Finite Group Databasebeta

← #33253754

Subgroups — #33253754

Order 18688.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989118C211yesmaximal, characteristic, complemented
2C22×D4×Dic73C211yesmaximal, characteristic, complemented
3#22614191C211yesmaximal, characteristic, complemented
4#22614176C211yesmaximal, characteristic, complemented
5#22614071C211yesmaximal, characteristic, complemented
6#22614056C211yesmaximal, characteristic, complemented
7#22613977C211yesmaximal, characteristic, complemented
8#22613962C211yesmaximal, characteristic, complemented
9#22613878C211yesmaximal, characteristic, complemented
10#22613863C211yesmaximal, characteristic, complemented
11#22613759C211yesmaximal, characteristic, complemented
12#22613677C211yesmaximal, characteristic, complemented
13#22613592C211yesmaximal, characteristic, complemented
14#22613488C211yesmaximal, characteristic, complemented
15#22613406C211yesmaximal, characteristic, complemented
16#22613328C211yesmaximal, characteristic, complemented
17#22613254C211yesmaximal, characteristic, complemented
18#22613219C211yesmaximal, characteristic, complemented
19#22613187C211yesmaximal, characteristic, complemented
20#22613166C211yesmaximal, characteristic, complemented
21#22613166C211yesmaximal, characteristic, complemented
22#22612463C211yesmaximal, characteristic, complemented
23#22612456C211yesmaximal, characteristic, complemented
24#121×Dic73C211yesmaximal, characteristic, complemented
25#120×Dic73C211yesmaximal, characteristic, complemented
26#120×Dic73C211yesmaximal, characteristic, complemented
27#22612371C211yesmaximal, characteristic, complemented
28#22612371C211yesmaximal, characteristic, complemented
29#22612309C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2410C211yesmaximal, characteristic
32C24×Dic73C2211yescharacteristic
33C24×Dic73C2211yescharacteristic
34#17989118—28no—
35C2×#14556584C2211yescharacteristic, complemented
36C2×#14556584C2211yescharacteristic, complemented
37C2×#14556582C2211yescharacteristic, complemented
38C2×#14556578C2211yescharacteristic, complemented
39C2×#14556572C2211yescharacteristic
40C2×#14556572C2211yescharacteristic
41C2×#14556572C2211yescharacteristic, complemented
42C2×#14556570C2211yescharacteristic, complemented
43C2×#14556568C2211yescharacteristic
44C2×#14556556C2211yescharacteristic, complemented
45C2×D4×Dic73—28no—
46C2×D4×Dic73C2211yescharacteristic
47C2×D4×Dic73C2211yescharacteristic
48C2×D4×Dic73C2211yescharacteristic
49C2×D4×Dic73C2211yescharacteristic
50C2×D4×Dic73C2211yescharacteristic
51C2×D4×Dic73C2211yescharacteristic
52C2×D4×Dic73C2211yescharacteristic
53C2×D4×Dic73C2211yescharacteristic
54C2×D4×Dic73C2211yescharacteristic
55C2×D4×Dic73C2211yescharacteristic, complemented
56C2×D4×Dic73C2211yescharacteristic, complemented
57C2×D4×Dic73C2211yescharacteristic, complemented
58C2×D4×Dic73C2211yescharacteristic, complemented
59C2×#14556547C2211yescharacteristic, complemented
60C2×#14556547C2211yescharacteristic, complemented
61C2×#14556547C2211yescharacteristic, complemented
62C22×C4⋊Dic73C2211yescharacteristic
63C22×C22⋊Dic73C2211yescharacteristic
64C22×C22⋊Dic73C2211yescharacteristic
65C22×C22⋊Dic73C2211yescharacteristic
66C22×C4×Dic73C2211yescharacteristic
67C22×C4×Dic73C2211yescharacteristic, complemented
68C22×C4×Dic73C2211yescharacteristic, complemented
69#17988529C2211yescharacteristic, complemented
70#17988527C2211yescharacteristic, complemented
71#17988526C2211yescharacteristic, complemented
72#17988523C2211yescharacteristic, complemented
73#17988520C2211yescharacteristic, complemented
74#17988519C2211yescharacteristic, complemented
75#17988519C2211yescharacteristic, complemented
76#17988515C2211yescharacteristic, complemented
77#17988515C2211yescharacteristic, complemented
78#17988515C2211yescharacteristic, complemented
79#17988515C2211yescharacteristic, complemented
80#17988512C2211yescharacteristic, complemented
81#17988512C2211yescharacteristic, complemented
82#17988512C2211yescharacteristic, complemented
83#17988510C2211yescharacteristic, complemented
84#17988510C2211yescharacteristic, complemented
85#17988510C2211yescharacteristic, complemented
86#17988510C2211yescharacteristic, complemented
87#17988501C2211yescharacteristic
88#17988501C2211yescharacteristic
89#17988501C2211yescharacteristic
90#17988501C2211yescharacteristic
91#17988501C2211yescharacteristic, complemented
92#17988501C2211yescharacteristic, complemented
93#17988501C2211yescharacteristic, complemented
94#17988501C2211yescharacteristic, complemented
95#17988499C2211yescharacteristic, complemented
96#17988499C2211yescharacteristic, complemented
97#17988491C2211yescharacteristic, complemented
98#17988490C2211yescharacteristic, complemented
99#17988486C2211yescharacteristic, complemented
100#17988482C2211yescharacteristic, complemented
101#17988481C2211yescharacteristic, complemented
102#17988481C2211yescharacteristic, complemented
103#17988481C2211yescharacteristic, complemented
104#17988481C2211yescharacteristic, complemented
105#17988480C2211yescharacteristic, complemented
106#17988480C2211yescharacteristic, complemented
107#17988475C2211yescharacteristic, complemented
108#17988475C2211yescharacteristic, complemented
109#17988474C2211yescharacteristic, complemented
110#17988474C2211yescharacteristic, complemented
111#17988472C2211yescharacteristic, complemented
112#17988472C2211yescharacteristic, complemented
113#17988472C2211yescharacteristic, complemented
114#17988470C2211yescharacteristic, complemented
115#17988470C2211yescharacteristic, complemented
116#17988468C2211yescharacteristic, complemented
117#17988467C2211yescharacteristic
118#17988467C2211yescharacteristic
119#17988467C2211yescharacteristic
120#17988467C2211yescharacteristic
121#17988467C2211yescharacteristic
122#17988467C2211yescharacteristic, complemented
123#17988467C2211yescharacteristic, complemented
124#17988467C2211yescharacteristic, complemented
125#17988467C2211yescharacteristic, complemented
126#17988467C2211yescharacteristic, complemented
127#17988462C2211yescharacteristic
128#17988462C2211yescharacteristic
129#17988462C2211yescharacteristic, complemented
130#17988462C2211yescharacteristic, complemented
131#17988462C2211yescharacteristic, complemented
132#17988462C2211yescharacteristic, complemented
133#17988460C2211yescharacteristic
134#17988460C2211yescharacteristic
135#17988460C2211yescharacteristic, complemented
136#17988460C2211yescharacteristic, complemented
137#17988459C2211yescharacteristic
138#17988459C2211yescharacteristic, complemented
139#17988448C2211yescharacteristic, complemented
140#17988448C2211yescharacteristic, complemented
141#17988448C2211yescharacteristic, complemented
142#17988447C2211yescharacteristic, complemented
143#17988445C2211yescharacteristic
144#17988445C2211yescharacteristic
145#17988445C2211yescharacteristic
146#17988445C2211yescharacteristic, complemented
147#17988445C2211yescharacteristic, complemented
148#17988443C2211yescharacteristic
149#17988443C2211yescharacteristic
150#17988443C2211yescharacteristic
151C4⋊C4×Dic73C2211yescharacteristic, complemented
152#17988438C2211yescharacteristic, complemented
153#17988438C2211yescharacteristic, complemented
154#17988438C2211yescharacteristic, complemented
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic, complemented
161C22⋊C4×Dic73C2211yescharacteristic, complemented
162C22⋊C4×Dic73C2211yescharacteristic, complemented
163C22⋊C4×Dic73C2211yescharacteristic, complemented
164C22⋊C4×Dic73C2211yescharacteristic, complemented
165C22⋊C4×Dic73C2211yescharacteristic, complemented
166C22⋊C4×Dic73C2211yescharacteristic, complemented
167C22⋊C4×Dic73C2211yescharacteristic, complemented
168C22⋊C4×Dic73C2211yescharacteristic, complemented
169C22⋊C4×Dic73C2211yescharacteristic, complemented
170C22⋊C4×Dic73C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic, complemented
173C2×#14556498C2211yescharacteristic, complemented
174C23×D4×C73C2211yescharacteristic
175C2×#121×C73C2211yescharacteristic
176C2×#121×C73C2211yescharacteristic
177C2×#120×C73C2211yescharacteristic
178C2×#120×C73C2211yescharacteristic
179C22×C22⋊C4×C73C2211yescharacteristic
180#394×C73C2211yescharacteristic
181#394×C73C2211yescharacteristic
182#392×C73C2211yescharacteristic
183#392×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic
185#386×C73C2211yescharacteristic
186#386×C73C2211yescharacteristic
187#385×C73C2211yescharacteristic
188#379×C73C2211yescharacteristic
189C22×Dic146C2311yescharacteristic
190C23×Dic73—24no—
191C23×Dic73—24no—
192C23×Dic73—24no—
193C23×Dic73—24no—
194C23×Dic73—42no—
195C23×Dic73—42no—
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C23×Dic73C2311yescharacteristic
200C23×Dic73C2311yescharacteristic
201C23×Dic73C2311yescharacteristic
202C23×Dic73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C23×Dic73C2311yescharacteristic
207C23×Dic73C2311yescharacteristic
208C23×Dic73C2311yescharacteristic
209C23×Dic73C2311yescharacteristic
210C23×Dic73C2311yescharacteristic
211#14556584—24no—
212#14556584—24no—
213#14556582—24no—
214#14556578—24no—
215#14556572—24no—
216#14556572—24no—
217#14556572—24no—
218#14556570—24no—
219#14556568—24no—
220#14556556—24no—
221D4×Dic73—24no—
222D4×Dic73—24no—
223D4×Dic73—24no—
224D4×Dic73—24no—
225D4×Dic73—24no—
226D4×Dic73—24no—
227D4×Dic73—24no—
228D4×Dic73—24no—
229D4×Dic73—24no—
230D4×Dic73—24no—
231D4×Dic73—42no—
232D4×Dic73—42no—
233D4×Dic73D418yescomplemented
234#14556547—24no—
235#14556547—24no—
236#14556547—42no—
237C2×C4⋊Dic73—24no—
238C2×C4⋊Dic73C2311yescharacteristic
239C2×C4⋊Dic73C2311yescharacteristic
240C2×C4⋊Dic73C2311yescharacteristic
241C2×C4⋊Dic73C2311yescharacteristic
242C2×C4⋊Dic73C2311yescharacteristic
243C2×C4⋊Dic73C2311yescharacteristic
244C2×C4⋊Dic73C2311yescharacteristic
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×C22⋊Dic73—24no—
263C2×C22⋊Dic73—24no—
264C2×C22⋊Dic73—24no—
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×C22⋊Dic73C2311yescharacteristic
271C2×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×C22⋊Dic73C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×C22⋊Dic73C2311yescharacteristic
285C2×C22⋊Dic73C2311yescharacteristic
286C2×C22⋊Dic73C2311yescharacteristic
287C2×C22⋊Dic73C2311yescharacteristic
288C2×C22⋊Dic73C2311yescharacteristic
289C2×C22⋊Dic73C2311yescharacteristic
290C2×C22⋊Dic73C2311yescharacteristic
291C2×C22⋊Dic73C2311yescharacteristic
292C2×C22⋊Dic73C2311yescharacteristic
293C2×C22⋊Dic73C2311yescharacteristic
294C2×C22⋊Dic73C2311yescharacteristic
295C2×C22⋊Dic73C2311yescharacteristic
296C2×C22⋊Dic73C2311yescharacteristic
297C2×C22⋊Dic73C2311yescharacteristic
298C2×C4×Dic73—24no—
299C2×C4×Dic73—24no—
300C2×C4×Dic73—42no—
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
305C2×C4×Dic73C2311yescharacteristic
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308C2×C4×Dic73C2311yescharacteristic
309C2×C4×Dic73C2311yescharacteristic
310C2×C4×Dic73C2311yescharacteristic
311C2×C4×Dic73C2311yescharacteristic
312C2×C4×Dic73C2311yescharacteristic
313C2×C4×Dic73C2311yescharacteristic
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348C25×C73C2311yescharacteristic
349C25×C73C2311yescharacteristic
350C22×D4×C73—24no—
351C22×D4×C73—24no—
352C22×D4×C73—24no—
353C22×D4×C73C2311yescharacteristic
354C22×D4×C73C2311yescharacteristic
355C22×D4×C73C2311yescharacteristic
356C22×D4×C73C2311yescharacteristic
357C22×D4×C73C2311yescharacteristic
358C22×D4×C73C2311yescharacteristic
359C22×D4×C73C2311yescharacteristic
360C22×D4×C73C2311yescharacteristic
361C22×D4×C73C2311yescharacteristic
362C23×C4×C73C2311yescharacteristic
363C23×C4×C73C2311yescharacteristic
364C23×C4×C73C2311yescharacteristic
365#121×C73—24no—
366#121×C73—24no—
367#120×C73—24no—
368#120×C73—24no—
369C2×C4⋊C4×C73C2311yescharacteristic
370C2×C4⋊C4×C73C2311yescharacteristic
371C2×C22⋊C4×C73—24no—
372C2×C22⋊C4×C73C2311yescharacteristic
373C2×C22⋊C4×C73C2311yescharacteristic
374C2×C22⋊C4×C73C2311yescharacteristic
375C2×C22⋊C4×C73C2311yescharacteristic
376C2×C22⋊C4×C73C2311yescharacteristic
377C2×C22⋊C4×C73C2311yescharacteristic
378C2×C22⋊C4×C73C2311yescharacteristic
379C2×C22⋊C4×C73C2311yescharacteristic
380C2×C22⋊C4×C73C2311yescharacteristic
381C2×C22⋊C4×C73C2311yescharacteristic
382C2×C22⋊C4×C73C2311yescharacteristic
383C2×C22⋊C4×C73C2311yescharacteristic
384C2×C22⋊C4×C73C2311yescharacteristic
385C2×C22⋊C4×C73C2311yescharacteristic
386C2×C22⋊C4×C73C2311yescharacteristic
387#95×C73C2311yescharacteristic
388#95×C73C2311yescharacteristic
389#95×C73C2311yescharacteristic
390#95×C73C2311yescharacteristic
391C2×Dic146—22no—
392C2×Dic146—22no—
393C2×Dic146—41no—
394C22×Dic73—22no—
395C22×Dic73—22no—
396C22×Dic73—22no—
397C22×Dic73—22no—
398C22×Dic73—22no—
399C22×Dic73—22no—
400C22×Dic73—22no—
401C22×Dic73—22no—
402C22×Dic73—22no—
403C22×Dic73—22no—
404C22×Dic73—22no—
405C22×Dic73—22no—
406C22×Dic73—22no—
407C22×Dic73—22no—
408C22×Dic73—22no—
409C22×Dic73—22no—
410C22×Dic73—22no—
411C22×Dic73—22no—
412C22×Dic73—22no—
413C22×Dic73—22no—
414C22×Dic73—22no—
415C22×Dic73—22no—
416C22×Dic73—22no—
417C22×Dic73—22no—
418C22×Dic73—22no—
419C22×Dic73—22no—
420C22×Dic73—22no—
421C22×Dic73—22no—
422C22×Dic73—22no—
423C22×Dic73—22no—
424C22×Dic73—22no—
425C22×Dic73—22no—
426C22×Dic73—22no—
427C22×Dic73—41no—
428C22×Dic73—41no—
429C22×Dic73—41no—
430C22×Dic73—41no—
431C22×Dic73—41no—
432C22×Dic73—41no—
433C22×Dic73—41no—
434C22×Dic73—41no—
435C22×Dic73—41no—
436C22×Dic73—416no—
437C22×Dic73—416no—
438C22×Dic73C2×D414yes—
439C22×Dic73C2×D414yes—
440C22×Dic73#4114yes—
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C22×Dic73C2411yescharacteristic
446C22×Dic73C2411yescharacteristic
447C22×Dic73C2411yescharacteristic
448C22×Dic73C2411yescharacteristic
449C22×Dic73C2411yescharacteristic
450C22×Dic73C2411yescharacteristic
451C22×Dic73C2411yescharacteristic
452C22×Dic73C2411yescharacteristic
453C22×Dic73C2411yescharacteristic
454C22×Dic73C2411yescharacteristic
455C22×Dic73C2411yescharacteristic
456C22×Dic73C2411yescharacteristic
457C4⋊Dic73—22no—
458C4⋊Dic73—22no—
459C4⋊Dic73—22no—
460C4⋊Dic73—22no—
461C4⋊Dic73—22no—
462C4⋊Dic73—22no—
463C4⋊Dic73—22no—
464C4⋊Dic73—41no—
465C4⋊Dic73—41no—
466C4⋊Dic73C2×D414yes—
467#11924007—22no—
468#11924007—22no—
469#11924007—22no—
470#11924007—22no—
471#11924007—22no—
472#11924007—22no—
473#11924007—22no—
474#11924007—22no—
475#11924007—22no—
476#11924007—22no—
477#11924007—41no—
478#11924007—41no—
479#11924007—41no—
480#11924007—41no—
481C22⋊Dic73—22no—
482C22⋊Dic73—22no—
483C22⋊Dic73—22no—
484C22⋊Dic73—22no—
485C22⋊Dic73—22no—
486C22⋊Dic73—22no—
487C22⋊Dic73—22no—
488C22⋊Dic73—22no—
489C22⋊Dic73—22no—
490C22⋊Dic73—22no—
491C22⋊Dic73—22no—
492C22⋊Dic73—22no—
493C22⋊Dic73—22no—
494C22⋊Dic73—22no—
495C22⋊Dic73—22no—
496C22⋊Dic73—22no—
497C22⋊Dic73—22no—
498C22⋊Dic73—22no—
499C22⋊Dic73—22no—
500C22⋊Dic73—22no—
501C22⋊Dic73—22no—
502C22⋊Dic73—22no—
503C22⋊Dic73—41no—
504C22⋊Dic73—41no—
505C22⋊Dic73—41no—
506C22⋊Dic73—41no—
507C22⋊Dic73—41no—
508C22⋊Dic73—41no—
509C22⋊Dic73—41no—
510C22⋊Dic73—41no—
511C22⋊Dic73—41no—
512C22⋊Dic73C2×D414yes—
513C22⋊Dic73C2×D414yes—
514C4×Dic73—22no—
515C4×Dic73—22no—
516C4×Dic73—22no—
517C4×Dic73—22no—
518C4×Dic73—22no—
519C4×Dic73—22no—
520C4×Dic73—22no—
521C4×Dic73—22no—
522C4×Dic73—22no—
523C4×Dic73—22no—
524C4×Dic73—22no—
525C4×Dic73—22no—
526C4×Dic73—41no—
527C4×Dic73—41no—
528C4×Dic73C2×D414yes—
529C24×C73—22no—
530C24×C73—22no—
531C24×C73—22no—
532C24×C73—22no—
533C24×C73—22no—
534C24×C73—22no—
535C24×C73—22no—
536C24×C73—22no—
537C24×C73—22no—
538C24×C73—41no—
539C24×C73—41no—
540C24×C73—41no—
541C24×C73—41no—
542C24×C73#4114yes—
543C24×C73C2411yescharacteristic
544C24×C73C2411yescharacteristic
545C24×C73C2411yescharacteristic
546C24×C73C2411yescharacteristic
547C24×C73C2411yescharacteristic
548C24×C73C2411yescharacteristic
549C2×D4×C73—232no—
550C2×D4×C73—22no—
551C2×D4×C73—22no—
552C2×D4×C73—22no—
553C2×D4×C73—22no—
554C2×D4×C73—22no—
555C2×D4×C73—22no—
556C2×D4×C73—22no—
557C2×D4×C73—22no—
558C2×D4×C73—22no—
559C2×D4×C73—22no—
560C2×D4×C73—22no—
561C2×D4×C73—22no—
562C2×D4×C73—22no—
563C2×D4×C73—22no—
564C2×D4×C73—22no—
565C2×D4×C73—22no—
566C2×D4×C73—22no—
567C2×D4×C73—22no—
568C2×D4×C73—22no—
569C2×D4×C73—22no—
570C2×D4×C73—22no—
571C2×D4×C73—41no—
572C2×D4×C73—41no—
573C2×D4×C73—41no—
574C2×D4×C73—41no—
575C2×D4×C73C2×D414yes—
576C2×D4×C73#4114yes—
577C22×C4×C73—22no—
578C22×C4×C73—22no—
579C22×C4×C73—22no—
580C22×C4×C73—22no—
581C22×C4×C73—22no—
582C22×C4×C73—22no—
583C22×C4×C73—22no—
584C22×C4×C73—41no—
585C22×C4×C73—41no—
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2411yescharacteristic
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C22×C4×C73C2411yescharacteristic
591C22×C4×C73C2411yescharacteristic
592C22×C4×C73C2411yescharacteristic
593C22×C4×C73C2411yescharacteristic
594C22×C4×C73C2411yescharacteristic
595C4⋊C4×C73—22no—
596C4⋊C4×C73—22no—
597C22⋊C4×C73—22no—
598C22⋊C4×C73—22no—
599C22⋊C4×C73—22no—
600C22⋊C4×C73—22no—
601C22⋊C4×C73—22no—
602C22⋊C4×C73—22no—
603C22⋊C4×C73—22no—
604C22⋊C4×C73—22no—
605C22⋊C4×C73—22no—
606C22⋊C4×C73—22no—
607C22⋊C4×C73—22no—
608C22⋊C4×C73—22no—
609C22⋊C4×C73—41no—
610C22⋊C4×C73—41no—
611C22⋊C4×C73#4114yes—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—21no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—28no—
621C23×C73—28no—
622C23×C73—28no—
623C23×C73—21no—
624C23×C73—21no—
625C23×C73—21no—
626C23×C73—21no—
627C23×C73—21no—
628C23×C73—21no—
629C23×C73—21no—
630C23×C73—21no—
631C23×C73—21no—
632C23×C73—21no—
633C23×C73—21no—
634C23×C73—21no—
635C23×C73—21no—
636C23×C73—21no—
637C23×C73—21no—
638C23×C73—21no—
639C23×C73—21no—
640C23×C73—21no—
641C23×C73—21no—
642C23×C73—21no—
643C23×C73—21no—
644C23×C73—21no—
645C23×C73—21no—
646C23×C73—21no—
647C23×C73—21no—
648C23×C73—44no—
649C23×C73—44no—
650C23×C73—44no—
651C23×C73—44no—
652C23×C73—44no—
653C23×C73—44no—
654C23×C73—44no—
655C23×C73—44no—
656C23×C73—44no—
657C23×C73—44no—
658C23×C73—44no—
659C23×C73C22×D412yes—
660C23×C73C22×D412yes—
661C23×C73C2×#4112yes—
662C23×C73C2×#4112yes—
663C23×C73C2×#4112yes—
664C23×C73C2×#4112yes—
665C23×C73C2×#4112yes—
666C23×C73C2×#4112yes—
667C23×C73C2×#4112yes—
668C23×C73C2511yescharacteristic
669D4×C73—28no—
670D4×C73—28no—
671D4×C73—28no—
672D4×C73—28no—
673D4×C73—44no—
674D4×C73—44no—
675D4×C73—44no—
676D4×C73—44no—
677D4×C73—44no—
678C2×C4×C73—28no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—21no—
694C2×C4×C73—21no—
695C2×C4×C73—21no—
696C2×C4×C73—21no—
697C2×C4×C73—21no—
698C2×C4×C73—21no—
699C2×C4×C73—21no—
700C2×C4×C73—21no—
701C2×C4×C73—21no—
702C2×C4×C73—44no—
703C2×C4×C73—44no—
704C2×C4×C73C22×D412yes—
705C2×C4×C73C2×#4112yes—
706C2×C4×C73C2×#4112yes—
707C2×C4×C73C2×#4112yes—
708C2×Dic73—21no—
709C2×Dic73—21no—
710C2×Dic73—21no—
711C2×Dic73—21no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—28no—
717C2×Dic73—28no—
718C2×Dic73—28no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—21no—
725C2×Dic73—21no—
726C2×Dic73—21no—
727C2×Dic73—21no—
728C2×Dic73—21no—
729C2×Dic73—21no—
730C2×Dic73—21no—
731C2×Dic73—21no—
732C2×Dic73—21no—
733C2×Dic73—21no—
734C2×Dic73—21no—
735C2×Dic73—21no—
736C2×Dic73—21no—
737C2×Dic73—21no—
738C2×Dic73—21no—
739C2×Dic73—21no—
740C2×Dic73—21no—
741C2×Dic73—21no—
742C2×Dic73—21no—
743C2×Dic73—21no—
744C2×Dic73—21no—
745C2×Dic73—21no—
746C2×Dic73—21no—
747C2×Dic73—21no—
748C2×Dic73—21no—
749C2×Dic73—21no—
750C2×Dic73—21no—
751C2×Dic73—21no—
752C2×Dic73—44no—
753C2×Dic73—44no—
754C2×Dic73—44no—
755C2×Dic73—44no—
756C2×Dic73—44no—
757C2×Dic73—44no—
758C2×Dic73—44no—
759C2×Dic73—44no—
760C2×Dic73—44no—
761C2×Dic73—44no—
762C2×Dic73—44no—
763C2×Dic73—44no—
764C2×Dic73C22×D412yes—
765C2×Dic73C22×D412yes—
766C2×Dic73C22×D412yes—
767C2×Dic73C22×D412yes—
768C2×Dic73C2×#4112yes—
769C2×Dic73C2×#4112yes—
770C2×Dic73H(5,𝔽2)12yes—
771Dic146—44no—
772C22×C73—22no—
773C22×C73—22no—
774C22×C73—22no—
775C22×C73—22no—
776C22×C73—22no—
777C22×C73—22no—
778C22×C73—22no—
779C22×C73—22no—
780C22×C73—22no—
781C22×C73—22no—
782C22×C73—22no—
783C22×C73—22no—
784C22×C73—22no—
785C22×C73—22no—
786C22×C73—22no—
787C22×C73—22no—
788C22×C73—22no—
789C22×C73—22no—
790C22×C73—22no—
791C22×C73—22no—
792C22×C73—22no—
793C22×C73—416no—
794C22×C73—416no—
795C22×C73—41no—
796C22×C73—41no—
797C22×C73—41no—
798C22×C73—41no—
799C22×C73—41no—
800C22×C73—41no—
801C22×C73—41no—
802C22×C73—41no—
803C22×C73—41no—
804C22×C73—41no—
805C22×C73—41no—
806C22×C73—41no—
807C22×C73—41no—
808C22×C73—41no—
809C22×C73—41no—
810C22×C73—41no—
811C22×C73—41no—
812C22×C73—41no—
813C22×C73—41no—
814C22×C73#52514yes—
815C22×C73#52914yescomplemented
816C22×C73C23×D411yescharacteristic
817C22×C73C22×#4111yescharacteristic
818C22×C73C22×#4111yescharacteristic
819C22×C73C22×#4111yescharacteristic
820C22×C73C22×#4111yescharacteristic
821C22×C73C2×H(5,𝔽2)11yescharacteristic
822C22×C73#58511yescharacteristic
823C4×C73—22no—
824C4×C73—22no—
825C4×C73—22no—
826C4×C73—22no—
827C4×C73—41no—
828C4×C73—41no—
829C4×C73—41no—
830C4×C73—41no—
831C4×C73—41no—
832Dic73—22no—
833Dic73—22no—
834Dic73—22no—
835Dic73—22no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73—41no—
840Dic73—41no—
841Dic73—41no—
842Dic73—41no—
843Dic73—41no—
844Dic73—41no—
845Dic73—41no—
846Dic73—41no—
847Dic73#54614yes—
848#34670—731nomaximal, Sylow
849C2×C73—24no—
850C2×C73—24no—
851C2×C73—42no—
852C2×C73—42no—
853C2×C73—42no—
854C2×C73—81no—
855C2×C73C2×#52511yescharacteristic
856C2×C73C2×#52911yescharacteristic
857C2×C73#345911yescharacteristic
858C2×C73C2×#54611yescharacteristic
859C2×C73D4×#4111yescharacteristic
860C2×C73#347511yescharacteristic
861C2×C73#348111yescharacteristic
862C2×#529—731no—
863C22×C4×D4—731no—
864#2481—731no—
865#2480—731no—
866#2473—731no—
867#2472—731no—
868#2467—731no—
869#2466—731no—
870#2460—731no—
871#2459—731no—
872#2450—731no—
873#2444—731no—
874#2437—731no—
875#2425—731no—
876#2419—731no—
877#2412—731no—
878#2410D7311yescharacteristic
879#2405—731no—
880#2398—731no—
881#2395—731no—
882#2392—731no—
883#2392—731no—
884C4×C22⋊Q8—731no—
885C4×#123—731no—
886C4×#121—731no—
887C4×#120—731no—
888C4×#120—731no—
889#2290—731no—
890#2290—731no—
891#2280—731no—
892C2×C4×C22⋊C4—731no—
893C73#3467011yescharacteristic, complemented, Sylow
894C23×D4C2×D7311yescharacteristic
895C24×C4—731no—
896C24×C4—731no—
897#529—1468no—
898C2×#126—731no—
899C2×#126—731no—
900C2×#125—731no—
901C2×#124—731no—
902C2×#123—731no—
903C2×#123—731no—
904C2×#123—731no—
905C2×C22⋊Q8—731no—
906C2×C22⋊Q8—731no—
907C2×#121C2×D7311yescharacteristic
908C2×#121C2×D7311yescharacteristic
909C2×#120C2×D7311yescharacteristic
910C2×#120C2×D7311yescharacteristic
911C2×C4×Q8—731no—
912C2×C4×D4—731no—
913C2×C4×D4—731no—
914C2×C4×D4—731no—
915C2×C4×D4—731no—
916C2×C4×D4—731no—
917C2×C4×D4—731no—
918C2×C4×D4—731no—
919C2×C4×D4—731no—
920C2×C4×D4—731no—
921C2×C4×D4—731no—
922C2×C4×D4—731no—
923C2×C4×D4—731no—
924C2×C4×D4—731no—
925C2×C4×D4—1468no—
926C2×#117—731no—
927C2×#117—731no—
928C2×#117—731no—
929C22×C4⋊C4—731no—
930C22×C22⋊C4—731no—
931C22×C22⋊C4—731no—
932C22×C22⋊C4—731no—
933C22×C22⋊C4C2×D7311yescharacteristic
934C22×C42—731no—
935C22×C42—731no—
936C22×C42—731no—
937#400—731no—
938#400—731no—
939#400—731no—
940#399—731no—
941#398—731no—
942#398—731no—
943#398—731no—
944#397—731no—
945#397—731no—
946#397—731no—
947#397—731no—
948#397—731no—
949#397—731no—
950#397—731no—
951#396—731no—
952#396—731no—
953#396—731no—
954#396—731no—
955#394—731no—
956#394—731no—
957#394—731no—
958#394—731no—
959#394—731no—
960#394—731no—
961#394—731no—
962#394—731no—
963#394C2×D7311yescharacteristic
964#394C2×D7311yescharacteristic
965#393—731no—
966#393—731no—
967#392C2×D7311yescharacteristic
968#392C2×D7311yescharacteristic
969#391—731no—
970#390—731no—
971#389—731no—
972#389—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#387—731no—
982#387—731no—
983#387—731no—
984#387—731no—
985#387—731no—
986#387—731no—
987#387—731no—
988#387—731no—
989#386—731no—
990#386—731no—
991#386—731no—
992#386—731no—
993#386—731no—
994#386—731no—
995#386—731no—
996#386—731no—
997#386—731no—
998#386—731no—
999#386C2×D7311yescharacteristic
1000#386C2×D7311yescharacteristic
1001#386C2×D7311yescharacteristic
1002#385—731no—
1003#385—731no—
1004#385—731no—
1005#385—731no—
1006#385—731no—
1007#385—731no—
1008#385—731no—
1009#385—731no—
1010#385—731no—
1011#385—731no—
1012#385—731no—
1013#385—731no—
1014#385C2×D7311yescharacteristic
1015#381—731no—
1016#381—731no—
1017#381—731no—
1018#380—731no—
1019#380—731no—
1020#380—731no—
1021#380—731no—
1022#380—731no—
1023#380—731no—
1024#379—731no—
1025#379—731no—
1026#379—731no—
1027#379C2×D7311yescharacteristic
1028C4×C4⋊C4—731no—
1029C4×C4⋊C4—731no—
1030C4×C4⋊C4—731no—
1031C4×C4⋊C4—731no—
1032C4×C22⋊C4—731no—
1033C4×C22⋊C4—731no—
1034C4×C22⋊C4—731no—
1035C4×C22⋊C4—731no—
1036C4×C22⋊C4—731no—
1037C4×C22⋊C4—731no—
1038C4×C22⋊C4—731no—
1039C4×C22⋊C4—731no—
1040C4×C22⋊C4—731no—
1041C4×C22⋊C4—731no—
1042C4×C22⋊C4—731no—
1043C4×C22⋊C4—731no—
1044C4×C22⋊C4—731no—
1045C4×C22⋊C4—731no—
1046C4×C22⋊C4—731no—
1047C4×C22⋊C4—731no—
1048#376—731no—
1049C2×#95—731no—
1050C2×#95—731no—
1051C25C22×D7311yescharacteristic
1052C25C22×D7311yescharacteristic
1053C22×Q8—731no—
1054C22×D4—24no—
1055C22×D4—24no—
1056C22×D4—24no—
1057C22×D4C22×D7311yescharacteristic
1058C22×D4C22×D7311yescharacteristic
1059C22×D4C22×D7311yescharacteristic
1060C22×D4C22×D7311yescharacteristic
1061C22×D4C22×D7311yescharacteristic
1062C22×D4C22×D7311yescharacteristic
1063C22×D4C22×D7311yescharacteristic
1064C22×D4C22×D7311yescharacteristic
1065C22×D4C22×D7311yescharacteristic
1066C23×C4—2922no—
1067C23×C4—2922no—
1068C23×C4—731no—
1069C23×C4—731no—
1070C23×C4—731no—
1071C23×C4—731no—
1072C23×C4—731no—
1073C23×C4—731no—
1074C23×C4—731no—
1075C23×C4—731no—
1076C23×C4—731no—
1077C23×C4—731no—
1078C23×C4—731no—
1079C23×C4—731no—
1080C23×C4—731no—
1081C23×C4—731no—
1082C23×C4—731no—
1083C23×C4—1464no—
1084C23×C4—1464no—
1085C23×C4—1464no—
1086C23×C4—1464no—
1087C23×C4C22×D7311yescharacteristic
1088C23×C4C22×D7311yescharacteristic
1089C23×C4C22×D7311yescharacteristic
1090#126—1464no—
1091#126—1464no—
1092#125—1464no—
1093#124—1464no—
1094#123—1464no—
1095#123—1464no—
1096#123—1464no—
1097C22⋊Q8—1464no—
1098C22⋊Q8—1464no—
1099#121—24no—
1100#121—24no—
1101#120—24no—
1102#120—24no—
1103C4×Q8—1464no—
1104C4×D4—2922no—
1105C4×D4—2922no—
1106C4×D4—738no—
1107C4×D4—1464no—
1108C4×D4—1464no—
1109C4×D4—1464no—
1110C4×D4—1464no—
1111C4×D4—1464no—
1112C4×D4—1464no—
1113C4×D4—1464no—
1114C4×D4—1464no—
1115C4×D4—1464no—
1116C4×D4—1464no—
1117#117—2922no—
1118#117—1464no—
1119#117—1464no—
1120C2×C4⋊C4—731no—
1121C2×C4⋊C4—731no—
1122C2×C4⋊C4—731no—
1123C2×C4⋊C4—731no—
1124C2×C4⋊C4—731no—
1125C2×C4⋊C4—731no—
1126C2×C4⋊C4—731no—
1127C2×C4⋊C4—731no—
1128C2×C4⋊C4—731no—
1129C2×C4⋊C4—731no—
1130C2×C4⋊C4—731no—
1131C2×C4⋊C4—731no—
1132C2×C4⋊C4—731no—
1133C2×C4⋊C4—731no—
1134C2×C4⋊C4—731no—
1135C2×C4⋊C4—731no—
1136C2×C4⋊C4—731no—
1137C2×C4⋊C4—731no—
1138C2×C4⋊C4—731no—
1139C2×C4⋊C4—731no—
1140C2×C4⋊C4—731no—
1141C2×C4⋊C4—731no—
1142C2×C4⋊C4—731no—
1143C2×C4⋊C4—731no—
1144C2×C4⋊C4—1464no—
1145C2×C4⋊C4C22×D7311yescharacteristic
1146C2×C4⋊C4C22×D7311yescharacteristic
1147C2×C22⋊C4—24no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—731no—
1165C2×C22⋊C4—731no—
1166C2×C22⋊C4—731no—
1167C2×C22⋊C4—731no—
1168C2×C22⋊C4—731no—
1169C2×C22⋊C4—731no—
1170C2×C22⋊C4—731no—
1171C2×C22⋊C4—731no—
1172C2×C22⋊C4—731no—
1173C2×C22⋊C4—731no—
1174C2×C22⋊C4—731no—
1175C2×C22⋊C4—731no—
1176C2×C22⋊C4—731no—
1177C2×C22⋊C4—731no—
1178C2×C22⋊C4—731no—
1179C2×C22⋊C4—731no—
1180C2×C22⋊C4—731no—
1181C2×C22⋊C4—1464no—
1182C2×C22⋊C4—1464no—
1183C2×C22⋊C4—1464no—
1184C2×C22⋊C4C22×D7311yescharacteristic
1185C2×C22⋊C4C22×D7311yescharacteristic
1186C2×C22⋊C4C22×D7311yescharacteristic
1187C2×C22⋊C4C22×D7311yescharacteristic
1188C2×C22⋊C4C22×D7311yescharacteristic
1189C2×C22⋊C4C22×D7311yescharacteristic
1190C2×C22⋊C4C22×D7311yescharacteristic
1191C2×C22⋊C4C22×D7311yescharacteristic
1192C2×C22⋊C4C22×D7311yescharacteristic
1193C2×C22⋊C4C22×D7311yescharacteristic
1194C2×C22⋊C4C22×D7311yescharacteristic
1195C2×C22⋊C4C22×D7311yescharacteristic
1196C2×C22⋊C4C22×D7311yescharacteristic
1197C2×C22⋊C4C22×D7311yescharacteristic
1198C2×C22⋊C4C22×D7311yescharacteristic
1199C2×C42—2922no—
1200C2×C42—731no—
1201C2×C42—731no—
1202C2×C42—731no—
1203C2×C42—731no—
1204C2×C42—731no—
1205C2×C42—731no—
1206C2×C42—731no—
1207C2×C42—731no—
1208C2×C42—731no—
1209C2×C42—731no—
1210C2×C42—731no—
1211C2×C42—731no—
1212C2×C42—731no—
1213C2×C42—731no—
1214C2×C42—731no—
1215C2×C42—1464no—
1216C2×C42—1464no—
1217#95—731no—
1218#95—731no—
1219#95—731no—
1220#95—731no—
1221#95—731no—
1222#95—731no—
1223#95—731no—
1224#95—731no—
1225#95—731no—
1226#95—731no—
1227#95—731no—
1228#95—731no—
1229#95—731no—
1230#95—731no—
1231#95—731no—
1232#95—731no—
1233#95—731no—
1234#95—731no—
1235#95—731no—
1236#95—731no—
1237#95—731no—
1238#95—731no—
1239#95—731no—
1240#95—731no—
1241#95—731no—
1242#95—731no—
1243#95—731no—
1244#95—731no—
1245#95—731no—
1246#95—731no—
1247#95—731no—
1248#95—731no—
1249#95C22×D7311yescharacteristic
1250#95C22×D7311yescharacteristic
1251#95C22×D7311yescharacteristic
1252#95C22×D7311yescharacteristic
1253C24—22no—
1254C24—22no—
1255C24—22no—
1256C24—22no—
1257C24—22no—
1258C24—22no—
1259C24—22no—
1260C24—22no—
1261C24—22no—
1262C24—41no—
1263C24—41no—
1264C24—41no—
1265C24—41no—
1266C24#1192402714yes—
1267C24C23×D7311yescharacteristic
1268C24C23×D7311yescharacteristic
1269C24C23×D7311yescharacteristic
1270C24C23×D7311yescharacteristic
1271C24C23×D7311yescharacteristic
1272C24C23×D7311yescharacteristic
1273C2×Q8—2921no—
1274C2×Q8—1462no—
1275C2×Q8—1462no—
1276C2×D4—232no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—22no—
1283C2×D4—22no—
1284C2×D4—22no—
1285C2×D4—22no—
1286C2×D4—22no—
1287C2×D4—22no—
1288C2×D4—22no—
1289C2×D4—22no—
1290C2×D4—22no—
1291C2×D4—22no—
1292C2×D4—22no—
1293C2×D4—22no—
1294C2×D4—22no—
1295C2×D4—22no—
1296C2×D4—22no—
1297C2×D4—22no—
1298C2×D4—41no—
1299C2×D4—41no—
1300C2×D4—41no—
1301C2×D4—41no—
1302C2×D4D4×D7314yes—
1303C2×D4#1192402714yes—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—2921no—
1314C22×C4—2921no—
1315C22×C4—2921no—
1316C22×C4—2921no—
1317C22×C4—2921no—
1318C22×C4—2921no—
1319C22×C4—2921no—
1320C22×C4—2921no—
1321C22×C4—2921no—
1322C22×C4—29216no—
1323C22×C4—29216no—
1324C22×C4—731no—
1325C22×C4—734no—
1326C22×C4—734no—
1327C22×C4—734no—
1328C22×C4—731no—
1329C22×C4—731no—
1330C22×C4—731no—
1331C22×C4—731no—
1332C22×C4—731no—
1333C22×C4—731no—
1334C22×C4—731no—
1335C22×C4—731no—
1336C22×C4—731no—
1337C22×C4—731no—
1338C22×C4—731no—
1339C22×C4—731no—
1340C22×C4—731no—
1341C22×C4—731no—
1342C22×C4—731no—
1343C22×C4—1462no—
1344C22×C4—1462no—
1345C22×C4—1462no—
1346C22×C4—1462no—
1347C22×C4—1462no—
1348C22×C4—1462no—
1349C22×C4—1462no—
1350C22×C4—1462no—
1351C22×C4—1462no—
1352C22×C4—1462no—
1353C22×C4—1462no—
1354C22×C4—1462no—
1355C22×C4—1462no—
1356C22×C4—1462no—
1357C22×C4—1462no—
1358C22×C4—1462no—
1359C22×C4—1462no—
1360C22×C4—1462no—
1361C22×C4—1462no—
1362C22×C4—1462no—
1363C22×C4—1462no—
1364C22×C4—1462no—
1365C22×C4—1462no—
1366C22×C4—1462no—
1367C22×C4—1462no—
1368C22×C4—1462no—
1369C22×C4—1462no—
1370C22×C4—1462no—
1371C22×C4—1462no—
1372C22×C4—1462no—
1373C22×C4—1462no—
1374C22×C4—1462no—
1375C22×C4—1462no—
1376C22×C4C23×D7311yescharacteristic
1377C22×C4C23×D7311yescharacteristic
1378C22×C4C23×D7311yescharacteristic
1379C22×C4C23×D7311yescharacteristic
1380C22×C4C23×D7311yescharacteristic
1381C22×C4C23×D7311yescharacteristic
1382C22×C4C23×D7311yescharacteristic
1383C22×C4C23×D7311yescharacteristic
1384C22×C4C23×D7311yescharacteristic
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—2921no—
1388C4⋊C4—2921no—
1389C4⋊C4—2921no—
1390C4⋊C4—2921no—
1391C4⋊C4—2921no—
1392C4⋊C4—2921no—
1393C4⋊C4—734no—
1394C4⋊C4—1462no—
1395C4⋊C4—1462no—
1396C4⋊C4—1462no—
1397C4⋊C4—1462no—
1398C4⋊C4—1462no—
1399C4⋊C4—1462no—
1400C4⋊C4—1462no—
1401C4⋊C4—1462no—
1402C4⋊C4—1462no—
1403C4⋊C4—1462no—
1404C4⋊C4—1462no—
1405C4⋊C4—1462no—
1406C4⋊C4—1462no—
1407C4⋊C4—1462no—
1408C4⋊C4—1462no—
1409C4⋊C4—1462no—
1410C4⋊C4—1462no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—22no—
1419C22⋊C4—22no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—2921no—
1426C22⋊C4—2921no—
1427C22⋊C4—2921no—
1428C22⋊C4—2921no—
1429C22⋊C4—2921no—
1430C22⋊C4—2921no—
1431C22⋊C4—2921no—
1432C22⋊C4—2921no—
1433C22⋊C4—2921no—
1434C22⋊C4—734no—
1435C22⋊C4—734no—
1436C22⋊C4—1462no—
1437C22⋊C4—1462no—
1438C22⋊C4—1462no—
1439C22⋊C4—1462no—
1440C22⋊C4—1462no—
1441C22⋊C4—1462no—
1442C22⋊C4—1462no—
1443C22⋊C4—1462no—
1444C22⋊C4—1462no—
1445C22⋊C4—1462no—
1446C22⋊C4—1462no—
1447C22⋊C4—1462no—
1448C22⋊C4—1462no—
1449C22⋊C4—1462no—
1450C22⋊C4—1462no—
1451C22⋊C4—1462no—
1452C22⋊C4—1462no—
1453C22⋊C4—1462no—
1454C22⋊C4—1462no—
1455C22⋊C4—1462no—
1456C22⋊C4—1462no—
1457C22⋊C4—1462no—
1458C22⋊C4#1192402714yes—
1459C42—2921no—
1460C42—2921no—
1461C42—734no—
1462C42—1462no—
1463C42—1462no—
1464C42—1462no—
1465C42—1462no—
1466C42—1462no—
1467C42—1462no—
1468C42—1462no—
1469C42—1462no—
1470C42—1462no—
1471C42—1462no—
1472C42—1462no—
1473C42—1462no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—28no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—21no—
1501C23—28no—
1502C23—28no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—44no—
1511C23—44no—
1512C23—44no—
1513C23—44no—
1514C23—44no—
1515C23—44no—
1516C23—44no—
1517C23—44no—
1518C23—44no—
1519C23—44no—
1520C23—44no—
1521C23C2×D4×D7312yes—
1522C23C2×D4×D7312yes—
1523C23#41×D7312yes—
1524C23C2×#1192402712yes—
1525C23C2×#1192402712yes—
1526C23C2×#1192402712yes—
1527C23C2×#1192402712yes—
1528C23C2×#1192402712yes—
1529C23C2×#1192402712yes—
1530C23C24×D7311yescharacteristic
1531Q8—2924no—
1532D4—28no—
1533D4—28no—
1534D4—28no—
1535D4—28no—
1536D4—44no—
1537D4—44no—
1538D4—44no—
1539D4—44no—
1540D4—44no—
1541C2×C4—28no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—44no—
1566C2×C4—44no—
1567C2×C4—2924no—
1568C2×C4—2924no—
1569C2×C4—2924no—
1570C2×C4—2924no—
1571C2×C4—2924no—
1572C2×C4—2924no—
1573C2×C4—2924no—
1574C2×C4—2924no—
1575C2×C4—2924no—
1576C2×C4—2924no—
1577C2×C4—2924no—
1578C2×C4—2924no—
1579C2×C4—732no—
1580C2×C4—732no—
1581C2×C4—732no—
1582C2×C4—732no—
1583C2×C4—732no—
1584C2×C4—732no—
1585C2×C4—732no—
1586C2×C4—1461no—
1587C2×C4—1461no—
1588C2×C4—1461no—
1589C2×C4—1461no—
1590C2×C4—1461no—
1591C2×C4—1461no—
1592C2×C4—1461no—
1593C2×C4—1461no—
1594C2×C4—1461no—
1595C2×C4—1461no—
1596C2×C4—1461no—
1597C2×C4—1461no—
1598C2×C4—1461no—
1599C2×C4—1461no—
1600C2×C4—1461no—
1601C2×C4—1461no—
1602C2×C4—1461no—
1603C2×C4—1461no—
1604C2×C4—1461no—
1605C2×C4—1461no—
1606C2×C4—1461no—
1607C2×C4—1461no—
1608C2×C4—1461no—
1609C2×C4—1461no—
1610C2×C4—1461no—
1611C2×C4—1461no—
1612C2×C4—1461no—
1613C2×C4—1461no—
1614C2×C4—1461no—
1615C2×C4—1461no—
1616C2×C4—1461no—
1617C2×C4—1461no—
1618C2×C4—1461no—
1619C2×C4—1468no—
1620C2×C4—1468no—
1621C2×C4—1468no—
1622C2×C4—1461no—
1623C2×C4—1461no—
1624C2×C4—1461no—
1625C2×C4—1461no—
1626C2×C4—1461no—
1627C2×C4—1461no—
1628C2×C4—1461no—
1629C2×C4—1461no—
1630C2×C4C2×D4×D7312yes—
1631C2×C4C2×#1192402712yes—
1632C2×C4C2×#1192402712yes—
1633C2×C4C2×#1192402712yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—22no—
1646C22—22no—
1647C22—22no—
1648C22—22no—
1649C22—22no—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—416no—
1656C22—416no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—41no—
1665C22—41no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22#1798909314yes—
1677C22#1798911814yescomplemented
1678C22C22×D4×D7311yescharacteristic
1679C22C2×#41×D7311yescharacteristic
1680C22C22×#1192402711yescharacteristic
1681C22C22×#1192402711yescharacteristic
1682C22C22×#1192402711yescharacteristic
1683C22H(5,𝔽2)×D7311yescharacteristic
1684C22#1798942211yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—22no—
1688C4—22no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—2921no—
1695C4—2921no—
1696C4—2921no—
1697C4—2921no—
1698C4—2921no—
1699C4—2921no—
1700C4—2921no—
1701C4—2921no—
1702C4—2921no—
1703C4—2921no—
1704C4—2921no—
1705C4—734no—
1706C4—1462no—
1707C4—1462no—
1708C4—1462no—
1709C4—1462no—
1710C2—24no—
1711C2—24no—
1712C2—42no—
1713C2—42no—
1714C2—42no—
1715C2—81no—
1716C2C2×#1798909311yescharacteristic
1717C2C2×#1798911811yescharacteristic
1718C2#2262333711yescharacteristic
1719C2#546×D7311yescharacteristic
1720C2D4×#1192402711yescharacteristic
1721C2#2262348211yescharacteristic
1722C2#2262353211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
Fitting, prime radicalC73×#2410C2
hypercenter#2410D73
hypocenterC73#34670
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2410

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989118C2semidirect
2. C22×D4×Dic73C2semidirect
3. #22614191C2semidirect
4. #22614176C2semidirect
5. #22614071C2semidirect
6. #22614056C2semidirect
7. #22613977C2semidirect
8. #22613962C2semidirect
9. #22613878C2semidirect
10. #22613863C2semidirect
11. #22613759C2semidirect
12. #22613677C2semidirect
13. #22613592C2semidirect
14. #22613488C2semidirect
15. #22613406C2semidirect
16. #22613328C2semidirect
17. #22613254C2semidirect
18. #22613219C2semidirect
19. #22613187C2semidirect
20. #22613166C2semidirect
21. #22613166C2semidirect
22. #22612463C2semidirect
23. #22612456C2semidirect
24. #121×Dic73C2semidirect
25. #120×Dic73C2semidirect
26. #120×Dic73C2semidirect
27. #22612371C2semidirect
28. #22612371C2semidirect
29. #22612309C2semidirect
30. C2×C22⋊C4×Dic73C2semidirect
35. C2×#14556584C22semidirect
36. C2×#14556584C22semidirect
37. C2×#14556582C22semidirect
38. C2×#14556578C22semidirect
41. C2×#14556572C22semidirect
42. C2×#14556570C22semidirect
44. C2×#14556556C22semidirect
55. C2×D4×Dic73C22semidirect
56. C2×D4×Dic73C22semidirect
57. C2×D4×Dic73C22semidirect
58. C2×D4×Dic73C22semidirect
59. C2×#14556547C22semidirect
60. C2×#14556547C22semidirect
61. C2×#14556547C22semidirect
67. C22×C4×Dic73C22semidirect
68. C22×C4×Dic73C22semidirect
69. #17988529C22semidirect
70. #17988527C22semidirect
71. #17988526C22semidirect
72. #17988523C22semidirect
73. #17988520C22semidirect
74. #17988519C22semidirect
75. #17988519C22semidirect
76. #17988515C22semidirect
77. #17988515C22semidirect
78. #17988515C22semidirect
79. #17988515C22semidirect
80. #17988512C22semidirect
81. #17988512C22semidirect
82. #17988512C22semidirect
83. #17988510C22semidirect
84. #17988510C22semidirect
85. #17988510C22semidirect
86. #17988510C22semidirect
91. #17988501C22semidirect
92. #17988501C22semidirect
93. #17988501C22semidirect
94. #17988501C22semidirect
95. #17988499C22semidirect
96. #17988499C22semidirect
97. #17988491C22semidirect
98. #17988490C22semidirect
99. #17988486C22semidirect
100. #17988482C22semidirect
101. #17988481C22semidirect
102. #17988481C22semidirect
103. #17988481C22semidirect
104. #17988481C22semidirect
105. #17988480C22semidirect
106. #17988480C22semidirect
107. #17988475C22semidirect
108. #17988475C22semidirect
109. #17988474C22semidirect
110. #17988474C22semidirect
111. #17988472C22semidirect
112. #17988472C22semidirect
113. #17988472C22semidirect
114. #17988470C22semidirect
115. #17988470C22semidirect
116. #17988468C22semidirect
122. #17988467C22semidirect
123. #17988467C22semidirect
124. #17988467C22semidirect
125. #17988467C22semidirect
126. #17988467C22semidirect
129. #17988462C22semidirect
130. #17988462C22semidirect
131. #17988462C22semidirect
132. #17988462C22semidirect
135. #17988460C22semidirect
136. #17988460C22semidirect
138. #17988459C22semidirect
139. #17988448C22semidirect
140. #17988448C22semidirect
141. #17988448C22semidirect
142. #17988447C22semidirect
146. #17988445C22semidirect
147. #17988445C22semidirect
151. C4⋊C4×Dic73C22semidirect
152. #17988438C22semidirect
153. #17988438C22semidirect
154. #17988438C22semidirect
160. C22⋊C4×Dic73C22semidirect
161. C22⋊C4×Dic73C22semidirect
162. C22⋊C4×Dic73C22semidirect
163. C22⋊C4×Dic73C22semidirect
164. C22⋊C4×Dic73C22semidirect
165. C22⋊C4×Dic73C22semidirect
166. C22⋊C4×Dic73C22semidirect
167. C22⋊C4×Dic73C22semidirect
168. C22⋊C4×Dic73C22semidirect
169. C22⋊C4×Dic73C22semidirect
170. C22⋊C4×Dic73C22semidirect
171. #17988432C22semidirect
172. C2×#14556498C22semidirect
173. C2×#14556498C22semidirect
233. D4×Dic73D4semidirect
815. C22×C73#529semidirect
893. C73#34670semidirect
1677. C22#17989118semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891182
C22×D4×Dic732
#226141912
#226141762
#226140712
#226140562
#226139772
#226139622
#226138782
#226138632
#226137592
#226136772
#226135922
#226134882
#226134062
#226133282
#226132542
#226132192
#226131872
#226131662
#226124632
#226124562
#121×Dic732
#120×Dic732
#226123712
#226123092
C2×C22⋊C4×Dic732
C73×#24102
#3467073