Finite Group Databasebeta

← #2465×D73 #33253952

Subgroups — #2465×D73 #33253952

Order 18688.

2854 conjugacy classes of subgroups.

The subgroup lattice has 1590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D73C211yesmaximal, characteristic
2C2×C4×Q8×D73C211yesmaximal, characteristic, complemented
3#22613959C211yesmaximal, characteristic, complemented
4#22613958C211yesmaximal, characteristic, complemented
5#22613957C211yesmaximal, characteristic, complemented
6#22613956C211yesmaximal, characteristic, complemented
7#22613955C211yesmaximal, characteristic, complemented
8#22613954C211yesmaximal, characteristic, complemented
9#22613953C211yesmaximal, characteristic, complemented
10#22613952C211yesmaximal, characteristic, complemented
11#22613951C211yesmaximal, characteristic, complemented
12#22613950C211yesmaximal, characteristic, complemented
13#22613949C211yesmaximal, characteristic, complemented
14#22613948C211yesmaximal, characteristic, complemented
15#22613947C211yesmaximal, characteristic, complemented
16#22613946C211yesmaximal, characteristic, complemented
17#22613945C211yesmaximal, characteristic, complemented
18#396×D73C211yesmaximal, characteristic
19#395×D73C211yesmaximal, characteristic, complemented
20#395×D73C211yesmaximal, characteristic, complemented
21#393×D73C211yesmaximal, characteristic
22#391×D73C211yesmaximal, characteristic, complemented
23#389×D73C211yesmaximal, characteristic, complemented
24#388×D73C211yesmaximal, characteristic
25#388×D73C211yesmaximal, characteristic
26#387×D73C211yesmaximal, characteristic, complemented
27#387×D73C211yesmaximal, characteristic, complemented
28#387×D73C211yesmaximal, characteristic, complemented
29#385×D73C211yesmaximal, characteristic
30C4×C22⋊C4×D73C211yesmaximal, characteristic
31C73×#2465C211yesmaximal, characteristic, complemented
32C22×Q8×D73C2211yescharacteristic
33C22×Q8×D73C2211yescharacteristic
34C23×C4×D73C2211yescharacteristic
35C2×#14556571C2211yescharacteristic
36C2×#14556570C2211yescharacteristic
37C2×#14556569C2211yescharacteristic
38C2×#14556569C2211yescharacteristic
39C2×#14556568C2211yescharacteristic
40C2×#14556568C2211yescharacteristic
41C2×#14556567C2211yescharacteristic
42C22⋊Q8×D73—28no—
43C2×Q8×Dic73C2211yescharacteristic, complemented
44C2×C4×Dic146C2211yescharacteristic, complemented
45C2×C4×Dic146C2211yescharacteristic, complemented
46C2×C4×Dic146C2211yescharacteristic, complemented
47C2×#14556556C2211yescharacteristic, complemented
48C2×#14556556C2211yescharacteristic, complemented
49C2×#14556556C2211yescharacteristic, complemented
50C4×Q8×D73—28no—
51C2×C4⋊C4×D73C2211yescharacteristic
52C2×C4⋊C4×D73C2211yescharacteristic
53C2×C4⋊C4×D73C2211yescharacteristic
54C2×C4⋊C4×D73C2211yescharacteristic
55C2×C4⋊C4×D73C2211yescharacteristic
56C2×C4⋊C4×D73C2211yescharacteristic
57C2×C4⋊C4×D73C2211yescharacteristic
58C2×C4⋊C4×D73C2211yescharacteristic
59C2×C4⋊C4×D73C2211yescharacteristic
60C2×C4⋊C4×D73C2211yescharacteristic
61C2×C22⋊C4×D73C2211yescharacteristic
62C2×C22⋊C4×D73C2211yescharacteristic
63C2×C22⋊C4×D73C2211yescharacteristic
64C2×C22⋊C4×D73C2211yescharacteristic
65C2×C22⋊C4×D73C2211yescharacteristic
66C2×C22⋊C4×D73C2211yescharacteristic
67C2×C42×D73C2211yescharacteristic
68C2×C42×D73C2211yescharacteristic
69C2×C42×D73C2211yescharacteristic
70C2×C42×D73C2211yescharacteristic
71#17988511C2211yescharacteristic
72#17988510C2211yescharacteristic
73#17988510C2211yescharacteristic
74#17988510C2211yescharacteristic
75#17988509C2211yescharacteristic
76#17988509C2211yescharacteristic
77#17988509C2211yescharacteristic
78#17988508C2211yescharacteristic, complemented
79#17988508C2211yescharacteristic, complemented
80#17988508C2211yescharacteristic, complemented
81#17988508C2211yescharacteristic, complemented
82#17988508C2211yescharacteristic, complemented
83#17988508C2211yescharacteristic, complemented
84#17988507C2211yescharacteristic, complemented
85#17988507C2211yescharacteristic, complemented
86#17988507C2211yescharacteristic, complemented
87#17988507C2211yescharacteristic, complemented
88#17988507C2211yescharacteristic, complemented
89#17988507C2211yescharacteristic, complemented
90#17988506C2211yescharacteristic, complemented
91#17988506C2211yescharacteristic, complemented
92#17988500C2211yescharacteristic
93#17988500C2211yescharacteristic
94#17988500C2211yescharacteristic
95#17988499C2211yescharacteristic
96#17988499C2211yescharacteristic
97#17988499C2211yescharacteristic
98#17988498C2211yescharacteristic
99#17988494C2211yescharacteristic, complemented
100#17988493C2211yescharacteristic, complemented
101#17988492C2211yescharacteristic, complemented
102#17988491C2211yescharacteristic, complemented
103#17988491C2211yescharacteristic, complemented
104#17988491C2211yescharacteristic, complemented
105#17988491C2211yescharacteristic, complemented
106#17988486C2211yescharacteristic, complemented
107#17988485C2211yescharacteristic, complemented
108#17988484C2211yescharacteristic, complemented
109#17988484C2211yescharacteristic, complemented
110#17988483C2211yescharacteristic, complemented
111#17988482C2211yescharacteristic, complemented
112#17988482C2211yescharacteristic, complemented
113#17988481C2211yescharacteristic
114#17988481C2211yescharacteristic
115#17988480C2211yescharacteristic
116#17988480C2211yescharacteristic
117#17988479C2211yescharacteristic
118#17988479C2211yescharacteristic
119#17988478C2211yescharacteristic
120#17988478C2211yescharacteristic
121#17988477C2211yescharacteristic
122#17988477C2211yescharacteristic
123#17988476C2211yescharacteristic
124#17988476C2211yescharacteristic
125#17988475C2211yescharacteristic
126#17988475C2211yescharacteristic
127#17988474C2211yescharacteristic, complemented
128#17988474C2211yescharacteristic, complemented
129#17988474C2211yescharacteristic, complemented
130#17988473C2211yescharacteristic, complemented
131#17988473C2211yescharacteristic, complemented
132#17988473C2211yescharacteristic, complemented
133#17988472C2211yescharacteristic, complemented
134#17988472C2211yescharacteristic, complemented
135#17988472C2211yescharacteristic, complemented
136#17988471C2211yescharacteristic, complemented
137#17988471C2211yescharacteristic, complemented
138#17988471C2211yescharacteristic, complemented
139#17988470C2211yescharacteristic, complemented
140#17988470C2211yescharacteristic, complemented
141#17988470C2211yescharacteristic, complemented
142#17988469C2211yescharacteristic, complemented
143#17988469C2211yescharacteristic, complemented
144#17988469C2211yescharacteristic, complemented
145#17988468C2211yescharacteristic, complemented
146#17988468C2211yescharacteristic, complemented
147#17988468C2211yescharacteristic, complemented
148#17988462C2211yescharacteristic
149#17988461C2211yescharacteristic
150#17988461C2211yescharacteristic
151#17988460C2211yescharacteristic
152#17988459C2211yescharacteristic
153#17988458C2211yescharacteristic
154#17988458C2211yescharacteristic
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C4×#11924005C2211yescharacteristic
158C4×#11924005C2211yescharacteristic
159C4×C22⋊Dic73C2211yescharacteristic
160#17988434C2211yescharacteristic
161#17988434C2211yescharacteristic
162#95×D73C2211yescharacteristic
163#95×D73C2211yescharacteristic
164#95×D73C2211yescharacteristic
165#95×D73C2211yescharacteristic
166#95×D73C2211yescharacteristic
167#95×D73C2211yescharacteristic
168#95×D73C2211yescharacteristic
169#95×D73C2211yescharacteristic
170#95×D73C2211yescharacteristic
171#95×D73C2211yescharacteristic
172#95×D73C2211yescharacteristic
173#95×D73C2211yescharacteristic
174C2×C22⋊Q8×C73C2211yescharacteristic
175C2×C4×Q8×C73C2211yescharacteristic, complemented
176#396×C73C2211yescharacteristic
177#395×C73C2211yescharacteristic, complemented
178#395×C73C2211yescharacteristic, complemented
179#393×C73C2211yescharacteristic
180#391×C73C2211yescharacteristic, complemented
181#389×C73C2211yescharacteristic, complemented
182#388×C73C2211yescharacteristic
183#388×C73C2211yescharacteristic
184#387×C73C2211yescharacteristic, complemented
185#387×C73C2211yescharacteristic, complemented
186#387×C73C2211yescharacteristic, complemented
187#385×C73C2211yescharacteristic
188C4×C22⋊C4×C73C2211yescharacteristic
189C24×D73C2311yescharacteristic
190C22×Dic146C2311yescharacteristic
191C22×Dic146C2311yescharacteristic
192C22×Dic146C2311yescharacteristic
193C22×Dic146C2311yescharacteristic
194C22×Dic146C2311yescharacteristic
195C22×Dic146C2311yescharacteristic
196C2×Q8×D73—24no—
197C2×Q8×D73—24no—
198C2×Q8×D73—24no—
199C2×Q8×D73—24no—
200C2×Q8×D73—24no—
201C2×Q8×D73—42no—
202C23×Dic73C2311yescharacteristic
203C22×C4×D73—24no—
204C22×C4×D73—24no—
205C22×C4×D73—42no—
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212C22×C4×D73C2311yescharacteristic
213C22×C4×D73C2311yescharacteristic
214C22×C4×D73C2311yescharacteristic
215C22×C4×D73C2311yescharacteristic
216C22×C4×D73C2311yescharacteristic
217C22×C4×D73C2311yescharacteristic
218C22×C4×D73C2311yescharacteristic
219C22×C4×D73C2311yescharacteristic
220C22×C4×D73C2311yescharacteristic
221C22×C4×D73C2311yescharacteristic
222#14556571—24no—
223#14556570—24no—
224#14556569—24no—
225#14556569—24no—
226#14556568—24no—
227#14556568—24no—
228#14556567—24no—
229Q8×Dic73—24no—
230C4×Dic146—24no—
231C4×Dic146—24no—
232C4×Dic146—24no—
233#14556556—24no—
234#14556556—24no—
235#14556556—24no—
236C2×C4⋊Dic73C2311yescharacteristic
237C2×C4⋊Dic73C2311yescharacteristic
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×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
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×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C4⋊C4×D73—24no—
267C4⋊C4×D73—24no—
268C4⋊C4×D73—24no—
269C4⋊C4×D73—24no—
270C4⋊C4×D73—24no—
271C4⋊C4×D73—24no—
272C4⋊C4×D73—24no—
273C4⋊C4×D73—42no—
274C4⋊C4×D73—42no—
275C4⋊C4×D73D418yes—
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C22⋊C4×D73—24no—
295C22⋊C4×D73—24no—
296C22⋊C4×D73—24no—
297C22⋊C4×D73—24no—
298C22⋊C4×D73—42no—
299C22⋊C4×D73Q818yescomplemented
300C2×C4×Dic73C2311yescharacteristic
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
312C42×D73—24no—
313C42×D73—24no—
314C42×D73—24no—
315C42×D73—42no—
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
348#14556498C2311yescharacteristic
349#14556498C2311yescharacteristic
350#14556498C2311yescharacteristic
351#14556498C2311yescharacteristic
352C22×Q8×C73C2311yescharacteristic
353C22×Q8×C73C2311yescharacteristic
354C23×C4×C73C2311yescharacteristic
355C22⋊Q8×C73—24no—
356C4×Q8×C73—24no—
357C2×C4⋊C4×C73C2311yescharacteristic
358C2×C4⋊C4×C73C2311yescharacteristic
359C2×C4⋊C4×C73C2311yescharacteristic
360C2×C4⋊C4×C73C2311yescharacteristic
361C2×C4⋊C4×C73C2311yescharacteristic
362C2×C4⋊C4×C73C2311yescharacteristic
363C2×C4⋊C4×C73C2311yescharacteristic
364C2×C4⋊C4×C73C2311yescharacteristic
365C2×C4⋊C4×C73C2311yescharacteristic
366C2×C4⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73C2311yescharacteristic
368C2×C22⋊C4×C73C2311yescharacteristic
369C2×C22⋊C4×C73C2311yescharacteristic
370C2×C22⋊C4×C73C2311yescharacteristic
371C2×C22⋊C4×C73C2311yescharacteristic
372C2×C22⋊C4×C73C2311yescharacteristic
373C2×C42×C73C2311yescharacteristic
374C2×C42×C73C2311yescharacteristic
375C2×C42×C73C2311yescharacteristic
376C2×C42×C73C2311yescharacteristic
377#95×C73C2311yescharacteristic
378#95×C73C2311yescharacteristic
379#95×C73C2311yescharacteristic
380#95×C73C2311yescharacteristic
381#95×C73C2311yescharacteristic
382#95×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385#95×C73C2311yescharacteristic
386#95×C73C2311yescharacteristic
387#95×C73C2311yescharacteristic
388#95×C73C2311yescharacteristic
389C23×D73—22no—
390C23×D73—22no—
391C23×D73—22no—
392C23×D73—22no—
393C23×D73—22no—
394C23×D73—22no—
395C23×D73C2×Q814yes—
396C23×D73C2411yescharacteristic
397C23×D73C2411yescharacteristic
398C2×Dic146—22no—
399C2×Dic146—22no—
400C2×Dic146—22no—
401C2×Dic146—22no—
402C2×Dic146—22no—
403C2×Dic146—22no—
404C2×Dic146—22no—
405C2×Dic146—22no—
406C2×Dic146—22no—
407C2×Dic146—22no—
408C2×Dic146—22no—
409C2×Dic146—22no—
410C2×Dic146—22no—
411C2×Dic146—22no—
412C2×Dic146—22no—
413C2×Dic146—41no—
414C2×Dic146—41no—
415C2×Dic146—41no—
416Q8×D73—232no—
417Q8×D73—416no—
418C22×Dic73—22no—
419C22×Dic73—22no—
420C22×Dic73—41no—
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C22×Dic73C2411yescharacteristic
430C22×Dic73C2411yescharacteristic
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C2×C4×D73—22no—
436C2×C4×D73—22no—
437C2×C4×D73—22no—
438C2×C4×D73—22no—
439C2×C4×D73—22no—
440C2×C4×D73—22no—
441C2×C4×D73—22no—
442C2×C4×D73—22no—
443C2×C4×D73—22no—
444C2×C4×D73—22no—
445C2×C4×D73—22no—
446C2×C4×D73—22no—
447C2×C4×D73—22no—
448C2×C4×D73—22no—
449C2×C4×D73—22no—
450C2×C4×D73—22no—
451C2×C4×D73—22no—
452C2×C4×D73—22no—
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—22no—
456C2×C4×D73—22no—
457C2×C4×D73—22no—
458C2×C4×D73—22no—
459C2×C4×D73—22no—
460C2×C4×D73—22no—
461C2×C4×D73—22no—
462C2×C4×D73—22no—
463C2×C4×D73—22no—
464C2×C4×D73—22no—
465C2×C4×D73—22no—
466C2×C4×D73—22no—
467C2×C4×D73—22no—
468C2×C4×D73—22no—
469C2×C4×D73—22no—
470C2×C4×D73—22no—
471C2×C4×D73—22no—
472C2×C4×D73—22no—
473C2×C4×D73—416no—
474C2×C4×D73—41no—
475C2×C4×D73—41no—
476C2×C4×D73C2×D414yes—
477C2×C4×D73C2×D414yes—
478C2×C4×D73C2×D414yes—
479C2×C4×D73C2×Q814yes—
480C2×C4×D73C2×Q814yes—
481C2×C4×D73#4114yes—
482C2×C4×D73#4114yes—
483C2×C4×D73#4114yes—
484C4⋊Dic73—22no—
485C4⋊Dic73—22no—
486C4⋊Dic73—22no—
487C4⋊Dic73—22no—
488C4⋊Dic73—22no—
489C4⋊Dic73—22no—
490C4⋊Dic73—22no—
491C4⋊Dic73—41no—
492C4⋊Dic73—41no—
493C4⋊Dic73C2×D414yes—
494#11924007—22no—
495#11924007—22no—
496#11924007—22no—
497#11924007—22no—
498#11924007—22no—
499#11924007—22no—
500#11924007—22no—
501#11924007—22no—
502#11924007—22no—
503#11924007—22no—
504#11924007—22no—
505#11924007—22no—
506#11924007—22no—
507#11924007—22no—
508#11924007—41no—
509#11924007—41no—
510#11924007—41no—
511#11924007—41no—
512#11924007C2×D414yes—
513#11924007C2×D414yes—
514C22⋊Dic73—22no—
515C22⋊Dic73—22no—
516C22⋊Dic73—22no—
517C22⋊Dic73—22no—
518C22⋊Dic73—41no—
519C22⋊Dic73C2×Q814yescomplemented
520#11924005—22no—
521#11924005—22no—
522#11924005—22no—
523#11924005—22no—
524#11924005—22no—
525#11924005—22no—
526#11924005—22no—
527#11924005—22no—
528#11924005—41no—
529#11924005—41no—
530#11924005C2×Q814yescomplemented
531#11924005C2×Q814yescomplemented
532C4×Dic73—22no—
533C4×Dic73—22no—
534C4×Dic73—22no—
535C4×Dic73—22no—
536C4×Dic73—22no—
537C4×Dic73—22no—
538C4×Dic73—22no—
539C4×Dic73—22no—
540C4×Dic73—22no—
541C4×Dic73—41no—
542C4×Dic73—41no—
543C4×Dic73—41no—
544C24×C73C2411yescharacteristic
545C2×Q8×C73—22no—
546C2×Q8×C73—22no—
547C2×Q8×C73—22no—
548C2×Q8×C73—22no—
549C2×Q8×C73—22no—
550C2×Q8×C73—41no—
551C22×C4×C73—22no—
552C22×C4×C73—22no—
553C22×C4×C73—41no—
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C22×C4×C73C2411yescharacteristic
559C22×C4×C73C2411yescharacteristic
560C22×C4×C73C2411yescharacteristic
561C22×C4×C73C2411yescharacteristic
562C22×C4×C73C2411yescharacteristic
563C22×C4×C73C2411yescharacteristic
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C4⋊C4×C73—22no—
569C4⋊C4×C73—22no—
570C4⋊C4×C73—22no—
571C4⋊C4×C73—22no—
572C4⋊C4×C73—22no—
573C4⋊C4×C73—22no—
574C4⋊C4×C73—22no—
575C4⋊C4×C73—41no—
576C4⋊C4×C73—41no—
577C4⋊C4×C73C2×D414yes—
578C22⋊C4×C73—22no—
579C22⋊C4×C73—22no—
580C22⋊C4×C73—22no—
581C22⋊C4×C73—22no—
582C22⋊C4×C73—41no—
583C22⋊C4×C73C2×Q814yescomplemented
584C42×C73—22no—
585C42×C73—22no—
586C42×C73—22no—
587C42×C73—41no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73C22×Q812yes—
595C23×C73C2511yescharacteristic
596C22×D73—21no—
597C22×D73—21no—
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—28no—
603C22×D73—28no—
604C22×D73—28no—
605C22×D73—44no—
606C22×D73—44no—
607C22×D73—44no—
608C22×D73—44no—
609C22×D73C22×D412yes—
610C22×D73C22×Q812yes—
611C22×D73C22×Q812yes—
612C22×D73C2×#4112yes—
613C22×D73C2×#4112yes—
614C22×D73C2×#4112yes—
615C22×D73H(5,𝔽2)12yes—
616C22×D732−1+412yes—
617Q8×C73—28no—
618Q8×C73—44no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—44no—
654C2×C4×C73C22×D412yes—
655C2×C4×C73C22×D412yes—
656C2×C4×C73C22×D412yes—
657C2×C4×C73C22×Q812yes—
658C2×C4×C73C22×Q812yes—
659C2×C4×C73C2×#4112yes—
660C2×C4×C73C2×#4112yes—
661C2×C4×C73C2×#4112yes—
662C2×Dic73—21no—
663C2×Dic73—21no—
664C2×Dic73—21no—
665C2×Dic73—21no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—44no—
697C2×Dic73C22×D412yes—
698C2×Dic73C22×D412yes—
699C2×Dic73C22×D412yes—
700C2×Dic73C22×Q812yes—
701C2×Dic73C22×Q812yes—
702C2×Dic73C2×#4112yes—
703C2×Dic73C2×#4112yes—
704C2×Dic73C2×#4112yes—
705C4×D73—28no—
706C4×D73—28no—
707C4×D73—28no—
708C4×D73—28no—
709C4×D73—28no—
710C4×D73—28no—
711C4×D73—28no—
712C4×D73—28no—
713C4×D73—44no—
714C4×D73—44no—
715C4×D73—44no—
716C4×D73—44no—
717C4×D73—44no—
718C4×D73—44no—
719C4×D73—44no—
720C4×D73—44no—
721Dic146—28no—
722Dic146—28no—
723Dic146—28no—
724Dic146—44no—
725Dic146—44no—
726Dic146—44no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—41no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73C23×D411yescharacteristic
735C22×C73C23×Q811yescharacteristic
736C22×C73C22×#4111yescharacteristic
737C22×C73C22×#4111yescharacteristic
738C22×C73C22×#4111yescharacteristic
739C22×C73C2×H(5,𝔽2)11yescharacteristic
740C22×C73C2×2−1+411yescharacteristic
741C2×D73—22no—
742C2×D73—22no—
743C2×D73—22no—
744C2×D73—41no—
745C2×D73—41no—
746C2×D73—41no—
747C2×D73—41no—
748C2×D73—416no—
749C2×D73#52514yes—
750C2×D73#53314yes—
751C2×D73#54214yes—
752C2×D73#54614yes—
753C2×D73D4×Q814yes—
754C2×D73#55414yes—
755C2×D73#55614yes—
756C4×C73—22no—
757C4×C73—22no—
758C4×C73—22no—
759C4×C73—22no—
760C4×C73—22no—
761C4×C73—22no—
762C4×C73—22no—
763C4×C73—22no—
764C4×C73—41no—
765C4×C73—41no—
766C4×C73—41no—
767C4×C73—41no—
768C4×C73—41no—
769C4×C73—41no—
770Dic73—22no—
771Dic73—22no—
772Dic73—22no—
773Dic73—22no—
774Dic73—22no—
775Dic73—22no—
776Dic73—22no—
777Dic73—22no—
778Dic73—41no—
779Dic73—41no—
780Dic73—41no—
781Dic73—41no—
782Dic73—41no—
783Dic73—41no—
784C2×#2465—731nomaximal, Sylow
785C2×C73—42no—
786C2×C73C2×#52511yescharacteristic
787C2×C73C2×#53311yescharacteristic
788C2×C73C2×#54211yescharacteristic
789C2×C73C2×#54611yescharacteristic
790C2×C73C2×D4×Q811yescharacteristic
791C2×C73C2×#55411yescharacteristic
792C2×C73C2×#55611yescharacteristic
793D73—42no—
794D73#246518yesdirect product factor
795C22×C22⋊Q8—731no—
796C22×C4×Q8—731no—
797#2465—731no—
798#2465—731no—
799#2465—731no—
800#2465—731no—
801#2465—731no—
802#2465—731no—
803#2465—731no—
804#2465—731no—
805#2465—731no—
806#2465—731no—
807#2465—731no—
808#2465—731no—
809#2465—731no—
810#2465—731no—
811#2465—731no—
812#2465D7311yescharacteristic, direct product factor
813C2×#396—731no—
814C2×#395—731no—
815C2×#395—731no—
816C2×#393—731no—
817C2×#391—731no—
818C2×#389—731no—
819C2×#388—731no—
820C2×#388—731no—
821C2×#387—731no—
822C2×#387—731no—
823C2×#387—731no—
824C2×#385—731no—
825C2×C4×C22⋊C4—731no—
826C73C2×#246511yescharacteristic, complemented, Sylow
827C23×Q8—731no—
828C23×Q8—731no—
829C24×C4—731no—
830C2×C22⋊Q8—731no—
831C2×C22⋊Q8—731no—
832C2×C22⋊Q8—731no—
833C2×C22⋊Q8—731no—
834C2×C22⋊Q8—731no—
835C2×C22⋊Q8—731no—
836C2×C22⋊Q8—731no—
837C2×C22⋊Q8—1468no—
838C2×C22⋊Q8C2×D7311yescharacteristic
839C2×C4×Q8—731no—
840C2×C4×Q8—731no—
841C2×C4×Q8—731no—
842C2×C4×Q8—731no—
843C2×C4×Q8—731no—
844C2×C4×Q8—731no—
845C2×C4×Q8—731no—
846C2×C4×Q8—1468no—
847C2×C4×Q8C2×D7311yescharacteristic, complemented
848C22×C4⋊C4—731no—
849C22×C4⋊C4—731no—
850C22×C4⋊C4—731no—
851C22×C4⋊C4—731no—
852C22×C4⋊C4—731no—
853C22×C4⋊C4—731no—
854C22×C4⋊C4—731no—
855C22×C4⋊C4—731no—
856C22×C4⋊C4—731no—
857C22×C4⋊C4—731no—
858C22×C22⋊C4—731no—
859C22×C22⋊C4—731no—
860C22×C22⋊C4—731no—
861C22×C22⋊C4—731no—
862C22×C22⋊C4—731no—
863C22×C22⋊C4—731no—
864C22×C42—731no—
865C22×C42—731no—
866C22×C42—731no—
867C22×C42—731no—
868#396—731no—
869#396—731no—
870#396—731no—
871#396—731no—
872#396—731no—
873#396—731no—
874#396—731no—
875#396C2×D7311yescharacteristic
876#395—731no—
877#395—731no—
878#395—731no—
879#395—731no—
880#395—731no—
881#395—731no—
882#395—731no—
883#395—731no—
884#395—731no—
885#395—731no—
886#395—731no—
887#395—731no—
888#395—731no—
889#395—731no—
890#395C2×D7311yescharacteristic, complemented
891#395C2×D7311yescharacteristic, complemented
892#393—731no—
893#393—731no—
894#393—731no—
895#393—731no—
896#393—731no—
897#393—731no—
898#393—731no—
899#393C2×D7311yescharacteristic
900#391—731no—
901#391—731no—
902#391—731no—
903#391—731no—
904#391—731no—
905#391—731no—
906#391—731no—
907#391C2×D7311yescharacteristic, complemented
908#389—731no—
909#389—731no—
910#389—731no—
911#389—731no—
912#389—731no—
913#389—731no—
914#389—731no—
915#389C2×D7311yescharacteristic, complemented
916#388—731no—
917#388—731no—
918#388—731no—
919#388—731no—
920#388—731no—
921#388—731no—
922#388—731no—
923#388—731no—
924#388—731no—
925#388—731no—
926#388—731no—
927#388—731no—
928#388—731no—
929#388—731no—
930#388C2×D7311yescharacteristic
931#388C2×D7311yescharacteristic
932#387—731no—
933#387—731no—
934#387—731no—
935#387—731no—
936#387—731no—
937#387—731no—
938#387—731no—
939#387—731no—
940#387—731no—
941#387—731no—
942#387—731no—
943#387—731no—
944#387—731no—
945#387—731no—
946#387—731no—
947#387—731no—
948#387—731no—
949#387—731no—
950#387—731no—
951#387—731no—
952#387—731no—
953#387C2×D7311yescharacteristic, complemented
954#387C2×D7311yescharacteristic, complemented
955#387C2×D7311yescharacteristic, complemented
956#385—731no—
957#385—731no—
958#385—731no—
959#385—731no—
960#385—731no—
961#385—731no—
962#385—731no—
963#385C2×D7311yescharacteristic
964C4×C22⋊C4—731no—
965C4×C22⋊C4—731no—
966C4×C22⋊C4—731no—
967C4×C22⋊C4—731no—
968C4×C22⋊C4—731no—
969C4×C22⋊C4—731no—
970C4×C22⋊C4—731no—
971C4×C22⋊C4C2×D7311yescharacteristic
972C2×#95—731no—
973C2×#95—731no—
974C2×#95—731no—
975C2×#95—731no—
976C2×#95—731no—
977C2×#95—731no—
978C2×#95—731no—
979C2×#95—731no—
980C2×#95—731no—
981C2×#95—731no—
982C2×#95—731no—
983C2×#95—731no—
984C25—731no—
985C22×Q8—2922no—
986C22×Q8—731no—
987C22×Q8—731no—
988C22×Q8—731no—
989C22×Q8—731no—
990C22×Q8—731no—
991C22×Q8—731no—
992C22×Q8—1464no—
993C22×Q8—1464no—
994C22×Q8—1464no—
995C22×Q8—1464no—
996C22×Q8—1464no—
997C22×Q8C22×D7311yescharacteristic
998C22×Q8C22×D7311yescharacteristic
999C23×C4—2922no—
1000C23×C4—731no—
1001C23×C4—731no—
1002C23×C4—731no—
1003C23×C4—731no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4—731no—
1010C23×C4—731no—
1011C23×C4—731no—
1012C23×C4—731no—
1013C23×C4—731no—
1014C23×C4—731no—
1015C23×C4—731no—
1016C23×C4—731no—
1017C23×C4—1464no—
1018C23×C4—1464no—
1019C23×C4C22×D7311yescharacteristic
1020C22⋊Q8—24no—
1021C22⋊Q8—1464no—
1022C22⋊Q8—1464no—
1023C22⋊Q8—1464no—
1024C22⋊Q8—1464no—
1025C22⋊Q8—1464no—
1026C22⋊Q8—1464no—
1027C22⋊Q8—1464no—
1028C4×Q8—24no—
1029C4×Q8—1464no—
1030C4×Q8—1464no—
1031C4×Q8—1464no—
1032C4×Q8—1464no—
1033C4×Q8—1464no—
1034C4×Q8—1464no—
1035C4×Q8—1464no—
1036C2×C4⋊C4—2922no—
1037C2×C4⋊C4—2922no—
1038C2×C4⋊C4—731no—
1039C2×C4⋊C4—731no—
1040C2×C4⋊C4—731no—
1041C2×C4⋊C4—731no—
1042C2×C4⋊C4—731no—
1043C2×C4⋊C4—731no—
1044C2×C4⋊C4—731no—
1045C2×C4⋊C4—731no—
1046C2×C4⋊C4—731no—
1047C2×C4⋊C4—738no—
1048C2×C4⋊C4—731no—
1049C2×C4⋊C4—731no—
1050C2×C4⋊C4—731no—
1051C2×C4⋊C4—731no—
1052C2×C4⋊C4—731no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4—731no—
1063C2×C4⋊C4—731no—
1064C2×C4⋊C4—731no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—731no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4—731no—
1069C2×C4⋊C4—1464no—
1070C2×C4⋊C4—1464no—
1071C2×C4⋊C4—1464no—
1072C2×C4⋊C4—1464no—
1073C2×C4⋊C4—1464no—
1074C2×C4⋊C4—1464no—
1075C2×C4⋊C4—1464no—
1076C2×C4⋊C4C22×D7311yescharacteristic
1077C2×C4⋊C4C22×D7311yescharacteristic
1078C2×C4⋊C4C22×D7311yescharacteristic
1079C2×C4⋊C4C22×D7311yescharacteristic
1080C2×C4⋊C4C22×D7311yescharacteristic
1081C2×C4⋊C4C22×D7311yescharacteristic
1082C2×C4⋊C4C22×D7311yescharacteristic
1083C2×C4⋊C4C22×D7311yescharacteristic
1084C2×C4⋊C4C22×D7311yescharacteristic
1085C2×C4⋊C4C22×D7311yescharacteristic
1086C2×C22⋊C4—2922no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—738no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—731no—
1098C2×C22⋊C4—731no—
1099C2×C22⋊C4—731no—
1100C2×C22⋊C4—731no—
1101C2×C22⋊C4—731no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—731no—
1104C2×C22⋊C4—731no—
1105C2×C22⋊C4—731no—
1106C2×C22⋊C4—1464no—
1107C2×C22⋊C4—1464no—
1108C2×C22⋊C4—1464no—
1109C2×C22⋊C4—1464no—
1110C2×C22⋊C4C22×D7311yescharacteristic
1111C2×C22⋊C4C22×D7311yescharacteristic
1112C2×C22⋊C4C22×D7311yescharacteristic
1113C2×C22⋊C4C22×D7311yescharacteristic
1114C2×C22⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4C22×D7311yescharacteristic
1116C2×C42—2922no—
1117C2×C42—731no—
1118C2×C42—731no—
1119C2×C42—731no—
1120C2×C42—731no—
1121C2×C42—731no—
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128C2×C42—731no—
1129C2×C42—1464no—
1130C2×C42—1464no—
1131C2×C42—1464no—
1132C2×C42C22×D7311yescharacteristic
1133C2×C42C22×D7311yescharacteristic
1134C2×C42C22×D7311yescharacteristic
1135C2×C42C22×D7311yescharacteristic
1136#95—731no—
1137#95—731no—
1138#95—731no—
1139#95—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95—731no—
1169#95—731no—
1170#95—731no—
1171#95—731no—
1172#95C22×D7311yescharacteristic
1173#95C22×D7311yescharacteristic
1174#95C22×D7311yescharacteristic
1175#95C22×D7311yescharacteristic
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180#95C22×D7311yescharacteristic
1181#95C22×D7311yescharacteristic
1182#95C22×D7311yescharacteristic
1183#95C22×D7311yescharacteristic
1184C24—731no—
1185C24—734no—
1186C24—731no—
1187C24—1462no—
1188C24—1462no—
1189C24—1462no—
1190C24—1462no—
1191C24—1462no—
1192C24—1462no—
1193C24C23×D7311yescharacteristic
1194C2×Q8—22no—
1195C2×Q8—22no—
1196C2×Q8—22no—
1197C2×Q8—22no—
1198C2×Q8—22no—
1199C2×Q8—41no—
1200C2×Q8—2921no—
1201C2×Q8—2921no—
1202C2×Q8—2921no—
1203C2×Q8—29216no—
1204C2×Q8—1462no—
1205C2×Q8—1462no—
1206C2×Q8—1462no—
1207C2×Q8—1462no—
1208C2×Q8—1462no—
1209C2×Q8—1462no—
1210C2×Q8—1462no—
1211C2×Q8—1462no—
1212C2×Q8—1462no—
1213C2×Q8—1462no—
1214C2×Q8—14632no—
1215C2×Q8—1462no—
1216C2×Q8—1462no—
1217C2×Q8—1462no—
1218C2×Q8—1462no—
1219C2×Q8—1462no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—41no—
1223C22×C4—2921no—
1224C22×C4—2921no—
1225C22×C4—29216no—
1226C22×C4—2921no—
1227C22×C4—731no—
1228C22×C4—731no—
1229C22×C4—731no—
1230C22×C4—731no—
1231C22×C4—731no—
1232C22×C4—731no—
1233C22×C4—731no—
1234C22×C4—731no—
1235C22×C4—734no—
1236C22×C4—734no—
1237C22×C4—734no—
1238C22×C4—734no—
1239C22×C4—734no—
1240C22×C4—734no—
1241C22×C4—734no—
1242C22×C4—734no—
1243C22×C4—731no—
1244C22×C4—731no—
1245C22×C4—731no—
1246C22×C4—731no—
1247C22×C4—731no—
1248C22×C4—731no—
1249C22×C4—1462no—
1250C22×C4—1462no—
1251C22×C4—1462no—
1252C22×C4—1462no—
1253C22×C4—1462no—
1254C22×C4—1462no—
1255C22×C4—1462no—
1256C22×C4—1462no—
1257C22×C4—1462no—
1258C22×C4—1462no—
1259C22×C4—1462no—
1260C22×C4—1462no—
1261C22×C4—1462no—
1262C22×C4—1462no—
1263C22×C4—1462no—
1264C22×C4—1462no—
1265C22×C4—1462no—
1266C22×C4—1462no—
1267C22×C4—1462no—
1268C22×C4—1462no—
1269C22×C4—1462no—
1270C22×C4—1462no—
1271C22×C4—1462no—
1272C22×C4—1462no—
1273C22×C4—1462no—
1274C22×C4—1462no—
1275C22×C4—1462no—
1276C22×C4—1462no—
1277C22×C4—1462no—
1278C22×C4—1462no—
1279C22×C4—1462no—
1280C22×C4—1462no—
1281C22×C4—1462no—
1282C22×C4—1462no—
1283C22×C4—1462no—
1284C22×C4—1462no—
1285C22×C4—1462no—
1286C22×C4—1462no—
1287C22×C4—1462no—
1288C22×C4—1462no—
1289C22×C4C23×D7311yescharacteristic
1290C22×C4C23×D7311yescharacteristic
1291C22×C4C23×D7311yescharacteristic
1292C22×C4C23×D7311yescharacteristic
1293C22×C4C23×D7311yescharacteristic
1294C22×C4C23×D7311yescharacteristic
1295C22×C4C23×D7311yescharacteristic
1296C22×C4C23×D7311yescharacteristic
1297C22×C4C23×D7311yescharacteristic
1298C22×C4C23×D7311yescharacteristic
1299C22×C4C23×D7311yescharacteristic
1300C22×C4C23×D7311yescharacteristic
1301C22×C4C23×D7311yescharacteristic
1302C22×C4C23×D7311yescharacteristic
1303C4⋊C4—22no—
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—22no—
1307C4⋊C4—22no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—41no—
1311C4⋊C4—41no—
1312C4⋊C4—2921no—
1313C4⋊C4—2921no—
1314C4⋊C4—2921no—
1315C4⋊C4—2921no—
1316C4⋊C4—2921no—
1317C4⋊C4—2921no—
1318C4⋊C4—734no—
1319C4⋊C4—734no—
1320C4⋊C4—734no—
1321C4⋊C4—1462no—
1322C4⋊C4—1462no—
1323C4⋊C4—1462no—
1324C4⋊C4—1462no—
1325C4⋊C4—1462no—
1326C4⋊C4—1462no—
1327C4⋊C4—1462no—
1328C4⋊C4—1462no—
1329C4⋊C4—1462no—
1330C4⋊C4—1462no—
1331C4⋊C4—1462no—
1332C4⋊C4—1462no—
1333C4⋊C4—1462no—
1334C4⋊C4—1462no—
1335C4⋊C4—1462no—
1336C4⋊C4—1462no—
1337C4⋊C4—1462no—
1338C4⋊C4—1462no—
1339C4⋊C4—1462no—
1340C4⋊C4—1462no—
1341C4⋊C4—1462no—
1342C4⋊C4D4×D7314yes—
1343C22⋊C4—22no—
1344C22⋊C4—22no—
1345C22⋊C4—22no—
1346C22⋊C4—22no—
1347C22⋊C4—41no—
1348C22⋊C4—2921no—
1349C22⋊C4—2921no—
1350C22⋊C4—2921no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—734no—
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⋊C4Q8×D7314yescomplemented
1367C42—22no—
1368C42—22no—
1369C42—22no—
1370C42—41no—
1371C42—2921no—
1372C42—2921no—
1373C42—2921no—
1374C42—1462no—
1375C42—1462no—
1376C42—1462no—
1377C42—1462no—
1378C42—1462no—
1379C42—1462no—
1380C42—1462no—
1381C42—1462no—
1382C42—1462no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—2924no—
1390C23—2924no—
1391C23—2924no—
1392C23—2924no—
1393C23—732no—
1394C23—732no—
1395C23—732no—
1396C23—732no—
1397C23—732no—
1398C23—732no—
1399C23—732no—
1400C23—732no—
1401C23—1468no—
1402C23—1468no—
1403C23—1468no—
1404C23—1461no—
1405C23—1461no—
1406C23—1461no—
1407C23—1461no—
1408C23—1461no—
1409C23—1461no—
1410C23C2×Q8×D7312yes—
1411C23C24×D7311yescharacteristic
1412Q8—28no—
1413Q8—44no—
1414Q8—2924no—
1415Q8—2924no—
1416Q8—2924no—
1417Q8—1468no—
1418Q8—1468no—
1419Q8—1468no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—44no—
1455C2×C4—2924no—
1456C2×C4—2924no—
1457C2×C4—2924no—
1458C2×C4—2924no—
1459C2×C4—2924no—
1460C2×C4—2924no—
1461C2×C4—2924no—
1462C2×C4—2924no—
1463C2×C4—2924no—
1464C2×C4—732no—
1465C2×C4—732no—
1466C2×C4—732no—
1467C2×C4—732no—
1468C2×C4—732no—
1469C2×C4—732no—
1470C2×C4—732no—
1471C2×C4—732no—
1472C2×C4—1468no—
1473C2×C4—1468no—
1474C2×C4—1468no—
1475C2×C4—1468no—
1476C2×C4—1468no—
1477C2×C4—1468no—
1478C2×C4—1468no—
1479C2×C4—1468no—
1480C2×C4—1461no—
1481C2×C4—1461no—
1482C2×C4—1461no—
1483C2×C4—1461no—
1484C2×C4—1461no—
1485C2×C4—1461no—
1486C2×C4—1461no—
1487C2×C4—1461no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4C2×D4×D7312yes—
1515C2×C4C2×D4×D7312yes—
1516C2×C4C2×D4×D7312yes—
1517C2×C4C2×Q8×D7312yes—
1518C2×C4C2×Q8×D7312yes—
1519C2×C4#41×D7312yes—
1520C2×C4#41×D7312yes—
1521C2×C4#41×D7312yes—
1522C22—22no—
1523C22—22no—
1524C22—22no—
1525C22—41no—
1526C22—41no—
1527C22—41no—
1528C22—41no—
1529C22—29216no—
1530C22—2921no—
1531C22—2921no—
1532C22—2921no—
1533C22—2921no—
1534C22—734no—
1535C22—734no—
1536C22—734no—
1537C22—734no—
1538C22—734no—
1539C22—734no—
1540C22—734no—
1541C22—1462no—
1542C22—1462no—
1543C22—1462no—
1544C22C22×D4×D7311yescharacteristic
1545C22C22×Q8×D7311yescharacteristic
1546C22C2×#41×D7311yescharacteristic
1547C22C2×#41×D7311yescharacteristic
1548C22C2×#41×D7311yescharacteristic
1549C22H(5,𝔽2)×D7311yescharacteristic
1550C222−1+4×D7311yescharacteristic
1551C4—22no—
1552C4—22no—
1553C4—22no—
1554C4—22no—
1555C4—22no—
1556C4—22no—
1557C4—22no—
1558C4—22no—
1559C4—41no—
1560C4—41no—
1561C4—41no—
1562C4—41no—
1563C4—41no—
1564C4—41no—
1565C4—2921no—
1566C4—2921no—
1567C4—2921no—
1568C4—2921no—
1569C4—2921no—
1570C4—2921no—
1571C4—1462no—
1572C4—1462no—
1573C4—1462no—
1574C4—1462no—
1575C4—1462no—
1576C4—1462no—
1577C4—1462no—
1578C4—1462no—
1579C2—42no—
1580C2—2922no—
1581C2—738no—
1582C2#525×D7311yescharacteristic
1583C2#533×D7311yescharacteristic
1584C2#542×D7311yescharacteristic
1585C2#546×D7311yescharacteristic
1586C2D4×Q8×D7311yescharacteristic
1587C2#554×D7311yescharacteristic
1588C2#556×D7311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2465C2
prime radicalC24×D73C23
hypercenter#2465D73
hypocenterC73C2×#2465
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2465

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D73C2semidirect
3. #22613959C2semidirect
4. #22613958C2semidirect
5. #22613957C2semidirect
6. #22613956C2semidirect
7. #22613955C2semidirect
8. #22613954C2semidirect
9. #22613953C2semidirect
10. #22613952C2semidirect
11. #22613951C2semidirect
12. #22613950C2semidirect
13. #22613949C2semidirect
14. #22613948C2semidirect
15. #22613947C2semidirect
16. #22613946C2semidirect
17. #22613945C2semidirect
19. #395×D73C2semidirect
20. #395×D73C2semidirect
22. #391×D73C2semidirect
23. #389×D73C2semidirect
26. #387×D73C2semidirect
27. #387×D73C2semidirect
28. #387×D73C2semidirect
31. C73×#2465C2semidirect
43. C2×Q8×Dic73C22semidirect
44. C2×C4×Dic146C22semidirect
45. C2×C4×Dic146C22semidirect
46. C2×C4×Dic146C22semidirect
47. C2×#14556556C22semidirect
48. C2×#14556556C22semidirect
49. C2×#14556556C22semidirect
78. #17988508C22semidirect
79. #17988508C22semidirect
80. #17988508C22semidirect
81. #17988508C22semidirect
82. #17988508C22semidirect
83. #17988508C22semidirect
84. #17988507C22semidirect
85. #17988507C22semidirect
86. #17988507C22semidirect
87. #17988507C22semidirect
88. #17988507C22semidirect
89. #17988507C22semidirect
90. #17988506C22semidirect
91. #17988506C22semidirect
99. #17988494C22semidirect
100. #17988493C22semidirect
101. #17988492C22semidirect
102. #17988491C22semidirect
103. #17988491C22semidirect
104. #17988491C22semidirect
105. #17988491C22semidirect
106. #17988486C22semidirect
107. #17988485C22semidirect
108. #17988484C22semidirect
109. #17988484C22semidirect
110. #17988483C22semidirect
111. #17988482C22semidirect
112. #17988482C22semidirect
127. #17988474C22semidirect
128. #17988474C22semidirect
129. #17988474C22semidirect
130. #17988473C22semidirect
131. #17988473C22semidirect
132. #17988473C22semidirect
133. #17988472C22semidirect
134. #17988472C22semidirect
135. #17988472C22semidirect
136. #17988471C22semidirect
137. #17988471C22semidirect
138. #17988471C22semidirect
139. #17988470C22semidirect
140. #17988470C22semidirect
141. #17988470C22semidirect
142. #17988469C22semidirect
143. #17988469C22semidirect
144. #17988469C22semidirect
145. #17988468C22semidirect
146. #17988468C22semidirect
147. #17988468C22semidirect
175. C2×C4×Q8×C73C22semidirect
177. #395×C73C22semidirect
178. #395×C73C22semidirect
180. #391×C73C22semidirect
181. #389×C73C22semidirect
184. #387×C73C22semidirect
185. #387×C73C22semidirect
186. #387×C73C22semidirect
299. C22⋊C4×D73Q8semidirect
519. C22⋊Dic73C2×Q8semidirect
530. #11924005C2×Q8semidirect
531. #11924005C2×Q8semidirect
583. C22⋊C4×C73C2×Q8semidirect
794. D73#2465direct (N × H)
812. #2465D73direct (N × H)
826. C73C2×#2465semidirect
847. C2×C4×Q8C2×D73semidirect
890. #395C2×D73semidirect
891. #395C2×D73semidirect
907. #391C2×D73semidirect
915. #389C2×D73semidirect
953. #387C2×D73semidirect
954. #387C2×D73semidirect
955. #387C2×D73semidirect
1366. C22⋊C4Q8×D73semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D732
C2×C4×Q8×D732
#226139592
#226139582
#226139572
#226139562
#226139552
#226139542
#226139532
#226139522
#226139512
#226139502
#226139492
#226139482
#226139472
#226139462
#226139452
#396×D732
#395×D732
#393×D732
#391×D732
#389×D732
#388×D732
#387×D732
#385×D732
C4×C22⋊C4×D732
C73×#24652
C2×#246573