Finite Group Databasebeta

← #33248903

Subgroups — #33248903

Order 18688.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×D73C211yesmaximal, characteristic
2#22613080C211yesmaximal, characteristic, complemented
3#22613078C211yesmaximal, characteristic, complemented
4#22613076C211yesmaximal, characteristic, complemented
5#22613073C211yesmaximal, characteristic, complemented
6#22612927C211yesmaximal, characteristic, complemented
7#22612923C211yesmaximal, characteristic, complemented
8#22612919C211yesmaximal, characteristic, complemented
9#22612805C211yesmaximal, characteristic, complemented
10#22612804C211yesmaximal, characteristic, complemented
11#22612779C211yesmaximal, characteristic, complemented
12#22612778C211yesmaximal, characteristic, complemented
13#22612774C211yesmaximal, characteristic, complemented
14#22612774C211yesmaximal, characteristic, complemented
15#22612749C211yesmaximal, characteristic
16D4×#11924005C211yesmaximal, characteristic
17#22612727C211yesmaximal, characteristic, complemented
18#22612723C211yesmaximal, characteristic, complemented
19#22612719C211yesmaximal, characteristic, complemented
20#22612715C211yesmaximal, characteristic, complemented
21#22612605C211yesmaximal, characteristic, complemented
22#22612602C211yesmaximal, characteristic, complemented
23#22612599C211yesmaximal, characteristic, complemented
24#22612596C211yesmaximal, characteristic, complemented
25#22612546C211yesmaximal, characteristic, complemented
26#22612542C211yesmaximal, characteristic, complemented
27#22612530C211yesmaximal, characteristic, complemented
28#22612525C211yesmaximal, characteristic, complemented
29#22612310C211yesmaximal, characteristic, complemented
30C2×#17988446C211yesmaximal, characteristic, complemented
31C73×#2359C211yesmaximal, characteristic, complemented
32C22×D4×D73C2211yescharacteristic
33C23×C4×D73C2211yescharacteristic
34C2×#14556576C2211yescharacteristic
35C2×#14556576C2211yescharacteristic
36C2×#14556575C2211yescharacteristic
37C2×#14556574C2211yescharacteristic
38C2×#14556573C2211yescharacteristic
39C2×#14556573C2211yescharacteristic
40C2×#14556572C2211yescharacteristic
41#123×D73C4116yescomplemented
42C2×D4×Dic73C2211yescharacteristic
43C2×C4×C22⋊D73C2211yescharacteristic
44C2×#14556551C2211yescharacteristic
45C2×#14556550C2211yescharacteristic, complemented
46C2×#14556549C2211yescharacteristic
47C2×#14556548C2211yescharacteristic
48C22×#11924007C2211yescharacteristic, complemented
49C22×#11924007C2211yescharacteristic, complemented
50C2×C4⋊C4×D73C2211yescharacteristic
51C2×C4⋊C4×D73C2211yescharacteristic
52C22×#11924005C2211yescharacteristic
53C22×#11924005C2211yescharacteristic
54C22×#11924005C2211yescharacteristic
55C2×C22⋊C4×D73C2211yescharacteristic
56C2×C22⋊C4×D73C2211yescharacteristic
57C2×C22⋊C4×D73C2211yescharacteristic
58C2×C22⋊C4×D73C2211yescharacteristic
59#17988489C2211yescharacteristic
60#17988488C2211yescharacteristic
61#17988487C2211yescharacteristic
62#17988487C2211yescharacteristic
63#17988486C2211yescharacteristic, complemented
64#17988485C2211yescharacteristic, complemented
65#17988485C2211yescharacteristic, complemented
66#17988484C2211yescharacteristic, complemented
67#17988484C2211yescharacteristic, complemented
68#17988484C2211yescharacteristic, complemented
69#17988483C2211yescharacteristic, complemented
70#17988483C2211yescharacteristic, complemented
71#17988482C2211yescharacteristic, complemented
72#17988482C2211yescharacteristic, complemented
73#17988482C2211yescharacteristic, complemented
74#17988481C2211yescharacteristic, complemented
75#17988481C2211yescharacteristic, complemented
76#17988480C2211yescharacteristic, complemented
77#17988480C2211yescharacteristic, complemented
78#17988479C2211yescharacteristic, complemented
79#17988479C2211yescharacteristic, complemented
80#17988479C2211yescharacteristic, complemented
81#17988478C2211yescharacteristic, complemented
82#17988478C2211yescharacteristic, complemented
83#17988478C2211yescharacteristic, complemented
84#17988478C2211yescharacteristic, complemented
85#17988478C2211yescharacteristic, complemented
86#17988477C2211yescharacteristic, complemented
87#17988477C2211yescharacteristic, complemented
88#17988477C2211yescharacteristic, complemented
89#17988476C2211yescharacteristic, complemented
90#17988476C2211yescharacteristic, complemented
91#17988476C2211yescharacteristic, complemented
92#17988476C2211yescharacteristic, complemented
93#17988476C2211yescharacteristic, complemented
94#17988475C2211yescharacteristic, complemented
95#17988475C2211yescharacteristic, complemented
96#17988474C2211yescharacteristic, complemented
97#17988473C2211yescharacteristic, complemented
98#17988473C2211yescharacteristic, complemented
99#17988472C2211yescharacteristic, complemented
100#17988472C2211yescharacteristic, complemented
101#17988471C2211yescharacteristic, complemented
102#17988471C2211yescharacteristic, complemented
103#17988471C2211yescharacteristic, complemented
104#17988470C2211yescharacteristic, complemented
105#17988470C2211yescharacteristic, complemented
106#17988469C2211yescharacteristic, complemented
107#17988469C2211yescharacteristic, complemented
108#17988469C2211yescharacteristic, complemented
109#17988468C2211yescharacteristic, complemented
110#17988467C2211yescharacteristic
111#17988466C2211yescharacteristic
112#17988466C2211yescharacteristic
113#17988465C2211yescharacteristic
114#17988465C2211yescharacteristic
115#17988464C2211yescharacteristic
116#17988464C2211yescharacteristic
117#17988462C2211yescharacteristic, complemented
118#17988462C2211yescharacteristic, complemented
119#17988461C2211yescharacteristic, complemented
120#17988461C2211yescharacteristic, complemented
121#17988461C2211yescharacteristic, complemented
122#17988460C2211yescharacteristic, complemented
123#17988460C2211yescharacteristic, complemented
124#17988460C2211yescharacteristic, complemented
125#17988459C2211yescharacteristic, complemented
126#17988459C2211yescharacteristic, complemented
127#17988459C2211yescharacteristic, complemented
128#17988458C2211yescharacteristic, complemented
129#17988458C2211yescharacteristic, complemented
130#17988458C2211yescharacteristic, complemented
131#17988449C2211yescharacteristic
132#17988449C2211yescharacteristic
133#17988448C2211yescharacteristic, complemented
134#17988448C2211yescharacteristic, complemented
135#17988446C2211yescharacteristic
136#17988446C2211yescharacteristic
137#17988446C2211yescharacteristic
138#17988446C2211yescharacteristic
139#17988446C2211yescharacteristic
140#17988446C2211yescharacteristic
141#17988446C2211yescharacteristic, complemented
142#17988446C2211yescharacteristic, complemented
143#17988446C2211yescharacteristic, complemented
144#17988446C2211yescharacteristic, complemented
145#17988444C2211yescharacteristic
146#17988444C2211yescharacteristic
147#17988444C2211yescharacteristic
148#17988444C2211yescharacteristic
149#17988444C2211yescharacteristic, complemented
150#17988444C2211yescharacteristic, complemented
151#17988442C2211yescharacteristic
152#17988442C2211yescharacteristic
153#17988442C2211yescharacteristic
154#17988442C2211yescharacteristic
155C4⋊C4×Dic73C2211yescharacteristic, complemented
156C4×#11924007C2211yescharacteristic, complemented
157#17988438C2211yescharacteristic, complemented
158C22⋊C4×Dic73C2211yescharacteristic, complemented
159C22⋊C4×Dic73C2211yescharacteristic, complemented
160C22⋊C4×Dic73C2211yescharacteristic, complemented
161C4×#11924005C2211yescharacteristic
162C4×#11924005C2211yescharacteristic
163C4×#11924005C2211yescharacteristic
164C4×#11924005C2211yescharacteristic
165C4×#11924005C2211yescharacteristic, complemented
166C4×#11924005C2211yescharacteristic, complemented
167C4×#11924005C2211yescharacteristic, complemented
168C4×C22⋊Dic73C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic
170#17988434C2211yescharacteristic
171#17988434C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic, complemented
173C2×#123×C73C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175C2×#117×C73C2211yescharacteristic, complemented
176#389×C73C2211yescharacteristic, complemented
177#388×C73C2211yescharacteristic, complemented
178#388×C73C2211yescharacteristic, complemented
179#387×C73C2211yescharacteristic, complemented
180#387×C73C2211yescharacteristic, complemented
181#386×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic, complemented
183#385×C73C2211yescharacteristic, complemented
184C4×C4⋊C4×C73C2211yescharacteristic, complemented
185C4×C22⋊C4×C73C2211yescharacteristic, complemented
186C4×C22⋊C4×C73C2211yescharacteristic, complemented
187C2×#95×C73C2211yescharacteristic, complemented
188C24×D73C2311yescharacteristic
189C24×D73C2311yescharacteristic
190C22×D292C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C2×D4×D73—42no—
194C2×D4×D73—42no—
195C2×D4×D73C2×C418yes—
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C23×Dic73C2311yescharacteristic
200C22×C4×D73—42no—
201C22×C4×D73—42no—
202C22×C4×D73C2×C418yescomplemented
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211C22×C4×D73C2311yescharacteristic
212#14556576C2×C418yescomplemented
213#14556576C2×C418yescomplemented
214#14556575C2×C418yescomplemented
215#14556574C2×C418yescomplemented
216#14556573C2×C418yescomplemented
217#14556573C2×C418yescomplemented
218#14556572C2×C418yescomplemented
219D4×Dic73—42no—
220C4×C22⋊D73—42no—
221#14556551—42no—
222#14556550—42no—
223#14556549—42no—
224#14556548—42no—
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×C4⋊Dic73C2311yescharacteristic
230C2×C4⋊Dic73C2311yescharacteristic
231C2×C4⋊Dic73C2311yescharacteristic
232C2×#11924007—42no—
233C2×#11924007—42no—
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C4⋊C4×D73C2×C418yescomplemented
253C4⋊C4×D73C2×C418yescomplemented
254C2×C22⋊Dic73C2311yescharacteristic
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×#11924005—42no—
263C2×#11924005—42no—
264C2×#11924005—42no—
265C2×#11924005C2311yescharacteristic
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C22⋊C4×D73—42no—
294C22⋊C4×D73C2×C418yescomplemented
295C22⋊C4×D73C2×C418yescomplemented
296C22⋊C4×D73C2×C418yescomplemented
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
305C2×C4×Dic73C2311yescharacteristic
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
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
338C22×D4×C73C2311yescharacteristic
339C23×C4×C73C2311yescharacteristic
340C23×C4×C73C2311yescharacteristic
341C23×C4×C73C2311yescharacteristic
342C23×C4×C73C2311yescharacteristic
343#123×C73C2×C418yescomplemented
344C4×D4×C73—42no—
345#117×C73—42no—
346C2×C4⋊C4×C73C2311yescharacteristic
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C42×C73C2311yescharacteristic
362C2×C42×C73C2311yescharacteristic
363C2×C42×C73C2311yescharacteristic
364C2×C42×C73C2311yescharacteristic
365C2×C42×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73—22no—
377C23×D73—22no—
378C23×D73—22no—
379C23×D73—22no—
380C23×D73—22no—
381C23×D73—22no—
382C23×D73—41no—
383C23×D73—41no—
384C23×D73—41no—
385C23×D73—41no—
386C23×D73—41no—
387C23×D73—41no—
388C23×D73C22×C414yes—
389C23×D73C22×C414yes—
390C23×D73C2411yescharacteristic
391C23×D73C2411yescharacteristic
392C23×D73C2411yescharacteristic
393C2×D292—41no—
394C2×D292—41no—
395C2×D292C22×C414yes—
396C2×C22⋊D73—22no—
397C2×C22⋊D73—22no—
398C2×C22⋊D73—41no—
399C2×C22⋊D73—41no—
400C2×C22⋊D73C22×C414yes—
401C2×C22⋊D73C22×C414yes—
402D4×D73—416no—
403C22×Dic73—22no—
404C22×Dic73—22no—
405C22×Dic73—22no—
406C22×Dic73—22no—
407C22×Dic73—41no—
408C22×Dic73—41no—
409C22×Dic73—41no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73C22×C414yes—
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C2×C4×D73—22no—
429C2×C4×D73—22no—
430C2×C4×D73—416no—
431C2×C4×D73—41no—
432C2×C4×D73—41no—
433C2×C4×D73—41no—
434C2×C4×D73—41no—
435C2×C4×D73—41no—
436C2×C4×D73—41no—
437C2×C4×D73—41no—
438C2×C4×D73—41no—
439C2×C4×D73—41no—
440C2×C4×D73—41no—
441C2×C4×D73—41no—
442C2×C4×D73—41no—
443C2×C4×D73—41no—
444C2×C4×D73—41no—
445C2×C4×D73—41no—
446C2×C4×D73—41no—
447C2×C4×D73—41no—
448C2×C4×D73—41no—
449C2×C4×D73C22×C414yes—
450C2×C4×D73C22×C414yes—
451C2×C4×D73C22×C414yes—
452C2×C4×D73C22×C414yes—
453C2×C4×D73C22×C414yes—
454C2×C4×D73C22×C414yes—
455C2×C4×D73C22×C414yes—
456C4⋊Dic73—41no—
457C4⋊Dic73—41no—
458C4⋊Dic73—41no—
459C4⋊Dic73—41no—
460C4⋊Dic73—41no—
461C4⋊Dic73C22×C414yes—
462C4⋊Dic73C22×C414yes—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
466#11924007—41no—
467#11924007—41no—
468#11924007—41no—
469#11924007—41no—
470#11924007—41no—
471#11924007—41no—
472#11924007—41no—
473#11924007—41no—
474#11924007—41no—
475#11924007—41no—
476#11924007—41no—
477#11924007C22×C414yes—
478#11924007C22×C414yes—
479#11924007C22×C414yes—
480#11924007C22×C414yes—
481C22⋊Dic73—22no—
482C22⋊Dic73—22no—
483C22⋊Dic73—41no—
484C22⋊Dic73—41no—
485C22⋊Dic73—41no—
486C22⋊Dic73C22×C414yes—
487C22⋊Dic73C22×C414yes—
488C22⋊Dic73C22×C414yes—
489#11924005—22no—
490#11924005—22no—
491#11924005—22no—
492#11924005—22no—
493#11924005—22no—
494#11924005—22no—
495#11924005—22no—
496#11924005—22no—
497#11924005—41no—
498#11924005—41no—
499#11924005—41no—
500#11924005—41no—
501#11924005—41no—
502#11924005—41no—
503#11924005—41no—
504#11924005—41no—
505#11924005—41no—
506#11924005—41no—
507#11924005—41no—
508#11924005—41no—
509#11924005—41no—
510#11924005—41no—
511#11924005C22×C414yes—
512#11924005C22×C414yes—
513#11924005C22×C414yes—
514#11924005C22×C414yes—
515#11924005C22×C414yes—
516#11924005C22×C414yes—
517C4×Dic73—41no—
518C4×Dic73—41no—
519C4×Dic73—41no—
520C4×Dic73—41no—
521C4×Dic73—41no—
522C4×Dic73—41no—
523C4×Dic73—41no—
524C4×Dic73—41no—
525C4×Dic73—41no—
526C4×Dic73—41no—
527C4×Dic73—41no—
528C24×C73C2411yescharacteristic
529C24×C73C2411yescharacteristic
530C2×D4×C73—22no—
531C2×D4×C73—22no—
532C2×D4×C73C22×C414yes—
533C22×C4×C73—22no—
534C22×C4×C73—22no—
535C22×C4×C73—22no—
536C22×C4×C73—22no—
537C22×C4×C73—41no—
538C22×C4×C73—41no—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73C22×C414yes—
545C22×C4×C73C2411yescharacteristic
546C22×C4×C73C2411yescharacteristic
547C22×C4×C73C2411yescharacteristic
548C22×C4×C73C2411yescharacteristic
549C22×C4×C73C2411yescharacteristic
550C22×C4×C73C2411yescharacteristic
551C22×C4×C73C2411yescharacteristic
552C22×C4×C73C2411yescharacteristic
553C22×C4×C73C2411yescharacteristic
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C4⋊C4×C73—41no—
559C4⋊C4×C73—41no—
560C4⋊C4×C73—41no—
561C4⋊C4×C73—41no—
562C4⋊C4×C73—41no—
563C4⋊C4×C73C22×C414yes—
564C4⋊C4×C73C22×C414yes—
565C22⋊C4×C73—22no—
566C22⋊C4×C73—22no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73C22×C414yes—
571C22⋊C4×C73C22×C414yes—
572C22⋊C4×C73C22×C414yes—
573C42×C73—41no—
574C42×C73—41no—
575C42×C73—41no—
576C42×C73—41no—
577C42×C73—41no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73C23×C412yes—
589C23×C73C23×C412yes—
590C23×C73H(5,𝔽2)12yes—
591C23×C73H(5,𝔽2)12yes—
592C23×C73C2511yescharacteristic
593C22×D73—21no—
594C22×D73—21no—
595C22×D73—21no—
596C22×D73—21no—
597C22×D73—28no—
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—21no—
610C22×D73—28no—
611C22×D73—28no—
612C22×D73—44no—
613C22×D73—44no—
614C22×D73—44no—
615C22×D73—44no—
616C22×D73—44no—
617C22×D73—44no—
618C22×D73—44no—
619C22×D73—82no—
620C22×D73—82no—
621C22×D73—82no—
622C22×D73—82no—
623C22×D73C23×C412yes—
624C22×D73C23×C412yes—
625C22×D73C23×C412yes—
626C22×D73H(5,𝔽2)12yes—
627C22×D732−1+412yes—
628D4×C73—28no—
629C2×C4×C73—28no—
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—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—82no—
665C2×C4×C73—82no—
666C2×C4×C73—82no—
667C2×C4×C73C23×C412yes—
668C2×C4×C73C23×C412yes—
669C2×C4×C73C23×C412yes—
670C2×C4×C73C23×C412yes—
671C2×C4×C73C23×C412yes—
672C22⋊D73—28no—
673C22⋊D73—44no—
674C2×Dic73—28no—
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—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—21no—
704C2×Dic73—21no—
705C2×Dic73—21no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73—21no—
709C2×Dic73—82no—
710C2×Dic73—82no—
711C2×Dic73—82no—
712C2×Dic73C23×C412yes—
713C2×Dic73C23×C412yes—
714C2×Dic73C23×C412yes—
715C2×Dic73C23×C412yes—
716C2×Dic73C23×C412yes—
717D292—44no—
718C4×D73—28no—
719C4×D73—44no—
720C4×D73—44no—
721C4×D73—44no—
722C4×D73—44no—
723C4×D73—44no—
724C4×D73—44no—
725C4×D73—82no—
726C4×D73—82no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—22no—
732C22×C73—22no—
733C22×C73—22no—
734C22×C73—22no—
735C22×C73—22no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73#51814yes—
741C22×C73C24×C411yescharacteristic
742C22×C73C2×H(5,𝔽2)11yescharacteristic
743C22×C73C2×H(5,𝔽2)11yescharacteristic
744C22×C73C2×H(5,𝔽2)11yescharacteristic
745C22×C73C2×2−1+411yescharacteristic
746C22×C73#58511yescharacteristic
747C22×C73#58511yescharacteristic
748C2×D73—22no—
749C2×D73—22no—
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—22no—
756C2×D73—22no—
757C2×D73—22no—
758C2×D73—22no—
759C2×D73—22no—
760C2×D73—416no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73—41no—
765C2×D73—41no—
766C2×D73—41no—
767C2×D73—41no—
768C2×D73—41no—
769C2×D73—88no—
770C2×D73#52014yes—
771C4×C73—22no—
772C4×C73—22no—
773C4×C73—22no—
774C4×C73—22no—
775C4×C73—22no—
776C4×C73—41no—
777C4×C73—41no—
778C4×C73—41no—
779C4×C73—41no—
780C4×C73—41no—
781C4×C73—41no—
782C4×C73—41no—
783C4×C73—41no—
784Dic73—22no—
785Dic73—22no—
786Dic73—22no—
787Dic73—22no—
788Dic73—22no—
789Dic73—41no—
790Dic73—41no—
791Dic73—41no—
792Dic73—41no—
793Dic73—41no—
794Dic73—41no—
795Dic73—41no—
796Dic73—41no—
797#34376—731nomaximal, Sylow
798C2×C73—24no—
799C2×C73—42no—
800C2×C73C2×#51811yescharacteristic
801C2×C73C2×#52011yescharacteristic
802C2×C73#342811yescharacteristic
803C2×C73#353411yescharacteristic
804C2×C73#353411yescharacteristic
805C2×C73#353511yescharacteristic
806C2×C73#353511yescharacteristic
807D73—24no—
808D73—42no—
809D73—42no—
810C22×#123—731no—
811#2376—731no—
812#2376—731no—
813#2376—731no—
814#2376—731no—
815#2359—731no—
816#2359—731no—
817#2359—731no—
818#2359D7311yescharacteristic, complemented
819#2345—731no—
820#2345—731no—
821#2342—731no—
822#2342—731no—
823#2342—731no—
824#2342—731no—
825D4×C22⋊C4—731no—
826D4×C22⋊C4—731no—
827#2335—731no—
828#2335—731no—
829#2335—731no—
830#2335—731no—
831#2322—731no—
832#2322—731no—
833#2322—731no—
834#2322—731no—
835#2316—731no—
836#2315—731no—
837#2313—731no—
838#2312—731no—
839#2280—731no—
840C2×#380—731no—
841C73#3437611yescharacteristic, complemented, Sylow
842C23×D4—731no—
843C24×C4—731no—
844C2×#123—731no—
845C2×#123—731no—
846C2×#123—7316no—
847C2×#123—731no—
848C2×#123—731no—
849C2×#123—731no—
850C2×#123—731no—
851C2×#123—731no—
852C2×#123C2×D7311yescharacteristic
853C2×C4×D4—731no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4C2×D7311yescharacteristic
857C2×#117—731no—
858C2×#117—731no—
859C2×#117—731no—
860C2×#117C2×D7311yescharacteristic, complemented
861C22×C4⋊C4—731no—
862C22×C4⋊C4—731no—
863C22×C4⋊C4—731no—
864C22×C4⋊C4—731no—
865C22×C22⋊C4—731no—
866C22×C22⋊C4—731no—
867C22×C22⋊C4—731no—
868C22×C22⋊C4—731no—
869C22×C22⋊C4—731no—
870C22×C22⋊C4—731no—
871C22×C22⋊C4—731no—
872#390—731no—
873#390—731no—
874#390—731no—
875#390—731no—
876#389—731no—
877#389—731no—
878#389—731no—
879#389—731no—
880#389—731no—
881#389—731no—
882#389—731no—
883#389—731no—
884#389—731no—
885#389—731no—
886#389—731no—
887#389C2×D7311yescharacteristic, complemented
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388—731no—
894#388—731no—
895#388—731no—
896#388—731no—
897#388—731no—
898#388—731no—
899#388—731no—
900#388—731no—
901#388—731no—
902#388—731no—
903#388—731no—
904#388—731no—
905#388—731no—
906#388—731no—
907#388—731no—
908#388—731no—
909#388—731no—
910#388C2×D7311yescharacteristic, complemented
911#388C2×D7311yescharacteristic, complemented
912#387—731no—
913#387—731no—
914#387—731no—
915#387—731no—
916#387—731no—
917#387—731no—
918#387—731no—
919#387—731no—
920#387—731no—
921#387—731no—
922#387—731no—
923#387—731no—
924#387—731no—
925#387—731no—
926#387C2×D7311yescharacteristic, complemented
927#387C2×D7311yescharacteristic, complemented
928#386—731no—
929#386—731no—
930#386—731no—
931#386—731no—
932#386—731no—
933#386—731no—
934#386—731no—
935#386C2×D7311yescharacteristic
936#385—731no—
937#385—731no—
938#385—731no—
939#385—731no—
940#385—731no—
941#385—731no—
942#385—731no—
943#385—731no—
944#385—731no—
945#385—731no—
946#385—731no—
947#385—731no—
948#385—731no—
949#385—731no—
950#385C2×D7311yescharacteristic, complemented
951#385C2×D7311yescharacteristic, complemented
952#381—731no—
953#381—731no—
954#381—731no—
955#381—731no—
956#380—731no—
957#380—731no—
958#380—731no—
959#380—731no—
960#380—731no—
961#380—731no—
962#380—731no—
963#380—731no—
964#380—731no—
965#380—731no—
966#380—731no—
967#380—731no—
968#380—731no—
969#380—731no—
970#380—731no—
971#380—731no—
972#379—731no—
973#379—731no—
974#379—731no—
975#379—731no—
976C4×C4⋊C4—731no—
977C4×C4⋊C4—731no—
978C4×C4⋊C4—731no—
979C4×C4⋊C4C2×D7311yescharacteristic, complemented
980C4×C22⋊C4—731no—
981C4×C22⋊C4—731no—
982C4×C22⋊C4—731no—
983C4×C22⋊C4—731no—
984C4×C22⋊C4—731no—
985C4×C22⋊C4—731no—
986C4×C22⋊C4—731no—
987C4×C22⋊C4—731no—
988C4×C22⋊C4—731no—
989C4×C22⋊C4—731no—
990C4×C22⋊C4—731no—
991C4×C22⋊C4—731no—
992C4×C22⋊C4—731no—
993C4×C22⋊C4—731no—
994C4×C22⋊C4C2×D7311yescharacteristic, complemented
995C4×C22⋊C4C2×D7311yescharacteristic, complemented
996C2×#95—731no—
997C2×#95C2×D7311yescharacteristic, complemented
998C25—731no—
999C25—731no—
1000C22×D4—2922no—
1001C22×D4—2922no—
1002C22×D4—731no—
1003C22×D4—738no—
1004C22×D4—731no—
1005C22×D4—731no—
1006C22×D4C22×D7311yescharacteristic
1007C23×C4—2922no—
1008C23×C4—2922no—
1009C23×C4—731no—
1010C23×C4—731no—
1011C23×C4—731no—
1012C23×C4—738no—
1013C23×C4—731no—
1014C23×C4—731no—
1015C23×C4—731no—
1016C23×C4—731no—
1017C23×C4—731no—
1018C23×C4—731no—
1019C23×C4—731no—
1020C23×C4—731no—
1021C23×C4—731no—
1022C23×C4—731no—
1023C23×C4C22×D7311yescharacteristic
1024C23×C4C22×D7311yescharacteristic
1025C23×C4C22×D7311yescharacteristic
1026C23×C4C22×D7311yescharacteristic
1027#123—738no—
1028#123—738no—
1029#123—738no—
1030#123—738no—
1031#123—738no—
1032#123—738no—
1033#123—738no—
1034#123C4×D7318yescomplemented
1035C4×D4—42no—
1036C4×D4—2922no—
1037C4×D4—2922no—
1038C4×D4—2922no—
1039#117—42no—
1040#117—2922no—
1041#117—2922no—
1042#117—2922no—
1043C2×C4⋊C4—2922no—
1044C2×C4⋊C4—2922no—
1045C2×C4⋊C4—731no—
1046C2×C4⋊C4—731no—
1047C2×C4⋊C4—731no—
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—731no—
1070C2×C4⋊C4—738no—
1071C2×C4⋊C4—738no—
1072C2×C4⋊C4C22×D7311yescharacteristic
1073C2×C4⋊C4C22×D7311yescharacteristic
1074C2×C4⋊C4C22×D7311yescharacteristic
1075C2×C4⋊C4C22×D7311yescharacteristic
1076C2×C4⋊C4C22×D7311yescharacteristic
1077C2×C4⋊C4C22×D7311yescharacteristic
1078C2×C4⋊C4C22×D7311yescharacteristic
1079C2×C22⋊C4—2922no—
1080C2×C22⋊C4—2922no—
1081C2×C22⋊C4—2922no—
1082C2×C22⋊C4—2922no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
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—731no—
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—731no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4—731no—
1109C2×C22⋊C4—738no—
1110C2×C22⋊C4—738no—
1111C2×C22⋊C4—738no—
1112C2×C22⋊C4—731no—
1113C2×C22⋊C4—731no—
1114C2×C22⋊C4—731no—
1115C2×C22⋊C4—731no—
1116C2×C22⋊C4—731no—
1117C2×C22⋊C4—731no—
1118C2×C22⋊C4—731no—
1119C2×C22⋊C4—731no—
1120C2×C22⋊C4—731no—
1121C2×C22⋊C4—731no—
1122C2×C22⋊C4C22×D7311yescharacteristic
1123C2×C22⋊C4C22×D7311yescharacteristic
1124C2×C22⋊C4C22×D7311yescharacteristic
1125C2×C22⋊C4C22×D7311yescharacteristic
1126C2×C22⋊C4C22×D7311yescharacteristic
1127C2×C22⋊C4C22×D7311yescharacteristic
1128C2×C22⋊C4C22×D7311yescharacteristic
1129C2×C22⋊C4C22×D7311yescharacteristic
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—731no—
1133C2×C42—731no—
1134C2×C42—731no—
1135C2×C42—731no—
1136C2×C42—731no—
1137C2×C42—731no—
1138C2×C42—731no—
1139C2×C42—731no—
1140C2×C42—731no—
1141C2×C42C22×D7311yescharacteristic
1142C2×C42C22×D7311yescharacteristic
1143C2×C42C22×D7311yescharacteristic
1144C2×C42C22×D7311yescharacteristic
1145C2×C42C22×D7311yescharacteristic
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#95—731no—
1173#95—731no—
1174#95—731no—
1175#95—731no—
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180#95C22×D7311yescharacteristic
1181#95C22×D7311yescharacteristic
1182#95C22×D7311yescharacteristic
1183#95C22×D7311yescharacteristic
1184#95C22×D7311yescharacteristic
1185#95C22×D7311yescharacteristic
1186C24—2921no—
1187C24—2921no—
1188C24—2921no—
1189C24—2921no—
1190C24—2921no—
1191C24—2921no—
1192C24—734no—
1193C24—734no—
1194C24—731no—
1195C24—731no—
1196C24—731no—
1197C24—1462no—
1198C24—1462no—
1199C24—1462no—
1200C24—1462no—
1201C24—1462no—
1202C24—1462no—
1203C24C23×D7311yescharacteristic
1204C24C23×D7311yescharacteristic
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—2921no—
1208C2×D4—2921no—
1209C2×D4—29216no—
1210C2×D4—2921no—
1211C2×D4—2921no—
1212C2×D4—734no—
1213C2×D4—734no—
1214C2×D4—734no—
1215C2×D4—1462no—
1216C2×D4—1462no—
1217C2×D4C2×C4×D7314yes—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—2921no—
1230C22×C4—2921no—
1231C22×C4—2921no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—2921no—
1237C22×C4—29216no—
1238C22×C4—2921no—
1239C22×C4—2921no—
1240C22×C4—2921no—
1241C22×C4—2921no—
1242C22×C4—2921no—
1243C22×C4—2921no—
1244C22×C4—2921no—
1245C22×C4—2921no—
1246C22×C4—2921no—
1247C22×C4—2921no—
1248C22×C4—2921no—
1249C22×C4—2921no—
1250C22×C4—2921no—
1251C22×C4—2921no—
1252C22×C4—2921no—
1253C22×C4—2921no—
1254C22×C4—2921no—
1255C22×C4—734no—
1256C22×C4—734no—
1257C22×C4—734no—
1258C22×C4—734no—
1259C22×C4—734no—
1260C22×C4—734no—
1261C22×C4—734no—
1262C22×C4—731no—
1263C22×C4—731no—
1264C22×C4—731no—
1265C22×C4—731no—
1266C22×C4—731no—
1267C22×C4—734no—
1268C22×C4—731no—
1269C22×C4—731no—
1270C22×C4—731no—
1271C22×C4—731no—
1272C22×C4—731no—
1273C22×C4—731no—
1274C22×C4—731no—
1275C22×C4—731no—
1276C22×C4—1462no—
1277C22×C4—1462no—
1278C22×C4—1462no—
1279C22×C4—1462no—
1280C22×C4—1462no—
1281C22×C4—1462no—
1282C22×C4C2×C4×D7314yes—
1283C22×C4C23×D7311yescharacteristic
1284C22×C4C23×D7311yescharacteristic
1285C22×C4C23×D7311yescharacteristic
1286C22×C4C23×D7311yescharacteristic
1287C22×C4C23×D7311yescharacteristic
1288C22×C4C23×D7311yescharacteristic
1289C22×C4C23×D7311yescharacteristic
1290C22×C4C23×D7311yescharacteristic
1291C22×C4C23×D7311yescharacteristic
1292C22×C4C23×D7311yescharacteristic
1293C22×C4C23×D7311yescharacteristic
1294C22×C4C23×D7311yescharacteristic
1295C22×C4C23×D7311yescharacteristic
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—41no—
1300C4⋊C4—41no—
1301C4⋊C4—2921no—
1302C4⋊C4—2921no—
1303C4⋊C4—2921no—
1304C4⋊C4—2921no—
1305C4⋊C4—2921no—
1306C4⋊C4—2921no—
1307C4⋊C4—2921no—
1308C4⋊C4—2921no—
1309C4⋊C4—2921no—
1310C4⋊C4—2921no—
1311C4⋊C4—2921no—
1312C4⋊C4—2921no—
1313C4⋊C4—2921no—
1314C4⋊C4—2921no—
1315C4⋊C4—2921no—
1316C4⋊C4—2921no—
1317C4⋊C4—2921no—
1318C4⋊C4—2921no—
1319C4⋊C4—2921no—
1320C4⋊C4—734no—
1321C4⋊C4—734no—
1322C4⋊C4—734no—
1323C4⋊C4—734no—
1324C4⋊C4—734no—
1325C4⋊C4—734no—
1326C4⋊C4C2×C4×D7314yes—
1327C4⋊C4C2×C4×D7314yes—
1328C22⋊C4—22no—
1329C22⋊C4—22no—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—2921no—
1334C22⋊C4—2921no—
1335C22⋊C4—2921no—
1336C22⋊C4—2921no—
1337C22⋊C4—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—2921no—
1341C22⋊C4—2921no—
1342C22⋊C4—2921no—
1343C22⋊C4—2921no—
1344C22⋊C4—2921no—
1345C22⋊C4—2921no—
1346C22⋊C4—2921no—
1347C22⋊C4—2921no—
1348C22⋊C4—2921no—
1349C22⋊C4—2921no—
1350C22⋊C4—734no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—734no—
1354C22⋊C4—734no—
1355C22⋊C4—734no—
1356C22⋊C4—734no—
1357C22⋊C4—734no—
1358C22⋊C4—734no—
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⋊C4C2×C4×D7314yes—
1370C22⋊C4C2×C4×D7314yes—
1371C22⋊C4C2×C4×D7314yes—
1372C42—41no—
1373C42—41no—
1374C42—41no—
1375C42—41no—
1376C42—41no—
1377C42—2921no—
1378C42—2921no—
1379C42—2921no—
1380C42—2921no—
1381C42—2921no—
1382C42—2921no—
1383C42—2921no—
1384C42—2921no—
1385C42—2921no—
1386C42—2921no—
1387C42—2921no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—2924no—
1399C23—2924no—
1400C23—2924no—
1401C23—2924no—
1402C23—2924no—
1403C23—2924no—
1404C23—2924no—
1405C23—5842no—
1406C23—5842no—
1407C23—5842no—
1408C23—5842no—
1409C23—732no—
1410C23—732no—
1411C23—732no—
1412C23—732no—
1413C23—732no—
1414C23—1468no—
1415C23—1468no—
1416C23—1461no—
1417C23—1461no—
1418C23—1461no—
1419C23—1461no—
1420C23—1461no—
1421C23—1461no—
1422C23—1461no—
1423C23—1461no—
1424C23—1461no—
1425C23—1461no—
1426C23—1461no—
1427C23—1461no—
1428C23—1468no—
1429C23—1461no—
1430C23—1461no—
1431C23—1461no—
1432C23—1461no—
1433C23C22×C4×D7312yes—
1434C23C22×C4×D7312yes—
1435C23#1455663612yes—
1436C23#1455663712yes—
1437C23C24×D7311yescharacteristic
1438D4—28no—
1439D4—2924no—
1440D4—2924no—
1441D4—1468no—
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—28no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—82no—
1478C2×C4—82no—
1479C2×C4—82no—
1480C2×C4—2924no—
1481C2×C4—2924no—
1482C2×C4—2924no—
1483C2×C4—2924no—
1484C2×C4—2924no—
1485C2×C4—2924no—
1486C2×C4—5842no—
1487C2×C4—5842no—
1488C2×C4—5842no—
1489C2×C4—5842no—
1490C2×C4—5842no—
1491C2×C4—732no—
1492C2×C4—732no—
1493C2×C4—732no—
1494C2×C4—732no—
1495C2×C4—732no—
1496C2×C4—1468no—
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×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4—1461no—
1521C2×C4—1461no—
1522C2×C4—1461no—
1523C2×C4—1461no—
1524C2×C4—1461no—
1525C2×C4—1461no—
1526C2×C4—1461no—
1527C2×C4—1461no—
1528C2×C4—1461no—
1529C2×C4—1461no—
1530C2×C4—1461no—
1531C2×C4—1468no—
1532C2×C4C22×C4×D7312yes—
1533C2×C4C22×C4×D7312yes—
1534C2×C4C22×C4×D7312yes—
1535C2×C4C22×C4×D7312yes—
1536C2×C4C22×C4×D7312yes—
1537C22—22no—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—22no—
1545C22—22no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—29216no—
1551C22—2921no—
1552C22—2921no—
1553C22—2921no—
1554C22—2921no—
1555C22—2921no—
1556C22—2921no—
1557C22—2921no—
1558C22—2921no—
1559C22—5848no—
1560C22—734no—
1561C22—1462no—
1562C22—1462no—
1563C22—1462no—
1564C22—1462no—
1565C22—1462no—
1566C22—1462no—
1567C22—1462no—
1568C22—1462no—
1569C22—1462no—
1570C22—1462no—
1571C22—1462no—
1572C22—1462no—
1573C22#1798905914yes—
1574C22C23×C4×D7311yescharacteristic
1575C22H(5,𝔽2)×D7311yescharacteristic
1576C22C2×#1455663611yescharacteristic
1577C22C2×#1455663711yescharacteristic
1578C222−1+4×D7311yescharacteristic
1579C22#1798942311yescharacteristic
1580C22#1798942311yescharacteristic
1581C4—22no—
1582C4—22no—
1583C4—22no—
1584C4—22no—
1585C4—22no—
1586C4—41no—
1587C4—41no—
1588C4—41no—
1589C4—41no—
1590C4—41no—
1591C4—41no—
1592C4—41no—
1593C4—41no—
1594C4—2921no—
1595C4—2921no—
1596C4—2921no—
1597C4—2921no—
1598C4—2921no—
1599C4—2921no—
1600C4—2921no—
1601C4—2921no—
1602C4—1462no—
1603C4—1462no—
1604C4—1462no—
1605C4—1462no—
1606C4—1462no—
1607C2—24no—
1608C2—42no—
1609C2—2922no—
1610C2—2922no—
1611C2—1464no—
1612C2C2×#1798905911yescharacteristic
1613C2#520×D7311yescharacteristic
1614C2#2262313011yescharacteristic
1615C2#2262411311yescharacteristic
1616C2#2262412411yescharacteristic
1617C2#2262413211yescharacteristic
1618C2#2262414311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2359C2
socle, cosocleC23×C73C25
prime radicalC22×D4×D73C22
hypercenter#2359D73
hypocenterC73#34376
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #22613080C2semidirect
3. #22613078C2semidirect
4. #22613076C2semidirect
5. #22613073C2semidirect
6. #22612927C2semidirect
7. #22612923C2semidirect
8. #22612919C2semidirect
9. #22612805C2semidirect
10. #22612804C2semidirect
11. #22612779C2semidirect
12. #22612778C2semidirect
13. #22612774C2semidirect
14. #22612774C2semidirect
17. #22612727C2semidirect
18. #22612723C2semidirect
19. #22612719C2semidirect
20. #22612715C2semidirect
21. #22612605C2semidirect
22. #22612602C2semidirect
23. #22612599C2semidirect
24. #22612596C2semidirect
25. #22612546C2semidirect
26. #22612542C2semidirect
27. #22612530C2semidirect
28. #22612525C2semidirect
29. #22612310C2semidirect
30. C2×#17988446C2semidirect
31. C73×#2359C2semidirect
41. #123×D73C4semidirect
45. C2×#14556550C22semidirect
48. C22×#11924007C22semidirect
49. C22×#11924007C22semidirect
63. #17988486C22semidirect
64. #17988485C22semidirect
65. #17988485C22semidirect
66. #17988484C22semidirect
67. #17988484C22semidirect
68. #17988484C22semidirect
69. #17988483C22semidirect
70. #17988483C22semidirect
71. #17988482C22semidirect
72. #17988482C22semidirect
73. #17988482C22semidirect
74. #17988481C22semidirect
75. #17988481C22semidirect
76. #17988480C22semidirect
77. #17988480C22semidirect
78. #17988479C22semidirect
79. #17988479C22semidirect
80. #17988479C22semidirect
81. #17988478C22semidirect
82. #17988478C22semidirect
83. #17988478C22semidirect
84. #17988478C22semidirect
85. #17988478C22semidirect
86. #17988477C22semidirect
87. #17988477C22semidirect
88. #17988477C22semidirect
89. #17988476C22semidirect
90. #17988476C22semidirect
91. #17988476C22semidirect
92. #17988476C22semidirect
93. #17988476C22semidirect
94. #17988475C22semidirect
95. #17988475C22semidirect
96. #17988474C22semidirect
97. #17988473C22semidirect
98. #17988473C22semidirect
99. #17988472C22semidirect
100. #17988472C22semidirect
101. #17988471C22semidirect
102. #17988471C22semidirect
103. #17988471C22semidirect
104. #17988470C22semidirect
105. #17988470C22semidirect
106. #17988469C22semidirect
107. #17988469C22semidirect
108. #17988469C22semidirect
109. #17988468C22semidirect
117. #17988462C22semidirect
118. #17988462C22semidirect
119. #17988461C22semidirect
120. #17988461C22semidirect
121. #17988461C22semidirect
122. #17988460C22semidirect
123. #17988460C22semidirect
124. #17988460C22semidirect
125. #17988459C22semidirect
126. #17988459C22semidirect
127. #17988459C22semidirect
128. #17988458C22semidirect
129. #17988458C22semidirect
130. #17988458C22semidirect
133. #17988448C22semidirect
134. #17988448C22semidirect
141. #17988446C22semidirect
142. #17988446C22semidirect
143. #17988446C22semidirect
144. #17988446C22semidirect
149. #17988444C22semidirect
150. #17988444C22semidirect
155. C4⋊C4×Dic73C22semidirect
156. C4×#11924007C22semidirect
157. #17988438C22semidirect
158. C22⋊C4×Dic73C22semidirect
159. C22⋊C4×Dic73C22semidirect
160. C22⋊C4×Dic73C22semidirect
165. C4×#11924005C22semidirect
166. C4×#11924005C22semidirect
167. C4×#11924005C22semidirect
168. C4×C22⋊Dic73C22semidirect
171. #17988434C22semidirect
172. C2×#14556498C22semidirect
175. C2×#117×C73C22semidirect
176. #389×C73C22semidirect
177. #388×C73C22semidirect
178. #388×C73C22semidirect
179. #387×C73C22semidirect
180. #387×C73C22semidirect
182. #385×C73C22semidirect
183. #385×C73C22semidirect
184. C4×C4⋊C4×C73C22semidirect
185. C4×C22⋊C4×C73C22semidirect
186. C4×C22⋊C4×C73C22semidirect
187. C2×#95×C73C22semidirect
202. C22×C4×D73C2×C4semidirect
212. #14556576C2×C4semidirect
213. #14556576C2×C4semidirect
214. #14556575C2×C4semidirect
215. #14556574C2×C4semidirect
216. #14556573C2×C4semidirect
217. #14556573C2×C4semidirect
218. #14556572C2×C4semidirect
252. C4⋊C4×D73C2×C4semidirect
253. C4⋊C4×D73C2×C4semidirect
294. C22⋊C4×D73C2×C4semidirect
295. C22⋊C4×D73C2×C4semidirect
296. C22⋊C4×D73C2×C4semidirect
343. #123×C73C2×C4semidirect
818. #2359D73semidirect
841. C73#34376semidirect
860. C2×#117C2×D73semidirect
887. #389C2×D73semidirect
910. #388C2×D73semidirect
911. #388C2×D73semidirect
926. #387C2×D73semidirect
927. #387C2×D73semidirect
950. #385C2×D73semidirect
951. #385C2×D73semidirect
979. C4×C4⋊C4C2×D73semidirect
994. C4×C22⋊C4C2×D73semidirect
995. C4×C22⋊C4C2×D73semidirect
997. C2×#95C2×D73semidirect
1034. #123C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#123×D732
#226130802
#226130782
#226130762
#226130732
#226129272
#226129232
#226129192
#226128052
#226128042
#226127792
#226127782
#226127742
#226127492
D4×#119240052
#226127272
#226127232
#226127192
#226127152
#226126052
#226126022
#226125992
#226125962
#226125462
#226125422
#226125302
#226125252
#226123102
C2×#179884462
C73×#23592
#3437673