Finite Group Databasebeta

← #33248752

Subgroups — #33248752

Order 18688.

2714 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989094C211yesmaximal, characteristic
2#22613081C212yesmaximal, complemented
3#22613074C212yesmaximal, complemented
4#22612914C212yesmaximal, complemented
5#22612912C212yesmaximal, complemented
6#22612861C212yesmaximal, complemented
7#22612853C212yesmaximal, complemented
8C4⋊C4×C22⋊D73C212yesmaximal, complemented
9#22612827C212yesmaximal, complemented
10#22612663C214yesmaximal, complemented
11#22612633C214yesmaximal, complemented
12#22612538C212yesmaximal, complemented
13#22612523C211yesmaximal, characteristic, complemented
14#380×D73C212yesmaximal, complemented
15C73×#2311C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17#17989094C4116yescomplemented
18C2×#14556572C2211yescharacteristic
19C2×#14556572C2211yescharacteristic
20C2×#14556567C2212yes—
21C2×#14556562C2212yes—
22C2×#14556559C2211yescharacteristic
23C2×#14556559C2211yescharacteristic
24C2×C4×C22⋊D73C2214yes—
25C2×C4×C22⋊D73C2212yes—
26C2×C4×C22⋊D73C2212yes—
27C2×#14556551C2214yes—
28C2×#14556550C2211yescharacteristic
29C2×#14556550C2211yescharacteristic, complemented
30C22×C4⋊Dic73C2211yescharacteristic, complemented
31C2×C4⋊C4×D73C2212yes—
32C2×C4⋊C4×D73C2212yes—
33C2×C22⋊C4×D73C2214yes—
34#17988494C2212yescomplemented
35#17988490C2212yes—
36#17988484C2214yescomplemented
37#17988482C2214yescomplemented
38#17988481C2214yes—
39#17988481C2214yescomplemented
40#17988475C2214yes—
41#17988475C2214yescomplemented
42#17988472C2214yescomplemented
43#17988471C2214yescomplemented
44#17988470C2214yescomplemented
45#17988469C2214yescomplemented
46#17988467C2212yes—
47#17988467C2212yescomplemented
48#17988463C2214yes—
49#17988463C2214yes—
50#17988461C2214yes—
51#17988460C2214yescomplemented
52#17988459C2214yescomplemented
53#17988458C2214yes—
54#17988456C2212yescomplemented
55#17988452C2212yescomplemented
56#17988447C2212yes—
57#17988447C2212yescomplemented
58#17988446C2214yes—
59#17988445C2214yes—
60#17988444C2212yes—
61#17988444C2212yes—
62C4⋊C4×Dic73C2212yescomplemented
63C4⋊C4×Dic73C2212yescomplemented
64C4×#11924005C2214yes—
65#17988434C2214yes—
66#95×D73C2214yes—
67C22×#41×C73C2211yescharacteristic
68C2×#117×C73C2211yescharacteristic, complemented
69C22×C4⋊C4×C73C2211yescharacteristic, complemented
70#391×C73C2212yescomplemented
71#390×C73C2212yes—
72#386×C73C2212yes—
73#386×C73C2212yescomplemented
74#380×C73C2212yes—
75#380×C73C2212yescomplemented
76C24×D73C2311yescharacteristic
77C22×C22⋊D73C2312yes—
78C22×C22⋊D73C2312yes—
79C23×Dic73C2312yes—
80C23×Dic73C2311yescharacteristic
81C22×C4×D73—42no—
82C22×C4×D73—42no—
83C22×C4×D73C2×C418yescomplemented
84C22×C4×D73C2312yes—
85C22×C4×D73C2314yes—
86C22×C4×D73C2314yes—
87C22×C4×D73C2312yes—
88#14556572C2×C418yescomplemented
89#14556572C2×C418yescomplemented
90#14556567C2×C4116yescomplemented
91#14556562C2×C4116yescomplemented
92#14556559C2×C418yescomplemented
93#14556559C2×C418yescomplemented
94C4×C22⋊D73—48no—
95C4×C22⋊D73C2×C4116yescomplemented
96C4×C22⋊D73C2×C4116yescomplemented
97#14556551—48no—
98#14556550—42no—
99#14556550C2×C418yescomplemented
100C2×C4⋊Dic73—42no—
101C2×C4⋊Dic73C2312yes—
102C2×C4⋊Dic73C2312yes—
103C2×C4⋊Dic73C2312yes—
104C2×C4⋊Dic73C2312yes—
105C2×#11924007C2314yes—
106C2×#11924007C2314yes—
107C2×#11924007C2314yes—
108C2×#11924007C2314yes—
109C2×#11924007C2312yes—
110C2×#11924007C2312yes—
111C4⋊C4×D73—44no—
112C4⋊C4×D73—44no—
113C2×C22⋊Dic73C2314yes—
114C2×C22⋊Dic73C2314yes—
115C2×C22⋊Dic73C2312yes—
116C2×C22⋊Dic73C2312yes—
117C2×C22⋊Dic73C2312yes—
118C2×C22⋊Dic73C2311yescharacteristic
119C2×C22⋊Dic73C2311yescharacteristic
120C2×#11924005C2314yes—
121C2×#11924005C2314yes—
122C2×#11924005C2312yes—
123C2×#11924005C2312yes—
124C22⋊C4×D73—48no—
125C2×C4×Dic73C2312yes—
126C2×C4×Dic73C2314yes—
127C2×C4×Dic73C2314yes—
128C2×C4×Dic73C2312yes—
129#14556498C2314yes—
130#14556498C2314yes—
131#14556498C2314yes—
132#14556498C2314yes—
133#14556498C2314yes—
134#14556498C2314yes—
135#14556498C2314yes—
136#14556498C2314yes—
137C2×#41×C73—42no—
138C2×#41×C73—42no—
139C2×#41×C73C2×C418yescomplemented
140C22×Q8×C73C2311yescharacteristic
141C22×D4×C73C2311yescharacteristic
142C22×D4×C73C2311yescharacteristic
143C22×D4×C73C2311yescharacteristic
144C23×C4×C73C2311yescharacteristic
145C23×C4×C73C2311yescharacteristic
146C23×C4×C73C2311yescharacteristic
147C23×C4×C73C2312yes—
148#117×C73—42no—
149C2×C4⋊C4×C73—42no—
150C2×C4⋊C4×C73C2312yes—
151C2×C4⋊C4×C73C2312yes—
152C2×C4⋊C4×C73C2312yes—
153C2×C22⋊C4×C73C2314yes—
154C2×C22⋊C4×C73C2314yes—
155C2×C22⋊C4×C73C2312yes—
156C2×C42×C73C2312yes—
157#95×C73C2314yes—
158#95×C73C2314yes—
159C23×D73—24no—
160C23×D73—24no—
161C23×D73—41no—
162C23×D73—41no—
163C23×D73C22×C414yes—
164C23×D73C2412yes—
165C2×C22⋊D73—24no—
166C2×C22⋊D73—24no—
167C2×C22⋊D73—24no—
168C2×C22⋊D73—24no—
169C2×C22⋊D73C22×C418yes—
170C2×C22⋊D73C22×C418yes—
171C22×Dic73—41no—
172C22×Dic73—41no—
173C22×Dic73—42no—
174C22×Dic73—44no—
175C22×Dic73C22×C414yes—
176C22×Dic73C2414yes—
177C22×Dic73C2414yes—
178C22×Dic73C2412yes—
179C22×Dic73C2412yes—
180C22×Dic73C2412yes—
181C2×C4×D73—24no—
182C2×C4×D73—24no—
183C2×C4×D73—28no—
184C2×C4×D73—28no—
185C2×C4×D73—416no—
186C2×C4×D73—42no—
187C2×C4×D73—42no—
188C2×C4×D73—44no—
189C2×C4×D73—44no—
190C2×C4×D73—44no—
191C2×C4×D73—44no—
192C2×C4×D73C22×C418yes—
193C2×C4×D73C22×C418yes—
194C4⋊Dic73—24no—
195C4⋊Dic73—24no—
196C4⋊Dic73—42no—
197C4⋊Dic73C22×C418yes—
198#11924007—44no—
199#11924007—44no—
200#11924007—44no—
201#11924007—44no—
202#11924007C22×C418yes—
203#11924007C22×C418yes—
204C22⋊Dic73—44no—
205C22⋊Dic73—42no—
206C22⋊Dic73—44no—
207C22⋊Dic73C22×C414yes—
208C22⋊Dic73C22×C414yes—
209C22⋊Dic73C22×C418yes—
210C22⋊Dic73C22×C418yes—
211#11924005—28no—
212#11924005—28no—
213#11924005C22×C418yes—
214#11924005C22×C418yes—
215C4×Dic73—42no—
216C4×Dic73—44no—
217C4×Dic73—44no—
218C4×Dic73C22×C418yes—
219C24×C73C2411yescharacteristic
220C24×C73C2411yescharacteristic
221C24×C73C2411yescharacteristic
222#41×C73—416no—
223C2×Q8×C73—41no—
224C2×Q8×C73—41no—
225C2×Q8×C73C22×C414yes—
226C2×D4×C73—41no—
227C2×D4×C73—41no—
228C2×D4×C73—41no—
229C2×D4×C73—41no—
230C2×D4×C73—41no—
231C2×D4×C73—41no—
232C2×D4×C73C22×C414yes—
233C2×D4×C73C22×C414yes—
234C2×D4×C73C22×C414yes—
235C22×C4×C73—22no—
236C22×C4×C73—22no—
237C22×C4×C73—22no—
238C22×C4×C73—22no—
239C22×C4×C73—22no—
240C22×C4×C73—22no—
241C22×C4×C73—42no—
242C22×C4×C73—44no—
243C22×C4×C73C22×C414yes—
244C22×C4×C73C22×C414yes—
245C22×C4×C73C22×C414yes—
246C22×C4×C73C2414yes—
247C22×C4×C73C2414yes—
248C22×C4×C73C2411yescharacteristic
249C22×C4×C73C2411yescharacteristic
250C22×C4×C73C2411yescharacteristic
251C22×C4×C73C2411yescharacteristic
252C4⋊C4×C73—24no—
253C4⋊C4×C73—24no—
254C4⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—44no—
257C22⋊C4×C73—44no—
258C42×C73—42no—
259C23×C73—21no—
260C23×C73—22no—
261C23×C73—22no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—22no—
270C23×C73—22no—
271C23×C73C23×C412yes—
272C23×C73C23×C412yes—
273C23×C73C23×C412yes—
274C23×C73C2511yescharacteristic
275C22×D73—22no—
276C22×D73—22no—
277C22×D73—22no—
278C22×D73—22no—
279C22×D73—216no—
280C22×D73—44no—
281C22×D73—48no—
282C22×D73—44no—
283C22×D73—44no—
284C22×D73C23×C414yes—
285C22×D73H(5,𝔽2)14yes—
286C22×D732−1+414yes—
287Q8×C73—44no—
288D4×C73—44no—
289D4×C73—44no—
290D4×C73—44no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—28no—
298C2×C4×C73—28no—
299C2×C4×C73—28no—
300C2×C4×C73—24no—
301C2×C4×C73—24no—
302C2×C4×C73—24no—
303C2×C4×C73—24no—
304C2×C4×C73—24no—
305C2×C4×C73—24no—
306C2×C4×C73—84no—
307C2×C4×C73C23×C412yes—
308C2×C4×C73C23×C412yes—
309C2×C4×C73C23×C412yes—
310C2×C4×C73C23×C412yes—
311C2×C4×C73H(5,𝔽2)12yes—
312C2×C4×C73H(5,𝔽2)12yes—
313C22⋊D73—216no—
314C22⋊D73—216no—
315C2×Dic73—22no—
316C2×Dic73—22no—
317C2×Dic73—22no—
318C2×Dic73—22no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—24no—
322C2×Dic73—24no—
323C2×Dic73—24no—
324C2×Dic73—24no—
325C2×Dic73—24no—
326C2×Dic73—24no—
327C2×Dic73—44no—
328C2×Dic73—84no—
329C2×Dic73C23×C414yes—
330C2×Dic73C23×C414yes—
331C2×Dic73C23×C414yes—
332C4×D73—216no—
333C4×D73—48no—
334C4×D73—88no—
335C4×D73—88no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—22no—
339C22×C73—24no—
340C22×C73—24no—
341C22×C73—24no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73C24×C411yescharacteristic
352C22×C73C2×H(5,𝔽2)12yes—
353C22×C73C2×H(5,𝔽2)11yescharacteristic
354C22×C73C2×H(5,𝔽2)11yescharacteristic
355C22×C73C2×2−1+412yes—
356C2×D73—24no—
357C2×D73—24no—
358C2×D73—24no—
359C2×D73—24no—
360C2×D73—24no—
361C2×D73—24no—
362C2×D73—416no—
363C2×D73#52018yes—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—22no—
367C4×C73—44no—
368C4×C73—44no—
369C4×C73#51814yes—
370Dic73—24no—
371Dic73—24no—
372Dic73—24no—
373Dic73—44no—
374Dic73—44no—
375#34360—731nomaximal, Sylow
376C2×C73—42no—
377C2×C73—42no—
378C2×C73—42no—
379C2×C73C2×#51811yescharacteristic
380C2×C73C2×#52012yes—
381C2×C73#353612yes—
382C2×C73#353711yescharacteristic
383C2×C73#353811yescharacteristic
384D73—28no—
385C2×#525—731no—
386#2376—732no—
387#2376—732no—
388#2358—732no—
389#2358—732no—
390#2352—732no—
391#2352—732no—
392D4×C4⋊C4—732no—
393D4×C4⋊C4—732no—
394#2329—734no—
395#2325—734no—
396#2314—732no—
397#2311—731no—
398#2311D7311yescharacteristic, complemented
399C2×#380—732no—
400C73#3436011yescharacteristic, complemented, Sylow
401C22×#41C2×D7311yescharacteristic
402C24×C4—731no—
403#525—7316no—
404C2×#123—731no—
405C2×#123—731no—
406C2×C22⋊Q8—732no—
407C2×#121—732no—
408C2×#120—731no—
409C2×#120—731no—
410C2×C4×D4—734no—
411C2×C4×D4—732no—
412C2×C4×D4—732no—
413C2×C4×D4—734no—
414C2×#117—731no—
415C2×#117—731no—
416C2×#117C2×D7311yescharacteristic, complemented
417C22×C4⋊C4—731no—
418C22×C4⋊C4—732no—
419C22×C4⋊C4—732no—
420C22×C4⋊C4C2×D7311yescharacteristic, complemented
421C22×C22⋊C4—734no—
422#391—732no—
423#391C2×D7312yescomplemented
424#390—732no—
425#390C2×D7312yes—
426#389—734no—
427#389—734no—
428#388—734no—
429#388—734no—
430#388—734no—
431#388—734no—
432#387—734no—
433#387—734no—
434#387—734no—
435#387—734no—
436#386—732no—
437#386—732no—
438#386—734no—
439#386—734no—
440#386C2×D7312yes—
441#386C2×D7312yescomplemented
442#385—734no—
443#385—734no—
444#385—734no—
445#385—734no—
446#384—732no—
447#382—732no—
448#380—732no—
449#380—732no—
450#380—732no—
451#380—732no—
452#380—734no—
453#380—734no—
454#380C2×D7312yes—
455#380C2×D7312yescomplemented
456C4×C4⋊C4—732no—
457C4×C4⋊C4—732no—
458C4×C22⋊C4—734no—
459C4×C22⋊C4—734no—
460C2×#95—734no—
461C25—731no—
462C2×#41—42no—
463C2×#41—42no—
464C2×#41C4×D7318yescomplemented
465C22×Q8C22×D7311yescharacteristic
466C22×D4—732no—
467C22×D4—732no—
468C22×D4C22×D7311yescharacteristic
469C22×D4C22×D7311yescharacteristic
470C22×D4C22×D7311yescharacteristic
471C23×C4—2922no—
472C23×C4—2922no—
473C23×C4—732no—
474C23×C4—731no—
475C23×C4—738no—
476C23×C4—732no—
477C23×C4—734no—
478C23×C4—734no—
479C23×C4—732no—
480C23×C4C22×D7311yescharacteristic
481C23×C4C22×D7311yescharacteristic
482C23×C4C22×D7311yescharacteristic
483C23×C4C22×D7312yes—
484#123—738no—
485#123—738no—
486C22⋊Q8—7316no—
487#121—7316no—
488#120—738no—
489#120—738no—
490C4×D4—2928no—
491C4×D4—2928no—
492C4×D4—7316no—
493C4×D4—7316no—
494#117—42no—
495#117—2922no—
496#117—738no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—2924no—
499C2×C4⋊C4—2924no—
500C2×C4⋊C4—2922no—
501C2×C4⋊C4—734no—
502C2×C4⋊C4—734no—
503C2×C4⋊C4—732no—
504C2×C4⋊C4—734no—
505C2×C4⋊C4—734no—
506C2×C4⋊C4—732no—
507C2×C4⋊C4—732no—
508C2×C4⋊C4—732no—
509C2×C4⋊C4—732no—
510C2×C4⋊C4—732no—
511C2×C4⋊C4C22×D7312yes—
512C2×C4⋊C4C22×D7312yes—
513C2×C4⋊C4C22×D7312yes—
514C2×C22⋊C4—2928no—
515C2×C22⋊C4—734no—
516C2×C22⋊C4—732no—
517C2×C22⋊C4—734no—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—731no—
520C2×C22⋊C4—732no—
521C2×C22⋊C4—732no—
522C2×C22⋊C4—732no—
523C2×C22⋊C4—732no—
524C2×C22⋊C4—734no—
525C2×C22⋊C4—734no—
526C2×C22⋊C4C22×D7314yes—
527C2×C22⋊C4C22×D7312yes—
528C2×C22⋊C4C22×D7314yes—
529C2×C42—732no—
530C2×C42—734no—
531C2×C42—734no—
532C2×C42—732no—
533C2×C42C22×D7312yes—
534#95—734no—
535#95—734no—
536#95—734no—
537#95—734no—
538#95—734no—
539#95—734no—
540#95—734no—
541#95—734no—
542#95C22×D7314yes—
543#95C22×D7314yes—
544C24—2921no—
545C24—2921no—
546C24—734no—
547C24—732no—
548C24—1464no—
549C24—1464no—
550C24C23×D7311yescharacteristic
551C24C23×D7311yescharacteristic
552C24C23×D7311yescharacteristic
553#41—416no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8C2×C4×D7314yes—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—738no—
564C2×D4—738no—
565C2×D4—1464no—
566C2×D4—1464no—
567C2×D4—1464no—
568C2×D4—1464no—
569C2×D4C2×C4×D7314yes—
570C2×D4C2×C4×D7314yes—
571C2×D4C2×C4×D7314yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—2922no—
581C22×C4—2922no—
582C22×C4—29216no—
583C22×C4—2924no—
584C22×C4—2924no—
585C22×C4—2924no—
586C22×C4—2924no—
587C22×C4—2921no—
588C22×C4—2921no—
589C22×C4—2922no—
590C22×C4—2924no—
591C22×C4—734no—
592C22×C4—738no—
593C22×C4—732no—
594C22×C4—732no—
595C22×C4—732no—
596C22×C4—738no—
597C22×C4—734no—
598C22×C4—734no—
599C22×C4—1468no—
600C22×C4—1468no—
601C22×C4—1464no—
602C22×C4—1464no—
603C22×C4C2×C4×D7314yes—
604C22×C4C2×C4×D7314yes—
605C22×C4C2×C4×D7314yes—
606C22×C4C23×D7314yes—
607C22×C4C23×D7314yes—
608C22×C4C23×D7311yescharacteristic
609C22×C4C23×D7311yescharacteristic
610C22×C4C23×D7311yescharacteristic
611C22×C4C23×D7311yescharacteristic
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—42no—
615C4⋊C4—2924no—
616C4⋊C4—2924no—
617C4⋊C4—2924no—
618C4⋊C4—2924no—
619C4⋊C4—2922no—
620C4⋊C4—738no—
621C4⋊C4—738no—
622C4⋊C4—738no—
623C4⋊C4—1464no—
624C4⋊C4—1464no—
625C22⋊C4—44no—
626C22⋊C4—42no—
627C22⋊C4—44no—
628C22⋊C4—2924no—
629C22⋊C4—2922no—
630C22⋊C4—2924no—
631C22⋊C4—734no—
632C22⋊C4—734no—
633C22⋊C4—738no—
634C22⋊C4—738no—
635C22⋊C4—738no—
636C22⋊C4—738no—
637C22⋊C4—1468no—
638C22⋊C4—1468no—
639C42—42no—
640C42—2922no—
641C42—2924no—
642C42—2924no—
643C42—738no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—2924no—
657C23—2928no—
658C23—2924no—
659C23—2924no—
660C23—734no—
661C23—734no—
662C23—734no—
663C23—14616no—
664C23—1462no—
665C23—1462no—
666C23—1462no—
667C23—1462no—
668C23C22×C4×D7312yes—
669C23C22×C4×D7312yes—
670C23C22×C4×D7312yes—
671C23C24×D7311yescharacteristic
672Q8—44no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—14616no—
677D4—14616no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—84no—
694C2×C4—2928no—
695C2×C4—2924no—
696C2×C4—5848no—
697C2×C4—5848no—
698C2×C4—5844no—
699C2×C4—734no—
700C2×C4—734no—
701C2×C4—734no—
702C2×C4—1464no—
703C2×C4—1464no—
704C2×C4—1464no—
705C2×C4—1464no—
706C2×C4—1464no—
707C2×C4—1464no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4—1462no—
711C2×C4—1462no—
712C2×C4—1462no—
713C2×C4—1462no—
714C2×C4—14616no—
715C2×C4C22×C4×D7312yes—
716C2×C4C22×C4×D7312yes—
717C2×C4C22×C4×D7312yes—
718C2×C4C22×C4×D7312yes—
719C2×C4#1455663612yes—
720C2×C4#1455663612yes—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—29216no—
737C22—738no—
738C22—1464no—
739C22—1464no—
740C22—1464no—
741C22—1464no—
742C22—1464no—
743C22—1464no—
744C22C23×C4×D7311yescharacteristic
745C22H(5,𝔽2)×D7312yes—
746C22C2×#1455663611yescharacteristic
747C22C2×#1455663611yescharacteristic
748C222−1+4×D7312yes—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—44no—
753C4—44no—
754C4—2924no—
755C4—2924no—
756C4—1464no—
757C4—1464no—
758C4—1464no—
759C4#1798906014yes—
760C2—42no—
761C2—42no—
762C2—42no—
763C2—1468no—
764C2C2×#1798906011yescharacteristic
765C2#520×D7312yes—
766C2#2262414912yes—
767C2#2262416411yescharacteristic
768C2#2262417411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2311C2
socle, cosocleC23×C73C25
prime radicalC2×#17989094C2
hypercenter#2311D73
hypocenterC73#34360
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #22613081C2semidirect
3. #22613074C2semidirect
4. #22612914C2semidirect
5. #22612912C2semidirect
6. #22612861C2semidirect
7. #22612853C2semidirect
8. C4⋊C4×C22⋊D73C2semidirect
9. #22612827C2semidirect
10. #22612663C2semidirect
11. #22612633C2semidirect
12. #22612538C2semidirect
13. #22612523C2semidirect
14. #380×D73C2semidirect
15. C73×#2311C2semidirect
17. #17989094C4semidirect
29. C2×#14556550C22semidirect
30. C22×C4⋊Dic73C22semidirect
34. #17988494C22semidirect
36. #17988484C22semidirect
37. #17988482C22semidirect
39. #17988481C22semidirect
41. #17988475C22semidirect
42. #17988472C22semidirect
43. #17988471C22semidirect
44. #17988470C22semidirect
45. #17988469C22semidirect
47. #17988467C22semidirect
51. #17988460C22semidirect
52. #17988459C22semidirect
54. #17988456C22semidirect
55. #17988452C22semidirect
57. #17988447C22semidirect
62. C4⋊C4×Dic73C22semidirect
63. C4⋊C4×Dic73C22semidirect
68. C2×#117×C73C22semidirect
69. C22×C4⋊C4×C73C22semidirect
70. #391×C73C22semidirect
73. #386×C73C22semidirect
75. #380×C73C22semidirect
83. C22×C4×D73C2×C4semidirect
88. #14556572C2×C4semidirect
89. #14556572C2×C4semidirect
90. #14556567C2×C4semidirect
91. #14556562C2×C4semidirect
92. #14556559C2×C4semidirect
93. #14556559C2×C4semidirect
95. C4×C22⋊D73C2×C4semidirect
96. C4×C22⋊D73C2×C4semidirect
99. #14556550C2×C4semidirect
139. C2×#41×C73C2×C4semidirect
398. #2311D73semidirect
400. C73#34360semidirect
416. C2×#117C2×D73semidirect
420. C22×C4⋊C4C2×D73semidirect
423. #391C2×D73semidirect
441. #386C2×D73semidirect
455. #380C2×D73semidirect
464. C2×#41C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179890942
#226130812
#226130742
#226129142
#226129122
#226128612
#226128532
C4⋊C4×C22⋊D732
#226128272
#226126632
#226126332
#226125382
#226125232
#380×D732
C73×#23112
#3436073