Finite Group Databasebeta

← #11658982

Subgroups — #11658982

Order 768.

2042 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85834C211yesmaximal, characteristic
2C3×#2923C211yesmaximal, characteristic, complemented
3#82513C211yesmaximal, characteristic, complemented
4#79375C214yesmaximal, complemented
5#79374C214yesmaximal, complemented
6#79334C214yesmaximal, complemented
7#79333C214yesmaximal, complemented
8#79080C211yesmaximal, characteristic, complemented
9D3×#424C211yesmaximal, characteristic, complemented
10#79071C211yesmaximal, characteristic, complemented
11#79070C211yesmaximal, characteristic, complemented
12#78662C211yesmaximal, characteristic
13D3×#408C211yesmaximal, characteristic
14#78649C211yesmaximal, characteristic, complemented
15#78648C211yesmaximal, characteristic, complemented
16#78519C211yesmaximal, characteristic, complemented
17#78514C211yesmaximal, characteristic, complemented
18#78489C211yesmaximal, characteristic, complemented
19C2×#4708C211yesmaximal, characteristic, complemented
20#60126—31nomaximal, Sylow
21C2×D3×#41C2211yescharacteristic
22C3×C4×#41C2211yescharacteristic
23Dic3×#41C2211yescharacteristic
24C2×D3×M16C2211yescharacteristic
25C2×D3×M16C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28#5574C412yes—
29#5572C412yes—
30#5546C412yes—
31#5546C414yes—
32#5545C414yes—
33#5545C412yes—
34#5522C2212yes—
35#5522C2211yescharacteristic
36D3×#117C2212yes—
37D3×#117C2211yescharacteristic
38C4×#235C2211yescharacteristic
39C4×#235C2212yes—
40C2×#872C2211yescharacteristic
41C2×#872C2212yes—
42C3×#433C2214yescomplemented
43C3×#432C2214yescomplemented
44C3×#424C2211yescharacteristic, complemented
45C3×#424C2211yescharacteristic, complemented
46C3×#408C2211yescharacteristic
47C3×#408C2211yescharacteristic
48C3×C4×M16C2211yescharacteristic, complemented
49C2×C3×#97C2211yescharacteristic, complemented
50#5234C2211yescharacteristic
51#5234C2211yescharacteristic
52#5129C2211yescharacteristic
53#5129C2211yescharacteristic
54#5119C2211yescharacteristic, complemented
55#5119C2211yescharacteristic, complemented
56Dic3×M16C2211yescharacteristic, complemented
57Dic3×M16C2211yescharacteristic, complemented
58#5110C2211yescharacteristic
59#5110C2211yescharacteristic
60#5102C2211yescharacteristic, complemented
61#5102C2211yescharacteristic, complemented
62C2×#815C2211yescharacteristic, complemented
63C2×C8×Dic3C2211yescharacteristic, complemented
64#5000C2214yescomplemented
65#4999C2211yescharacteristic, complemented
66#4999C2211yescharacteristic, complemented
67#4925C2214yescomplemented
68C4×#208C2211yescharacteristic, complemented
69C2×C4×C3⋊C8C2211yescharacteristic, complemented
70#4840C2214yescomplemented
71#4840C2214yescomplemented
72#4839C2214yes—
73#4839C2214yes—
74#4837C2214yescomplemented
75#4835C2214yescomplemented
76#4833C2214yescomplemented
77D3×C4⋊C8C2214yescomplemented
78#4727C2214yes—
79#4727C2214yes—
80#4726C2214yes—
81D3×C22⋊C8C2214yes—
82#4720C2214yescomplemented
83#4720C2214yescomplemented
84#4719C2214yescomplemented
85#4718C2214yescomplemented
86#4709C2214yescomplemented
87#4709C2214yescomplemented
88#4708C2212yes—
89#4708C2212yes—
90#4708C2212yes—
91#4708C2212yescomplemented
92#4708C2212yescomplemented
93#4708C2212yescomplemented
94#4705C2214yescomplemented
95#4689C2212yes—
96#4689C2212yescomplemented
97#4685C2214yescomplemented
98#3428—31no—
99#2925—34no—
100#2925—34no—
101#2924—34no—
102#2924—34no—
103#2923—31no—
104#2923—31no—
105#2923—31no—
106#2923D311yescharacteristic, complemented
107#2922—31no—
108#2922—31no—
109#2922—31no—
110#2922—31no—
111#2905—31no—
112C2×#424—31no—
113#2879—31no—
114C2×#408—31no—
115#2873—31no—
116C2×#405—31no—
117C2×C3×#41C2311yescharacteristic
118D3×#41—24no—
119D3×#41—24no—
120C2×#239C2×C411yescharacteristic
121C2×D3×Q8C2×C411yescharacteristic
122C2×#237C2×C412yes—
123C2×#237C2×C411yescharacteristic
124C2×D3×D4C2×C412yes—
125C2×D3×D4C2×C411yescharacteristic
126C2×#235C2311yescharacteristic
127C2×#235C2312yes—
128C22×C4×D3C2312yes—
129C22×C4×D3C2311yescharacteristic
130C2×C3×M16C2311yescharacteristic
131C2×C3×M16C2311yescharacteristic
132C22×C3×C8C2311yescharacteristic
133C22×C3×C8C2311yescharacteristic
134C3×C4×Q8C2×C412yes—
135C3×C4×D4C2×C414yes—
136C3×C4×D4C2×C412yes—
137C3×#117C2311yescharacteristic
138C3×#117C2312yes—
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2312yes—
141Q8×Dic3C2×C412yes—
142D4×Dic3C2×C414yes—
143D4×Dic3C2×C412yes—
144C4×#67C2×C414yes—
145C4×#67C2×C414yes—
146C4×#67C2×C414yes—
147C2×(C2×D3)⋊C4C2×C414yes—
148C2×(C2×D3)⋊C4C2×C412yes—
149#926C2312yes—
150#926C2311yescharacteristic
151C2×Dic3⋊C4C2×C414yes—
152C2×Dic3⋊C4C2×C412yes—
153C2×C4×Dic3C2312yes—
154C2×C4×Dic3C2311yescharacteristic
155C2×#208C2311yescharacteristic
156C2×#208C2311yescharacteristic
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159D3×M16—24no—
160D3×M16—24no—
161C2×ΓL(1,𝔽25)—24no—
162C2×ΓL(1,𝔽25)C2312yes—
163C2×ΓL(1,𝔽25)C2312yes—
164C2×ΓL(1,𝔽25)C2312yes—
165C2×ΓL(1,𝔽25)C2312yes—
166C2×D3×C8—24no—
167C2×D3×C8C2312yes—
168C2×D3×C8C2312yes—
169C2×D3×C8C2312yes—
170C2×D3×C8C2312yes—
171#893C2×C414yes—
172#893C2×C412yes—
173#892C2×C414yes—
174#892C2×C412yes—
175D3×C4⋊C4C2×C414yes—
176D3×C4⋊C4C2×C412yes—
177#887C2×C414yes—
178#887C2×C412yes—
179#67⋊C4C2×C414yes—
180#67⋊C4C2×C414yes—
181#67⋊C4C2×C414yes—
182D3×C22⋊C4C2×C414yes—
183D3×C22⋊C4C2×C412yes—
184#877C2×C414yes—
185#877C2×C412yes—
186C4×D12C2×C412yes—
187C4×D12C2×C414yes—
188#872C2×C414yes—
189#872C2×C412yes—
190#872C2×C414yes—
191#872C2×C412yes—
192#872C2311yescharacteristic
193#872C2311yescharacteristic
194#872C2311yescharacteristic
195#872C2311yescharacteristic
196#872C2312yes—
197#872C2312yes—
198#872C2312yes—
199C42×D3C2312yes—
200C42×D3C2312yes—
201C42×D3C2312yes—
202C4×Dic6C2×C412yes—
203C4×Dic6C2×C414yes—
204C3×C4⋊C8C2314yes—
205C3×C4⋊C8C2314yes—
206C3×C22⋊C8C2314yes—
207C3×C22⋊C8C2314yes—
208C3×#97C2312yes—
209C3×#97C2312yes—
210C3×#97C2312yes—
211C3×C4×C8C2312yes—
212#830C2314yes—
213#830C2314yes—
214(C2×D3)⋊C8C2314yes—
215(C2×D3)⋊C8C2314yes—
216(C2×D3)⋊C8C2314yes—
217(C2×D3)⋊C8C2314yes—
218#815C2312yes—
219#815C2312yes—
220#815C2312yes—
221#815C2312yes—
222Dic3⋊C8C2314yes—
223Dic3⋊C8C2314yes—
224Dic3⋊C8C2314yes—
225Dic3⋊C8C2314yes—
226C8×Dic3C2312yes—
227C8×Dic3C2312yes—
228C8×Dic3C2312yes—
229C8×Dic3C2312yes—
230C4⋊(C3⋊C8)C2314yes—
231C4⋊(C3⋊C8)C2314yes—
232#803C2312yes—
233C4×C3⋊C8C2312yes—
234C4×C3⋊C8C2312yes—
235C4×C3⋊C8C2312yes—
236C22×#41—31no—
237C22×M16—31no—
238C22×M16—31no—
239C22×M16—31no—
240C23×C8—31no—
241#520—32no—
242#520—34no—
243#520—32no—
244#519—32no—
245#518—34no—
246#518—32no—
247C4×#41—31no—
248C4×#41—31no—
249C4×#41—32no—
250C4×#41—31no—
251C4×#41—32no—
252C4×#41C2×D311yescharacteristic
253C2×#117—31no—
254C2×#117—32no—
255C2×#117—31no—
256C2×#117—32no—
257#433—34no—
258#433—34no—
259#433—34no—
260#433—34no—
261#433—34no—
262#433—34no—
263#433—34no—
264#433C2×D314yescomplemented
265#432—34no—
266#432—34no—
267#432—34no—
268#432C2×D314yescomplemented
269#431—34no—
270#431—34no—
271#431—34no—
272#431—34no—
273#424—31no—
274#424—31no—
275#424—31no—
276#424—31no—
277#424—31no—
278#424—31no—
279#424—34no—
280#424—34no—
281#424C2×D311yescharacteristic, complemented
282#424C2×D311yescharacteristic, complemented
283#423—34no—
284C2×C4⋊C8—34no—
285#408—31no—
286#408—31no—
287#408—31no—
288#408—31no—
289#408—31no—
290#408—31no—
291#408—34no—
292#408—34no—
293#408C2×D311yescharacteristic
294#408C2×D311yescharacteristic
295#407—34no—
296C2×C22⋊C8—34no—
297#405—32no—
298#405—32no—
299#405—32no—
300#405—32no—
301#405—32no—
302#405—32no—
303#405—32no—
304#405—32no—
305C4×M16—31no—
306C4×M16—31no—
307C4×M16—31no—
308C4×M16C2×D311yescharacteristic, complemented
309C2×#97—31no—
310C2×#97C2×D311yescharacteristic, complemented
311C2×C4×C8—31no—
312C2×C4×C8—31no—
313C23×D3C22×C412yes—
314C23×D3C22×C411yescharacteristic
315C3×#41—22no—
316C3×#41—22no—
317C2×C3×Q8C22×C411yescharacteristic
318C2×C3×D4C22×C412yes—
319C2×C3×D4C22×C411yescharacteristic
320C22×C3×C4C22×C414yes—
321C22×C3×C4C22×C412yes—
322C22×C3×C4C2412yes—
323C22×C3×C4C2411yescharacteristic
324C2×#67C22×C412yes—
325C2×#67C22×C412yes—
326C2×#67C22×C412yes—
327C22×Dic3C22×C412yes—
328C22×Dic3C22×C414yes—
329C22×Dic3C22×C412yes—
330C22×Dic3C22×C411yescharacteristic
331#239—24no—
332D3×Q8—24no—
333#237—28no—
334#237—24no—
335D3×D4—28no—
336D3×D4—24no—
337#235—22no—
338#235—22no—
339#235—24no—
340#235—24no—
341C2×D12C22×C412yes—
342C2×D12C22×C411yescharacteristic
343C2×C4×D3—24no—
344C2×C4×D3—24no—
345C2×C4×D3C22×C412yes—
346C2×C4×D3C22×C412yes—
347C2×C4×D3C22×C414yes—
348C2×C4×D3C22×C414yes—
349C2×C4×D3C22×C414yes—
350C2×C4×D3C22×C411yescharacteristic
351C2×C4×D3C22×C411yescharacteristic
352C2×C4×D3#4114yes—
353C2×C4×D3#4114yes—
354C2×C4×D3C2412yes—
355C2×C4×D3C2411yescharacteristic
356C2×C4×D3C2411yescharacteristic
357C2×Dic6C22×C411yescharacteristic
358C2×Dic6C22×C412yes—
359C3×M16—22no—
360C3×M16—22no—
361C2×C3×C8—22no—
362C2×C3×C8—22no—
363C2×C3×C8C2412yes—
364C2×C3×C8C2412yes—
365C2×C3×C8C2412yes—
366C2×C3×C8C2412yes—
367C3×C4⋊C4C22×C414yes—
368C3×C4⋊C4C22×C412yes—
369C3×C22⋊C4C22×C414yes—
370C3×C22⋊C4C22×C412yes—
371C3×C42C22×C414yes—
372C3×C42C22×C412yes—
373C3×C42C2411yescharacteristic
374C3×C42C2411yescharacteristic
375C3×C42C2412yes—
376#217C22×C414yes—
377#217C22×C412yes—
378(C2×D3)⋊C4C22×C412yes—
379(C2×D3)⋊C4C22×C414yes—
380(C2×D3)⋊C4C22×C412yes—
381(C2×D3)⋊C4C22×C412yes—
382(C2×D3)⋊C4C22×C414yes—
383(C2×D3)⋊C4C22×C414yes—
384(C2×D3)⋊C4C22×C412yes—
385C4⋊Dic3C22×C414yes—
386C4⋊Dic3C22×C412yes—
387Dic3⋊C4C22×C414yes—
388Dic3⋊C4C22×C412yes—
389Dic3⋊C4C22×C412yes—
390Dic3⋊C4C22×C412yes—
391Dic3⋊C4C22×C414yes—
392Dic3⋊C4C22×C414yes—
393Dic3⋊C4C22×C412yes—
394C4×Dic3C22×C414yes—
395C4×Dic3C22×C414yes—
396C4×Dic3C22×C414yes—
397C4×Dic3C22×C414yes—
398C4×Dic3C22×C412yes—
399C4×Dic3C2411yescharacteristic
400C4×Dic3C2411yescharacteristic
401C4×Dic3C2412yes—
402#208—22no—
403#208—22no—
404C2×C3⋊C8—22no—
405C2×C3⋊C8—22no—
406C2×C3⋊C8C2412yes—
407C2×C3⋊C8C2412yes—
408C2×C3⋊C8C2412yes—
409C2×C3⋊C8C2412yes—
410ΓL(1,𝔽25)—24no—
411ΓL(1,𝔽25)—24no—
412ΓL(1,𝔽25)—24no—
413ΓL(1,𝔽25)—24no—
414D3×C8—24no—
415D3×C8—24no—
416D3×C8—24no—
417D3×C8—24no—
418C2×#41—31no—
419C2×#41—32no—
420C2×#41—31no—
421C2×#41—32no—
422C2×#41—31no—
423C2×#41—64no—
424C2×#41—64no—
425C2×#41C22×D311yescharacteristic
426C22×Q8—31no—
427C22×D4—31no—
428C22×D4—32no—
429C23×C4—31no—
430C23×C4—32no—
431C2×M16—31no—
432C2×M16—31no—
433C2×M16—32no—
434C2×M16—32no—
435C2×M16—32no—
436C2×M16—32no—
437C2×M16—64no—
438C2×M16—64no—
439C2×M16—64no—
440C2×M16C22×D311yescharacteristic
441C2×M16C22×D311yescharacteristic
442C22×C8—31no—
443C22×C8—31no—
444C22×C8—32no—
445C22×C8—32no—
446C22×C8—32no—
447C22×C8—32no—
448C22×C8—64no—
449C22×C8C22×D311yescharacteristic
450C22×C8C22×D311yescharacteristic
451C4×Q8—32no—
452C4×Q8—32no—
453C4×Q8—34no—
454C4×Q8—32no—
455C4×Q8—34no—
456C4×Q8C4×D312yes—
457C4×D4—34no—
458C4×D4—32no—
459C4×D4—34no—
460C4×D4—34no—
461C4×D4—34no—
462C4×D4—32no—
463C4×D4—34no—
464C4×D4—34no—
465C4×D4—34no—
466C4×D4—34no—
467C4×D4—32no—
468C4×D4—34no—
469C4×D4C4×D314yes—
470C4×D4C4×D312yes—
471#117—31no—
472#117—32no—
473#117—32no—
474#117—34no—
475#117—32no—
476#117—34no—
477#117—32no—
478#117—34no—
479#117—32no—
480#117—34no—
481#117—31no—
482#117—31no—
483#117—32no—
484#117—31no—
485#117—31no—
486#117—32no—
487#117—32no—
488#117C22×D311yescharacteristic
489#117C22×D312yes—
490C2×C4⋊C4—32no—
491C2×C4⋊C4—34no—
492C2×C4⋊C4—32no—
493C2×C4⋊C4—34no—
494C2×C22⋊C4—32no—
495C2×C22⋊C4—34no—
496C2×C22⋊C4—32no—
497C2×C22⋊C4—34no—
498C2×C42—31no—
499C2×C42—32no—
500C2×C42—32no—
501C2×C42—32no—
502C2×C42—32no—
503C2×C42C22×D311yescharacteristic
504C2×C42C22×D312yes—
505C4⋊C8—34no—
506C4⋊C8—34no—
507C4⋊C8—34no—
508C4⋊C8—34no—
509C4⋊C8—34no—
510C4⋊C8—34no—
511C4⋊C8C22×D314yes—
512C4⋊C8C22×D314yes—
513C22⋊C8—34no—
514C22⋊C8—34no—
515C22⋊C8—34no—
516C22⋊C8—34no—
517C22⋊C8—34no—
518C22⋊C8—34no—
519C22⋊C8C22×D314yes—
520C22⋊C8C22×D314yes—
521#97—32no—
522#97—32no—
523#97—32no—
524#97—32no—
525#97—32no—
526#97C22×D312yes—
527#97C22×D312yes—
528#97C22×D312yes—
529C4×C8—32no—
530C4×C8—32no—
531C4×C8—32no—
532C4×C8—32no—
533C4×C8—32no—
534C4×C8—32no—
535C4×C8—32no—
536C4×C8C22×D312yes—
537C23×C3C23×C412yes—
538C23×C3C23×C411yescharacteristic
539C22×D3—24no—
540C22×D3—42no—
541C22×D3—44no—
542C22×D3#11714yes—
543C22×D3C23×C412yes—
544C22×D3C23×C411yescharacteristic
545C22×D3C23×C411yescharacteristic
546C3×Q8—22no—
547C3×D4—24no—
548C3×D4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—42no—
552C2×C3×C4—44no—
553C2×C3×C4C23×C412yes—
554C2×C3×C4C23×C414yes—
555C2×C3×C4C23×C412yes—
556C2×C3×C4C23×C412yes—
557C2×C3×C4C23×C411yescharacteristic
558C2×C3×C4C2×#4112yes—
559C2×C3×C4C2×#4112yes—
560C2×C3×C4C2511yescharacteristic
561#67—24no—
562#67—24no—
563#67—24no—
564C2×Dic3—24no—
565C2×Dic3—42no—
566C2×Dic3—44no—
567C2×Dic3#11714yes—
568C2×Dic3C23×C412yes—
569C2×Dic3C23×C412yes—
570C2×Dic3C23×C412yes—
571C2×Dic3C23×C414yes—
572C2×Dic3C23×C411yescharacteristic
573C2×Dic3C23×C411yescharacteristic
574D12—24no—
575D12—22no—
576C4×D3—24no—
577C4×D3—22no—
578C4×D3—22no—
579C4×D3—24no—
580C4×D3—44no—
581C4×D3—44no—
582C4×D3—44no—
583C4×D3#11714yes—
584C4×D3#11714yes—
585C4×D3C2×#4112yes—
586C4×D3C2×#4112yes—
587C4×D3C2×#4112yes—
588C4×D3C2×#4112yes—
589Dic6—22no—
590Dic6—24no—
591C3×C8—22no—
592C3×C8—22no—
593C3×C8—22no—
594C3×C8—22no—
595C3⋊C8—22no—
596C3⋊C8—22no—
597C3⋊C8—22no—
598C3⋊C8—22no—
599C24—31no—
600C24—32no—
601#41—22no—
602#41—22no—
603#41—64no—
604#41—64no—
605#41—68no—
606#41—64no—
607#41—64no—
608#41—62no—
609#41—62no—
610C2×Q8—32no—
611C2×Q8—31no—
612C2×Q8—64no—
613C2×Q8C2×C4×D311yescharacteristic
614C2×D4—32no—
615C2×D4—32no—
616C2×D4—32no—
617C2×D4—32no—
618C2×D4—31no—
619C2×D4—64no—
620C2×D4—68no—
621C2×D4C2×C4×D312yes—
622C2×D4C2×C4×D311yescharacteristic
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—34no—
627C22×C4—34no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—32no—
631C22×C4—34no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—32no—
635C22×C4—32no—
636C22×C4—34no—
637C22×C4—34no—
638C22×C4—34no—
639C22×C4—64no—
640C22×C4—64no—
641C22×C4C2×C4×D314yes—
642C22×C4C2×C4×D312yes—
643C22×C4C23×D312yes—
644C22×C4C23×D311yescharacteristic
645M16—22no—
646M16—22no—
647M16—64no—
648M16—64no—
649M16—64no—
650M16—64no—
651M16—62no—
652M16—62no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—32no—
656C2×C8—32no—
657C2×C8—32no—
658C2×C8—32no—
659C2×C8—64no—
660C2×C8—64no—
661C2×C8—64no—
662C2×C8—64no—
663C2×C8—62no—
664C2×C8—62no—
665C2×C8C23×D312yes—
666C2×C8C23×D312yes—
667C2×C8C23×D312yes—
668C2×C8C23×D312yes—
669C4⋊C4—32no—
670C4⋊C4—34no—
671C4⋊C4—32no—
672C4⋊C4—32no—
673C4⋊C4—32no—
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—34no—
677C4⋊C4—32no—
678C4⋊C4C2×C4×D314yes—
679C4⋊C4C2×C4×D312yes—
680C22⋊C4—34no—
681C22⋊C4—32no—
682C22⋊C4—32no—
683C22⋊C4—34no—
684C22⋊C4—32no—
685C22⋊C4—32no—
686C22⋊C4—34no—
687C22⋊C4—32no—
688C22⋊C4—34no—
689C22⋊C4C2×C4×D314yes—
690C22⋊C4C2×C4×D312yes—
691C42—34no—
692C42—34no—
693C42—32no—
694C42—34no—
695C42—34no—
696C42—31no—
697C42—31no—
698C42—32no—
699C42C2×C4×D314yes—
700C42C2×C4×D312yes—
701C42C23×D311yescharacteristic
702C42C23×D311yescharacteristic
703C42C23×D312yes—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—24no—
707C22×C3C2×#11712yes—
708C22×C3C24×C411yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—24no—
713C2×D3—44no—
714C2×D3—84no—
715C2×D3C2×#11712yes—
716C2×D3C2×#11712yes—
717C3×C4—22no—
718C3×C4—24no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4C2×#11712yes—
722C3×C4C22×#4111yescharacteristic
723C3×C4C22×#4111yescharacteristic
724Dic3—22no—
725Dic3—24no—
726Dic3—22no—
727Dic3—22no—
728Dic3C2×#11712yes—
729Dic3C2×#11712yes—
730C23—31no—
731C23—31no—
732C23—34no—
733C23—32no—
734C23—64no—
735C23—122no—
736C23—124no—
737C23C22×C4×D312yes—
738C23C22×C4×D311yescharacteristic
739Q8—22no—
740Q8—64no—
741Q8—62no—
742D4—24no—
743D4—22no—
744D4—64no—
745D4—64no—
746D4—64no—
747D4—64no—
748D4—62no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—34no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—34no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—34no—
763C2×C4—32no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—64no—
767C2×C4—64no—
768C2×C4—64no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—124no—
772C2×C4—124no—
773C2×C4—124no—
774C2×C4—122no—
775C2×C4—124no—
776C2×C4C22×C4×D312yes—
777C2×C4C22×C4×D312yes—
778C2×C4C22×C4×D314yes—
779C2×C4C22×C4×D312yes—
780C2×C4C22×C4×D311yescharacteristic
781C2×C4D3×#4112yes—
782C2×C4D3×#4112yes—
783C2×C4C24×D311yescharacteristic
784C8—22no—
785C8—22no—
786C8—22no—
787C8—22no—
788C8—62no—
789C8—62no—
790C8—62no—
791C8—62no—
792C2×C3—22no—
793C2×C3—42no—
794C2×C3C22×#11711yescharacteristic
795C2×C3#357312yes—
796D3—22no—
797D3—22no—
798D3—42no—
799C22—22no—
800C22—24no—
801C22—22no—
802C22—32no—
803C22—32no—
804C22—62no—
805C22—62no—
806C22—64no—
807C22—62no—
808C22—124no—
809C22—244no—
810C22D3×#11712yes—
811C22C23×C4×D311yescharacteristic
812C4—22no—
813C4—22no—
814C4—24no—
815C4—22no—
816C4—32no—
817C4—32no—
818C4—62no—
819C4—64no—
820C4—62no—
821C4—62no—
822C4D3×#11712yes—
823C4C2×D3×#4111yescharacteristic
824C4C2×D3×#4111yescharacteristic
825C3#6012611yescharacteristic, complemented, Sylow
826C2—22no—
827C2—42no—
828C2—62no—
829C2—62no—
830C2—122no—
831C2C2×D3×#11711yescharacteristic
832C2#8716612yes—
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2923C2
prime radicalC2×D3×#41C22
cosocleC2×C3×C4C25
hypercenter#2923D3
hypocenterC3#60126
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. C3×#2923C2semidirect
3. #82513C2semidirect
4. #79375C2semidirect
5. #79374C2semidirect
6. #79334C2semidirect
7. #79333C2semidirect
8. #79080C2semidirect
9. D3×#424C2semidirect
10. #79071C2semidirect
11. #79070C2semidirect
14. #78649C2semidirect
15. #78648C2semidirect
16. #78519C2semidirect
17. #78514C2semidirect
18. #78489C2semidirect
19. C2×#4708C2semidirect
42. C3×#433C22semidirect
43. C3×#432C22semidirect
44. C3×#424C22semidirect
45. C3×#424C22semidirect
48. C3×C4×M16C22semidirect
49. C2×C3×#97C22semidirect
54. #5119C22semidirect
55. #5119C22semidirect
56. Dic3×M16C22semidirect
57. Dic3×M16C22semidirect
60. #5102C22semidirect
61. #5102C22semidirect
62. C2×#815C22semidirect
63. C2×C8×Dic3C22semidirect
64. #5000C22semidirect
65. #4999C22semidirect
66. #4999C22semidirect
67. #4925C22semidirect
68. C4×#208C22semidirect
69. C2×C4×C3⋊C8C22semidirect
70. #4840C22semidirect
71. #4840C22semidirect
74. #4837C22semidirect
75. #4835C22semidirect
76. #4833C22semidirect
77. D3×C4⋊C8C22semidirect
82. #4720C22semidirect
83. #4720C22semidirect
84. #4719C22semidirect
85. #4718C22semidirect
86. #4709C22semidirect
87. #4709C22semidirect
91. #4708C22semidirect
92. #4708C22semidirect
93. #4708C22semidirect
94. #4705C22semidirect
96. #4689C22semidirect
97. #4685C22semidirect
106. #2923D3semidirect
264. #433C2×D3semidirect
268. #432C2×D3semidirect
281. #424C2×D3semidirect
282. #424C2×D3semidirect
308. C4×M16C2×D3semidirect
310. C2×#97C2×D3semidirect
825. C3#60126semidirect

Maximal subgroups

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

subgroupindex
#858342
C3×#29232
#825132
#793752
#793742
#793342
#793332
#790802
D3×#4242
#790712
#790702
#786622
D3×#4082
#786492
#786482
#785192
#785142
#784892
C2×#47082
#601263