Finite Group Databasebeta

← #11901807

Subgroups — #11901807

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595995C211yesmaximal, characteristic, complemented
2C3×#5522C211yesmaximal, characteristic, complemented
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595034C211yesmaximal, characteristic, complemented
5#10595029C211yesmaximal, characteristic, complemented
6#10594954C211yesmaximal, characteristic, complemented
7C2×#63874C211yesmaximal, characteristic, complemented
8#10594594C212yesmaximal, complemented
9#10594355C212yesmaximal, complemented
10#10594352C212yesmaximal, complemented
11#10594341C212yesmaximal, complemented
12#10594243C214yesmaximal, complemented
13#10594241C214yesmaximal, complemented
14#10593934C214yesmaximal, complemented
15#10593870C214yesmaximal, complemented
16#86273—31nomaximal
17#85837—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#117C2211yescharacteristic
22#64106C2212yes—
23#64104C2212yes—
24#64095C2212yes—
25#64091C2212yes—
26C4×C4⋊(C3⋊D3)C2214yes—
27C3×#926C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C3×#893C2212yescomplemented
31C3×#890C2212yescomplemented
32C3×#888C2212yescomplemented
33C3×#887C2212yescomplemented
34C3×#67⋊C4C2214yes—
35C3×#878C2214yes—
36C3×#872C2212yescomplemented
37C3×C42×D3C2212yescomplemented
38C3×C4×Dic6C2214yescomplemented
39#63981C2212yes—
40#63978C2214yes—
41C2×#3724C2212yes—
42C2×#3722C2212yes—
43#63962C2212yes—
44#63952C2214yes—
45#63916C2212yes—
46#63911C2211yescharacteristic, complemented
47#63910C2214yes—
48#63909C2214yes—
49#63907C2214yes—
50C4×#626C2214yes—
51C4×#626C2214yescomplemented
52#63897C2214yes—
53#63894C2212yescomplemented
54#63888C2214yescomplemented
55C4×#624C2212yescomplemented
56#63874C2212yes—
57#63874C2212yes—
58#63874C2212yes—
59#63874C2212yes—
60#63874C2212yescomplemented
61#63871C2212yes—
62#63869C2214yescomplemented
63#63868C2214yes—
64#63868C2214yescomplemented
65#63866C2211yescharacteristic, complemented
66#63864C2214yes—
67#63864C2211yescharacteristic, complemented
68#63861C2214yescomplemented
69#63860C2211yescharacteristic, complemented
70#63856C2214yescomplemented
71#63854C2214yescomplemented
72#63850C2214yes—
73#63850C2214yescomplemented
74#63848C2214yes—
75#63845C2214yescomplemented
76#63844C2212yescomplemented
77C3×#533—31no—
78C3×C4×#41—31no—
79#5832—31no—
80#5828—31no—
81#5733—32no—
82#5733—32no—
83#5698—32no—
84#5697—32no—
85#5645—34no—
86#5644—34no—
87#5583—32no—
88#5582—32no—
89#5580—34no—
90#5580—34no—
91#5564—34no—
92#5562—32no—
93#5561—32no—
94#5560—34no—
95#5528—34no—
96#5524—31no—
97#5524—31no—
98#5524—31no—
99#5524—61no—
100#5522—31no—
101#5522D311yescharacteristic, complemented
102#5517D311yescharacteristic, complemented
103#5479—34no—
104#5477—31no—
105C4×#235—31no—
106C2×#872—31no—
107C2×#872—31no—
108C23×C3⋊D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×#638C2312yes—
111C22×C3⋊Dic3C2311yescharacteristic
112#3828—24no—
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4⋊(C3⋊D3)C2314yes—
115C2×C4×C3⋊D3—24no—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2312yes—
118C2×C4×C3⋊D3C2312yes—
119C2×#634C2311yescharacteristic
120C2×C3×#67C2312yes—
121C22×C3×Dic3C2312yes—
122C22×C3×Dic3C2312yes—
123C3×#235—24no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6C2311yescharacteristic
128C2×C3×Dic6C2314yes—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#624C2314yes—
132C32×C4⋊C4C2312yes—
133C32×C22⋊C4C2312yes—
134C32×C42C2312yes—
135#3752C2314yes—
136#3752C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138C3×#217C2312yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×C4⋊Dic3C2314yes—
141C3×C4⋊Dic3C2312yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2312yes—
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2311yescharacteristic
150C3×C4×Dic3C2311yescharacteristic
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2312yes—
153#3724C2314yes—
154#3724C2312yes—
155#3724C2312yes—
156#3724C2312yes—
157#3724C2312yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160#3722C2312yes—
161#3722C2314yes—
162#3722C2312yes—
163#3722C2314yes—
164#3722C2314yes—
165#3722C2312yes—
166#3722C2312yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169Dic32C2314yes—
170#3455—91noSylow
171C2×C3×#41—31no—
172C2×#235—31no—
173C2×#235—31no—
174C2×#235—61no—
175C2×#235C2×D311yescharacteristic
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—61no—
179C3×C4⋊Q8—32no—
180C3×#125—32no—
181C3×C22⋊Q8—34no—
182C3×C4×Q8—32no—
183C3×C4×Q8—34no—
184C3×C4×D4—32no—
185C3×C4×D4—34no—
186C3×#117—21no—
187C3×#117—31no—
188C3×#117—32no—
189C3×#117C2×D311yescharacteristic
190C3×#117C2×D311yescharacteristic
191C2×C3×C42—31no—
192C2×C3×C42—31no—
193C2×C3×C42—32no—
194#947—34no—
195#947—34no—
196#947—31no—
197#946—34no—
198#946—32no—
199#946—34no—
200#944—31no—
201#940—31no—
202#939—34no—
203#938—32no—
204#937—32no—
205#936—31no—
206#935—32no—
207#930—34no—
208#930—34no—
209#929—34no—
210#929—34no—
211C4×#67—34no—
212C4×#67—34no—
213C4×#67—34no—
214C2×(C2×D3)⋊C4—32no—
215C2×(C2×D3)⋊C4—32no—
216#926C2×D311yescharacteristic
217#924—34no—
218C2×Dic3⋊C4—32no—
219C2×Dic3⋊C4—32no—
220C2×C4×Dic3C2×D311yescharacteristic
221C2×C4×Dic3C2×D311yescharacteristic
222#898—34no—
223#898—34no—
224#898—34no—
225#898—34no—
226#898—34no—
227#897—32no—
228#897—32no—
229#897—32no—
230#897—62no—
231#896—34no—
232#895—32no—
233#895—34no—
234#895—32no—
235#895—32no—
236#895—34no—
237#895—62no—
238#894—34no—
239#894—34no—
240#894—34no—
241#894—34no—
242#894—34no—
243#893—32no—
244#893C2×D312yescomplemented
245#890—34no—
246#890—34no—
247#890C2×D312yescomplemented
248#889—34no—
249#888C2×D312yescomplemented
250#887—32no—
251#887C2×D312yescomplemented
252#886—32no—
253#886—32no—
254#886—32no—
255#886—62no—
256#885—34no—
257#884—34no—
258#883—34no—
259#882—32no—
260#882—32no—
261#882—32no—
262#882—62no—
263#67⋊C4—34no—
264#67⋊C4C2×D314yes—
265#879—34no—
266#878C2×D314yes—
267#876—34no—
268#876—34no—
269#875—31no—
270#875—31no—
271#875—34no—
272#874—31no—
273C4×D12—34no—
274C4×D12—34no—
275C4×D12—34no—
276C4×D12—34no—
277C4×D12—32no—
278C4×D12—64no—
279#872—32no—
280#872—32no—
281#872—32no—
282#872—32no—
283#872—32no—
284#872—32no—
285#872—32no—
286#872—32no—
287#872—32no—
288#872—32no—
289#872C2×D312yescomplemented
290C42×D3—32no—
291C42×D3—32no—
292C42×D3C2×D312yescomplemented
293#870—34no—
294#869—31no—
295C4×Dic6—32no—
296C4×Dic6C2×D314yescomplemented
297C23×C32C2411yescharacteristic
298C22×C3⋊D3—22no—
299C22×C3⋊D3—42no—
300C22×C3⋊D3C2412yes—
301C22×C3⋊D3C2412yes—
302C22×C3×D3C2412yes—
303C2×C32×C4#4114yes—
304C2×C32×C4C2414yes—
305C2×C32×C4C2411yescharacteristic
306C2×C32×C4C2411yescharacteristic
307#638—24no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2412yes—
311C4⋊(C3⋊D3)—22no—
312C4⋊(C3⋊D3)—44no—
313C4×C3⋊D3—24no—
314C4×C3⋊D3—24no—
315C4×C3⋊D3—24no—
316#634—22no—
317C3×#67—24no—
318C2×C3×Dic3—42no—
319C2×C3×Dic3—42no—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2414yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C3×D12—22no—
327C3×C4×D3—24no—
328C3×C4×D3—44no—
329C3×Dic6—22no—
330C3×Dic6—44no—
331#626—44no—
332#626—44no—
333#624—44no—
334#542—92no—
335#542—92no—
336#541—92no—
337#540—92no—
338#539—94no—
339#538—94no—
340#533—31no—
341#532—91no—
342#529—94no—
343#529—94no—
344#525—91no—
345#525—91no—
346C4×#41—31no—
347C4×#41—91no—
348C2×#117—91no—
349C23×D3—31no—
350C23×D3—31no—
351C23×D3—61no—
352C3×#41—64no—
353C2×C3×Q8—31no—
354C2×C3×Q8—34no—
355C2×C3×D4—32no—
356C2×C3×D4—31no—
357C22×C3×C4—21no—
358C22×C3×C4—32no—
359C22×C3×C4—32no—
360C22×C3×C4—32no—
361C22×C3×C4—34no—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—32no—
365C2×#67—32no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—62no—
369C2×#67C22×D312yes—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—61no—
373C22×Dic3C22×D312yes—
374C22×Dic3C22×D312yes—
375#235—24no—
376#235—64no—
377#235—64no—
378#235—124no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—34no—
382C2×D12—34no—
383C2×D12—34no—
384C2×D12—34no—
385C2×D12—64no—
386C2×D12—61no—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—32no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3—32no—
393C2×C4×D3—32no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—64no—
400C2×C4×D3—64no—
401C2×C4×D3—124no—
402C2×C4×D3C22×D312yes—
403C2×C4×D3C22×D314yes—
404C2×Dic6—31no—
405C2×Dic6—31no—
406C2×Dic6—61no—
407C2×Dic6C22×D311yescharacteristic
408C2×Dic6C22×D314yes—
409C3×C4⋊C4—22no—
410C3×C4⋊C4—32no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4C22×D312yes—
416C3×C4⋊C4C22×D312yes—
417C3×C22⋊C4—22no—
418C3×C22⋊C4—32no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4C22×D312yes—
421C3×C22⋊C4C22×D312yes—
422C3×C42—22no—
423C3×C42—32no—
424C3×C42—31no—
425C3×C42—34no—
426C3×C42—31no—
427C3×C42—32no—
428C3×C42—31no—
429C3×C42—32no—
430C3×C42—31no—
431C3×C42C22×D312yes—
432C3×C42C22×D312yes—
433#217—34no—
434#217—34no—
435#217C22×D312yes—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—32no—
443(C2×D3)⋊C4—32no—
444(C2×D3)⋊C4—32no—
445(C2×D3)⋊C4—32no—
446(C2×D3)⋊C4—32no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—32no—
449(C2×D3)⋊C4—32no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—64no—
457(C2×D3)⋊C4—64no—
458(C2×D3)⋊C4C22×D314yes—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—64no—
464C4⋊Dic3C22×D312yes—
465C4⋊Dic3C22×D314yes—
466Dic3⋊C4—34no—
467Dic3⋊C4—32no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—32no—
471Dic3⋊C4—32no—
472Dic3⋊C4—32no—
473Dic3⋊C4—32no—
474Dic3⋊C4—32no—
475Dic3⋊C4—32no—
476Dic3⋊C4—32no—
477Dic3⋊C4—34no—
478Dic3⋊C4C22×D314yes—
479Dic3⋊C4C22×D314yes—
480Dic3⋊C4C22×D314yes—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3C22×D312yes—
484C4×Dic3C22×D312yes—
485C4×Dic3C22×D311yescharacteristic
486C4×Dic3C22×D311yescharacteristic
487C4×Dic3C22×D314yes—
488C4×Dic3C22×D312yes—
489C4×Dic3C22×D311yescharacteristic
490C4×Dic3C22×D311yescharacteristic
491C22×C32—22no—
492C22×C32C2×#4112yes—
493C22×C32C2511yescharacteristic
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—24no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—44no—
500C2×C3×D3—22no—
501C2×C3×D3—24no—
502C32×C4—24no—
503C32×C4C2×#4112yes—
504C32×C4C2×#4112yes—
505C3⋊Dic3—22no—
506C3⋊Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—24no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C2×#41—31no—
514C2×#41—91no—
515C23×C4—91no—
516C4⋊Q8—32no—
517C4⋊Q8—91no—
518#127—91no—
519#126—94no—
520#126—94no—
521#126—94no—
522#126—94no—
523#125—32no—
524#125—94no—
525#125—94no—
526#124—91no—
527#124—94no—
528#124—91no—
529#124—94no—
530#123—94no—
531#123—92no—
532#123—94no—
533#123—94no—
534#123—94no—
535#123—92no—
536C22⋊Q8—34no—
537C22⋊Q8—92no—
538C22⋊Q8—94no—
539C22⋊Q8—94no—
540C22⋊Q8—92no—
541#121—94no—
542#121—94no—
543#121—92no—
544#121—94no—
545#121—92no—
546#120—92no—
547#120—92no—
548C4×Q8—32no—
549C4×Q8—34no—
550C4×Q8—92no—
551C4×D4—32no—
552C4×D4—34no—
553C4×D4—92no—
554C4×D4—94no—
555C4×D4—94no—
556C4×D4—94no—
557C4×D4—94no—
558#117—31no—
559#117—32no—
560#117—92no—
561#117—92no—
562#117—92no—
563#117—92no—
564#117—92no—
565#117D3211yescharacteristic
566C2×C4⋊C4—92no—
567C2×C22⋊C4—92no—
568C2×C42—31no—
569C2×C42—31no—
570C2×C42—32no—
571C2×C42—92no—
572C23×C3—21no—
573C23×C3—32no—
574C23×C3C23×D311yescharacteristic
575C23×C3C23×D311yescharacteristic
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—32no—
579C22×D3—32no—
580C22×D3—62no—
581C22×D3—62no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3—122no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—124no—
588C22×D3C23×D312yes—
589C3×Q8—62no—
590C3×Q8—124no—
591C3×D4—64no—
592C3×D4—62no—
593C2×C3×C4—21no—
594C2×C3×C4—24no—
595C2×C3×C4—21no—
596C2×C3×C4—24no—
597C2×C3×C4—32no—
598C2×C3×C4—34no—
599C2×C3×C4—32no—
600C2×C3×C4—32no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—64no—
604C2×C3×C4—124no—
605C2×C3×C4—122no—
606C2×C3×C4—122no—
607C2×C3×C4#23514yes—
608C2×C3×C4#23914yes—
609C2×C3×C4C23×D314yes—
610C2×C3×C4C23×D314yes—
611C2×C3×C4C23×D311yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615#67—24no—
616#67—64no—
617#67—64no—
618#67—124no—
619#67—124no—
620#67—124no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—32no—
625C2×Dic3—42no—
626C2×Dic3—42no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—122no—
632C2×Dic3C23×D312yes—
633C2×Dic3C23×D314yes—
634C2×Dic3C23×D312yes—
635C2×Dic3C23×D312yes—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638D12—22no—
639D12—62no—
640D12—62no—
641D12—122no—
642D12—124no—
643D12—124no—
644D12—128no—
645D12—124no—
646D12—124no—
647C4×D3—24no—
648C4×D3—44no—
649C4×D3—64no—
650C4×D3—64no—
651C4×D3—64no—
652C4×D3—64no—
653C4×D3—64no—
654C4×D3—64no—
655C4×D3—124no—
656C4×D3—124no—
657C4×D3—124no—
658C4×D3—124no—
659C4×D3—124no—
660Dic6—22no—
661Dic6—44no—
662Dic6—62no—
663Dic6—62no—
664Dic6—122no—
665C2×C32—22no—
666C2×C32C22×#4111yescharacteristic
667C2×C32#58512yes—
668C3⋊D3—42no—
669C3⋊D3—42no—
670C3×D3—42no—
671C24—91no—
672#41—64no—
673#41—184no—
674C2×Q8—31no—
675C2×Q8—34no—
676C2×Q8—91no—
677C2×D4—32no—
678C2×D4—31no—
679C2×D4—94no—
680C2×D4—94no—
681C2×D4—92no—
682C2×D4—91no—
683C2×D4—94no—
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—34no—
688C22×C4—94no—
689C22×C4—91no—
690C22×C4—92no—
691C22×C4—92no—
692C22×C4—92no—
693C22×C4—184no—
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—34no—
696C4⋊C4—32no—
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—92no—
701C4⋊C4—92no—
702C4⋊C4—92no—
703C4⋊C4—92no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4C2×D3212yes—
709C22⋊C4—32no—
710C22⋊C4—34no—
711C22⋊C4—92no—
712C22⋊C4—92no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C22⋊C4—94no—
720C22⋊C4—94no—
721C22⋊C4—94no—
722C22⋊C4C2×D3212yes—
723C42—32no—
724C42—31no—
725C42—31no—
726C42—34no—
727C42—31no—
728C42—31no—
729C42—32no—
730C42—32no—
731C42—94no—
732C42C2×D3212yes—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—21no—
737C22×C3—42no—
738C22×C3—62no—
739C22×C3—64no—
740C22×C3C2×#23512yes—
741C22×C3C2×#23912yes—
742C22×C3C24×D311yescharacteristic
743C22×C3C24×D311yescharacteristic
744C2×D3—22no—
745C2×D3—24no—
746C2×D3—64no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—64no—
752C2×D3—64no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—122no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—124no—
761C2×D3—124no—
762C2×D3—124no—
763C2×D3—128no—
764C3×C4—24no—
765C3×C4—24no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—44no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—64no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4C2×#23512yes—
776C3×C4C2×#23512yes—
777C3×C4C2×#23912yes—
778C3×C4C2×#23912yes—
779Dic3—22no—
780Dic3—22no—
781Dic3—24no—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—122no—
790Dic3—122no—
791C32#345511yescharacteristic, complemented, Sylow
792C23—32no—
793C23—92no—
794C23—92no—
795C23—182no—
796C23—362no—
797C23C22×D3211yescharacteristic
798Q8—62no—
799Q8—124no—
800Q8—182no—
801D4—64no—
802D4—62no—
803D4—184no—
804D4—182no—
805D4—364no—
806D4—364no—
807D4—364no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—34no—
814C2×C4—64no—
815C2×C4—92no—
816C2×C4—92no—
817C2×C4—124no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4—182no—
821C2×C4—184no—
822C2×C4—184no—
823C2×C4—184no—
824C2×C4—364no—
825C2×C4#379914yes—
826C2×C4C22×D3214yes—
827C2×C4C22×D3211yescharacteristic
828C2×C4C22×D3211yescharacteristic
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—21no—
832C2×C3—22no—
833C2×C3—42no—
834C2×C3—122no—
835C2×C3C22×#23511yescharacteristic
836C2×C3C22×#23911yescharacteristic
837C2×C3#596412yes—
838C2×C3#596412yes—
839D3—42no—
840D3—124no—
841D3—122no—
842D3—122no—
843D3—122no—
844D3—122no—
845D3—242no—
846C22—22no—
847C22—62no—
848C22—64no—
849C22—182no—
850C22—182no—
851C22—184no—
852C22—182no—
853C22—182no—
854C22—364no—
855C22C2×#379912yes—
856C22C23×D3211yescharacteristic
857C4—24no—
858C4—62no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—62no—
863C4—64no—
864C4—182no—
865C4—182no—
866C4C2×#379912yes—
867C4C2×#379912yes—
868C3—21no—
869C3#8583711yescharacteristic, complemented
870C3#8627311yescharacteristic, complemented
871C2—22no—
872C2—122no—
873C2—362no—
874C2—362no—
875C2C22×#379911yescharacteristic
876C2#1059669512yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595995C2semidirect
2. C3×#5522C2semidirect
3. C3×#5517C2semidirect
4. #10595034C2semidirect
5. #10595029C2semidirect
6. #10594954C2semidirect
7. C2×#63874C2semidirect
8. #10594594C2semidirect
9. #10594355C2semidirect
10. #10594352C2semidirect
11. #10594341C2semidirect
12. #10594243C2semidirect
13. #10594241C2semidirect
14. #10593934C2semidirect
15. #10593870C2semidirect
30. C3×#893C22semidirect
31. C3×#890C22semidirect
32. C3×#888C22semidirect
33. C3×#887C22semidirect
36. C3×#872C22semidirect
37. C3×C42×D3C22semidirect
38. C3×C4×Dic6C22semidirect
46. #63911C22semidirect
51. C4×#626C22semidirect
53. #63894C22semidirect
54. #63888C22semidirect
55. C4×#624C22semidirect
60. #63874C22semidirect
62. #63869C22semidirect
64. #63868C22semidirect
65. #63866C22semidirect
67. #63864C22semidirect
68. #63861C22semidirect
69. #63860C22semidirect
70. #63856C22semidirect
71. #63854C22semidirect
73. #63850C22semidirect
75. #63845C22semidirect
76. #63844C22semidirect
101. #5522D3semidirect
102. #5517D3semidirect
244. #893C2×D3semidirect
247. #890C2×D3semidirect
249. #888C2×D3semidirect
251. #887C2×D3semidirect
289. #872C2×D3semidirect
292. C42×D3C2×D3semidirect
296. C4×Dic6C2×D3semidirect
791. C32#3455semidirect
869. C3#85837semidirect
870. C3#86273semidirect

Maximal subgroups

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

subgroupindex
#105959952
C3×#55222
C3×#55172
#105950342
#105950292
#105949542
C2×#638742
#105945942
#105943552
#105943522
#105943412
#105942432
#105942412
#105939342
#105938702
#862733
#858373