Finite Group Databasebeta

← #11901800

Subgroups — #11901800

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#10596299C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4#10595395C212yesmaximal, complemented
5#10595354C212yesmaximal, complemented
6#10595221C214yesmaximal, complemented
7#10595218C212yesmaximal, complemented
8#10595216C214yesmaximal, complemented
9#10595121C212yesmaximal, complemented
10#10595049C211yesmaximal, characteristic, complemented
11#10595034C211yesmaximal, characteristic, complemented
12Dic3×#235C211yesmaximal, characteristic, complemented
13#10594933C214yesmaximal, complemented
14C2×#63874C211yesmaximal, characteristic, complemented
15#10594839C214yesmaximal, complemented
16#86236—31nomaximal
17#85837—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21#64155C2212yes—
22#64147C2212yes—
23#64146C2212yes—
24#64144C2212yes—
25C4×#638C2214yes—
26#64135C2211yescharacteristic
27C3×#947C2211yescharacteristic, complemented
28C3×Q8×Dic3C2212yescomplemented
29C3×#944C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic, complemented
31C3×#939C2214yes—
32C3×#936C2211yescharacteristic, complemented
33C3×D4×Dic3C2214yes—
34C3×D4×Dic3C2212yescomplemented
35C3×C4×#67C2214yescomplemented
36C3×#926C2211yescharacteristic
37C3×#926C2212yescomplemented
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2212yescomplemented
41#63981C2212yes—
42#63978C2214yes—
43Dic3×#67C2214yes—
44#63971C2214yes—
45#63969C2214yescomplemented
46C2×#3724C2212yes—
47#63966C2214yes—
48#63964C2214yes—
49#63964C2214yescomplemented
50C2×#3722C2212yes—
51#63962C2212yes—
52#63961C2214yescomplemented
53#63956C2214yescomplemented
54#63953C2214yes—
55#63918C2212yescomplemented
56C4×#627C2214yescomplemented
57#63916C2212yes—
58C4×#626C2214yes—
59#63899C2214yescomplemented
60Dic3×D12C2212yescomplemented
61#63890C2214yes—
62C4×D3×Dic3C2212yescomplemented
63#63874C2212yes—
64#63874C2212yes—
65#63874C2212yes—
66#63874C2212yes—
67#63871C2212yes—
68#63869C2212yescomplemented
69#63868C2214yes—
70#63867C2214yescomplemented
71#63859C2214yescomplemented
72#63855C2212yescomplemented
73#63852C2214yes—
74#63848C2214yes—
75#63847C2214yescomplemented
76Dic3×Dic6C2212yescomplemented
77C3×#532—31no—
78C3×C4×#41—31no—
79#5832D311yescharacteristic, complemented
80#5828—31no—
81#5828—31no—
82#5828—31no—
83#5828—61no—
84Dic3×#41—31no—
85Dic3×#41D311yescharacteristic, complemented
86#5731—32no—
87#5719—32no—
88#5682—32no—
89#5682—32no—
90#5617—34no—
91#5602—34no—
92#5583—32no—
93#5582—32no—
94#5564—34no—
95#5562—32no—
96#5561—32no—
97#5560—34no—
98#5538—34no—
99#5538—34no—
100#5528—34no—
101#5524—31no—
102#5517—31no—
103#5479—34no—
104C4×#235—31no—
105C2×#872—31no—
106C2×#872—31no—
107#5470—31no—
108C23×C3⋊D3C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2311yescharacteristic
113C22×C32×C4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638C2314yes—
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C4×C3⋊D3—24no—
118C2×C4×C3⋊D3C2312yes—
119C2×C4×C3⋊D3C2312yes—
120C2×C3×#67C2312yes—
121C2×C3×#67C2314yes—
122C22×C3×Dic3C2312yes—
123C22×C3×Dic3C2312yes—
124C22×C3×Dic3C2314yes—
125C3×#235—24no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×#627C2314yes—
130C2×#626C2314yes—
131C2×D3×Dic3C2314yes—
132#3757C2312yes—
133#3757C2314yes—
134#3752C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136#3750C2314yes—
137C4×C3⋊Dic3C2312yes—
138C3×#217C2312yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×C4⋊Dic3C2312yes—
143C3×C4⋊Dic3C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2311yescharacteristic
146C3×C4×Dic3C2311yescharacteristic
147C3×C4×Dic3C2312yes—
148C3×C4×Dic3C2312yes—
149C3×C4×Dic3C2311yescharacteristic
150C3×C4×Dic3C2311yescharacteristic
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2314yes—
153#3724C2312yes—
154#3724C2314yes—
155#3724C2312yes—
156#3724C2312yes—
157#3724C2312yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162#3722C2312yes—
163#3722C2314yes—
164#3722C2312yes—
165#3722C2312yes—
166#3722C2312yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169Dic32C2314yes—
170#3455—91noSylow
171C2×C3×#41—21no—
172C2×C3×#41—31no—
173C2×C3×#41C2×D311yescharacteristic
174C2×C3×#41C2×D311yescharacteristic
175C2×#235C2×D311yescharacteristic
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—61no—
179C3×C4⋊Q8—31no—
180C3×#127—31no—
181C3×#124—31no—
182C3×#124—31no—
183C3×#121—34no—
184C3×C4×Q8—32no—
185C3×C4×D4—34no—
186C3×C4×D4—32no—
187C3×C4×D4—34no—
188C3×#117—31no—
189C3×#117—32no—
190C2×C3×C42—31no—
191C2×C3×C42—31no—
192C2×C3×C42—32no—
193#947C2×D311yescharacteristic, complemented
194#946—32no—
195#946—32no—
196#946—32no—
197#946—62no—
198Q8×Dic3—32no—
199Q8×Dic3C2×D312yescomplemented
200#944C2×D311yescharacteristic, complemented
201#940C2×D311yescharacteristic, complemented
202#939—34no—
203#939—34no—
204#939C2×D314yes—
205#938—32no—
206#938—32no—
207#938—32no—
208#938—62no—
209#937—32no—
210#937—32no—
211#937—32no—
212#937—62no—
213#936C2×D311yescharacteristic, complemented
214#935—32no—
215#935—32no—
216#935—34no—
217#935—34no—
218#935—32no—
219#935—62no—
220D4×Dic3—34no—
221D4×Dic3—32no—
222D4×Dic3C2×D314yes—
223D4×Dic3C2×D312yescomplemented
224#930—34no—
225#929—34no—
226#929—34no—
227C4×#67—34no—
228C4×#67—34no—
229C4×#67—34no—
230C4×#67—34no—
231C4×#67—64no—
232C4×#67C2×D314yescomplemented
233C2×(C2×D3)⋊C4—32no—
234C2×(C2×D3)⋊C4—32no—
235#926—31no—
236#926—31no—
237#926—32no—
238#926—61no—
239#926C2×D311yescharacteristic
240#926C2×D312yescomplemented
241#924—34no—
242#924—34no—
243C2×Dic3⋊C4—32no—
244C2×Dic3⋊C4—32no—
245C2×C4×Dic3—32no—
246C2×C4×Dic3C2×D311yescharacteristic
247C2×C4×Dic3C2×D311yescharacteristic
248C2×C4×Dic3C2×D312yescomplemented
249#898—34no—
250#898—34no—
251#898—34no—
252#897—32no—
253#896—34no—
254#895—32no—
255#894—34no—
256#890—32no—
257#889—34no—
258#889—34no—
259#889—34no—
260#888—32no—
261#886—32no—
262#886—34no—
263#886—34no—
264#885—34no—
265#885—34no—
266#885—34no—
267#884—34no—
268#883—34no—
269#882—32no—
270#879—34no—
271#879—34no—
272#879—34no—
273#878—34no—
274#878—34no—
275#878—34no—
276#876—34no—
277#876—34no—
278#875—34no—
279C4×D12—32no—
280C4×D12—34no—
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#872—32no—
290C42×D3—32no—
291#870—32no—
292#870—34no—
293#869—32no—
294C4×Dic6—32no—
295C4×Dic6—34no—
296C4×Dic6—34no—
297C23×C32C2412yes—
298C23×C32C2411yescharacteristic
299C22×C3⋊D3—22no—
300C22×C3⋊D3—42no—
301C22×C3⋊D3C2412yes—
302C22×C3×D3C2412yes—
303C32×Q8—22no—
304C32×D4—24no—
305C32×D4—22no—
306C2×C32×C4—24no—
307C2×C32×C4#4114yes—
308C2×C32×C4C2412yes—
309C2×C32×C4C2411yescharacteristic
310C2×C32×C4C2411yescharacteristic
311#638—44no—
312C2×C3⋊Dic3—22no—
313C2×C3⋊Dic3C2414yes—
314C2×C3⋊Dic3C2412yes—
315C4×C3⋊D3—24no—
316C4×C3⋊D3—24no—
317C3×#67—24no—
318C3×#67—44no—
319C2×C3×Dic3—42no—
320C2×C3×Dic3—44no—
321C2×C3×Dic3—42no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2414yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C3×D12—22no—
329C3×C4×D3—24no—
330C3×Dic6—22no—
331#627—44no—
332#626—44no—
333D3×Dic3—44no—
334#542—92no—
335#542—92no—
336#541—92no—
337#540—92no—
338#539—94no—
339#538—94no—
340#533—91no—
341#532—31no—
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—24no—
353C3×#41—24no—
354C3×#41—44no—
355C3×#41—64no—
356C2×C3×Q8—21no—
357C2×C3×Q8—31no—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×D4—22no—
361C2×C3×D4—21no—
362C2×C3×D4—32no—
363C2×C3×D4—34no—
364C2×C3×D4—31no—
365C2×C3×D4C22×D312yes—
366C2×C3×D4C22×D311yescharacteristic
367C2×C3×D4C22×D312yes—
368C2×C3×D4C22×D311yescharacteristic
369C22×C3×C4—21no—
370C22×C3×C4—22no—
371C22×C3×C4—32no—
372C22×C3×C4—32no—
373C22×C3×C4—34no—
374C22×C3×C4—32no—
375C22×C3×C4C22×D312yes—
376C22×C3×C4C22×D312yes—
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—64no—
383C2×#67C22×D312yes—
384C2×#67C22×D314yes—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—34no—
388C22×Dic3—61no—
389C22×Dic3C22×D312yes—
390C22×Dic3C22×D314yes—
391C22×Dic3C22×D312yes—
392#235—24no—
393C2×D12—34no—
394C2×D12C22×D311yescharacteristic
395C2×C4×D3—32no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—34no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—64no—
403C2×C4×D3—64no—
404C2×C4×D3—124no—
405C2×C4×D3C22×D312yes—
406C2×Dic6—34no—
407C2×Dic6—34no—
408C2×Dic6C22×D311yescharacteristic
409C3×C4⋊C4—32no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C22⋊C4—32no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C42—32no—
417C3×C42—32no—
418C3×C42—32no—
419C3×C42—31no—
420C3×C42—31no—
421C3×C42—34no—
422C3×C42—31no—
423C3×C42—31no—
424#217—32no—
425#217—34no—
426#217—34no—
427#217—32no—
428#217—34no—
429#217—34no—
430#217—62no—
431#217—64no—
432#217C22×D314yes—
433#217C22×D314yes—
434#217C22×D312yes—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—32no—
441(C2×D3)⋊C4—32no—
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—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—64no—
450(C2×D3)⋊C4C22×D314yes—
451C4⋊Dic3—32no—
452C4⋊Dic3—32no—
453C4⋊Dic3—34no—
454C4⋊Dic3—34no—
455C4⋊Dic3—34no—
456C4⋊Dic3—34no—
457C4⋊Dic3—62no—
458C4⋊Dic3C22×D312yes—
459C4⋊Dic3C22×D314yes—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—32no—
468Dic3⋊C4—32no—
469Dic3⋊C4—32no—
470Dic3⋊C4—32no—
471Dic3⋊C4—32no—
472Dic3⋊C4—32no—
473Dic3⋊C4—32no—
474Dic3⋊C4—32no—
475Dic3⋊C4—34no—
476Dic3⋊C4—64no—
477Dic3⋊C4C22×D314yes—
478C4×Dic3—32no—
479C4×Dic3—32no—
480C4×Dic3—34no—
481C4×Dic3—34no—
482C4×Dic3—62no—
483C4×Dic3C22×D312yes—
484C4×Dic3C22×D312yes—
485C4×Dic3C22×D311yescharacteristic
486C4×Dic3C22×D311yescharacteristic
487C4×Dic3C22×D311yescharacteristic
488C4×Dic3C22×D311yescharacteristic
489C4×Dic3C22×D312yes—
490C4×Dic3C22×D314yes—
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—24no—
494C22×C32C2×#4112yes—
495C22×C32C2511yescharacteristic
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—44no—
500C2×C3×D3—22no—
501C2×C3×D3—24no—
502C32×C4—22no—
503C32×C4C2×#4112yes—
504C32×C4C2×#4112yes—
505C3⋊Dic3—22no—
506C3⋊Dic3—24no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—24no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C2×#41—31no—
514C2×#41D3211yescharacteristic
515C23×C4—91no—
516C4⋊Q8—31no—
517C4⋊Q8—92no—
518#127—31no—
519#126—94no—
520#126—94no—
521#126—94no—
522#126—94no—
523#125—94no—
524#125—92no—
525#125—94no—
526#124—31no—
527#124—31no—
528#124—94no—
529#124—94no—
530#123—94no—
531#123—94no—
532#123—92no—
533#123—94no—
534#123—94no—
535#123—92no—
536C22⋊Q8—94no—
537C22⋊Q8—94no—
538C22⋊Q8—94no—
539C22⋊Q8—92no—
540C22⋊Q8—92no—
541#121—34no—
542#121—94no—
543#121—92no—
544#121—94no—
545#121—92no—
546#120—92no—
547#120—92no—
548C4×Q8—32no—
549C4×Q8—94no—
550C4×Q8—92no—
551C4×D4—34no—
552C4×D4—32no—
553C4×D4—34no—
554C4×D4—94no—
555C4×D4—92no—
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#117—91no—
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—22no—
574C23×C3—32no—
575C23×C3C23×D312yes—
576C23×C3C23×D312yes—
577C23×C3C23×D311yescharacteristic
578C23×C3C23×D311yescharacteristic
579C22×D3—32no—
580C22×D3—32no—
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—22no—
590C3×Q8—22no—
591C3×Q8—42no—
592C3×Q8—62no—
593C3×D4—24no—
594C3×D4—24no—
595C3×D4—22no—
596C3×D4—22no—
597C3×D4—42no—
598C3×D4—44no—
599C3×D4—64no—
600C3×D4—62no—
601C3×D4—124no—
602C2×C3×C4—24no—
603C2×C3×C4—24no—
604C2×C3×C4—21no—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—24no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—34no—
614C2×C3×C4—44no—
615C2×C3×C4—64no—
616C2×C3×C4—122no—
617C2×C3×C4—124no—
618C2×C3×C4—122no—
619C2×C3×C4#23514yes—
620C2×C3×C4#23714yes—
621C2×C3×C4C23×D312yes—
622C2×C3×C4C23×D312yes—
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C23×D311yescharacteristic
625C2×C3×C4C23×D311yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627#67—24no—
628#67—44no—
629#67—124no—
630#67—124no—
631#67—124no—
632#67—128no—
633C2×Dic3—34no—
634C2×Dic3—34no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—42no—
638C2×Dic3—44no—
639C2×Dic3—42no—
640C2×Dic3—64no—
641C2×Dic3—62no—
642C2×Dic3—62no—
643C2×Dic3—62no—
644C2×Dic3—122no—
645C2×Dic3—124no—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D314yes—
652D12—22no—
653D12—124no—
654C4×D3—24no—
655C4×D3—64no—
656C4×D3—64no—
657C4×D3—64no—
658C4×D3—64no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—124no—
662Dic6—22no—
663Dic6—124no—
664Dic6—124no—
665C2×C32—22no—
666C2×C32—42no—
667C2×C32C22×#4111yescharacteristic
668C2×C32#58512yes—
669C3⋊D3—42no—
670C3×D3—42no—
671C24—91no—
672#41—24no—
673#41—64no—
674C2×Q8—31no—
675C2×Q8—94no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—32no—
678C2×D4—34no—
679C2×D4—31no—
680C2×D4—94no—
681C2×D4—94no—
682C2×D4C2×D3212yes—
683C2×D4C2×D3211yescharacteristic
684C22×C4—32no—
685C22×C4—32no—
686C22×C4—34no—
687C22×C4—32no—
688C22×C4—94no—
689C22×C4—91no—
690C22×C4—92no—
691C22×C4—92no—
692C22×C4—184no—
693C22×C4C2×D3212yes—
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—32no—
696C4⋊C4—34no—
697C4⋊C4—34no—
698C4⋊C4—92no—
699C4⋊C4—92no—
700C4⋊C4—92no—
701C4⋊C4—92no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C4⋊C4—92no—
708C4⋊C4—94no—
709C22⋊C4—32no—
710C22⋊C4—34no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4—92no—
716C22⋊C4—92no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C22⋊C4—94no—
720C22⋊C4—92no—
721C22⋊C4—94no—
722C22⋊C4—94no—
723C42—32no—
724C42—31no—
725C42—31no—
726C42—34no—
727C42—31no—
728C42—31no—
729C42—32no—
730C42—32no—
731C42—94no—
732C42—92no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—24no—
738C22×C3—24no—
739C22×C3—22no—
740C22×C3—21no—
741C22×C3—42no—
742C22×C3—44no—
743C22×C3—42no—
744C22×C3—62no—
745C22×C3—64no—
746C22×C3C2×#23512yes—
747C22×C3C2×#23712yes—
748C22×C3C24×D311yescharacteristic
749C22×C3C24×D311yescharacteristic
750C2×D3—22no—
751C2×D3—24no—
752C2×D3—64no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—124no—
762C2×D3—124no—
763C2×D3—128no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—42no—
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×#23712yes—
778C3×C4C2×#23712yes—
779Dic3—22no—
780Dic3—22no—
781Dic3—24no—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—62no—
786Dic3—62no—
787Dic3—64no—
788Dic3—64no—
789Dic3—122no—
790Dic3—124no—
791C32#345511yescharacteristic, complemented, Sylow
792C23—32no—
793C23—92no—
794C23—182no—
795C23—362no—
796C23C22×D3212yes—
797C23C22×D3211yescharacteristic
798Q8—22no—
799Q8—62no—
800Q8—364no—
801D4—24no—
802D4—22no—
803D4—64no—
804D4—62no—
805D4—124no—
806D4—364no—
807D4—364no—
808C2×C4—24no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—34no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—64no—
816C2×C4—94no—
817C2×C4—92no—
818C2×C4—122no—
819C2×C4—124no—
820C2×C4—122no—
821C2×C4—182no—
822C2×C4—184no—
823C2×C4—184no—
824C2×C4—364no—
825C2×C4#380414yes—
826C2×C4C22×D3212yes—
827C2×C4C22×D3211yescharacteristic
828C2×C4C22×D3211yescharacteristic
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—82no—
837C2×C3—122no—
838C2×C3C22×#23511yescharacteristic
839C2×C3C22×#23711yescharacteristic
840C2×C3#596412yes—
841C2×C3#596412yes—
842D3—42no—
843D3—124no—
844D3—122no—
845D3—122no—
846C22—22no—
847C22—24no—
848C22—22no—
849C22—64no—
850C22—62no—
851C22—182no—
852C22—182no—
853C22—182no—
854C22—364no—
855C22C2×#380412yes—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—62no—
859C4—62no—
860C4—62no—
861C4—64no—
862C4—62no—
863C4—62no—
864C4—184no—
865C4—182no—
866C4C2×#380412yes—
867C4C2×#380412yes—
868C3—21no—
869C3#8583711yescharacteristic, complemented
870C3#8623611yescharacteristic, complemented
871C2—22no—
872C2—42no—
873C2—122no—
874C2—362no—
875C2#1059669512yes—
876C2C22×#380411yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596299C2semidirect
2. C3×#5832C2semidirect
3. C3×Dic3×#41C2semidirect
4. #10595395C2semidirect
5. #10595354C2semidirect
6. #10595221C2semidirect
7. #10595218C2semidirect
8. #10595216C2semidirect
9. #10595121C2semidirect
10. #10595049C2semidirect
11. #10595034C2semidirect
12. Dic3×#235C2semidirect
13. #10594933C2semidirect
14. C2×#63874C2semidirect
15. #10594839C2semidirect
27. C3×#947C22semidirect
28. C3×Q8×Dic3C22semidirect
29. C3×#944C22semidirect
30. C3×#940C22semidirect
32. C3×#936C22semidirect
34. C3×D4×Dic3C22semidirect
35. C3×C4×#67C22semidirect
37. C3×#926C22semidirect
40. C2×C3×C4×Dic3C22semidirect
45. #63969C22semidirect
49. #63964C22semidirect
52. #63961C22semidirect
53. #63956C22semidirect
55. #63918C22semidirect
56. C4×#627C22semidirect
59. #63899C22semidirect
60. Dic3×D12C22semidirect
62. C4×D3×Dic3C22semidirect
68. #63869C22semidirect
70. #63867C22semidirect
71. #63859C22semidirect
72. #63855C22semidirect
75. #63847C22semidirect
76. Dic3×Dic6C22semidirect
79. #5832D3semidirect
85. Dic3×#41D3semidirect
193. #947C2×D3semidirect
199. Q8×Dic3C2×D3semidirect
200. #944C2×D3semidirect
201. #940C2×D3semidirect
213. #936C2×D3semidirect
223. D4×Dic3C2×D3semidirect
232. C4×#67C2×D3semidirect
240. #926C2×D3semidirect
248. C2×C4×Dic3C2×D3semidirect
791. C32#3455semidirect
869. C3#85837semidirect
870. C3#86236semidirect

Maximal subgroups

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

subgroupindex
#105962992
C3×#58322
C3×Dic3×#412
#105953952
#105953542
#105952212
#105952182
#105952162
#105951212
#105950492
#105950342
Dic3×#2352
#105949332
C2×#638742
#105948392
#862363
#858373