Finite Group Databasebeta

← #11901804

Subgroups — #11901804

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#10596262C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C2×C3×#926C211yesmaximal, characteristic, complemented
4#10595507C214yesmaximal, complemented
5#10595049C211yesmaximal, characteristic, complemented
6#10595029C211yesmaximal, characteristic, complemented
7#10594987C214yesmaximal, complemented
8#10594985C212yesmaximal, complemented
9#10594983C212yesmaximal, complemented
10#10594954C211yesmaximal, characteristic, complemented
11Dic3×#235C211yesmaximal, characteristic, complemented
12#10594933C214yesmaximal, complemented
13#10594836C214yesmaximal, complemented
14#10594824C212yesmaximal, complemented
15#10594814C212yesmaximal, complemented
16#86019—31nomaximal
17#85738—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21#64162C2212yes—
22#64139C2212yes—
23#64138C2212yes—
24C4×#638C2214yes—
25#64135C2211yescharacteristic
26#64133C2212yes—
27C3×#953C2212yes—
28C2×C3×#217C2212yes—
29C3×#930C2212yes—
30C3×#929C2212yes—
31C3×C4×#67C2214yes—
32C3×#926C2212yes—
33C3×#926C2212yes—
34C3×#926C2212yes—
35C3×#926C2212yes—
36C3×#926C2211yescharacteristic
37C2×C3×C4⋊Dic3C2212yes—
38C3×#924C2212yes—
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41#63978C2214yes—
42#63975C2214yes—
43Dic3×#67C2214yes—
44#63971C2214yes—
45#63969C2214yes—
46#63964C2214yes—
47#63959C2214yes—
48#63958C2214yes—
49#63956C2214yes—
50#63956C2214yes—
51#63953C2214yes—
52#63952C2214yes—
53#63918C2212yescomplemented
54C4×#627C2214yescomplemented
55#63911C2211yescharacteristic, complemented
56C4×#626C2214yescomplemented
57#63899C2214yescomplemented
58#63895C2214yescomplemented
59#63894C2212yescomplemented
60Dic3×D12C2212yescomplemented
61#63890C2214yescomplemented
62C4×#624C2212yescomplemented
63C4×D3×Dic3C2212yescomplemented
64#63874C2212yescomplemented
65#63869C2212yescomplemented
66#63866C2211yescharacteristic, complemented
67#63864C2211yescharacteristic, complemented
68#63860C2211yescharacteristic, complemented
69#63858C2214yescomplemented
70#63855C2212yescomplemented
71#63854C2214yescomplemented
72#63848C2214yescomplemented
73#63847C2214yescomplemented
74#63846C2214yescomplemented
75#63844C2212yescomplemented
76Dic3×Dic6C2212yescomplemented
77C3×#525—31no—
78C2×C3×#117—31no—
79#5832—31no—
80Dic3×#41—31no—
81#5791—31no—
82#5791—31no—
83#5791—61no—
84#5791D311yescharacteristic, complemented
85C2×#926D311yescharacteristic, complemented
86#5665—34no—
87#5643—32no—
88#5625—32no—
89#5619—32no—
90#5603—32no—
91#5593—34no—
92#5557—34no—
93#5538—34no—
94#5535—32no—
95#5534—32no—
96#5534—32no—
97#5528—34no—
98#5528—34no—
99#5522—31no—
100#5518—32no—
101#5517—31no—
102#5515—34no—
103#5494—34no—
104#5477—31no—
105C4×#235—31no—
106C4×#235—31no—
107#5470—31no—
108C24×C32C2311yescharacteristic
109C22×C32×C4—24no—
110C22×C32×C4C2312yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2312yes—
113C22×C32×C4C2311yescharacteristic
114C2×#638C2312yes—
115C2×#638C2314yes—
116#3828—24no—
117C2×C4⋊(C3⋊D3)C2311yescharacteristic
118C2×C4×C3⋊D3C2312yes—
119C2×#634C2311yescharacteristic
120C2×C3×#67C2312yes—
121C2×C3×#67C2314yes—
122C22×C3×Dic3C2312yes—
123C22×C3×Dic3C2312yes—
124C3×#235—24no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×C4×D3C2312yes—
127C2×C3×Dic6C2311yescharacteristic
128C2×#627C2314yes—
129C2×#626C2314yes—
130C2×#624C2314yes—
131C2×D3×Dic3C2314yes—
132#3757C2314yes—
133#3757C2312yes—
134#3752C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136#3750C2314yes—
137C4×C3⋊Dic3C2312yes—
138C3×#217C2314yes—
139C3×#217C2312yes—
140C3×#217C2312yes—
141C3×#217C2312yes—
142C3×#217C2312yes—
143C3×#217C2312yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×C4⋊Dic3C2312yes—
146C3×C4⋊Dic3C2312yes—
147C3×C4⋊Dic3C2312yes—
148C3×C4⋊Dic3C2312yes—
149C3×C4⋊Dic3C2312yes—
150C3×Dic3⋊C4C2314yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2311yescharacteristic
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2312yes—
158#3724C2314yes—
159#3724C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164#3722C2314yes—
165#3722C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168Dic32C2314yes—
169Dic32C2314yes—
170#3455—91noSylow
171C2×C3×#41—31no—
172C23×C3×C4—21no—
173C23×C3×C4C2×D311yescharacteristic
174C23×C3×C4C2×D311yescharacteristic
175C2×#235—31no—
176C2×#235—31no—
177C2×#235—61no—
178C2×#235C2×D311yescharacteristic
179C3×#123—32no—
180C3×C22⋊Q8—32no—
181C3×#121—32no—
182C3×#120—32no—
183C3×C4×D4—34no—
184C3×#117—31no—
185C3×#117—32no—
186C3×#117—32no—
187C3×#117—32no—
188C3×#117—32no—
189C2×C3×C4⋊C4—32no—
190C2×C3×C22⋊C4—32no—
191C2×C3×C42—31no—
192C2×C3×C42—31no—
193#953—32no—
194#953—32no—
195#953—62no—
196#953C2×D312yes—
197C2×#217C2×D312yes—
198#947—31no—
199Q8×Dic3—32no—
200#944—31no—
201#940—31no—
202#939—34no—
203#939—34no—
204#938—34no—
205#936—34no—
206#936—31no—
207#935—34no—
208D4×Dic3—34no—
209D4×Dic3—32no—
210#930—32no—
211#930—32no—
212#930—34no—
213#930—62no—
214#930C2×D312yes—
215#929—32no—
216#929—32no—
217#929—62no—
218#929C2×D312yes—
219C4×#67—34no—
220C4×#67—34no—
221C4×#67—34no—
222C4×#67—34no—
223C4×#67—34no—
224C4×#67—64no—
225C4×#67C2×D314yes—
226#926—31no—
227#926—31no—
228#926—32no—
229#926—61no—
230#926C2×D312yes—
231#926C2×D311yescharacteristic
232#926C2×D312yes—
233#926C2×D312yes—
234#926C2×D312yes—
235C2×C4⋊Dic3C2×D312yes—
236#924—32no—
237#924—32no—
238#924—34no—
239#924—62no—
240#924C2×D312yes—
241C2×C4×Dic3—32no—
242C2×C4×Dic3C2×D311yescharacteristic
243C2×C4×Dic3C2×D311yescharacteristic
244#898—34no—
245#898—34no—
246#898—34no—
247#897—34no—
248#896—34no—
249#896—34no—
250#894—34no—
251#894—34no—
252#893—32no—
253#890—34no—
254#890—32no—
255#889—34no—
256#889—34no—
257#889—34no—
258#888—32no—
259#887—32no—
260#886—34no—
261#885—34no—
262#885—34no—
263#885—34no—
264#884—34no—
265#884—34no—
266#883—34no—
267#883—34no—
268#883—34no—
269#883—34no—
270#67⋊C4—34no—
271#879—34no—
272#879—34no—
273#879—34no—
274#879—34no—
275#879—34no—
276#878—34no—
277#878—34no—
278#875—31no—
279#875—31no—
280#874—31no—
281C4×D12—32no—
282C4×D12—34no—
283C4×D12—32no—
284#872—32no—
285#872—32no—
286#872—32no—
287C42×D3—32no—
288C42×D3—32no—
289C42×D3—32no—
290#870—32no—
291#869—31no—
292#869—32no—
293C4×Dic6—32no—
294C4×Dic6—32no—
295C4×Dic6—34no—
296C4×Dic6—34no—
297C23×C32—22no—
298C23×C32—42no—
299C23×C32C2412yes—
300C23×C32C2411yescharacteristic
301C22×C3⋊D3C2412yes—
302C22×C3×D3C2412yes—
303C2×C32×C4—22no—
304C2×C32×C4—24no—
305C2×C32×C4—24no—
306C2×C32×C4#4114yes—
307C2×C32×C4C2412yes—
308C2×C32×C4C2411yescharacteristic
309C2×C32×C4C2411yescharacteristic
310#638—24no—
311#638—44no—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2414yes—
314C4⋊(C3⋊D3)—22no—
315C4×C3⋊D3—24no—
316#634—22no—
317C3×#67—24no—
318C3×#67—44no—
319C2×C3×Dic3—42no—
320C2×C3×Dic3—42no—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2414yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C3×D12—22no—
328C3×C4×D3—24no—
329C3×Dic6—22no—
330#627—44no—
331#626—44no—
332#624—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—91no—
342#529—94no—
343#529—94no—
344#525—31no—
345#525—91no—
346C4×#41—91no—
347C4×#41—91no—
348C2×#117—31no—
349C24×C3—21no—
350C24×C3C22×D311yescharacteristic
351C24×C3C22×D311yescharacteristic
352C3×#41—64no—
353C2×C3×Q8—31no—
354C2×C3×D4—32no—
355C2×C3×D4—34no—
356C2×C3×D4—31no—
357C22×C3×C4—24no—
358C22×C3×C4—24no—
359C22×C3×C4—21no—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4—21no—
363C22×C3×C4—32no—
364C22×C3×C4—32no—
365C22×C3×C4—32no—
366C22×C3×C4—44no—
367C22×C3×C4C22×D312yes—
368C22×C3×C4C22×D312yes—
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D312yes—
371C22×C3×C4C22×D312yes—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C2×#67—32no—
376C2×#67—32no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—64no—
381C2×#67—62no—
382C2×#67C22×D312yes—
383C2×#67C22×D314yes—
384C22×Dic3—34no—
385C22×Dic3C22×D312yes—
386C22×Dic3C22×D312yes—
387#235—24no—
388#235—64no—
389#235—64no—
390#235—124no—
391C2×D12—31no—
392C2×D12—31no—
393C2×D12—34no—
394C2×D12—61no—
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—34no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—62no—
402C2×C4×D3C22×D312yes—
403C2×Dic6—31no—
404C2×Dic6—31no—
405C2×Dic6—34no—
406C2×Dic6—34no—
407C2×Dic6—61no—
408C2×Dic6C22×D311yescharacteristic
409C3×C4⋊C4—32no—
410C3×C4⋊C4—32no—
411C3×C4⋊C4—32no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—32no—
414C3×C4⋊C4—32no—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—32no—
418C3×C22⋊C4—32no—
419C3×C22⋊C4—32no—
420C3×C22⋊C4—32no—
421C3×C22⋊C4—34no—
422C3×C42—32no—
423C3×C42—32no—
424C3×C42—32no—
425C3×C42—31no—
426C3×C42—31no—
427C3×C42—31no—
428C3×C42—31no—
429#217—32no—
430#217—34no—
431#217—34no—
432#217—32no—
433#217—34no—
434#217—34no—
435#217—64no—
436#217—62no—
437#217C22×D314yes—
438#217C22×D312yes—
439#217C22×D312yes—
440#217C22×D312yes—
441#217C22×D312yes—
442#217C22×D312yes—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—64no—
452(C2×D3)⋊C4C22×D314yes—
453C4⋊Dic3—32no—
454C4⋊Dic3—32no—
455C4⋊Dic3—34no—
456C4⋊Dic3—34no—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3—62no—
460C4⋊Dic3C22×D312yes—
461C4⋊Dic3C22×D312yes—
462C4⋊Dic3C22×D312yes—
463C4⋊Dic3C22×D312yes—
464C4⋊Dic3C22×D312yes—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—64no—
476Dic3⋊C4C22×D314yes—
477C4×Dic3—32no—
478C4×Dic3—32no—
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3—62no—
484C4×Dic3C22×D312yes—
485C4×Dic3C22×D312yes—
486C4×Dic3C22×D311yescharacteristic
487C4×Dic3C22×D311yescharacteristic
488C4×Dic3C22×D312yes—
489C4×Dic3C22×D311yescharacteristic
490C4×Dic3C22×D311yescharacteristic
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—44no—
496C22×C32C2×#4112yes—
497C22×C32C2511yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—24no—
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—22no—
510C3×Dic3—24no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C2×#41—31no—
514C2×#41—91no—
515C23×C4D3211yescharacteristic
516C4⋊Q8—92no—
517C4⋊Q8—91no—
518#127—91no—
519#126—94no—
520#126—94no—
521#126—94no—
522#126—94no—
523#125—92no—
524#125—94no—
525#125—94no—
526#124—91no—
527#124—91no—
528#124—94no—
529#124—94no—
530#123—32no—
531#123—94no—
532#123—94no—
533#123—94no—
534#123—94no—
535#123—92no—
536C22⋊Q8—32no—
537C22⋊Q8—94no—
538C22⋊Q8—94no—
539C22⋊Q8—94no—
540C22⋊Q8—92no—
541#121—32no—
542#121—94no—
543#121—94no—
544#121—94no—
545#121—92no—
546#120—32no—
547#120—92no—
548C4×Q8—94no—
549C4×Q8—92no—
550C4×Q8—92no—
551C4×D4—34no—
552C4×D4—92no—
553C4×D4—94no—
554C4×D4—92no—
555C4×D4—94no—
556C4×D4—94no—
557C4×D4—94no—
558#117—32no—
559#117—32no—
560#117—32no—
561#117—32no—
562#117—31no—
563#117—92no—
564#117—92no—
565#117—91no—
566C2×C4⋊C4—32no—
567C2×C22⋊C4—32no—
568C2×C42—31no—
569C2×C42—31no—
570C2×C42—92no—
571C2×C42—92no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—32no—
577C23×C3—42no—
578C23×C3—42no—
579C23×C3—42no—
580C23×C3—44no—
581C23×C3C23×D312yes—
582C23×C3C23×D312yes—
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—62no—
588C22×D3C23×D312yes—
589C3×Q8—62no—
590C3×D4—64no—
591C3×D4—62no—
592C3×D4—124no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—24no—
596C2×C3×C4—24no—
597C2×C3×C4—24no—
598C2×C3×C4—24no—
599C2×C3×C4—21no—
600C2×C3×C4—22no—
601C2×C3×C4—21no—
602C2×C3×C4—24no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—34no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—44no—
610C2×C3×C4—44no—
611C2×C3×C4—42no—
612C2×C3×C4—64no—
613C2×C3×C4—122no—
614C2×C3×C4—122no—
615C2×C3×C4#23514yes—
616C2×C3×C4#23714yes—
617C2×C3×C4C23×D312yes—
618C2×C3×C4C23×D312yes—
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623#67—24no—
624#67—44no—
625#67—64no—
626#67—64no—
627#67—124no—
628#67—124no—
629#67—124no—
630#67—124no—
631#67—128no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—34no—
635C2×Dic3—34no—
636C2×Dic3—42no—
637C2×Dic3—42no—
638C2×Dic3—64no—
639C2×Dic3—62no—
640C2×Dic3—124no—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D314yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647D12—22no—
648D12—62no—
649D12—62no—
650D12—122no—
651D12—124no—
652C4×D3—24no—
653C4×D3—64no—
654C4×D3—64no—
655C4×D3—124no—
656C4×D3—124no—
657C4×D3—124no—
658C4×D3—124no—
659Dic6—22no—
660Dic6—62no—
661Dic6—62no—
662Dic6—122no—
663Dic6—124no—
664Dic6—124no—
665C2×C32—22no—
666C2×C32—42no—
667C2×C32C22×#4111yescharacteristic
668C2×C32#58512yes—
669C3⋊D3—42no—
670C3×D3—42no—
671C24C2×D3211yescharacteristic
672#41—64no—
673#41—184no—
674C2×Q8—31no—
675C2×Q8—94no—
676C2×Q8—91no—
677C2×D4—32no—
678C2×D4—34no—
679C2×D4—31no—
680C2×D4—94no—
681C2×D4—92no—
682C2×D4—94no—
683C2×D4—91no—
684C22×C4—24no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—32no—
688C22×C4—94no—
689C22×C4—94no—
690C22×C4—92no—
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3212yes—
693C22×C4C2×D3212yes—
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—32no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—32no—
699C4⋊C4—32no—
700C4⋊C4—34no—
701C4⋊C4—94no—
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—32no—
711C22⋊C4—32no—
712C22⋊C4—32no—
713C22⋊C4—32no—
714C22⋊C4—34no—
715C22⋊C4—34no—
716C22⋊C4—94no—
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—31no—
727C42—31no—
728C42—32no—
729C42—32no—
730C42—94no—
731C42—94no—
732C42—92no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—24no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—42no—
747C22×C3—44no—
748C22×C3—44no—
749C22×C3—48no—
750C22×C3—62no—
751C22×C3—64no—
752C22×C3C2×#23512yes—
753C22×C3C2×#23712yes—
754C22×C3C24×D311yescharacteristic
755C22×C3C24×D311yescharacteristic
756C2×D3—22no—
757C2×D3—24no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—64no—
761C2×D3—64no—
762C2×D3—122no—
763C2×D3—124no—
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—22no—
793C23—32no—
794C23—42no—
795C23—92no—
796C23C22×D3212yes—
797C23C22×D3211yescharacteristic
798Q8—62no—
799Q8—182no—
800Q8—364no—
801D4—64no—
802D4—62no—
803D4—124no—
804D4—184no—
805D4—182no—
806D4—364no—
807D4—364no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—34no—
816C2×C4—32no—
817C2×C4—64no—
818C2×C4—94no—
819C2×C4—92no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—184no—
823C2×C4—364no—
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—44no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—122no—
838C2×C3C22×#23511yescharacteristic
839C2×C3C22×#23711yescharacteristic
840C2×C3#596412yes—
841C2×C3#596412yes—
842D3—42no—
843D3—122no—
844D3—122no—
845D3—242no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—64no—
852C22—62no—
853C22—184no—
854C22—182no—
855C22C2×#380412yes—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—62no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—64no—
863C4—62no—
864C4—184no—
865C4—182no—
866C4C2×#380412yes—
867C4C2×#380412yes—
868C3—21no—
869C3#8573811yescharacteristic, complemented
870C3#8601911yescharacteristic, complemented
871C2—22no—
872C2—42no—
873C2—122no—
874C2—362no—
875C2#1059666912yes—
876C2C22×#380411yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #10596262C2semidirect
2. C3×#5791C2semidirect
3. C2×C3×#926C2semidirect
4. #10595507C2semidirect
5. #10595049C2semidirect
6. #10595029C2semidirect
7. #10594987C2semidirect
8. #10594985C2semidirect
9. #10594983C2semidirect
10. #10594954C2semidirect
11. Dic3×#235C2semidirect
12. #10594933C2semidirect
13. #10594836C2semidirect
14. #10594824C2semidirect
15. #10594814C2semidirect
53. #63918C22semidirect
54. C4×#627C22semidirect
55. #63911C22semidirect
56. C4×#626C22semidirect
57. #63899C22semidirect
58. #63895C22semidirect
59. #63894C22semidirect
60. Dic3×D12C22semidirect
61. #63890C22semidirect
62. C4×#624C22semidirect
63. C4×D3×Dic3C22semidirect
64. #63874C22semidirect
65. #63869C22semidirect
66. #63866C22semidirect
67. #63864C22semidirect
68. #63860C22semidirect
69. #63858C22semidirect
70. #63855C22semidirect
71. #63854C22semidirect
72. #63848C22semidirect
73. #63847C22semidirect
74. #63846C22semidirect
75. #63844C22semidirect
76. Dic3×Dic6C22semidirect
84. #5791D3semidirect
85. C2×#926D3semidirect
791. C32#3455semidirect
869. C3#85738semidirect
870. C3#86019semidirect

Maximal subgroups

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

subgroupindex
#105962622
C3×#57912
C2×C3×#9262
#105955072
#105950492
#105950292
#105949872
#105949852
#105949832
#105949542
Dic3×#2352
#105949332
#105948362
#105948242
#105948142
#860193
#857383