Finite Group Databasebeta

← #11901801

Subgroups — #11901801

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic, complemented
2C3×#5828C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4#10595348C212yesmaximal, complemented
5#10595346C212yesmaximal, complemented
6#10595127C214yesmaximal, complemented
7#10595125C212yesmaximal, complemented
8#10595124C212yesmaximal, complemented
9#10595123C214yesmaximal, complemented
10#10595050C211yesmaximal, characteristic, complemented
11#10595023C211yesmaximal, characteristic, complemented
12#10594954C211yesmaximal, characteristic, complemented
13C2×#63855C211yesmaximal, characteristic, complemented
14#10594839C214yesmaximal, complemented
15#10594836C214yesmaximal, complemented
16#86019—31nomaximal
17#85837—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21#64156C2211yescharacteristic, complemented
22#64153C2211yescharacteristic, complemented
23#64149C2211yescharacteristic, complemented
24#64148C2214yes—
25#64145C2211yescharacteristic, complemented
26C4×#638C2214yescomplemented
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C3×#946C2212yes—
29C3×Q8×Dic3C2212yescomplemented
30C3×#938C2212yes—
31C3×#937C2212yes—
32C3×#935C2212yes—
33C3×D4×Dic3C2214yes—
34C3×D4×Dic3C2212yescomplemented
35C3×C4×#67C2214yes—
36C3×#926C2211yescharacteristic
37C3×#926C2211yescharacteristic
38C3×#926C2212yescomplemented
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2212yescomplemented
41#63982C2214yes—
42#63978C2214yes—
43#63977C2212yes—
44#63975C2214yescomplemented
45#63966C2212yes—
46#63966C2214yescomplemented
47C2×Dic3⋊Dic3C2212yes—
48#63964C2214yescomplemented
49#63961C2214yes—
50C2×(C2×D3)⋊Dic3C2212yes—
51#63959C2214yes—
52#63958C2214yes—
53#63956C2214yescomplemented
54#63952C2214yes—
55#63919C2212yescomplemented
56C4×#627C2214yescomplemented
57#63909C2212yes—
58C4×#626C2214yes—
59#63895C2214yescomplemented
60#63894C2212yescomplemented
61C4×#624C2212yescomplemented
62#63874C2212yescomplemented
63#63872C2212yescomplemented
64#63868C2214yescomplemented
65#63867C2214yescomplemented
66#63859C2214yes—
67#63858C2214yes—
68#63857C2212yes—
69#63855C2212yes—
70#63855C2212yes—
71#63855C2212yes—
72#63855C2212yes—
73#63854C2214yes—
74#63852C2214yes—
75#63846C2214yescomplemented
76#63844C2212yescomplemented
77C3×#525—31no—
78C3×C4×#41—31no—
79#5832—31no—
80#5832—31no—
81#5832—61no—
82#5828D311yescharacteristic, complemented
83Dic3×#41D311yescharacteristic, complemented
84#5791—31no—
85C2×#926—31no—
86#5665—34no—
87#5643—32no—
88#5625—32no—
89#5619—32no—
90#5603—32no—
91#5593—34no—
92#5583—32no—
93#5582—32no—
94#5564—34no—
95#5562—32no—
96#5561—32no—
97#5560—34no—
98#5557—34no—
99#5538—34no—
100#5528—34no—
101#5524—31no—
102#5522—31no—
103#5517—31no—
104#5517—31no—
105#5479—34no—
106C4×#235—31no—
107C2×#872—31no—
108C23×C3×D3C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2311yescharacteristic
113C22×C32×C4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638C2312yes—
116C2×#638C2314yes—
117C22×C3⋊Dic3C2312yes—
118#3828—24no—
119C2×C4⋊(C3⋊D3)C2311yescharacteristic
120C2×C4×C3⋊D3C2312yes—
121C2×#634C2311yescharacteristic
122C2×C3×#67C2314yes—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2312yes—
125C22×C3×Dic3C2314yes—
126C2×C3×C4×D3—24no—
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2312yes—
129C2×#627C2314yes—
130C2×#626C2314yes—
131C2×#624C2314yes—
132#3757C2314yes—
133#3752C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2311yescharacteristic
136C4×C3⋊Dic3C2312yes—
137C4×C3⋊Dic3C2311yescharacteristic
138C3×#217C2312yes—
139C3×#217C2312yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×C4⋊Dic3C2312yes—
144C3×C4⋊Dic3C2312yes—
145C3×C4⋊Dic3C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2311yescharacteristic
149C3×C4×Dic3C2312yes—
150C3×C4×Dic3C2312yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2312yes—
153#3724C2314yes—
154#3724C2314yes—
155Dic3⋊Dic3C2312yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2312yes—
159Dic3⋊Dic3C2312yes—
160Dic3⋊Dic3C2312yes—
161Dic3⋊Dic3C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164(C2×D3)⋊Dic3C2312yes—
165(C2×D3)⋊Dic3C2312yes—
166(C2×D3)⋊Dic3C2312yes—
167(C2×D3)⋊Dic3C2312yes—
168(C2×D3)⋊Dic3C2314yes—
169Dic32C2314yes—
170#3455—91noSylow
171C2×C3×#41—21no—
172C2×C3×#41C2×D311yescharacteristic
173C2×C3×#41C2×D311yescharacteristic
174C23×C3×C4—31no—
175C2×#235—31no—
176C2×#235—31no—
177C2×#235—61no—
178C22×C4×D3C2×D311yescharacteristic
179C3×#123—32no—
180C3×C22⋊Q8—32no—
181C3×#121—32no—
182C3×#120—32no—
183C3×C4×Q8—32no—
184C3×C4×D4—34no—
185C3×C4×D4—32no—
186C3×C4×D4—34no—
187C3×#117—31no—
188C3×#117—31no—
189C3×#117—32no—
190C2×C3×C42—31no—
191C2×C3×C42—32no—
192#953—32no—
193C2×#217—32no—
194#947—31no—
195#947—31no—
196#947—61no—
197#946C2×D312yes—
198Q8×Dic3C2×D312yescomplemented
199#944—31no—
200#944—31no—
201#944—61no—
202#940—31no—
203#940—31no—
204#940—61no—
205#939—34no—
206#939—34no—
207#939—34no—
208#939—64no—
209#938—34no—
210#938C2×D312yes—
211#937C2×D312yes—
212#936—31no—
213#936—31no—
214#936—34no—
215#936—61no—
216#935—34no—
217#935C2×D312yes—
218D4×Dic3C2×D314yes—
219D4×Dic3C2×D312yescomplemented
220#930—34no—
221#930—32no—
222#929—34no—
223#929—32no—
224#929—34no—
225C4×#67—34no—
226C4×#67—34no—
227C4×#67—34no—
228C4×#67—34no—
229C4×#67—64no—
230C4×#67C2×D314yes—
231C2×(C2×D3)⋊C4—32no—
232#926—32no—
233#926—32no—
234#926—32no—
235#926—32no—
236#926C2×D311yescharacteristic
237#926C2×D311yescharacteristic
238#926C2×D312yescomplemented
239C2×C4⋊Dic3—32no—
240#924—34no—
241#924—32no—
242C2×Dic3⋊C4—32no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—61no—
246C2×C4×Dic3C2×D311yescharacteristic
247C2×C4×Dic3C2×D312yescomplemented
248#898—34no—
249#898—34no—
250#897—32no—
251#897—34no—
252#896—34no—
253#895—32no—
254#894—34no—
255#893—32no—
256#890—34no—
257#890—32no—
258#890—32no—
259#889—34no—
260#889—34no—
261#888—32no—
262#888—32no—
263#887—32no—
264#886—34no—
265#886—32no—
266#885—34no—
267#885—34no—
268#884—34no—
269#883—34no—
270#883—34no—
271#883—34no—
272#882—32no—
273#67⋊C4—34no—
274#879—34no—
275#879—34no—
276#879—34no—
277#879—34no—
278#878—34no—
279#878—34no—
280#878—34no—
281#876—34no—
282#876—34no—
283#875—34no—
284C4×D12—34no—
285C4×D12—32no—
286#872—32no—
287#872—32no—
288#872—32no—
289#872—32no—
290#872—32no—
291#872—32no—
292C42×D3—32no—
293C42×D3—32no—
294#870—34no—
295C4×Dic6—32no—
296C4×Dic6—34no—
297C4×Dic6—34no—
298C23×C32C2412yes—
299C23×C32C2411yescharacteristic
300C22×C3⋊D3C2412yes—
301C22×C3×D3—22no—
302C22×C3×D3—42no—
303C22×C3×D3C2412yes—
304C32×Q8—22no—
305C32×D4—24no—
306C32×D4—22no—
307C2×C32×C4—24no—
308C2×C32×C4#4114yes—
309C2×C32×C4C2412yes—
310C2×C32×C4C2411yescharacteristic
311C2×C32×C4C2411yescharacteristic
312#638—24no—
313#638—44no—
314C2×C3⋊Dic3—42no—
315C2×C3⋊Dic3C2412yes—
316C2×C3⋊Dic3C2412yes—
317C2×C3⋊Dic3C2412yes—
318C4⋊(C3⋊D3)—22no—
319C4×C3⋊D3—24no—
320#634—22no—
321C3×#67—44no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—42no—
324C2×C3×Dic3—44no—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2414yes—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2414yes—
329C2×C3×Dic3C2412yes—
330C3×C4×D3—24no—
331C3×C4×D3—24no—
332#627—44no—
333#626—44no—
334#624—44no—
335#542—92no—
336#542—92no—
337#541—92no—
338#540—92no—
339#539—94no—
340#538—94no—
341#533—91no—
342#532—91no—
343#529—94no—
344#529—94no—
345#525—31no—
346#525—91no—
347C4×#41—31no—
348C4×#41—91no—
349C2×#117—91no—
350C24×C3—31no—
351C23×D3C22×D311yescharacteristic
352C3×#41—24no—
353C3×#41—24no—
354C3×#41—44no—
355C2×C3×Q8—21no—
356C2×C3×Q8C22×D311yescharacteristic
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×D4—21no—
359C2×C3×D4—22no—
360C2×C3×D4—34no—
361C2×C3×D4C22×D312yes—
362C2×C3×D4C22×D311yescharacteristic
363C2×C3×D4C22×D312yes—
364C2×C3×D4C22×D311yescharacteristic
365C22×C3×C4—21no—
366C22×C3×C4—22no—
367C22×C3×C4—31no—
368C22×C3×C4—32no—
369C22×C3×C4—34no—
370C22×C3×C4—32no—
371C22×C3×C4—32no—
372C22×C3×C4—64no—
373C22×C3×C4C22×D312yes—
374C22×C3×C4C22×D312yes—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—32no—
378C2×#67—32no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—64no—
383C2×#67—62no—
384C2×#67C22×D314yes—
385C22×Dic3—32no—
386C22×Dic3—32no—
387C22×Dic3—62no—
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D314yes—
390C22×Dic3C22×D312yes—
391#235—64no—
392#235—64no—
393#235—124no—
394C2×D12—31no—
395C2×D12—31no—
396C2×D12—34no—
397C2×D12—61no—
398C2×C4×D3—24no—
399C2×C4×D3—32no—
400C2×C4×D3—32no—
401C2×C4×D3—34no—
402C2×C4×D3—34no—
403C2×C4×D3—62no—
404C2×C4×D3C22×D312yes—
405C2×C4×D3C22×D312yes—
406C2×Dic6—31no—
407C2×Dic6—31no—
408C2×Dic6—34no—
409C2×Dic6—34no—
410C2×Dic6—61no—
411C3×C4⋊C4—32no—
412C3×C4⋊C4—32no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—32no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C42—32no—
421C3×C42—32no—
422C3×C42—32no—
423C3×C42—34no—
424C3×C42—31no—
425C3×C42—31no—
426#217—34no—
427#217—34no—
428#217—34no—
429#217—32no—
430#217—32no—
431#217—32no—
432#217—32no—
433#217—64no—
434#217C22×D312yes—
435#217C22×D312yes—
436#217C22×D314yes—
437#217C22×D314yes—
438(C2×D3)⋊C4—32no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—32no—
441(C2×D3)⋊C4—32no—
442(C2×D3)⋊C4—34no—
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—64no—
450(C2×D3)⋊C4C22×D314yes—
451C4⋊Dic3—34no—
452C4⋊Dic3—34no—
453C4⋊Dic3—34no—
454C4⋊Dic3—32no—
455C4⋊Dic3—32no—
456C4⋊Dic3—32no—
457C4⋊Dic3—32no—
458C4⋊Dic3C22×D312yes—
459C4⋊Dic3C22×D314yes—
460C4⋊Dic3C22×D312yes—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—32no—
469Dic3⋊C4—32no—
470Dic3⋊C4—32no—
471Dic3⋊C4—32no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—64no—
475Dic3⋊C4C22×D314yes—
476C4×Dic3—32no—
477C4×Dic3—32no—
478C4×Dic3—31no—
479C4×Dic3—31no—
480C4×Dic3—31no—
481C4×Dic3—31no—
482C4×Dic3—34no—
483C4×Dic3—34no—
484C4×Dic3—62no—
485C4×Dic3—61no—
486C4×Dic3—61no—
487C4×Dic3C22×D312yes—
488C4×Dic3C22×D312yes—
489C4×Dic3C22×D311yescharacteristic
490C4×Dic3C22×D311yescharacteristic
491C4×Dic3C22×D314yes—
492C4×Dic3C22×D312yes—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—24no—
496C22×C32C2×#4112yes—
497C22×C32C2511yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—24no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—44no—
504C32×C4—22no—
505C32×C4C2×#4112yes—
506C32×C4C2×#4112yes—
507C3⋊Dic3—22no—
508C3⋊Dic3—22no—
509C3⋊Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—24no—
513C3×Dic3—24no—
514C3×Dic3—22no—
515C2×#41—91no—
516C2×#41D3211yescharacteristic
517C23×C4—31no—
518C4⋊Q8—92no—
519C4⋊Q8—91no—
520#127—91no—
521#126—94no—
522#126—94no—
523#126—94no—
524#126—94no—
525#125—94no—
526#125—94no—
527#125—92no—
528#124—94no—
529#124—94no—
530#124—91no—
531#124—91no—
532#123—32no—
533#123—94no—
534#123—94no—
535#123—92no—
536#123—94no—
537#123—94no—
538C22⋊Q8—32no—
539C22⋊Q8—94no—
540C22⋊Q8—94no—
541C22⋊Q8—94no—
542C22⋊Q8—92no—
543#121—32no—
544#121—94no—
545#121—92no—
546#121—94no—
547#121—94no—
548#120—32no—
549#120—92no—
550C4×Q8—32no—
551C4×Q8—94no—
552C4×Q8—92no—
553C4×D4—34no—
554C4×D4—32no—
555C4×D4—34no—
556C4×D4—92no—
557C4×D4—94no—
558C4×D4—94no—
559C4×D4—94no—
560#117—31no—
561#117—32no—
562#117—31no—
563#117—92no—
564#117—92no—
565#117—92no—
566#117—92no—
567#117—92no—
568C2×C4⋊C4—92no—
569C2×C22⋊C4—92no—
570C2×C42—31no—
571C2×C42—32no—
572C2×C42—92no—
573C2×C42—91no—
574C23×C3—21no—
575C23×C3—22no—
576C23×C3—32no—
577C23×C3—62no—
578C23×C3—122no—
579C23×C3C23×D312yes—
580C23×C3C23×D312yes—
581C23×C3C23×D311yescharacteristic
582C23×C3C23×D311yescharacteristic
583C22×D3—22no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—42no—
587C22×D3—62no—
588C22×D3C23×D312yes—
589C3×Q8—22no—
590C3×Q8—22no—
591C3×Q8—42no—
592C3×D4—24no—
593C3×D4—24no—
594C3×D4—22no—
595C3×D4—22no—
596C3×D4—42no—
597C3×D4—44no—
598C3×D4—124no—
599C2×C3×C4—24no—
600C2×C3×C4—24no—
601C2×C3×C4—21no—
602C2×C3×C4—22no—
603C2×C3×C4—21no—
604C2×C3×C4—24no—
605C2×C3×C4—32no—
606C2×C3×C4—34no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—34no—
610C2×C3×C4—44no—
611C2×C3×C4—62no—
612C2×C3×C4—64no—
613C2×C3×C4—64no—
614C2×C3×C4—124no—
615C2×C3×C4—122no—
616C2×C3×C4#23514yes—
617C2×C3×C4#23714yes—
618C2×C3×C4C23×D312yes—
619C2×C3×C4C23×D312yes—
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
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—22no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—44no—
640C2×Dic3—42no—
641C2×Dic3—62no—
642C2×Dic3—62no—
643C2×Dic3—62no—
644C2×Dic3—122no—
645C2×Dic3—122no—
646C2×Dic3—124no—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D314yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D314yes—
651C2×Dic3C23×D312yes—
652D12—62no—
653D12—62no—
654D12—122no—
655D12—124no—
656C4×D3—24no—
657C4×D3—24no—
658C4×D3—64no—
659C4×D3—64no—
660C4×D3—124no—
661C4×D3—124no—
662C4×D3—124no—
663Dic6—62no—
664Dic6—62no—
665Dic6—122no—
666Dic6—124no—
667Dic6—124no—
668C2×C32—22no—
669C2×C32—42no—
670C2×C32C22×#4111yescharacteristic
671C2×C32#58512yes—
672C3⋊D3—42no—
673C3×D3—42no—
674C24—31no—
675#41—24no—
676#41—184no—
677C2×Q8—94no—
678C2×Q8—91no—
679C2×Q8C2×D3211yescharacteristic
680C2×D4—34no—
681C2×D4—94no—
682C2×D4—92no—
683C2×D4—94no—
684C2×D4—91no—
685C2×D4C2×D3212yes—
686C2×D4C2×D3211yescharacteristic
687C22×C4—31no—
688C22×C4—32no—
689C22×C4—34no—
690C22×C4—32no—
691C22×C4—32no—
692C22×C4—64no—
693C22×C4—94no—
694C22×C4—92no—
695C22×C4—92no—
696C22×C4C2×D3212yes—
697C22×C4C2×D3211yescharacteristic
698C4⋊C4—32no—
699C4⋊C4—34no—
700C4⋊C4—32no—
701C4⋊C4—34no—
702C4⋊C4—92no—
703C4⋊C4—92no—
704C4⋊C4—92no—
705C4⋊C4—92no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C4⋊C4—94no—
712C22⋊C4—32no—
713C22⋊C4—34no—
714C22⋊C4—32no—
715C22⋊C4—34no—
716C22⋊C4—34no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C22⋊C4—92no—
720C22⋊C4—92no—
721C22⋊C4—92no—
722C22⋊C4—92no—
723C22⋊C4—94no—
724C22⋊C4—94no—
725C22⋊C4—94no—
726C42—32no—
727C42—34no—
728C42—31no—
729C42—31no—
730C42—32no—
731C42—32no—
732C42—94no—
733C42—91no—
734C42—91no—
735C42—92no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—24no—
741C22×C3—24no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—42no—
745C22×C3—44no—
746C22×C3—42no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—62no—
750C22×C3—124no—
751C22×C3C2×#23512yes—
752C22×C3C2×#23712yes—
753C22×C3C24×D311yescharacteristic
754C22×C3C24×D311yescharacteristic
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—44no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—64no—
762C2×D3—64no—
763C2×D3—122no—
764C2×D3—124no—
765C3×C4—22no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—42no—
770C3×C4—62no—
771C3×C4—64no—
772C3×C4—64no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4C2×#23512yes—
776C3×C4C2×#23512yes—
777C3×C4C2×#23712yes—
778C3×C4C2×#23712yes—
779Dic3—22no—
780Dic3—24no—
781Dic3—24no—
782Dic3—22no—
783Dic3—22no—
784Dic3—64no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—62no—
789Dic3—62no—
790Dic3—62no—
791Dic3—122no—
792Dic3—122no—
793C32#345511yescharacteristic, complemented, Sylow
794C23—32no—
795C23—62no—
796C23—92no—
797C23—122no—
798C23C22×D3212yes—
799C23C22×D3211yescharacteristic
800Q8—22no—
801Q8—182no—
802Q8—364no—
803D4—24no—
804D4—22no—
805D4—124no—
806D4—184no—
807D4—182no—
808D4—364no—
809D4—364no—
810C2×C4—24no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—34no—
814C2×C4—34no—
815C2×C4—32no—
816C2×C4—62no—
817C2×C4—64no—
818C2×C4—64no—
819C2×C4—92no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4—122no—
823C2×C4—124no—
824C2×C4—184no—
825C2×C4—364no—
826C2×C4—362no—
827C2×C4#380414yes—
828C2×C4C22×D3212yes—
829C2×C4C22×D3211yescharacteristic
830C2×C4C22×D3211yescharacteristic
831C2×C3—22no—
832C2×C3—22no—
833C2×C3—22no—
834C2×C3—21no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—82no—
839C2×C3—122no—
840C2×C3C22×#23511yescharacteristic
841C2×C3C22×#23711yescharacteristic
842C2×C3#596412yes—
843C2×C3#596412yes—
844D3—42no—
845D3—122no—
846D3—122no—
847D3—242no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—124no—
855C22—184no—
856C22—182no—
857C22C2×#380412yes—
858C22C23×D3211yescharacteristic
859C4—22no—
860C4—62no—
861C4—62no—
862C4—64no—
863C4—64no—
864C4—62no—
865C4—182no—
866C4—182no—
867C4—182no—
868C4C2×#380412yes—
869C4C2×#380412yes—
870C3—21no—
871C3#8583711yescharacteristic, complemented
872C3#8601911yescharacteristic, complemented
873C2—22no—
874C2—42no—
875C2—122no—
876C2—362no—
877C2#1059669512yes—
878C2C22×#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. #10596303C2semidirect
2. C3×#5828C2semidirect
3. C3×Dic3×#41C2semidirect
4. #10595348C2semidirect
5. #10595346C2semidirect
6. #10595127C2semidirect
7. #10595125C2semidirect
8. #10595124C2semidirect
9. #10595123C2semidirect
10. #10595050C2semidirect
11. #10595023C2semidirect
12. #10594954C2semidirect
13. C2×#63855C2semidirect
14. #10594839C2semidirect
15. #10594836C2semidirect
21. #64156C22semidirect
22. #64153C22semidirect
23. #64149C22semidirect
25. #64145C22semidirect
26. C4×#638C22semidirect
29. C3×Q8×Dic3C22semidirect
34. C3×D4×Dic3C22semidirect
38. C3×#926C22semidirect
40. C2×C3×C4×Dic3C22semidirect
44. #63975C22semidirect
46. #63966C22semidirect
48. #63964C22semidirect
53. #63956C22semidirect
55. #63919C22semidirect
56. C4×#627C22semidirect
59. #63895C22semidirect
60. #63894C22semidirect
61. C4×#624C22semidirect
62. #63874C22semidirect
63. #63872C22semidirect
64. #63868C22semidirect
65. #63867C22semidirect
75. #63846C22semidirect
76. #63844C22semidirect
82. #5828D3semidirect
83. Dic3×#41D3semidirect
198. Q8×Dic3C2×D3semidirect
219. D4×Dic3C2×D3semidirect
238. #926C2×D3semidirect
247. C2×C4×Dic3C2×D3semidirect
793. C32#3455semidirect
871. C3#85837semidirect
872. C3#86019semidirect

Maximal subgroups

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

subgroupindex
#105963032
C3×#58282
C3×Dic3×#412
#105953482
#105953462
#105951272
#105951252
#105951242
#105951232
#105950502
#105950232
#105949542
C2×#638552
#105948392
#105948362
#860193
#858373