Finite Group Databasebeta

← #11664857

Subgroups — #11664857

Order 768.

1798 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86274C211yesmaximal, characteristic
2C2×#5689C211yesmaximal, characteristic
3C3×#3166C211yesmaximal, characteristic, complemented
4#83341C211yesmaximal, characteristic, complemented
5#83015C211yesmaximal, characteristic, complemented
6#81975C214yesmaximal, complemented
7#81974C214yesmaximal, complemented
8#81918C214yesmaximal, complemented
9#81917C214yesmaximal, complemented
10#79208C212yesmaximal
11D3×#428C212yesmaximal
12#79204C212yesmaximal, complemented
13#79203C212yesmaximal, complemented
14#78514C211yesmaximal, characteristic
15#78506C211yesmaximal, characteristic, complemented
16#60664—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×D3×M16C2212yes—
20#5729C2212yes—
21#5729C2212yes—
22#5689—22no—
23#5689—22no—
24#5689C2212yes—
25#5689C2212yes—
26#5689C2214yes—
27#5689C2214yes—
28#5634—21no—
29#5634—21no—
30#5623—21no—
31#5623—21no—
32#5578—22no—
33#5578—22no—
34D3×#117C2212yes—
35#5517C2212yes—
36C2×#897—21no—
37C2×#896—21no—
38C2×#892C2211yescharacteristic
39C2×D3×C4⋊C4C2211yescharacteristic
40C2×#890C2211yescharacteristic
41C2×#889—21no—
42C2×#888—21no—
43C2×#888C2211yescharacteristic
44C2×#872C2211yescharacteristic
45#5470C2211yescharacteristic
46C2×#869C2211yescharacteristic
47C3×#501C2212yescomplemented
48C3×#501C2212yescomplemented
49C3×#499C2214yescomplemented
50C3×#428C2212yes—
51C3×#428C2212yes—
52C3×C4×M16C2211yescharacteristic
53#5121C2212yes—
54#5121C2212yes—
55Dic3×M16C2212yes—
56#5080C2212yescomplemented
57#5078C2212yescomplemented
58#5065C2214yescomplemented
59#5064C2212yescomplemented
60#5064C2212yescomplemented
61#5064C2214yescomplemented
62#4995C2212yes—
63#4995C2212yes—
64#4964C2212yes—
65#4964C2212yes—
66C4×#208C2211yescharacteristic
67#4881C2214yes—
68#4881C2214yes—
69#4880C2214yes—
70D3×#107C2214yes—
71#4878C2214yescomplemented
72#4876C2214yescomplemented
73#4876C2214yescomplemented
74#4874C2214yescomplemented
75#4861C2214yes—
76#4861C2214yes—
77#4860C2214yes—
78D3×#106C2214yes—
79#4858C2214yescomplemented
80#4856C2214yescomplemented
81#4856C2214yescomplemented
82#4855C2214yescomplemented
83#4708C2214yes—
84#4702C2214yescomplemented
85#4689C2214yes—
86#4682C2212yescomplemented
87#4680C2212yescomplemented
88#3458—31no—
89C2×#544—31no—
90#3166—32no—
91#3166—31no—
92#3166D311yescharacteristic, complemented
93#3165—32no—
94#3165—31no—
95#3165—31no—
96#3164—34no—
97#3164—34no—
98#3163—34no—
99#3163—34no—
100#2911—32no—
101C2×#428—32no—
102#2873—31no—
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×Dic6—21no—
106C22×Dic6—21no—
107C2×C3×M16C2312yes—
108C3×C4⋊Q8C2311yescharacteristic
109C3×C4⋊Q8C2311yescharacteristic
110C3×#125—21no—
111C3×#125—21no—
112C3×#125C2312yes—
113C3×#125C2312yes—
114C3×#125C2312yes—
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—21no—
117C3×C4×Q8—21no—
118C3×C4×Q8—21no—
119C3×#117C2312yes—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125#946—22no—
126#946—22no—
127#944—22no—
128#944—22no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4D411yescharacteristic
131C2×(C2×D3)⋊C4D411yescharacteristic
132#926C2312yes—
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3C2311yescharacteristic
136C2×C4⋊Dic3C2311yescharacteristic
137#924—21no—
138#924—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4D411yescharacteristic
143C2×Dic3⋊C4D411yescharacteristic
144C2×C4×Dic3—21no—
145C2×C4×Dic3C2311yescharacteristic
146C2×#208C2312yes—
147D3×M16Q8116yescomplemented
148C2×ΓL(1,𝔽25)C2314yes—
149C2×D3×C8C2314yes—
150#897—22no—
151#897—22no—
152#897—24no—
153#897—24no—
154#896—22no—
155#896—22no—
156#896—22no—
157#896—22no—
158#896—24no—
159#896—24no—
160#892—22no—
161#892C2312yes—
162#892C2314yes—
163#892C2312yes—
164D3×C4⋊C4—22no—
165D3×C4⋊C4C2312yes—
166D3×C4⋊C4C2314yes—
167D3×C4⋊C4C2312yes—
168#890—22no—
169#890C2312yes—
170#890C2314yes—
171#890C2312yes—
172#889—24no—
173#889—24no—
174#889—22no—
175#889—22no—
176#889—22no—
177#889—22no—
178#888—24no—
179#888—24no—
180#888—22no—
181#888—22no—
182#888—22no—
183#888C2312yes—
184#888C2314yes—
185#888C2312yes—
186D3×C22⋊C4—22no—
187#878—22no—
188#878—22no—
189#877—22no—
190#872—22no—
191#872D412yes—
192#872D412yes—
193#872C2312yes—
194#872C2312yes—
195C42×D3—22no—
196#870C2312yes—
197#869—21no—
198#869—21no—
199#869C2311yescharacteristic
200#869C2312yes—
201#869C2311yescharacteristic
202#869C2312yes—
203C4×Dic6—21no—
204C4×Dic6—21no—
205C4×Dic6—22no—
206C4×Dic6—22no—
207C3×#107C2314yes—
208C3×#107C2314yes—
209C3×#106C2314yes—
210C3×#106C2314yes—
211C3×#97C2312yes—
212C3×C4×C8C2312yes—
213#818C2314yes—
214#818C2314yes—
215#817C2314yes—
216#817C2314yes—
217#815C2314yes—
218C8×Dic3C2314yes—
219#808C2314yes—
220#808C2314yes—
221#808C2314yes—
222#808C2314yes—
223#807C2314yes—
224#807C2314yes—
225#807C2314yes—
226#807C2314yes—
227#803C2312yes—
228C4×C3⋊C8C2312yes—
229C22×M16—32no—
230#544—32no—
231#544—32no—
232#544—32no—
233#544—34no—
234#544—34no—
235#544—32no—
236#544—61no—
237#544—61no—
238#544—62no—
239#544—62no—
240#543—61no—
241#543—61no—
242#533—32no—
243#533—31no—
244#533—62no—
245#533—62no—
246#533C2×D311yescharacteristic
247C2×C4⋊Q8—31no—
248C2×C4⋊Q8—31no—
249C2×C4⋊Q8—61no—
250C2×#125—31no—
251C2×#125—61no—
252C2×#125C2×D311yescharacteristic
253C2×C22⋊Q8—61no—
254C2×C22⋊Q8—61no—
255C2×#117—31no—
256C2×#117—32no—
257C2×#117—31no—
258C22×C4⋊C4—31no—
259#501—32no—
260#501—34no—
261#501—32no—
262#501—34no—
263#501—34no—
264#501—34no—
265#501—34no—
266#501—34no—
267#501C2×D312yescomplemented
268#501C2×D312yescomplemented
269#500—32no—
270#500—34no—
271#500—32no—
272#499—34no—
273#499—34no—
274#499—34no—
275#499C2×D314yescomplemented
276#498—32no—
277#498—34no—
278#498—32no—
279#428—32no—
280#428—32no—
281#428—32no—
282#428—32no—
283#428—32no—
284#428—32no—
285#428—34no—
286#428—34no—
287#428—34no—
288#428—34no—
289#428C2×D312yes—
290#428C2×D312yes—
291#427—34no—
292#427—34no—
293C2×#107—34no—
294C2×#106—34no—
295#405—34no—
296#405—34no—
297C4×M16—32no—
298C4×M16—31no—
299C4×M16C2×D311yescharacteristic
300C23×D3C2×D411yescharacteristic
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3C2×D411yescharacteristic
311C22×Dic3C2×D411yescharacteristic
312C22×Dic3C2×D411yescharacteristic
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—24no—
316C2×C4×D3—82no—
317C2×C4×D3C2×D412yes—
318C2×C4×D3C2×Q818yes—
319C2×C4×D3C2412yes—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—22no—
323C2×Dic6—22no—
324C2×Dic6—22no—
325C2×Dic6—22no—
326C2×Dic6—24no—
327C2×Dic6—82no—
328C2×Dic6—82no—
329C3×M16C2×Q818yes—
330C2×C3×C8C2414yes—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—22no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4C2412yes—
342C3×C4⋊C4C2412yes—
343C3×C4⋊C4C2412yes—
344C3×C4⋊C4C2412yes—
345C3×C22⋊C4—22no—
346C3×C42—22no—
347C3×C42C2×D411yescharacteristic
348C3×C42C2×D411yescharacteristic
349C3×C42C2411yescharacteristic
350C3×C42C2411yescharacteristic
351#217—22no—
352(C2×D3)⋊C4—22no—
353(C2×D3)⋊C4—22no—
354(C2×D3)⋊C4—24no—
355(C2×D3)⋊C4C2×D412yes—
356(C2×D3)⋊C4C2×D412yes—
357(C2×D3)⋊C4C2×D412yes—
358(C2×D3)⋊C4C2×D412yes—
359C4⋊Dic3—21no—
360C4⋊Dic3—21no—
361C4⋊Dic3—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3—22no—
364C4⋊Dic3—22no—
365C4⋊Dic3—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—24no—
368C4⋊Dic3C2412yes—
369C4⋊Dic3C2412yes—
370C4⋊Dic3C2412yes—
371C4⋊Dic3C2412yes—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—22no—
377Dic3⋊C4—22no—
378Dic3⋊C4—22no—
379Dic3⋊C4—22no—
380Dic3⋊C4—24no—
381Dic3⋊C4—24no—
382Dic3⋊C4—24no—
383Dic3⋊C4C2×D412yes—
384Dic3⋊C4C2×D412yes—
385Dic3⋊C4C2×D412yes—
386Dic3⋊C4C2×D412yes—
387C4×Dic3—22no—
388C4×Dic3—22no—
389C4×Dic3—22no—
390C4×Dic3—24no—
391C4×Dic3C2×D412yes—
392C4×Dic3C2412yes—
393#208C2×Q818yes—
394C2×C3⋊C8C2414yes—
395ΓL(1,𝔽25)C2×Q8116yescomplemented
396D3×C8C2×Q8116yescomplemented
397C22×Q8—61no—
398C22×Q8—61no—
399C23×C4—31no—
400C23×C4—61no—
401C2×M16—32no—
402C2×M16—316no—
403C2×M16—34no—
404C2×M16C22×D312yes—
405C22×C8—34no—
406C4⋊Q8—34no—
407C4⋊Q8—32no—
408C4⋊Q8—32no—
409C4⋊Q8—32no—
410C4⋊Q8—32no—
411C4⋊Q8—31no—
412C4⋊Q8—31no—
413C4⋊Q8—62no—
414C4⋊Q8—64no—
415C4⋊Q8—64no—
416C4⋊Q8—62no—
417C4⋊Q8—62no—
418C4⋊Q8—62no—
419C4⋊Q8—62no—
420C4⋊Q8—61no—
421C4⋊Q8—61no—
422C4⋊Q8C22×D311yescharacteristic
423C4⋊Q8C22×D311yescharacteristic
424#125—21no—
425#125—21no—
426#125—34no—
427#125—32no—
428#125—32no—
429#125—32no—
430#125—62no—
431#125—64no—
432#125—64no—
433#125—62no—
434#125—62no—
435#125—62no—
436#125—62no—
437#125C22×D312yes—
438#125C22×D312yes—
439#125C22×D312yes—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—62no—
443C22⋊Q8—62no—
444C22⋊Q8—64no—
445C22⋊Q8—64no—
446C22⋊Q8—64no—
447C22⋊Q8—64no—
448C22⋊Q8—62no—
449C22⋊Q8—62no—
450C22⋊Q8—62no—
451C22⋊Q8—62no—
452C22⋊Q8—62no—
453C22⋊Q8—62no—
454C22⋊Q8—62no—
455C22⋊Q8—62no—
456C22⋊Q8—61no—
457C22⋊Q8—61no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8—62no—
461C4×Q8—62no—
462C4×Q8—61no—
463C4×Q8—61no—
464#117—32no—
465#117—32no—
466#117—32no—
467#117—32no—
468#117—32no—
469#117—32no—
470#117—34no—
471#117—32no—
472#117—62no—
473#117—62no—
474#117—62no—
475#117C22×D312yes—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—34no—
483C2×C4⋊C4—32no—
484C2×C4⋊C4—32no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4—61no—
487C2×C4⋊C4—61no—
488C2×C4⋊C4—61no—
489C2×C4⋊C4—61no—
490C2×C4⋊C4—61no—
491C2×C4⋊C4C22×D311yescharacteristic
492C2×C4⋊C4C22×D311yescharacteristic
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—62no—
496C2×C22⋊C4—61no—
497C2×C42—31no—
498C2×C42—62no—
499C2×C42—61no—
500C2×C42C22×D311yescharacteristic
501#107—34no—
502#107—34no—
503#107—34no—
504#107—34no—
505#107—34no—
506#107—34no—
507#107C22×D314yes—
508#107C22×D314yes—
509#106—34no—
510#106—34no—
511#106—34no—
512#106—34no—
513#106—34no—
514#106—34no—
515#106C22×D314yes—
516#106C22×D314yes—
517#97—34no—
518#97—32no—
519#97C22×D312yes—
520C4×C8—34no—
521C4×C8—32no—
522C4×C8C22×D312yes—
523C23×C3C22×D411yescharacteristic
524C22×D3—41no—
525C22×D3—41no—
526C22×D3C4⋊Q814yes—
527C22×D3C22×D412yes—
528C3×Q8—81no—
529C3×Q8—81no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—42no—
537C2×C3×C4—42no—
538C2×C3×C4C22×D411yescharacteristic
539C2×C3×C4C22×D411yescharacteristic
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4C22×Q814yes—
544C2×C3×C4C2511yescharacteristic
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—42no—
552C2×Dic3—42no—
553C2×Dic3C4⋊Q814yes—
554C2×Dic3C22×D412yes—
555C2×Dic3C22×D412yes—
556C2×Dic3C22×D412yes—
557C4×D3—82no—
558C4×D3—82no—
559C4×D3—84no—
560C4×D3C4⋊Q818yes—
561C4×D3C22×Q814yes—
562C4×D3C22×Q814yes—
563Dic6—82no—
564Dic6—82no—
565Dic6—84no—
566Dic6—81no—
567Dic6—81no—
568Dic6—82no—
569Dic6—82no—
570C3×C8C22×Q818yes—
571C3⋊C8C22×Q818yes—
572C24—31no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—62no—
576C2×Q8—62no—
577C2×Q8—64no—
578C2×Q8—61no—
579C2×Q8—61no—
580C2×Q8—62no—
581C2×Q8—62no—
582C2×Q8—242no—
583C2×Q8—242no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—31no—
587C22×C4—32no—
588C22×C4—38no—
589C22×C4—32no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—62no—
593C22×C4—62no—
594C22×C4—64no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—242no—
598C22×C4D3×D411yescharacteristic
599C22×C4D3×D411yescharacteristic
600C22×C4C23×D311yescharacteristic
601M16—38no—
602M16—316no—
603M16D3×Q818yes—
604C2×C8—34no—
605C2×C8—316no—
606C2×C8C23×D314yes—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—32no—
618C4⋊C4—32no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—32no—
622C4⋊C4—32no—
623C4⋊C4—32no—
624C4⋊C4—32no—
625C4⋊C4—64no—
626C4⋊C4—62no—
627C4⋊C4—62no—
628C4⋊C4—64no—
629C4⋊C4—64no—
630C4⋊C4—64no—
631C4⋊C4—62no—
632C4⋊C4—62no—
633C4⋊C4—62no—
634C4⋊C4—62no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C4⋊C4—62no—
642C4⋊C4—62no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4C23×D312yes—
646C4⋊C4C23×D312yes—
647C4⋊C4C23×D312yes—
648C4⋊C4C23×D312yes—
649C22⋊C4—22no—
650C22⋊C4—32no—
651C22⋊C4—32no—
652C22⋊C4—32no—
653C22⋊C4—32no—
654C22⋊C4—62no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—62no—
658C42—22no—
659C42—32no—
660C42—32no—
661C42—62no—
662C42—62no—
663C42—64no—
664C42—62no—
665C42D3×D411yescharacteristic
666C42D3×D411yescharacteristic
667C42C23×D311yescharacteristic
668C42C23×D311yescharacteristic
669C22×C3—21no—
670C22×C3—21no—
671C22×C3C2×C4⋊Q812yes—
672C22×C3C23×D411yescharacteristic
673C2×D3—22no—
674C2×D3—22no—
675C2×D3—44no—
676C2×D3C2×C4⋊Q814yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4C2×C4⋊Q812yes—
686C3×C4C23×Q812yes—
687Dic3—22no—
688Dic3—22no—
689Dic3—42no—
690Dic3—42no—
691Dic3—42no—
692Dic3—42no—
693Dic3C2×C4⋊Q814yes—
694C23—32no—
695C23—34no—
696C23—121no—
697C23—121no—
698C23C2×D3×D411yescharacteristic
699Q8—81no—
700Q8—81no—
701Q8—242no—
702Q8—242no—
703Q8—241no—
704Q8—241no—
705Q8—244no—
706Q8—242no—
707Q8—242no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—32no—
713C2×C4—34no—
714C2×C4—34no—
715C2×C4—34no—
716C2×C4—38no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—244no—
732C2×C4—242no—
733C2×C4—242no—
734C2×C4C2×D3×D411yescharacteristic
735C2×C4C2×D3×D411yescharacteristic
736C2×C4C2×D3×D411yescharacteristic
737C2×C4C2×D3×D411yescharacteristic
738C2×C4C2×D3×D411yescharacteristic
739C2×C4C2×D3×Q814yes—
740C2×C4C24×D311yescharacteristic
741C8—38no—
742C8C2×D3×Q818yes—
743C2×C3—22no—
744C2×C3C22×C4⋊Q811yescharacteristic
745C2×C3#358511yescharacteristic
746C2×C3#358611yescharacteristic
747D3—24no—
748C22—21no—
749C22—21no—
750C22—34no—
751C22—62no—
752C22—62no—
753C22—124no—
754C22D3×C4⋊Q812yes—
755C22C22×D3×D411yescharacteristic
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—34no—
761C4—42no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—62no—
766C4—62no—
767C4—122no—
768C4—122no—
769C4—122no—
770C4—122no—
771C4D3×C4⋊Q812yes—
772C4C22×D3×Q812yes—
773C3#6066411yescharacteristic, complemented, Sylow
774C2—22no—
775C2—64no—
776C2C2×D3×C4⋊Q811yescharacteristic
777C2#8720011yescharacteristic
778C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3166C2
socleC22×C3C23×D4
prime radicalC23×D3C2×D4
hypercenter#3166D3
hypocenterC3#60664
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
3. C3×#3166C2semidirect
4. #83341C2semidirect
5. #83015C2semidirect
6. #81975C2semidirect
7. #81974C2semidirect
8. #81918C2semidirect
9. #81917C2semidirect
12. #79204C2semidirect
13. #79203C2semidirect
15. #78506C2semidirect
47. C3×#501C22semidirect
48. C3×#501C22semidirect
49. C3×#499C22semidirect
56. #5080C22semidirect
57. #5078C22semidirect
58. #5065C22semidirect
59. #5064C22semidirect
60. #5064C22semidirect
61. #5064C22semidirect
71. #4878C22semidirect
72. #4876C22semidirect
73. #4876C22semidirect
74. #4874C22semidirect
79. #4858C22semidirect
80. #4856C22semidirect
81. #4856C22semidirect
82. #4855C22semidirect
84. #4702C22semidirect
86. #4682C22semidirect
87. #4680C22semidirect
92. #3166D3semidirect
147. D3×M16Q8semidirect
267. #501C2×D3semidirect
268. #501C2×D3semidirect
275. #499C2×D3semidirect
395. ΓL(1,𝔽25)C2×Q8semidirect
396. D3×C8C2×Q8semidirect
773. C3#60664semidirect

Maximal subgroups

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

subgroupindex
#862742
C2×#56892
C3×#31662
#833412
#830152
#819752
#819742
#819182
#819172
#792082
D3×#4282
#792042
#792032
#785142
#785062
#606643