Finite Group Databasebeta

← #11664852

Subgroups — #11664852

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×#5729C211yesmaximal, characteristic
3C3×#3165C211yesmaximal, characteristic, complemented
4#83342C211yesmaximal, characteristic, complemented
5#83207C211yesmaximal, characteristic, complemented
6#81975C214yesmaximal, complemented
7#81974C214yesmaximal, complemented
8#81939C214yesmaximal, complemented
9#81892C214yesmaximal, complemented
10#79208C212yesmaximal
11D3×#428C212yesmaximal
12#79204C212yesmaximal, complemented
13#79203C212yesmaximal, complemented
14#78514C211yesmaximal, characteristic
15#78507C211yesmaximal, characteristic, complemented
16#60664—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×#946—21no—
20C2×#944—21no—
21C2×D3×M16C2212yes—
22#5729—22no—
23#5729—22no—
24#5729C2212yes—
25#5729C2212yes—
26#5729C2214yes—
27#5729C2214yes—
28#5689C2212yes—
29#5689C2212yes—
30#5634—21no—
31#5634—21no—
32#5623—21no—
33#5623—21no—
34#5578—22no—
35#5578—22no—
36D3×#117C2212yes—
37#5517C2212yes—
38C2×#896—21no—
39C2×#892C2211yescharacteristic
40C2×D3×C4⋊C4C2211yescharacteristic
41C2×#890C2211yescharacteristic
42C2×#889—21no—
43C2×#888C2211yescharacteristic
44C2×#872C2211yescharacteristic
45#5470C2211yescharacteristic
46C2×#870C2211yescharacteristic
47C3×#501C2214yescomplemented
48C3×#500C2212yescomplemented
49C3×#498C2212yescomplemented
50C3×#428C2212yes—
51C3×#428C2212yes—
52C3×C4×M16C2211yescharacteristic
53#5121C2212yes—
54#5121C2212yes—
55Dic3×M16C2212yes—
56#5081C2214yescomplemented
57#5081C2212yescomplemented
58#5081C2212yescomplemented
59#5080C2212yescomplemented
60#5078C2212yescomplemented
61#5065C2214yescomplemented
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#4702C2212yescomplemented
85#4702C2212yescomplemented
86#4689C2214yes—
87#4683C2214yescomplemented
88#3458—31no—
89C2×#544—31no—
90#3166—32no—
91#3166—31no—
92#3166—31no—
93#3165—32no—
94#3165—31no—
95#3165D311yescharacteristic, complemented
96#3164—34no—
97#3164—34no—
98#3163—34no—
99#3163—34no—
100#2911—32no—
101C2×#428—32no—
102#2873—31no—
103C22×C3×Q8—21no—
104C22×C4×D3—21no—
105C22×C4×D3C2311yescharacteristic
106C22×Dic6—21no—
107C2×C3×M16C2312yes—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8C2312yes—
111C3×C4⋊Q8C2312yes—
112C3×C4⋊Q8C2311yescharacteristic
113C3×C4⋊Q8C2311yescharacteristic
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⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124#946—22no—
125#946—22no—
126#946—24no—
127#946—24no—
128#944—24no—
129#944—24no—
130#944—22no—
131#944—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4D411yescharacteristic
134C2×(C2×D3)⋊C4D411yescharacteristic
135#926C2312yes—
136C2×C4⋊Dic3—21no—
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139#924—21no—
140#924—21no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4—21no—
143C2×Dic3⋊C4—21no—
144C2×Dic3⋊C4—21no—
145C2×Dic3⋊C4—21no—
146C2×Dic3⋊C4D411yescharacteristic
147C2×Dic3⋊C4D411yescharacteristic
148C2×C4×Dic3—21no—
149C2×C4×Dic3C2311yescharacteristic
150C2×#208C2312yes—
151D3×M16Q8116yescomplemented
152C2×ΓL(1,𝔽25)C2314yes—
153C2×D3×C8C2314yes—
154#897—22no—
155#897—22no—
156#896—22no—
157#896—22no—
158#896—22no—
159#896—22no—
160#896—24no—
161#896—24no—
162#892—22no—
163#892C2312yes—
164#892C2314yes—
165#892C2312yes—
166D3×C4⋊C4—22no—
167D3×C4⋊C4C2312yes—
168D3×C4⋊C4C2314yes—
169D3×C4⋊C4C2312yes—
170#890—22no—
171#890C2312yes—
172#890C2314yes—
173#890C2312yes—
174#889—22no—
175#889—22no—
176#889—24no—
177#889—24no—
178#889—22no—
179#889—22no—
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#870—21no—
197#870—21no—
198#870C2312yes—
199#870C2312yes—
200#870C2312yes—
201#869C2311yescharacteristic
202#869C2311yescharacteristic
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—34no—
232#544—34no—
233#544—32no—
234#544—32no—
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—61no—
249C2×C4⋊Q8C2×D311yescharacteristic
250C2×#125—31no—
251C2×#125—31no—
252C2×#125—61no—
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—32no—
267#501—32no—
268#501C2×D314yescomplemented
269#500—32no—
270#500—34no—
271#500C2×D312yescomplemented
272#499—34no—
273#499—34no—
274#499—34no—
275#499—34no—
276#498—32no—
277#498—34no—
278#498C2×D312yescomplemented
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—
303C2×C3×Q8—22no—
304C2×C3×Q8—22no—
305C2×C3×Q8—82no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2411yescharacteristic
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3C2×D411yescharacteristic
314C22×Dic3C2×D411yescharacteristic
315C22×Dic3C2×D411yescharacteristic
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—24no—
319C2×C4×D3—82no—
320C2×C4×D3C2×D412yes—
321C2×C4×D3C2×Q818yes—
322C2×C4×D3C2412yes—
323C2×Dic6—21no—
324C2×Dic6—21no—
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6—24no—
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—21no—
339C3×C4⋊C4C2412yes—
340C3×C4⋊C4C2412yes—
341C3×C4⋊C4C2412yes—
342C3×C4⋊C4C2412yes—
343C3×C22⋊C4—22no—
344C3×C42—22no—
345C3×C42C2×D411yescharacteristic
346C3×C42C2×D411yescharacteristic
347C3×C42C2411yescharacteristic
348C3×C42C2411yescharacteristic
349#217—22no—
350(C2×D3)⋊C4—22no—
351(C2×D3)⋊C4—22no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4C2×D412yes—
354(C2×D3)⋊C4C2×D412yes—
355(C2×D3)⋊C4C2×D412yes—
356(C2×D3)⋊C4C2×D412yes—
357C4⋊Dic3—21no—
358C4⋊Dic3—21no—
359C4⋊Dic3—21no—
360C4⋊Dic3—21no—
361C4⋊Dic3—22no—
362C4⋊Dic3—22no—
363C4⋊Dic3—24no—
364C4⋊Dic3C2412yes—
365C4⋊Dic3C2412yes—
366C4⋊Dic3C2412yes—
367C4⋊Dic3C2412yes—
368Dic3⋊C4—22no—
369Dic3⋊C4—22no—
370Dic3⋊C4—22no—
371Dic3⋊C4—22no—
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—21no—
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—21no—
407C4⋊Q8—21no—
408C4⋊Q8—34no—
409C4⋊Q8—32no—
410C4⋊Q8—32no—
411C4⋊Q8—31no—
412C4⋊Q8—31no—
413C4⋊Q8—62no—
414C4⋊Q8—62no—
415C4⋊Q8—62no—
416C4⋊Q8—64no—
417C4⋊Q8—64no—
418C4⋊Q8—62no—
419C4⋊Q8—62no—
420C4⋊Q8C22×D312yes—
421C4⋊Q8C22×D312yes—
422C4⋊Q8C22×D311yescharacteristic
423C4⋊Q8C22×D311yescharacteristic
424#125—34no—
425#125—32no—
426#125—32no—
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#125—61no—
438#125—61no—
439#125C22×D312yes—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—62no—
443C22⋊Q8—62no—
444C22⋊Q8—64no—
445C22⋊Q8—64no—
446C22⋊Q8—62no—
447C22⋊Q8—62no—
448C22⋊Q8—62no—
449C22⋊Q8—62no—
450C22⋊Q8—62no—
451C22⋊Q8—62no—
452C22⋊Q8—64no—
453C22⋊Q8—64no—
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—31no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—31no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—34no—
482C2×C4⋊C4—32no—
483C2×C4⋊C4—32no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4—61no—
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—
530C3×Q8—82no—
531C3×Q8—82no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×Q814yes—
546C2×C3×C4C2511yescharacteristic
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—22no—
550C2×Dic3—22no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—42no—
554C2×Dic3—42no—
555C2×Dic3C4⋊Q814yes—
556C2×Dic3C22×D412yes—
557C2×Dic3C22×D412yes—
558C2×Dic3C22×D412yes—
559C4×D3—82no—
560C4×D3—82no—
561C4×D3—84no—
562C4×D3C4⋊Q818yes—
563C4×D3C22×Q814yes—
564C4×D3C22×Q814yes—
565Dic6—82no—
566Dic6—82no—
567Dic6—84no—
568Dic6—81no—
569Dic6—81no—
570C3×C8C22×Q818yes—
571C3⋊C8C22×Q818yes—
572C24—31no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—62no—
578C2×Q8—62no—
579C2×Q8—64no—
580C2×Q8—61no—
581C2×Q8—61no—
582C2×Q8—82no—
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—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—32no—
616C4⋊C4—32no—
617C4⋊C4—32no—
618C4⋊C4—32no—
619C4⋊C4—32no—
620C4⋊C4—32no—
621C4⋊C4—32no—
622C4⋊C4—32no—
623C4⋊C4—64no—
624C4⋊C4—62no—
625C4⋊C4—62no—
626C4⋊C4—64no—
627C4⋊C4—64no—
628C4⋊C4—64no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—62no—
632C4⋊C4—62no—
633C4⋊C4—62no—
634C4⋊C4—62no—
635C4⋊C4—61no—
636C4⋊C4—61no—
637C4⋊C4—62no—
638C4⋊C4—62no—
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—82no—
700Q8—82no—
701Q8—81no—
702Q8—81no—
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#8719211yescharacteristic
778C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3165C2
socleC22×C3C23×D4
prime radicalC23×D3C2×D4
hypercenter#3165D3
hypocenterC3#60664
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. C3×#3165C2semidirect
4. #83342C2semidirect
5. #83207C2semidirect
6. #81975C2semidirect
7. #81974C2semidirect
8. #81939C2semidirect
9. #81892C2semidirect
12. #79204C2semidirect
13. #79203C2semidirect
15. #78507C2semidirect
47. C3×#501C22semidirect
48. C3×#500C22semidirect
49. C3×#498C22semidirect
56. #5081C22semidirect
57. #5081C22semidirect
58. #5081C22semidirect
59. #5080C22semidirect
60. #5078C22semidirect
61. #5065C22semidirect
71. #4878C22semidirect
72. #4876C22semidirect
73. #4876C22semidirect
74. #4874C22semidirect
79. #4858C22semidirect
80. #4856C22semidirect
81. #4856C22semidirect
82. #4855C22semidirect
84. #4702C22semidirect
85. #4702C22semidirect
87. #4683C22semidirect
95. #3165D3semidirect
151. D3×M16Q8semidirect
268. #501C2×D3semidirect
271. #500C2×D3semidirect
278. #498C2×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×#57292
C3×#31652
#833422
#832072
#819752
#819742
#819392
#818922
#792082
D3×#4282
#792042
#792032
#785142
#785072
#606643