Finite Group Databasebeta

← #11675136

Subgroups — #11675136

Order 768.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86280C211yesmaximal, characteristic, complemented
2#85788C211yesmaximal, characteristic, complemented
3C3×#3077C211yesmaximal, characteristic, complemented
4#83334C211yesmaximal, characteristic, complemented
5C2×C4×#213C211yesmaximal, characteristic, complemented
6#81202C214yesmaximal, complemented
7#81150C214yesmaximal, complemented
8#81088C212yesmaximal, complemented
9#81087C212yesmaximal, complemented
10#80993C212yesmaximal, complemented
11#80992C212yesmaximal, complemented
12#79243C212yesmaximal, complemented
13#79201C212yesmaximal, complemented
14#79055C211yesmaximal, characteristic, complemented
15#79044C211yesmaximal, characteristic, complemented
16#78944C212yesmaximal, complemented
17#78920C212yesmaximal, complemented
18#61325—31nomaximal, Sylow
19C3×#533C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21#5805C2212yes—
22C22×#213C2211yescharacteristic
23#5791—22no—
24C2×#908C2212yes—
25#5730C2212yescomplemented
26#5727C2212yescomplemented
27#5690C2214yescomplemented
28#5634—22no—
29D3×C22⋊Q8—22no—
30#5579—22no—
31#5579—21no—
32Q8×D12—21no—
33#5563—21no—
34#5559C2214yescomplemented
35#5558—22no—
36#5553C2212yescomplemented
37#5551—21no—
38#5542C2212yescomplemented
39#5521C2212yes—
40#5519C2212yes—
41#5504C2212yes—
42#5494—22no—
43#5477C2211yescharacteristic
44C2×C4×D12C2211yescharacteristic
45#5470C2211yescharacteristic
46C3×#478C2214yescomplemented
47C3×#476C2212yescomplemented
48C3×#474C2212yescomplemented
49C3×#428C2212yes—
50C3×#423C2211yescharacteristic
51C3×#418C2212yes—
52C2×#832C2211yescharacteristic
53#5133C2212yes—
54#5122C2212yes—
55#5119C2212yes—
56#5093C2211yescharacteristic, complemented
57#5093C2211yescharacteristic, complemented
58#5088C2211yescharacteristic, complemented
59#5088C2211yescharacteristic, complemented
60#5068C2212yescomplemented
61#5068C2212yescomplemented
62C4×#213C2212yes—
63C4×#213C2212yes—
64C4×#213C2212yes—
65C4×#213C2212yes—
66#5002C2212yes—
67#5002C2212yes—
68C2×#809C2211yescharacteristic
69C2×#807C2211yescharacteristic
70C2×C4×C3⋊C8C2211yescharacteristic
71#4890C2214yescomplemented
72#4889C2214yescomplemented
73#4875C2214yescomplemented
74#4872C2214yescomplemented
75#4871C2214yescomplemented
76#4869C2214yescomplemented
77#4857C2214yescomplemented
78#4852C2214yescomplemented
79#4844C2214yescomplemented
80#4843C2212yescomplemented
81#4841C2212yescomplemented
82#4831C2212yescomplemented
83#4831C2212yescomplemented
84#4830C2212yescomplemented
85#4830C2212yescomplemented
86#4787C2214yes—
87#4787C2214yes—
88#4786C2214yes—
89#4786C2214yes—
90#4768C2214yescomplemented
91#4765C2214yescomplemented
92#4764C2214yescomplemented
93#4760C2214yescomplemented
94#3506—31no—
95#3501—31no—
96#3370—34no—
97#3367—32no—
98#3366—32no—
99#3361—34no—
100#3360—32no—
101#3358—32no—
102#3136—32no—
103#3131—31no—
104#3083—32no—
105#3077D311yescharacteristic, complemented
106#3041—32no—
107#3036—31no—
108#2960—31no—
109#2946—32no—
110C2×C4×D8—31no—
111C22×C3×D4C2311yescharacteristic
112C23×C3×C4—21no—
113C2×D3×Q8—22no—
114C2×#235—22no—
115C2×#235C2312yes—
116C22×D12C2311yescharacteristic
117C22×C4×D3—21no—
118C2×C3×M16C2312yes—
119C3×C4⋊Q8C2311yescharacteristic
120C3×C4⋊Q8C2311yescharacteristic
121C3×#125C2312yes—
122C3×C22⋊Q8—21no—
123C3×C22⋊Q8—21no—
124C3×C4×Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×D4—21no—
127C3×C4×D4—21no—
128C3×C4×D4C2312yes—
129C3×C4×D4C2312yes—
130C3×#117C2312yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4—21no—
133C2×C3×C42C2311yescharacteristic
134#953—24no—
135#946—22no—
136#946—24no—
137#940C2314yes—
138#938—22no—
139#938—22no—
140#936C2314yes—
141C2×#213—24no—
142C2×#213C2312yes—
143C2×#213C2312yes—
144#930—21no—
145#930—21no—
146#930—22no—
147#929—24no—
148C4×#67—24no—
149C4×#67—24no—
150C2×(C2×D3)⋊C4—21no—
151#926—22no—
152#926C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154#924—22no—
155#924D412yes—
156#924D412yes—
157C22×C3⋊C8C2311yescharacteristic
158C22×C3⋊C8C2311yescharacteristic
159#908—28no—
160C2×D24C2314yes—
161C2×#204C2314yes—
162#897—22no—
163#897—24no—
164#896—24no—
165#896—24no—
166#896—24no—
167#893C2314yes—
168#893C2314yes—
169#893C2314yes—
170#892—22no—
171D3×C4⋊C4—22no—
172D3×C4⋊C4—22no—
173D3×C4⋊C4—24no—
174#890C2314yes—
175#888C2314yes—
176#887C2314yes—
177#885—24no—
178#884—24no—
179#883—24no—
180D3×C22⋊C4—24no—
181#879—24no—
182#878—24no—
183#875C2312yes—
184#874C2311yescharacteristic
185C4×D12—21no—
186C4×D12—21no—
187C4×D12—21no—
188C4×D12—21no—
189C4×D12—22no—
190C4×D12—22no—
191C4×D12C2312yes—
192C4×D12C2312yes—
193#870—22no—
194#870D412yes—
195#869—22no—
196#869D411yescharacteristic
197#869D411yescharacteristic
198#869C2311yescharacteristic
199C4×Dic6C2312yes—
200C4×Dic6C2312yes—
201C3×#107C2314yes—
202C3×#106C2314yes—
203C3×C4⋊C8C2312yes—
204C3×C4⋊C8C2312yes—
205C3×#102C2314yes—
206C3×#102C2314yes—
207#832C2312yes—
208#832C2312yes—
209#821C2314yes—
210#816C2314yes—
211#815C2314yes—
212Dic3⋊C8C2314yes—
213Dic3⋊C8C2314yes—
214C8×Dic3C2314yes—
215#810C2312yes—
216#810C2312yes—
217#810C2312yes—
218#810C2312yes—
219#809C2312yes—
220#809C2312yes—
221#809C2312yes—
222#809C2312yes—
223#809C2312yes—
224#809C2312yes—
225#807C2312yes—
226#807C2312yes—
227C4×C3⋊C8C2311yescharacteristic
228C4×C3⋊C8C2311yescharacteristic
229C4×C3⋊C8C2311yescharacteristic
230C4×C3⋊C8C2311yescharacteristic
231C2×AGL(1,ℤ/8)—32no—
232C22×D8—31no—
233#559—34no—
234#556—32no—
235#555—61no—
236#554—32no—
237#554—34no—
238#554—62no—
239#554—61no—
240#553—62no—
241#550—32no—
242D4×Q8—32no—
243D4×Q8—61no—
244#547—61no—
245#544—32no—
246#543—62no—
247#538—62no—
248#535—32no—
249#533—31no—
250#533C2×D311yescharacteristic
251#532—31no—
252#525—62no—
253C2×C22⋊Q8—62no—
254#520—32no—
255#518—32no—
256C2×C4×D4—31no—
257C2×C4×D4C2×D311yescharacteristic
258#490—34no—
259#489—34no—
260#488—32no—
261#488—32no—
262#488—34no—
263#487—31no—
264#487—31no—
265#486—31no—
266#486—31no—
267#486—34no—
268#479—34no—
269#478—34no—
270#478C2×D314yescomplemented
271#477—34no—
272#476C2×D312yescomplemented
273#474—34no—
274#474C2×D312yescomplemented
275#463—34no—
276#463—34no—
277#463—34no—
278#461—32no—
279#459—32no—
280#459—34no—
281#459—34no—
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#442—34no—
287#440—34no—
288C4×SD16—34no—
289C4×D8—32no—
290C4×D8—32no—
291C4×D8—32no—
292C4×D8—32no—
293C4×D8—34no—
294#428C2×D312yes—
295C2×#107—31no—
296#424—32no—
297#423C2×D311yescharacteristic
298#418C2×D312yes—
299#417—32no—
300#416—32no—
301#416—32no—
302C2×#102—31no—
303C2×#102—31no—
304#405—32no—
305C2×C4×C8—31no—
306C24×C3—21no—
307C23×D3—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×D4—21no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4C2412yes—
314C22×C3×C4—21no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—82no—
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C22×C3×C4C2411yescharacteristic
321C2×#67—22no—
322C2×#67—24no—
323C2×#67—24no—
324C22×Dic3—21no—
325D3×Q8—84no—
326#235—24no—
327#235—24no—
328#235—84no—
329C2×D12—21no—
330C2×D12—22no—
331C2×D12—21no—
332C2×D12—21no—
333C2×D12#4114yescomplemented
334C2×D12C2412yes—
335C2×D12C2412yes—
336C2×C4×D3—22no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—24no—
340C2×C4×D3—24no—
341C2×C4×D3—24no—
342C2×C4×D3—82no—
343C2×Dic6—24no—
344C2×Dic6C2×D412yes—
345C2×Dic6C2×D412yes—
346C2×Dic6C2412yes—
347C3×M16—24no—
348C2×C3×C8C2414yes—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4C2412yes—
355C3×C4⋊C4C2412yes—
356C3×C4⋊C4C2412yes—
357C3×C22⋊C4—22no—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—22no—
360C3×C42—22no—
361C3×C42C2×D411yescharacteristic
362C3×C42C2×D411yescharacteristic
363C3×C42C2411yescharacteristic
364C3×C42C2411yescharacteristic
365#217—24no—
366#217—24no—
367#217C2×D414yes—
368#213—24no—
369#213—24no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—22no—
373(C2×D3)⋊C4—22no—
374(C2×D3)⋊C4—24no—
375(C2×D3)⋊C4—24no—
376(C2×D3)⋊C4—24no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—24no—
381C4⋊Dic3C2×D412yes—
382C4⋊Dic3C2×D412yes—
383C4⋊Dic3C2×D412yes—
384C4⋊Dic3C2×D412yes—
385C4⋊Dic3C2412yes—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4C2×D414yes—
390Dic3⋊C4C2×D414yes—
391C4×Dic3—24no—
392C4×Dic3C2414yes—
393C2×C3⋊C8—22no—
394C2×C3⋊C8—22no—
395C2×C3⋊C8C2411yescharacteristic
396C2×C3⋊C8C2411yescharacteristic
397C2×C3⋊C8C2411yescharacteristic
398C2×C3⋊C8C2411yescharacteristic
399D24—28no—
400#204—28no—
401C2×#41—32no—
402C2×#41—62no—
403C22×Q8—62no—
404C22×D4—31no—
405C22×D4C22×D311yescharacteristic
406C23×C4—21no—
407C23×C4—61no—
408AGL(1,ℤ/8)—68no—
409C2×SD16—34no—
410C2×D8—32no—
411C2×D8—32no—
412C2×D8—34no—
413C2×D8—64no—
414C2×M16C22×D312yes—
415C22×C8—31no—
416C22×C8—31no—
417C4⋊Q8—34no—
418C4⋊Q8—31no—
419C4⋊Q8—31no—
420C4⋊Q8—31no—
421C4⋊Q8—62no—
422C4⋊Q8C22×D311yescharacteristic
423C4⋊Q8C22×D311yescharacteristic
424#127—34no—
425#127—31no—
426#126—64no—
427#125—34no—
428#125—32no—
429#125—62no—
430#125C22×D312yes—
431#124—34no—
432#124—32no—
433#124—64no—
434#123—64no—
435#123—64no—
436C22⋊Q8—21no—
437C22⋊Q8—21no—
438C22⋊Q8—32no—
439C22⋊Q8—32no—
440C22⋊Q8—64no—
441C22⋊Q8—64no—
442C22⋊Q8—64no—
443C22⋊Q8—64no—
444C22⋊Q8—62no—
445C22⋊Q8—64no—
446C22⋊Q8—62no—
447C22⋊Q8—64no—
448C22⋊Q8—62no—
449#121—64no—
450#121—62no—
451#121—62no—
452#121—62no—
453#121—61no—
454#121—61no—
455#120—64no—
456C4×Q8—21no—
457C4×Q8—21no—
458C4×Q8—32no—
459C4×Q8—32no—
460C4×Q8—34no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—34no—
464C4×D4—34no—
465C4×D4—34no—
466C4×D4—32no—
467C4×D4—32no—
468C4×D4—62no—
469C4×D4—62no—
470C4×D4—64no—
471C4×D4—64no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4C22×D312yes—
477C4×D4C22×D312yes—
478#117—32no—
479#117—62no—
480#117—62no—
481#117C22×D312yes—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4—64no—
485C2×C4⋊C4—62no—
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—64no—
489C2×C22⋊C4—61no—
490C2×C42C22×D311yescharacteristic
491#107—32no—
492#107—32no—
493#107C22×D314yes—
494#106C22×D314yes—
495C4⋊C8—34no—
496C4⋊C8—34no—
497C4⋊C8C22×D312yes—
498C4⋊C8C22×D312yes—
499#103—34no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103—32no—
504#102—32no—
505#102—32no—
506#102—34no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—32no—
511#102—32no—
512#102—32no—
513#102C22×D314yes—
514#102C22×D314yes—
515#97—34no—
516C4×C8—34no—
517C4×C8—31no—
518C4×C8—31no—
519C4×C8—31no—
520C4×C8—31no—
521C23×C3—22no—
522C23×C3—42no—
523C23×C3—81no—
524C23×C3—81no—
525C23×C3C22×D411yescharacteristic
526C22×D3—22no—
527C22×D3—24no—
528C22×D3—22no—
529C22×D3—81no—
530C22×D3—81no—
531C3×Q8—42no—
532C3×Q8—81no—
533C3×D4—22no—
534C3×D4—22no—
535C3×D4—42no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—41no—
541C2×C3×C4—44no—
542C2×C3×C4—82no—
543C2×C3×C4—81no—
544C2×C3×C4C22×D411yescharacteristic
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4C22×D411yescharacteristic
549C2×C3×C4C2×#4112yes—
550C2×C3×C42−1+412yes—
551C2×C3×C4C2511yescharacteristic
552#67—44no—
553#67—84no—
554#67—84no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—81no—
558C2×Dic3C22×D414yes—
559C2×Dic3C22×D414yes—
560D12—24no—
561D12—22no—
562D12—22no—
563D12—22no—
564D12—42no—
565D12—81no—
566D12C2×#4114yes—
567C4×D3—44no—
568C4×D3—44no—
569C4×D3—84no—
570C4×D3—84no—
571C4×D3—84no—
572C4×D3—82no—
573Dic6—24no—
574Dic6—22no—
575Dic6—22no—
576Dic6—42no—
577Dic6—84no—
578C3×C8—24no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C24—21no—
584C24—61no—
585#41—64no—
586#41—64no—
587#41—244no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—32no—
591C2×Q8—32no—
592C2×Q8—32no—
593C2×Q8—64no—
594C2×Q8—244no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—34no—
599C2×D4—32no—
600C2×D4—32no—
601C2×D4—64no—
602C2×D4—64no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—62no—
608C2×D4C23×D312yes—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—64no—
613C22×C4—64no—
614C22×C4—64no—
615C22×C4—61no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—82no—
620C22×C4—242no—
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624SD16—68no—
625D8—68no—
626D8—64no—
627D8—64no—
628M16—24no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8—62no—
634C2×C8—62no—
635C2×C8C23×D314yes—
636C4⋊C4—21no—
637C4⋊C4—22no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—32no—
642C4⋊C4—32no—
643C4⋊C4—34no—
644C4⋊C4—32no—
645C4⋊C4—34no—
646C4⋊C4—32no—
647C4⋊C4—32no—
648C4⋊C4—64no—
649C4⋊C4—64no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4C23×D312yes—
656C4⋊C4C23×D312yes—
657C4⋊C4C23×D312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—34no—
662C22⋊C4—64no—
663C22⋊C4—64no—
664C22⋊C4—64no—
665C22⋊C4—64no—
666C22⋊C4—64no—
667C22⋊C4—62no—
668C22⋊C4—62no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C42—22no—
672C42—34no—
673C42—64no—
674C42D3×D411yescharacteristic
675C42D3×D411yescharacteristic
676C42C23×D311yescharacteristic
677C42C23×D311yescharacteristic
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—84no—
684C22×C3#54812yes—
685C22×C3C23×D411yescharacteristic
686C2×D3—24no—
687C2×D3—42no—
688C2×D3—42no—
689C2×D3—42no—
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—84no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4—42no—
699C3×C4#54812yes—
700C3×C4#57612yes—
701C3×C4C22×#4111yescharacteristic
702C3×C4C2×2−1+411yescharacteristic
703Dic3—24no—
704Dic3—24no—
705Dic3—42no—
706Dic3—42no—
707C23—22no—
708C23—42no—
709C23—62no—
710C23—64no—
711C23—62no—
712C23—81no—
713C23—81no—
714C23—241no—
715C23—241no—
716C23C2×D3×D411yescharacteristic
717Q8—42no—
718Q8—64no—
719Q8—62no—
720Q8—62no—
721Q8—81no—
722Q8—122no—
723Q8—244no—
724D4—22no—
725D4—22no—
726D4—34no—
727D4—42no—
728D4—64no—
729D4—62no—
730D4—62no—
731D4—62no—
732D4—124no—
733D4—122no—
734D4—241no—
735D4—244no—
736D4—244no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—34no—
742C2×C4—34no—
743C2×C4—41no—
744C2×C4—44no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—82no—
748C2×C4—81no—
749C2×C4—124no—
750C2×C4—124no—
751C2×C4—242no—
752C2×C4—244no—
753C2×C4—244no—
754C2×C4—244no—
755C2×C4—241no—
756C2×C4C2×D3×D411yescharacteristic
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4#100712yes—
762C2×C4D3×#4112yes—
763C2×C4C24×D311yescharacteristic
764C8—24no—
765C8—61no—
766C8—61no—
767C8—61no—
768C8—61no—
769C2×C3—22no—
770C2×C3—82no—
771C2×C3C2×#54811yescharacteristic
772C2×C3C2×#57611yescharacteristic
773C2×C3#358411yescharacteristic
774D3—44no—
775D3—82no—
776C22—21no—
777C22—21no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—64no—
782C22—84no—
783C22—122no—
784C22—122no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—244no—
789C22#563312yes—
790C22C22×D3×D411yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—64no—
798C4—64no—
799C4—122no—
800C4—122no—
801C4#563312yes—
802C4#577412yes—
803C4C2×#100711yescharacteristic
804C4C2×D3×#4111yescharacteristic
805C3#6132511yescharacteristic, complemented, Sylow
806C2—22no—
807C2—82no—
808C2—124no—
809C2—242no—
810C2C2×#563311yescharacteristic
811C2C2×#577411yescharacteristic
812C2#8719911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
hypercenter#3077D3
hypocenterC3#61325
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #86280C2semidirect
2. #85788C2semidirect
3. C3×#3077C2semidirect
4. #83334C2semidirect
5. C2×C4×#213C2semidirect
6. #81202C2semidirect
7. #81150C2semidirect
8. #81088C2semidirect
9. #81087C2semidirect
10. #80993C2semidirect
11. #80992C2semidirect
12. #79243C2semidirect
13. #79201C2semidirect
14. #79055C2semidirect
15. #79044C2semidirect
16. #78944C2semidirect
17. #78920C2semidirect
25. #5730C22semidirect
26. #5727C22semidirect
27. #5690C22semidirect
34. #5559C22semidirect
36. #5553C22semidirect
38. #5542C22semidirect
46. C3×#478C22semidirect
47. C3×#476C22semidirect
48. C3×#474C22semidirect
56. #5093C22semidirect
57. #5093C22semidirect
58. #5088C22semidirect
59. #5088C22semidirect
60. #5068C22semidirect
61. #5068C22semidirect
71. #4890C22semidirect
72. #4889C22semidirect
73. #4875C22semidirect
74. #4872C22semidirect
75. #4871C22semidirect
76. #4869C22semidirect
77. #4857C22semidirect
78. #4852C22semidirect
79. #4844C22semidirect
80. #4843C22semidirect
81. #4841C22semidirect
82. #4831C22semidirect
83. #4831C22semidirect
84. #4830C22semidirect
85. #4830C22semidirect
90. #4768C22semidirect
91. #4765C22semidirect
92. #4764C22semidirect
93. #4760C22semidirect
105. #3077D3semidirect
270. #478C2×D3semidirect
272. #476C2×D3semidirect
274. #474C2×D3semidirect
333. C2×D12#41semidirect
805. C3#61325semidirect

Maximal subgroups

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

subgroupindex
#862802
#857882
C3×#30772
#833342
C2×C4×#2132
#812022
#811502
#810882
#810872
#809932
#809922
#792432
#792012
#790552
#790442
#789442
#789202
#613253