Finite Group Databasebeta

← #11675119

Subgroups — #11675119

Order 768.

1878 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#86277C211yesmaximal, characteristic, complemented
2C2×#5585C211yesmaximal, characteristic, complemented
3C3×#3078C211yesmaximal, characteristic, complemented
4#83336C211yesmaximal, characteristic, complemented
5C4×#942C211yesmaximal, characteristic, complemented
6#81218C214yesmaximal, complemented
7#81217C214yesmaximal, complemented
8#81139C212yesmaximal, complemented
9#81134C212yesmaximal, complemented
10#81041C212yesmaximal, complemented
11#81038C212yesmaximal, complemented
12#79239C212yesmaximal, complemented
13#79199C212yesmaximal, complemented
14#79056C211yesmaximal, characteristic
15#79046C211yesmaximal, characteristic, complemented
16#78975C212yesmaximal, complemented
17#78954C212yesmaximal, complemented
18#61324—31nomaximal, Sylow
19C3×#533C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×#947C2212yes—
22C2×#942C2211yescharacteristic
23C2×#908C2212yes—
24#5730C2211yescharacteristic, complemented
25#5727C2211yescharacteristic, complemented
26#5722C2211yescharacteristic, complemented
27#5721C2211yescharacteristic, complemented
28#5690C2212yescomplemented
29#5685C2212yescomplemented
30#5636—22no—
31#5635—21no—
32#5632—21no—
33#5585—21no—
34#5585—22no—
35#5585—21no—
36#5585C2214yes—
37#5585C2212yes—
38#5585C2212yes—
39#5578—22no—
40#5578—21no—
41C4×D3×Q8—21no—
42#5522C2212yes—
43#5517C2212yes—
44C2×#894—22no—
45C2×#893C2212yes—
46C2×#875—21no—
47C2×#874C2211yescharacteristic
48C4×#235C2211yescharacteristic
49C2×C4×D12—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#479C2214yescomplemented
52C3×#477C2212yescomplemented
53C3×#475C2212yescomplemented
54C3×#428C2212yes—
55C3×#423C2211yescharacteristic
56C3×#419C2212yes—
57#5225C2211yescharacteristic
58#5131C2212yes—
59#5118C2212yes—
60Dic3×M16C2212yes—
61#5088C2212yes—
62#5088C2212yes—
63#5067C2214yes—
64#5030C2212yescomplemented
65C4×#216C2212yescomplemented
66#5026C2212yescomplemented
67C4×#215C2212yescomplemented
68#5001C2212yes—
69#5001C2212yes—
70#4966C2211yescharacteristic
71#4964C2211yescharacteristic
72C4×#208C2211yescharacteristic
73#4891C2214yescomplemented
74#4890C2214yescomplemented
75#4889C2214yescomplemented
76#4872C2214yescomplemented
77#4871C2214yescomplemented
78#4870C2214yescomplemented
79#4869C2214yescomplemented
80#4852C2214yescomplemented
81#4848C2212yes—
82#4848C2212yes—
83#4843C2212yes—
84#4843C2212yes—
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4819C2214yescomplemented
89#4819C2214yescomplemented
90#4800C2214yescomplemented
91#4800C2214yescomplemented
92#4798C2214yescomplemented
93#4798C2214yescomplemented
94#4794C2214yescomplemented
95#4794C2214yescomplemented
96C2×#559—31no—
97Q8×#41—31no—
98#3375—32no—
99#3373—32no—
100#3371—34no—
101#3370—34no—
102#3365—32no—
103#3361—32no—
104#3140—32no—
105#3138—31no—
106#3078D311yescharacteristic, complemented
107#3077—32no—
108#3040—32no—
109#3038—31no—
110Q8×M16—31no—
111C4×#137—31no—
112C4×AGL(1,ℤ/8)—32no—
113C22×C3×Q8C2311yescharacteristic
114C2×D3×Q8—21no—
115C2×#235C2311yescharacteristic
116C22×D12—21no—
117C22×D12—21no—
118C22×D12C2312yes—
119C22×C4×D3—22no—
120C22×Dic6D411yescharacteristic
121C2×C3×M16C2312yes—
122C3×C4⋊Q8C2311yescharacteristic
123C3×C4⋊Q8C2311yescharacteristic
124C3×#125C2312yes—
125C3×C22⋊Q8—21no—
126C3×C22⋊Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×Q8—21no—
129C3×C4×Q8—21no—
130C3×C4×Q8—21no—
131C3×C4×Q8C2312yes—
132C3×C4×Q8C2312yes—
133C3×#117C2312yes—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C42—21no—
137C2×C3×C42C2311yescharacteristic
138#947—22no—
139#947—22no—
140#947C2314yes—
141#947C2314yes—
142#946—21no—
143#946—22no—
144Q8×Dic3—21no—
145#944—21no—
146#944—22no—
147C2×#216C2312yes—
148#942—24no—
149C2×#215C2312yes—
150C4×#67—21no—
151C4×#67—21no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—22no—
154C2×(C2×D3)⋊C4—22no—
155#926C2311yescharacteristic
156C2×C4⋊Dic3D411yescharacteristic
157C2×Dic3⋊C4D412yes—
158C2×C4×Dic3C2312yes—
159C2×#208C2311yescharacteristic
160C2×#208C2311yescharacteristic
161#908—28no—
162C2×D24C2314yes—
163C2×#204C2314yes—
164#897—21no—
165#897—22no—
166#896—22no—
167#896—22no—
168#896—22no—
169#894—24no—
170#894—24no—
171#894—24no—
172#894—24no—
173#893—22no—
174#893—22no—
175#893C2312yes—
176#893C2314yes—
177#893C2314yes—
178#893C2312yes—
179D3×C4⋊C4—21no—
180D3×C4⋊C4—22no—
181#890C2312yes—
182#890C2312yes—
183#889—22no—
184#889—22no—
185#889—22no—
186#888—22no—
187#888—21no—
188#888C2312yes—
189#888C2312yes—
190#887—21no—
191#887—22no—
192#887C2312yes—
193#887C2312yes—
194#67⋊C4—22no—
195#67⋊C4—22no—
196#878—22no—
197#878—22no—
198#875—22no—
199#875—22no—
200#875—24no—
201#874—21no—
202#874—21no—
203#874C2312yes—
204#874C2312yes—
205C4×D12—22no—
206C4×D12—24no—
207C4×D12—22no—
208C4×D12C2311yescharacteristic
209C4×D12C2311yescharacteristic
210#872—21no—
211#872—22no—
212C42×D3—21no—
213C42×D3—22no—
214C4×Dic6—22no—
215C4×Dic6—22no—
216C4×Dic6D411yescharacteristic
217C4×Dic6D412yes—
218C4×Dic6D411yescharacteristic
219C4×Dic6C2311yescharacteristic
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2312yes—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2311yescharacteristic
224C3×#107C2314yes—
225C3×#106C2314yes—
226C3×C4⋊C8C2312yes—
227C3×C4⋊C8C2312yes—
228C3×#103C2314yes—
229C3×#103C2314yes—
230#835C2312yes—
231#835C2312yes—
232#821C2314yes—
233#821C2314yes—
234#815C2314yes—
235Dic3⋊C8C2314yes—
236Dic3⋊C8C2314yes—
237C8×Dic3C2314yes—
238#810C2312yes—
239#809C2312yes—
240#809C2314yes—
241#809C2314yes—
242#809C2314yes—
243#809C2314yes—
244#808C2312yes—
245#807C2312yes—
246#803C2312yes—
247C4×C3⋊C8C2312yes—
248C2×#137—31no—
249C2×AGL(1,ℤ/8)—32no—
250#559—32no—
251#559—34no—
252#559—32no—
253#559—61no—
254#559—62no—
255#559—61no—
256Q82—31no—
257#557—31no—
258#557—32no—
259#554—31no—
260#554—32no—
261#554—61no—
262#554—62no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—32no—
266#533—62no—
267#533—61no—
268#533C2×D311yescharacteristic
269C2×#127—31no—
270C2×#124—32no—
271C2×#124—61no—
272C2×#123—62no—
273C4×#41—32no—
274C4×#41—31no—
275C2×C4×Q8—31no—
276C2×C4×Q8—61no—
277C2×C4×Q8C2×D311yescharacteristic
278C2×C4×D4—32no—
279C2×C4×D4—61no—
280#490—34no—
281#489—34no—
282#489—34no—
283#488—34no—
284#488—34no—
285#486—32no—
286#486—32no—
287#479C2×D314yescomplemented
288#478—34no—
289#478—34no—
290#477C2×D312yescomplemented
291#476—34no—
292#475C2×D312yescomplemented
293#474—34no—
294#464—34no—
295#464—34no—
296#463—34no—
297#463—34no—
298#460—32no—
299#460—32no—
300#459—32no—
301#459—32no—
302#446—34no—
303#446—32no—
304C8×Q8—32no—
305#442—34no—
306#441—32no—
307#440—32no—
308#440—34no—
309C4×Q16—32no—
310C4×SD16—32no—
311C4×SD16—34no—
312C4×D8—34no—
313#428—31no—
314#428C2×D312yes—
315#423—32no—
316#423C2×D311yescharacteristic
317#419—31no—
318#419C2×D312yes—
319#418—32no—
320#418—32no—
321#418—32no—
322#417—31no—
323C4×M16—32no—
324C4×M16—31no—
325C23×D3—22no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—21no—
329C2×C3×Q8—22no—
330C2×C3×Q8—22no—
331C2×C3×Q8C2412yes—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2411yescharacteristic
337C2×#67—21no—
338C22×Dic3C2×D412yes—
339C22×Dic3C2×D412yes—
340D3×Q8—44no—
341#235—22no—
342#235#4114yes—
343C2×D12—24no—
344C2×D12—24no—
345C2×D12—22no—
346C2×D12—22no—
347C2×D12—22no—
348C2×D12—22no—
349C2×D12—22no—
350C2×D12—44no—
351C2×D12—82no—
352C2×D12C2414yes—
353C2×D12C2411yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—22no—
357C2×C4×D3—21no—
358C2×C4×D3—22no—
359C2×C4×D3—24no—
360C2×C4×D3—24no—
361C2×C4×D3—84no—
362C2×Dic6—22no—
363C2×Dic6—22no—
364C2×Dic6—42no—
365C2×Dic6C2×D411yescharacteristic
366C2×Dic6C2×D411yescharacteristic
367C2×Dic6C2×D412yes—
368C2×Dic6C2411yescharacteristic
369C3×M16—24no—
370C2×C3×C8C2414yes—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—22no—
378C3×C4⋊C4C2412yes—
379C3×C4⋊C4C2412yes—
380C3×C4⋊C4C2412yes—
381C3×C22⋊C4—22no—
382C3×C42—22no—
383C3×C42—22no—
384C3×C42—22no—
385C3×C42C2×D411yescharacteristic
386C3×C42C2×D411yescharacteristic
387C3×C42C2411yescharacteristic
388C3×C42C2411yescharacteristic
389#217—21no—
390#216—24no—
391#215—24no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—24no—
397(C2×D3)⋊C4—24no—
398(C2×D3)⋊C4—24no—
399(C2×D3)⋊C4—24no—
400(C2×D3)⋊C4—24no—
401(C2×D3)⋊C4—24no—
402C4⋊Dic3—22no—
403C4⋊Dic3—22no—
404C4⋊Dic3C2×D411yescharacteristic
405C4⋊Dic3C2×D412yes—
406C4⋊Dic3C2×D411yescharacteristic
407C4⋊Dic3C2411yescharacteristic
408C4⋊Dic3C2411yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4C2×D412yes—
418Dic3⋊C4C2×D412yes—
419Dic3⋊C4C2×D412yes—
420Dic3⋊C4C2×D412yes—
421C4×Dic3—21no—
422C4×Dic3—21no—
423C4×Dic3—21no—
424C4×Dic3—22no—
425C4×Dic3—22no—
426C4×Dic3C2×D412yes—
427C4×Dic3C2×D412yes—
428C4×Dic3C2412yes—
429C4×Dic3C2412yes—
430#208—22no—
431#208—22no—
432C2×C3⋊C8C2412yes—
433C2×C3⋊C8C2412yes—
434D24—28no—
435#204—28no—
436C2×#41—31no—
437C22×Q8—31no—
438C22×Q8—61no—
439C22×Q8C22×D311yescharacteristic
440C22×D4—32no—
441C22×D4—61no—
442C22×D4—61no—
443C23×C4—62no—
444#137—64no—
445AGL(1,ℤ/8)—68no—
446C2×Q16—32no—
447C2×SD16—32no—
448C2×SD16—34no—
449C2×D8—34no—
450C2×M16—31no—
451C2×M16—31no—
452C2×M16C22×D312yes—
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—61no—
456C4⋊Q8—62no—
457C4⋊Q8—62no—
458C4⋊Q8—61no—
459C4⋊Q8C22×D311yescharacteristic
460C4⋊Q8C22×D311yescharacteristic
461#127—32no—
462#127—32no—
463#127—61no—
464#127—61no—
465#125—32no—
466#125—32no—
467#125—62no—
468#125—62no—
469#125—62no—
470#125C22×D312yes—
471#124—34no—
472#124—34no—
473#124—62no—
474#124—62no—
475#124—64no—
476#124—62no—
477#124—62no—
478#123—64no—
479#123—64no—
480#123—64no—
481#123—64no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489C22⋊Q8—62no—
490C22⋊Q8—61no—
491C22⋊Q8—61no—
492C22⋊Q8—62no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8—31no—
498C4×Q8—32no—
499C4×Q8—31no—
500C4×Q8—31no—
501C4×Q8—31no—
502C4×Q8—32no—
503C4×Q8—32no—
504C4×Q8—32no—
505C4×Q8—31no—
506C4×Q8—31no—
507C4×Q8—62no—
508C4×Q8—62no—
509C4×Q8—62no—
510C4×Q8—61no—
511C4×Q8—61no—
512C4×Q8C22×D312yes—
513C4×Q8C22×D312yes—
514C4×D4—34no—
515C4×D4—34no—
516C4×D4—32no—
517C4×D4—32no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—62no—
521C4×D4—64no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4—61no—
528C4×D4—61no—
529#117—31no—
530#117—62no—
531#117—61no—
532#117C22×D312yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—31no—
535C2×C4⋊C4—32no—
536C2×C4⋊C4—62no—
537C2×C4⋊C4—61no—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C42—21no—
543C2×C42—32no—
544C2×C42—62no—
545C2×C42—61no—
546C2×C42C22×D311yescharacteristic
547#107—32no—
548#107C22×D314yes—
549#106—32no—
550#106C22×D314yes—
551C4⋊C8—34no—
552C4⋊C8—34no—
553C4⋊C8C22×D312yes—
554C4⋊C8C22×D312yes—
555#103—32no—
556#103—32no—
557#103—32no—
558#103C22×D314yes—
559#103C22×D314yes—
560#102—34no—
561#102—34no—
562#102—32no—
563#102—34no—
564#102—34no—
565#102—34no—
566#102—34no—
567#97—34no—
568#97—32no—
569C4×C8—34no—
570C4×C8—32no—
571C23×C3C22×D411yescharacteristic
572C22×D3—21no—
573C22×D3—24no—
574C22×D3—44no—
575C22×D3—44no—
576C22×D3—44no—
577C3×Q8—22no—
578C3×Q8—22no—
579C3×Q8—42no—
580C3×Q8—42no—
581C3×Q8—81no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—41no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C22×D411yescharacteristic
595C2×C3×C4C2×#4112yes—
596C2×C3×C42−1+412yes—
597C2×C3×C4C2511yescharacteristic
598#67—24no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—42no—
603C2×Dic3—42no—
604C2×Dic3C22×D412yes—
605C2×Dic3C22×D412yes—
606C2×Dic3C22×D412yes—
607C2×Dic3C22×D412yes—
608D12—24no—
609D12—21no—
610D12—24no—
611D12—44no—
612D12—44no—
613D12—44no—
614D12—82no—
615D12—82no—
616D12C2×#4112yes—
617C4×D3—24no—
618C4×D3—44no—
619C4×D3—42no—
620C4×D3—82no—
621C4×D3—84no—
622C4×D3—84no—
623C4×D3—81no—
624Dic6—22no—
625Dic6—22no—
626Dic6—21no—
627Dic6—42no—
628Dic6—44no—
629Dic6—82no—
630Dic6C2×#4112yes—
631C3×C8—24no—
632C3⋊C8—22no—
633C3⋊C8—22no—
634C24—62no—
635#41—34no—
636#41—62no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—31no—
643C2×Q8—31no—
644C2×Q8—32no—
645C2×Q8—31no—
646C2×Q8—62no—
647C2×Q8—62no—
648C2×Q8—122no—
649C2×Q8—124no—
650C2×Q8C23×D312yes—
651C2×D4—31no—
652C2×D4—34no—
653C2×D4—61no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—64no—
660C2×D4—64no—
661C2×D4—124no—
662C2×D4—242no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—32no—
666C22×C4—32no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—64no—
670C22×C4—64no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—244no—
675C22×C4D3×D411yescharacteristic
676C22×C4D3×D411yescharacteristic
677C22×C4C23×D311yescharacteristic
678Q16—64no—
679SD16—68no—
680SD16—64no—
681D8—68no—
682M16—24no—
683M16—62no—
684M16—62no—
685C2×C8—32no—
686C2×C8—32no—
687C2×C8C23×D314yes—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—31no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—31no—
699C4⋊C4—32no—
700C4⋊C4—32no—
701C4⋊C4—32no—
702C4⋊C4—31no—
703C4⋊C4—31no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—61no—
713C4⋊C4—61no—
714C4⋊C4C23×D312yes—
715C4⋊C4C23×D312yes—
716C4⋊C4C23×D312yes—
717C22⋊C4—22no—
718C22⋊C4—64no—
719C22⋊C4—64no—
720C22⋊C4—64no—
721C22⋊C4—64no—
722C22⋊C4—64no—
723C22⋊C4—64no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C42—22no—
730C42—22no—
731C42—22no—
732C42—32no—
733C42—32no—
734C42—32no—
735C42—32no—
736C42—62no—
737C42—62no—
738C42—61no—
739C42—61no—
740C42—61no—
741C42D3×D411yescharacteristic
742C42D3×D411yescharacteristic
743C42C23×D311yescharacteristic
744C42C23×D311yescharacteristic
745C22×C3—21no—
746C22×C3—21no—
747C22×C3#54812yes—
748C22×C3C23×D411yescharacteristic
749C2×D3—22no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—44no—
753C2×D3—44no—
754C2×D3—44no—
755C2×D3—88no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—42no—
760C3×C4—42no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4#54812yes—
764C3×C4#57512yes—
765C3×C4C22×#4111yescharacteristic
766C3×C4C2×2−1+411yescharacteristic
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—41no—
773Dic3—41no—
774C23—61no—
775C23—64no—
776C23—124no—
777C23—124no—
778C23—124no—
779C23C2×D3×D411yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—32no—
783Q8—42no—
784Q8—42no—
785Q8—61no—
786Q8—62no—
787Q8—62no—
788Q8—81no—
789Q8—122no—
790Q8—124no—
791Q8—242no—
792D4—32no—
793D4—64no—
794D4—61no—
795D4—64no—
796D4—64no—
797D4—124no—
798D4—124no—
799D4—124no—
800D4—242no—
801D4—242no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—61no—
815C2×C4—64no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—124no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—241no—
823C2×C4—244no—
824C2×C4—244no—
825C2×C4—242no—
826C2×C4C2×D3×D411yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4C2×D3×D411yescharacteristic
831C2×C4#100712yes—
832C2×C4D3×#4112yes—
833C2×C4C24×D311yescharacteristic
834C8—24no—
835C8—62no—
836C8—62no—
837C2×C3—22no—
838C2×C3C2×#54811yescharacteristic
839C2×C3C2×#57511yescharacteristic
840C2×C3#358511yescharacteristic
841D3—42no—
842D3—84no—
843C22—21no—
844C22—21no—
845C22—62no—
846C22—121no—
847C22—121no—
848C22—124no—
849C22—124no—
850C22—124no—
851C22—248no—
852C22#563312yes—
853C22C22×D3×D411yescharacteristic
854C4—21no—
855C4—21no—
856C4—21no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—62no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—121no—
867C4—121no—
868C4#563312yes—
869C4#577712yes—
870C4C2×#100711yescharacteristic
871C4C2×D3×#4111yescharacteristic
872C3#6132411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—122no—
875C2—244no—
876C2C2×#563311yescharacteristic
877C2C2×#577711yescharacteristic
878C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3078C2
socleC22×C3C23×D4
prime radical#79056C2
hypercenter#3078D3
hypocenterC3#61324
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
1. #86277C2semidirect
2. C2×#5585C2semidirect
3. C3×#3078C2semidirect
4. #83336C2semidirect
5. C4×#942C2semidirect
6. #81218C2semidirect
7. #81217C2semidirect
8. #81139C2semidirect
9. #81134C2semidirect
10. #81041C2semidirect
11. #81038C2semidirect
12. #79239C2semidirect
13. #79199C2semidirect
15. #79046C2semidirect
16. #78975C2semidirect
17. #78954C2semidirect
24. #5730C22semidirect
25. #5727C22semidirect
26. #5722C22semidirect
27. #5721C22semidirect
28. #5690C22semidirect
29. #5685C22semidirect
51. C3×#479C22semidirect
52. C3×#477C22semidirect
53. C3×#475C22semidirect
64. #5030C22semidirect
65. C4×#216C22semidirect
66. #5026C22semidirect
67. C4×#215C22semidirect
73. #4891C22semidirect
74. #4890C22semidirect
75. #4889C22semidirect
76. #4872C22semidirect
77. #4871C22semidirect
78. #4870C22semidirect
79. #4869C22semidirect
80. #4852C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
88. #4819C22semidirect
89. #4819C22semidirect
90. #4800C22semidirect
91. #4800C22semidirect
92. #4798C22semidirect
93. #4798C22semidirect
94. #4794C22semidirect
95. #4794C22semidirect
106. #3078D3semidirect
287. #479C2×D3semidirect
290. #477C2×D3semidirect
292. #475C2×D3semidirect
872. C3#61324semidirect

Maximal subgroups

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

subgroupindex
#862772
C2×#55852
C3×#30782
#833362
C4×#9422
#812182
#812172
#811392
#811342
#810412
#810382
#792392
#791992
#790562
#790462
#789752
#789542
#613243