Finite Group Databasebeta

← #11675117

Subgroups — #11675117

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#41×Dic6C211yesmaximal, characteristic, complemented
2C2×#5585C211yesmaximal, characteristic, complemented
3C3×C4×#137C211yesmaximal, characteristic, complemented
4#83968C212yesmaximal, complemented
5#82526C211yesmaximal, characteristic
6#82431C211yesmaximal, characteristic, complemented
7#79816C214yesmaximal, complemented
8#79753C214yesmaximal, complemented
9#79703C212yesmaximal, complemented
10#79701C212yesmaximal, complemented
11#79629C212yesmaximal, complemented
12#79621C212yesmaximal, complemented
13#79239C212yesmaximal, complemented
14#78954C212yesmaximal, complemented
15#78866C212yesmaximal, complemented
16#78526C211yesmaximal, characteristic, complemented
17M16×Dic6C211yesmaximal, characteristic, complemented
18#61324—31nomaximal, Sylow
19C2×C3×#137C2211yescharacteristic
20C3×C4×#41C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22Dic3×#41C2212yes—
23C2×#949C2212yes—
24C2×#947C2212yes—
25#5585—21no—
26#5585—21no—
27#5585—22no—
28#5585C2212yes—
29#5585C2212yes—
30#5585C2214yes—
31#5570C2211yescharacteristic, complemented
32#5569C2212yescomplemented
33Q8×Dic6C2211yescharacteristic, complemented
34#5543—21no—
35#5543C2211yescharacteristic, complemented
36#5539—22no—
37#5539C2212yescomplemented
38D4×Dic6—21no—
39D4×Dic6C2211yescharacteristic, complemented
40#5517—22no—
41#5517C2212yes—
42C2×#894—22no—
43C2×#893C2212yes—
44C2×#875—21no—
45C2×#874C2211yescharacteristic
46C2×C4×D12—21no—
47#5470—21no—
48#5470C2211yescharacteristic
49C2×C4×Dic6—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#441C2212yescomplemented
52C3×#440C2212yescomplemented
53C3×C4×Q16C2212yescomplemented
54C3×C4×SD16C2212yescomplemented
55C3×#428C2211yescharacteristic
56C3×#419C2211yescharacteristic
57C3×#417C2211yescharacteristic
58C3×C4×M16C2211yescharacteristic
59#5225C2212yes—
60#5185C2214yescomplemented
61#5185C2214yescomplemented
62#5165C2214yescomplemented
63#5165C2214yescomplemented
64#5131C2212yes—
65#5131C2212yes—
66#5118C2212yes—
67Dic3×M16C2212yes—
68#5027C2212yes—
69#5027C2212yes—
70#5022C2214yescomplemented
71#5021C2212yescomplemented
72#5020C2212yescomplemented
73#5015C2212yes—
74#5015C2212yes—
75#5001C2212yes—
76#4964C2212yes—
77#4924C2211yescharacteristic
78#4891C2214yescomplemented
79#4890C2214yescomplemented
80#4871C2214yescomplemented
81#4870C2214yescomplemented
82#4817C2214yescomplemented
83#4800C2214yescomplemented
84#4800C2214yescomplemented
85#4794C2214yescomplemented
86#4794C2214yescomplemented
87#4788C2214yescomplemented
88#4785C2214yescomplemented
89#4756C2214yescomplemented
90#4713C2214yes—
91#4701C2214yescomplemented
92#4694C2212yes—
93#4694C2212yes—
94#4679C2212yescomplemented
95C8×Dic6C2212yescomplemented
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#3078—31no—
107#3077—32no—
108#3040—32no—
109#3038—31no—
110Q8×M16—31no—
111C4×#137D311yescharacteristic, complemented
112C4×AGL(1,ℤ/8)—32no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8C2311yescharacteristic
115C22×D12—21no—
116C22×D12—21no—
117C22×D12C2312yes—
118C22×C4×D3—22no—
119C22×Dic6—21no—
120C22×Dic6D411yescharacteristic
121C3×#137—24no—
122C2×C3×Q16C2312yes—
123C2×C3×SD16C2312yes—
124C2×C3×M16C2311yescharacteristic
125C2×C3×M16C2311yescharacteristic
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×Q8C2312yes—
129C3×C4×Q8C2312yes—
130C3×C4×Q8C2311yescharacteristic
131C3×C4×Q8C2311yescharacteristic
132C3×C4×D4—21no—
133C3×C4×D4—21no—
134C3×C4×D4C2311yescharacteristic
135C3×C4×D4C2311yescharacteristic
136C3×#117—21no—
137C3×#117C2311yescharacteristic
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C42—21no—
141C2×C3×C42—21no—
142C2×C3×C42C2311yescharacteristic
143#949—28no—
144#947—22no—
145#947—22no—
146#947C2314yes—
147#947C2314yes—
148Q8×Dic3C2312yes—
149Q8×Dic3C2312yes—
150C2×#215C2314yes—
151D4×Dic3—22no—
152D4×Dic3—22no—
153D4×Dic3C2312yes—
154D4×Dic3C2312yes—
155C2×#213C2314yes—
156C2×(C2×D3)⋊C4—22no—
157C2×(C2×D3)⋊C4—22no—
158C2×(C2×D3)⋊C4—22no—
159#926—22no—
160#926C2312yes—
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3D411yescharacteristic
163#924—21no—
164#924—21no—
165#924—21no—
166#924—21no—
167#924—22no—
168C2×Dic3⋊C4—22no—
169C2×Dic3⋊C4D412yes—
170C2×C4×Dic3—22no—
171C2×C4×Dic3C2312yes—
172C2×#208C2312yes—
173#894—24no—
174#894—24no—
175#894—24no—
176#894—24no—
177#893—22no—
178#893—22no—
179#893C2314yes—
180#893C2314yes—
181#890—22no—
182#890—22no—
183#890C2312yes—
184#890C2312yes—
185#888—22no—
186#888—22no—
187#888C2312yes—
188#888C2312yes—
189#878—22no—
190#878—22no—
191#878—22no—
192#878—22no—
193#878—22no—
194#878—22no—
195#875—22no—
196#875—22no—
197#875—24no—
198#874—21no—
199#874—21no—
200#874C2312yes—
201#874C2312yes—
202C4×D12—22no—
203C4×D12—22no—
204C4×D12—24no—
205#870—22no—
206#870C2312yes—
207#869—21no—
208#869—21no—
209#869C2311yescharacteristic
210#869C2311yescharacteristic
211C4×Dic6—21no—
212C4×Dic6—21no—
213C4×Dic6—21no—
214C4×Dic6—21no—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C4×Dic6—22no—
218C4×Dic6D411yescharacteristic
219C4×Dic6D411yescharacteristic
220C4×Dic6D412yes—
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2312yes—
224C3×#107C2312yes—
225C3×#106C2312yes—
226C3×#103C2312yes—
227C3×#103C2312yes—
228C3×#103C2312yes—
229C3×#102C2312yes—
230C3×#97C2312yes—
231C3×C4×C8C2312yes—
232#835C2314yes—
233#835C2314yes—
234#821C2314yes—
235#821C2314yes—
236#821C2314yes—
237#821C2314yes—
238#815C2314yes—
239Dic3⋊C8C2314yes—
240Dic3⋊C8C2314yes—
241C8×Dic3C2314yes—
242#809C2314yes—
243#809C2314yes—
244#808C2314yes—
245#807C2314yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248C2×#137C2×D311yescharacteristic
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—62no—
262#554—61no—
263D4×Q8—31no—
264D4×Q8—61no—
265#533—32no—
266#533—31no—
267#533—61no—
268#533—62no—
269C2×#127—31no—
270C2×#124—32no—
271C2×#124—61no—
272C2×#123—62no—
273C4×#41—32no—
274C4×#41C2×D311yescharacteristic
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#479—34no—
288#478—34no—
289#478—34no—
290#477—32no—
291#476—34no—
292#475—32no—
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#441C2×D312yescomplemented
307#440—34no—
308#440C2×D312yescomplemented
309C4×Q16C2×D312yescomplemented
310C4×SD16—34no—
311C4×SD16C2×D312yescomplemented
312C4×D8—34no—
313#428—32no—
314#428C2×D311yescharacteristic
315#423—32no—
316#423—31no—
317#419—32no—
318#419C2×D311yescharacteristic
319#418—32no—
320#418—32no—
321#418—32no—
322#417C2×D311yescharacteristic
323C4×M16—32no—
324C4×M16C2×D311yescharacteristic
325C23×D3—22no—
326C3×#41—22no—
327C3×#41#4114yes—
328C2×C3×Q8—21no—
329C2×C3×Q8—22no—
330C2×C3×Q8—22no—
331C2×C3×Q8C2412yes—
332C2×C3×Q8C2411yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4C2411yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2411yescharacteristic
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3C2×D412yes—
346C22×Dic3C2×D412yes—
347C2×D12—24no—
348C2×D12—24no—
349C2×D12—22no—
350C2×D12—22no—
351C2×D12—22no—
352C2×D12—22no—
353C2×D12—22no—
354C2×D12—44no—
355C2×D12—82no—
356C2×D12C2414yes—
357C2×C4×D3—24no—
358C2×C4×D3—24no—
359C2×C4×D3—84no—
360C2×Dic6—21no—
361C2×Dic6—22no—
362C2×Dic6—21no—
363C2×Dic6—22no—
364C2×Dic6—42no—
365C2×Dic6—44no—
366C2×Dic6C2×D411yescharacteristic
367C2×Dic6C2×D411yescharacteristic
368C2×Dic6C2×D412yes—
369C3×Q16—24no—
370C3×SD16—24no—
371C3×M16—22no—
372C3×M16—22no—
373C2×C3×C8C2412yes—
374C2×C3×C8C2412yes—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—22no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4C2412yes—
381C3×C4⋊C4C2411yescharacteristic
382C3×C4⋊C4C2411yescharacteristic
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C42—21no—
387C3×C42—21no—
388C3×C42—21no—
389C3×C42—22no—
390C3×C42—22no—
391C3×C42C2×D411yescharacteristic
392C3×C42C2×D411yescharacteristic
393C3×C42C2411yescharacteristic
394C3×C42C2411yescharacteristic
395#217—22no—
396#217—22no—
397#217—22no—
398#215—28no—
399#213—28no—
400(C2×D3)⋊C4—24no—
401(C2×D3)⋊C4—24no—
402(C2×D3)⋊C4—24no—
403(C2×D3)⋊C4—24no—
404(C2×D3)⋊C4—24no—
405(C2×D3)⋊C4—24no—
406C4⋊Dic3—21no—
407C4⋊Dic3—21no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3C2×D411yescharacteristic
413C4⋊Dic3C2×D411yescharacteristic
414C4⋊Dic3C2×D412yes—
415C4⋊Dic3C2412yes—
416C4⋊Dic3C2412yes—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—22no—
423Dic3⋊C4C2×D412yes—
424Dic3⋊C4C2×D412yes—
425Dic3⋊C4C2×D412yes—
426Dic3⋊C4C2×D412yes—
427C4×Dic3—22no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430C4×Dic3C2×D412yes—
431C4×Dic3C2×D412yes—
432C4×Dic3C2412yes—
433C4×Dic3C2412yes—
434#208—24no—
435C2×C3⋊C8C2414yes—
436C2×#41C22×D311yescharacteristic
437C22×Q8—31no—
438C22×Q8—61no—
439C22×Q8C22×D311yescharacteristic
440C22×D4—32no—
441C22×D4—61no—
442C22×D4—61no—
443C23×C4—62no—
444#137—24no—
445AGL(1,ℤ/8)—68no—
446C2×Q16C22×D312yes—
447C2×SD16—34no—
448C2×SD16C22×D312yes—
449C2×D8—34no—
450C2×M16—32no—
451C2×M16C22×D311yescharacteristic
452C2×M16C22×D311yescharacteristic
453C4⋊Q8—32no—
454C4⋊Q8—32no—
455C4⋊Q8—31no—
456C4⋊Q8—31no—
457C4⋊Q8—61no—
458C4⋊Q8—61no—
459C4⋊Q8—62no—
460C4⋊Q8—62no—
461#127—32no—
462#127—32no—
463#127—61no—
464#127—61no—
465#125—32no—
466#125—32no—
467#125—32no—
468#125—62no—
469#125—62no—
470#125—62no—
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—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—61no—
489C22⋊Q8—62no—
490C22⋊Q8—61no—
491C22⋊Q8—61no—
492C22⋊Q8—61no—
493C4×Q8—21no—
494C4×Q8—21no—
495C4×Q8—31no—
496C4×Q8—32no—
497C4×Q8—31no—
498C4×Q8—31no—
499C4×Q8—31no—
500C4×Q8—32no—
501C4×Q8—32no—
502C4×Q8—32no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8—61no—
509C4×Q8—61no—
510C4×Q8C22×D312yes—
511C4×Q8C22×D312yes—
512C4×Q8C22×D311yescharacteristic
513C4×Q8C22×D311yescharacteristic
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—32no—
517C4×D4—32no—
518C4×D4—34no—
519C4×D4—34no—
520C4×D4—62no—
521C4×D4—64no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4C22×D311yescharacteristic
528C4×D4C22×D311yescharacteristic
529#117—21no—
530#117—32no—
531#117—62no—
532#117C22×D311yescharacteristic
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—21no—
544C2×C42—32no—
545C2×C42—62no—
546C2×C42C22×D311yescharacteristic
547#107—34no—
548#107C22×D312yes—
549#106—34no—
550#106C22×D312yes—
551C4⋊C8—34no—
552C4⋊C8—34no—
553C4⋊C8—32no—
554C4⋊C8—32no—
555#103—34no—
556#103—34no—
557#103C22×D312yes—
558#103C22×D312yes—
559#103C22×D312yes—
560#102—34no—
561#102—34no—
562#102—34no—
563#102—34no—
564#102—34no—
565#102—34no—
566#102C22×D312yes—
567#97—34no—
568#97C22×D312yes—
569C4×C8—34no—
570C4×C8C22×D312yes—
571C23×C3—21no—
572C23×C3C22×D411yescharacteristic
573C22×D3—24no—
574C22×D3—44no—
575C22×D3—44no—
576C22×D3—44no—
577C3×Q8—21no—
578C3×Q8—22no—
579C3×Q8—22no—
580C3×Q8—42no—
581C3×Q8C2×#4112yes—
582C3×D4—24no—
583C3×D4—21no—
584C3×D4C2×#4112yes—
585C2×C3×C4—21no—
586C2×C3×C4—24no—
587C2×C3×C4—22no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—41no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—81no—
597C2×C3×C4C22×D411yescharacteristic
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C2×#4112yes—
603C2×C3×C42−1+412yes—
604C2×C3×C4C2511yescharacteristic
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—42no—
608C2×Dic3—42no—
609C2×Dic3—44no—
610C2×Dic3—82no—
611C2×Dic3C22×D412yes—
612C2×Dic3C22×D412yes—
613C2×Dic3C22×D412yes—
614C2×Dic3C22×D412yes—
615D12—24no—
616D12—24no—
617D12—44no—
618D12—44no—
619D12—44no—
620D12—82no—
621D12—82no—
622C4×D3—84no—
623C4×D3—84no—
624Dic6—22no—
625Dic6—22no—
626Dic6—42no—
627Dic6—44no—
628Dic6—42no—
629Dic6—82no—
630Dic6—81no—
631C3×C8—22no—
632C3×C8—22no—
633C3⋊C8—24no—
634C24—62no—
635#41—22no—
636#41#23514yes—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—31no—
641C2×Q8—31no—
642C2×Q8—32no—
643C2×Q8—62no—
644C2×Q8—62no—
645C2×Q8—61no—
646C2×Q8—61no—
647C2×Q8—122no—
648C2×Q8—124no—
649C2×Q8C23×D312yes—
650C2×Q8C23×D311yescharacteristic
651C2×D4—21no—
652C2×D4—34no—
653C2×D4—64no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—64no—
660C2×D4—124no—
661C2×D4—242no—
662C2×D4C23×D311yescharacteristic
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—32no—
669C22×C4—32no—
670C22×C4—64no—
671C22×C4—64no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—244no—
675C22×C4D3×D411yescharacteristic
676C22×C4D3×D411yescharacteristic
677C22×C4C23×D311yescharacteristic
678Q16—24no—
679SD16—24no—
680SD16—68no—
681D8—68no—
682M16—22no—
683M16—22no—
684M16—64no—
685C2×C8—34no—
686C2×C8C23×D312yes—
687C2×C8C23×D312yes—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—31no—
694C4⋊C4—32no—
695C4⋊C4—32no—
696C4⋊C4—31no—
697C4⋊C4—32no—
698C4⋊C4—32no—
699C4⋊C4—32no—
700C4⋊C4—32no—
701C4⋊C4—32no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—61no—
712C4⋊C4—62no—
713C4⋊C4—61no—
714C4⋊C4C23×D311yescharacteristic
715C4⋊C4C23×D311yescharacteristic
716C4⋊C4C23×D312yes—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—64no—
721C22⋊C4—64no—
722C22⋊C4—64no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—64no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—22no—
733C42—22no—
734C42—32no—
735C42—32no—
736C42—32no—
737C42—32no—
738C42—62no—
739C42—62no—
740C42—62no—
741C42D3×D411yescharacteristic
742C42D3×D411yescharacteristic
743C42C23×D311yescharacteristic
744C42C23×D311yescharacteristic
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3#54812yes—
751C22×C3C23×D411yescharacteristic
752C2×D3—44no—
753C2×D3—44no—
754C2×D3—44no—
755C2×D3—88no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—22no—
759C3×C4—21no—
760C3×C4—41no—
761C3×C4—42no—
762C3×C4—42no—
763C3×C4—41no—
764C3×C4#54812yes—
765C3×C4#57512yes—
766C3×C4C22×#4111yescharacteristic
767C3×C4C2×2−1+411yescharacteristic
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—42no—
773Dic3—42no—
774C23—21no—
775C23—64no—
776C23—124no—
777C23—124no—
778C23—124no—
779C23C2×D3×D411yescharacteristic
780Q8—21no—
781Q8—22no—
782Q8—22no—
783Q8—42no—
784Q8—62no—
785Q8—62no—
786Q8—122no—
787Q8—124no—
788Q8—122no—
789Q8—241no—
790Q8—242no—
791Q8C2×#23512yes—
792D4—24no—
793D4—21no—
794D4—64no—
795D4—64no—
796D4—124no—
797D4—124no—
798D4—124no—
799D4—242no—
800D4—242no—
801D4C2×#23512yes—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—81no—
820C2×C4—122no—
821C2×C4—122no—
822C2×C4—124no—
823C2×C4—244no—
824C2×C4—244no—
825C2×C4—242no—
826C2×C4C2×#23512yes—
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4C2×D3×D411yescharacteristic
831C2×C4C2×D3×D411yescharacteristic
832C2×C4#101012yes—
833C2×C4C24×D311yescharacteristic
834C8—22no—
835C8—22no—
836C8—64no—
837C2×C3—22no—
838C2×C3—42no—
839C2×C3C2×#54811yescharacteristic
840C2×C3C2×#57511yescharacteristic
841C2×C3#358511yescharacteristic
842D3—84no—
843C22—21no—
844C22—21no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—124no—
849C22—124no—
850C22—124no—
851C22—248no—
852C22#555212yes—
853C22C22×D3×D411yescharacteristic
854C4—21no—
855C4—21no—
856C4—21no—
857C4—22no—
858C4—41no—
859C4—42no—
860C4—41no—
861C4—42no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—122no—
867C4—122no—
868C4#555212yes—
869C4#577712yes—
870C4C22×#23511yescharacteristic
871C4C2×#101011yescharacteristic
872C3#6132411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—42no—
875C2—244no—
876C2C2×#555211yescharacteristic
877C2C2×#577711yescharacteristic
878C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×#137C2
socleC22×C3C23×D4
prime radical#82526C2
hypercenterC4×#137D3
hypocenterC3#61324
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
1. #41×Dic6C2semidirect
2. C2×#5585C2semidirect
3. C3×C4×#137C2semidirect
4. #83968C2semidirect
6. #82431C2semidirect
7. #79816C2semidirect
8. #79753C2semidirect
9. #79703C2semidirect
10. #79701C2semidirect
11. #79629C2semidirect
12. #79621C2semidirect
13. #79239C2semidirect
14. #78954C2semidirect
15. #78866C2semidirect
16. #78526C2semidirect
17. M16×Dic6C2semidirect
31. #5570C22semidirect
32. #5569C22semidirect
33. Q8×Dic6C22semidirect
35. #5543C22semidirect
37. #5539C22semidirect
39. D4×Dic6C22semidirect
51. C3×#441C22semidirect
52. C3×#440C22semidirect
53. C3×C4×Q16C22semidirect
54. C3×C4×SD16C22semidirect
60. #5185C22semidirect
61. #5185C22semidirect
62. #5165C22semidirect
63. #5165C22semidirect
70. #5022C22semidirect
71. #5021C22semidirect
72. #5020C22semidirect
78. #4891C22semidirect
79. #4890C22semidirect
80. #4871C22semidirect
81. #4870C22semidirect
82. #4817C22semidirect
83. #4800C22semidirect
84. #4800C22semidirect
85. #4794C22semidirect
86. #4794C22semidirect
87. #4788C22semidirect
88. #4785C22semidirect
89. #4756C22semidirect
91. #4701C22semidirect
94. #4679C22semidirect
95. C8×Dic6C22semidirect
111. C4×#137D3semidirect
306. #441C2×D3semidirect
308. #440C2×D3semidirect
309. C4×Q16C2×D3semidirect
311. C4×SD16C2×D3semidirect
872. C3#61324semidirect

Maximal subgroups

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

subgroupindex
#41×Dic62
C2×#55852
C3×C4×#1372
#839682
#825262
#824312
#798162
#797532
#797032
#797012
#796292
#796212
#792392
#789542
#788662
#785262
M16×Dic62
#613243