Finite Group Databasebeta

← #11664156

Subgroups — #11664156

Order 768.

2194 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86261C211yesmaximal, characteristic, complemented
2C4×#1004C211yesmaximal, characteristic, complemented
3C3×#3077C211yesmaximal, characteristic, complemented
4#83349C211yesmaximal, characteristic, complemented
5C2×#5015C211yesmaximal, characteristic, complemented
6#81146C214yesmaximal, complemented
7#81144C214yesmaximal, complemented
8#81046C212yesmaximal, complemented
9#81045C212yesmaximal, complemented
10#80951C212yesmaximal, complemented
11#80948C212yesmaximal, complemented
12#79219C212yesmaximal, complemented
13#79201C212yesmaximal, complemented
14#79056C211yesmaximal, characteristic, complemented
15#79040C211yesmaximal, characteristic, complemented
16#78928C212yesmaximal, complemented
17#78915C212yesmaximal, complemented
18#60590—31nomaximal, Sylow
19C2×#1004C2211yescharacteristic
20C3×#533C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22#5798C2211yescharacteristic
23C22×#213C2212yes—
24C2×C4×#67—22no—
25C2×#908C2212yes—
26#5725C2212yescomplemented
27#5725C2212yescomplemented
28#5697C2214yescomplemented
29#5630—22no—
30#5630—22no—
31#5585—21no—
32#5585—21no—
33#5577—21no—
34#5577—21no—
35#5546—21no—
36#5546C2212yescomplemented
37#5545—21no—
38#5545C2212yescomplemented
39C4×D3×D4—21no—
40C4×D3×D4C2212yescomplemented
41C4×#237—21no—
42C4×#237C2212yescomplemented
43#5525C2212yes—
44#5521C2212yescomplemented
45#5504C2211yescharacteristic
46#5504C2211yescharacteristic
47#5486—22no—
48C2×#874C2211yescharacteristic, complemented
49C4×#235C2211yescharacteristic
50C4×#235C2211yescharacteristic
51C3×#478C2214yescomplemented
52C3×#476C2212yescomplemented
53C3×#474C2212yescomplemented
54C3×#428C2212yescomplemented
55C3×#423C2211yescharacteristic, complemented
56C3×#418C2212yes—
57#5131C2212yescomplemented
58#5129C2212yes—
59#5122C2212yescomplemented
60#5094C2211yescharacteristic, complemented
61#5091C2211yescharacteristic, complemented
62#5087C2211yescharacteristic, complemented
63#5084C2211yescharacteristic, complemented
64#5066C2212yescomplemented
65#5063C2212yescomplemented
66#5015C2212yescomplemented
67#5015C2212yescomplemented
68#5015C2214yescomplemented
69#5002C2212yes—
70#4998C2212yescomplemented
71C2×#809C2212yescomplemented
72C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
73#4889C2214yescomplemented
74#4885C2214yescomplemented
75#4882C2214yescomplemented
76#4872C2214yescomplemented
77#4869C2214yescomplemented
78#4866C2214yescomplemented
79#4863C2214yescomplemented
80#4852C2214yescomplemented
81#4848C2212yescomplemented
82#4848C2212yescomplemented
83#4843C2212yescomplemented
84#4843C2212yescomplemented
85#4840C2214yescomplemented
86#4835C2212yescomplemented
87#4833C2212yescomplemented
88#4785C2214yescomplemented
89#4785C2214yescomplemented
90#4781C2214yescomplemented
91#4781C2214yescomplemented
92#4773C2214yescomplemented
93#4773C2214yescomplemented
94#4756C2214yescomplemented
95#4756C2214yescomplemented
96#3508—31no—
97C4×H(5,𝔽2)—31no—
98#3122—34no—
99#3119—34no—
100#3115—32no—
101#3109—32no—
102#3106—32no—
103#3100—32no—
104#3096—32no—
105#3077D311yescharacteristic, complemented
106#3076—31no—
107#3038—31no—
108C2×#459—31no—
109#3008—32no—
110#2948—32no—
111#2946—32no—
112#2925—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C22×#67—22no—
116C2×#239—22no—
117C2×#239—22no—
118#1004—24no—
119#1004—24no—
120C2×#237—21no—
121C2×#237C2312yes—
122C2×D3×D4—21no—
123C2×D3×D4C2312yes—
124C2×#235C2311yescharacteristic
125C2×#235C2311yescharacteristic
126C22×D12—21no—
127C22×D12—21no—
128C22×D12C2312yes—
129C22×C4×D3—22no—
130C2×C3×M16C2312yes—
131C3×C4⋊Q8C2311yescharacteristic
132C3×C4⋊Q8C2311yescharacteristic
133C3×#125C2312yes—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C4×Q8—21no—
137C3×C4×Q8—21no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4C2312yes—
141C3×C4×D4C2312yes—
142C3×#117C2312yes—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×C3×C42C2311yescharacteristic
146C2×#217—22no—
147#947—22no—
148#947—22no—
149D4×Dic3—21no—
150D4×Dic3—21no—
151D4×Dic3C2312yes—
152D4×Dic3C2312yes—
153C2×#213—28no—
154C2×#213C2314yes—
155C2×#213C2314yes—
156C4×#67—21no—
157C4×#67—21no—
158C4×#67—22no—
159C4×#67—22no—
160C4×#67—22no—
161C4×#67—22no—
162C4×#67—22no—
163C4×#67—22no—
164C4×#67D412yes—
165C4×#67D412yes—
166C2×(C2×D3)⋊C4—22no—
167#926C2311yescharacteristic
168#926C2311yescharacteristic
169C2×Dic3⋊C4—22no—
170C2×C4×Dic3—22no—
171C22×C3⋊C8C2312yes—
172#908—28no—
173C2×D24C2314yes—
174C2×#204C2314yes—
175#895—22no—
176#895—22no—
177#895—24no—
178#895—24no—
179#895C2314yes—
180#895C2314yes—
181#894—24no—
182#894—24no—
183#893—21no—
184#893—22no—
185#893—22no—
186#893C2312yes—
187#893C2314yes—
188#893C2314yes—
189#892—21no—
190#892C2312yes—
191D3×C4⋊C4—21no—
192D3×C4⋊C4C2312yes—
193#887—21no—
194#887C2312yes—
195#882—24no—
196#67⋊C4—22no—
197#67⋊C4—22no—
198#67⋊C4—22no—
199#67⋊C4—22no—
200D3×C22⋊C4—22no—
201D3×C22⋊C4—24no—
202D3×C22⋊C4—22no—
203#877—22no—
204#877—22no—
205#875—22no—
206#874—22no—
207#874—21no—
208#874—21no—
209#874C2312yes—
210#874C2312yes—
211C4×D12—22no—
212C4×D12—22no—
213C4×D12D411yescharacteristic
214C4×D12D411yescharacteristic
215C4×D12C2311yescharacteristic
216C4×D12C2311yescharacteristic
217#872—21no—
218#872C2312yes—
219C42×D3—21no—
220C42×D3C2312yes—
221C4×Dic6D411yescharacteristic
222C4×Dic6D411yescharacteristic
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2311yescharacteristic
225C3×#107C2314yes—
226C3×#106C2314yes—
227C3×C4⋊C8C2312yes—
228C3×C4⋊C8C2312yes—
229C3×#102C2314yes—
230C3×#102C2314yes—
231#821C2314yes—
232#821C2314yes—
233(C2×D3)⋊C8C2314yes—
234(C2×D3)⋊C8C2314yes—
235#815C2314yes—
236C8×Dic3C2314yes—
237#810C2312yes—
238#810C2312yes—
239#809C2314yes—
240#809C2312yes—
241#809C2314yes—
242#809C2312yes—
243#808C2312yes—
244#808C2312yes—
245#807C2312yes—
246#807C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248C4⋊(C3⋊C8)C2311yescharacteristic
249C4⋊(C3⋊C8)C2311yescharacteristic
250C2×H(5,𝔽2)—31no—
251C2×AGL(1,ℤ/8)—32no—
252C22×D8—32no—
253#559—61no—
254#559—61no—
255#550—61no—
256#550—61no—
257#546—62no—
258#546—62no—
259#540—34no—
260#535—32no—
261#533C2×D311yescharacteristic, complemented
262#532—32no—
263#532—32no—
264C2×#127—31no—
265#520—31no—
266#520—32no—
267#520—31no—
268#520—61no—
269#518—31no—
270#518—32no—
271#518—32no—
272#518—62no—
273#518—61no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—31no—
277C4×#41—61no—
278C2×C4×D4—32no—
279C2×C4×D4—61no—
280C2×C4×D4—62no—
281C2×C4×D4C2×D311yescharacteristic
282#482—34no—
283#482—34no—
284#481—34no—
285#480—34no—
286#479—32no—
287#478—32no—
288#478C2×D314yescomplemented
289#477—31no—
290#476—31no—
291#476C2×D312yescomplemented
292#475—31no—
293#474—31no—
294#474C2×D312yescomplemented
295#460—32no—
296#460—32no—
297#459—32no—
298#459—32no—
299#459—34no—
300#459—32no—
301#459—32no—
302#449—34no—
303#449—34no—
304#447—34no—
305#447—34no—
306#442—34no—
307#442—34no—
308#442—34no—
309#440—34no—
310C4×SD16—34no—
311C4×D8—34no—
312C4×D8—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428C2×D312yescomplemented
318#427—32no—
319#423C2×D311yescharacteristic, complemented
320C2×C4⋊C8—31no—
321#418—32no—
322#418C2×D312yes—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C24×C3—21no—
328C23×D3—22no—
329C23×D3—22no—
330C2×C3×Q8—21no—
331C2×C3×Q8—21no—
332C2×C3×D4—21no—
333C2×C3×D4—22no—
334C2×C3×D4#4114yescomplemented
335C2×C3×D4C2412yes—
336C22×C3×C4—21no—
337C22×C3×C4—22no—
338C22×C3×C4—22no—
339C22×C3×C4—82no—
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2411yescharacteristic
343C2×#67—216no—
344C2×#67—21no—
345C2×#67—22no—
346C2×#67—22no—
347C2×#67C2×D412yes—
348C22×Dic3—22no—
349C22×Dic3—22no—
350C22×Dic3—22no—
351#239—84no—
352#239—84no—
353#237—28no—
354#237—24no—
355#237—24no—
356D3×D4—28no—
357D3×D4—24no—
358D3×D4—24no—
359#235—22no—
360#235—22no—
361#235—22no—
362#235#4114yescomplemented
363C2×D12—24no—
364C2×D12—24no—
365C2×D12—22no—
366C2×D12—22no—
367C2×D12—22no—
368C2×D12—24no—
369C2×D12—24no—
370C2×D12—22no—
371C2×D12—22no—
372C2×D12—82no—
373C2×D12—82no—
374C2×D12C2×D411yescharacteristic
375C2×D12C2414yes—
376C2×D12C2411yescharacteristic
377C2×C4×D3—21no—
378C2×C4×D3—21no—
379C2×C4×D3—22no—
380C2×C4×D3—21no—
381C2×C4×D3—24no—
382C2×C4×D3—24no—
383C2×C4×D3—22no—
384C2×C4×D3—84no—
385C2×C4×D3C2×D412yes—
386C2×C4×D3C2×D412yes—
387C2×C4×D3C2412yes—
388C2×Dic6C2×D411yescharacteristic
389C2×Dic6C2411yescharacteristic
390C3×M16—24no—
391C2×C3×C8C2414yes—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—22no—
396C3×C4⋊C4—22no—
397C3×C4⋊C4C2412yes—
398C3×C4⋊C4C2412yes—
399C3×C4⋊C4C2412yes—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4—22no—
403C3×C42—22no—
404C3×C42C2×D411yescharacteristic
405C3×C42C2×D411yescharacteristic
406C3×C42C2411yescharacteristic
407C3×C42C2411yescharacteristic
408#217—21no—
409#217—22no—
410#217—22no—
411#217C2×D412yes—
412#213—28no—
413#213—28no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—24no—
418(C2×D3)⋊C4—24no—
419(C2×D3)⋊C4—24no—
420(C2×D3)⋊C4—24no—
421(C2×D3)⋊C4—22no—
422(C2×D3)⋊C4C2×D412yes—
423(C2×D3)⋊C4C2×D412yes—
424C4⋊Dic3C2×D411yescharacteristic
425C4⋊Dic3C2×D411yescharacteristic
426C4⋊Dic3C2411yescharacteristic
427C4⋊Dic3C2411yescharacteristic
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4C2×D412yes—
433Dic3⋊C4C2×D412yes—
434C4×Dic3—21no—
435C4×Dic3—21no—
436C4×Dic3—21no—
437C4×Dic3—22no—
438C4×Dic3—22no—
439C4×Dic3C2×D412yes—
440C4×Dic3C2×D412yes—
441C4×Dic3C2412yes—
442C2×C3⋊C8—24no—
443C2×C3⋊C8C2412yes—
444C2×C3⋊C8C2412yes—
445D24—28no—
446#204—28no—
447H(5,𝔽2)—64no—
448H(5,𝔽2)—64no—
449C2×#41—31no—
450C2×#41—32no—
451C2×#41—31no—
452C2×#41—62no—
453C2×#41—62no—
454C2×#41—61no—
455C22×D4—32no—
456C22×D4—32no—
457C22×D4—61no—
458C22×D4—62no—
459C22×D4—61no—
460C22×D4—61no—
461C22×D4C22×D311yescharacteristic
462C23×C4—21no—
463C23×C4—62no—
464AGL(1,ℤ/8)—68no—
465C2×SD16—34no—
466C2×D8—34no—
467C2×D8—34no—
468C2×D8—34no—
469C2×D8—68no—
470C2×M16C22×D312yes—
471C22×C8—32no—
472C4⋊Q8C22×D311yescharacteristic
473C4⋊Q8C22×D311yescharacteristic
474#127—32no—
475#127—32no—
476#127—62no—
477#127—61no—
478#127—61no—
479#125C22×D312yes—
480#124—62no—
481#124—62no—
482#124—62no—
483#123—64no—
484#123—64no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487#121—34no—
488#121—34no—
489#121—64no—
490#121—64no—
491#121—62no—
492#121—62no—
493#120—64no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—31no—
497C4×Q8—31no—
498C4×Q8—32no—
499C4×Q8—31no—
500C4×Q8—31no—
501C4×Q8—61no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—32no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—34no—
510C4×D4—34no—
511C4×D4—31no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—31no—
515C4×D4—62no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—61no—
527C4×D4—62no—
528C4×D4—61no—
529C4×D4—61no—
530C4×D4—62no—
531C4×D4—62no—
532C4×D4—61no—
533C4×D4—61no—
534C4×D4C22×D312yes—
535C4×D4C22×D312yes—
536#117—31no—
537#117—32no—
538#117—31no—
539#117—32no—
540#117—62no—
541#117—62no—
542#117—61no—
543#117—61no—
544#117C22×D312yes—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—61no—
547C2×C4⋊C4—62no—
548C2×C4⋊C4C22×D311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—62no—
551C2×C22⋊C4—64no—
552C2×C22⋊C4—62no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C42—32no—
556C2×C42—62no—
557C2×C42—61no—
558C2×C42C22×D311yescharacteristic
559#107—32no—
560#107—32no—
561#107C22×D314yes—
562#106—32no—
563#106—32no—
564#106C22×D314yes—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8C22×D312yes—
569C4⋊C8C22×D312yes—
570#103—32no—
571#103—32no—
572#102—34no—
573#102—34no—
574#102—34no—
575#102—34no—
576#102—32no—
577#102—32no—
578#102C22×D314yes—
579#102C22×D314yes—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—22no—
585C23×C3—24no—
586C23×C3—81no—
587C23×C3—81no—
588C23×C3C22×D411yescharacteristic
589C22×D3—21no—
590C22×D3—28no—
591C22×D3—24no—
592C22×D3—44no—
593C22×D3—82no—
594C22×D3—82no—
595C22×D3—82no—
596C22×D3—82no—
597C22×D3C22×D412yes—
598C3×Q8—42no—
599C3×Q8—42no—
600C3×D4—24no—
601C3×D4—22no—
602C3×D4C2×#4114yes—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—41no—
608C2×C3×C4—44no—
609C2×C3×C4—82no—
610C2×C3×C4—81no—
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C2×#4112yes—
617C2×C3×C4C2×#4112yes—
618C2×C3×C4C2511yescharacteristic
619#67—28no—
620#67—28no—
621#67—24no—
622#67—24no—
623C2×Dic3—28no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—82no—
628C2×Dic3—82no—
629C2×Dic3C22×D412yes—
630C2×Dic3C22×D412yes—
631C2×Dic3C22×D412yes—
632D12—22no—
633D12—21no—
634D12—24no—
635D12—24no—
636D12—44no—
637D12—44no—
638D12—44no—
639D12—82no—
640D12—82no—
641D12—84no—
642D12—84no—
643D12C2×#4112yes—
644C4×D3—24no—
645C4×D3—24no—
646C4×D3—22no—
647C4×D3—22no—
648C4×D3—42no—
649C4×D3—42no—
650C4×D3—82no—
651C4×D3—84no—
652C4×D3—84no—
653C4×D3—81no—
654C4×D3—82no—
655Dic6—22no—
656Dic6—21no—
657Dic6C2×#4112yes—
658C3×C8—24no—
659C3⋊C8—22no—
660C3⋊C8—22no—
661C24—21no—
662C24—62no—
663C24—62no—
664#41—34no—
665#41—64no—
666#41—68no—
667#41—64no—
668#41—62no—
669#41—62no—
670#41—62no—
671#41—244no—
672#41—244no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—31no—
676C2×Q8—31no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—32no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—34no—
683C2×D4—64no—
684C2×D4—64no—
685C2×D4—62no—
686C2×D4—64no—
687C2×D4—68no—
688C2×D4—62no—
689C2×D4—616no—
690C2×D4—61no—
691C2×D4—64no—
692C2×D4—62no—
693C2×D4—62no—
694C2×D4—62no—
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—64no—
698C2×D4—64no—
699C2×D4—242no—
700C2×D4—242no—
701C2×D4#23914yescomplemented
702C2×D4C23×D312yes—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—62no—
710C22×C4—64no—
711C22×C4—64no—
712C22×C4—62no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—61no—
717C22×C4—61no—
718C22×C4—61no—
719C22×C4—82no—
720C22×C4—244no—
721C22×C4D3×D411yescharacteristic
722C22×C4D3×D411yescharacteristic
723C22×C4C23×D311yescharacteristic
724SD16—68no—
725D8—68no—
726D8—68no—
727D8—68no—
728M16—24no—
729C2×C8—32no—
730C2×C8—32no—
731C2×C8—64no—
732C2×C8C23×D314yes—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—22no—
737C4⋊C4—22no—
738C4⋊C4—31no—
739C4⋊C4—32no—
740C4⋊C4—31no—
741C4⋊C4—32no—
742C4⋊C4—31no—
743C4⋊C4—31no—
744C4⋊C4—62no—
745C4⋊C4—62no—
746C4⋊C4—61no—
747C4⋊C4—61no—
748C4⋊C4C23×D312yes—
749C4⋊C4C23×D312yes—
750C4⋊C4C23×D312yes—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—32no—
755C22⋊C4—32no—
756C22⋊C4—32no—
757C22⋊C4—62no—
758C22⋊C4—64no—
759C22⋊C4—64no—
760C22⋊C4—64no—
761C22⋊C4—64no—
762C22⋊C4—62no—
763C22⋊C4—62no—
764C22⋊C4—62no—
765C22⋊C4—61no—
766C22⋊C4—61no—
767C22⋊C4—61no—
768C42—22no—
769C42—32no—
770C42—32no—
771C42—32no—
772C42—62no—
773C42—62no—
774C42—61no—
775C42—61no—
776C42—61no—
777C42D3×D411yescharacteristic
778C42D3×D411yescharacteristic
779C42C23×D311yescharacteristic
780C42C23×D311yescharacteristic
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—24no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—84no—
787C22×C3#52512yes—
788C22×C3C23×D411yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—41no—
794C2×D3—41no—
795C2×D3—44no—
796C2×D3—44no—
797C2×D3—44no—
798C2×D3—88no—
799C2×D3—164no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—42no—
806C3×C4#52512yes—
807C3×C4#57612yes—
808C3×C4C22×#4111yescharacteristic
809C3×C4C22×#4111yescharacteristic
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—22no—
814Dic3—41no—
815Dic3—41no—
816C23—22no—
817C23—24no—
818C23—32no—
819C23—68no—
820C23—61no—
821C23—64no—
822C23—81no—
823C23—81no—
824C23—124no—
825C23—242no—
826C23—242no—
827C23—242no—
828C23—242no—
829C23C2×D3×D411yescharacteristic
830Q8—32no—
831Q8—42no—
832Q8—42no—
833Q8—61no—
834Q8—62no—
835D4—22no—
836D4—24no—
837D4—32no—
838D4—68no—
839D4—68no—
840D4—64no—
841D4—64no—
842D4—61no—
843D4—64no—
844D4—64no—
845D4—62no—
846D4—124no—
847D4—124no—
848D4—124no—
849D4—242no—
850D4—242no—
851D4—244no—
852D4—244no—
853D4C2×#23914yes—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—41no—
862C2×C4—44no—
863C2×C4—68no—
864C2×C4—61no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—64no—
868C2×C4—64no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—82no—
872C2×C4—81no—
873C2×C4—122no—
874C2×C4—122no—
875C2×C4—241no—
876C2×C4—242no—
877C2×C4—244no—
878C2×C4—244no—
879C2×C4—242no—
880C2×C4—242no—
881C2×C4—242no—
882C2×C4C2×D3×D411yescharacteristic
883C2×C4C2×D3×D411yescharacteristic
884C2×C4C2×D3×D411yescharacteristic
885C2×C4C2×D3×D411yescharacteristic
886C2×C4C2×D3×D411yescharacteristic
887C2×C4C2×#23912yes—
888C2×C4D3×#4112yes—
889C2×C4C24×D311yescharacteristic
890C8—24no—
891C8—62no—
892C8—62no—
893C2×C3—22no—
894C2×C3—44no—
895C2×C3C2×#52511yescharacteristic
896C2×C3C2×#57611yescharacteristic
897C2×C3#358511yescharacteristic
898D3—42no—
899D3—42no—
900D3—84no—
901C22—21no—
902C22—21no—
903C22—24no—
904C22—42no—
905C22—42no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—84no—
911C22—121no—
912C22—121no—
913C22—124no—
914C22—124no—
915C22—124no—
916C22—248no—
917C22—484no—
918C22#562712yes—
919C22C22×D3×D411yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—121no—
931C4—121no—
932C4#562712yes—
933C4#577412yes—
934C4C22×#23911yescharacteristic
935C4C2×D3×#4111yescharacteristic
936C3#6059011yescharacteristic, complemented, Sylow
937C2—22no—
938C2—44no—
939C2—122no—
940C2—122no—
941C2—244no—
942C2C2×#562711yescharacteristic
943C2C2×#577411yescharacteristic
944C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
hypercenter#3077D3
hypocenterC3#60590
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. #86261C2semidirect
2. C4×#1004C2semidirect
3. C3×#3077C2semidirect
4. #83349C2semidirect
5. C2×#5015C2semidirect
6. #81146C2semidirect
7. #81144C2semidirect
8. #81046C2semidirect
9. #81045C2semidirect
10. #80951C2semidirect
11. #80948C2semidirect
12. #79219C2semidirect
13. #79201C2semidirect
14. #79056C2semidirect
15. #79040C2semidirect
16. #78928C2semidirect
17. #78915C2semidirect
20. C3×#533C22semidirect
26. #5725C22semidirect
27. #5725C22semidirect
28. #5697C22semidirect
36. #5546C22semidirect
38. #5545C22semidirect
40. C4×D3×D4C22semidirect
42. C4×#237C22semidirect
44. #5521C22semidirect
48. C2×#874C22semidirect
51. C3×#478C22semidirect
52. C3×#476C22semidirect
53. C3×#474C22semidirect
54. C3×#428C22semidirect
55. C3×#423C22semidirect
57. #5131C22semidirect
59. #5122C22semidirect
60. #5094C22semidirect
61. #5091C22semidirect
62. #5087C22semidirect
63. #5084C22semidirect
64. #5066C22semidirect
65. #5063C22semidirect
66. #5015C22semidirect
67. #5015C22semidirect
68. #5015C22semidirect
70. #4998C22semidirect
71. C2×#809C22semidirect
72. C2×C4⋊(C3⋊C8)C22semidirect
73. #4889C22semidirect
74. #4885C22semidirect
75. #4882C22semidirect
76. #4872C22semidirect
77. #4869C22semidirect
78. #4866C22semidirect
79. #4863C22semidirect
80. #4852C22semidirect
81. #4848C22semidirect
82. #4848C22semidirect
83. #4843C22semidirect
84. #4843C22semidirect
85. #4840C22semidirect
86. #4835C22semidirect
87. #4833C22semidirect
88. #4785C22semidirect
89. #4785C22semidirect
90. #4781C22semidirect
91. #4781C22semidirect
92. #4773C22semidirect
93. #4773C22semidirect
94. #4756C22semidirect
95. #4756C22semidirect
105. #3077D3semidirect
261. #533C2×D3semidirect
288. #478C2×D3semidirect
291. #476C2×D3semidirect
294. #474C2×D3semidirect
317. #428C2×D3semidirect
319. #423C2×D3semidirect
334. C2×C3×D4#41semidirect
362. #235#41semidirect
701. C2×D4#239semidirect
936. C3#60590semidirect

Maximal subgroups

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

subgroupindex
#862612
C4×#10042
C3×#30772
#833492
C2×#50152
#811462
#811442
#810462
#810452
#809512
#809482
#792192
#792012
#790562
#790402
#789282
#789152
#605903