Finite Group Databasebeta

← #11664173

Subgroups — #11664173

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86262C211yesmaximal, characteristic, complemented
2C4×#1004C211yesmaximal, characteristic
3C3×#3077C211yesmaximal, characteristic, complemented
4#83349C211yesmaximal, characteristic, complemented
5C2×#5019C211yesmaximal, characteristic, complemented
6#81147C214yesmaximal, complemented
7#81145C214yesmaximal, complemented
8#81047C212yesmaximal, complemented
9#81044C212yesmaximal, complemented
10#80950C212yesmaximal, complemented
11#80949C212yesmaximal, complemented
12#79220C212yesmaximal, complemented
13#79202C212yesmaximal, complemented
14#79057C211yesmaximal, characteristic, complemented
15#79040C211yesmaximal, characteristic, complemented
16#78929C212yesmaximal
17#78916C212yesmaximal, complemented
18#60591—31nomaximal, Sylow
19C2×#1004C2211yescharacteristic
20C3×#533C2211yescharacteristic, complemented
21C2×C3×C4×D4C2211yescharacteristic
22#5798C2211yescharacteristic
23C22×#214C2212yes—
24C2×C4×#67—22no—
25C2×#909C2212yes—
26#5728C2212yescomplemented
27#5728C2212yescomplemented
28#5698C2214yescomplemented
29#5642—22no—
30#5642—22no—
31#5584—21no—
32#5584—21no—
33#5570—21no—
34#5570—21no—
35#5546—21no—
36#5546C2212yes—
37#5545—21no—
38#5545C2212yes—
39C4×D3×D4—21no—
40C4×D3×D4C2212yes—
41C4×#237—21no—
42C4×#237C2212yes—
43#5526C2212yes—
44#5516C2212yescomplemented
45#5504C2211yescharacteristic
46#5504C2211yescharacteristic
47#5486—22no—
48C4×#235C2211yescharacteristic
49C4×#235C2211yescharacteristic
50C2×#869C2211yescharacteristic, complemented
51C3×#478C2214yescomplemented
52C3×#476C2212yescomplemented
53C3×#474C2212yescomplemented
54C3×#428C2212yescomplemented
55C3×#423C2211yescharacteristic, complemented
56C3×#418C2212yes—
57#5129C2212yes—
58#5122C2212yescomplemented
59#5120C2212yescomplemented
60#5094C2211yescharacteristic, complemented
61#5091C2211yescharacteristic, complemented
62#5087C2211yescharacteristic, complemented
63#5084C2211yescharacteristic, complemented
64#5066C2212yescomplemented
65#5063C2212yescomplemented
66#5019C2212yescomplemented
67#5019C2212yescomplemented
68#5019C2214yescomplemented
69#5002C2212yes—
70#4998C2212yescomplemented
71C2×#810C2212yescomplemented
72C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
73#4889C2214yescomplemented
74#4888C2214yescomplemented
75#4884C2214yescomplemented
76#4873C2214yescomplemented
77#4868C2214yescomplemented
78#4862C2214yescomplemented
79#4853C2214yescomplemented
80#4852C2214yescomplemented
81#4849C2212yescomplemented
82#4849C2212yescomplemented
83#4841C2212yescomplemented
84#4841C2212yescomplemented
85#4840C2214yescomplemented
86#4835C2212yescomplemented
87#4833C2212yescomplemented
88#4783C2214yes—
89#4783C2214yes—
90#4776C2214yes—
91#4776C2214yes—
92#4758C2214yescomplemented
93#4758C2214yescomplemented
94#4757C2214yescomplemented
95#4757C2214yescomplemented
96#3509—31no—
97C4×H(5,𝔽2)—31no—
98#3123—34no—
99#3120—34no—
100#3116—32no—
101#3110—32no—
102#3107—32no—
103#3101—32no—
104#3097—32no—
105#3077D311yescharacteristic, complemented
106#3076—31no—
107#3039—31no—
108C2×#461—31no—
109#3009—32no—
110#2949—32no—
111#2947—32no—
112#2925—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C22×#67—22no—
116#1004—24no—
117#1004—24no—
118C2×#237—21no—
119C2×#237C2312yes—
120C2×D3×D4—21no—
121C2×D3×D4C2312yes—
122C2×#235C2311yescharacteristic
123C2×#235C2311yescharacteristic
124C22×C4×D3—22no—
125C22×Dic6C2312yes—
126C2×C3×M16C2312yes—
127C3×C4⋊Q8C2311yescharacteristic
128C3×C4⋊Q8C2311yescharacteristic
129C3×#125C2312yes—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C4×Q8—21no—
133C3×C4×Q8—21no—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4C2312yes—
137C3×C4×D4C2312yes—
138C3×#117C2312yes—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C22⋊C4—21no—
141C2×C3×C42C2311yescharacteristic
142C2×#217—22no—
143#946—22no—
144#946—22no—
145Q8×Dic3—22no—
146Q8×Dic3—22no—
147D4×Dic3—21no—
148D4×Dic3—21no—
149D4×Dic3C2312yes—
150D4×Dic3C2312yes—
151C2×#214—28no—
152C2×#214C2314yes—
153C2×#214C2314yes—
154C4×#67—21no—
155C4×#67—21no—
156C4×#67—22no—
157C4×#67—22no—
158C4×#67—22no—
159C4×#67—22no—
160C4×#67—22no—
161C4×#67—22no—
162C4×#67D412yes—
163C4×#67D412yes—
164C2×(C2×D3)⋊C4—22no—
165#926C2311yescharacteristic
166#926C2311yescharacteristic
167C2×C4⋊Dic3—21no—
168C2×C4⋊Dic3—21no—
169C2×Dic3⋊C4—22no—
170C2×C4×Dic3—22no—
171C22×C3⋊C8C2312yes—
172#909—28no—
173C2×Dic12C2314yes—
174C2×#204C2314yes—
175#898—24no—
176#898—24no—
177#897C2314yes—
178#897C2314yes—
179#893—21no—
180#893C2312yes—
181#892—22no—
182#892—22no—
183#892—21no—
184#892C2312yes—
185D3×C4⋊C4—21no—
186D3×C4⋊C4C2312yes—
187#890—24no—
188#890—24no—
189#890—22no—
190#890—22no—
191#887—21no—
192#887C2312yes—
193#887C2314yes—
194#887C2314yes—
195#886—24no—
196#67⋊C4—22no—
197#67⋊C4—22no—
198#67⋊C4—22no—
199#67⋊C4—22no—
200D3×C22⋊C4—22no—
201D3×C22⋊C4—22no—
202#877—24no—
203#877—22no—
204#877—22no—
205#875—22no—
206C4×D12D411yescharacteristic
207C4×D12D411yescharacteristic
208C4×D12C2311yescharacteristic
209C4×D12C2311yescharacteristic
210#872—21no—
211#872C2312yes—
212C42×D3—21no—
213C42×D3C2312yes—
214#869—22no—
215#869—21no—
216#869—21no—
217#869C2312yes—
218#869C2312yes—
219C4×Dic6—22no—
220C4×Dic6—22no—
221C4×Dic6D411yescharacteristic
222C4×Dic6D411yescharacteristic
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2311yescharacteristic
225C3×#107C2314yes—
226C3×#106C2314yes—
227C3×C4⋊C8C2312yes—
228C3×C4⋊C8C2312yes—
229C3×#102C2314yes—
230C3×#102C2314yes—
231(C2×D3)⋊C8C2314yes—
232(C2×D3)⋊C8C2314yes—
233#816C2314yes—
234#816C2314yes—
235#815C2314yes—
236C8×Dic3C2314yes—
237#810C2314yes—
238#810C2312yes—
239#810C2314yes—
240#810C2312yes—
241#809C2312yes—
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×#137—32no—
252C22×SD16—32no—
253#557—61no—
254#557—61no—
255#556—61no—
256#556—61no—
257#552—62no—
258#552—62no—
259#541—34no—
260#536—32no—
261#533—32no—
262#533—32no—
263#533C2×D311yescharacteristic, complemented
264C2×C4⋊Q8—31no—
265#520—31no—
266#520—32no—
267#520—31no—
268#520—61no—
269#519—32no—
270#518—31no—
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#485—34no—
283#485—34no—
284#484—34no—
285#483—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#462—32no—
296#462—32no—
297#461—32no—
298#461—32no—
299#461—34no—
300#461—32no—
301#461—32no—
302#452—34no—
303#452—34no—
304#450—34no—
305#450—34no—
306#441—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×SD16—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#419—32no—
322#418C2×D312yes—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C24×C3—21no—
328C23×D3—22no—
329C2×C3×Q8—21no—
330C2×C3×Q8—21no—
331C2×C3×D4—21no—
332C2×C3×D4—22no—
333C2×C3×D4#4114yes—
334C2×C3×D4C2412yes—
335C22×C3×C4—21no—
336C22×C3×C4—22no—
337C22×C3×C4—22no—
338C22×C3×C4—82no—
339C22×C3×C4C2×D411yescharacteristic
340C22×C3×C4C2×D411yescharacteristic
341C22×C3×C4C2411yescharacteristic
342C2×#67—216no—
343C2×#67—21no—
344C2×#67—22no—
345C2×#67—22no—
346C2×#67C2×D412yes—
347C22×Dic3—22no—
348C22×Dic3—22no—
349C22×Dic3—22no—
350C22×Dic3—22no—
351#237—28no—
352#237—24no—
353#237—24no—
354D3×D4—28no—
355D3×D4—24no—
356D3×D4—24no—
357#235—22no—
358#235—22no—
359#235—22no—
360#235#4114yes—
361C2×D12C2×D411yescharacteristic
362C2×D12C2411yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—21no—
365C2×C4×D3—22no—
366C2×C4×D3—21no—
367C2×C4×D3—22no—
368C2×C4×D3—84no—
369C2×C4×D3C2×D412yes—
370C2×C4×D3C2×D412yes—
371C2×C4×D3C2412yes—
372C2×Dic6—24no—
373C2×Dic6—24no—
374C2×Dic6—22no—
375C2×Dic6C2×D411yescharacteristic
376C2×Dic6C2414yes—
377C2×Dic6C2411yescharacteristic
378C3×M16—24no—
379C2×C3×C8C2414yes—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4C2412yes—
386C3×C4⋊C4C2412yes—
387C3×C4⋊C4C2412yes—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—22no—
390C3×C22⋊C4—22no—
391C3×C42—22no—
392C3×C42C2×D411yescharacteristic
393C3×C42C2×D411yescharacteristic
394C3×C42C2411yescharacteristic
395C3×C42C2411yescharacteristic
396#217—21no—
397#217—22no—
398#217—22no—
399#217C2×D412yes—
400#214—28no—
401#214—28no—
402(C2×D3)⋊C4—24no—
403(C2×D3)⋊C4—24no—
404(C2×D3)⋊C4—22no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4C2×D412yes—
409(C2×D3)⋊C4C2×D412yes—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3—22no—
413C4⋊Dic3—22no—
414C4⋊Dic3—24no—
415C4⋊Dic3—24no—
416C4⋊Dic3C2×D411yescharacteristic
417C4⋊Dic3C2×D411yescharacteristic
418C4⋊Dic3C2411yescharacteristic
419C4⋊Dic3C2411yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422Dic3⋊C4—24no—
423Dic3⋊C4—24no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4C2×D412yes—
427Dic3⋊C4C2×D412yes—
428C4×Dic3—21no—
429C4×Dic3—21no—
430C4×Dic3—21no—
431C4×Dic3—24no—
432C4×Dic3—24no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3C2×D412yes—
436C4×Dic3C2×D412yes—
437C4×Dic3C2412yes—
438C2×C3⋊C8—24no—
439C2×C3⋊C8C2412yes—
440C2×C3⋊C8C2412yes—
441Dic12—28no—
442#204—28no—
443H(5,𝔽2)—64no—
444H(5,𝔽2)—64no—
445C2×#41—31no—
446C2×#41—32no—
447C2×#41—31no—
448C2×#41—61no—
449C22×Q8—32no—
450C22×D4—32no—
451C22×D4—61no—
452C22×D4—62no—
453C22×D4C22×D311yescharacteristic
454C23×C4—21no—
455C23×C4—62no—
456#137—68no—
457C2×Q16—34no—
458C2×SD16—34no—
459C2×SD16—34no—
460C2×SD16—34no—
461C2×SD16—68no—
462C2×M16C22×D312yes—
463C22×C8—32no—
464C4⋊Q8—32no—
465C4⋊Q8—32no—
466C4⋊Q8—62no—
467C4⋊Q8—61no—
468C4⋊Q8—61no—
469C4⋊Q8C22×D311yescharacteristic
470C4⋊Q8C22×D311yescharacteristic
471#126—64no—
472#126—64no—
473#125—62no—
474#125—62no—
475#125—64no—
476#125—64no—
477#125C22×D312yes—
478#124—62no—
479#123—64no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—34no—
483C22⋊Q8—34no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—31no—
489C4×Q8—31no—
490C4×Q8—32no—
491C4×Q8—34no—
492C4×Q8—34no—
493C4×Q8—31no—
494C4×Q8—31no—
495C4×Q8—62no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8—61no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—32no—
503C4×D4—32no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—32no—
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—31no—
510C4×D4—31no—
511C4×D4—62no—
512C4×D4—62no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—62no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—62no—
520C4×D4—61no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—61no—
525C4×D4—61no—
526C4×D4C22×D312yes—
527C4×D4C22×D312yes—
528#117—31no—
529#117—32no—
530#117—31no—
531#117—32no—
532#117—62no—
533#117—64no—
534#117—62no—
535#117—61no—
536#117—62no—
537#117—62no—
538#117—61no—
539#117C22×D312yes—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—61no—
542C2×C4⋊C4—62no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—61no—
545C2×C4⋊C4C22×D311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—62no—
548C2×C22⋊C4—62no—
549C2×C22⋊C4—62no—
550C2×C22⋊C4—62no—
551C2×C42—32no—
552C2×C42—62no—
553C2×C42—61no—
554C2×C42C22×D311yescharacteristic
555#107—32no—
556#107—32no—
557#107C22×D314yes—
558#106—32no—
559#106—32no—
560#106C22×D314yes—
561C4⋊C8—31no—
562C4⋊C8—31no—
563C4⋊C8—32no—
564C4⋊C8C22×D312yes—
565C4⋊C8C22×D312yes—
566#103—34no—
567#103—34no—
568#103—34no—
569#103—34no—
570#103—32no—
571#103—32no—
572#102—32no—
573#102—32no—
574#102C22×D314yes—
575#102C22×D314yes—
576C22⋊C8—34no—
577C22⋊C8—34no—
578#97—34no—
579C4×C8—34no—
580C23×C3—22no—
581C23×C3—24no—
582C23×C3—81no—
583C23×C3—81no—
584C23×C3C22×D411yescharacteristic
585C22×D3—21no—
586C22×D3—28no—
587C22×D3—82no—
588C22×D3—82no—
589C22×D3C22×D412yes—
590C3×Q8—42no—
591C3×Q8—42no—
592C3×D4—24no—
593C3×D4—22no—
594C3×D4C2×#4114yes—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—41no—
600C2×C3×C4—44no—
601C2×C3×C4—82no—
602C2×C3×C4—81no—
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C2×#4112yes—
609C2×C3×C4C2×#4112yes—
610C2×C3×C4C2511yescharacteristic
611#67—28no—
612#67—28no—
613#67—24no—
614#67—24no—
615C2×Dic3—28no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—24no—
620C2×Dic3—44no—
621C2×Dic3—82no—
622C2×Dic3—82no—
623C2×Dic3C22×D412yes—
624C2×Dic3C22×D412yes—
625C2×Dic3C22×D412yes—
626D12—22no—
627D12—21no—
628D12C2×#4112yes—
629C4×D3—24no—
630C4×D3—24no—
631C4×D3—22no—
632C4×D3—22no—
633C4×D3—42no—
634C4×D3—42no—
635C4×D3—82no—
636C4×D3—81no—
637C4×D3—82no—
638Dic6—22no—
639Dic6—21no—
640Dic6—24no—
641Dic6—24no—
642Dic6—44no—
643Dic6C2×#4112yes—
644C3×C8—24no—
645C3⋊C8—22no—
646C3⋊C8—22no—
647C24—21no—
648C24—62no—
649#41—34no—
650#41—64no—
651#41—68no—
652#41—64no—
653#41—62no—
654#41—62no—
655#41—62no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—31no—
659C2×Q8—31no—
660C2×Q8—34no—
661C2×Q8—62no—
662C2×Q8—64no—
663C2×Q8—64no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—32no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—62no—
670C2×D4—64no—
671C2×D4—68no—
672C2×D4—62no—
673C2×D4—616no—
674C2×D4—61no—
675C2×D4—64no—
676C2×D4#23914yes—
677C2×D4C23×D312yes—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—61no—
690C22×C4—62no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—82no—
694C22×C4—244no—
695C22×C4D3×D411yescharacteristic
696C22×C4D3×D411yescharacteristic
697C22×C4C23×D311yescharacteristic
698Q16—68no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702M16—24no—
703C2×C8—32no—
704C2×C8—32no—
705C2×C8—64no—
706C2×C8C23×D314yes—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—31no—
713C4⋊C4—32no—
714C4⋊C4—31no—
715C4⋊C4—32no—
716C4⋊C4—31no—
717C4⋊C4—31no—
718C4⋊C4—62no—
719C4⋊C4—62no—
720C4⋊C4—64no—
721C4⋊C4—64no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4—61no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—61no—
730C4⋊C4C23×D312yes—
731C4⋊C4C23×D312yes—
732C4⋊C4C23×D312yes—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—32no—
737C22⋊C4—32no—
738C22⋊C4—32no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—62no—
744C22⋊C4—62no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C42—22no—
749C42—32no—
750C42—32no—
751C42—32no—
752C42—62no—
753C42—62no—
754C42—64no—
755C42—64no—
756C42—61no—
757C42—61no—
758C42—61no—
759C42D3×D411yescharacteristic
760C42D3×D411yescharacteristic
761C42C23×D311yescharacteristic
762C42C23×D311yescharacteristic
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—24no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—84no—
769C22×C3#52512yes—
770C22×C3C23×D411yescharacteristic
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—88no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—42no—
784C3×C4#52512yes—
785C3×C4#57712yes—
786C3×C4C22×#4111yescharacteristic
787C3×C4C22×#4111yescharacteristic
788Dic3—22no—
789Dic3—22no—
790Dic3—22no—
791Dic3—22no—
792Dic3—41no—
793Dic3—44no—
794Dic3—41no—
795C23—22no—
796C23—24no—
797C23—32no—
798C23—68no—
799C23—61no—
800C23—81no—
801C23—81no—
802C23—242no—
803C23—242no—
804C23C2×D3×D411yescharacteristic
805Q8—32no—
806Q8—42no—
807Q8—42no—
808Q8—61no—
809Q8—62no—
810Q8—64no—
811Q8—64no—
812Q8—124no—
813D4—22no—
814D4—24no—
815D4—32no—
816D4—68no—
817D4—68no—
818D4—64no—
819D4—64no—
820D4—61no—
821D4—62no—
822D4C2×#23914yes—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—41no—
831C2×C4—44no—
832C2×C4—68no—
833C2×C4—61no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—64no—
837C2×C4—64no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—64no—
841C2×C4—82no—
842C2×C4—81no—
843C2×C4—122no—
844C2×C4—124no—
845C2×C4—122no—
846C2×C4—241no—
847C2×C4—242no—
848C2×C4—242no—
849C2×C4—242no—
850C2×C4—242no—
851C2×C4C2×D3×D411yescharacteristic
852C2×C4C2×D3×D411yescharacteristic
853C2×C4C2×D3×D411yescharacteristic
854C2×C4C2×D3×D411yescharacteristic
855C2×C4C2×D3×D411yescharacteristic
856C2×C4C2×#23912yes—
857C2×C4D3×#4112yes—
858C2×C4C24×D311yescharacteristic
859C8—24no—
860C8—62no—
861C8—62no—
862C2×C3—22no—
863C2×C3—44no—
864C2×C3C2×#52511yescharacteristic
865C2×C3C2×#57711yescharacteristic
866C2×C3#358611yescharacteristic
867D3—42no—
868D3—42no—
869C22—21no—
870C22—21no—
871C22—24no—
872C22—42no—
873C22—42no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—84no—
879C22—121no—
880C22—121no—
881C22—248no—
882C22#562712yes—
883C22C22×D3×D411yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—62no—
891C4—62no—
892C4—62no—
893C4—62no—
894C4—121no—
895C4—121no—
896C4—124no—
897C4#562712yes—
898C4#577512yes—
899C4C22×#23911yescharacteristic
900C4C2×D3×#4111yescharacteristic
901C3#6059111yescharacteristic, complemented, Sylow
902C2—22no—
903C2—44no—
904C2—122no—
905C2—122no—
906C2C2×#562711yescharacteristic
907C2C2×#577511yescharacteristic
908C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
prime radicalC2×#1004C22
hypercenter#3077D3
hypocenterC3#60591
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. #86262C2semidirect
3. C3×#3077C2semidirect
4. #83349C2semidirect
5. C2×#5019C2semidirect
6. #81147C2semidirect
7. #81145C2semidirect
8. #81047C2semidirect
9. #81044C2semidirect
10. #80950C2semidirect
11. #80949C2semidirect
12. #79220C2semidirect
13. #79202C2semidirect
14. #79057C2semidirect
15. #79040C2semidirect
17. #78916C2semidirect
20. C3×#533C22semidirect
26. #5728C22semidirect
27. #5728C22semidirect
28. #5698C22semidirect
44. #5516C22semidirect
50. C2×#869C22semidirect
51. C3×#478C22semidirect
52. C3×#476C22semidirect
53. C3×#474C22semidirect
54. C3×#428C22semidirect
55. C3×#423C22semidirect
58. #5122C22semidirect
59. #5120C22semidirect
60. #5094C22semidirect
61. #5091C22semidirect
62. #5087C22semidirect
63. #5084C22semidirect
64. #5066C22semidirect
65. #5063C22semidirect
66. #5019C22semidirect
67. #5019C22semidirect
68. #5019C22semidirect
70. #4998C22semidirect
71. C2×#810C22semidirect
72. C2×C4⋊(C3⋊C8)C22semidirect
73. #4889C22semidirect
74. #4888C22semidirect
75. #4884C22semidirect
76. #4873C22semidirect
77. #4868C22semidirect
78. #4862C22semidirect
79. #4853C22semidirect
80. #4852C22semidirect
81. #4849C22semidirect
82. #4849C22semidirect
83. #4841C22semidirect
84. #4841C22semidirect
85. #4840C22semidirect
86. #4835C22semidirect
87. #4833C22semidirect
92. #4758C22semidirect
93. #4758C22semidirect
94. #4757C22semidirect
95. #4757C22semidirect
105. #3077D3semidirect
263. #533C2×D3semidirect
288. #478C2×D3semidirect
291. #476C2×D3semidirect
294. #474C2×D3semidirect
317. #428C2×D3semidirect
319. #423C2×D3semidirect
901. C3#60591semidirect

Maximal subgroups

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

subgroupindex
#862622
C4×#10042
C3×#30772
#833492
C2×#50192
#811472
#811452
#810472
#810442
#809502
#809492
#792202
#792022
#790572
#790402
#789292
#789162
#605913