Finite Group Databasebeta

← #11664166

Subgroups — #11664166

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#86204C211yesmaximal, characteristic, complemented
2C4×#1004C211yesmaximal, characteristic
3C2×C3×#461C211yesmaximal, characteristic, complemented
4#83859C212yesmaximal
5#83843C212yesmaximal, complemented
6#83209C211yesmaximal, characteristic, complemented
7#82296C211yesmaximal, characteristic, complemented
8#80413C214yesmaximal, complemented
9#80412C214yesmaximal, complemented
10#80411C212yesmaximal, complemented
11#80410C212yesmaximal, complemented
12#80409C212yesmaximal, complemented
13#80408C212yesmaximal, complemented
14#79025C211yesmaximal, characteristic, complemented
15#79000C211yesmaximal, characteristic, complemented
16#78804C212yesmaximal, complemented
17#78774C212yesmaximal, complemented
18#60591—31nomaximal, Sylow
19C2×#1004C2211yescharacteristic
20C22×C3×SD16C2212yes—
21C2×C3×C4⋊Q8C2211yescharacteristic, complemented
22C2×C3×C4×D4C2211yescharacteristic
23#5816C2212yes—
24#5812C2212yescomplemented
25C2×#942C2212yes—
26#5798C2211yescharacteristic
27C2×C4×#67—22no—
28#5732—21no—
29#5732—21no—
30#5731C2214yescomplemented
31#5728C2212yescomplemented
32#5728C2212yescomplemented
33#5721—21no—
34#5721—21no—
35#5546—21no—
36#5546C2212yes—
37#5545—21no—
38#5545C2212yes—
39C4×D3×D4—21no—
40C4×D3×D4C2212yes—
41C4×#237—21no—
42C4×#237C2212yes—
43#5513—22no—
44#5513—22no—
45#5504C2211yescharacteristic
46#5504C2211yescharacteristic
47#5486—22no—
48C4×#235C2211yescharacteristic
49C4×#235C2211yescharacteristic
50#5470C2211yescharacteristic, complemented
51C3×#461C2212yescomplemented
52C3×#461C2212yescomplemented
53C3×#461C2214yescomplemented
54C2×C3×C4⋊C8C2211yescharacteristic, complemented
55C2×C3×#103C2212yescomplemented
56#5225C2212yescomplemented
57#5215C2212yes—
58#5173C2214yes—
59#5173C2214yes—
60#5169C2214yes—
61#5169C2214yes—
62#5164C2214yescomplemented
63#5164C2214yescomplemented
64Dic3×SD16C2214yescomplemented
65Dic3×SD16C2214yescomplemented
66#5113C2212yes—
67#5110C2212yes—
68#5106C2212yescomplemented
69#5101C2212yescomplemented
70#5090C2212yescomplemented
71#5090C2212yescomplemented
72#5083C2212yescomplemented
73#5083C2212yescomplemented
74#5009C2214yescomplemented
75#5008C2212yescomplemented
76#5007C2212yescomplemented
77#4964C2212yescomplemented
78#4924C2211yescharacteristic, complemented
79#4851C2211yescharacteristic, complemented
80#4850C2211yescharacteristic, complemented
81#4847C2212yescomplemented
82#4846C2211yescharacteristic, complemented
83#4842C2211yescharacteristic, complemented
84#4840C2214yescomplemented
85#4835C2212yescomplemented
86#4833C2212yescomplemented
87#4829C2212yescomplemented
88#4817C2214yescomplemented
89#4815C2214yescomplemented
90#4814C2214yescomplemented
91#4811C2214yescomplemented
92#4805C2214yescomplemented
93#4790C2214yescomplemented
94#4789C2214yescomplemented
95#4788C2214yescomplemented
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#3077—31no—
106#3076—31no—
107#3039—31no—
108C2×#461D311yescharacteristic, complemented
109#3009—32no—
110#2949—32no—
111#2947—32no—
112#2925—31no—
113C22×C3×Q8C2312yes—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C22×#67—22no—
117#1004—24no—
118#1004—24no—
119C2×#237—21no—
120C2×#237C2312yes—
121C2×D3×D4—21no—
122C2×D3×D4C2312yes—
123C2×#235C2311yescharacteristic
124C2×#235C2311yescharacteristic
125C22×C4×D3—22no—
126C2×C3×SD16—28no—
127C2×C3×SD16C2314yes—
128C2×C3×SD16C2314yes—
129C22×C3×C8C2312yes—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8C2312yes—
133C3×C4⋊Q8C2312yes—
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4C2312yes—
137C3×C4×D4C2312yes—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C22⋊C4—21no—
142C2×C3×C42C2311yescharacteristic
143C2×#217—22no—
144#947—22no—
145#946C2314yes—
146#946C2314yes—
147Q8×Dic3—22no—
148Q8×Dic3—22no—
149Q8×Dic3C2314yes—
150Q8×Dic3C2314yes—
151#944—22no—
152C2×#216C2314yes—
153#942—28no—
154C2×#215C2314yes—
155D4×Dic3—21no—
156D4×Dic3—21no—
157D4×Dic3C2312yes—
158D4×Dic3C2312yes—
159#929—24no—
160C4×#67—21no—
161C4×#67—21no—
162C4×#67—22no—
163C4×#67—22no—
164C4×#67—22no—
165C4×#67—22no—
166C4×#67—22no—
167C4×#67—22no—
168C4×#67D412yes—
169C4×#67D412yes—
170C2×(C2×D3)⋊C4—22no—
171#926—24no—
172#926C2312yes—
173#926C2311yescharacteristic
174#926C2311yescharacteristic
175#924—21no—
176#924—21no—
177C2×Dic3⋊C4—22no—
178C2×C4×Dic3—22no—
179C2×#208C2312yes—
180#898—24no—
181#898—24no—
182#897—22no—
183#897—22no—
184#893—21no—
185#893C2312yes—
186#892—22no—
187#892—22no—
188#892—21no—
189#892C2312yes—
190D3×C4⋊C4—21no—
191D3×C4⋊C4C2312yes—
192#890—22no—
193#890—22no—
194#889—24no—
195#889—24no—
196#887—21no—
197#887—22no—
198#887—22no—
199#887C2312yes—
200#67⋊C4—22no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#67⋊C4—22no—
204D3×C22⋊C4—22no—
205D3×C22⋊C4—22no—
206#877—22no—
207#877—22no—
208C4×D12D411yescharacteristic
209C4×D12D411yescharacteristic
210C4×D12C2311yescharacteristic
211C4×D12C2311yescharacteristic
212#872—21no—
213#872C2312yes—
214C42×D3—21no—
215C42×D3C2312yes—
216#870C2312yes—
217#869C2311yescharacteristic
218#869C2311yescharacteristic
219C4×Dic6—21no—
220C4×Dic6—21no—
221C4×Dic6D411yescharacteristic
222C4×Dic6D411yescharacteristic
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2311yescharacteristic
225C3×C4⋊C8C2312yes—
226C3×C4⋊C8C2311yescharacteristic
227C3×C4⋊C8C2311yescharacteristic
228C3×#103C2314yes—
229C3×#103C2314yes—
230#835C2314yes—
231#835C2314yes—
232#832C2314yes—
233#832C2314yes—
234#821C2312yes—
235#821C2312yes—
236(C2×D3)⋊C8C2314yes—
237(C2×D3)⋊C8C2314yes—
238#818C2312yes—
239#818C2312yes—
240#817C2312yes—
241#817C2312yes—
242#816C2312yes—
243#816C2312yes—
244#815C2314yes—
245C8×Dic3C2314yes—
246#808C2314yes—
247#807C2314yes—
248C4⋊(C3⋊C8)C2312yes—
249C4⋊(C3⋊C8)C2312yes—
250C2×H(5,𝔽2)—31no—
251C2×#137—32no—
252C22×SD16C2×D312yes—
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#533—31no—
264C2×C4⋊Q8C2×D311yescharacteristic, complemented
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—34no—
288#478—32no—
289#477—31no—
290#476—32no—
291#476—31no—
292#475—31no—
293#474—32no—
294#474—31no—
295#462—32no—
296#462—32no—
297#461—32no—
298#461—32no—
299#461C2×D312yescomplemented
300#461C2×D312yescomplemented
301#461C2×D314yescomplemented
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#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8C2×D311yescharacteristic, complemented
321#419—32no—
322#418—32no—
323#416—32no—
324C2×#103C2×D312yescomplemented
325#408—32no—
326#405—32no—
327C24×C3—21no—
328C23×D3—22no—
329C2×C3×Q8—22no—
330C2×C3×Q8—24no—
331C2×C3×Q8—24no—
332C2×C3×Q8C2414yes—
333C2×C3×D4—21no—
334C2×C3×D4—22no—
335C2×C3×D4#4114yes—
336C2×C3×D4C2412yes—
337C22×C3×C4—22no—
338C22×C3×C4—21no—
339C22×C3×C4—22no—
340C22×C3×C4—22no—
341C22×C3×C4—82no—
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2411yescharacteristic
345C2×#67—216no—
346C2×#67—21no—
347C2×#67—22no—
348C2×#67—22no—
349C2×#67C2×D412yes—
350C22×Dic3—22no—
351C22×Dic3—22no—
352C22×Dic3—22no—
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#4114yes—
363C2×D12C2×D411yescharacteristic
364C2×D12C2411yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3—22no—
368C2×C4×D3—21no—
369C2×C4×D3—22no—
370C2×C4×D3—84no—
371C2×C4×D3C2×D412yes—
372C2×C4×D3C2×D412yes—
373C2×C4×D3C2412yes—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6C2×D411yescharacteristic
377C2×Dic6C2411yescharacteristic
378C3×SD16—28no—
379C3×SD16—28no—
380C2×C3×C8—24no—
381C2×C3×C8C2412yes—
382C2×C3×C8C2412yes—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4C2412yes—
389C3×C22⋊C4—22no—
390C3×C22⋊C4—22no—
391C3×C42C2×D411yescharacteristic
392C3×C42C2×D411yescharacteristic
393C3×C42C2411yescharacteristic
394C3×C42C2411yescharacteristic
395#217—22no—
396#217—21no—
397#217—22no—
398#217—22no—
399#217C2×D412yes—
400#216—28no—
401#215—28no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—24no—
404(C2×D3)⋊C4—24no—
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—21no—
411C4⋊Dic3—21no—
412C4⋊Dic3—24no—
413C4⋊Dic3—24no—
414C4⋊Dic3C2×D411yescharacteristic
415C4⋊Dic3C2×D411yescharacteristic
416C4⋊Dic3C2412yes—
417C4⋊Dic3C2412yes—
418C4⋊Dic3C2411yescharacteristic
419C4⋊Dic3C2411yescharacteristic
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—21no—
423Dic3⋊C4—21no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—24no—
427Dic3⋊C4—24no—
428Dic3⋊C4C2×D412yes—
429Dic3⋊C4C2×D412yes—
430C4×Dic3—22no—
431C4×Dic3—21no—
432C4×Dic3—21no—
433C4×Dic3—21no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—24no—
437C4×Dic3—24no—
438C4×Dic3C2×D412yes—
439C4×Dic3C2×D412yes—
440C4×Dic3C2412yes—
441#208—24no—
442C2×C3⋊C8C2414yes—
443H(5,𝔽2)—64no—
444H(5,𝔽2)—64no—
445C2×#41—31no—
446C2×#41—32no—
447C2×#41—31no—
448C2×#41—61no—
449C22×Q8C22×D312yes—
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—28no—
459C2×SD16—34no—
460C2×SD16C22×D314yes—
461C2×SD16C22×D314yes—
462C2×M16—32no—
463C22×C8C22×D312yes—
464C4⋊Q8—21no—
465C4⋊Q8—21no—
466C4⋊Q8—31no—
467C4⋊Q8—31no—
468C4⋊Q8—62no—
469C4⋊Q8C22×D312yes—
470C4⋊Q8C22×D312yes—
471#126—64no—
472#126—64no—
473#125—32no—
474#125—62no—
475#125—62no—
476#125—64no—
477#125—64no—
478#124—62no—
479#123—64no—
480C22⋊Q8—34no—
481C22⋊Q8—34no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—61no—
485C22⋊Q8—61no—
486C4×Q8—31no—
487C4×Q8—31no—
488C4×Q8—34no—
489C4×Q8—34no—
490C4×Q8—32no—
491C4×Q8—31no—
492C4×Q8—31no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—61no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8—61no—
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—32no—
533#117—62no—
534#117—62no—
535#117—64no—
536#117—61no—
537#117—62no—
538#117—62no—
539#117—61no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—32no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—62no—
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#107—34no—
558#106—32no—
559#106—32no—
560#106—34no—
561C4⋊C8—32no—
562C4⋊C8—32no—
563C4⋊C8C22×D311yescharacteristic
564C4⋊C8C22×D311yescharacteristic
565C4⋊C8C22×D312yes—
566#103—34no—
567#103—34no—
568#103—32no—
569#103—32no—
570#103C22×D314yes—
571#103C22×D314yes—
572#102—34no—
573#102—34no—
574#102—32no—
575#102—32no—
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—24no—
591C3×Q8—24no—
592C3×Q8—44no—
593C3×D4—24no—
594C3×D4—22no—
595C3×D4C2×#4114yes—
596C2×C3×C4—22no—
597C2×C3×C4—24no—
598C2×C3×C4—22no—
599C2×C3×C4—41no—
600C2×C3×C4—44no—
601C2×C3×C4—44no—
602C2×C3×C4—82no—
603C2×C3×C4—81no—
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C22×D411yescharacteristic
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C2×#4112yes—
610C2×C3×C4C2×#4112yes—
611C2×C3×C4C2511yescharacteristic
612#67—28no—
613#67—28no—
614#67—24no—
615#67—24no—
616C2×Dic3—28no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—21no—
622C2×Dic3—82no—
623C2×Dic3—82no—
624C2×Dic3C22×D412yes—
625C2×Dic3C22×D412yes—
626C2×Dic3C22×D412yes—
627D12—22no—
628D12—21no—
629D12C2×#4112yes—
630C4×D3—24no—
631C4×D3—24no—
632C4×D3—22no—
633C4×D3—22no—
634C4×D3—42no—
635C4×D3—42no—
636C4×D3—82no—
637C4×D3—81no—
638C4×D3—82no—
639Dic6—22no—
640Dic6—21no—
641Dic6—42no—
642Dic6—42no—
643Dic6C2×#4112yes—
644C3×C8—22no—
645C3×C8—22no—
646C3⋊C8—24no—
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—22no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—31no—
660C2×Q8—31no—
661C2×Q8—61no—
662C2×Q8—61no—
663C2×Q8C23×D314yes—
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#23714yes—
677C2×D4C23×D312yes—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—82no—
694C22×C4—244no—
695C22×C4D3×D411yescharacteristic
696C22×C4D3×D411yescharacteristic
697C22×C4C23×D311yescharacteristic
698Q16—68no—
699SD16—28no—
700SD16—28no—
701SD16—68no—
702M16—64no—
703C2×C8—24no—
704C2×C8—34no—
705C2×C8C23×D312yes—
706C2×C8C23×D312yes—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—31no—
713C4⋊C4—32no—
714C4⋊C4—31no—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—32no—
718C4⋊C4—31no—
719C4⋊C4—31no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4—64no—
725C4⋊C4—64no—
726C4⋊C4—61no—
727C4⋊C4—61no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4—62no—
731C4⋊C4—62no—
732C4⋊C4C23×D312yes—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—32no—
736C22⋊C4—32no—
737C22⋊C4—32no—
738C22⋊C4—62no—
739C22⋊C4—62no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—61no—
745C22⋊C4—62no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C42—32no—
749C42—32no—
750C42—32no—
751C42—62no—
752C42—62no—
753C42—64no—
754C42—64no—
755C42—61no—
756C42—61no—
757C42—61no—
758C42—62no—
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—44no—
782C3×C4—42no—
783C3×C4#52512yes—
784C3×C4#57712yes—
785C3×C4C22×#4111yescharacteristic
786C3×C4C22×#4111yescharacteristic
787Dic3—22no—
788Dic3—22no—
789Dic3—22no—
790Dic3—22no—
791Dic3—42no—
792Dic3—41no—
793Dic3—42no—
794Dic3—41no—
795C23—22no—
796C23—24no—
797C23—32no—
798C23—68no—
799C23—61no—
800C23—81no—
801C23—81no—
802C23—242no—
803C23—242no—
804C23C2×D3×D411yescharacteristic
805Q8—24no—
806Q8—24no—
807Q8—32no—
808Q8—44no—
809Q8—61no—
810Q8—62no—
811Q8—122no—
812Q8—122no—
813D4—22no—
814D4—24no—
815D4—32no—
816D4—68no—
817D4—68no—
818D4—64no—
819D4—64no—
820D4—61no—
821D4—62no—
822D4C2×#23714yes—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—41no—
830C2×C4—44no—
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—62no—
840C2×C4—62no—
841C2×C4—61no—
842C2×C4—82no—
843C2×C4—81no—
844C2×C4—122no—
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×#23712yes—
857C2×C4D3×#4112yes—
858C2×C4C24×D311yescharacteristic
859C8—22no—
860C8—22no—
861C8—64no—
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#560612yes—
883C22C22×D3×D411yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—42no—
888C4—44no—
889C4—62no—
890C4—62no—
891C4—62no—
892C4—62no—
893C4—121no—
894C4—122no—
895C4—121no—
896C4—122no—
897C4#560612yes—
898C4#576212yes—
899C4C22×#23711yescharacteristic
900C4C2×D3×#4111yescharacteristic
901C3#6059111yescharacteristic, complemented, Sylow
902C2—22no—
903C2—44no—
904C2—122no—
905C2—122no—
906C2C2×#560611yescharacteristic
907C2C2×#576211yescharacteristic
908C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#461C2
socleC22×C3C23×D4
prime radicalC2×#1004C22
hypercenterC2×#461D3
hypocenterC3#60591
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. #86204C2semidirect
3. C2×C3×#461C2semidirect
5. #83843C2semidirect
6. #83209C2semidirect
7. #82296C2semidirect
8. #80413C2semidirect
9. #80412C2semidirect
10. #80411C2semidirect
11. #80410C2semidirect
12. #80409C2semidirect
13. #80408C2semidirect
14. #79025C2semidirect
15. #79000C2semidirect
16. #78804C2semidirect
17. #78774C2semidirect
21. C2×C3×C4⋊Q8C22semidirect
24. #5812C22semidirect
30. #5731C22semidirect
31. #5728C22semidirect
32. #5728C22semidirect
50. #5470C22semidirect
51. C3×#461C22semidirect
52. C3×#461C22semidirect
53. C3×#461C22semidirect
54. C2×C3×C4⋊C8C22semidirect
55. C2×C3×#103C22semidirect
56. #5225C22semidirect
62. #5164C22semidirect
63. #5164C22semidirect
64. Dic3×SD16C22semidirect
65. Dic3×SD16C22semidirect
68. #5106C22semidirect
69. #5101C22semidirect
70. #5090C22semidirect
71. #5090C22semidirect
72. #5083C22semidirect
73. #5083C22semidirect
74. #5009C22semidirect
75. #5008C22semidirect
76. #5007C22semidirect
77. #4964C22semidirect
78. #4924C22semidirect
79. #4851C22semidirect
80. #4850C22semidirect
81. #4847C22semidirect
82. #4846C22semidirect
83. #4842C22semidirect
84. #4840C22semidirect
85. #4835C22semidirect
86. #4833C22semidirect
87. #4829C22semidirect
88. #4817C22semidirect
89. #4815C22semidirect
90. #4814C22semidirect
91. #4811C22semidirect
92. #4805C22semidirect
93. #4790C22semidirect
94. #4789C22semidirect
95. #4788C22semidirect
108. C2×#461D3semidirect
264. C2×C4⋊Q8C2×D3semidirect
299. #461C2×D3semidirect
300. #461C2×D3semidirect
301. #461C2×D3semidirect
320. C2×C4⋊C8C2×D3semidirect
324. C2×#103C2×D3semidirect
901. C3#60591semidirect

Maximal subgroups

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

subgroupindex
#862042
C4×#10042
C2×C3×#4612
#838592
#838432
#832092
#822962
#804132
#804122
#804112
#804102
#804092
#804082
#790252
#790002
#788042
#787742
#605913