Finite Group Databasebeta

← #11675016

Subgroups — #11675016

Order 768.

2064 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86220C211yesmaximal, characteristic, complemented
2C2×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×#3036C211yesmaximal, characteristic, complemented
4#83931C212yesmaximal, complemented
5Dic3×AGL(1,ℤ/8)C212yesmaximal, complemented
6#83283C211yesmaximal, characteristic, complemented
7C4×#932C211yesmaximal, characteristic, complemented
8#80521C214yesmaximal, complemented
9#80518C214yesmaximal, complemented
10#80416C212yesmaximal, complemented
11#80414C212yesmaximal, complemented
12#80323C212yesmaximal, complemented
13#80318C212yesmaximal, complemented
14#79060C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78878C212yesmaximal, complemented
17#78870C212yesmaximal, complemented
18#61317—31nomaximal, Sylow
19C23×Dic6—21no—
20C2×C3×AGL(1,ℤ/8)C2212yes—
21C3×#532C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23#5832C2212yes—
24Dic3×#41C2212yes—
25C2×D4×Dic3C2212yes—
26C2×#932C2211yescharacteristic
27C2×#924—21no—
28#5732C2211yescharacteristic, complemented
29#5721C2211yescharacteristic, complemented
30#5718C2211yescharacteristic, complemented
31#5713C2211yescharacteristic, complemented
32#5681C2212yescomplemented
33#5671C2212yescomplemented
34#5618—21no—
35#5601—22no—
36#5598—21no—
37#5557—21no—
38#5538—22no—
39D4×Dic6—21no—
40D4×Dic6—22no—
41D4×Dic6—21no—
42D4×Dic6C2212yes—
43D4×Dic6C2212yes—
44D4×Dic6C2214yes—
45C4×#237—21no—
46C2×#888C2212yes—
47C2×#878—22no—
48C4×#235C2211yescharacteristic
49C2×#869C2211yescharacteristic
50C2×C4×Dic6C2211yescharacteristic
51C3×#463C2214yes—
52C3×#461C2212yes—
53C3×#459C2212yes—
54C3×#423C2211yescharacteristic
55C3×#417C2212yes—
56#5232C2212yes—
57#5232C2212yes—
58#5215C2211yescharacteristic
59#5165C2214yes—
60#5164C2214yes—
61#5162C2214yes—
62Dic3×SD16C2214yes—
63#5153C2214yes—
64#5152C2214yes—
65#5150C2214yes—
66Dic3×D8C2214yes—
67#5133C2212yes—
68#5121C2212yes—
69#5118C2212yes—
70Dic3×M16C2212yes—
71#5079C2212yescomplemented
72#5070C2212yescomplemented
73#5055C2214yescomplemented
74#5018C2212yes—
75C4×#214C2212yes—
76#5014C2212yes—
77C4×#213C2212yes—
78#4966C2211yescharacteristic
79#4964C2211yescharacteristic
80C4×#208C2211yescharacteristic
81#4851C2212yescomplemented
82#4850C2212yescomplemented
83#4846C2212yescomplemented
84#4842C2212yescomplemented
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4794C2214yescomplemented
89#4793C2214yescomplemented
90#4792C2214yescomplemented
91#4791C2214yescomplemented
92#4765C2214yescomplemented
93#4761C2214yescomplemented
94#4760C2214yescomplemented
95#4759C2214yescomplemented
96#3480—31no—
97C2×D4×Q8—31no—
98#3373—34no—
99#3373—32no—
100#3367—34no—
101#3367—32no—
102#3359—32no—
103#3358—32no—
104#3141—32no—
105#3141—31no—
106#3079—31no—
107#3079—32no—
108#3036—32no—
109#3036D311yescharacteristic, complemented
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)—31no—
113C2×C3×#41C2312yes—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C23×Dic3—22no—
117C2×#237—21no—
118C2×#235C2311yescharacteristic
119C22×Dic6—21no—
120C22×Dic6—22no—
121C22×Dic6—24no—
122C22×Dic6—22no—
123C22×Dic6—22no—
124C22×Dic6—48no—
125C22×Dic6D411yescharacteristic
126C3×AGL(1,ℤ/8)—28no—
127C2×C3×SD16C2314yes—
128C2×C3×D8C2314yes—
129C2×C3×M16C2312yes—
130C3×C4⋊Q8C2311yescharacteristic
131C3×#127C2311yescharacteristic
132C3×#124C2312yes—
133C3×#121—21no—
134C3×#121—21no—
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4C2312yes—
140C3×C4×D4C2312yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×C3×C42C2311yescharacteristic
144C2×#217—22no—
145#947C2312yes—
146Q8×Dic3C2312yes—
147Q8×Dic3C2312yes—
148#944C2312yes—
149#940C2312yes—
150#939—22no—
151#939—22no—
152#939—22no—
153#938—21no—
154#936—21no—
155#936C2312yes—
156#935—22no—
157D4×Dic3—22no—
158D4×Dic3—22no—
159D4×Dic3—21no—
160D4×Dic3—22no—
161D4×Dic3—22no—
162D4×Dic3C2312yes—
163D4×Dic3C2314yes—
164D4×Dic3C2312yes—
165D4×Dic3C2314yes—
166C2×#214C2312yes—
167#932—24no—
168C2×#213C2312yes—
169C4×#67—21no—
170C4×#67—21no—
171C4×#67—22no—
172C4×#67—22no—
173#926—22no—
174#926C2311yescharacteristic
175C2×C4⋊Dic3—21no—
176C2×C4⋊Dic3D411yescharacteristic
177C2×C4⋊Dic3C2312yes—
178#924—24no—
179#924—22no—
180#924—22no—
181C2×Dic3⋊C4—22no—
182C2×Dic3⋊C4D412yes—
183C2×C4×Dic3—22no—
184C2×C4×Dic3C2312yes—
185C2×#208C2311yescharacteristic
186C2×#208C2311yescharacteristic
187#898—22no—
188#897—21no—
189#892—21no—
190#890—21no—
191#889—22no—
192#888—22no—
193#888—22no—
194#888C2314yes—
195#888C2314yes—
196#887—21no—
197#886—22no—
198#885—22no—
199#883—22no—
200#67⋊C4—22no—
201#879—22no—
202#879—22no—
203#878—22no—
204#878—24no—
205#878—24no—
206#878—24no—
207#878—24no—
208#877—22no—
209C4×D12C2311yescharacteristic
210C4×D12C2311yescharacteristic
211#872—21no—
212C42×D3—21no—
213#869—21no—
214#869—21no—
215#869C2312yes—
216#869C2312yes—
217C4×Dic6D411yescharacteristic
218C4×Dic6D412yes—
219C4×Dic6D411yescharacteristic
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2312yes—
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2311yescharacteristic
225C3×C4⋊C8C2312yes—
226C3×C4⋊C8C2312yes—
227C3×#103C2314yes—
228C3×#102C2314yes—
229#835C2314yes—
230#835C2314yes—
231#832C2312yes—
232#832C2314yes—
233#832C2314yes—
234#832C2312yes—
235#821C2314yes—
236#818C2314yes—
237#817C2314yes—
238#816C2314yes—
239#815C2314yes—
240Dic3⋊C8C2314yes—
241Dic3⋊C8C2314yes—
242C8×Dic3C2314yes—
243#810C2312yes—
244#809C2312yes—
245#808C2312yes—
246#807C2312yes—
247#803C2312yes—
248C4×C3⋊C8C2312yes—
249C23×Q8—61no—
250C2×AGL(1,ℤ/8)—31no—
251C2×AGL(1,ℤ/8)C2×D312yes—
252#559—31no—
253#559—32no—
254#557—31no—
255#556—31no—
256#556—32no—
257#553—62no—
258#553—61no—
259#550—31no—
260D4×Q8—32no—
261D4×Q8—34no—
262D4×Q8—32no—
263D4×Q8—61no—
264D4×Q8—61no—
265D4×Q8—62no—
266#548—61no—
267#532—32no—
268#532C2×D311yescharacteristic
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8—31no—
271#529—62no—
272#529—61no—
273C2×C22⋊Q8—62no—
274C2×C22⋊Q8—61no—
275C4×#41—32no—
276C4×#41—31no—
277C4×#41—61no—
278C2×C4×Q8—31no—
279C2×C4×D4—32no—
280C2×C4×D4C2×D311yescharacteristic
281#489—34no—
282#489—34no—
283#489—34no—
284#487—32no—
285#487—34no—
286#486—32no—
287#486—34no—
288#477—32no—
289#477—34no—
290#476—32no—
291#476—34no—
292#475—32no—
293#475—34no—
294#474—32no—
295#474—34no—
296#463—34no—
297#463—34no—
298#463C2×D314yes—
299#461—34no—
300#461C2×D312yes—
301#459—34no—
302#459C2×D312yes—
303#446—34no—
304#446—32no—
305C8×Q8—32no—
306#442—34no—
307#442—32no—
308#440—34no—
309#440—32no—
310C4×SD16—34no—
311C4×SD16—32no—
312C4×D8—34no—
313C4×D8—32no—
314#428—32no—
315#428—31no—
316#423—32no—
317#423C2×D311yescharacteristic
318#418—31no—
319#417—32no—
320#417—32no—
321#417—32no—
322#417—31no—
323#417C2×D312yes—
324C4×M16—32no—
325C4×M16—31no—
326C24×C3—21no—
327C3×#41—24no—
328C3×#41—24no—
329C2×C3×Q8C2412yes—
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—22no—
335C2×C3×D4#4114yescomplemented
336C2×C3×D4C2412yes—
337C2×C3×D4C2412yes—
338C22×C3×C4—21no—
339C22×C3×C4—22no—
340C22×C3×C4—22no—
341C22×C3×C4—22no—
342C22×C3×C4—44no—
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2411yescharacteristic
346C2×#67—21no—
347C2×#67—22no—
348C2×#67—22no—
349C22×Dic3—22no—
350C22×Dic3—22no—
351C22×Dic3—24no—
352C22×Dic3—24no—
353C22×Dic3—22no—
354C22×Dic3—48no—
355C22×Dic3C2×D412yes—
356C22×Dic3C2×D412yes—
357#237—44no—
358#235—22no—
359#235—22no—
360C2×D12C2411yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—21no—
363C2×C4×D3—21no—
364C2×Dic6—24no—
365C2×Dic6—22no—
366C2×Dic6—22no—
367C2×Dic6—24no—
368C2×Dic6—24no—
369C2×Dic6—48no—
370C2×Dic6—416no—
371C2×Dic6—48no—
372C2×Dic6—44no—
373C2×Dic6—48no—
374C2×Dic6C2×D412yes—
375C2×Dic6C2×D411yescharacteristic
376C2×Dic6C2×D411yescharacteristic
377C2×Dic6C2411yescharacteristic
378C3×SD16—28no—
379C3×D8—28no—
380C3×M16—24no—
381C2×C3×C8C2414yes—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4C2412yes—
386C3×C22⋊C4—22no—
387C3×C22⋊C4—22no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—22no—
390C3×C42C2×D411yescharacteristic
391C3×C42C2×D411yescharacteristic
392C3×C42C2411yescharacteristic
393C3×C42C2411yescharacteristic
394#217—21no—
395#217—22no—
396#217—24no—
397#217—24no—
398#217—22no—
399#217—22no—
400#217—22no—
401#214—24no—
402#213—24no—
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407C4⋊Dic3—22no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3C2×D412yes—
413C4⋊Dic3C2×D411yescharacteristic
414C4⋊Dic3C2×D411yescharacteristic
415C4⋊Dic3C2411yescharacteristic
416C4⋊Dic3C2411yescharacteristic
417C4⋊Dic3C2414yes—
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—22no—
421Dic3⋊C4—24no—
422Dic3⋊C4—24no—
423Dic3⋊C4—22no—
424Dic3⋊C4C2×D412yes—
425Dic3⋊C4C2×D412yes—
426Dic3⋊C4C2×D412yes—
427Dic3⋊C4C2×D412yes—
428C4×Dic3—21no—
429C4×Dic3—21no—
430C4×Dic3—21no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3C2×D412yes—
434C4×Dic3C2×D412yes—
435C4×Dic3C2412yes—
436C4×Dic3C2412yes—
437#208—22no—
438#208—22no—
439C2×C3⋊C8C2412yes—
440C2×C3⋊C8C2412yes—
441C2×#41—31no—
442C2×#41—61no—
443C2×#41C22×D312yes—
444C22×Q8—31no—
445C22×Q8—62no—
446C22×Q8—62no—
447C22×Q8—64no—
448C22×Q8—62no—
449C22×Q8—61no—
450C22×Q8—128no—
451C22×D4C22×D311yescharacteristic
452C23×C4—21no—
453C23×C4—62no—
454AGL(1,ℤ/8)—28no—
455AGL(1,ℤ/8)—64no—
456C2×SD16—32no—
457C2×SD16C22×D314yes—
458C2×D8—32no—
459C2×D8C22×D314yes—
460C2×M16—31no—
461C2×M16—31no—
462C2×M16C22×D312yes—
463C4⋊Q8—34no—
464C4⋊Q8—34no—
465C4⋊Q8—32no—
466C4⋊Q8—32no—
467C4⋊Q8—32no—
468C4⋊Q8—62no—
469C4⋊Q8—62no—
470C4⋊Q8—61no—
471C4⋊Q8—61no—
472C4⋊Q8C22×D311yescharacteristic
473#127—32no—
474#127C22×D311yescharacteristic
475#126—62no—
476#126—62no—
477#126—62no—
478#125—62no—
479#125—61no—
480#124—32no—
481#124—32no—
482#124—62no—
483#124—61no—
484#124C22×D312yes—
485#123—62no—
486#123—62no—
487#123—62no—
488C22⋊Q8—64no—
489C22⋊Q8—64no—
490C22⋊Q8—64no—
491C22⋊Q8—64no—
492C22⋊Q8—62no—
493C22⋊Q8—61no—
494C22⋊Q8—62no—
495C22⋊Q8—62no—
496C22⋊Q8—64no—
497#121—21no—
498#121—21no—
499#121—61no—
500#121—62no—
501#121—62no—
502#121—62no—
503C4×Q8—31no—
504C4×Q8—32no—
505C4×Q8—31no—
506C4×Q8—31no—
507C4×Q8—32no—
508C4×Q8—31no—
509C4×Q8—32no—
510C4×Q8—32no—
511C4×Q8—31no—
512C4×Q8—31no—
513C4×Q8—61no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—34no—
519C4×D4—34no—
520C4×D4—32no—
521C4×D4—32no—
522C4×D4—31no—
523C4×D4—31no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4—62no—
528C4×D4—62no—
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—62no—
538#117—62no—
539#117—61no—
540#117—61no—
541C2×C4⋊C4—32no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—32no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—61no—
546C2×C4⋊C4C22×D311yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—62no—
549C2×C42—32no—
550C2×C42—62no—
551C2×C42—61no—
552C2×C42C22×D311yescharacteristic
553#107—34no—
554#107—32no—
555#106—34no—
556#106—32no—
557C4⋊C8—34no—
558C4⋊C8—34no—
559C4⋊C8C22×D312yes—
560C4⋊C8C22×D312yes—
561#103—34no—
562#103—34no—
563#103—34no—
564#103—32no—
565#103C22×D314yes—
566#102—34no—
567#102—34no—
568#102—32no—
569#102—32no—
570#102—34no—
571#102—32no—
572#102C22×D314yes—
573#97—34no—
574#97—32no—
575C4×C8—34no—
576C4×C8—32no—
577C23×C3—24no—
578C23×C3—22no—
579C23×C3—22no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3C22×D411yescharacteristic
583C22×D3—21no—
584C3×Q8—22no—
585C3×Q8—22no—
586C3×D4—24no—
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—22no—
590C3×D4—44no—
591C3×D4—42no—
592C3×D4—81no—
593C3×D4C2×#4114yes—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—41no—
598C2×C3×C4—44no—
599C2×C3×C4—42no—
600C2×C3×C4—44no—
601C2×C3×C4—44no—
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C22×D411yescharacteristic
604C2×C3×C4C22×D411yescharacteristic
605C2×C3×C4C22×D411yescharacteristic
606C2×C3×C4C22×D411yescharacteristic
607C2×C3×C4C2×#4112yes—
608C2×C3×C42−1+412yes—
609C2×C3×C4C2511yescharacteristic
610#67—42no—
611#67—44no—
612#67—82no—
613C2×Dic3—24no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—24no—
618C2×Dic3—42no—
619C2×Dic3—48no—
620C2×Dic3—44no—
621C2×Dic3—48no—
622C2×Dic3—44no—
623C2×Dic3—82no—
624C2×Dic3C22×D412yes—
625C2×Dic3C22×D412yes—
626C2×Dic3C22×D412yes—
627C2×Dic3C22×D412yes—
628D12—21no—
629D12—21no—
630C4×D3—42no—
631C4×D3—42no—
632C4×D3—81no—
633Dic6—22no—
634Dic6—24no—
635Dic6—21no—
636Dic6—21no—
637Dic6—48no—
638Dic6—44no—
639Dic6—44no—
640Dic6—48no—
641Dic6AGL(1,ℤ/8)14yescomplemented
642C3×C8—24no—
643C3⋊C8—22no—
644C3⋊C8—22no—
645C24—21no—
646#41—24no—
647#41—24no—
648#41—62no—
649#41—62no—
650#41—124no—
651C2×Q8—31no—
652C2×Q8—32no—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—64no—
656C2×Q8—64no—
657C2×Q8—64no—
658C2×Q8—62no—
659C2×Q8—62no—
660C2×Q8—124no—
661C2×Q8—128no—
662C2×Q8—128no—
663C2×Q8—1216no—
664C2×Q8—128no—
665C2×Q8C23×D312yes—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—22no—
671C2×D4—31no—
672C2×D4—62no—
673C2×D4—62no—
674C2×D4—61no—
675C2×D4#23714yescomplemented
676C2×D4C23×D312yes—
677C2×D4C23×D312yes—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—44no—
685C22×C4—62no—
686C22×C4—64no—
687C22×C4—64no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—128no—
694C22×C4D3×D411yescharacteristic
695C22×C4D3×D411yescharacteristic
696C22×C4C23×D311yescharacteristic
697SD16—28no—
698SD16—64no—
699D8—28no—
700D8—64no—
701M16—24no—
702M16—62no—
703M16—62no—
704C2×C8—32no—
705C2×C8—32no—
706C2×C8C23×D314yes—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—32no—
711C4⋊C4—31no—
712C4⋊C4—32no—
713C4⋊C4—31no—
714C4⋊C4—32no—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—34no—
718C4⋊C4—31no—
719C4⋊C4—31no—
720C4⋊C4—64no—
721C4⋊C4—64no—
722C4⋊C4—62no—
723C4⋊C4—62no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—62no—
729C4⋊C4—61no—
730C4⋊C4—61no—
731C4⋊C4C23×D312yes—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—62no—
737C22⋊C4—62no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—61no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C42—32no—
748C42—32no—
749C42—32no—
750C42—32no—
751C42—62no—
752C42—62no—
753C42—61no—
754C42—61no—
755C42—61no—
756C42D3×D411yescharacteristic
757C42D3×D411yescharacteristic
758C42C23×D311yescharacteristic
759C42C23×D311yescharacteristic
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—24no—
763C22×C3—48no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3#54812yes—
770C22×C3C23×D411yescharacteristic
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C3×C4—21no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—42no—
778C3×C4—42no—
779C3×C4#54812yes—
780C3×C4C2×AGL(1,ℤ/8)12yes—
781C3×C4C22×#4111yescharacteristic
782C3×C4C2×2−1+411yescharacteristic
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—41no—
787Dic3—41no—
788Dic3—44no—
789Dic3—41no—
790Dic3C2×AGL(1,ℤ/8)14yes—
791C23—22no—
792C23—24no—
793C23—22no—
794C23—42no—
795C23—42no—
796C23—61no—
797C23C2×D3×D411yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—34no—
801Q8—64no—
802Q8—62no—
803Q8—61no—
804Q8—61no—
805Q8—124no—
806Q8—128no—
807Q8—128no—
808Q8—124no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—24no—
813D4—44no—
814D4—42no—
815D4—61no—
816D4—61no—
817D4—81no—
818D4—124no—
819D4—122no—
820D4—242no—
821D4C2×#23714yes—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—41no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—64no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—64no—
839C2×C4—128no—
840C2×C4—124no—
841C2×C4—122no—
842C2×C4—128no—
843C2×C4—124no—
844C2×C4—122no—
845C2×C4—122no—
846C2×C4—241no—
847C2×C4—242no—
848C2×C4C2×D3×D411yescharacteristic
849C2×C4C2×D3×D411yescharacteristic
850C2×C4C2×D3×D411yescharacteristic
851C2×C4C2×D3×D411yescharacteristic
852C2×C4C2×D3×D411yescharacteristic
853C2×C4C2×#23712yes—
854C2×C4#101012yes—
855C2×C4C24×D311yescharacteristic
856C8—24no—
857C8—62no—
858C8—62no—
859C2×C3—22no—
860C2×C3—44no—
861C2×C3—82no—
862C2×C3C2×#54811yescharacteristic
863C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
864C2×C3#358611yescharacteristic
865D3—81no—
866C22—21no—
867C22—21no—
868C22—24no—
869C22—48no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22#559812yes—
879C22C22×D3×D411yescharacteristic
880C4—21no—
881C4—21no—
882C4—21no—
883C4—34no—
884C4—42no—
885C4—42no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—124no—
890C4—121no—
891C4—121no—
892C4—121no—
893C4#559812yes—
894C4D3×AGL(1,ℤ/8)12yes—
895C4C22×#23711yescharacteristic
896C4C2×#101011yescharacteristic
897C3#6131711yescharacteristic, complemented, Sylow
898C2—22no—
899C2—44no—
900C2—82no—
901C2—241no—
902C2C2×#559811yescharacteristic
903C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
904C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3036C2
socleC22×C3C23×D4
hypercenter#3036D3
hypocenterC3#61317
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #86220C2semidirect
2. C2×D4×Dic6C2semidirect
3. C3×#3036C2semidirect
4. #83931C2semidirect
5. Dic3×AGL(1,ℤ/8)C2semidirect
6. #83283C2semidirect
7. C4×#932C2semidirect
8. #80521C2semidirect
9. #80518C2semidirect
10. #80416C2semidirect
11. #80414C2semidirect
12. #80323C2semidirect
13. #80318C2semidirect
14. #79060C2semidirect
15. #79046C2semidirect
16. #78878C2semidirect
17. #78870C2semidirect
28. #5732C22semidirect
29. #5721C22semidirect
30. #5718C22semidirect
31. #5713C22semidirect
32. #5681C22semidirect
33. #5671C22semidirect
71. #5079C22semidirect
72. #5070C22semidirect
73. #5055C22semidirect
81. #4851C22semidirect
82. #4850C22semidirect
83. #4846C22semidirect
84. #4842C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
88. #4794C22semidirect
89. #4793C22semidirect
90. #4792C22semidirect
91. #4791C22semidirect
92. #4765C22semidirect
93. #4761C22semidirect
94. #4760C22semidirect
95. #4759C22semidirect
109. #3036D3semidirect
335. C2×C3×D4#41semidirect
641. Dic6AGL(1,ℤ/8)semidirect
675. C2×D4#237semidirect
897. C3#61317semidirect

Maximal subgroups

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

subgroupindex
#862202
C2×D4×Dic62
C3×#30362
#839312
Dic3×AGL(1,ℤ/8)2
#832832
C4×#9322
#805212
#805182
#804162
#804142
#803232
#803182
#790602
#790462
#788782
#788702
#613173