Finite Group Databasebeta

← #11664282

Subgroups — #11664282

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86225C211yesmaximal, characteristic, complemented
2C4×#1004C211yesmaximal, characteristic, complemented
3C3×#3036C211yesmaximal, characteristic, complemented
4#83949C212yesmaximal, complemented
5#83930C212yesmaximal, complemented
6#83296C211yesmaximal, characteristic, complemented
7C2×#5008C211yesmaximal, characteristic, complemented
8#80511C214yesmaximal, complemented
9#80508C214yesmaximal, complemented
10#80411C212yesmaximal, complemented
11#80408C212yesmaximal, complemented
12#80314C212yesmaximal, complemented
13#80313C212yesmaximal, complemented
14#79060C211yesmaximal, characteristic, complemented
15#79040C211yesmaximal, characteristic, complemented
16#78875C212yesmaximal, complemented
17#78869C212yesmaximal, complemented
18#60597—31nomaximal, Sylow
19C2×#1004C2211yescharacteristic
20C2×C3×AGL(1,ℤ/8)C2212yes—
21C3×#532C2211yescharacteristic, complemented
22C2×C3×C4×D4C2211yescharacteristic
23#5833C2212yes—
24#5827C2212yescomplemented
25C2×#950C2212yes—
26#5798C2211yescharacteristic
27C2×C4×#67—22no—
28#5728C2212yescomplemented
29#5716C2212yescomplemented
30#5682C2214yescomplemented
31#5618—22no—
32#5598—22no—
33#5563—21no—
34#5555—21no—
35#5546—21no—
36#5546C2212yes—
37#5545—21no—
38#5545C2212yes—
39C4×D3×D4—21no—
40C4×D3×D4C2212yes—
41#5543—21no—
42#5542—21no—
43C4×#237—21no—
44C4×#237C2212yes—
45#5504C2211yescharacteristic
46#5504C2211yescharacteristic
47#5486—22no—
48C4×#235C2211yescharacteristic
49C4×#235C2211yescharacteristic
50C2×#869C2211yescharacteristic, complemented
51C3×#463C2214yescomplemented
52C3×#461C2212yescomplemented
53C3×#459C2212yescomplemented
54C3×#423C2211yescharacteristic, complemented
55C3×#417C2212yescomplemented
56#5233C2212yescomplemented
57C2×#832C2212yes—
58#5173C2214yes—
59#5169C2214yes—
60#5164C2214yescomplemented
61Dic3×SD16C2214yescomplemented
62#5158C2214yes—
63#5156C2214yes—
64#5152C2214yescomplemented
65Dic3×D8C2214yescomplemented
66#5133C2212yes—
67#5129C2212yes—
68#5122C2212yescomplemented
69#5121C2212yescomplemented
70#5090C2211yescharacteristic, complemented
71#5083C2211yescharacteristic, complemented
72#5075C2211yescharacteristic, complemented
73#5072C2211yescharacteristic, complemented
74#5057C2212yescomplemented
75#5054C2212yescomplemented
76#5008C2212yescomplemented
77#5008C2212yescomplemented
78#5008C2214yescomplemented
79C2×#808C2212yescomplemented
80C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
81#4851C2212yescomplemented
82#4850C2212yescomplemented
83#4846C2212yescomplemented
84#4842C2212yescomplemented
85#4840C2214yescomplemented
86#4835C2212yescomplemented
87#4833C2212yescomplemented
88#4814C2214yescomplemented
89#4805C2214yescomplemented
90#4789C2214yescomplemented
91#4788C2214yescomplemented
92#4785C2214yescomplemented
93#4784C2214yescomplemented
94#4777C2214yescomplemented
95#4758C2214yescomplemented
96#3511—31no—
97C4×H(5,𝔽2)—31no—
98#3125—34no—
99#3118—34no—
100#3116—32no—
101#3109—32no—
102#3106—32no—
103#3101—32no—
104#3099—32no—
105#3079—31no—
106C2×#476—31no—
107#3036D311yescharacteristic, complemented
108#3035—31no—
109#3012—32no—
110#2952—32no—
111#2946—32no—
112#2925—31no—
113C2×C3×#41C2312yes—
114C22×C3×D4C2311yescharacteristic
115C23×C3×C4—21no—
116C22×#67—22no—
117#1004—24no—
118#1004—24no—
119C2×#237—22no—
120C2×#237—21no—
121C2×#237C2312yes—
122C2×D3×D4—21no—
123C2×D3×D4C2312yes—
124C2×#235C2311yescharacteristic
125C2×#235C2311yescharacteristic
126C22×C4×D3—22no—
127C22×Dic6—21no—
128C3×AGL(1,ℤ/8)—28no—
129C2×C3×SD16C2314yes—
130C2×C3×D8C2314yes—
131C2×C3×M16C2312yes—
132C3×C4⋊Q8C2311yescharacteristic
133C3×#127C2311yescharacteristic
134C3×#124C2312yes—
135C3×#121—21no—
136C3×#121—21no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4C2312yes—
142C3×C4×D4C2312yes—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C22⋊C4—21no—
145C2×C3×C42C2311yescharacteristic
146C2×#217—22no—
147#950—28no—
148#946C2314yes—
149Q8×Dic3C2314yes—
150C2×#216C2312yes—
151C2×#215C2312yes—
152#939—24no—
153#938—22no—
154#938C2314yes—
155#936—22no—
156D4×Dic3—24no—
157D4×Dic3—21no—
158D4×Dic3—21no—
159D4×Dic3—22no—
160D4×Dic3C2312yes—
161D4×Dic3C2314yes—
162D4×Dic3C2312yes—
163C2×#214C2312yes—
164C2×#213C2312yes—
165#930—22no—
166C4×#67—21no—
167C4×#67—21no—
168C4×#67—22no—
169C4×#67—22no—
170C4×#67—22no—
171C4×#67—22no—
172C4×#67—22no—
173C4×#67—22no—
174C4×#67D412yes—
175C4×#67D412yes—
176C2×(C2×D3)⋊C4—22no—
177#926—22no—
178#926C2311yescharacteristic
179#926C2311yescharacteristic
180C2×C4⋊Dic3—21no—
181C2×C4⋊Dic3—22no—
182C2×C4⋊Dic3C2312yes—
183#924—22no—
184C2×Dic3⋊C4—22no—
185C2×C4×Dic3—22no—
186C22×C3⋊C8C2312yes—
187#897—22no—
188#893—21no—
189#893C2312yes—
190#892—22no—
191#892—21no—
192#892C2312yes—
193D3×C4⋊C4—21no—
194D3×C4⋊C4C2312yes—
195#890—22no—
196#887—21no—
197#887—22no—
198#887C2312yes—
199#886—24no—
200#885—24no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#67⋊C4—22no—
204#67⋊C4—22no—
205D3×C22⋊C4—22no—
206D3×C22⋊C4—22no—
207#879—24no—
208#878—24no—
209#877—22no—
210#877—22no—
211C4×D12D411yescharacteristic
212C4×D12D411yescharacteristic
213C4×D12C2311yescharacteristic
214C4×D12C2311yescharacteristic
215#872—21no—
216#872C2312yes—
217C42×D3—21no—
218C42×D3C2312yes—
219#869—21no—
220#869—21no—
221#869C2312yes—
222#869C2312yes—
223C4×Dic6D411yescharacteristic
224C4×Dic6D411yescharacteristic
225C4×Dic6C2311yescharacteristic
226C4×Dic6C2311yescharacteristic
227C3×C4⋊C8C2312yes—
228C3×C4⋊C8C2312yes—
229C3×#103C2314yes—
230C3×#102C2314yes—
231#835C2312yes—
232#835C2312yes—
233#832C2312yes—
234#832C2314yes—
235#832C2312yes—
236#832C2314yes—
237#821C2314yes—
238(C2×D3)⋊C8C2314yes—
239(C2×D3)⋊C8C2314yes—
240#818C2314yes—
241#817C2314yes—
242#816C2314yes—
243#815C2314yes—
244C8×Dic3C2314yes—
245#808C2314yes—
246#808C2314yes—
247C4⋊(C3⋊C8)C2312yes—
248C4⋊(C3⋊C8)C2311yescharacteristic
249C4⋊(C3⋊C8)C2311yescharacteristic
250C2×H(5,𝔽2)—31no—
251C2×AGL(1,ℤ/8)C2×D312yes—
252C2×#135—32no—
253#556—61no—
254#555—61no—
255#554—61no—
256#553—62no—
257#548—62no—
258#547—61no—
259#542—34no—
260#537—32no—
261#533—32no—
262#532—32no—
263#532C2×D311yescharacteristic, complemented
264C2×C4⋊Q8—31no—
265#520—31no—
266#520—32no—
267#520—32no—
268#520—31no—
269#520—61no—
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#483—34no—
284#482—34no—
285#481—34no—
286#477—32no—
287#476—32no—
288#476—32no—
289#476—34no—
290#476—32no—
291#475—32no—
292#474—32no—
293#464—32no—
294#463—32no—
295#463C2×D314yescomplemented
296#462—31no—
297#461—31no—
298#461C2×D312yescomplemented
299#460—31no—
300#459—31no—
301#459C2×D312yescomplemented
302#452—34no—
303#450—34no—
304#449—34no—
305#447—34no—
306#442—34no—
307#442—34no—
308#441—34no—
309#440—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#106—32no—
319#423C2×D311yescharacteristic, complemented
320C2×C4⋊C8—31no—
321#417—32no—
322#417C2×D312yescomplemented
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C24×C3—21no—
328C23×D3—22no—
329C3×#41—24no—
330C3×#41—24no—
331C2×C3×Q8C2412yes—
332C2×C3×D4—22no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—22no—
337C2×C3×D4#4114yescomplemented
338C2×C3×D4C2412yes—
339C2×C3×D4C2412yes—
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—22no—
343C22×C3×C4—22no—
344C22×C3×C4—82no—
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D411yescharacteristic
347C22×C3×C4C2411yescharacteristic
348C2×#67—216no—
349C2×#67—21no—
350C2×#67—22no—
351C2×#67—24no—
352C2×#67—22no—
353C2×#67C2×D412yes—
354C22×Dic3—22no—
355C22×Dic3—22no—
356C22×Dic3—24no—
357C22×Dic3—22no—
358C22×Dic3—22no—
359#237—28no—
360#237—24no—
361#237—24no—
362#237—84no—
363D3×D4—28no—
364D3×D4—24no—
365D3×D4—24no—
366#235—22no—
367#235—22no—
368#235—22no—
369#235#4114yescomplemented
370C2×D12C2×D411yescharacteristic
371C2×D12C2411yescharacteristic
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—22no—
375C2×C4×D3—21no—
376C2×C4×D3—22no—
377C2×C4×D3—84no—
378C2×C4×D3C2×D412yes—
379C2×C4×D3C2×D412yes—
380C2×C4×D3C2412yes—
381C2×Dic6—22no—
382C2×Dic6—22no—
383C2×Dic6—82no—
384C2×Dic6C2×D411yescharacteristic
385C2×Dic6C2411yescharacteristic
386C3×SD16—28no—
387C3×D8—28no—
388C3×M16—24no—
389C2×C3×C8C2414yes—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4C2412yes—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C42C2×D411yescharacteristic
399C3×C42C2×D411yescharacteristic
400C3×C42C2411yescharacteristic
401C3×C42C2411yescharacteristic
402#217—21no—
403#217—22no—
404#217—22no—
405#217—24no—
406#217—24no—
407#217C2×D412yes—
408#216—24no—
409#215—24no—
410#214—24no—
411#213—24no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—24no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4C2×D412yes—
418(C2×D3)⋊C4C2×D412yes—
419C4⋊Dic3—22no—
420C4⋊Dic3—22no—
421C4⋊Dic3—22no—
422C4⋊Dic3—24no—
423C4⋊Dic3C2×D411yescharacteristic
424C4⋊Dic3C2×D411yescharacteristic
425C4⋊Dic3C2414yes—
426C4⋊Dic3C2411yescharacteristic
427C4⋊Dic3C2411yescharacteristic
428Dic3⋊C4—21no—
429Dic3⋊C4—21no—
430Dic3⋊C4—22no—
431Dic3⋊C4—22no—
432Dic3⋊C4—24no—
433Dic3⋊C4C2×D412yes—
434Dic3⋊C4C2×D412yes—
435C4×Dic3—21no—
436C4×Dic3—21no—
437C4×Dic3—21no—
438C4×Dic3—22no—
439C4×Dic3—22no—
440C4×Dic3—24no—
441C4×Dic3C2×D412yes—
442C4×Dic3C2×D412yes—
443C4×Dic3C2412yes—
444C2×C3⋊C8—24no—
445C2×C3⋊C8C2412yes—
446C2×C3⋊C8C2412yes—
447H(5,𝔽2)—64no—
448H(5,𝔽2)—64no—
449C2×#41—31no—
450C2×#41—32no—
451C2×#41—31no—
452C2×#41—62no—
453C2×#41—61no—
454C2×#41C22×D312yes—
455C22×Q8—61no—
456C22×D4—32no—
457C22×D4—61no—
458C22×D4—62no—
459C22×D4C22×D311yescharacteristic
460C23×C4—21no—
461C23×C4—62no—
462AGL(1,ℤ/8)—28no—
463#135—68no—
464C2×Q16—32no—
465C2×SD16—32no—
466C2×SD16—32no—
467C2×SD16C22×D314yes—
468C2×D8—32no—
469C2×D8C22×D314yes—
470C2×M16C22×D312yes—
471C22×C8—32no—
472C4⋊Q8—32no—
473C4⋊Q8—32no—
474C4⋊Q8—61no—
475C4⋊Q8—61no—
476C4⋊Q8C22×D311yescharacteristic
477#127C22×D311yescharacteristic
478#126—64no—
479#125—62no—
480#124—62no—
481#124—64no—
482#124C22×D312yes—
483#123—64no—
484C22⋊Q8—34no—
485C22⋊Q8—64no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488#121—21no—
489#121—21no—
490#121—34no—
491#121—62no—
492#121—62no—
493#121—64no—
494C4×Q8—31no—
495C4×Q8—31no—
496C4×Q8—34no—
497C4×Q8—32no—
498C4×Q8—31no—
499C4×Q8—31no—
500C4×Q8—62no—
501C4×Q8—61no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—32no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—32no—
510C4×D4—34no—
511C4×D4—32no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4—31no—
515C4×D4—31no—
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—64no—
525C4×D4—61no—
526C4×D4—62no—
527C4×D4—61no—
528C4×D4—61no—
529C4×D4—62no—
530C4×D4—62no—
531C4×D4—61no—
532C4×D4—61no—
533C4×D4C22×D312yes—
534C4×D4C22×D312yes—
535#117—31no—
536#117—32no—
537#117—31no—
538#117—32no—
539#117—62no—
540#117—62no—
541#117—61no—
542#117—62no—
543#117—62no—
544#117—61no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—62no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4—61no—
551C2×C4⋊C4C22×D311yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C22⋊C4—62no—
556C2×C22⋊C4—62no—
557C2×C42—32no—
558C2×C42—62no—
559C2×C42—61no—
560C2×C42C22×D311yescharacteristic
561#107—34no—
562#106—34no—
563#106—34no—
564#106—34no—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8C22×D312yes—
569C4⋊C8C22×D312yes—
570#103—32no—
571#103—32no—
572#103—34no—
573#103C22×D314yes—
574#102—34no—
575#102—34no—
576#102—32no—
577#102—32no—
578#102—34no—
579#102C22×D314yes—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—22no—
585C23×C3—24no—
586C23×C3—22no—
587C23×C3—81no—
588C23×C3—81no—
589C23×C3C22×D411yescharacteristic
590C22×D3—21no—
591C22×D3—28no—
592C22×D3—82no—
593C22×D3—82no—
594C22×D3C22×D412yes—
595C3×Q8—22no—
596C3×Q8—22no—
597C3×D4—24no—
598C3×D4—22no—
599C3×D4—22no—
600C3×D4—22no—
601C3×D4—42no—
602C3×D4—44no—
603C3×D4—42no—
604C3×D4C2×#4114yes—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—41no—
609C2×C3×C4—44no—
610C2×C3×C4—44no—
611C2×C3×C4—82no—
612C2×C3×C4—81no—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C2×#4112yes—
619C2×C3×C4C2×#4112yes—
620C2×C3×C4C2511yescharacteristic
621#67—28no—
622#67—28no—
623#67—24no—
624#67—24no—
625#67—84no—
626C2×Dic3—28no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—24no—
631C2×Dic3—82no—
632C2×Dic3—84no—
633C2×Dic3—82no—
634C2×Dic3—82no—
635C2×Dic3C22×D412yes—
636C2×Dic3C22×D412yes—
637C2×Dic3C22×D412yes—
638D12—22no—
639D12—21no—
640D12C2×#4112yes—
641C4×D3—24no—
642C4×D3—24no—
643C4×D3—22no—
644C4×D3—22no—
645C4×D3—42no—
646C4×D3—42no—
647C4×D3—82no—
648C4×D3—81no—
649C4×D3—82no—
650Dic6—22no—
651Dic6—21no—
652Dic6—44no—
653Dic6—82no—
654Dic6C2×#4112yes—
655C3×C8—24no—
656C3⋊C8—22no—
657C3⋊C8—22no—
658C24—21no—
659C24—62no—
660#41—24no—
661#41—24no—
662#41—34no—
663#41—64no—
664#41—68no—
665#41—64no—
666#41—62no—
667#41—62no—
668#41—62no—
669#41—244no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×Q8—62no—
673C2×Q8—62no—
674C2×Q8—242no—
675C2×Q8C23×D312yes—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—22no—
681C2×D4—32no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—62no—
685C2×D4—64no—
686C2×D4—68no—
687C2×D4—62no—
688C2×D4—616no—
689C2×D4—61no—
690C2×D4—64no—
691C2×D4—64no—
692C2×D4#23714yescomplemented
693C2×D4C23×D312yes—
694C2×D4C23×D312yes—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—32no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—62no—
706C22×C4—62no—
707C22×C4—64no—
708C22×C4—61no—
709C22×C4—62no—
710C22×C4—61no—
711C22×C4—61no—
712C22×C4—82no—
713C22×C4—244no—
714C22×C4D3×D411yescharacteristic
715C22×C4D3×D411yescharacteristic
716C22×C4C23×D311yescharacteristic
717Q16—64no—
718SD16—28no—
719SD16—64no—
720SD16—64no—
721D8—28no—
722D8—64no—
723M16—24no—
724C2×C8—32no—
725C2×C8—32no—
726C2×C8—64no—
727C2×C8C23×D314yes—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—31no—
732C4⋊C4—31no—
733C4⋊C4—32no—
734C4⋊C4—32no—
735C4⋊C4—34no—
736C4⋊C4—31no—
737C4⋊C4—31no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—64no—
741C4⋊C4—64no—
742C4⋊C4—62no—
743C4⋊C4—61no—
744C4⋊C4—62no—
745C4⋊C4—62no—
746C4⋊C4—61no—
747C4⋊C4C23×D312yes—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—22no—
751C22⋊C4—22no—
752C22⋊C4—32no—
753C22⋊C4—32no—
754C22⋊C4—32no—
755C22⋊C4—62no—
756C22⋊C4—62no—
757C22⋊C4—64no—
758C22⋊C4—62no—
759C22⋊C4—62no—
760C22⋊C4—64no—
761C22⋊C4—64no—
762C22⋊C4—61no—
763C22⋊C4—61no—
764C22⋊C4—61no—
765C42—32no—
766C42—32no—
767C42—32no—
768C42—62no—
769C42—62no—
770C42—64no—
771C42—61no—
772C42—61no—
773C42—61no—
774C42D3×D411yescharacteristic
775C42D3×D411yescharacteristic
776C42C23×D311yescharacteristic
777C42C23×D311yescharacteristic
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—24no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
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—88no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—42no—
800C3×C4—42no—
801C3×C4#52512yes—
802C3×C4#57712yes—
803C3×C4C22×#4111yescharacteristic
804C3×C4C22×#4111yescharacteristic
805Dic3—22no—
806Dic3—22no—
807Dic3—22no—
808Dic3—22no—
809Dic3—44no—
810Dic3—41no—
811Dic3—41no—
812C23—22no—
813C23—24no—
814C23—22no—
815C23—32no—
816C23—68no—
817C23—61no—
818C23—81no—
819C23—81no—
820C23—242no—
821C23—242no—
822C23C2×D3×D411yescharacteristic
823Q8—22no—
824Q8—22no—
825Q8—32no—
826Q8—61no—
827Q8—62no—
828Q8—124no—
829Q8—242no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—24no—
834D4—32no—
835D4—42no—
836D4—44no—
837D4—42no—
838D4—68no—
839D4—68no—
840D4—64no—
841D4—64no—
842D4—61no—
843D4—62no—
844D4—244no—
845D4C2×#23714yes—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—41no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—68no—
856C2×C4—61no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—64no—
860C2×C4—64no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—64no—
864C2×C4—82no—
865C2×C4—81no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—241no—
869C2×C4—242no—
870C2×C4—242no—
871C2×C4—242no—
872C2×C4—244no—
873C2×C4—242no—
874C2×C4—242no—
875C2×C4C2×D3×D411yescharacteristic
876C2×C4C2×D3×D411yescharacteristic
877C2×C4C2×D3×D411yescharacteristic
878C2×C4C2×D3×D411yescharacteristic
879C2×C4C2×D3×D411yescharacteristic
880C2×C4C2×#23712yes—
881C2×C4D3×#4112yes—
882C2×C4C24×D311yescharacteristic
883C8—24no—
884C8—62no—
885C8—62no—
886C2×C3—22no—
887C2×C3—44no—
888C2×C3—82no—
889C2×C3C2×#52511yescharacteristic
890C2×C3C2×#57711yescharacteristic
891C2×C3#358511yescharacteristic
892D3—42no—
893D3—42no—
894C22—21no—
895C22—21no—
896C22—24no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—84no—
907C22—121no—
908C22—121no—
909C22—248no—
910C22#560612yes—
911C22C22×D3×D411yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—62no—
918C4—62no—
919C4—62no—
920C4—62no—
921C4—121no—
922C4—121no—
923C4—124no—
924C4#560612yes—
925C4#577512yes—
926C4C22×#23711yescharacteristic
927C4C2×D3×#4111yescharacteristic
928C3#6059711yescharacteristic, complemented, Sylow
929C2—22no—
930C2—44no—
931C2—82no—
932C2—122no—
933C2—122no—
934C2C2×#560611yescharacteristic
935C2C2×#577511yescharacteristic
936C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3036C2
socleC22×C3C23×D4
hypercenter#3036D3
hypocenterC3#60597
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. #86225C2semidirect
2. C4×#1004C2semidirect
3. C3×#3036C2semidirect
4. #83949C2semidirect
5. #83930C2semidirect
6. #83296C2semidirect
7. C2×#5008C2semidirect
8. #80511C2semidirect
9. #80508C2semidirect
10. #80411C2semidirect
11. #80408C2semidirect
12. #80314C2semidirect
13. #80313C2semidirect
14. #79060C2semidirect
15. #79040C2semidirect
16. #78875C2semidirect
17. #78869C2semidirect
21. C3×#532C22semidirect
24. #5827C22semidirect
28. #5728C22semidirect
29. #5716C22semidirect
30. #5682C22semidirect
50. C2×#869C22semidirect
51. C3×#463C22semidirect
52. C3×#461C22semidirect
53. C3×#459C22semidirect
54. C3×#423C22semidirect
55. C3×#417C22semidirect
56. #5233C22semidirect
60. #5164C22semidirect
61. Dic3×SD16C22semidirect
64. #5152C22semidirect
65. Dic3×D8C22semidirect
68. #5122C22semidirect
69. #5121C22semidirect
70. #5090C22semidirect
71. #5083C22semidirect
72. #5075C22semidirect
73. #5072C22semidirect
74. #5057C22semidirect
75. #5054C22semidirect
76. #5008C22semidirect
77. #5008C22semidirect
78. #5008C22semidirect
79. C2×#808C22semidirect
80. C2×C4⋊(C3⋊C8)C22semidirect
81. #4851C22semidirect
82. #4850C22semidirect
83. #4846C22semidirect
84. #4842C22semidirect
85. #4840C22semidirect
86. #4835C22semidirect
87. #4833C22semidirect
88. #4814C22semidirect
89. #4805C22semidirect
90. #4789C22semidirect
91. #4788C22semidirect
92. #4785C22semidirect
93. #4784C22semidirect
94. #4777C22semidirect
95. #4758C22semidirect
107. #3036D3semidirect
263. #532C2×D3semidirect
295. #463C2×D3semidirect
298. #461C2×D3semidirect
301. #459C2×D3semidirect
319. #423C2×D3semidirect
322. #417C2×D3semidirect
337. C2×C3×D4#41semidirect
369. #235#41semidirect
692. C2×D4#237semidirect
928. C3#60597semidirect

Maximal subgroups

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

subgroupindex
#862252
C4×#10042
C3×#30362
#839492
#839302
#832962
C2×#50082
#805112
#805082
#804112
#804082
#803142
#803132
#790602
#790402
#788752
#788692
#605973