Finite Group Databasebeta

← #10833395

Subgroups — #10833395

Order 768.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87275C211yesmaximal, characteristic
2C3×#3007C211yesmaximal, characteristic, complemented
3C22×#837C211yesmaximal, characteristic, complemented
4C2×#5202C211yesmaximal, characteristic, complemented
5#82809C211yesmaximal, characteristic, complemented
6#82732C211yesmaximal, characteristic, complemented
7#72110C211yesmaximal, characteristic, complemented
8#72106C211yesmaximal, characteristic, complemented
9#72100C211yesmaximal, characteristic, complemented
10#70312C211yesmaximal, characteristic, complemented
11#70306C211yesmaximal, characteristic, complemented
12#70305C211yesmaximal, characteristic, complemented
13#70298C211yesmaximal, characteristic, complemented
14#69985C211yesmaximal, characteristic, complemented
15#69965C211yesmaximal, characteristic, complemented
16#24467—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×#1009C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C2×C3×#137C2211yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic, complemented
22#5834—21no—
23#5833—21no—
24#5833C2211yescharacteristic
25#5830—21no—
26#5830C2211yescharacteristic
27#5829—21no—
28#5829—22no—
29#5827C2211yescharacteristic
30#5817—21no—
31C2×#947C2211yescharacteristic, complemented
32C2×#942C2211yescharacteristic, complemented
33D4×#67—21no—
34D4×#67—22no—
35#5791—21no—
36#5791C2211yescharacteristic
37C2×#930—21no—
38C2×#930C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic, complemented
40C22×#208C2211yescharacteristic, complemented
41C3×#452—21no—
42C3×#452—21no—
43C3×#451—21no—
44C3×#450—21no—
45C3×#417C2211yescharacteristic
46C3×#417C2211yescharacteristic, complemented
47C3×#407C2211yescharacteristic, complemented
48C2×#837—24no—
49C2×#837C2211yescharacteristic
50C2×#837C2211yescharacteristic
51C2×#837C2211yescharacteristic, complemented
52C2×#837C2211yescharacteristic, complemented
53#5229C2211yescharacteristic, complemented
54#5225C2211yescharacteristic, complemented
55#5202—24no—
56C2×#825C2211yescharacteristic, complemented
57C2×#825C2211yescharacteristic, complemented
58C2×#823C2211yescharacteristic, complemented
59C2×#823C2211yescharacteristic, complemented
60#5052—21no—
61#5051—21no—
62#5049—21no—
63#5048—21no—
64#4990—22no—
65#4988C2211yescharacteristic, complemented
66#4977C2211yescharacteristic, complemented
67#4966C2211yescharacteristic, complemented
68#4964C2211yescharacteristic, complemented
69#4958—22no—
70#4555C2211yescharacteristic, complemented
71#4555C2211yescharacteristic, complemented
72#4554C2211yescharacteristic, complemented
73#4554C2211yescharacteristic, complemented
74#3488—31no—
75#3056—31no—
76C2×#455—31no—
77#3007D311yescharacteristic, complemented
78C22×#104—31no—
79#2850—31no—
80#2040—31no—
81#2037—31no—
82#2007—31no—
83#2004—31no—
84#1900—31no—
85#1896—31no—
86#1882—31no—
87#1860—31no—
88#1792—31no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41—22no—
92C2×C3×#41—22no—
93C2×C3×#41—41no—
94C2×C3×#41—41no—
95C2×C3×#41D411yescharacteristic
96C2×C3×#41D411yescharacteristic
97C2×C3×#41C2311yescharacteristic
98C2×C3×#41C2311yescharacteristic
99C22×C3×Q8D411yescharacteristic
100C22×C3×Q8C2311yescharacteristic
101C22×C3×D4—21no—
102C22×C3×D4D411yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C22×#67—22no—
106C22×#67D412yes—
107C23×Dic3—21no—
108#1009—22no—
109#1009—22no—
110#1009—41no—
111#1009—41no—
112C2×#239—21no—
113C2×D3×D4—22no—
114C2×D3×D4—21no—
115C2×#235—21no—
116C2×#235C2311yescharacteristic
117C22×D12—21no—
118C22×D12C2311yescharacteristic
119C3×#137—22no—
120C3×#137—22no—
121C3×#137—41no—
122C3×#137—41no—
123C2×C3×Q16—21no—
124C2×C3×Q16—21no—
125C2×C3×SD16—21no—
126C2×C3×SD16—21no—
127C2×C3×M16C2311yescharacteristic
128C2×C3×M16C2311yescharacteristic
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4—21no—
136#953—22no—
137#953—21no—
138#947—22no—
139#947—21no—
140#947—22no—
141#947—41no—
142#946—22no—
143#946—21no—
144Q8×Dic3—21no—
145C2×#216—21no—
146#942—22no—
147#942—41no—
148C2×#215—21no—
149#940—22no—
150#940—21no—
151#939—22no—
152#939—22no—
153#939—22no—
154#938—22no—
155#938—21no—
156#937—22no—
157#937—22no—
158#937—22no—
159D4×Dic3—21no—
160D4×Dic3—22no—
161#930—22no—
162#930—22no—
163#930—21no—
164#930—21no—
165#930—21no—
166#930—21no—
167#930—21no—
168#930—21no—
169#930—21no—
170#930D411yescharacteristic
171#930D411yescharacteristic
172#929—22no—
173#929—21no—
174C4×#67—22no—
175C4×#67—22no—
176C4×#67—21no—
177C4×#67—21no—
178C2×(C2×D3)⋊C4—22no—
179C2×(C2×D3)⋊C4—22no—
180C2×(C2×D3)⋊C4—22no—
181C2×(C2×D3)⋊C4D412yes—
182#926—21no—
183#926C2311yescharacteristic
184C2×C4⋊Dic3—21no—
185C2×C4⋊Dic3C2311yescharacteristic
186#924—21no—
187#924D411yescharacteristic
188#924D411yescharacteristic
189C2×C4×Dic3—22no—
190C2×C4×Dic3—21no—
191C2×C4×Dic3—41no—
192C2×C4×Dic3C2311yescharacteristic
193C2×C4×Dic3C2311yescharacteristic
194C2×#208—21no—
195C2×#208—22no—
196C2×#208—41no—
197C2×#208C2311yescharacteristic
198C2×#208C2311yescharacteristic
199C22×C3⋊C8—21no—
200C3×#103—21no—
201C3×#103—21no—
202C3×#102—21no—
203C3×#102—21no—
204C3×C22⋊C8—21no—
205C3×C22⋊C8—21no—
206#837—22no—
207#837—22no—
208#837—22no—
209#837D414yescomplemented
210#835—21no—
211#835—21no—
212C3⋊#95—22no—
213C3⋊#95—22no—
214#825—22no—
215#825—41no—
216#823—22no—
217#823—41no—
218#810—21no—
219#809—21no—
220#808—21no—
221#807—21no—
222C2×H(5,𝔽2)—31no—
223C22×#41C2×D311yescharacteristic
224C2×#137—31no—
225C2×#137C2×D311yescharacteristic
226C2×#137C2×D311yescharacteristic, complemented
227C22×M16—31no—
228#550—61no—
229#548—61no—
230#546—62no—
231#546—61no—
232D42—62no—
233D42—61no—
234#537—31no—
235#537—61no—
236#535—31no—
237#535—61no—
238C2×#124—31no—
239#525—31no—
240#525—61no—
241C2×C22⋊Q8C2×D311yescharacteristic, complemented
242C2×#121—31no—
243C2×#121—61no—
244#520—31no—
245C22×C42—31no—
246#470—61no—
247#468—61no—
248#467—61no—
249#465—61no—
250#455—64no—
251#452—21no—
252#452—21no—
253#451—21no—
254#450—21no—
255#428—31no—
256C2×#104—31no—
257C2×#104—31no—
258C2×#104—31no—
259C2×#104—31no—
260C2×#104—31no—
261C2×#104—31no—
262C2×#104—64no—
263#419—31no—
264#417—31no—
265#417C2×D311yescharacteristic
266#417C2×D311yescharacteristic, complemented
267C2×#100—31no—
268C2×#100—31no—
269#407C2×D311yescharacteristic, complemented
270#391—31no—
271#390—31no—
272#388—62no—
273#386—62no—
274#382—31no—
275#343—31no—
276#343—31no—
277#339—31no—
278#339—31no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—22no—
282C23×D3C2×D412yes—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—22no—
286C3×#41—22no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—42no—
292C3×#41—42no—
293C3×#41—41no—
294C3×#41—41no—
295C3×#41—42no—
296C3×#41—42no—
297C3×#41C2×D412yes—
298C3×#41#4112yes—
299C2×C3×Q8—21no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—21no—
304C2×C3×Q8—21no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—41no—
308C2×C3×Q8C2×D411yescharacteristic
309C2×C3×Q8C2×D411yescharacteristic
310C2×C3×D4—21no—
311C2×C3×D4—22no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—41no—
317C2×C3×D4—42no—
318C2×C3×D4—42no—
319C2×C3×D4C2×D411yescharacteristic
320C2×C3×D4C2×D411yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—42no—
333C22×C3×C4—42no—
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2411yescharacteristic
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—22no—
345C2×#67—22no—
346C2×#67—22no—
347C2×#67—21no—
348C2×#67—22no—
349C2×#67—44no—
350C2×#67—84no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—22no—
354C22×Dic3—42no—
355C22×Dic3—42no—
356C22×Dic3—42no—
357C22×Dic3C2×D412yes—
358#239—42no—
359#239—42no—
360D3×D4—44no—
361D3×D4—44no—
362D3×D4—42no—
363D3×D4—42no—
364#235—21no—
365#235—21no—
366#235—21no—
367#235—21no—
368#235—42no—
369#235—42no—
370C2×D12—22no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—21no—
375C2×D12—21no—
376C2×D12—21no—
377C2×D12—42no—
378C2×D12—42no—
379C2×D12C2×D411yescharacteristic
380C2×C4×D3—22no—
381C2×C4×D3—21no—
382C2×Dic6C2×D411yescharacteristic
383C3×Q16—42no—
384C3×Q16—42no—
385C3×SD16—42no—
386C3×SD16—42no—
387C3×M16—21no—
388C3×M16—21no—
389C3×M16—21no—
390C3×M16—21no—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—41no—
396C3×C4⋊C4—41no—
397C3×C22⋊C4—41no—
398C3×C22⋊C4—41no—
399#217—22no—
400#217—22no—
401#217—21no—
402#217—21no—
403#217—21no—
404#216—42no—
405#215—42no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—44no—
414(C2×D3)⋊C4—44no—
415C4⋊Dic3—22no—
416C4⋊Dic3—21no—
417C4⋊Dic3—21no—
418C4⋊Dic3C2×D411yescharacteristic
419C4⋊Dic3C2×D411yescharacteristic
420Dic3⋊C4—22no—
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423C4×Dic3—22no—
424C4×Dic3—21no—
425C4×Dic3—21no—
426C4×Dic3—21no—
427C4×Dic3—21no—
428C4×Dic3—42no—
429C4×Dic3C2×D412yescomplemented
430#208—21no—
431#208—21no—
432#208—21no—
433#208—42no—
434#208C2×D412yescomplemented
435C2×C3⋊C8—21no—
436C2×C3⋊C8—21no—
437C2×C3⋊C8—42no—
438H(5,𝔽2)—62no—
439H(5,𝔽2)—62no—
440H(5,𝔽2)—121no—
441H(5,𝔽2)—121no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—31no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41—61no—
450C2×#41—61no—
451C2×#41#6711yescharacteristic
452C2×#41#6711yescharacteristic
453C2×#41C22×D311yescharacteristic
454C2×#41C22×D311yescharacteristic
455C22×Q8#6711yescharacteristic
456C22×Q8C22×D311yescharacteristic
457C22×D4—21no—
458C22×D4—32no—
459C22×D4—31no—
460C22×D4—61no—
461C22×D4—62no—
462C22×D4—62no—
463C22×D4—61no—
464C22×D4#6711yescharacteristic
465C23×C4—21no—
466C23×C4—61no—
467C23×C4C22×D311yescharacteristic
468#137—22no—
469#137—22no—
470#137—41no—
471#137—41no—
472#137—62no—
473#137—121no—
474C2×Q16—21no—
475C2×Q16—21no—
476C2×Q16—61no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—61no—
480C2×M16—31no—
481C2×M16—31no—
482C2×M16—61no—
483C2×M16—62no—
484C2×M16—121no—
485C2×M16C22×D311yescharacteristic
486C2×M16C22×D311yescharacteristic
487C22×C8—61no—
488#127—62no—
489#127—61no—
490#124—62no—
491#124—62no—
492#124—61no—
493#124—121no—
494#123—62no—
495#123—61no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—31no—
501C22⋊Q8—31no—
502C22⋊Q8—61no—
503C22⋊Q8—62no—
504C22⋊Q8—61no—
505#121—31no—
506#121—31no—
507#121—61no—
508#121—61no—
509#121—61no—
510#121—62no—
511#121—62no—
512#121—62no—
513#121—62no—
514#121—62no—
515#121—62no—
516#121—61no—
517#121—61no—
518#121—61no—
519#121—61no—
520#121—61no—
521#120—62no—
522#120—62no—
523#120—62no—
524#120—62no—
525#120—61no—
526C4×Q8—61no—
527C4×D4—62no—
528C4×D4—62no—
529C4×D4—62no—
530C4×D4—61no—
531C4×D4—61no—
532C4×D4—61no—
533#117—31no—
534#117—61no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—61no—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—32no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4—62no—
543C2×C22⋊C4—62no—
544C2×C42—31no—
545C2×C42—31no—
546C2×C42—62no—
547C2×C42—61no—
548C2×C42—121no—
549#107—61no—
550#106—61no—
551#104—34no—
552#104—62no—
553#104—62no—
554#104—62no—
555#104—62no—
556#104—121no—
557#103—21no—
558#103—21no—
559#103—61no—
560#103—61no—
561#103—61no—
562#102—21no—
563#102—21no—
564#102—61no—
565#100—62no—
566#100—121no—
567C22⋊C8—21no—
568C22⋊C8—21no—
569#95—62no—
570#95—62no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—41no—
577C23×C3—42no—
578C23×C3—42no—
579C23×C3—81no—
580C23×C3#12011yescharacteristic
581C23×C3#12011yescharacteristic
582C23×C3C22×D411yescharacteristic
583C22×D3—22no—
584C22×D3—21no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—44no—
588C22×D3—42no—
589C22×D3—42no—
590C22×D3—82no—
591C22×D3—82no—
592C3×Q8—21no—
593C3×Q8—21no—
594C3×Q8—21no—
595C3×Q8—42no—
596C3×Q8—41no—
597C3×Q8—41no—
598C3×Q8—41no—
599C3×Q8—41no—
600C3×Q8#12112yes—
601C3×D4—22no—
602C3×D4—22no—
603C3×D4—21no—
604C3×D4—21no—
605C3×D4—21no—
606C3×D4—42no—
607C3×D4—42no—
608C3×D4—42no—
609C3×D4—41no—
610C3×D4—41no—
611C3×D4#12112yes—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—42no—
627C2×C3×C4—42no—
628C2×C3×C4—42no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—42no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4#12011yescharacteristic
637C2×C3×C4#12011yescharacteristic
638C2×C3×C4C22×D411yescharacteristic
639C2×C3×C4C22×D411yescharacteristic
640C2×C3×C4C22×D411yescharacteristic
641C2×C3×C4C2×#4111yescharacteristic
642C2×C3×C4H(5,𝔽2)11yescharacteristic
643C2×C3×C4H(5,𝔽2)11yescharacteristic
644#67—44no—
645#67—41no—
646#67—41no—
647#67—44no—
648#67—42no—
649#67—81no—
650#67—82no—
651#67—82no—
652#67—82no—
653#67—82no—
654C2×Dic3—22no—
655C2×Dic3—21no—
656C2×Dic3—22no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—22no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—48no—
664C2×Dic3—41no—
665C2×Dic3—42no—
666C2×Dic3—82no—
667D12—21no—
668D12—21no—
669D12—44no—
670D12—41no—
671D12—41no—
672D12—41no—
673D12—41no—
674C4×D3—44no—
675C4×D3—41no—
676C4×D3—41no—
677Dic6—21no—
678Dic6—21no—
679C3×C8—41no—
680C3×C8—41no—
681C3⋊C8—22no—
682C3⋊C8—41no—
683C24—21no—
684C24—32no—
685C24—62no—
686C24D3×D411yescharacteristic
687#41—21no—
688#41—21no—
689#41—22no—
690#41—22no—
691#41—21no—
692#41—21no—
693#41—21no—
694#41—21no—
695#41—42no—
696#41—42no—
697#41—41no—
698#41—41no—
699#41—42no—
700#41—42no—
701#41—61no—
702#41—61no—
703#41—61no—
704#41—61no—
705#41—122no—
706#41—122no—
707#41—122no—
708#41—122no—
709#41D3×D412yes—
710#41#23712yes—
711C2×Q8—21no—
712C2×Q8—22no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8—31no—
720C2×Q8—41no—
721C2×Q8C2×#6711yescharacteristic
722C2×Q8C2×#6711yescharacteristic
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—31no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—62no—
734C2×D4—62no—
735C2×D4—61no—
736C2×D4—62no—
737C2×D4—61no—
738C2×D4—62no—
739C2×D4—62no—
740C2×D4—62no—
741C2×D4—61no—
742C2×D4—62no—
743C2×D4—61no—
744C2×D4—61no—
745C2×D4—61no—
746C2×D4—61no—
747C2×D4—61no—
748C2×D4—61no—
749C2×D4—122no—
750C2×D4—122no—
751C2×D4—124no—
752C2×D4—124no—
753C2×D4—122no—
754C2×D4—122no—
755C2×D4—124no—
756C2×D4—244no—
757C2×D4C2×#6711yescharacteristic
758C2×D4C2×#6711yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—32no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—62no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—62no—
777C22×C4—61no—
778C22×C4—122no—
779C22×C4—122no—
780C22×C4—122no—
781C22×C4D3×D411yescharacteristic
782C22×C4D3×D411yescharacteristic
783C22×C4D3×D411yescharacteristic
784C22×C4C2×#6711yescharacteristic
785C22×C4C2×#6711yescharacteristic
786C22×C4C23×D311yescharacteristic
787Q16—42no—
788Q16—42no—
789Q16—122no—
790SD16—42no—
791SD16—42no—
792SD16—122no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—32no—
798M16—61no—
799M16—61no—
800M16—61no—
801M16—122no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—61no—
805C2×C8—61no—
806C2×C8—122no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—31no—
810C4⋊C4—31no—
811C4⋊C4—41no—
812C4⋊C4—41no—
813C4⋊C4—62no—
814C4⋊C4—62no—
815C4⋊C4—61no—
816C4⋊C4—61no—
817C4⋊C4—61no—
818C4⋊C4—61no—
819C22⋊C4—41no—
820C22⋊C4—41no—
821C22⋊C4—62no—
822C22⋊C4—62no—
823C22⋊C4—62no—
824C22⋊C4—62no—
825C22⋊C4—62no—
826C22⋊C4—61no—
827C22⋊C4—61no—
828C22⋊C4—61no—
829C22⋊C4—62no—
830C22⋊C4—62no—
831C22⋊C4—61no—
832C22⋊C4—61no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C42—32no—
836C42—62no—
837C42—61no—
838C42—61no—
839C42—61no—
840C42—61no—
841C42—122no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—22no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—41no—
853C22×C3—41no—
854C22×C3—41no—
855C22×C3—41no—
856C22×C3—41no—
857C22×C3—84no—
858C22×C3#45512yescomplemented
859C22×C3C2×#12011yescharacteristic
860C22×C3D4211yescharacteristic
861C22×C3#54611yescharacteristic
862C2×D3—41no—
863C2×D3—42no—
864C2×D3—42no—
865C2×D3—41no—
866C2×D3—42no—
867C2×D3—41no—
868C2×D3—82no—
869C2×D3—82no—
870C2×D3—164no—
871C3×C4—22no—
872C3×C4—21no—
873C3×C4—21no—
874C3×C4—41no—
875C3×C4—81no—
876C3×C4—81no—
877C3×C4C2×#12111yescharacteristic
878C3×C4#53411yescharacteristic
879C3×C4D4211yescharacteristic
880C3×C4#54611yescharacteristic
881Dic3—42no—
882Dic3—42no—
883Dic3—41no—
884Dic3—42no—
885Dic3—41no—
886Dic3—41no—
887C23—22no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—41no—
893C23—42no—
894C23—42no—
895C23—61no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—81no—
900C23—124no—
901C23—122no—
902C23—122no—
903C23—242no—
904C23—242no—
905C23#93711yescharacteristic
906C23#93711yescharacteristic
907C23C2×D3×D411yescharacteristic
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—42no—
912Q8—41no—
913Q8—41no—
914Q8—41no—
915Q8—41no—
916Q8—61no—
917Q8—61no—
918Q8#93912yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—41no—
928D4—41no—
929D4—61no—
930D4—61no—
931D4—124no—
932D4—124no—
933D4—124no—
934D4—122no—
935D4—121no—
936D4—121no—
937D4—121no—
938D4—121no—
939D4—121no—
940D4—121no—
941D4—242no—
942D4—241no—
943D4—242no—
944D4—242no—
945D4—242no—
946D4#93912yes—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—62no—
975C2×C4—61no—
976C2×C4—62no—
977C2×C4—124no—
978C2×C4—121no—
979C2×C4—121no—
980C2×C4—121no—
981C2×C4—128no—
982C2×C4—121no—
983C2×C4—121no—
984C2×C4—121no—
985C2×C4—122no—
986C2×C4—242no—
987C2×C4#93711yescharacteristic
988C2×C4#93711yescharacteristic
989C2×C4C2×D3×D411yescharacteristic
990C2×C4C2×D3×D411yescharacteristic
991C2×C4C2×#23711yescharacteristic
992C2×C4#100411yescharacteristic
993C2×C4#100411yescharacteristic
994C2×C4C22×#6711yescharacteristic
995C8—41no—
996C8—41no—
997C8—62no—
998C8—121no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—22no—
1002C2×C3—42no—
1003C2×C3—41no—
1004C2×C3—81no—
1005C2×C3#241011yescharacteristic
1006C2×C3C2×#45511yescharacteristic
1007C2×C3#301811yescharacteristic
1008D3—82no—
1009D3—81no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—22no—
1018C22—42no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—84no—
1026C22—122no—
1027C22—121no—
1028C22—122no—
1029C22—121no—
1030C22—121no—
1031C22—122no—
1032C22—242no—
1033C22—242no—
1034C22—484no—
1035C22#520212yescomplemented
1036C22#559011yescharacteristic
1037C22#559111yescharacteristic
1038C22C2×#93711yescharacteristic
1039C4—21no—
1040C4—21no—
1041C4—22no—
1042C4—41no—
1043C4—81no—
1044C4—81no—
1045C4—122no—
1046C4—122no—
1047C4—122no—
1048C4—121no—
1049C4—121no—
1050C4—121no—
1051C4#559011yescharacteristic
1052C4#559111yescharacteristic
1053C4C2×#93911yescharacteristic
1054C4#580411yescharacteristic
1055C3#2446711yescharacteristic, complemented, Sylow
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—242no—
1063C2—241no—
1064C2#8260611yescharacteristic
1065C2C2×#520211yescharacteristic
1066C2#8400411yescharacteristic
subgroupG/H
centerC22C2×#937
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3007C2
socleC22×C3C2×#120
prime radical#87275C2
hypercenter#3007D3
hypocenterC3#24467
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
2. C3×#3007C2semidirect
3. C22×#837C2semidirect
4. C2×#5202C2semidirect
5. #82809C2semidirect
6. #82732C2semidirect
7. #72110C2semidirect
8. #72106C2semidirect
9. #72100C2semidirect
10. #70312C2semidirect
11. #70306C2semidirect
12. #70305C2semidirect
13. #70298C2semidirect
14. #69985C2semidirect
15. #69965C2semidirect
20. C2×C3×#137C22semidirect
21. C2×C3×C22⋊Q8C22semidirect
31. C2×#947C22semidirect
32. C2×#942C22semidirect
39. C22×C4×Dic3C22semidirect
40. C22×#208C22semidirect
46. C3×#417C22semidirect
47. C3×#407C22semidirect
51. C2×#837C22semidirect
52. C2×#837C22semidirect
53. #5229C22semidirect
54. #5225C22semidirect
56. C2×#825C22semidirect
57. C2×#825C22semidirect
58. C2×#823C22semidirect
59. C2×#823C22semidirect
65. #4988C22semidirect
66. #4977C22semidirect
67. #4966C22semidirect
68. #4964C22semidirect
70. #4555C22semidirect
71. #4555C22semidirect
72. #4554C22semidirect
73. #4554C22semidirect
77. #3007D3semidirect
209. #837D4semidirect
226. C2×#137C2×D3semidirect
241. C2×C22⋊Q8C2×D3semidirect
266. #417C2×D3semidirect
269. #407C2×D3semidirect
429. C4×Dic3C2×D4semidirect
434. #208C2×D4semidirect
858. C22×C3#455semidirect
1035. C22#5202semidirect
1055. C3#24467semidirect

Maximal subgroups

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

subgroupindex
#872752
C3×#30072
C22×#8372
C2×#52022
#828092
#827322
#721102
#721062
#721002
#703122
#703062
#703052
#702982
#699852
#699652
#244673