Finite Group Databasebeta

← #10815972

Subgroups — #10815972

Order 768.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83911C211yesmaximal, characteristic
2#83796C211yesmaximal, characteristic, complemented
3C2×#5144C211yesmaximal, characteristic, complemented
4C2×#4821C211yesmaximal, characteristic, complemented
5#78663C211yesmaximal, characteristic, complemented
6C3×#1876C211yesmaximal, characteristic, complemented
7#72085C211yesmaximal, characteristic, complemented
8#70390C211yesmaximal, characteristic, complemented
9#70383C211yesmaximal, characteristic, complemented
10#70367C211yesmaximal, characteristic, complemented
11#69997C211yesmaximal, characteristic, complemented
12#68941C211yesmaximal, characteristic, complemented
13#68927C211yesmaximal, characteristic, complemented
14#68694C211yesmaximal, characteristic, complemented
15#68601C211yesmaximal, characteristic, complemented
16#22889—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×C3×#135C2211yescharacteristic
19C2×C3×#131C2211yescharacteristic, complemented
20#5828C2211yescharacteristic
21C2×#950C2211yescharacteristic
22C2×#907C2211yescharacteristic
23C2×D3×M16C2211yescharacteristic
24C2×#901C2211yescharacteristic
25C2×#872C2211yescharacteristic
26C2×C3×#104C2211yescharacteristic
27C2×C3×#104C2211yescharacteristic, complemented
28C3×#408C2211yescharacteristic
29C2×#837C2211yescharacteristic
30C2×#837C2211yescharacteristic, complemented
31#5234C2211yescharacteristic
32#5234C2211yescharacteristic, complemented
33#5233C2211yescharacteristic
34#5187C411yescharacteristic, complemented
35#5186C411yescharacteristic, complemented
36#5173C411yescharacteristic, complemented
37#5172C411yescharacteristic, complemented
38#5170C411yescharacteristic, complemented
39#5169C411yescharacteristic, complemented
40#5158C411yescharacteristic, complemented
41#5156C411yescharacteristic, complemented
42#5144—24no—
43C2×#825C2211yescharacteristic
44#5128—21no—
45#5127—21no—
46#5126C2211yescharacteristic
47C2×#822C2211yescharacteristic, complemented
48#5122C2211yescharacteristic, complemented
49#5113C2211yescharacteristic
50#5111—21no—
51C8×#67—21no—
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×#819C2211yescharacteristic, complemented
55#5102C2211yescharacteristic, complemented
56C2×#815C2211yescharacteristic, complemented
57C2×C8×Dic3C2211yescharacteristic, complemented
58C2×#805C2211yescharacteristic
59#4821—24no—
60#4727—21no—
61#4727—21no—
62#4726—21no—
63D3×C22⋊C8—21no—
64C3×#341C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66#4558C2211yescharacteristic, complemented
67#4555C2211yescharacteristic, complemented
68#4524C2211yescharacteristic, complemented
69#4523C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933—31no—
73C2×#421—31no—
74#2880—31no—
75#1975—31no—
76#1937—31no—
77#1929—31no—
78#1897—31no—
79#1876—31no—
80#1876D311yescharacteristic, complemented
81#1866—31no—
82#1855—31no—
83#1765—31no—
84#1750—31no—
85C2×C3×#41C2311yescharacteristic
86C2×C3×#41C2311yescharacteristic
87D3×#41—22no—
88D3×#41—22no—
89D3×#41—41no—
90D3×#41—41no—
91C2×#239C2×C411yescharacteristic
92C2×D3×Q8C2×C411yescharacteristic
93C2×#237—21no—
94C2×#237C2×C411yescharacteristic
95C2×D3×D4—21no—
96C2×D3×D4C2×C411yescharacteristic
97C2×#235—21no—
98C2×#235C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3C2311yescharacteristic
101C3×#135—41no—
102C3×#135—41no—
103C2×C3×Q16C2×C411yescharacteristic
104C2×C3×SD16C2×C411yescharacteristic
105C2×C3×SD16C2×C411yescharacteristic
106C2×C3×D8C2×C411yescharacteristic
107C3×#131—22no—
108C3×#131—41no—
109C2×C3×M16—21no—
110C2×C3×M16C2311yescharacteristic
111C2×C3×M16C2311yescharacteristic
112C22×C3×C8—21no—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C2×C3×C42C2311yescharacteristic
116#950—22no—
117#950—22no—
118#946C2×C411yescharacteristic
119#946C2×C411yescharacteristic
120C2×#216C2×C411yescharacteristic
121C2×#215C2×C411yescharacteristic
122#938C2×C411yescharacteristic
123#938C2×C411yescharacteristic
124#937—21no—
125#935—21no—
126C2×#214C2×C411yescharacteristic
127C2×#213C2×C411yescharacteristic
128C4×#67—21no—
129C4×#67—21no—
130C2×(C2×D3)⋊C4—21no—
131#926C2311yescharacteristic
132C2×Dic3⋊C4—21no—
133C2×C4×Dic3C2311yescharacteristic
134C2×#208C2311yescharacteristic
135C2×#208C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#907—22no—
139#907—41no—
140D3×M16—22no—
141D3×M16—41no—
142#901—22no—
143#901—41no—
144C2×ΓL(1,𝔽25)—21no—
145C2×ΓL(1,𝔽25)—21no—
146C2×ΓL(1,𝔽25)—21no—
147C2×D3×C8—21no—
148C2×D3×C8—21no—
149C2×D3×C8—21no—
150#872—22no—
151#872—41no—
152C3×#104—22no—
153C3×#104—41no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156#837—22no—
157#837—22no—
158#835C2×C411yescharacteristic
159#835C2×C411yescharacteristic
160#832C2×C411yescharacteristic
161#832C2×C411yescharacteristic
162#830—21no—
163#830—21no—
164#830—21no—
165#830—21no—
166#825D414yescomplemented
167#822—22no—
168#821C2×C411yescharacteristic
169#821C2×C411yescharacteristic
170(C2×D3)⋊C8—21no—
171(C2×D3)⋊C8—21no—
172(C2×D3)⋊C8C2×C411yescharacteristic
173(C2×D3)⋊C8C2×C411yescharacteristic
174(C2×D3)⋊C8C2×C411yescharacteristic
175(C2×D3)⋊C8C2×C411yescharacteristic
176(C2×D3)⋊C8D411yescharacteristic
177(C2×D3)⋊C8D411yescharacteristic
178(C2×D3)⋊C8D411yescharacteristic
179(C2×D3)⋊C8D411yescharacteristic
180#819—41no—
181#816C2×C411yescharacteristic
182#816C2×C411yescharacteristic
183#815—21no—
184#815—41no—
185Dic3⋊C8—21no—
186Dic3⋊C8—21no—
187C8×Dic3—22no—
188C8×Dic3—21no—
189#805—22no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135C2×D311yescharacteristic
193C2×#131—31no—
194C2×#131—31no—
195C2×#131C2×D311yescharacteristic, complemented
196C22×M16—31no—
197#525—31no—
198C2×#117—31no—
199#452—31no—
200#452—31no—
201#451—31no—
202#450—31no—
203#449—31no—
204#449—31no—
205#448—31no—
206#447—31no—
207#443—64no—
208#436—61no—
209#435—61no—
210#435—61no—
211C8×D4—61no—
212C2×#108—31no—
213C2×#108—31no—
214#424—31no—
215#421—64no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104C2×D311yescharacteristic
221C2×#104C2×D311yescharacteristic, complemented
222#416—31no—
223#416—31no—
224#408—31no—
225#408—31no—
226#408—61no—
227#408—61no—
228#408C2×D311yescharacteristic
229#407—31no—
230#407—61no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—61no—
234#405—31no—
235C2×#97—31no—
236C2×C4×C8—31no—
237#341—31no—
238#341C2×D311yescharacteristic, complemented
239#339—31no—
240#339—31no—
241#336—31no—
242#336C2×D311yescharacteristic, complemented
243C23×D3—21no—
244C23×D3#4111yescharacteristic
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C2×C3×Q8C22×C411yescharacteristic
254C2×C3×Q8C22×C411yescharacteristic
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4C22×C411yescharacteristic
258C2×C3×D4C22×C411yescharacteristic
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4C2411yescharacteristic
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—21no—
266C2×#67—21no—
267C2×#67—21no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3#4111yescharacteristic
271#239—22no—
272#239—41no—
273D3×Q8—22no—
274D3×Q8—41no—
275#237—22no—
276#237—41no—
277#237—42no—
278#237—42no—
279D3×D4—22no—
280D3×D4—41no—
281D3×D4—42no—
282D3×D4—42no—
283#235—21no—
284#235—21no—
285#235—42no—
286#235—42no—
287#235C2×D412yes—
288#235#4112yes—
289C2×D12—21no—
290C2×D12C22×C411yescharacteristic
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3C22×C411yescharacteristic
301C2×C4×D3C22×C411yescharacteristic
302C2×C4×D3C2×D411yescharacteristic
303C2×C4×D3C2×D411yescharacteristic
304C2×Dic6—21no—
305C2×Dic6C22×C411yescharacteristic
306C3×Q16—41no—
307C3×SD16—41no—
308C3×SD16—41no—
309C3×D8—41no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—42no—
314C3×M16C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—42no—
322C2×C3×C8C22×C411yescharacteristic
323C2×C3×C8C22×C411yescharacteristic
324C2×C3×C8C2×D411yescharacteristic
325C2×C3×C8C2×D411yescharacteristic
326C3×C42—21no—
327C3×C42—21no—
328#217—21no—
329#217—21no—
330#217—21no—
331#216—22no—
332#215—22no—
333#214—22no—
334#213—22no—
335(C2×D3)⋊C4—21no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—42no—
338C4⋊Dic3C22×C411yescharacteristic
339C4⋊Dic3C22×C411yescharacteristic
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—42no—
343C4×Dic3—21no—
344C4×Dic3—21no—
345C4×Dic3C2×D412yes—
346#208—21no—
347#208—21no—
348#208—21no—
349#208—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C22×C411yescharacteristic
357C2×C3⋊C8C22×C411yescharacteristic
358C2×C3⋊C8C2×D411yescharacteristic
359C2×C3⋊C8C2×D411yescharacteristic
360ΓL(1,𝔽25)—42no—
361ΓL(1,𝔽25)—42no—
362ΓL(1,𝔽25)—42no—
363D3×C8—42no—
364D3×C8—42no—
365D3×C8—42no—
366C2×#41—31no—
367C2×#41—31no—
368C2×#41—31no—
369C2×#41—61no—
370C2×#41—61no—
371C2×#41—62no—
372C2×#41—62no—
373C2×#41—121no—
374C2×#41—121no—
375C2×#41C22×D311yescharacteristic
376C2×#41C22×D311yescharacteristic
377C22×Q8—31no—
378C22×D4—31no—
379C22×D4—61no—
380C23×C4—31no—
381C23×C4—61no—
382#135—41no—
383#135—41no—
384#135—62no—
385#135—62no—
386C2×Q16—31no—
387C2×Q16C4×D311yescharacteristic
388C2×SD16—31no—
389C2×SD16—31no—
390C2×SD16C4×D311yescharacteristic
391C2×SD16C4×D311yescharacteristic
392C2×D8—31no—
393C2×D8C4×D311yescharacteristic
394#131—22no—
395#131—41no—
396#131—62no—
397#131—62no—
398#131—121no—
399#131—121no—
400C2×M16—21no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—61no—
404C2×M16—61no—
405C2×M16—61no—
406C2×M16—62no—
407C2×M16—121no—
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—21no—
411C22×C8—31no—
412C22×C8—31no—
413C22×C8—61no—
414C22×C8—61no—
415C22×C8—61no—
416C22×C8C22×D311yescharacteristic
417C22×C8C22×D311yescharacteristic
418#123—61no—
419C22⋊Q8—31no—
420C22⋊Q8—31no—
421#121—31no—
422#121—31no—
423#120—61no—
424C4×D4—61no—
425C4×D4—61no—
426#117—31no—
427#117—62no—
428#117—121no—
429C2×C4⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42—31no—
432C2×C42C22×D311yescharacteristic
433#108—62no—
434#108—121no—
435C4⋊C8—61no—
436C4⋊C8—61no—
437#104—22no—
438#104—34no—
439#104—41no—
440#104—62no—
441#104—62no—
442#104—62no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102—31no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—31no—
460C22⋊C8—31no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8—61no—
466C22⋊C8—61no—
467#97—61no—
468#97—121no—
469C4×C8—62no—
470C4×C8—61no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3C2×#4111yescharacteristic
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—81no—
482C22×D3C4×D411yescharacteristic
483C22×D3C4×D411yescharacteristic
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—41no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4C23×C411yescharacteristic
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C2×#4111yescharacteristic
509C2×C3×C4H(5,𝔽2)11yescharacteristic
510C2×C3×C4H(5,𝔽2)11yescharacteristic
511#67—22no—
512#67—22no—
513#67—42no—
514#67—42no—
515#67—42no—
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—22no—
523C2×Dic3—42no—
524C2×Dic3—41no—
525C2×Dic3—41no—
526C2×Dic3C4×D411yescharacteristic
527C2×Dic3C4×D411yescharacteristic
528D12—21no—
529D12—42no—
530D12C4×D412yes—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—22no—
537C4×D3—21no—
538C4×D3—22no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—42no—
542C4×D3—42no—
543Dic6—21no—
544Dic6—42no—
545Dic6C4×D412yes—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—22no—
550C3×C8—21no—
551C3×C8—41no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—41no—
557C3⋊C8—41no—
558C24—31no—
559C24—61no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—32no—
569#41—32no—
570#41—61no—
571#41—61no—
572#41—62no—
573#41—62no—
574#41—122no—
575#41—122no—
576#41—121no—
577#41—122no—
578#41—122no—
579#41—121no—
580C2×Q8—31no—
581C2×Q8—61no—
582C2×Q8—62no—
583C2×Q8—121no—
584C2×Q8C2×C4×D311yescharacteristic
585C2×Q8C2×C4×D311yescharacteristic
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—121no—
597C2×D4—122no—
598C2×D4—122no—
599C2×D4C2×C4×D311yescharacteristic
600C2×D4C2×C4×D311yescharacteristic
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4C23×D311yescharacteristic
621Q16—41no—
622Q16—62no—
623SD16—41no—
624SD16—41no—
625SD16—62no—
626SD16—62no—
627D8—41no—
628D8—62no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—61no—
634M16—61no—
635M16—61no—
636M16—61no—
637M16—122no—
638M16—122no—
639M16—122no—
640M16D3×D412yes—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—42no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—122no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8C2×C4×D311yescharacteristic
662C2×C8C2×C4×D311yescharacteristic
663C2×C8D3×D411yescharacteristic
664C2×C8D3×D411yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—122no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—122no—
676C42—21no—
677C42—21no—
678C42—32no—
679C42—61no—
680C42—61no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3C2×C4×D411yescharacteristic
690C22×C3#54611yescharacteristic
691C22×C3#55111yescharacteristic
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—22no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—81no—
702C2×D3—81no—
703C2×D3—84no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—81no—
707C3×C4C2×C4×D411yescharacteristic
708C3×C4#51811yescharacteristic
709C3×C4D4211yescharacteristic
710C3×C4#54611yescharacteristic
711Dic3—22no—
712Dic3—21no—
713Dic3—21no—
714Dic3—42no—
715Dic3—41no—
716Dic3—41no—
717C23—21no—
718C23—21no—
719C23—31no—
720C23—31no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—121no—
725C23—121no—
726C23—122no—
727C23—122no—
728C23—241no—
729C23D3×#4111yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—21no—
734Q8—32no—
735Q8—61no—
736Q8—122no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—21no—
741D4—32no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—62no—
747D4—62no—
748D4—61no—
749D4—122no—
750D4—122no—
751D4—122no—
752D4—122no—
753D4—241no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—62no—
774C2×C4—61no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—62no—
781C2×C4—122no—
782C2×C4—122no—
783C2×C4—122no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4#100411yescharacteristic
791C2×C4D3×#4111yescharacteristic
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—22no—
797C8—41no—
798C8—61no—
799C8—61no—
800C8—61no—
801C8—61no—
802C8—121no—
803C8—121no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—81no—
807C2×C3—81no—
808C2×C3#235811yescharacteristic
809C2×C3#295511yescharacteristic
810C2×C3#295711yescharacteristic
811D3—41no—
812D3—41no—
813D3—42no—
814C22—21no—
815C22—21no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—61no—
826C22—61no—
827C22—61no—
828C22—62no—
829C22—121no—
830C22—121no—
831C22—241no—
832C22—241no—
833C22—244no—
834C22C4×D3×D411yescharacteristic
835C22#561211yescharacteristic
836C22#565911yescharacteristic
837C4—41no—
838C4—41no—
839C4—61no—
840C4—61no—
841C4—62no—
842C4—81no—
843C4—122no—
844C4—121no—
845C4—121no—
846C4#548611yescharacteristic
847C4C4×D3×D411yescharacteristic
848C4#559011yescharacteristic
849C4#561211yescharacteristic
850C3#2288911yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—81no—
854C2—81no—
855C2—121no—
856C2—121no—
857C2—122no—
858C2#7488011yescharacteristic
859C2#7988811yescharacteristic
860C2#7989911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1876C2
socleC22×C3C2×C4×D4
prime radical#83911C2
cosocleC22×C3×C4C24
hypercenter#1876D3
hypocenterC3#22889
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #83796C2semidirect
3. C2×#5144C2semidirect
4. C2×#4821C2semidirect
5. #78663C2semidirect
6. C3×#1876C2semidirect
7. #72085C2semidirect
8. #70390C2semidirect
9. #70383C2semidirect
10. #70367C2semidirect
11. #69997C2semidirect
12. #68941C2semidirect
13. #68927C2semidirect
14. #68694C2semidirect
15. #68601C2semidirect
19. C2×C3×#131C22semidirect
27. C2×C3×#104C22semidirect
30. C2×#837C22semidirect
32. #5234C22semidirect
34. #5187C4semidirect
35. #5186C4semidirect
36. #5173C4semidirect
37. #5172C4semidirect
38. #5170C4semidirect
39. #5169C4semidirect
40. #5158C4semidirect
41. #5156C4semidirect
47. C2×#822C22semidirect
48. #5122C22semidirect
54. C2×#819C22semidirect
55. #5102C22semidirect
56. C2×#815C22semidirect
57. C2×C8×Dic3C22semidirect
64. C3×#341C22semidirect
65. C3×#336C22semidirect
66. #4558C22semidirect
67. #4555C22semidirect
68. #4524C22semidirect
69. #4523C22semidirect
80. #1876D3semidirect
166. #825D4semidirect
195. C2×#131C2×D3semidirect
221. C2×#104C2×D3semidirect
238. #341C2×D3semidirect
242. #336C2×D3semidirect
850. C3#22889semidirect

Maximal subgroups

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

subgroupindex
#839112
#837962
C2×#51442
C2×#48212
#786632
C3×#18762
#720852
#703902
#703832
#703672
#699972
#689412
#689272
#686942
#686012
#228893