Finite Group Databasebeta

← #10815960

Subgroups — #10815960

Order 768.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83911C211yesmaximal, characteristic
2C2×#5196C211yesmaximal, characteristic, complemented
3#83793C211yesmaximal, characteristic, complemented
4C2×D3×#104C211yesmaximal, characteristic, complemented
5#78659C211yesmaximal, characteristic, complemented
6C3×#1876C211yesmaximal, characteristic, complemented
7#72008C211yesmaximal, characteristic, complemented
8#70382C211yesmaximal, characteristic, complemented
9#70377C211yesmaximal, characteristic, complemented
10#70376C211yesmaximal, characteristic, complemented
11#69999C211yesmaximal, characteristic, complemented
12#68941C211yesmaximal, characteristic, complemented
13#68918C211yesmaximal, characteristic, complemented
14#68646C211yesmaximal, characteristic, complemented
15#68599C211yesmaximal, characteristic, complemented
16#22888—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×C3×#135C2211yescharacteristic
19C2×C3×#131C2211yescharacteristic
20#5828C2211yescharacteristic
21C2×#950C2211yescharacteristic
22C2×#948C2211yescharacteristic
23C2×#948C2211yescharacteristic, complemented
24C2×D3×M16C2211yescharacteristic
25C2×C42×D3C2211yescharacteristic
26C2×C3×#104C2211yescharacteristic
27C2×C3×#104C2211yescharacteristic, complemented
28C3×#408C2211yescharacteristic, complemented
29C2×#837C2211yescharacteristic
30C2×#837C2211yescharacteristic, complemented
31#5233C2211yescharacteristic
32#5196—24no—
33#5187C411yescharacteristic, complemented
34#5186C411yescharacteristic, complemented
35#5173C411yescharacteristic, complemented
36#5172C411yescharacteristic, complemented
37#5170C411yescharacteristic, complemented
38#5169C411yescharacteristic, complemented
39#5158C411yescharacteristic, complemented
40#5156C411yescharacteristic, complemented
41C2×#825C2211yescharacteristic
42#5129—21no—
43#5129C2211yescharacteristic
44#5126—21no—
45#5126C2211yescharacteristic
46C2×#822C2211yescharacteristic, complemented
47#5119C2211yescharacteristic, complemented
48#5113C2211yescharacteristic
49#5110—21no—
50#5110C2211yescharacteristic
51C2×(C2×D3)⋊C8—21no—
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic
54C2×#819C2211yescharacteristic, complemented
55#5101C2211yescharacteristic, complemented
56C2×C8×Dic3C2211yescharacteristic, complemented
57C2×C8×Dic3C2211yescharacteristic, complemented
58C2×#805C2211yescharacteristic
59D3×#104—24no—
60#4730—21no—
61#4729—21no—
62#4728—21no—
63#67⋊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—
73C22×#104—31no—
74#2880—31no—
75#1974—31no—
76#1937—31no—
77#1929—31no—
78#1896—31no—
79#1876—31no—
80#1876D311yescharacteristic, complemented
81#1866—31no—
82#1855—31no—
83#1764—31no—
84C4×C22⋊C8—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×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C3×#135—22no—
103C3×#135—22no—
104C2×C3×Q16C2×C411yescharacteristic, complemented
105C2×C3×SD16C2×C411yescharacteristic, complemented
106C2×C3×SD16C2×C411yescharacteristic, complemented
107C2×C3×D8C2×C411yescharacteristic, complemented
108C3×#131—22no—
109C3×#131—41no—
110C2×C3×M16—21no—
111C2×C3×M16C2311yescharacteristic
112C2×C3×M16C2311yescharacteristic
113C22×C3×C8—21no—
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C2×C3×C42C2311yescharacteristic
117#950—41no—
118#950—41no—
119#948—22no—
120#948—22no—
121#948—41no—
122#948—41no—
123#946C2×C411yescharacteristic
124#946C2×C411yescharacteristic
125C2×#216C2×C411yescharacteristic, complemented
126C2×#215C2×C411yescharacteristic, complemented
127#938C2×C411yescharacteristic
128#938C2×C411yescharacteristic
129#937—21no—
130#935—21no—
131C2×#214C2×C411yescharacteristic, complemented
132C2×#213C2×C411yescharacteristic, complemented
133C4×#67—21no—
134C4×#67—21no—
135#926C2311yescharacteristic
136C2×C4×Dic3—21no—
137C2×C4×Dic3C2311yescharacteristic
138C2×#208—21no—
139C2×#208—21no—
140C2×#208C2311yescharacteristic
141C2×#208C2311yescharacteristic
142C22×C3⋊C8—21no—
143C22×C3⋊C8—21no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146D3×M16—22no—
147D3×M16—41no—
148C2×ΓL(1,𝔽25)—21no—
149C2×D3×C8—21no—
150C42×D3—22no—
151C42×D3—41no—
152C3×#104—22no—
153C3×#104—41no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156#837—22no—
157#837D414yescomplemented
158#835C2×C411yescharacteristic, complemented
159#835C2×C411yescharacteristic, complemented
160#832C2×C411yescharacteristic, complemented
161#832C2×C411yescharacteristic, complemented
162#825—22no—
163#822—41no—
164#821C2×C411yescharacteristic, complemented
165#821C2×C411yescharacteristic, complemented
166(C2×D3)⋊C8—21no—
167(C2×D3)⋊C8—21no—
168(C2×D3)⋊C8—21no—
169(C2×D3)⋊C8—21no—
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—22no—
181#816C2×C411yescharacteristic, complemented
182#816C2×C411yescharacteristic, complemented
183#815—21no—
184Dic3⋊C8—21no—
185Dic3⋊C8—21no—
186C8×Dic3—21no—
187C8×Dic3—22no—
188C8×Dic3—41no—
189#805—22no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135C2×D311yescharacteristic
193C2×#131—31no—
194C2×#131—31no—
195C2×#131C2×D311yescharacteristic
196C22×M16—31no—
197#525—31no—
198C22×C42—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—
215C2×#104—31no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—64no—
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, complemented
229#407—31no—
230#407—61no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—61no—
234#405—31no—
235C2×C4×C8—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×#41C2×D412yes—
252C3×#41#4112yes—
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—21no—
286#235—21no—
287#235—42no—
288#235—42no—
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—24no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×C4×D3C22×C411yescharacteristic
304C2×C4×D3C22×C411yescharacteristic
305C2×C4×D3C2×D411yescharacteristic
306C2×C4×D3C2×D411yescharacteristic
307C2×Dic6—21no—
308C2×Dic6C22×C411yescharacteristic
309C3×Q16—22no—
310C3×SD16—22no—
311C3×SD16—22no—
312C3×D8—22no—
313C3×M16—21no—
314C3×M16—21no—
315C3×M16—21no—
316C3×M16—21no—
317C3×M16—42no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—42no—
325C2×C3×C8C22×C411yescharacteristic
326C2×C3×C8C22×C411yescharacteristic
327C2×C3×C8C2×D411yescharacteristic
328C2×C3×C8C2×D411yescharacteristic
329C3×C42—21no—
330C3×C42—21no—
331#217—21no—
332#217—21no—
333#217—21no—
334#216—41no—
335#215—41no—
336#214—41no—
337#213—41no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—21no—
340C4⋊Dic3C22×C411yescharacteristic
341C4⋊Dic3C22×C411yescharacteristic
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344C4×Dic3—21no—
345C4×Dic3—21no—
346C4×Dic3—42no—
347C4×Dic3C2×D412yes—
348#208—21no—
349#208—21no—
350#208—21no—
351#208—42no—
352#208—42no—
353#208C2×D412yes—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—42no—
361C2×C3⋊C8—42no—
362C2×C3⋊C8C22×C411yescharacteristic
363C2×C3⋊C8C22×C411yescharacteristic
364C2×C3⋊C8C2×D411yescharacteristic
365C2×C3⋊C8C2×D411yescharacteristic
366ΓL(1,𝔽25)—42no—
367D3×C8—42no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—31no—
371C2×#41—61no—
372C2×#41—61no—
373C2×#41—62no—
374C2×#41—62no—
375C2×#41—121no—
376C2×#41—121no—
377C2×#41C22×D311yescharacteristic
378C2×#41C22×D311yescharacteristic
379C22×Q8—31no—
380C22×D4—31no—
381C22×D4—61no—
382C23×C4—31no—
383C23×C4—61no—
384C23×C4—61no—
385#135—22no—
386#135—22no—
387#135—121no—
388#135—121no—
389C2×Q16—31no—
390C2×Q16C4×D311yescharacteristic, complemented
391C2×SD16—31no—
392C2×SD16—31no—
393C2×SD16C4×D311yescharacteristic, complemented
394C2×SD16C4×D311yescharacteristic, complemented
395C2×D8—31no—
396C2×D8C4×D311yescharacteristic, complemented
397#131—22no—
398#131—41no—
399#131—62no—
400#131—62no—
401#131—121no—
402#131—121no—
403C2×M16—21no—
404C2×M16—31no—
405C2×M16—31no—
406C2×M16—61no—
407C2×M16—61no—
408C2×M16—61no—
409C2×M16—62no—
410C2×M16—121no—
411C2×M16C22×D311yescharacteristic
412C2×M16C22×D311yescharacteristic
413C22×C8—21no—
414C22×C8—31no—
415C22×C8—31no—
416C22×C8—61no—
417C22×C8—61no—
418C22×C8—61no—
419C22×C8C22×D311yescharacteristic
420C22×C8C22×D311yescharacteristic
421#123—61no—
422C22⋊Q8—31no—
423C22⋊Q8—31no—
424#121—31no—
425#121—31no—
426#120—61no—
427C4×D4—61no—
428C4×D4—61no—
429#117—31no—
430C2×C42—31no—
431C2×C42—62no—
432C2×C42—61no—
433C2×C42—121no—
434C2×C42C22×D311yescharacteristic
435#108—62no—
436#108—121no—
437C4⋊C8—61no—
438C4⋊C8—61no—
439#104—22no—
440#104—34no—
441#104—41no—
442#104—62no—
443#104—62no—
444#104—62no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—31no—
460C22⋊C8—31no—
461C22⋊C8—31no—
462C22⋊C8—31no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8—61no—
466C22⋊C8—61no—
467C22⋊C8—61no—
468C22⋊C8—61no—
469#97—61no—
470C4×C8—62no—
471C4×C8—61no—
472C4×C8—121no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3C2×#4111yescharacteristic
476C22×D3—21no—
477C22×D3—21no—
478C22×D3—22no—
479C22×D3—21no—
480C22×D3—41no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—81no—
484C22×D3C4×D411yescharacteristic
485C22×D3C4×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8C4×D412yes—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4C4×D412yes—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4C23×C411yescharacteristic
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4H(5,𝔽2)11yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513#67—42no—
514#67—42no—
515#67—41no—
516#67—41no—
517#67—42no—
518#67—81no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—42no—
528C2×Dic3C4×D411yescharacteristic
529C2×Dic3C4×D411yescharacteristic
530D12—21no—
531D12—21no—
532D12—42no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—42no—
542C4×D3—48no—
543C4×D3—42no—
544C4×D3—41no—
545C4×D3—41no—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—22no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—41no—
561C24—31no—
562C24—61no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—62no—
570#41—62no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—61no—
575#41—122no—
576#41—122no—
577#41—121no—
578#41—122no—
579#41—122no—
580#41—121no—
581#41D3×D412yes—
582#41#23712yes—
583C2×Q8—31no—
584C2×Q8—61no—
585C2×Q8—62no—
586C2×Q8—121no—
587C2×Q8C2×C4×D311yescharacteristic
588C2×Q8C2×C4×D311yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—62no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—121no—
600C2×D4—122no—
601C2×D4—122no—
602C2×D4C2×C4×D311yescharacteristic
603C2×D4C2×C4×D311yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—64no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—122no—
623C22×C4—122no—
624C22×C4—122no—
625C22×C4—122no—
626C22×C4C23×D311yescharacteristic
627Q16—22no—
628Q16—121no—
629SD16—22no—
630SD16—22no—
631SD16—121no—
632SD16—121no—
633D8—22no—
634D8—121no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—32no—
640M16—42no—
641M16—61no—
642M16—61no—
643M16—61no—
644M16—122no—
645M16—122no—
646M16—122no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—42no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C2×C8—61no—
664C2×C8—122no—
665C2×C8—122no—
666C2×C8—122no—
667C2×C8C2×C4×D311yescharacteristic
668C2×C8C2×C4×D311yescharacteristic
669C2×C8D3×D411yescharacteristic
670C2×C8D3×D411yescharacteristic
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—61no—
674C4⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—61no—
680C42—21no—
681C42—21no—
682C42—32no—
683C42—61no—
684C42—61no—
685C42—122no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3C2×C4×D411yescharacteristic
695C22×C3#54611yescharacteristic
696C22×C3#55111yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—42no—
703C2×D3—42no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—84no—
708C2×D3#44312yescomplemented
709C3×C4—22no—
710C3×C4—42no—
711C3×C4—41no—
712C3×C4C2×C4×D411yescharacteristic
713C3×C4#51811yescharacteristic
714C3×C4D4211yescharacteristic
715C3×C4#54611yescharacteristic
716Dic3—24no—
717Dic3—21no—
718Dic3—21no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722C23—21no—
723C23—21no—
724C23—31no—
725C23—31no—
726C23—62no—
727C23—61no—
728C23—61no—
729C23—61no—
730C23—121no—
731C23—122no—
732C23—122no—
733C23—241no—
734C23D3×#4111yescharacteristic
735Q8—21no—
736Q8—21no—
737Q8—21no—
738Q8—61no—
739Q8—61no—
740Q8—122no—
741Q8#67⋊C412yes—
742D4—22no—
743D4—22no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—41no—
748D4—41no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—122no—
753D4—122no—
754D4—122no—
755D4—121no—
756D4—121no—
757D4—241no—
758D4#67⋊C412yes—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—61no—
773C2×C4—62no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—122no—
787C2×C4—122no—
788C2×C4—128no—
789C2×C4—122no—
790C2×C4—121no—
791C2×C4—121no—
792C2×C4C22×C4×D311yescharacteristic
793C2×C4C2×D3×D411yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4C2×#23711yescharacteristic
796C2×C4#100411yescharacteristic
797C2×C4#100911yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—41no—
803C8—41no—
804C8—61no—
805C8—61no—
806C8—61no—
807C8—61no—
808C8—62no—
809C8—121no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—42no—
813C2×C3—81no—
814C2×C3#235811yescharacteristic
815C2×C3C2×#44311yescharacteristic
816C2×C3#295611yescharacteristic
817D3—22no—
818D3—41no—
819D3—81no—
820C22—21no—
821C22—21no—
822C22—22no—
823C22—32no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—122no—
835C22—122no—
836C22—121no—
837C22—121no—
838C22—121no—
839C22—244no—
840C22C4×D3×D411yescharacteristic
841C22#561011yescharacteristic
842C22#565811yescharacteristic
843C4—22no—
844C4—42no—
845C4—41no—
846C4—64no—
847C4—61no—
848C4—61no—
849C4—121no—
850C4—121no—
851C4—121no—
852C4C2×#67⋊C411yescharacteristic
853C4#554511yescharacteristic
854C4#559111yescharacteristic
855C4#560911yescharacteristic
856C3#2288811yescharacteristic, complemented, Sylow
857C2—21no—
858C2—21no—
859C2—42no—
860C2—62no—
861C2—81no—
862C2—121no—
863C2—241no—
864C2#7487911yescharacteristic
865C2D3×#44311yescharacteristic
866C2#7989811yescharacteristic
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#22888
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. C2×#5196C2semidirect
3. #83793C2semidirect
4. C2×D3×#104C2semidirect
5. #78659C2semidirect
6. C3×#1876C2semidirect
7. #72008C2semidirect
8. #70382C2semidirect
9. #70377C2semidirect
10. #70376C2semidirect
11. #69999C2semidirect
12. #68941C2semidirect
13. #68918C2semidirect
14. #68646C2semidirect
15. #68599C2semidirect
23. C2×#948C22semidirect
27. C2×C3×#104C22semidirect
28. C3×#408C22semidirect
30. C2×#837C22semidirect
33. #5187C4semidirect
34. #5186C4semidirect
35. #5173C4semidirect
36. #5172C4semidirect
37. #5170C4semidirect
38. #5169C4semidirect
39. #5158C4semidirect
40. #5156C4semidirect
46. C2×#822C22semidirect
47. #5119C22semidirect
54. C2×#819C22semidirect
55. #5101C22semidirect
56. C2×C8×Dic3C22semidirect
57. C2×C8×Dic3C22semidirect
64. C3×#341C22semidirect
65. C3×#336C22semidirect
66. #4558C22semidirect
67. #4555C22semidirect
68. #4524C22semidirect
69. #4523C22semidirect
80. #1876D3semidirect
104. C2×C3×Q16C2×C4semidirect
105. C2×C3×SD16C2×C4semidirect
106. C2×C3×SD16C2×C4semidirect
107. C2×C3×D8C2×C4semidirect
125. C2×#216C2×C4semidirect
126. C2×#215C2×C4semidirect
131. C2×#214C2×C4semidirect
132. C2×#213C2×C4semidirect
157. #837D4semidirect
158. #835C2×C4semidirect
159. #835C2×C4semidirect
160. #832C2×C4semidirect
161. #832C2×C4semidirect
164. #821C2×C4semidirect
165. #821C2×C4semidirect
181. #816C2×C4semidirect
182. #816C2×C4semidirect
221. C2×#104C2×D3semidirect
228. #408C2×D3semidirect
238. #341C2×D3semidirect
242. #336C2×D3semidirect
390. C2×Q16C4×D3semidirect
393. C2×SD16C4×D3semidirect
394. C2×SD16C4×D3semidirect
396. C2×D8C4×D3semidirect
708. C2×D3#443semidirect
856. C3#22888semidirect

Maximal subgroups

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

subgroupindex
#839112
C2×#51962
#837932
C2×D3×#1042
#786592
C3×#18762
#720082
#703822
#703772
#703762
#699992
#689412
#689182
#686462
#685992
#228883