Finite Group Databasebeta

← #10815970

Subgroups — #10815970

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
1C3×#2933C211yesmaximal, characteristic, complemented
2C2×#5144C211yesmaximal, characteristic, complemented
3C2×#5139C211yesmaximal, characteristic, complemented
4#82926C211yesmaximal, characteristic
5#78600C211yesmaximal, characteristic, complemented
6#72010C211yesmaximal, characteristic, complemented
7#72001C211yesmaximal, characteristic, complemented
8#71712C211yesmaximal, characteristic, complemented
9#70545C211yesmaximal, characteristic, complemented
10#70535C211yesmaximal, characteristic, complemented
11#70011C211yesmaximal, characteristic, complemented
12#70000C211yesmaximal, characteristic, complemented
13#69907C211yesmaximal, characteristic, complemented
14#69900C211yesmaximal, characteristic, complemented
15#69888C211yesmaximal, characteristic, complemented
16#22889—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic, complemented
19C22×C3×M16C2211yescharacteristic
20C3×#525C2211yescharacteristic
21C2×#950C2211yescharacteristic
22C2×#950C2211yescharacteristic
23C2×#926C2211yescharacteristic
24C2×#901C2211yescharacteristic
25C2×#901C2211yescharacteristic
26C3×#436—21no—
27C3×#435—21no—
28C3×#435—21no—
29C3×C8×D4—21no—
30C3×#424C2211yescharacteristic, complemented
31C3×#408C2211yescharacteristic, complemented
32C2×C3×C22⋊C8C2211yescharacteristic
33C3×#405C2211yescharacteristic, complemented
34C2×#837C2211yescharacteristic, complemented
35C2×#837C2211yescharacteristic, complemented
36#5207C2211yescharacteristic
37C2×#830C2211yescharacteristic
38#5144—24no—
39#5139—24no—
40C2×#825C2211yescharacteristic
41C2×#825C2211yescharacteristic
42C2×#825C2211yescharacteristic
43C2×#825C2211yescharacteristic
44C2×#822C2211yescharacteristic, complemented
45C2×#822C2211yescharacteristic, complemented
46#5110C2211yescharacteristic
47#5110C2211yescharacteristic
48C2×#815C2211yescharacteristic, complemented
49C2×C8×Dic3C2211yescharacteristic, complemented
50#5050C411yescharacteristic, complemented
51#5047C411yescharacteristic, complemented
52#5047C411yescharacteristic, complemented
53#5046C411yescharacteristic, complemented
54#5040C411yescharacteristic, complemented
55#5037C411yescharacteristic, complemented
56#5037C411yescharacteristic, complemented
57#5036C411yescharacteristic, complemented
58#5002C2211yescharacteristic
59#5002C2211yescharacteristic
60#4727—21no—
61#4727—21no—
62#4726—21no—
63D3×C22⋊C8—21no—
64#4558C2211yescharacteristic, complemented
65#4558C2211yescharacteristic, complemented
66#4550C2211yescharacteristic, complemented
67#4550C2211yescharacteristic, complemented
68#4532C2211yescharacteristic, complemented
69#4532C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933D311yescharacteristic, complemented
73C2×#421—31no—
74#2880—31no—
75#1975—31no—
76#1937—31no—
77#1929—31no—
78#1897—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1765—31no—
84#1750—31no—
85C2×C3×#41C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—41no—
93C2×#235—41no—
94C2×#235C2×C411yescharacteristic
95C2×#235C2×C411yescharacteristic
96C2×#235C2311yescharacteristic
97C2×#235C2311yescharacteristic
98C22×D12C2×C411yescharacteristic
99C22×C4×D3—21no—
100C22×Dic6C2×C411yescharacteristic
101C3×#131—22no—
102C3×#131—41no—
103C2×C3×M16—21no—
104C2×C3×M16—21no—
105C2×C3×M16—22no—
106C2×C3×M16—41no—
107C2×C3×M16C2311yescharacteristic
108C2×C3×M16C2311yescharacteristic
109C22×C3×C8—21no—
110C22×C3×C8—21no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×#123—21no—
114C3×C22⋊Q8C2×C411yescharacteristic
115C3×C22⋊Q8C2×C411yescharacteristic
116C3×#121C2×C411yescharacteristic
117C3×#121C2×C411yescharacteristic
118C3×#120—21no—
119C3×C4×D4—21no—
120C3×C4×D4—21no—
121C3×#117C2311yescharacteristic
122C2×#217—21no—
123#950—22no—
124#950—22no—
125#950—41no—
126#950—41no—
127C2×#216C2×C411yescharacteristic
128C2×#216C2×C411yescharacteristic
129C2×#215C2×C411yescharacteristic
130C2×#215C2×C411yescharacteristic
131C2×#214C2×C411yescharacteristic
132C2×#214C2×C411yescharacteristic
133C2×#213C2×C411yescharacteristic
134C2×#213C2×C411yescharacteristic
135#926—22no—
136#926—41no—
137C2×C4⋊Dic3—21no—
138C2×C4×Dic3C2311yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C2×#208C2311yescharacteristic
141C2×#208C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#901—22no—
145#901—22no—
146#901—41no—
147#901—41no—
148C2×ΓL(1,𝔽25)—21no—
149C2×ΓL(1,𝔽25)—21no—
150C2×D3×C8—21no—
151C2×D3×C8—21no—
152C3×C4⋊C8—21no—
153C3×C4⋊C8—21no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156C3×C22⋊C8D411yescharacteristic
157C3×C22⋊C8D411yescharacteristic
158C3×C22⋊C8D411yescharacteristic
159C3×C22⋊C8D411yescharacteristic
160C3×#97—21no—
161C3×C4×C8—21no—
162#837—22no—
163#837—41no—
164#830—21no—
165#830—21no—
166#830C2×C411yescharacteristic
167#830C2×C411yescharacteristic
168#830C2×C411yescharacteristic
169#830C2×C411yescharacteristic
170#825—22no—
171#825—22no—
172#825—22no—
173#825D414yescomplemented
174#822—22no—
175#822—41no—
176(C2×D3)⋊C8—21no—
177(C2×D3)⋊C8—21no—
178(C2×D3)⋊C8—21no—
179(C2×D3)⋊C8—21no—
180#815—41no—
181C8×Dic3—22no—
182#810C2×C411yescharacteristic
183#810C2×C411yescharacteristic
184#810C2×C411yescharacteristic
185#810C2×C411yescharacteristic
186#809C2×C411yescharacteristic
187#809C2×C411yescharacteristic
188#809C2×C411yescharacteristic
189#809C2×C411yescharacteristic
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131C2×D311yescharacteristic, complemented
196C22×M16C2×D311yescharacteristic
197#525C2×D311yescharacteristic
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—21no—
209#435—21no—
210#435—21no—
211C8×D4—21no—
212C2×#108—31no—
213C2×#108—31no—
214#424C2×D311yescharacteristic, complemented
215#421—64no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104—31no—
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—61no—
233C2×C22⋊C8C2×D311yescharacteristic
234#405C2×D311yescharacteristic, complemented
235C2×#97—31no—
236C2×C4×C8—31no—
237#341—31no—
238#341—31no—
239#339—31no—
240#339—31no—
241#336—31no—
242#336—31no—
243C24×C3#4111yescharacteristic
244C23×D3—21no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C2×C3×Q8C22×C411yescharacteristic
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4C22×C411yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4C22×C411yescharacteristic
260C22×C3×C4C22×C411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4#4111yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C2×#67—21no—
266C2×#67—21no—
267C2×#67—21no—
268C2×#67—21no—
269C2×#67—42no—
270C2×#67—42no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—21no—
278#235—21no—
279#235—21no—
280#235—22no—
281#235—22no—
282#235—41no—
283#235—41no—
284#235—42no—
285#235—42no—
286#235—42no—
287#235—42no—
288#235C2×D412yes—
289#235#4112yes—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—41no—
293C2×D12C22×C411yescharacteristic
294C2×D12C22×C411yescharacteristic
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×Dic6—22no—
302C2×Dic6—21no—
303C2×Dic6—41no—
304C2×Dic6C22×C411yescharacteristic
305C2×Dic6C22×C411yescharacteristic
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—42no—
310C3×M16—42no—
311C3×M16C2×D412yes—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—42no—
319C2×C3×C8—42no—
320C2×C3×C8C2×D411yescharacteristic
321C2×C3×C8C2×D411yescharacteristic
322C2×C3×C8C2×D411yescharacteristic
323C2×C3×C8C2×D411yescharacteristic
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4C22×C411yescharacteristic
327C3×C4⋊C4C22×C411yescharacteristic
328C3×C22⋊C4—21no—
329C3×C22⋊C4—21no—
330C3×C22⋊C4—21no—
331C3×C22⋊C4—21no—
332C3×C22⋊C4—21no—
333C3×C42—21no—
334#217—42no—
335#216—22no—
336#216—41no—
337#215—22no—
338#215—41no—
339#214—22no—
340#214—41no—
341#213—22no—
342#213—41no—
343C4⋊Dic3—42no—
344C4×Dic3—21no—
345C4×Dic3—21no—
346C4×Dic3—21no—
347C4×Dic3C2×D412yes—
348#208—21no—
349#208—21no—
350#208—21no—
351#208—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8C22×C411yescharacteristic
359C2×C3⋊C8C22×C411yescharacteristic
360C2×C3⋊C8C22×C411yescharacteristic
361C2×C3⋊C8C22×C411yescharacteristic
362ΓL(1,𝔽25)—42no—
363ΓL(1,𝔽25)—42no—
364D3×C8—42no—
365D3×C8—42no—
366C2×#41—31no—
367C2×#41—31no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—62no—
371C2×#41—62no—
372C2×#41—61no—
373C2×#41—61no—
374C2×#41—121no—
375C2×#41—121no—
376C2×#41C22×D311yescharacteristic
377C22×Q8—31no—
378C22×D4—31no—
379C22×D4—61no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382#135—62no—
383#135—62no—
384#135—121no—
385#135—121no—
386C2×Q16—31no—
387C2×Q16—31no—
388C2×SD16—31no—
389C2×SD16—31no—
390C2×SD16—31no—
391C2×SD16—31no—
392C2×D8—31no—
393C2×D8—31no—
394#131—22no—
395#131—41no—
396#131—62no—
397#131—62no—
398#131—121no—
399#131—121no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—22no—
403C2×M16—31no—
404C2×M16—31no—
405C2×M16—41no—
406C2×M16—61no—
407C2×M16—61no—
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—31no—
413C22×C8—31no—
414C22×C8—61no—
415C22×C8—61no—
416C22×C8C22×D311yescharacteristic
417C22×C8C22×D311yescharacteristic
418#123—21no—
419C22⋊Q8C4×D311yescharacteristic
420C22⋊Q8C4×D311yescharacteristic
421#121C4×D311yescharacteristic
422#121C4×D311yescharacteristic
423#120—21no—
424C4×D4—21no—
425C4×D4—21no—
426#117—62no—
427#117—121no—
428#117C22×D311yescharacteristic
429C2×C4⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42—31no—
432C2×C42—31no—
433#108—62no—
434#108—121no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437#104—34no—
438#104—62no—
439#104—62no—
440#104—62no—
441#104—62no—
442#104—121no—
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—61no—
458C22⋊C8—61no—
459C22⋊C8—61no—
460C22⋊C8—61no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8#6711yescharacteristic
464C22⋊C8#6711yescharacteristic
465C22⋊C8#6711yescharacteristic
466C22⋊C8#6711yescharacteristic
467#97—21no—
468#97—121no—
469C4×C8—21no—
470C4×C8—62no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3C4×D411yescharacteristic
477C23×C3C4×D411yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—81no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—42no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—81no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4C4×D411yescharacteristic
508C2×C3×C4C4×D411yescharacteristic
509C2×C3×C4C23×C411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C2×#4111yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515#67—22no—
516#67—22no—
517#67—42no—
518#67—42no—
519#67—41no—
520#67—41no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—42no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530D12—21no—
531D12—21no—
532D12—21no—
533D12—42no—
534D12C4×D412yes—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—41no—
540C4×D3—41no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6C4×D412yes—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—22no—
549C3×C8—21no—
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—61no—
559C24#23511yescharacteristic
560#41—21no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—32no—
565#41—32no—
566#41—62no—
567#41—62no—
568#41—61no—
569#41—61no—
570#41—61no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—122no—
575#41—122no—
576#41—121no—
577#41—121no—
578#41—122no—
579#41—122no—
580C2×Q8—31no—
581C2×Q8—31no—
582C2×Q8—62no—
583C2×Q8—61no—
584C2×Q8—121no—
585C2×Q8C2×C4×D311yescharacteristic
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—121no—
598C2×D4—122no—
599C2×D4—122no—
600C2×D4C2×C4×D311yescharacteristic
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—122no—
614C22×C4—122no—
615C22×C4C2×C4×D311yescharacteristic
616C22×C4C2×C4×D311yescharacteristic
617C22×C4#23511yescharacteristic
618C22×C4C2×#6711yescharacteristic
619C22×C4C2×#6711yescharacteristic
620C22×C4C23×D311yescharacteristic
621Q16—62no—
622Q16—121no—
623SD16—62no—
624SD16—62no—
625SD16—121no—
626SD16—121no—
627D8—62no—
628D8—121no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—61no—
635M16—61no—
636M16—61no—
637M16—61no—
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—42no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8C2×#6711yescharacteristic
662C2×C8C2×#6711yescharacteristic
663C2×C8C2×#6711yescharacteristic
664C2×C8C2×#6711yescharacteristic
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—122no—
668C4⋊C4C2×C4×D311yescharacteristic
669C4⋊C4C2×C4×D311yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—122no—
676C42—21no—
677C42—32no—
678C42—61no—
679C42—61no—
680C42—61no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3C2×C4×D411yescharacteristic
695C22×C3#54611yescharacteristic
696C22×C3#55111yescharacteristic
697C2×D3—22no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—84no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4C2×C4×D411yescharacteristic
710C3×C4#51811yescharacteristic
711C3×C4D4211yescharacteristic
712C3×C4#54611yescharacteristic
713Dic3—22no—
714Dic3—42no—
715Dic3—41no—
716Dic3—81no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726C23—241no—
727C23C4×#6711yescharacteristic
728C23C4×#6711yescharacteristic
729C23C2×#23511yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—32no—
733Q8—61no—
734Q8—61no—
735Q8—61no—
736Q8—122no—
737D4—21no—
738D4—21no—
739D4—32no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—62no—
744D4—62no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—81no—
749D4—122no—
750D4—122no—
751D4—122no—
752D4—121no—
753D4—121no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—61no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—61no—
773C2×C4—62no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—122no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4C4×#6711yescharacteristic
785C2×C4C4×#6711yescharacteristic
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4#100411yescharacteristic
789C2×C4D3×#4111yescharacteristic
790C2×C4#100911yescharacteristic
791C2×C4C22×#6711yescharacteristic
792C8—21no—
793C8—21no—
794C8—22no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—61no—
799C8—61no—
800C8—61no—
801C8—61no—
802C8—121no—
803C8—121no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—81no—
809C2×C3#235811yescharacteristic
810C2×C3#295511yescharacteristic
811C2×C3#295711yescharacteristic
812D3—42no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—62no—
826C22—81no—
827C22—81no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22#555011yescharacteristic
835C22#555611yescharacteristic
836C22C2×C4×#6711yescharacteristic
837C4—21no—
838C4—21no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—62no—
843C4—122no—
844C4—121no—
845C4—241no—
846C4C4×D3×D411yescharacteristic
847C4#554511yescharacteristic
848C4D4×#6711yescharacteristic
849C4#582911yescharacteristic
850C3#2288911yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—122no—
857C2—241no—
858C2#8239811yescharacteristic
859C2#8379211yescharacteristic
860C2#8381211yescharacteristic
subgroupG/H
centerC2×C4C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2933C2
socleC22×C3C2×C4×D4
prime radical#82926C2
cosocleC22×C3×C4C24
hypercenter#2933D3
hypocenterC3#22889
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
1. C3×#2933C2semidirect
2. C2×#5144C2semidirect
3. C2×#5139C2semidirect
5. #78600C2semidirect
6. #72010C2semidirect
7. #72001C2semidirect
8. #71712C2semidirect
9. #70545C2semidirect
10. #70535C2semidirect
11. #70011C2semidirect
12. #70000C2semidirect
13. #69907C2semidirect
14. #69900C2semidirect
15. #69888C2semidirect
18. C2×C3×#131C22semidirect
30. C3×#424C22semidirect
31. C3×#408C22semidirect
33. C3×#405C22semidirect
34. C2×#837C22semidirect
35. C2×#837C22semidirect
44. C2×#822C22semidirect
45. C2×#822C22semidirect
48. C2×#815C22semidirect
49. C2×C8×Dic3C22semidirect
50. #5050C4semidirect
51. #5047C4semidirect
52. #5047C4semidirect
53. #5046C4semidirect
54. #5040C4semidirect
55. #5037C4semidirect
56. #5037C4semidirect
57. #5036C4semidirect
64. #4558C22semidirect
65. #4558C22semidirect
66. #4550C22semidirect
67. #4550C22semidirect
68. #4532C22semidirect
69. #4532C22semidirect
72. #2933D3semidirect
173. #825D4semidirect
195. C2×#131C2×D3semidirect
214. #424C2×D3semidirect
228. #408C2×D3semidirect
234. #405C2×D3semidirect
850. C3#22889semidirect

Maximal subgroups

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

subgroupindex
C3×#29332
C2×#51442
C2×#51392
#829262
#786002
#720102
#720012
#717122
#705452
#705352
#700112
#700002
#699072
#699002
#698882
#228893