Finite Group Databasebeta

← #30622200

Subgroups — #30622200

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840801C211yesmaximal, characteristic, complemented
2C2×SD16×#6923C211yesmaximal, characteristic, complemented
3#21462349C211yesmaximal, characteristic
4#21462334C211yesmaximal, characteristic, complemented
5#21461951C211yesmaximal, characteristic
6#21461932C211yesmaximal, characteristic, complemented
7#21461911C211yesmaximal, characteristic, complemented
8#21461909C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461815C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461782C211yesmaximal, characteristic, complemented
13#21461620C211yesmaximal, characteristic, complemented
14#21461591C211yesmaximal, characteristic, complemented
15#460×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×D4×#6923—21no—
19C2×D4×#6923C2211yescharacteristic
20C2×D4×#6923C2211yescharacteristic
21#16840801—24no—
22SD16×#6923—24no—
23C2×#14519846C2211yescharacteristic
24C2×#14519845C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31#16840721C2211yescharacteristic
32C2×#14519831C2211yescharacteristic
33C2×C8×#6923C2211yescharacteristic
34#16840714—21no—
35#16840714C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840713—21no—
38#16840713—21no—
39#16840713C2211yescharacteristic
40#16840713C2211yescharacteristic
41#16840710—21no—
42#16840710—21no—
43#16840706—21no—
44#16840706C2211yescharacteristic
45C4×C4⋊#6923—21no—
46C4×C4⋊#6923C2211yescharacteristic
47C4×C4⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×SD16×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56#127×D61C2211yescharacteristic
57C4×Q8×D61C2211yescharacteristic
58#16839963C411yescharacteristic, complemented
59#16839962C411yescharacteristic, complemented
60#16839961C411yescharacteristic, complemented
61#16839961C411yescharacteristic, complemented
62#16839960C411yescharacteristic, complemented
63#16839960C411yescharacteristic, complemented
64#16839959C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#460C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C2×D61⋊C8C2311yescharacteristic
72C2×D61⋊C8C2311yescharacteristic
73Q8×#6923—22no—
74Q8×#6923—22no—
75Q8×#6923—41no—
76Q8×#6923—41no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—41no—
80D4×#6923—41no—
81D4×#6923—44no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923D411yescharacteristic
87C2×C4⋊#6923D411yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923C2311yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103#14519846—22no—
104#14519845—22no—
105#14519840—22no—
106#14519840D414yescomplemented
107#14519839—22no—
108#14519839—22no—
109#14519839—41no—
110#14519839—41no—
111#14519832—21no—
112#14519832—21no—
113#14519831—22no—
114C8×#6923—22no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4D411yescharacteristic
121(C2×#6923)⋊C4D411yescharacteristic
122C2×Q8×D61C2311yescharacteristic
123C2×D4×D61—21no—
124C2×D4×D61—21no—
125C2×D4×D61C2311yescharacteristic
126C2×D4×D61C2311yescharacteristic
127C2×#11758190C2×C411yescharacteristic, complemented
128C2×#11758190C2×C411yescharacteristic, complemented
129C2×#11758200C2×C411yescharacteristic, complemented
130C2×#11758200C2×C411yescharacteristic, complemented
131C2×#11758201C2×C411yescharacteristic, complemented
132C2×#11758201C2×C411yescharacteristic, complemented
133SD16×D61—22no—
134SD16×D61—22no—
135SD16×D61—22no—
136SD16×D61—22no—
137C2×C8×D61C2311yescharacteristic
138C2×C8×D61C2311yescharacteristic
139#14519774C2×C411yescharacteristic
140#14519773—21no—
141#14519773—21no—
142#14519773C2×C411yescharacteristic
143#14519773C2×C411yescharacteristic
144Q8×Dic61C2×C411yescharacteristic, complemented
145C4×Dic122—21no—
146C4×Dic122C2×C411yescharacteristic, complemented
147#14519742—21no—
148#14519742C2×C411yescharacteristic, complemented
149C4⋊C4×D61—21no—
150C4⋊C4×D61C2311yescharacteristic
151C42×D61—21no—
152C42×D61C2311yescharacteristic
153C4⋊#92418C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519706C2×C411yescharacteristic, complemented
156#14519699C2×C411yescharacteristic, complemented
157#14519699C2×C411yescharacteristic, complemented
158#14519698C2×C411yescharacteristic, complemented
159#14519698C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161#14519697C2×C411yescharacteristic, complemented
162C2×SD16×C61C2×C411yescharacteristic, complemented
163C2×SD16×C61C2×C411yescharacteristic, complemented
164#127×C61C2×C411yescharacteristic
165C4×Q8×C61C2×C411yescharacteristic, complemented
166C4⋊C8×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168#102×C61C2×C411yescharacteristic, complemented
169C23×D61—21no—
170C23×D61—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—21no—
174C22×#6923—21no—
175C22×#6923—42no—
176C22×#6923—42no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—81no—
180C22×#6923—81no—
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C22×#6923C2×D411yescharacteristic
184C22×#6923C2×D411yescharacteristic
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196Q8×D61—21no—
197Q8×D61—21no—
198Q8×D61C2×D412yes—
199Q8×D61#4112yes—
200D4×D61—21no—
201D4×D61—21no—
202D4×D61—21no—
203D4×D61—21no—
204D4×D61—21no—
205D4×D61—21no—
206D4×D61—21no—
207D4×D61—21no—
208D4×D61—42no—
209D4×D61—42no—
210D4×D61—81no—
211D4×D61—81no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244C22×C411yescharacteristic
215C2×D244C22×C411yescharacteristic
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61C2×D411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2411yescharacteristic
221C2×Dic122—21no—
222C2×Dic122C22×C411yescharacteristic
223C22⋊#6923—42no—
224C22⋊#6923—42no—
225C22⋊#6923—42no—
226C22⋊#6923—42no—
227C22⋊#6923—81no—
228C22⋊#6923—81no—
229C2×#92420—21no—
230C2×#92420—21no—
231C4⋊#6923—22no—
232C4⋊#6923—21no—
233C4⋊#6923—21no—
234C4⋊#6923—21no—
235C4⋊#6923—21no—
236C4⋊#6923—21no—
237C4⋊#6923—21no—
238C4⋊#6923—21no—
239C4⋊#6923—41no—
240C4⋊#6923—42no—
241C4⋊#6923—42no—
242C4⋊#6923—42no—
243C4⋊#6923—42no—
244C4⋊#6923C2×D412yes—
245C4×#6923—21no—
246C4×#6923—21no—
247C4×#6923—21no—
248C4×#6923—21no—
249C4×#6923—42no—
250C4×#6923—42no—
251C4×#6923—42no—
252D61⋊C8—21no—
253D61⋊C8—21no—
254D61⋊C8—21no—
255D61⋊C8C2×D412yes—
256SD16×C61—22no—
257SD16×C61—22no—
258C2×C8×C61C22×C411yescharacteristic
259C2×C8×C61C22×C411yescharacteristic
260C4⋊C4×C61—21no—
261C4⋊C4×C61C22×C411yescharacteristic
262C42×C61—21no—
263C42×C61C22×C411yescharacteristic
264#11758201—22no—
265#11758201—22no—
266#11758200—22no—
267#11758200—22no—
268C4⋊Dic61—21no—
269C4⋊Dic61C22×C411yescharacteristic
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61C22×C411yescharacteristic
277C4×Dic61#4111yescharacteristic
278C4×Dic61#4111yescharacteristic
279C2×#92418C22×C411yescharacteristic
280C2×#92418C22×C411yescharacteristic
281#11758190—22no—
282#11758190—22no—
283C8×D61—21no—
284C8×D61—21no—
285C8×D61—21no—
286C8×D61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C22×D411yescharacteristic
304C2×#6923—21no—
305C2×#6923—21no—
306C2×#6923—21no—
307C2×#6923—21no—
308C2×#6923—21no—
309C2×#6923—22no—
310C2×#6923—21no—
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—21no—
315C2×#6923—21no—
316C2×#6923—41no—
317C2×#6923—41no—
318C2×#6923—41no—
319C2×#6923—41no—
320C2×#6923—41no—
321C2×#6923—41no—
322C2×#6923—41no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—84no—
328C2×#6923—84no—
329C2×#6923AGL(1,ℤ/8)12yes—
330Q8×C61—21no—
331Q8×C61C4×D412yescomplemented
332D4×C61—21no—
333D4×C61—21no—
334D4×C61—21no—
335D4×C61—21no—
336D4×C61—42no—
337D4×C61—81no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61C4×D411yescharacteristic
341C2×C4×C61C4×D411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C22⋊D61—42no—
344C22⋊D61—42no—
345C22⋊D61—41no—
346C22⋊D61—41no—
347C22⋊D61—41no—
348C22⋊D61—41no—
349C22⋊D61—81no—
350C22⋊D61—81no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61C4×D411yescharacteristic
354C2×Dic61C4×D411yescharacteristic
355C2×Dic61C2×#4111yescharacteristic
356D244—21no—
357D244—21no—
358D244—21no—
359D244—21no—
360D244—42no—
361D244—81no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61C22×D411yescharacteristic
371C4×D61C2×#4111yescharacteristic
372C4×D61H(5,𝔽2)11yescharacteristic
373C4×D612−1+411yescharacteristic
374Dic122—21no—
375Dic122—22no—
376Dic122—22no—
377Dic122C4×D412yescomplemented
378#92420—22no—
379#92420—41no—
380C8×C61—21no—
381C8×C61—21no—
382#92418—21no—
383#92418—21no—
384#23010—611nomaximal, Sylow
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61C2×C4×D411yescharacteristic
392C2×D61—41no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—81no—
399C2×D61—81no—
400C2×D61—81no—
401C2×D61—81no—
402C2×D61—81no—
403C2×D61—81no—
404C2×D61—81no—
405C2×D61—81no—
406C2×D61D4211yescharacteristic
407C2×D61#54811yescharacteristic
408C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
409C2×D61#57511yescharacteristic
410C2×D61#57711yescharacteristic
411C2×D61#57711yescharacteristic
412#6923—22no—
413#6923—41no—
414#6923—42no—
415#6923—41no—
416#6923—41no—
417#6923—81no—
418#6923—81no—
419#6923—81no—
420C4×C61—22no—
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—41no—
424C4×C61C2×C4×D411yescharacteristic
425C4×C61#52011yescharacteristic
426Dic61—22no—
427Dic61—21no—
428Dic61—21no—
429Dic61—41no—
430Dic61#54711yescharacteristic
431Dic61#55311yescharacteristic
432C2×#460—611no—
433C2×#440—611no—
434C2×C4×SD16—611no—
435#2366—611no—
436#2351—611no—
437#1961—611no—
438#1949—611no—
439#1936—611no—
440#1934—611no—
441#1880—611no—
442#1880—611no—
443#1864—611no—
444#1862—611no—
445#1771—611no—
446#1763—611no—
447C2×C61—81no—
448C2×C61—81no—
449C2×C61#236111yescharacteristic
450C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C61#294911yescharacteristic
452D61—81no—
453D61—81no—
454D61#326511yescharacteristic
455D61#327111yescharacteristic
456D61#336811yescharacteristic
457D61#337111yescharacteristic
458C22×SD16—611no—
459C22×SD16—611no—
460C2×#127—611no—
461C2×C4×Q8—611no—
462C2×C4×Q8—611no—
463C2×C4×Q8—611no—
464C2×C4×D4—611no—
465C2×C4×D4—611no—
466C2×C4×D4—1221no—
467#460—611no—
468#460—611no—
469#460—611no—
470#460—611no—
471#460—611no—
472#460—611no—
473#460—611no—
474#460#692311yescharacteristic, complemented
475#440—1224no—
476C4×SD16—1224no—
477C2×#107—611no—
478C2×#106—611no—
479C2×C4⋊C8—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#97—611no—
489C2×#97—611no—
490C2×C4×C8—611no—
491#390—611no—
492#390—611no—
493#390—1221no—
494#389—611no—
495#389—611no—
496#389—1221no—
497#389—1221no—
498#386—1221no—
499#386—1221no—
500#382—611no—
501#382—1221no—
502C4×C4⋊C4—611no—
503C4×C4⋊C4—611no—
504C4×C4⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
509#336—611no—
510#336—611no—
511C61#2301011yescharacteristic, complemented, Sylow
512C22×Q8—611no—
513C22×D4—611no—
514C22×D4—611no—
515C22×D4—1221no—
516C22×D4—1221no—
517C23×C4—1221no—
518C23×C4—1221no—
519C2×SD16—611no—
520C2×SD16—611no—
521C2×SD16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—1222no—
526C2×SD16—1222no—
527C2×SD16—1222no—
528C2×SD16—1222no—
529C2×SD16C2×#692311yescharacteristic, complemented
530C2×SD16C2×#692311yescharacteristic, complemented
531C22×C8—611no—
532C22×C8—611no—
533C22×C8—611no—
534C22×C8—611no—
535#127—611no—
536#127—611no—
537#127—611no—
538#127—1221no—
539#127—1221no—
540#127C2×#692311yescharacteristic
541C4×Q8—611no—
542C4×Q8—611no—
543C4×Q8—611no—
544C4×Q8—1221no—
545C4×Q8—1221no—
546C4×Q8—1222no—
547C4×Q8—1222no—
548C4×Q8—2441no—
549C4×Q8—2441no—
550C4×Q8C2×#692311yescharacteristic, complemented
551C4×D4—1222no—
552C4×D4—1222no—
553C4×D4—2441no—
554C4×D4—2441no—
555C4×D4—2444no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—1221no—
568C2×C22⋊C4—1221no—
569C2×C22⋊C4—1221no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—1221no—
578C2×C42—1221no—
579C2×C42—1221no—
580C2×C42—1221no—
581#107—1222no—
582#106—1222no—
583C4⋊C8—611no—
584C4⋊C8—611no—
585C4⋊C8—611no—
586C4⋊C8C2×#692311yescharacteristic, complemented
587#103—614no—
588#103—1222no—
589#102—611no—
590#102—611no—
591#102—611no—
592#102—611no—
593#102—611no—
594#102—611no—
595#102—1222no—
596#102—1222no—
597#102—2441no—
598#102—2441no—
599#102C2×#692311yescharacteristic, complemented
600#102C2×#692311yescharacteristic, complemented
601#97—1221no—
602#97—1221no—
603#97—1222no—
604C4×C8—1222no—
605#95—611no—
606#95—611no—
607#95—1221no—
608#95—1221no—
609#95—1221no—
610#95—1221no—
611#95—1221no—
612C24—1221no—
613C24—1221no—
614C2×Q8—612no—
615C2×Q8—612no—
616C2×Q8—611no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8C22×#692311yescharacteristic
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—611no—
624C2×D4—611no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4—1221no—
632C2×D4—1221no—
633C2×D4—1221no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—2442no—
644C2×D4—2442no—
645C2×D4C22×#692311yescharacteristic
646C2×D4C22×#692311yescharacteristic
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—4881no—
661C22×C4—4881no—
662C22×C4—2442no—
663C22×C4—2442no—
664C22×C4—2442no—
665C22×C4—2442no—
666SD16—22no—
667SD16—22no—
668SD16—1222no—
669SD16—1222no—
670SD16—1222no—
671SD16—1222no—
672SD16—1222no—
673SD16—1222no—
674C2×C8—612no—
675C2×C8—611no—
676C2×C8—611no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—1221no—
683C2×C8—1221no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8C22×#692311yescharacteristic
687C2×C8C22×#692311yescharacteristic
688C4⋊C4—21no—
689C4⋊C4—612no—
690C4⋊C4—611no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1222no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—2442no—
704C4⋊C4—2441no—
705C4⋊C4—2442no—
706C4⋊C4—2442no—
707C4⋊C4—2442no—
708C4⋊C4C22×#692311yescharacteristic
709C22⋊C4—4881no—
710C22⋊C4—4881no—
711C22⋊C4—2442no—
712C22⋊C4—2442no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C42—21no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—1221no—
720C42—1221no—
721C42—1221no—
722C42—1221no—
723C42—1221no—
724C42—1221no—
725C42—1221no—
726C42—2442no—
727C42—2442no—
728C42—2442no—
729C42C22×#692311yescharacteristic
730C23—21no—
731C23—21no—
732C23—611no—
733C23—1221no—
734C23—1221no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2441no—
739C23—2441no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747Q8—21no—
748Q8—612no—
749Q8—1222no—
750Q8—1222no—
751Q8—1221no—
752Q8D4×#692312yescomplemented
753D4—21no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—81no—
759D4—1221no—
760D4—1221no—
761D4—1221no—
762D4—1221no—
763D4—4881no—
764D4—4881no—
765D4—4881no—
766D4—2442no—
767D4—2441no—
768D4—2441no—
769D4—2441no—
770D4—2441no—
771D4—2442no—
772D4—2442no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—612no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1222no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—4884no—
804C2×C4—4884no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4D4×#692311yescharacteristic
819C2×C4D4×#692311yescharacteristic
820C2×C4C23×#692311yescharacteristic
821C8—21no—
822C8—21no—
823C8—1222no—
824C8—1221no—
825C8—1221no—
826C8—2441no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—611no—
834C22—611no—
835C22—611no—
836C22—611no—
837C22—611no—
838C22—611no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—4881no—
843C22—4881no—
844C22—4881no—
845C22—4881no—
846C22—4881no—
847C22—2441no—
848C22—2441no—
849C22—2441no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22C2×D4×#692311yescharacteristic
854C4—21no—
855C4—21no—
856C4—22no—
857C4—41no—
858C4—611no—
859C4—611no—
860C4—1222no—
861C4—1221no—
862C4—1221no—
863C4—1222no—
864C4—4881no—
865C4—4881no—
866C4—4881no—
867C4—2441no—
868C4—2441no—
869C4—2441no—
870C4—2442no—
871C4—2441no—
872C4C2×D4×#692311yescharacteristic
873C4#1684083111yescharacteristic
874C2—81no—
875C2—81no—
876C2—611no—
877C2—611no—
878C2—611no—
879C2—611no—
880C2—4881no—
881C2—4881no—
882C2#2146234411yescharacteristic
883C2AGL(1,ℤ/8)×#692311yescharacteristic
884C2#2146257911yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#460C4
socleC22×C61C2×C4×D4
prime radical#127×D61C22
cosocleC2×C4×D61C24
hypercenter#460#6923
hypocenterC61#23010
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#16840801C2semidirect
2. C2×SD16×#6923C2semidirect
4. #21462334C2semidirect
6. #21461932C2semidirect
7. #21461911C2semidirect
8. #21461909C2semidirect
9. #21461815C2semidirect
10. #21461815C2semidirect
11. #21461784C2semidirect
12. #21461782C2semidirect
13. #21461620C2semidirect
14. #21461591C2semidirect
58. #16839963C4semidirect
59. #16839962C4semidirect
60. #16839961C4semidirect
61. #16839961C4semidirect
62. #16839960C4semidirect
63. #16839960C4semidirect
64. #16839959C4semidirect
68. C61×#460C4semidirect
106. #14519840D4semidirect
127. C2×#11758190C2×C4semidirect
128. C2×#11758190C2×C4semidirect
129. C2×#11758200C2×C4semidirect
130. C2×#11758200C2×C4semidirect
131. C2×#11758201C2×C4semidirect
132. C2×#11758201C2×C4semidirect
144. Q8×Dic61C2×C4semidirect
146. C4×Dic122C2×C4semidirect
148. #14519742C2×C4semidirect
153. C4⋊#92418C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519706C2×C4semidirect
156. #14519699C2×C4semidirect
157. #14519699C2×C4semidirect
158. #14519698C2×C4semidirect
159. #14519698C2×C4semidirect
160. #14519697C2×C4semidirect
161. #14519697C2×C4semidirect
162. C2×SD16×C61C2×C4semidirect
163. C2×SD16×C61C2×C4semidirect
165. C4×Q8×C61C2×C4semidirect
166. C4⋊C8×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
168. #102×C61C2×C4semidirect
331. Q8×C61C4×D4semidirect
377. Dic122C4×D4semidirect
474. #460#6923semidirect
511. C61#23010semidirect
529. C2×SD16C2×#6923semidirect
530. C2×SD16C2×#6923semidirect
550. C4×Q8C2×#6923semidirect
586. C4⋊C8C2×#6923semidirect
599. #102C2×#6923semidirect
600. #102C2×#6923semidirect
752. Q8D4×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408012
C2×SD16×#69232
#214623492
#214623342
#214619512
#214619322
#214619112
#214619092
#214618152
#214617842
#214617822
#214616202
#214615912
#460×D612
#2301061