Subgroups — #28417353

Order 14912.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418610	C₂	1	1	yes	maximal, characteristic, complemented
2	#21418605	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₂₃₃	C₂	1	1	yes	maximal, characteristic
4	#16836604	—	2	1	no	—
5	#16836597	—	2	1	no	—
6	D₄×D₂₃₃	—	2	1	no	—
7	D₁₈₆₄	C₄	1	1	yes	characteristic
8	#16836579	—	2	1	no	—
9	C₈×D₂₃₃	C₂²	1	1	yes	characteristic
10	D₈×C₂₃₃	C₄	1	1	yes	characteristic
11	#14272345	—	4	1	no	—
12	C₂²×D₂₃₃	—	4	1	no	—
13	D₉₃₂	—	2	1	no	—
14	C₂²⋊D₂₃₃	—	4	1	no	—
15	C₄×D₂₃₃	D₄	1	1	yes	characteristic
16	#14272338	D₄	1	1	yes	characteristic
17	D₄×C₂₃₃	—	2	1	no	—
18	C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₂₃₃	—	4	1	no	—
20	C₂×D₂₃₃	—	4	1	no	—
21	C₂×D₂₃₃	—	8	2	no	—
22	C₂×D₂₃₃	SD₁₆	1	1	yes	characteristic
23	C₄×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₂₃₃	D₈	1	1	yes	characteristic
25	C₂×C₂₃₃	—	8	1	no	—
26	C₂×C₂₃₃	#102	1	1	yes	characteristic
27	D₂₃₃	—	2	1	no	—
28	D₂₃₃	—	8	1	no	—
29	C₂₃₃	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	233	1	no	maximal, Sylow
31	C₂×D₈	—	233	1	no	—
32	M₃₂	—	233	1	no	—
33	#108	—	233	1	no	—
34	C₂×D₄	—	466	1	no	—
35	D₈	—	466	1	no	—
36	D₈	—	233	1	no	—
37	D₈	#11745400	1	1	yes	characteristic
38	M₁₆	—	466	1	no	—
39	C₂×C₈	—	233	1	no	—
40	C₁₆	—	466	1	no	—
41	C₂³	—	932	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	932	1	no	—
44	D₄	—	466	1	no	—
45	C₂×C₄	—	233	1	no	—
46	C₈	—	932	1	no	—
47	C₈	—	233	1	no	—
48	C₈	C₂×#11745400	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	1864	2	no	—
51	C₂²	—	932	1	no	—
52	C₂²	—	233	1	no	—
53	C₄	—	233	1	no	—
54	C₄	C₂²⋊#11745400	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	1864	1	no	—
57	C₂	—	466	1	no	—
58	C₂	#21418597	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21418597
commutator	C₈×C₂₃₃	C₂×C₄
Frattini	C₈	C₂×#11745400
Fitting	D₈×C₂₃₃	C₄
socle	C₂×C₂₃₃	#102
prime radical	D₈×D₂₃₃	C₂
cosocle	C₈×D₂₃₃	C₂²
hypercenter	D₈	#11745400
hypocenter	C₂₃₃	#361
LCS	G ▷ C₈×C₂₃₃ ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #21418610	C₂	semidirect
2. #21418605	C₂	semidirect
29. C₂₃₃	#361	semidirect

Maximal subgroups

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

subgroup	index
#21418610	2
#21418605	2
D₈×D₂₃₃	2
#361	233