Subgroups — #44529261

Order 31168.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₄₈	C₂	1	2	yes	maximal
2	#29510215	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₉₇₄	C₂	1	1	yes	maximal, characteristic
4	#29510140	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₇₄	C₂²	1	2	yes	—
7	C₂×Dic₉₇₄	C₂²	1	1	yes	characteristic
8	Dic₁₉₄₈	—	2	4	no	—
9	C₄⋊Dic₄₈₇	—	2	1	no	—
10	C₄⋊Dic₄₈₇	—	2	1	no	—
11	C₄⋊Dic₄₈₇	C₂²	1	1	yes	characteristic
12	Dic₄₈₇⋊C₄	—	2	1	no	—
13	C₄×Dic₄₈₇	—	2	1	no	—
14	C₂×C₈×C₄₈₇	C₂²	1	2	yes	—
15	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
16	Dic₉₇₄	—	2	1	no	—
17	Dic₉₇₄	—	2	2	no	—
18	Dic₉₇₄	—	2	2	no	—
19	Dic₉₇₄	D₄	1	2	yes	—
20	C₂×Dic₄₈₇	—	2	1	no	—
21	C₂×Dic₄₈₇	—	2	1	no	—
22	C₂×Dic₄₈₇	—	2	2	no	—
23	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
25	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
26	C₈×C₄₈₇	—	2	2	no	—
27	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₈₇	—	2	1	no	—
29	C₄×C₄₈₇	Q₁₆	1	2	yes	complemented
30	C₄×C₄₈₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₈₇	#41	1	1	yes	characteristic
32	Dic₄₈₇	—	2	2	no	—
33	Dic₄₈₇	—	4	2	no	—
34	Dic₄₈₇	—	4	1	no	—
35	C₂×C₄₈₇	#121	1	1	yes	characteristic
36	C₂×C₄₈₇	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₄₈₇	#137	1	1	yes	characteristic
38	C₄₈₇	#462	1	1	yes	characteristic, complemented, Sylow
39	#462	—	487	1	no	maximal, Sylow
40	C₂×Q₁₆	—	487	2	no	—
41	C₄⋊Q₈	—	487	1	no	—
42	C₄×Q₈	—	487	1	no	—
43	C₄⋊C₈	D₄₈₇	1	1	yes	characteristic
44	#103	—	487	2	no	—
45	C₂×Q₈	—	487	2	no	—
46	C₂×Q₈	—	487	1	no	—
47	Q₁₆	—	974	4	no	—
48	C₂×C₈	C₂×D₄₈₇	1	2	yes	—
49	C₄⋊C₄	—	974	1	no	—
50	C₄⋊C₄	—	974	1	no	—
51	C₄⋊C₄	—	974	1	no	—
52	C₄⋊C₄	—	487	1	no	—
53	C₄²	—	974	1	no	—
54	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
55	Q₈	—	974	2	no	—
56	Q₈	—	974	2	no	—
57	Q₈	—	974	1	no	—
58	Q₈	—	487	2	no	—
59	C₂×C₄	—	974	1	no	—
60	C₂×C₄	—	974	2	no	—
61	C₂×C₄	—	974	1	no	—
62	C₂×C₄	D₁₉₄₈	1	1	yes	characteristic
63	C₂×C₄	D₁₉₄₈	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₁₉₄₈	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	1948	2	no	—
69	C₄	—	1948	1	no	—
70	C₄	—	974	2	no	—
71	C₄	Dic₁₉₄₈	1	2	yes	complemented
72	C₄	D₄×D₄₈₇	1	1	yes	characteristic
73	C₄	#21441262	1	1	yes	characteristic
74	C₂	#29510190	1	1	yes	characteristic
75	C₂	C₂×Dic₁₉₄₈	1	1	yes	characteristic
76	C₂	#29510248	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₉₄₈
commutator, cosocle	C₂×C₄×C₄₈₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	C₄⋊C₈×C₄₈₇	C₂
socle, prime radical	C₂²×C₄₈₇	C₂×D₄
hypercenter	C₄⋊C₈	D₄₈₇
hypocenter	C₄₈₇	#462
LCS	G ▷ C₂×C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
29. C₄×C₄₈₇	Q₁₆	semidirect
38. C₄₈₇	#462	semidirect
71. C₄	Dic₁₉₄₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₉₄₈	2
#29510215	2
C₄×Dic₉₇₄	2
#29510140	2
C₄⋊C₈×C₄₈₇	2
#462	487