Subgroups — #44529347

Order 31168.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₉₄₈	C₂	1	1	yes	maximal, characteristic
2	#29510148	C₂	1	1	yes	maximal, characteristic, complemented
3	#29510146	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊(C₄₈₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#29510135	C₂	1	1	yes	maximal, characteristic
6	#29510135	C₂	1	1	yes	maximal, characteristic
7	#125×C₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₉₄₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄₈₇	—	2	1	no	—
10	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄₈₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₈₇	C₂²	1	1	yes	characteristic
13	(C₂×D₄₈₇)⋊C₄	—	2	1	no	—
14	C₄⋊C₄×C₄₈₇	—	2	1	no	—
15	C₄⋊C₄×C₄₈₇	—	2	1	no	—
16	C₄⋊C₄×C₄₈₇	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₄₈₇	C₂²	1	1	yes	characteristic
18	C₄²×C₄₈₇	C₂²	1	1	yes	characteristic
19	C₂²×D₄₈₇	—	2	1	no	—
20	D₁₉₄₈	—	2	1	no	—
21	D₁₉₄₈	Q₈	1	2	yes	—
22	C₂×Dic₄₈₇	—	2	1	no	—
23	C₄×D₄₈₇	—	4	2	no	—
24	C₄₈₇⋊C₈	—	2	1	no	—
25	C₄₈₇⋊C₈	—	2	1	no	—
26	C₂×C₄×C₄₈₇	—	2	1	no	—
27	C₂×C₄×C₄₈₇	—	2	1	no	—
28	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
29	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
31	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₄₈₇	—	2	2	no	—
33	C₂×D₄₈₇	—	4	1	no	—
34	C₂×D₄₈₇	—	4	1	no	—
35	C₄×C₄₈₇	—	2	1	no	—
36	C₄×C₄₈₇	—	2	1	no	—
37	C₄×C₄₈₇	—	4	1	no	—
38	C₄×C₄₈₇	—	4	1	no	—
39	C₄×C₄₈₇	C₂×Q₈	1	1	yes	characteristic
40	C₄×C₄₈₇	#41	1	1	yes	characteristic
41	Dic₄₈₇	—	4	1	no	—
42	C₂×C₄₈₇	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₄₈₇	#135	1	1	yes	characteristic
44	C₂×C₄₈₇	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₄₈₇	—	4	2	no	—
46	C₄₈₇	#478	1	1	yes	characteristic, complemented, Sylow
47	#478	—	487	1	no	maximal, Sylow
48	#125	D₄₈₇	1	1	yes	characteristic, complemented
49	C₄×D₄	—	487	1	no	—
50	#107	—	487	1	no	—
51	#106	—	487	1	no	—
52	C₄⋊C₈	—	487	1	no	—
53	#102	—	487	1	no	—
54	#102	—	487	1	no	—
55	C₂×D₄	—	487	1	no	—
56	C₂²×C₄	—	974	1	no	—
57	C₂×C₈	—	487	1	no	—
58	C₂×C₈	—	487	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	487	1	no	—
62	C₄⋊C₄	C₂×D₄₈₇	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₄₈₇	1	1	yes	characteristic
64	C₂²⋊C₄	—	974	1	no	—
65	C₄²	C₂×D₄₈₇	1	1	yes	characteristic
66	C₂³	—	974	1	no	—
67	D₄	—	974	1	no	—
68	D₄	—	487	2	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	1948	2	no	—
72	C₂×C₄	—	974	1	no	—
73	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊D₄₈₇	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
76	C₈	—	974	1	no	—
77	C₈	—	974	1	no	—
78	C₂²	—	1948	1	no	—
79	C₂²	—	1948	1	no	—
80	C₂²	—	974	2	no	—
81	C₂²	C₂×C₂²⋊D₄₈₇	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	1948	1	no	—
87	C₄	Q₈×D₄₈₇	1	1	yes	characteristic
88	C₄	#21441262	1	1	yes	characteristic
89	C₂	—	1948	2	no	—
90	C₂	#29510191	1	1	yes	characteristic
91	C₂	#29510235	1	1	yes	characteristic
92	C₂	#29510240	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₈₇
commutator, cosocle	C₂×C₄×C₄₈₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	#125×C₄₈₇	C₂
socle	C₂²×C₄₈₇	C₂×D₄
prime radical	C₂×D₁₉₄₈	C₂²
hypercenter	#125	D₄₈₇
hypocenter	C₄₈₇	#478
LCS	G ▷ C₂×C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #29510148	C₂	semidirect
3. #29510146	C₂	semidirect
4. C₄⋊(C₄₈₇⋊C₈)	C₂	semidirect
7. #125×C₄₈₇	C₂	semidirect
46. C₄₈₇	#478	semidirect
48. #125	D₄₈₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₉₄₈	2
#29510148	2
#29510146	2
C₄⋊(C₄₈₇⋊C₈)	2
#29510135	2
#125×C₄₈₇	2
#478	487