Subgroups — #44529286

Order 31168.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₈₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#29510189	C₂	1	2	yes	maximal, complemented
3	#29510149	C₂	1	1	yes	maximal, characteristic, complemented
4	#29510137	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×C₄₈₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₉₄₈	C₂²	1	2	yes	—
7	C₂×C₂²⋊D₄₈₇	—	2	2	no	—
8	D₃₈₉₆	—	2	2	no	—
9	C₄⋊Dic₄₈₇	C₂²	1	2	yes	—
10	(C₂×D₄₈₇)⋊C₄	—	2	2	no	—
11	C₂²×C₄×C₄₈₇	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₄₈₇	—	2	2	no	—
13	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₄₈₇	C₂²	1	1	yes	characteristic
15	C₂²×D₄₈₇	—	2	2	no	—
16	D₁₉₄₈	—	2	2	no	—
17	D₁₉₄₈	—	2	2	no	—
18	C₂²⋊D₄₈₇	—	4	4	no	—
19	C₂×Dic₄₈₇	—	2	2	no	—
20	C₂³×C₄₈₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₈₇	—	2	1	no	—
22	C₂×C₄×C₄₈₇	—	2	1	no	—
23	C₂×C₄×C₄₈₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₈₇	C₂³	1	1	yes	characteristic
25	C₈×C₄₈₇	—	2	1	no	—
26	C₈×C₄₈₇	D₄	1	2	yes	complemented
27	C₂²×C₄₈₇	—	2	1	no	—
28	C₂²×C₄₈₇	—	2	1	no	—
29	C₂²×C₄₈₇	D₈	1	2	yes	complemented
30	C₂²×C₄₈₇	C₂×D₄	1	1	yes	characteristic
31	C₂×D₄₈₇	—	4	2	no	—
32	C₂×D₄₈₇	—	4	2	no	—
33	C₂×D₄₈₇	—	4	2	no	—
34	C₄×C₄₈₇	—	2	1	no	—
35	C₄×C₄₈₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₈₇	#41	1	1	yes	characteristic
37	Dic₄₈₇	—	4	2	no	—
38	C₂×C₄₈₇	—	2	2	no	—
39	C₂×C₄₈₇	#121	1	1	yes	characteristic
40	C₂×C₄₈₇	C₂×D₈	1	1	yes	characteristic
41	C₂×C₄₈₇	#135	1	1	yes	characteristic
42	D₄₈₇	—	8	2	no	—
43	C₄₈₇	#466	1	1	yes	characteristic, complemented, Sylow
44	#466	—	487	1	no	maximal, Sylow
45	C₂×D₈	—	487	1	no	—
46	C₂²×C₈	D₄₈₇	1	1	yes	characteristic, complemented
47	#121	—	487	2	no	—
48	#107	—	487	1	no	—
49	#102	—	487	2	no	—
50	C₂×D₄	—	974	2	no	—
51	C₂×D₄	—	487	2	no	—
52	C₂²×C₄	C₂×D₄₈₇	1	1	yes	characteristic
53	D₈	—	974	2	no	—
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
56	C₂×C₈	C₂×D₄₈₇	1	1	yes	characteristic
57	C₄⋊C₄	—	487	2	no	—
58	C₂²⋊C₄	—	974	2	no	—
59	C₂³	—	974	2	no	—
60	C₂³	D₁₉₄₈	1	1	yes	characteristic
61	D₄	—	1948	4	no	—
62	D₄	—	974	2	no	—
63	D₄	—	974	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	974	2	no	—
67	C₂×C₄	D₁₉₄₈	1	1	yes	characteristic
68	C₂×C₄	C₂²×D₄₈₇	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	C₂²⋊D₄₈₇	1	2	yes	complemented
71	C₂²	—	2	1	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	1948	2	no	—
74	C₂²	—	1948	2	no	—
75	C₂²	—	1948	2	no	—
76	C₂²	D₃₈₉₆	1	2	yes	complemented
77	C₂²	C₂×D₁₉₄₈	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	1948	2	no	—
80	C₄	C₂×C₂²⋊D₄₈₇	1	1	yes	characteristic
81	C₄	#21441261	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	—	3896	2	no	—
84	C₂	#29510189	1	1	yes	characteristic
85	C₂	C₂×D₃₈₉₆	1	1	yes	characteristic
86	C₂	#29510237	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₉₄₈
commutator, cosocle	C₂×C₄×C₄₈₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₈₇
Fitting	C₂²×C₈×C₄₈₇	C₂
socle	C₂²×C₄₈₇	C₂×D₄
hypercenter	C₂²×C₈	D₄₈₇
hypocenter	C₄₈₇	#466
LCS	G ▷ C₂×C₄×C₄₈₇ ▷ C₂×C₄₈₇ ▷ C₄₈₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₈₉₆	C₂	semidirect
2. #29510189	C₂	semidirect
3. #29510149	C₂	semidirect
4. #29510137	C₂	semidirect
5. C₂²×C₈×C₄₈₇	C₂	semidirect
26. C₈×C₄₈₇	D₄	semidirect
29. C₂²×C₄₈₇	D₈	semidirect
43. C₄₈₇	#466	semidirect
46. C₂²×C₈	D₄₈₇	semidirect
70. C₈	C₂²⋊D₄₈₇	semidirect
76. C₂²	D₃₈₉₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₈₉₆	2
#29510189	2
#29510149	2
#29510137	2
C₂²×C₈×C₄₈₇	2
#466	487