Subgroups — #14580477

Order 2624.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10620273	C₂	1	2	yes	maximal, complemented
3	#13050138	C₂	1	1	yes	maximal, characteristic
4	#13050089	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₄₁	—	2	1	no	—
8	C₂²×Dic₄₁	—	2	1	no	—
9	C₂×D₁₆₄	C₂²	1	1	yes	characteristic
10	C₂×Dic₈₂	—	2	1	no	—
11	C₂×Dic₈₂	—	2	4	no	—
12	C₂×Dic₈₂	C₂²	1	2	yes	—
13	C₂×C₈×C₄₁	C₂²	1	2	yes	—
14	#10620281	—	2	1	no	—
15	C₄⋊Dic₄₁	C₂²	1	1	yes	characteristic
16	#10620273	—	2	4	no	—
17	C₂³×C₄₁	D₄	1	1	yes	characteristic
18	C₂²×D₄₁	—	2	1	no	—
19	C₂×C₄×C₄₁	—	2	2	no	—
20	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
22	C₂²⋊D₄₁	—	4	2	no	—
23	C₂×Dic₄₁	—	2	4	no	—
24	C₂×Dic₄₁	—	2	2	no	—
25	C₂×Dic₄₁	—	2	1	no	—
26	D₁₆₄	—	2	2	no	—
27	Dic₈₂	—	2	4	no	—
28	Dic₈₂	—	2	2	no	—
29	Dic₈₂	D₄	1	4	yes	complemented
30	C₈×C₄₁	—	2	2	no	—
31	C₂²×C₄₁	—	2	1	no	—
32	C₂²×C₄₁	—	2	1	no	—
33	C₂²×C₄₁	SD₁₆	1	2	yes	complemented
34	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
35	C₂×D₄₁	—	4	1	no	—
36	C₂×D₄₁	—	4	1	no	—
37	C₂×D₄₁	—	4	1	no	—
38	C₄×C₄₁	—	2	1	no	—
39	C₄×C₄₁	C₂×D₄	1	2	yes	—
40	Dic₄₁	—	2	4	no	—
41	Dic₄₁	—	4	1	no	—
42	C₂×C₄₁	—	2	2	no	—
43	C₂×C₄₁	#120	1	1	yes	characteristic
44	C₂×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₄₁	#137	1	1	yes	characteristic
46	D₄₁	—	8	1	no	—
47	#448	—	41	1	no	maximal, Sylow
48	C₄₁	#448	1	1	yes	characteristic, complemented, Sylow
49	C₂²×Q₈	—	41	1	no	—
50	C₂×SD₁₆	—	41	2	no	—
51	#121	—	41	1	no	—
52	#103	—	41	2	no	—
53	C₂²⋊C₈	D₄₁	1	1	yes	characteristic, complemented
54	C₂×Q₈	—	41	2	no	—
55	C₂×Q₈	—	82	4	no	—
56	C₂×Q₈	—	82	1	no	—
57	C₂×D₄	—	41	1	no	—
58	C₂×D₄	—	82	1	no	—
59	C₂²×C₄	—	82	1	no	—
60	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
61	SD₁₆	—	82	4	no	—
62	C₂×C₈	C₂×D₄₁	1	2	yes	—
63	C₄⋊C₄	—	41	1	no	—
64	C₂²⋊C₄	—	82	1	no	—
65	C₂³	—	82	1	no	—
66	C₂³	D₁₆₄	1	1	yes	characteristic
67	Q₈	—	41	4	no	—
68	Q₈	—	82	4	no	—
69	Q₈	—	82	2	no	—
70	D₄	—	82	2	no	—
71	D₄	—	164	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	82	4	no	—
74	C₂×C₄	—	82	2	no	—
75	C₂×C₄	—	82	1	no	—
76	C₂×C₄	D₁₆₄	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
78	C₈	—	2	2	no	—
79	C₂²	—	2	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	164	1	no	—
82	C₂²	—	164	1	no	—
83	C₂²	—	164	1	no	—
84	C₂²	#10620273	1	2	yes	complemented
85	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	82	4	no	—
88	C₄	—	164	1	no	—
89	C₄	D₄×D₄₁	1	2	yes	—
90	C₂	—	2	2	no	—
91	C₂	—	328	1	no	—
92	C₂	#13050134	1	1	yes	characteristic
93	C₂	C₂×#10620273	1	1	yes	characteristic
94	C₂	#13050197	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₆₄
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₂²⋊C₈×C₄₁	C₂
socle	C₂²×C₄₁	C₂×D₄
prime radical	#13050138	C₂
hypercenter	C₂²⋊C₈	D₄₁
hypocenter	C₄₁	#448
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₈₂	C₂	semidirect
2. C₂×#10620273	C₂	semidirect
4. #13050089	C₂	semidirect
5. C₂²⋊C₈×C₄₁	C₂	semidirect
29. Dic₈₂	D₄	semidirect
33. C₂²×C₄₁	SD₁₆	semidirect
48. C₄₁	#448	semidirect
53. C₂²⋊C₈	D₄₁	semidirect
84. C₂²	#10620273	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₂	2
C₂×#10620273	2
#13050138	2
#13050089	2
C₂²⋊C₈×C₄₁	2
#448	41