Subgroups — #14580545

Order 2624.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#10620285	C₂	1	1	yes	maximal, characteristic
3	#13050162	C₂	1	1	yes	maximal, characteristic
4	#13050129	C₂	1	1	yes	maximal, characteristic
5	#13050093	C₂	1	1	yes	maximal, characteristic
6	#13050087	C₂	1	1	yes	maximal, characteristic
7	#103×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
10	C₂×Dic₈₂	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
13	#10620285	—	2	2	no	—
14	#10620279	—	2	1	no	—
15	#10620279	—	2	1	no	—
16	#10620279	—	2	1	no	—
17	C₄×Dic₄₁	—	2	1	no	—
18	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
19	C₂×#66491	C₂²	1	1	yes	characteristic
20	Dic₁₆₄	—	2	2	no	—
21	Q₈×C₄₁	—	2	1	no	—
22	Q₈×C₄₁	—	2	1	no	—
23	C₂×C₄×C₄₁	—	2	1	no	—
24	C₂×C₄×C₄₁	—	2	1	no	—
25	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
26	C₂×Dic₄₁	—	2	1	no	—
27	C₂×Dic₄₁	—	2	1	no	—
28	C₂×Dic₄₁	D₄	1	1	yes	characteristic
29	C₂×Dic₄₁	D₄	1	1	yes	characteristic
30	Dic₈₂	—	2	1	no	—
31	Dic₈₂	—	2	1	no	—
32	Dic₈₂	—	2	1	no	—
33	Dic₈₂	D₄	1	2	yes	—
34	C₈×C₄₁	—	2	1	no	—
35	#66491	—	2	1	no	—
36	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
37	C₄×C₄₁	—	4	1	no	—
38	C₄×C₄₁	—	4	1	no	—
39	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
40	C₄×C₄₁	#41	1	1	yes	characteristic
41	Dic₄₁	—	2	2	no	—
42	Dic₄₁	—	2	1	no	—
43	Dic₄₁	—	4	1	no	—
44	Dic₄₁	Q₁₆	1	2	yes	complemented
45	C₂×C₄₁	#121	1	1	yes	characteristic
46	C₂×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₄₁	#137	1	1	yes	characteristic
48	#462	—	41	1	no	maximal, Sylow
49	C₄₁	#462	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	41	1	no	—
51	C₂×Q₁₆	—	41	1	no	—
52	C₄⋊Q₈	—	41	1	no	—
53	C₄×Q₈	—	41	1	no	—
54	C₄⋊C₈	—	41	1	no	—
55	#103	—	41	1	no	—
56	#103	D₄₁	1	1	yes	characteristic
57	C₂×Q₈	—	41	1	no	—
58	C₂×Q₈	—	41	1	no	—
59	C₂×Q₈	C₂×D₄₁	1	1	yes	characteristic
60	Q₁₆	—	82	2	no	—
61	Q₁₆	—	82	2	no	—
62	C₂×C₈	—	41	1	no	—
63	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
64	C₄⋊C₄	—	82	1	no	—
65	C₄⋊C₄	—	82	1	no	—
66	C₄⋊C₄	—	82	1	no	—
67	C₄⋊C₄	C₂×D₄₁	1	1	yes	characteristic
68	C₄²	—	41	1	no	—
69	C₄²	—	82	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	41	2	no	—
73	Q₈	—	82	1	no	—
74	Q₈	—	82	1	no	—
75	Q₈	—	82	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	41	1	no	—
79	C₂×C₄	—	41	1	no	—
80	C₂×C₄	—	82	1	no	—
81	C₂×C₄	—	82	1	no	—
82	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	82	1	no	—
85	C₂²	D₄×D₄₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	41	2	no	—
89	C₄	—	82	2	no	—
90	C₄	—	82	1	no	—
91	C₄	—	164	1	no	—
92	C₄	#10620306	1	1	yes	characteristic
93	C₄	D₄×D₄₁	1	1	yes	characteristic
94	C₂	#13050137	1	1	yes	characteristic
95	C₂	Q₁₆×D₄₁	1	1	yes	characteristic
96	C₂	#13050193	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#103×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
hypercenter	#103	D₄₁
hypocenter	C₄₁	#462
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
44. Dic₄₁	Q₁₆	semidirect
49. C₄₁	#462	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₆₄	2
C₂×#10620285	2
#13050162	2
#13050129	2
#13050093	2
#13050087	2
#103×C₄₁	2
#462	41