Subgroups — #14581343

Order 2624.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620297	C₂	1	1	yes	maximal, characteristic
2	C₂×#10620296	C₂	1	1	yes	maximal, characteristic
3	#13050231	C₂	1	2	yes	maximal, complemented
4	C₄⋊#66493	C₂	1	2	yes	maximal, complemented
5	#13050122	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
7	C₂×#66493	C₂²	1	1	yes	characteristic
8	C₂×#66493	C₂²	1	2	yes	—
9	C₂×#66493	C₂²	1	1	yes	characteristic
10	#10620297	—	2	2	no	—
11	#10620296	—	2	2	no	—
12	C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
13	#10620281	C₄	1	2	yes	—
14	C₄⋊Dic₄₁	C₄	1	1	yes	characteristic
15	C₄×Dic₄₁	C₂²	1	2	yes	—
16	C₂²×D₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
20	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
21	C₄×D₄₁	D₄	1	2	yes	—
22	C₄×D₄₁	Q₈	1	2	yes	—
23	#66493	—	2	1	no	—
24	#66493	—	2	1	no	—
25	#66493	—	2	2	no	—
26	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₄₁	—	2	1	no	—
28	C₂×D₄₁	—	2	1	no	—
29	C₂×D₄₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₄₁	—	2	2	no	—
31	C₄×C₄₁	C₄⋊C₄	1	2	yes	—
32	Dic₄₁	—	2	2	no	—
33	Dic₄₁	C₂×D₄	1	1	yes	characteristic
34	Dic₄₁	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄₁	#131	1	1	yes	characteristic
37	C₂×C₄₁	#131	1	1	yes	characteristic
38	D₄₁	—	2	2	no	—
39	#424	—	41	1	no	maximal, Sylow
40	C₄₁	#424	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	41	1	no	—
42	C₂²×C₈	—	41	1	no	—
43	#117	—	41	1	no	—
44	C₄⋊C₈	—	41	2	no	—
45	C₄⋊C₈	—	41	2	no	—
46	C₂²×C₄	—	41	1	no	—
47	M₁₆	—	82	2	no	—
48	C₂×C₈	—	41	1	no	—
49	C₂×C₈	—	41	1	no	—
50	C₂×C₈	—	41	2	no	—
51	C₂×C₈	—	82	2	no	—
52	C₄⋊C₄	—	41	1	no	—
53	C₄⋊C₄	#4223	1	1	yes	characteristic
54	C₂²⋊C₄	—	41	2	no	—
55	C₄²	—	41	2	no	—
56	C₂³	—	41	1	no	—
57	C₂×C₄	—	41	1	no	—
58	C₂×C₄	—	41	2	no	—
59	C₂×C₄	—	41	2	no	—
60	C₂×C₄	—	41	2	no	—
61	C₂×C₄	C₂×#4223	1	2	yes	—
62	C₂×C₄	C₂×#4223	1	1	yes	characteristic
63	C₈	—	82	1	no	—
64	C₈	—	82	1	no	—
65	C₈	—	82	2	no	—
66	C₂²	—	41	2	no	—
67	C₂²	—	82	1	no	—
68	C₂²	—	82	1	no	—
69	C₂²	C₂²×#4223	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	41	1	no	—
72	C₄	—	41	1	no	—
73	C₄	—	82	2	no	—
74	C₄	C₄⋊#4223	1	2	yes	—
75	C₂	—	82	2	no	—
76	C₂	C₂×C₄⋊#4223	1	1	yes	characteristic
77	C₂	#13050251	1	1	yes	characteristic
78	C₂	#13050252	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#4223
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting	C₄⋊C₄×C₄₁	C₄
prime radical	C₂²×D₄₁	C₂×C₄
cosocle	C₂×Dic₄₁	C₂³
hypercenter	C₄⋊C₄	#4223
hypocenter	C₄₁	#424
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #13050231	C₂	semidirect
4. C₄⋊#66493	C₂	semidirect
40. C₄₁	#424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620297	2
C₂×#10620296	2
#13050231	2
C₄⋊#66493	2
#13050122	2
#424	41