Subgroups — #14581378

Order 2624.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050251	C₂	1	2	yes	maximal, complemented
2	#13050235	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050228	C₂	1	2	yes	maximal, complemented
4	C₈×#4223	C₂	1	1	yes	maximal, characteristic, complemented
5	#13050183	C₂	1	1	yes	maximal, characteristic
6	#10620308	C₂²	1	2	yes	—
7	#10620301	—	2	2	no	—
8	C₂×#66493	—	2	2	no	—
9	C₄×#4223	C₂²	1	1	yes	characteristic
10	#10620297	C₂²	1	2	yes	—
11	#10620296	C₂²	1	1	yes	characteristic
12	D₈×C₄₁	C₄	1	1	yes	characteristic, complemented
13	#10620283	C₄	1	2	yes	complemented
14	Dic₁₆₄	C₄	1	1	yes	characteristic, complemented
15	C₈×D₄₁	C₂²	1	1	yes	characteristic
16	C₂×#4223	—	2	1	no	—
17	D₄×C₄₁	C₂×C₄	1	2	yes	—
18	C₂²⋊D₄₁	—	2	2	no	—
19	C₂×Dic₄₁	—	2	2	no	—
20	C₄×D₄₁	C₂³	1	1	yes	characteristic
21	Dic₈₂	C₂×C₄	1	2	yes	—
22	#66493	—	2	2	no	—
23	#66493	D₄	1	1	yes	characteristic
24	#66493	D₄	1	1	yes	characteristic
25	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
26	#66491	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄₁	—	2	2	no	—
28	C₂×D₄₁	#41	1	1	yes	characteristic
29	#4223	—	2	2	no	—
30	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	Dic₄₁	—	2	2	no	—
32	Dic₄₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄₁	—	4	2	no	—
34	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
35	D₄₁	—	2	1	no	—
36	#443	—	41	1	no	maximal, Sylow
37	C₄₁	#443	1	1	yes	characteristic, complemented, Sylow
38	#135	—	41	1	no	—
39	#131	—	41	2	no	—
40	#108	—	41	1	no	—
41	#104	—	41	2	no	—
42	C₄×C₈	—	41	1	no	—
43	#41	—	41	2	no	—
44	Q₁₆	—	41	1	no	—
45	SD₁₆	—	41	2	no	—
46	D₈	#4223	1	1	yes	characteristic, complemented
47	M₁₆	—	41	2	no	—
48	M₁₆	—	82	2	no	—
49	C₂×C₈	—	41	1	no	—
50	C₂×C₈	—	41	1	no	—
51	C₂×C₈	—	82	2	no	—
52	C₄²	—	41	1	no	—
53	Q₈	—	41	2	no	—
54	D₄	—	82	2	no	—
55	D₄	C₂×#4223	1	2	yes	—
56	C₂×C₄	—	41	1	no	—
57	C₂×C₄	—	82	2	no	—
58	C₂×C₄	—	82	1	no	—
59	C₈	—	41	1	no	—
60	C₈	—	41	1	no	—
61	C₈	—	41	1	no	—
62	C₈	—	82	2	no	—
63	C₈	C₂×#4223	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	—	41	1	no	—
66	C₄	—	41	1	no	—
67	C₄	—	82	2	no	—
68	C₄	—	82	2	no	—
69	C₄	C₂²×#4223	1	1	yes	characteristic
70	C₂	—	4	2	no	—
71	C₂	—	82	1	no	—
72	C₂	D₄×#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#4223
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₄	C₂²×#4223
Fitting	D₈×C₄₁	C₄
socle	C₂×C₄₁	C₄×D₄
prime radical	#13050183	C₂
cosocle	C₄×D₄₁	C₂³
hypercenter	D₈	#4223
hypocenter	C₄₁	#443
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #13050251	C₂	semidirect
2. #13050235	C₂	semidirect
3. #13050228	C₂	semidirect
4. C₈×#4223	C₂	semidirect
12. D₈×C₄₁	C₄	semidirect
13. #10620283	C₄	semidirect
14. Dic₁₆₄	C₄	semidirect
37. C₄₁	#443	semidirect
46. D₈	#4223	semidirect

Maximal subgroups

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

subgroup	index
#13050251	2
#13050235	2
#13050228	2
C₈×#4223	2
#13050183	2
#443	41