Subgroups — #14580384

Order 2624.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620277	C₂	1	1	yes	maximal, characteristic
2	C₂×#10620277	C₂	1	1	yes	maximal, characteristic
3	#13050099	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	M₁₆×C₄₁	—	2	1	no	—
7	M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂×C₈×C₄₁	—	2	1	no	—
9	#10620277	—	2	1	no	—
10	#10620277	C₄	1	2	yes	—
11	#10620277	C₄	1	2	yes	—
12	#10620277	C₂²	1	2	yes	—
13	C₂×#66491	—	2	1	no	—
14	C₂×#66491	C₂²	1	2	yes	—
15	C₂³×C₄₁	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	Q₈	1	1	yes	characteristic
21	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
22	C₈×C₄₁	—	2	2	no	—
23	#66491	—	2	2	no	—
24	#66491	C₂×C₄	1	4	yes	—
25	C₂²×C₄₁	—	4	1	no	—
26	C₂²×C₄₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₄₁	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄₁	—	2	1	no	—
34	C₂×C₄₁	—	2	1	no	—
35	C₂×C₄₁	—	2	1	no	—
36	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
37	#430	—	41	1	no	maximal, Sylow
38	C₄₁	#430	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	—	41	1	no	—
40	C₂×M₁₆	—	41	1	no	—
41	C₂×M₁₆	D₄₁	1	1	yes	characteristic
42	#108	—	41	4	no	—
43	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
44	M₁₆	—	2	1	no	—
45	M₁₆	—	41	2	no	—
46	M₁₆	—	41	2	no	—
47	M₁₆	—	41	2	no	—
48	M₁₆	—	82	1	no	—
49	M₁₆	C₂×D₄₁	1	2	yes	—
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	—	41	2	no	—
52	C₂×C₈	—	82	1	no	—
53	C₂³	Dic₈₂	1	1	yes	characteristic
54	C₂×C₄	Dic₈₂	1	1	yes	characteristic
55	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
56	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₄₁	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	41	4	no	—
62	C₈	—	82	2	no	—
63	C₂²	—	4	1	no	—
64	C₂²	#10620279	1	1	yes	characteristic
65	C₂²	#10620279	1	1	yes	characteristic
66	C₂²	C₂×Dic₈₂	1	1	yes	characteristic
67	C₄	#10620279	1	1	yes	characteristic
68	C₄	#10620279	1	1	yes	characteristic
69	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
70	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	C₂×#10620279	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊D₄₁
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₂×M₁₆×C₄₁	C₂
socle	C₂×C₄₁	C₂×C₄⋊C₄
prime radical	C₂³×C₄₁	Q₈
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂×M₁₆	D₄₁
hypocenter	C₄₁	#430
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13050099	C₂	semidirect
38. C₄₁	#430	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10620277	2
#13050099	2
C₂×M₁₆×C₄₁	2
#430	41