Subgroups — #14581317

Order 2624.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050243	C₂	1	2	yes	maximal, complemented
2	#13050223	C₂	1	4	yes	maximal, complemented
3	C₂×#10620310	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
5	#10620310	—	2	2	no	—
6	#10620310	—	2	2	no	—
7	C₂×D₁₆₄	C₄	1	1	yes	characteristic, complemented
8	C₂×D₁₆₄	C₂²	1	2	yes	—
9	C₂×C₄×D₄₁	C₄	1	2	yes	complemented
10	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
11	C₂²⋊#4223	C₂²	1	4	yes	—
12	C₄⋊#4223	—	2	2	no	—
13	C₄×#4223	—	2	2	no	—
14	C₂²×D₄₁	C₂×C₄	1	2	yes	—
15	C₂²×D₄₁	C₂³	1	1	yes	characteristic
16	C₂×#4223	—	2	4	no	—
17	Q₈×C₄₁	—	2	2	no	—
18	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
21	D₁₆₄	—	2	4	no	—
22	D₁₆₄	—	2	2	no	—
23	C₄×D₄₁	—	2	2	no	—
24	C₄×D₄₁	—	2	2	no	—
25	C₄×D₄₁	D₄	1	2	yes	—
26	C₄×D₄₁	D₄	1	2	yes	—
27	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₁	—	2	2	no	—
29	C₂×D₄₁	—	4	1	no	—
30	C₂×D₄₁	—	4	2	no	—
31	C₂×D₄₁	C₂×D₄	1	2	yes	—
32	#4223	—	4	4	no	—
33	C₄×C₄₁	—	2	2	no	—
34	C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
35	Dic₄₁	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₄₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄₁	—	2	1	no	—
38	C₂×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	D₄₁	—	2	2	no	—
40	D₄₁	—	4	2	no	—
41	#410	—	41	1	no	maximal, Sylow
42	C₄₁	#410	1	1	yes	characteristic, complemented, Sylow
43	C₂×#41	—	41	1	no	—
44	#117	—	41	2	no	—
45	#99	—	41	4	no	—
46	#41	—	82	2	no	—
47	#41	—	82	2	no	—
48	C₂×Q₈	#4223	1	1	yes	characteristic, complemented
49	C₂×D₄	—	41	2	no	—
50	C₂×D₄	—	41	1	no	—
51	C₂²×C₄	—	41	1	no	—
52	C₂²×C₄	—	41	2	no	—
53	C₄⋊C₄	—	82	2	no	—
54	C₂²⋊C₄	—	41	4	no	—
55	C₄²	—	82	2	no	—
56	C₂³	—	41	1	no	—
57	C₂³	—	41	2	no	—
58	Q₈	—	2	2	no	—
59	D₄	—	82	4	no	—
60	D₄	—	82	2	no	—
61	C₂×C₄	—	41	1	no	—
62	C₂×C₄	—	41	2	no	—
63	C₂×C₄	—	41	2	no	—
64	C₂×C₄	—	82	2	no	—
65	C₂×C₄	—	82	2	no	—
66	C₂×C₄	—	82	4	no	—
67	C₂×C₄	C₂×#4223	1	2	yes	—
68	C₂×C₄	C₂×#4223	1	1	yes	characteristic
69	C₂²	—	41	2	no	—
70	C₂²	—	82	2	no	—
71	C₂²	—	164	1	no	—
72	C₂²	—	164	2	no	—
73	C₂²	C₂²×#4223	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	41	1	no	—
76	C₄	—	41	1	no	—
77	C₄	—	164	4	no	—
78	C₄	C₂²⋊#4223	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	82	2	no	—
81	C₂	—	164	2	no	—
82	C₂	C₂×C₂²⋊#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#4223
commutator	C₂²×C₄₁	C₂²×C₄
Frattini	C₂²	C₂²×#4223
Fitting	C₂×Q₈×C₄₁	C₄
socle	C₂×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂×#10620310	C₂
cosocle	C₂²×D₄₁	C₂³
hypercenter	C₂×Q₈	#4223
hypocenter	C₄₁	#410
LCS	G ▷ C₂²×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #13050243	C₂	semidirect
2. #13050223	C₂	semidirect
4. C₂×Q₈×C₄₁	C₄	semidirect
7. C₂×D₁₆₄	C₄	semidirect
9. C₂×C₄×D₄₁	C₄	semidirect
42. C₄₁	#410	semidirect
48. C₂×Q₈	#4223	semidirect

Maximal subgroups

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

subgroup	index
#13050243	2
#13050223	2
C₂×#10620310	2
#410	41