Subgroups — #14580396

Order 2624.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050121	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#66491	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050076	C₂	1	1	yes	maximal, characteristic
4	#13050076	C₂	1	1	yes	maximal, characteristic
5	#13050074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	#10620281	C₄	1	1	yes	characteristic
13	#10620281	C₄	1	1	yes	characteristic
14	#10620279	C₄	1	1	yes	characteristic
15	#10620279	C₄	1	1	yes	characteristic
16	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
17	C₂×#66491	C₂²	1	1	yes	characteristic
18	C₂×#66491	C₂²	1	1	yes	characteristic
19	C₂²×D₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
23	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
26	C₄×D₄₁	—	2	1	no	—
27	C₄×D₄₁	—	2	1	no	—
28	C₈×C₄₁	—	2	1	no	—
29	C₈×C₄₁	—	2	1	no	—
30	#66491	—	2	1	no	—
31	#66491	—	2	1	no	—
32	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₄₁	—	2	1	no	—
34	C₂×D₄₁	—	2	1	no	—
35	C₂×D₄₁	—	2	1	no	—
36	C₄×C₄₁	—	2	1	no	—
37	C₄×C₄₁	—	2	1	no	—
38	C₄×C₄₁	#41	1	1	yes	characteristic
39	C₄×C₄₁	#41	1	1	yes	characteristic
40	Dic₄₁	—	2	1	no	—
41	Dic₄₁	—	2	1	no	—
42	Dic₄₁	—	2	1	no	—
43	C₂×C₄₁	#117	1	1	yes	characteristic
44	C₂×C₄₁	#131	1	1	yes	characteristic
45	C₂×C₄₁	#131	1	1	yes	characteristic
46	D₄₁	—	4	1	no	—
47	#433	—	41	1	no	maximal, Sylow
48	C₄₁	#433	1	1	yes	characteristic, complemented, Sylow
49	#117	—	41	1	no	—
50	C₄⋊C₈	—	41	1	no	—
51	C₄⋊C₈	D₄₁	1	1	yes	characteristic, complemented
52	C₂²⋊C₈	—	41	1	no	—
53	C₂²⋊C₈	—	41	1	no	—
54	#97	—	41	1	no	—
55	C₄×C₈	—	41	1	no	—
56	C₂²×C₄	—	41	1	no	—
57	C₂×C₈	—	41	1	no	—
58	C₂×C₈	—	41	1	no	—
59	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
60	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
61	C₄⋊C₄	—	41	1	no	—
62	C₄⋊C₄	—	41	1	no	—
63	C₂²⋊C₄	—	41	1	no	—
64	C₂²⋊C₄	—	41	1	no	—
65	C₄²	—	41	1	no	—
66	C₄²	C₂×D₄₁	1	1	yes	characteristic
67	C₂³	—	41	1	no	—
68	C₂×C₄	—	41	1	no	—
69	C₂×C₄	—	41	1	no	—
70	C₂×C₄	—	41	1	no	—
71	C₂×C₄	—	82	1	no	—
72	C₂×C₄	—	82	1	no	—
73	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
74	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	2	1	no	—
78	C₈	—	82	1	no	—
79	C₈	—	82	1	no	—
80	C₂²	—	82	1	no	—
81	C₂²	—	82	1	no	—
82	C₂²	—	82	1	no	—
83	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	2	1	no	—
86	C₄	—	82	1	no	—
87	C₄	—	82	1	no	—
88	C₄	—	82	1	no	—
89	C₄	#10620308	1	1	yes	characteristic
90	C₄	#10620310	1	1	yes	characteristic
91	C₂	—	164	1	no	—
92	C₂	#13050122	1	1	yes	characteristic
93	C₂	#13050170	1	1	yes	characteristic
94	C₂	#13050172	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting	C₄⋊C₈×C₄₁	C₂
prime radical	C₂²×D₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄⋊C₈	D₄₁
hypocenter	C₄₁	#433
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊#66491	C₂	semidirect
5. #13050074	C₂	semidirect
6. C₈×Dic₄₁	C₂	semidirect
7. C₄⋊C₈×C₄₁	C₂	semidirect
48. C₄₁	#433	semidirect
51. C₄⋊C₈	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050121	2
C₄⋊#66491	2
#13050076	2
#13050074	2
C₈×Dic₄₁	2
C₄⋊C₈×C₄₁	2
#433	41