Subgroups — C₂×#24905674 #35325441

Order 21248.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24905674	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₈₃⋊C₆₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃₂×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₈₃⋊C₆₄	C₂²	1	4	yes	complemented
5	C₂²×C₁₆×C₈₃	C₄	1	1	yes	characteristic
6	C₂×C₃₂×C₈₃	C₄	1	1	yes	characteristic
7	C₂×C₃₂×C₈₃	C₄	1	2	yes	—
8	C₂×C₃₂×C₈₃	C₂²	1	2	yes	—
9	C₂×C₃₂×C₈₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₈₃	C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₈₃	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₈₃	C₈	1	2	yes	—
13	C₂×C₁₆×C₈₃	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₃₂×C₈₃	C₂×C₄	1	2	yes	—
16	C₃₂×C₈₃	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₈₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₈₃	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₈₃	C₁₆	1	2	yes	—
20	C₂×C₈×C₈₃	C₁₆	1	1	yes	characteristic
21	C₂×C₈×C₈₃	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₈₃	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₈₃	C₂×C₈	1	2	yes	—
24	C₁₆×C₈₃	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₈₃	C₂²×C₄	1	1	yes	characteristic
26	C₂³×C₈₃	C₃₂	1	1	yes	characteristic
27	C₂×C₄×C₈₃	C₃₂	1	2	yes	—
28	C₂×C₄×C₈₃	C₃₂	1	1	yes	characteristic
29	C₂×C₄×C₈₃	C₂×C₁₆	1	2	yes	—
30	C₂×C₄×C₈₃	C₂×C₁₆	1	1	yes	characteristic
31	C₈×C₈₃	C₂×C₁₆	1	2	yes	—
32	C₈×C₈₃	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₈₃	C₂²×C₈	1	1	yes	characteristic
34	C₂²×C₈₃	—	2	2	no	—
35	C₂²×C₈₃	C₂×C₃₂	1	2	yes	—
36	C₂²×C₈₃	C₂×C₃₂	1	1	yes	characteristic
37	C₄×C₈₃	C₂×C₃₂	1	1	yes	characteristic
38	C₄×C₈₃	C₂×C₃₂	1	2	yes	—
39	C₄×C₈₃	C₂²×C₁₆	1	1	yes	characteristic
40	C₂×M₁₂₈	—	83	1	no	maximal, Sylow
41	C₂×C₈₃	—	2	2	no	—
42	C₂×C₈₃	M₁₂₈	1	2	yes	complemented
43	C₂×C₈₃	C₂²×C₃₂	1	1	yes	characteristic
44	C₂²×C₃₂	D₈₃	1	1	yes	characteristic
45	M₁₂₈	—	83	4	no	—
46	C₂×C₆₄	—	83	2	no	—
47	C₈₃	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₁₆	Dic₈₃	1	1	yes	characteristic
49	C₂×C₃₂	Dic₈₃	1	1	yes	characteristic
50	C₂×C₃₂	Dic₈₃	1	2	yes	—
51	C₂×C₃₂	C₂×D₈₃	1	2	yes	—
52	C₂×C₃₂	C₂×D₈₃	1	1	yes	characteristic
53	C₆₄	—	83	4	no	—
54	C₂²×C₈	C₈₃⋊C₈	1	1	yes	characteristic
55	C₂×C₁₆	C₈₃⋊C₈	1	1	yes	characteristic
56	C₂×C₁₆	C₈₃⋊C₈	1	2	yes	—
57	C₂×C₁₆	C₂×Dic₈₃	1	2	yes	—
58	C₂×C₁₆	C₂×Dic₈₃	1	1	yes	characteristic
59	C₃₂	C₂×Dic₈₃	1	2	yes	—
60	C₃₂	C₂×Dic₈₃	1	1	yes	characteristic
61	C₃₂	C₂²×D₈₃	1	1	yes	characteristic
62	C₂²×C₄	C₈₃⋊C₁₆	1	1	yes	characteristic
63	C₂×C₈	C₈₃⋊C₁₆	1	2	yes	—
64	C₂×C₈	C₈₃⋊C₁₆	1	1	yes	characteristic
65	C₂×C₈	C₂×C₈₃⋊C₈	1	2	yes	—
66	C₂×C₈	C₂×C₈₃⋊C₈	1	1	yes	characteristic
67	C₁₆	C₂×C₈₃⋊C₈	1	2	yes	—
68	C₁₆	C₂×C₈₃⋊C₈	1	1	yes	characteristic
69	C₁₆	C₂²×Dic₈₃	1	1	yes	characteristic
70	C₂³	C₈₃⋊C₃₂	1	1	yes	characteristic
71	C₂×C₄	C₈₃⋊C₃₂	1	2	yes	—
72	C₂×C₄	C₈₃⋊C₃₂	1	1	yes	characteristic
73	C₂×C₄	C₂×C₈₃⋊C₁₆	1	2	yes	—
74	C₂×C₄	C₂×C₈₃⋊C₁₆	1	1	yes	characteristic
75	C₈	C₂×C₈₃⋊C₁₆	1	2	yes	—
76	C₈	C₂×C₈₃⋊C₁₆	1	1	yes	characteristic
77	C₈	C₂²×C₈₃⋊C₈	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×C₈₃⋊C₃₂	1	2	yes	—
80	C₂²	C₂×C₈₃⋊C₃₂	1	1	yes	characteristic
81	C₄	C₂×C₈₃⋊C₃₂	1	1	yes	characteristic
82	C₄	C₂×C₈₃⋊C₃₂	1	2	yes	—
83	C₄	C₂²×C₈₃⋊C₁₆	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#24905674	1	2	yes	direct product factor
86	C₂	C₂²×C₈₃⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃₂	C₂×D₈₃
commutator	C₂×C₈₃	C₂²×C₃₂
Frattini	C₃₂	C₂²×D₈₃
Fitting	C₂²×C₃₂×C₈₃	C₂
socle	C₂²×C₈₃	C₂×C₃₂
prime radical	C₂³×C₈₃	C₃₂
cosocle	C₃₂×C₈₃	C₂³
hypercenter	C₂²×C₃₂	D₈₃
hypocenter	C₈₃	C₂×M₁₂₈
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
1. #24905674	C₂	direct (N × H)
2. C₂×C₈₃⋊C₆₄	C₂	semidirect
4. C₈₃⋊C₆₄	C₂²	semidirect
42. C₂×C₈₃	M₁₂₈	semidirect
47. C₈₃	C₂×M₁₂₈	semidirect
85. C₂	#24905674	direct (N × H)

Maximal subgroups

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

subgroup	index
#24905674	2
C₂×C₈₃⋊C₆₄	2
C₂²×C₃₂×C₈₃	2
C₂×M₁₂₈	83

Subgroups — C2×#24905674 #35325441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#24905674 #35325441