Subgroups — C₂×#16863236 #22562513

Order 8576.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₃₆	C₂	1	1	yes	maximal, characteristic
2	#16863236	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₆₈	—	2	1	no	—
6	Dic₅₃₆	—	2	1	no	—
7	Dic₅₃₆	C₂²	1	2	yes	—
8	C₆₇⋊C₃₂	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₆₇	—	2	1	no	—
10	Q₃₂×C₆₇	—	2	1	no	—
11	Q₃₂×C₆₇	C₂²	1	2	yes	—
12	C₂×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₃₄	—	4	1	no	—
14	Dic₂₆₈	—	2	2	no	—
15	Dic₂₆₈	—	4	1	no	—
16	C₂×Q₈×C₆₇	—	4	1	no	—
17	Q₁₆×C₆₇	—	2	2	no	—
18	Q₁₆×C₆₇	—	4	1	no	—
19	C₂×C₈×C₆₇	D₄	1	1	yes	characteristic
20	C₁₆×C₆₇	D₄	1	1	yes	characteristic
21	C₁₆×C₆₇	C₂³	1	1	yes	characteristic
22	Q₈×C₆₇	—	4	2	no	—
23	Q₈×C₆₇	—	8	1	no	—
24	C₂×C₄×C₆₇	—	8	1	no	—
25	C₂×C₄×C₆₇	D₈	1	1	yes	characteristic
26	C₂×Dic₆₇	—	8	1	no	—
27	Dic₁₃₄	—	4	2	no	—
28	Dic₁₃₄	—	8	1	no	—
29	C₈×C₆₇	D₈	1	1	yes	characteristic
30	C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₆₇	D₁₆	1	1	yes	characteristic
32	C₄×C₆₇	—	8	2	no	—
33	C₄×C₆₇	D₁₆	1	1	yes	characteristic
34	C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
35	Dic₆₇	—	8	2	no	—
36	C₂×C₆₇	Q₆₄	1	2	yes	complemented
37	C₂×C₆₇	C₂×D₁₆	1	1	yes	characteristic
38	C₂×Q₆₄	—	67	1	no	maximal, Sylow
39	C₆₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₃₂	—	67	1	no	—
41	C₂×Q₃₂	D₆₇	1	1	yes	characteristic
42	Q₆₄	—	67	4	no	—
43	C₂×C₃₂	—	67	1	no	—
44	C₂×Q₁₆	—	2	1	no	—
45	C₂×Q₁₆	—	134	1	no	—
46	Q₃₂	—	2	1	no	—
47	Q₃₂	—	67	2	no	—
48	Q₃₂	—	134	1	no	—
49	Q₃₂	C₂×D₆₇	1	2	yes	—
50	C₂×C₁₆	C₂×D₆₇	1	1	yes	characteristic
51	C₃₂	—	67	2	no	—
52	C₂×Q₈	—	4	1	no	—
53	C₂×Q₈	—	268	1	no	—
54	Q₁₆	—	2	2	no	—
55	Q₁₆	—	4	1	no	—
56	Q₁₆	—	268	1	no	—
57	Q₁₆	—	134	2	no	—
58	C₂×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
59	C₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
60	C₁₆	C₂²×D₆₇	1	1	yes	characteristic
61	Q₈	—	4	2	no	—
62	Q₈	—	8	1	no	—
63	Q₈	—	268	2	no	—
64	Q₈	—	536	1	no	—
65	C₂×C₄	—	8	1	no	—
66	C₂×C₄	—	536	1	no	—
67	C₂×C₄	#11761613	1	1	yes	characteristic
68	C₈	#11761613	1	1	yes	characteristic
69	C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
70	C₂²	#14523984	1	1	yes	characteristic
71	C₄	—	8	2	no	—
72	C₄	—	536	2	no	—
73	C₄	#14523984	1	1	yes	characteristic
74	C₄	C₂×#11761613	1	1	yes	characteristic
75	C₂	#16863236	1	2	yes	direct product factor
76	C₂	C₂×#14523984	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14523984
commutator	C₁₆×C₆₇	C₂³
Frattini	C₁₆	C₂²×D₆₇
Fitting	C₂×Q₃₂×C₆₇	C₂
socle	C₂²×C₆₇	D₁₆
hypercenter	C₂×Q₃₂	D₆₇
hypocenter	C₆₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₆₇ ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #16863236	C₂	direct (N × H)
36. C₂×C₆₇	Q₆₄	semidirect
39. C₆₇	C₂×Q₆₄	semidirect
75. C₂	#16863236	direct (N × H)

Subgroups — C2×#16863236 #22562513

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16863236 #22562513