Subgroups — C₂×#89315 #11729213

Order 896.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#89315	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×D₈	—	2	1	no	—
6	C₂×Dic₂₈	—	2	1	no	—
7	C₇×D₁₆	—	2	1	no	—
8	C₇×D₁₆	C₂²	1	2	yes	—
9	C₂×C₇×C₁₆	C₂²	1	1	yes	characteristic
10	Dic₅₆	—	2	1	no	—
11	Dic₅₆	C₂²	1	2	yes	complemented
12	C₇⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂×SD₆₄	—	7	1	no	maximal, Sylow
14	C₂×C₇×D₄	—	4	1	no	—
15	C₂×Dic₁₄	—	4	1	no	—
16	C₇×D₈	—	2	2	no	—
17	C₇×D₈	—	4	1	no	—
18	C₂×C₇×C₈	D₄	1	1	yes	characteristic
19	Dic₂₈	—	2	2	no	—
20	Dic₂₈	—	4	1	no	—
21	C₇×C₁₆	D₄	1	1	yes	characteristic
22	C₇×C₁₆	C₂³	1	1	yes	characteristic
23	C₂×Q₃₂	—	7	1	no	—
24	C₂×D₁₆	D₇	1	1	yes	characteristic
25	SD₆₄	—	7	4	no	—
26	C₂×C₃₂	—	7	1	no	—
27	C₂³×C₇	—	8	1	no	—
28	C₇×D₄	—	4	2	no	—
29	C₇×D₄	—	8	1	no	—
30	C₂×C₄×C₇	D₈	1	1	yes	characteristic
31	C₂×Dic₇	—	8	1	no	—
32	Dic₁₄	—	4	2	no	—
33	Dic₁₄	—	8	1	no	—
34	C₇×C₈	D₈	1	1	yes	characteristic
35	C₇×C₈	C₂×D₄	1	1	yes	characteristic
36	C₂×Q₁₆	—	14	1	no	—
37	C₂×D₈	—	2	1	no	—
38	Q₃₂	—	7	2	no	—
39	Q₃₂	—	14	1	no	—
40	D₁₆	—	2	1	no	—
41	D₁₆	C₂×D₇	1	2	yes	—
42	C₂×C₁₆	C₂×D₇	1	1	yes	characteristic
43	C₃₂	—	7	2	no	—
44	C₂²×C₇	—	8	2	no	—
45	C₂²×C₇	—	16	2	no	—
46	C₂²×C₇	D₁₆	1	1	yes	characteristic
47	C₄×C₇	D₁₆	1	1	yes	characteristic
48	C₄×C₇	C₂×D₈	1	1	yes	characteristic
49	Dic₇	—	8	2	no	—
50	C₂×Q₈	—	28	1	no	—
51	C₂×D₄	—	4	1	no	—
52	Q₁₆	—	14	2	no	—
53	Q₁₆	—	28	1	no	—
54	D₈	—	2	2	no	—
55	D₈	—	4	1	no	—
56	C₂×C₈	C₂²⋊D₇	1	1	yes	characteristic
57	C₁₆	C₂²⋊D₇	1	1	yes	characteristic
58	C₁₆	C₂²×D₇	1	1	yes	characteristic
59	C₂×C₇	—	16	2	no	—
60	C₂×C₇	SD₆₄	1	2	yes	complemented
61	C₂×C₇	C₂×D₁₆	1	1	yes	characteristic
62	C₂³	—	8	1	no	—
63	Q₈	—	28	2	no	—
64	Q₈	—	56	1	no	—
65	D₄	—	4	2	no	—
66	D₄	—	8	1	no	—
67	C₂×C₄	—	56	1	no	—
68	C₂×C₄	#1141	1	1	yes	characteristic
69	C₈	#1141	1	1	yes	characteristic
70	C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
71	C₇	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
72	C₂²	—	8	2	no	—
73	C₂²	—	16	2	no	—
74	C₂²	#6400	1	1	yes	characteristic
75	C₄	—	56	2	no	—
76	C₄	#6400	1	1	yes	characteristic
77	C₄	C₂×#1141	1	1	yes	characteristic
78	C₂	—	16	2	no	—
79	C₂	#89315	1	2	yes	direct product factor
80	C₂	C₂×#6400	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#6400
commutator, cosocle	C₇×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₇
Fitting, prime radical	C₂×C₇×D₁₆	C₂
socle	C₂²×C₇	D₁₆
hypercenter	C₂×D₁₆	D₇
hypocenter	C₇	C₂×SD₆₄
LCS	G ▷ C₇×C₁₆ ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₅₆	C₂	semidirect
3. #89315	C₂	direct (N × H)
4. C₂×C₇⋊C₃₂	C₂	semidirect
11. Dic₅₆	C₂²	semidirect
12. C₇⋊C₃₂	C₂²	semidirect
60. C₂×C₇	SD₆₄	semidirect
71. C₇	C₂×SD₆₄	semidirect
79. C₂	#89315	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×D₁₆	2
C₂×Dic₅₆	2
#89315	2
C₂×C₇⋊C₃₂	2
C₂×SD₆₄	7

Subgroups — C2×#89315 #11729213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#89315 #11729213