Subgroups — C₂×#10622087 #13070918

Order 1408.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₇₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622087	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₄₄	—	2	1	no	—
6	C₂×D₈₈	—	2	1	no	—
7	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	Dic₈₈	—	2	1	no	—
9	Dic₈₈	C₂²	1	2	yes	complemented
10	D₁₇₆	—	2	1	no	—
11	D₁₇₆	C₂²	1	2	yes	—
12	C₁₁×C₃₂	C₂²	1	2	yes	complemented
13	C₂×D₄₄	—	4	1	no	—
14	C₂×Dic₂₂	—	4	1	no	—
15	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
16	Dic₄₄	—	2	2	no	—
17	Dic₄₄	—	4	1	no	—
18	D₈₈	—	2	2	no	—
19	D₈₈	—	4	1	no	—
20	C₁₁×C₁₆	D₄	1	1	yes	characteristic
21	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
22	C₂×SD₆₄	—	11	1	no	maximal, Sylow
23	C₂²×D₁₁	—	8	1	no	—
24	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
25	C₂×Dic₁₁	—	8	1	no	—
26	D₄₄	—	4	2	no	—
27	D₄₄	—	8	1	no	—
28	Dic₂₂	—	4	2	no	—
29	Dic₂₂	—	8	1	no	—
30	C₈×C₁₁	D₈	1	1	yes	characteristic
31	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
32	C₂×Q₃₂	—	11	1	no	—
33	C₂×D₁₆	—	11	1	no	—
34	SD₆₄	—	11	4	no	—
35	C₂×C₃₂	D₁₁	1	1	yes	characteristic, complemented
36	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
37	C₂×D₁₁	—	8	2	no	—
38	C₂×D₁₁	—	16	2	no	—
39	C₄×C₁₁	D₁₆	1	1	yes	characteristic
40	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
41	Dic₁₁	—	8	2	no	—
42	C₂×Q₁₆	—	22	1	no	—
43	C₂×D₈	—	22	1	no	—
44	Q₃₂	—	11	2	no	—
45	Q₃₂	—	22	1	no	—
46	D₁₆	—	11	2	no	—
47	D₁₆	—	22	1	no	—
48	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
49	C₃₂	C₂×D₁₁	1	2	yes	complemented
50	C₂×C₁₁	SD₆₄	1	2	yes	complemented
51	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
52	D₁₁	—	16	2	no	—
53	C₂×Q₈	—	44	1	no	—
54	C₂×D₄	—	44	1	no	—
55	Q₁₆	—	22	2	no	—
56	Q₁₆	—	44	1	no	—
57	D₈	—	22	2	no	—
58	D₈	—	44	1	no	—
59	C₂×C₈	D₄₄	1	1	yes	characteristic
60	C₁₆	D₄₄	1	1	yes	characteristic
61	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
62	C₁₁	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
63	C₂³	—	88	1	no	—
64	Q₈	—	44	2	no	—
65	Q₈	—	88	1	no	—
66	D₄	—	44	2	no	—
67	D₄	—	88	1	no	—
68	C₂×C₄	—	88	1	no	—
69	C₂×C₄	D₈₈	1	1	yes	characteristic
70	C₈	D₈₈	1	1	yes	characteristic
71	C₈	C₂×D₄₄	1	1	yes	characteristic
72	C₂²	—	88	2	no	—
73	C₂²	—	176	2	no	—
74	C₂²	D₁₇₆	1	1	yes	characteristic
75	C₄	—	88	2	no	—
76	C₄	D₁₇₆	1	1	yes	characteristic
77	C₄	C₂×D₈₈	1	1	yes	characteristic
78	C₂	—	176	2	no	—
79	C₂	#10622087	1	2	yes	direct product factor
80	C₂	C₂×D₁₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₇₆
commutator, cosocle	C₁₁×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₁
Fitting	C₂×C₁₁×C₃₂	C₂
socle	C₂²×C₁₁	D₁₆
prime radical	C₂×D₁₇₆	C₂
hypercenter	C₂×C₃₂	D₁₁
hypocenter	C₁₁	C₂×SD₆₄
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₈₈	C₂	semidirect
3. C₂×C₁₁×C₃₂	C₂	semidirect
4. #10622087	C₂	direct (N × H)
9. Dic₈₈	C₂²	semidirect
12. C₁₁×C₃₂	C₂²	semidirect
35. C₂×C₃₂	D₁₁	semidirect
49. C₃₂	C₂×D₁₁	semidirect
50. C₂×C₁₁	SD₆₄	semidirect
62. C₁₁	C₂×SD₆₄	semidirect
79. C₂	#10622087	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×Dic₈₈	2
C₂×D₁₇₆	2
C₂×C₁₁×C₃₂	2
#10622087	2
C₂×SD₆₄	11

Subgroups — C2×#10622087 #13070918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10622087 #13070918