Subgroups — C₂×#6482 #90456

Order 448.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1161	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1143	C₂	1	2	yes	maximal, complemented
4	#6482	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₅₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×Q₈	C₂²	1	2	yes	—
8	#1161	—	2	4	no	—
9	#1161	C₂²	1	8	yes	complemented
10	C₂×D₂₈	—	2	2	no	—
11	C₂×D₂₈	C₂²	1	2	yes	—
12	C₂×C₄×D₇	—	2	2	no	—
13	C₂×C₄×D₇	C₂²	1	1	yes	characteristic
14	C₇×Q₁₆	C₂²	1	4	yes	complemented
15	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
16	#1143	C₂²	1	8	yes	complemented
17	C₂×C₇⋊C₈	C₂²	1	1	yes	characteristic
18	D₅₆	C₂²	1	4	yes	complemented
19	C₈×D₇	C₂²	1	4	yes	complemented
20	C₂×#135	—	7	1	no	maximal, Sylow
21	C₂²×D₇	—	2	2	no	—
22	C₂²×D₇	D₄	1	1	yes	characteristic
23	C₇×Q₈	—	2	2	no	—
24	C₇×Q₈	C₂³	1	4	yes	—
25	C₂×C₄×C₇	—	2	2	no	—
26	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₇	D₄	1	1	yes	characteristic
28	D₂₈	—	2	8	no	—
29	D₂₈	—	2	2	no	—
30	D₂₈	C₂³	1	4	yes	—
31	C₄×D₇	—	2	8	no	—
32	C₄×D₇	D₄	1	2	yes	—
33	C₄×D₇	C₂³	1	2	yes	—
34	C₇×C₈	C₂³	1	2	yes	—
35	C₇⋊C₈	C₂³	1	2	yes	—
36	C₂×#41	—	7	2	no	—
37	#135	—	7	8	no	—
38	C₂×Q₁₆	D₇	1	1	yes	characteristic, complemented
39	C₂×SD₁₆	—	7	2	no	—
40	C₂×D₈	—	7	1	no	—
41	C₂²×C₈	—	7	1	no	—
42	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
43	C₂×D₇	—	2	2	no	—
44	C₂×D₇	—	2	4	no	—
45	C₂×D₇	—	4	4	no	—
46	C₂×D₇	C₂×D₄	1	2	yes	—
47	C₄×C₇	—	2	4	no	—
48	C₄×C₇	C₂×D₄	1	1	yes	characteristic
49	C₄×C₇	C₂⁴	1	1	yes	characteristic
50	Dic₇	C₂×D₄	1	2	yes	—
51	#41	—	7	8	no	—
52	#41	—	14	4	no	—
53	C₂×Q₈	C₂×D₇	1	2	yes	—
54	C₂×D₄	—	7	2	no	—
55	C₂×D₄	—	14	2	no	—
56	C₂²×C₄	—	7	1	no	—
57	C₂²×C₄	—	14	2	no	—
58	Q₁₆	C₂×D₇	1	4	yes	complemented
59	SD₁₆	—	7	8	no	—
60	D₈	—	7	4	no	—
61	C₂×C₈	—	7	1	no	—
62	C₂×C₈	—	7	4	no	—
63	C₂×C₈	C₂×D₇	1	1	yes	characteristic
64	C₂×C₇	#135	1	2	yes	complemented
65	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
66	D₇	—	2	2	no	—
67	D₇	—	4	4	no	—
68	C₂³	—	7	1	no	—
69	C₂³	—	14	2	no	—
70	Q₈	—	2	2	no	—
71	Q₈	C₂²×D₇	1	4	yes	—
72	D₄	—	7	4	no	—
73	D₄	—	14	8	no	—
74	D₄	—	14	2	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	7	1	no	—
77	C₂×C₄	—	7	2	no	—
78	C₂×C₄	—	7	2	no	—
79	C₂×C₄	—	14	8	no	—
80	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
81	C₈	—	7	2	no	—
82	C₈	C₂²×D₇	1	2	yes	—
83	C₇	C₂×#135	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	7	2	no	—
85	C₂²	—	14	2	no	—
86	C₂²	—	14	4	no	—
87	C₂²	—	28	4	no	—
88	C₂²	D₄×D₇	1	1	yes	characteristic
89	C₄	—	2	4	no	—
90	C₄	—	7	2	no	—
91	C₄	D₄×D₇	1	1	yes	characteristic
92	C₄	C₂³×D₇	1	1	yes	characteristic
93	C₂	—	14	2	no	—
94	C₂	—	28	4	no	—
95	C₂	#6482	1	2	yes	direct product factor
96	C₂	C₂×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₇
commutator, cosocle	C₄×C₇	C₂⁴
Frattini	C₄	C₂³×D₇
Fitting	C₂×C₇×Q₁₆	C₂
socle	C₂²×C₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₇
hypocenter	C₇	C₂×#135
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#1161	C₂	semidirect
2. C₂×C₇×Q₁₆	C₂	semidirect
3. C₂×#1143	C₂	semidirect
4. #6482	C₂	direct (N × H)
5. C₂×D₅₆	C₂	semidirect
6. C₂×C₈×D₇	C₂	semidirect
9. #1161	C₂²	semidirect
14. C₇×Q₁₆	C₂²	semidirect
16. #1143	C₂²	semidirect
18. D₅₆	C₂²	semidirect
19. C₈×D₇	C₂²	semidirect
38. C₂×Q₁₆	D₇	semidirect
58. Q₁₆	C₂×D₇	semidirect
64. C₂×C₇	#135	semidirect
83. C₇	C₂×#135	semidirect
95. C₂	#6482	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×#1161	2
C₂×C₇×Q₁₆	2
C₂×#1143	2
#6482	2
C₂×D₅₆	2
C₂×C₈×D₇	2
C₂×#135	7

Subgroups — C2×#6482 #90456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6482 #90456