Subgroups — C₂×D₇×Q₁₆ #90454

Order 448.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₇	C₂	1	2	yes	maximal
2	C₂×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1144	C₂	1	2	yes	maximal, complemented
4	D₇×Q₁₆	C₂	1	8	yes	maximal, direct product factor
5	C₂×Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇	C₂	1	1	yes	maximal, characteristic
7	C₂×C₇×Q₈	C₂²	1	2	yes	—
8	Q₈×D₇	—	2	4	no	—
9	Q₈×D₇	C₂²	1	8	yes	—
10	C₂×C₄×D₇	—	2	2	no	—
11	C₂×C₄×D₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₄	—	2	2	no	—
13	C₂×Dic₁₄	C₂²	1	2	yes	—
14	C₇×Q₁₆	C₂²	1	4	yes	complemented
15	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
16	#1144	C₂²	1	8	yes	complemented
17	C₂×C₇⋊C₈	C₂²	1	1	yes	characteristic
18	Dic₂₈	C₂²	1	4	yes	complemented
19	C₈×D₇	C₂²	1	4	yes	—
20	C₂²×Q₁₆	—	7	1	no	maximal, Sylow
21	C₂²×D₇	D₄	1	1	yes	characteristic
22	C₇×Q₈	—	2	2	no	—
23	C₇×Q₈	C₂³	1	4	yes	—
24	C₂×C₄×C₇	—	2	2	no	—
25	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₇	—	2	2	no	—
27	C₂×Dic₇	D₄	1	1	yes	characteristic
28	C₄×D₇	—	2	8	no	—
29	C₄×D₇	D₄	1	2	yes	—
30	C₄×D₇	C₂³	1	2	yes	—
31	Dic₁₄	—	2	2	no	—
32	Dic₁₄	—	2	8	no	—
33	Dic₁₄	C₂³	1	4	yes	—
34	C₇×C₈	C₂³	1	2	yes	—
35	C₇⋊C₈	C₂³	1	2	yes	—
36	C₂²×Q₈	—	7	2	no	—
37	C₂×Q₁₆	—	7	2	no	—
38	C₂×Q₁₆	—	7	8	no	—
39	C₂×Q₁₆	—	7	1	no	—
40	C₂×Q₁₆	D₇	1	1	yes	characteristic, direct product factor
41	C₂²×C₈	—	7	1	no	—
42	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
43	C₂×D₇	Q₁₆	1	4	yes	direct product factor
44	C₂×D₇	C₂×D₄	1	2	yes	—
45	C₄×C₇	—	2	4	no	—
46	C₄×C₇	C₂×D₄	1	1	yes	characteristic
47	C₄×C₇	C₂⁴	1	1	yes	characteristic
48	Dic₇	—	2	4	no	—
49	Dic₇	C₂×D₄	1	2	yes	—
50	C₂×Q₈	—	7	8	no	—
51	C₂×Q₈	—	7	2	no	—
52	C₂×Q₈	—	14	2	no	—
53	C₂×Q₈	—	14	4	no	—
54	C₂×Q₈	C₂×D₇	1	2	yes	—
55	C₂²×C₄	—	7	1	no	—
56	C₂²×C₄	—	14	2	no	—
57	Q₁₆	—	7	8	no	—
58	Q₁₆	—	7	4	no	—
59	Q₁₆	C₂×D₇	1	4	yes	direct product factor
60	C₂×C₈	—	7	1	no	—
61	C₂×C₈	—	7	4	no	—
62	C₂×C₈	C₂×D₇	1	1	yes	characteristic
63	C₂×C₇	C₂×Q₁₆	1	2	yes	complemented
64	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
65	D₇	C₂×Q₁₆	1	4	yes	direct product factor
66	C₂³	—	7	1	no	—
67	Q₈	—	2	2	no	—
68	Q₈	—	7	4	no	—
69	Q₈	—	14	8	no	—
70	Q₈	—	14	2	no	—
71	Q₈	C₂²×D₇	1	4	yes	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	7	1	no	—
74	C₂×C₄	—	7	2	no	—
75	C₂×C₄	—	7	2	no	—
76	C₂×C₄	—	14	8	no	—
77	C₂×C₄	—	14	2	no	—
78	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
79	C₈	—	7	2	no	—
80	C₈	C₂²×D₇	1	2	yes	—
81	C₇	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	7	4	no	—
83	C₂²	—	7	2	no	—
84	C₂²	D₄×D₇	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	7	2	no	—
87	C₄	—	14	4	no	—
88	C₄	D₄×D₇	1	1	yes	characteristic
89	C₄	C₂³×D₇	1	1	yes	characteristic
90	C₂	—	7	4	no	—
91	C₂	D₇×Q₁₆	1	2	yes	direct product factor
92	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
prime radical	C₂²×D₇	D₄
hypercenter	C₂×Q₁₆	D₇
hypocenter	C₇	C₂²×Q₁₆
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
2. C₂×C₇×Q₁₆	C₂	semidirect
3. C₂×#1144	C₂	semidirect
4. D₇×Q₁₆	C₂	direct (N × H)
5. C₂×Dic₂₈	C₂	semidirect
14. C₇×Q₁₆	C₂²	semidirect
16. #1144	C₂²	semidirect
18. Dic₂₈	C₂²	semidirect
40. C₂×Q₁₆	D₇	direct (N × H)
43. C₂×D₇	Q₁₆	direct (N × H)
59. Q₁₆	C₂×D₇	direct (N × H)
63. C₂×C₇	C₂×Q₁₆	semidirect
65. D₇	C₂×Q₁₆	direct (N × H)
81. C₇	C₂²×Q₁₆	semidirect
91. C₂	D₇×Q₁₆	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×Q₈×D₇	2
C₂×C₇×Q₁₆	2
C₂×#1144	2
D₇×Q₁₆	2
C₂×Dic₂₈	2
C₂×C₈×D₇	2
C₂²×Q₁₆	7

Subgroups — C2×D7×Q16 #90454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₇×Q₁₆ #90454