Subgroups — C₄×Q₈×D₇ #90262

Order 448.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₄⋊C₄	C₂	1	3	yes	maximal
5	#6450	C₂	1	3	yes	maximal, complemented
6	C₄²×D₇	C₂	1	3	yes	maximal
7	C₄×Dic₁₄	C₂	1	3	yes	maximal, complemented
8	C₂×C₇×Q₈	C₂²	1	1	yes	characteristic
9	Q₈×D₇	C₄	1	8	yes	direct product factor
10	C₂×C₄×D₇	C₂²	1	3	yes	—
11	C₂×C₄×D₇	C₂²	1	3	yes	—
12	C₂×C₄×D₇	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₄	C₂²	1	3	yes	—
14	C₇×C₄⋊C₄	C₂²	1	3	yes	—
15	C₄²×C₇	C₂²	1	3	yes	—
16	C₄⋊Dic₇	C₂²	1	3	yes	—
17	Dic₇⋊C₄	C₂²	1	6	yes	—
18	C₄×Dic₇	C₂²	1	3	yes	—
19	C₄×Dic₇	C₂²	1	3	yes	—
20	C₄×Dic₇	C₂²	1	3	yes	—
21	C₂×C₄×Q₈	—	7	1	no	maximal, Sylow
22	C₂²×D₇	C₂³	1	1	yes	characteristic
23	C₇×Q₈	C₂×C₄	1	4	yes	complemented
24	C₂×C₄×C₇	C₂³	1	3	yes	—
25	C₂×C₄×C₇	C₂³	1	3	yes	—
26	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₇	C₂³	1	3	yes	—
28	C₂×Dic₇	C₂³	1	3	yes	—
29	C₂×Dic₇	C₂³	1	1	yes	characteristic
30	C₄×D₇	—	2	6	no	—
31	C₄×D₇	C₂×C₄	1	12	yes	—
32	C₄×D₇	Q₈	1	4	yes	direct product factor
33	Dic₁₄	C₂×C₄	1	12	yes	complemented
34	C₂²×Q₈	—	7	1	no	—
35	C₄×Q₈	—	7	1	no	—
36	C₄×Q₈	—	7	3	no	—
37	C₄×Q₈	—	7	3	no	—
38	C₄×Q₈	D₇	1	1	yes	characteristic, direct product factor
39	C₂×C₄⋊C₄	—	7	3	no	—
40	C₂×C₄²	—	7	3	no	—
41	C₂²×C₇	C₂⁴	1	1	yes	characteristic
42	C₂×D₇	C₂²×C₄	1	2	yes	—
43	C₂×D₇	C₂×Q₈	1	2	yes	—
44	C₂×D₇	#41	1	2	yes	—
45	C₄×C₇	—	2	3	no	—
46	C₄×C₇	C₂²×C₄	1	6	yes	—
47	C₄×C₇	C₂×Q₈	1	2	yes	complemented
48	Dic₇	—	2	3	no	—
49	Dic₇	C₂²×C₄	1	6	yes	—
50	Dic₇	C₂×Q₈	1	2	yes	complemented
51	C₂×Q₈	—	7	8	no	—
52	C₂×Q₈	—	7	3	no	—
53	C₂×Q₈	C₂×D₇	1	1	yes	characteristic
54	C₂²×C₄	—	7	3	no	—
55	C₂²×C₄	—	7	1	no	—
56	C₂²×C₄	—	7	3	no	—
57	C₄⋊C₄	—	7	6	no	—
58	C₄⋊C₄	—	7	3	no	—
59	C₄⋊C₄	C₂×D₇	1	3	yes	—
60	C₄²	—	7	3	no	—
61	C₄²	—	7	3	no	—
62	C₄²	—	7	3	no	—
63	C₄²	C₂×D₇	1	3	yes	—
64	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
65	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
66	C₂×C₇	C₂×#41	1	1	yes	characteristic
67	D₇	C₄×Q₈	1	4	yes	direct product factor
68	C₂³	—	7	1	no	—
69	Q₈	—	7	12	no	—
70	Q₈	C₄×D₇	1	4	yes	direct product factor
71	C₂×C₄	—	7	1	no	—
72	C₂×C₄	—	7	3	no	—
73	C₂×C₄	—	7	12	no	—
74	C₂×C₄	—	7	4	no	—
75	C₂×C₄	—	7	3	no	—
76	C₂×C₄	—	14	6	no	—
77	C₂×C₄	C₂²×D₇	1	3	yes	—
78	C₂×C₄	C₂²×D₇	1	3	yes	—
79	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
80	C₇	C₂×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
81	C₂²	—	7	2	no	—
82	C₂²	—	7	2	no	—
83	C₂²	—	7	2	no	—
84	C₂²	C₂³×D₇	1	1	yes	characteristic
85	C₄	—	2	3	no	—
86	C₄	—	7	6	no	—
87	C₄	—	7	2	no	—
88	C₄	—	14	3	no	—
89	C₄	C₂×C₄×D₇	1	6	yes	—
90	C₄	Q₈×D₇	1	2	yes	direct product factor
91	C₂	—	7	4	no	—
92	C₂	C₂²×C₄×D₇	1	1	yes	characteristic
93	C₂	C₂×Q₈×D₇	1	1	yes	characteristic
94	C₂	D₇×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₇
commutator	C₂×C₇	C₂³×C₄
Frattini	C₂²	C₂³×D₇
Fitting	C₄×C₇×Q₈	C₂
socle, cosocle	C₂²×C₇	C₂⁴
prime radical	C₂²×D₇	C₂³
hypercenter	C₄×Q₈	D₇
hypocenter	C₇	C₂×C₄×Q₈
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×Q₈	C₂	semidirect
3. Q₈×Dic₇	C₂	semidirect
5. #6450	C₂	semidirect
7. C₄×Dic₁₄	C₂	semidirect
9. Q₈×D₇	C₄	direct (N × H)
23. C₇×Q₈	C₂×C₄	semidirect
32. C₄×D₇	Q₈	direct (N × H)
33. Dic₁₄	C₂×C₄	semidirect
38. C₄×Q₈	D₇	direct (N × H)
47. C₄×C₇	C₂×Q₈	semidirect
50. Dic₇	C₂×Q₈	semidirect
67. D₇	C₄×Q₈	direct (N × H)
70. Q₈	C₄×D₇	direct (N × H)
80. C₇	C₂×C₄×Q₈	semidirect
90. C₄	Q₈×D₇	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
C₄×C₇×Q₈	2
Q₈×Dic₇	2
D₇×C₄⋊C₄	2
#6450	2
C₄²×D₇	2
C₄×Dic₁₄	2
C₂×C₄×Q₈	7

Subgroups — C4×Q8×D7 #90262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×D₇ #90262