Subgroups — D₇×#95 #89435

Order 448.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₇	C₂	1	3	yes	maximal
2	C₇×#95	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇⋊#95	C₂	1	3	yes	maximal, complemented
4	C₂³×D₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₇	C₂²	1	3	yes	—
6	C₂²×Dic₇	C₂²	1	3	yes	—
7	C₂×C₄×D₇	—	2	12	no	—
8	C₂×C₄×D₇	C₄	1	12	yes	complemented
9	C₂×#95	—	7	1	no	maximal, Sylow
10	C₂³×C₇	C₂³	1	1	yes	characteristic
11	C₂²×D₇	C₂×C₄	1	6	yes	—
12	C₂²×D₇	D₄	1	6	yes	—
13	C₂²×D₇	Q₈	1	2	yes	—
14	C₂×C₄×C₇	—	2	6	no	—
15	C₂×C₄×C₇	C₂×C₄	1	6	yes	complemented
16	C₂×Dic₇	—	2	6	no	—
17	C₂×Dic₇	C₂×C₄	1	6	yes	complemented
18	C₄×D₇	—	2	24	no	—
19	C₂³×C₄	—	7	3	no	—
20	#95	—	7	3	no	—
21	#95	D₇	1	1	yes	characteristic, direct product factor
22	C₂²×C₇	C₂²×C₄	1	3	yes	—
23	C₂²×C₇	C₂×D₄	1	3	yes	—
24	C₂²×C₇	C₂×Q₈	1	1	yes	characteristic
25	C₂×D₇	C₄²	1	4	yes	—
26	C₂×D₇	C₂²⋊C₄	1	12	yes	—
27	C₂×D₇	C₄⋊C₄	1	12	yes	—
28	C₄×C₇	—	2	6	no	—
29	Dic₇	—	2	6	no	—
30	C₂⁴	—	7	1	no	—
31	C₂²×C₄	—	7	3	no	—
32	C₂²×C₄	—	7	12	no	—
33	C₂²×C₄	—	14	12	no	—
34	C₂²×C₄	C₂×D₇	1	3	yes	—
35	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₇	C₂×C₂²⋊C₄	1	3	yes	—
37	C₂×C₇	C₂×C₄⋊C₄	1	3	yes	—
38	D₇	#95	1	8	yes	direct product factor
39	C₂³	—	7	6	no	—
40	C₂³	—	7	6	no	—
41	C₂³	—	7	2	no	—
42	C₂³	C₂²×D₇	1	1	yes	characteristic
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	7	6	no	—
45	C₂×C₄	—	14	24	no	—
46	C₂×C₄	—	14	6	no	—
47	C₂×C₄	C₄×D₇	1	6	yes	complemented
48	C₇	C₂×#95	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	7	4	no	—
50	C₂²	—	7	12	no	—
51	C₂²	—	7	12	no	—
52	C₂²	C₂×C₄×D₇	1	3	yes	—
53	C₂²	D₄×D₇	1	3	yes	—
54	C₂²	Q₈×D₇	1	1	yes	characteristic
55	C₄	—	2	6	no	—
56	C₄	—	14	6	no	—
57	C₂	—	7	8	no	—
58	C₂	C₄²×D₇	1	1	yes	characteristic
59	C₂	D₇×C₂²⋊C₄	1	3	yes	—
60	C₂	D₇×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₇
commutator	C₂×C₇	C₂×C₄²
Fitting	C₇×#95	C₂
socle, cosocle	C₂³×C₇	C₂³
prime radical	C₂³×D₇	C₂²
hypercenter	#95	D₇
hypocenter	C₇	C₂×#95
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₇×#95	C₂	semidirect
3. C₇⋊#95	C₂	semidirect
8. C₂×C₄×D₇	C₄	semidirect
15. C₂×C₄×C₇	C₂×C₄	semidirect
17. C₂×Dic₇	C₂×C₄	semidirect
21. #95	D₇	direct (N × H)
38. D₇	#95	direct (N × H)
47. C₂×C₄	C₄×D₇	semidirect
48. C₇	C₂×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₇	2
C₇×#95	2
C₇⋊#95	2
C₂×#95	7

Subgroups — D7×#95 #89435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#95 #89435