Subgroups — C₂×#6453 #90190

Order 448.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₇	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₇	C₂	1	1	yes	maximal, characteristic
6	#6453	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₇	C₂²	1	2	yes	—
8	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₇	C₂²	1	1	yes	characteristic
11	C₂²×Dic₇	C₂²	1	2	yes	—
12	C₇×C₄⋊C₄	C₂²	1	4	yes	—
13	C₄⋊Dic₇	C₂²	1	8	yes	—
14	C₄⋊Dic₇	C₂²	1	4	yes	—
15	Dic₇⋊C₄	C₂²	1	8	yes	—
16	C₄×Dic₇	C₂²	1	4	yes	—
17	C₂×#125	—	7	1	no	maximal, Sylow
18	C₂³×C₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₇	—	2	4	no	—
20	C₂×C₄×C₇	Q₈	1	4	yes	—
21	C₂×C₄×C₇	C₂³	1	4	yes	—
22	C₂×C₄×C₇	C₂³	1	2	yes	—
23	C₂×Dic₇	—	2	2	no	—
24	C₂×Dic₇	—	2	2	no	—
25	C₂×Dic₇	—	2	4	no	—
26	C₂×Dic₇	C₂³	1	2	yes	—
27	C₂×Dic₇	C₂³	1	2	yes	—
28	C₂×Dic₇	C₂³	1	4	yes	—
29	#125	—	7	8	no	—
30	C₂×C₄⋊C₄	—	7	2	no	—
31	C₂×C₄⋊C₄	—	7	2	no	—
32	C₂×C₄⋊C₄	—	7	1	no	—
33	C₂×C₄⋊C₄	D₇	1	1	yes	characteristic
34	C₂×C₄²	—	7	1	no	—
35	C₂²×C₇	C₂×Q₈	1	2	yes	—
36	C₂²×C₇	#41	1	2	yes	—
37	C₂²×C₇	#41	1	2	yes	—
38	C₂²×C₇	C₂⁴	1	1	yes	characteristic
39	C₄×C₇	—	2	4	no	—
40	C₄×C₇	C₂×Q₈	1	4	yes	—
41	Dic₇	—	2	2	no	—
42	Dic₇	—	2	2	no	—
43	Dic₇	—	2	4	no	—
44	C₂²×C₄	—	7	1	no	—
45	C₂²×C₄	—	7	1	no	—
46	C₂²×C₄	—	7	2	no	—
47	C₂²×C₄	C₂×D₇	1	2	yes	—
48	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
49	C₄⋊C₄	—	7	8	no	—
50	C₄⋊C₄	—	7	8	no	—
51	C₄⋊C₄	—	7	4	no	—
52	C₄⋊C₄	C₂×D₇	1	4	yes	—
53	C₄²	—	7	4	no	—
54	C₂×C₇	#125	1	4	yes	complemented
55	C₂×C₇	C₂²×Q₈	1	1	yes	characteristic
56	C₂×C₇	C₂×#41	1	1	yes	characteristic
57	C₂×C₇	C₂×#41	1	1	yes	characteristic
58	C₂³	C₂²×D₇	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	7	2	no	—
61	C₂×C₄	—	7	2	no	—
62	C₂×C₄	—	7	4	no	—
63	C₂×C₄	—	14	2	no	—
64	C₂×C₄	—	14	2	no	—
65	C₂×C₄	—	14	4	no	—
66	C₂×C₄	Dic₁₄	1	4	yes	—
67	C₂×C₄	C₂²×D₇	1	4	yes	—
68	C₂×C₄	C₂²×D₇	1	2	yes	—
69	C₇	C₂×#125	1	1	yes	characteristic, complemented, Sylow
70	C₂²	C₂×Dic₁₄	1	2	yes	—
71	C₂²	#1159	1	2	yes	—
72	C₂²	#1161	1	2	yes	—
73	C₂²	C₂³×D₇	1	1	yes	characteristic
74	C₄	—	2	4	no	—
75	C₄	—	14	2	no	—
76	C₄	—	14	2	no	—
77	C₄	—	14	4	no	—
78	C₄	C₂×Dic₁₄	1	4	yes	—
79	C₂	#6453	1	4	yes	direct product factor
80	C₂	C₂²×Dic₁₄	1	1	yes	characteristic
81	C₂	C₂×#1159	1	1	yes	characteristic
82	C₂	C₂×#1161	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂⁴
Frattini	C₂²	C₂³×D₇
Fitting	C₂×C₇×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₇	C₂³
hypercenter	C₂×C₄⋊C₄	D₇
hypocenter	C₇	C₂×#125
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #6453	C₂	direct (N × H)
54. C₂×C₇	#125	semidirect
69. C₇	C₂×#125	semidirect
79. C₂	#6453	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×C₇×C₄⋊C₄	2
C₂×C₄⋊Dic₇	2
C₂×Dic₇⋊C₄	2
C₂×C₄×Dic₇	2
#6453	2
C₂×#125	7

Subgroups — C2×#6453 #90190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6453 #90190