Subgroups — #13285000

Order 1792.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic
2	#11729288	C₂	1	14	yes	maximal
3	C₂²×C₄²×C₇	C₂²	1	7	yes	—
4	C₄³×C₇	C₄	1	8	yes	complemented
5	C₂×C₇⋊#95	C₂²	1	28	yes	—
6	#14691	—	7	1	no	maximal, Sylow
7	C₂³×C₄×C₇	C₂³	1	7	yes	—
8	C₂³×Dic₇	C₂³	1	8	yes	—
9	C₂×C₄²×C₇	—	2	28	no	—
10	C₂×C₄²×C₇	C₂×C₄	1	28	yes	—
11	C₇⋊#95	—	2	56	no	—
12	C₂×C₄³	D₇	1	1	yes	characteristic
13	#1434	—	7	14	no	—
14	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
15	C₂²×C₄×C₇	—	2	28	no	—
16	C₂²×C₄×C₇	C₂²×C₄	1	14	yes	—
17	C₂²×C₄×C₇	#41	1	28	yes	—
18	C₂²×Dic₇	—	2	56	no	—
19	C₄²×C₇	—	2	56	no	—
20	C₂²×C₄²	C₂×D₇	1	7	yes	—
21	C₂×#95	—	7	28	no	—
22	C₄³	Dic₇	1	8	yes	complemented
23	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
24	C₂³×C₇	C₂×#41	1	14	yes	—
25	C₂×C₄×C₇	—	2	28	no	—
26	C₂×C₄×C₇	—	2	56	no	—
27	C₂×C₄×C₇	#117	1	28	yes	—
28	C₂×Dic₇	—	4	56	no	—
29	C₂³×C₄	—	7	8	no	—
30	C₂³×C₄	C₂²×D₇	1	7	yes	—
31	C₂×C₄²	—	2	28	no	—
32	C₂×C₄²	C₂×Dic₇	1	28	yes	—
33	#95	—	14	56	no	—
34	C₂²×C₇	C₂×#117	1	7	yes	—
35	C₂²×C₇	#529	1	28	yes	—
36	C₄×C₇	—	2	28	no	—
37	Dic₇	—	8	8	no	—
38	C₂⁴	C₂³×D₇	1	1	yes	characteristic
39	C₂²×C₄	—	2	28	no	—
40	C₂²×C₄	—	14	56	no	—
41	C₂²×C₄	#1157	1	28	yes	—
42	C₂²×C₄	C₂²×Dic₇	1	14	yes	—
43	C₄²	—	2	56	no	—
44	C₂×C₇	#2283	1	7	yes	—
45	C₂×C₇	#2866	1	8	yes	—
46	C₂³	C₂×#1157	1	14	yes	—
47	C₂³	C₂³×Dic₇	1	1	yes	characteristic
48	C₂×C₄	—	2	56	no	—
49	C₂×C₄	—	2	28	no	—
50	C₂×C₄	—	28	56	no	—
51	C₂×C₄	#6489	1	28	yes	—
52	C₇	#14691	1	1	yes	characteristic, complemented, Sylow
53	C₂²	#90170	1	28	yes	—
54	C₂²	C₂×#6489	1	7	yes	—
55	C₄	—	2	28	no	—
56	C₄	—	56	8	no	—
57	C₂	#11730762	1	8	yes	—
58	C₂	#11739505	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₇
commutator	C₂³×C₇	C₂³×C₄
Fitting	C₂×C₄³×C₇	C₂
socle, prime radical, cosocle	C₂⁴×C₇	C₂⁴
hypercenter	C₂×C₄³	D₇
hypocenter	C₇	#14691
LCS	G ▷ C₂³×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
4. C₄³×C₇	C₄	semidirect
22. C₄³	Dic₇	semidirect
52. C₇	#14691	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄³×C₇	2
#11729288	2
#14691	7