Subgroups — C₂×#30628335 #44537267

Order 31424.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₉₈₂	C₂	1	1	yes	maximal, characteristic
2	#30628335	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₄₉₁⋊C₄	C₂	1	4	yes	maximal
4	C₂×C₄×Dic₄₉₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₄₉₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₈₂	—	2	4	no	—
7	C₂×Dic₉₈₂	C₂²	1	4	yes	—
8	C₂²×Dic₄₉₁	C₂²	1	2	yes	—
9	C₂²×Dic₄₉₁	C₂²	1	2	yes	—
10	Dic₄₉₁⋊C₄	C₂²	1	16	yes	—
11	C₄×Dic₄₉₁	C₂²	1	4	yes	—
12	C₂×Q₈×C₄₉₁	—	2	4	no	—
13	C₂×Q₈×C₄₉₁	C₂²	1	4	yes	—
14	C₂²×C₄×C₄₉₁	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₉₁	C₂²	1	1	yes	characteristic
16	Dic₉₈₂	—	2	8	no	—
17	C₂×Dic₄₉₁	—	2	4	no	—
18	C₂×Dic₄₉₁	Q₈	1	8	yes	complemented
19	C₂×Dic₄₉₁	C₂³	1	4	yes	—
20	C₂×Dic₄₉₁	C₂³	1	4	yes	—
21	C₂³×C₄₉₁	C₂³	1	1	yes	characteristic
22	Q₈×C₄₉₁	—	2	8	no	—
23	C₂×C₄×C₄₉₁	—	2	4	no	—
24	C₂×C₄×C₄₉₁	D₄	1	4	yes	—
25	C₂×C₄×C₄₉₁	C₂³	1	4	yes	—
26	C₂×C₄×C₄₉₁	C₂³	1	2	yes	—
27	C₂²×C₄₉₁	C₂×D₄	1	2	yes	—
28	C₂²×C₄₉₁	C₂×Q₈	1	4	yes	—
29	C₂²×C₄₉₁	C₂⁴	1	1	yes	characteristic
30	C₄×C₄₉₁	—	2	4	no	—
31	C₄×C₄₉₁	C₂×D₄	1	4	yes	—
32	Dic₄₉₁	—	2	4	no	—
33	Dic₄₉₁	C₂×Q₈	1	8	yes	complemented
34	C₂×C₄₉₁	C₄⋊Q₈	1	4	yes	complemented
35	C₂×C₄₉₁	C₂²×D₄	1	1	yes	characteristic
36	C₂×C₄₉₁	C₂²×Q₈	1	2	yes	—
37	C₄₉₁	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₄⋊Q₈	—	491	1	no	maximal, Sylow
39	C₂²×Q₈	—	491	1	no	—
40	C₂²×Q₈	D₄₉₁	1	1	yes	characteristic
41	C₄⋊Q₈	—	491	8	no	—
42	C₂×C₄⋊C₄	—	491	4	no	—
43	C₂×C₄²	—	491	1	no	—
44	C₂×Q₈	—	2	4	no	—
45	C₂×Q₈	—	982	4	no	—
46	C₂×Q₈	—	491	4	no	—
47	C₂×Q₈	C₂×D₄₉₁	1	4	yes	—
48	C₂²×C₄	—	491	2	no	—
49	C₂²×C₄	—	491	2	no	—
50	C₂²×C₄	C₂×D₄₉₁	1	2	yes	—
51	C₂²×C₄	C₂×D₄₉₁	1	1	yes	characteristic
52	C₄⋊C₄	—	491	16	no	—
53	C₄²	—	491	4	no	—
54	C₂³	C₂²×D₄₉₁	1	1	yes	characteristic
55	Q₈	—	2	8	no	—
56	Q₈	—	982	8	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	—	982	4	no	—
59	C₂×C₄	—	491	4	no	—
60	C₂×C₄	—	491	8	no	—
61	C₂×C₄	—	491	4	no	—
62	C₂×C₄	C₂²⋊D₄₉₁	1	4	yes	—
63	C₂×C₄	C₂²×D₄₉₁	1	4	yes	—
64	C₂×C₄	C₂²×D₄₉₁	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₄₉₁	1	2	yes	—
66	C₂²	Q₈×D₄₉₁	1	4	yes	—
67	C₂²	C₂³×D₄₉₁	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	982	4	no	—
70	C₄	—	491	8	no	—
71	C₄	C₂×C₂²⋊D₄₉₁	1	4	yes	—
72	C₂	#30628335	1	4	yes	direct product factor
73	C₂	C₂²×C₂²⋊D₄₉₁	1	1	yes	characteristic
74	C₂	C₂×Q₈×D₄₉₁	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₄₉₁
commutator, cosocle	C₂²×C₄₉₁	C₂⁴
Frattini	C₂²	C₂³×D₄₉₁
Fitting	C₂²×Q₈×C₄₉₁	C₂
socle, prime radical	C₂³×C₄₉₁	C₂³
hypercenter	C₂²×Q₈	D₄₉₁
hypocenter	C₄₉₁	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. #30628335	C₂	direct (N × H)
18. C₂×Dic₄₉₁	Q₈	semidirect
33. Dic₄₉₁	C₂×Q₈	semidirect
34. C₂×C₄₉₁	C₄⋊Q₈	semidirect
37. C₄₉₁	C₂×C₄⋊Q₈	semidirect
72. C₂	#30628335	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₉₈₂	2
#30628335	2
C₂×Dic₄₉₁⋊C₄	2
C₂×C₄×Dic₄₉₁	2
C₂²×Q₈×C₄₉₁	2
C₂×C₄⋊Q₈	491

Subgroups — C2×#30628335 #44537267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30628335 #44537267