Subgroups — #44507063

Order 30848.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508122	C₂	1	4	yes	maximal
2	#29508097	C₂	1	2	yes	maximal
3	C₈²×C₂₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₉₆₄	—	2	4	no	—
5	#21440642	C₂²	1	4	yes	—
6	#21440576	—	2	8	no	—
7	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₂₄₁	C₂²	1	2	yes	—
9	C₂×Dic₄₈₂	—	2	4	no	—
10	Dic₉₆₄	—	4	8	no	—
11	C₄⋊Dic₂₄₁	—	2	8	no	—
12	C₂×C₈×C₂₄₁	D₄	1	2	yes	—
13	C₂×C₈×C₂₄₁	D₄	1	4	yes	—
14	C₄²×C₂₄₁	C₂³	1	1	yes	characteristic
15	Dic₄₈₂	—	4	8	no	—
16	C₂×Dic₂₄₁	—	4	4	no	—
17	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₂₄₁	C₂×D₄	1	2	yes	—
19	C₈×C₂₄₁	D₈	1	4	yes	—
20	C₈×C₂₄₁	Q₁₆	1	8	yes	complemented
21	C₂²×C₂₄₁	#127	1	1	yes	characteristic
22	C₄×C₂₄₁	C₂×D₈	1	2	yes	—
23	C₄×C₂₄₁	C₂×Q₁₆	1	4	yes	—
24	Dic₂₄₁	—	8	4	no	—
25	C₂×C₂₄₁	#493	1	1	yes	characteristic
26	C₂×C₂₄₁	#494	1	2	yes	—
27	C₂₄₁	#1713	1	1	yes	characteristic, complemented, Sylow
28	#1713	—	241	1	no	maximal, Sylow
29	#500	—	241	4	no	—
30	#494	—	241	2	no	—
31	C₈²	D₂₄₁	1	1	yes	characteristic
32	C₂×Q₁₆	—	482	4	no	—
33	C₄⋊Q₈	—	241	4	no	—
34	#107	—	482	8	no	—
35	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
36	C₄×C₈	C₂×D₂₄₁	1	2	yes	—
37	C₂×Q₈	—	482	4	no	—
38	Q₁₆	—	964	8	no	—
39	C₂×C₈	D₉₆₄	1	2	yes	—
40	C₂×C₈	D₉₆₄	1	4	yes	—
41	C₄⋊C₄	—	482	8	no	—
42	C₄²	C₂²×D₂₄₁	1	1	yes	characteristic
43	Q₈	—	964	8	no	—
44	C₂×C₄	—	964	4	no	—
45	C₂×C₄	C₂×D₉₆₄	1	1	yes	characteristic
46	C₂×C₄	C₂×D₉₆₄	1	2	yes	—
47	C₈	D₁₉₂₈	1	4	yes	—
48	C₈	Dic₉₆₄	1	8	yes	complemented
49	C₂²	#21440639	1	1	yes	characteristic
50	C₄	—	1928	4	no	—
51	C₄	C₂×D₁₉₂₈	1	2	yes	—
52	C₄	C₂×Dic₉₆₄	1	4	yes	—
53	C₂	#29508094	1	1	yes	characteristic
54	C₂	#29508097	1	2	yes	—

	subgroup	G/H
center	C₂²	#21440639
commutator, cosocle	C₄²×C₂₄₁	C₂³
Frattini	C₄²	C₂²×D₂₄₁
Fitting	C₈²×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	#127
hypercenter	C₈²	D₂₄₁
hypocenter	C₂₄₁	#1713
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂²×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₂₄₁	Q₁₆	semidirect
27. C₂₄₁	#1713	semidirect
48. C₈	Dic₉₆₄	semidirect

Maximal subgroups

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

subgroup	index
#29508122	2
#29508097	2
C₈²×C₂₄₁	2
#1713	241