Subgroups — #44509691

Order 30848.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508119	C₂	1	1	yes	maximal, characteristic
2	#29508097	C₂	1	1	yes	maximal, characteristic
3	#29507522	C₂	1	4	yes	maximal
4	#346×C₂₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₉₆₄	—	2	1	no	—
6	C₂×Dic₉₆₄	C₂²	1	2	yes	—
7	#21440642	—	2	1	no	—
8	#21440634	—	2	1	no	—
9	#21440576	C₂²	1	2	yes	—
10	#21440574	—	2	1	no	—
11	C₂×C₁₆×C₂₄₁	C₂²	1	2	yes	—
12	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₈₂	—	2	2	no	—
14	Dic₉₆₄	—	2	4	no	—
15	Dic₉₆₄	—	4	2	no	—
16	C₄⋊Dic₂₄₁	—	2	2	no	—
17	C₄⋊Dic₂₄₁	—	4	2	no	—
18	#16838749	—	4	2	no	—
19	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
20	C₂×C₈×C₂₄₁	C₂³	1	1	yes	characteristic
21	C₄²×C₂₄₁	D₄	1	1	yes	characteristic
22	C₁₆×C₂₄₁	—	2	2	no	—
23	Dic₄₈₂	—	4	2	no	—
24	Dic₄₈₂	—	4	2	no	—
25	C₂×Dic₂₄₁	—	4	2	no	—
26	C₂×Dic₂₄₁	—	4	2	no	—
27	C₂×C₄×C₂₄₁	D₈	1	2	yes	—
28	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
29	C₈×C₂₄₁	SD₁₆	1	2	yes	—
30	C₈×C₂₄₁	#41	1	2	yes	—
31	C₂²×C₂₄₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₂₄₁	—	2	2	no	—
33	C₄×C₂₄₁	#124	1	1	yes	characteristic
34	C₄×C₂₄₁	C₂×SD₁₆	1	1	yes	characteristic
35	Dic₂₄₁	—	8	2	no	—
36	Dic₂₄₁	—	8	2	no	—
37	C₂×C₂₄₁	#486	1	1	yes	characteristic
38	C₂×C₂₄₁	#510	1	2	yes	—
39	C₂₄₁	#2245	1	1	yes	characteristic, complemented, Sylow
40	#2245	—	241	1	no	maximal, Sylow
41	#499	—	241	1	no	—
42	#494	—	241	1	no	—
43	#358	—	241	4	no	—
44	#346	D₂₄₁	1	1	yes	characteristic
45	C₂×Q₁₆	—	482	1	no	—
46	C₂×Q₁₆	—	241	2	no	—
47	C₄⋊Q₈	—	482	1	no	—
48	#125	—	482	1	no	—
49	C₂×C₁₆	C₂×D₂₄₁	1	2	yes	—
50	#107	—	241	2	no	—
51	#106	—	482	1	no	—
52	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
53	C₂×Q₈	—	482	2	no	—
54	Q₁₆	—	964	2	no	—
55	Q₁₆	—	482	4	no	—
56	C₂×C₈	D₉₆₄	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₂₄₁	1	1	yes	characteristic
58	C₄⋊C₄	—	964	2	no	—
59	C₄⋊C₄	—	964	2	no	—
60	C₄⋊C₄	—	482	2	no	—
61	C₄²	D₉₆₄	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	964	2	no	—
64	Q₈	—	964	2	no	—
65	C₂×C₄	—	964	2	no	—
66	C₂×C₄	—	964	2	no	—
67	C₂×C₄	D₁₉₂₈	1	2	yes	—
68	C₂×C₄	C₂×D₉₆₄	1	1	yes	characteristic
69	C₈	#16838759	1	2	yes	—
70	C₈	#16838770	1	2	yes	—
71	C₂²	C₂×D₁₉₂₈	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	1928	2	no	—
74	C₄	—	1928	2	no	—
75	C₄	#21440630	1	1	yes	characteristic
76	C₄	C₂×#16838759	1	1	yes	characteristic
77	C₂	#29508064	1	1	yes	characteristic
78	C₂	#29508160	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₉₂₈
commutator, cosocle	C₂×C₈×C₂₄₁	C₂³
Frattini	C₂×C₈	C₂²×D₂₄₁
Fitting	#346×C₂₄₁	C₂
socle, prime radical	C₂²×C₂₄₁	C₂×D₈
hypercenter	#346	D₂₄₁
hypocenter	C₂₄₁	#2245
LCS	G ▷ C₂×C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
39. C₂₄₁	#2245	semidirect

Maximal subgroups

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

subgroup	index
#29508119	2
#29508097	2
#29507522	2
#346×C₂₄₁	2
#2245	241