Subgroups — #44505481

Order 30848.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29508094	C₂	1	1	yes	maximal, characteristic
2	#29507538	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₉₂₈	—	2	1	no	—
5	C₂×D₁₉₂₈	—	2	1	no	—
6	#21440639	C₄	1	2	yes	—
7	#21440582	—	2	1	no	—
8	M₃₂×C₂₄₁	—	2	1	no	—
9	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
10	C₂×D₉₆₄	—	2	2	no	—
11	C₂×D₉₆₄	—	4	2	no	—
12	D₁₉₂₈	—	4	1	no	—
13	D₁₉₂₈	—	4	1	no	—
14	D₁₉₂₈	—	4	1	no	—
15	D₁₉₂₈	—	4	1	no	—
16	#16838745	—	4	1	no	—
17	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
19	C₄²×C₂₄₁	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₂₄₁	—	4	1	no	—
21	C₂²×D₂₄₁	—	4	2	no	—
22	D₉₆₄	—	4	2	no	—
23	D₉₆₄	—	4	2	no	—
24	D₉₆₄	—	8	4	no	—
25	C₂×C₄×C₂₄₁	—	2	1	no	—
26	C₂×C₄×C₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₂₄₁	D₈	1	1	yes	characteristic
28	C₈×C₂₄₁	D₈	1	1	yes	characteristic
29	C₈×C₂₄₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₄₁	SD₁₆	1	1	yes	characteristic
31	C₂²×C₂₄₁	#100	1	1	yes	characteristic
32	C₂×D₂₄₁	—	8	4	no	—
33	C₂×D₂₄₁	—	8	2	no	—
34	C₄×C₂₄₁	—	2	2	no	—
35	C₄×C₂₄₁	#102	1	1	yes	characteristic
36	C₄×C₂₄₁	#102	1	1	yes	characteristic
37	C₂×C₂₄₁	—	2	1	no	—
38	C₂×C₂₄₁	#331	1	1	yes	characteristic
39	D₂₄₁	—	16	2	no	—
40	C₂₄₁	#1357	1	1	yes	characteristic, complemented, Sylow
41	#1357	—	241	1	no	maximal, Sylow
42	#493	—	241	1	no	—
43	#364	—	241	1	no	—
44	#364	D₂₄₁	1	1	yes	characteristic, complemented
45	C₂×D₈	—	482	1	no	—
46	C₂×D₈	—	482	1	no	—
47	#127	—	241	2	no	—
48	M₃₂	—	2	1	no	—
49	M₃₂	—	482	1	no	—
50	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
51	C₂×D₄	—	964	2	no	—
52	C₂×D₄	—	482	2	no	—
53	D₈	—	964	1	no	—
54	D₈	—	964	1	no	—
55	D₈	—	964	1	no	—
56	D₈	—	964	1	no	—
57	C₂×C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
58	C₂×C₈	D₉₆₄	1	1	yes	characteristic
59	C₄²	C₄×D₂₄₁	1	1	yes	characteristic
60	C₁₆	—	4	1	no	—
61	C₁₆	—	964	1	no	—
62	C₂³	—	964	2	no	—
63	D₄	—	1928	4	no	—
64	D₄	—	964	2	no	—
65	D₄	—	964	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#16838747	1	1	yes	characteristic
68	C₈	#16838755	1	1	yes	characteristic
69	C₈	D₁₉₂₈	1	1	yes	characteristic
70	C₈	#16838757	1	1	yes	characteristic
71	C₈	#16838759	1	1	yes	characteristic
72	C₂²	—	1928	4	no	—
73	C₂²	—	1928	2	no	—
74	C₂²	#21440558	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	#21440562	1	1	yes	characteristic
77	C₄	#21440564	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	3856	2	no	—
80	C₂	#29507460	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#29507460
commutator	C₄²×C₂₄₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₄₁
Fitting	#364×C₂₄₁	C₂
socle	C₂×C₂₄₁	#331
prime radical	#29508094	C₂
cosocle	C₄×C₈×C₂₄₁	C₂²
hypercenter	#364	D₂₄₁
hypocenter	C₂₄₁	#1357
LCS	G ▷ C₄²×C₂₄₁ ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #29507538	C₂	semidirect
3. #364×C₂₄₁	C₂	semidirect
40. C₂₄₁	#1357	semidirect
44. #364	D₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
#29508094	2
#29507538	2
#364×C₂₄₁	2
#1357	241