Subgroups — #44505490

Order 30848.

118 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	C₄⋊#16838745	C₂	1	1	yes	maximal, characteristic, complemented
3	#335×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₉₂₈	—	2	1	no	—
5	C₂×D₁₉₂₈	C₄	1	2	yes	—
6	#21440639	—	2	1	no	—
7	C₂×#16838745	—	2	1	no	—
8	C₄⋊C₈×C₂₄₁	—	2	1	no	—
9	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
10	C₂×D₉₆₄	—	2	2	no	—
11	C₂×D₉₆₄	—	4	1	no	—
12	C₂×D₉₆₄	—	4	1	no	—
13	D₁₉₂₈	—	4	2	no	—
14	D₁₉₂₈	—	4	1	no	—
15	D₁₉₂₈	—	4	1	no	—
16	#16838745	—	4	1	no	—
17	C₂×C₈×C₂₄₁	—	4	1	no	—
18	C₂×C₈×C₂₄₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
20	C₄²×C₂₄₁	D₄	1	1	yes	characteristic
21	C₂²×D₂₄₁	—	4	2	no	—
22	D₉₆₄	—	4	2	no	—
23	D₉₆₄	—	4	2	no	—
24	D₉₆₄	—	8	2	no	—
25	D₉₆₄	—	8	1	no	—
26	D₉₆₄	—	8	1	no	—
27	C₂×C₄×C₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₄₁	D₈	1	1	yes	characteristic
29	C₂×C₄×C₂₄₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₂₄₁	—	2	1	no	—
31	C₈×C₂₄₁	—	8	1	no	—
32	C₈×C₂₄₁	D₈	1	1	yes	characteristic
33	C₈×C₂₄₁	SD₁₆	1	1	yes	characteristic
34	C₂²×C₂₄₁	#102	1	1	yes	characteristic
35	C₂×D₂₄₁	—	8	2	no	—
36	C₂×D₂₄₁	—	8	2	no	—
37	C₂×D₂₄₁	—	8	2	no	—
38	C₄×C₂₄₁	—	2	1	no	—
39	C₄×C₂₄₁	#100	1	1	yes	characteristic
40	C₄×C₂₄₁	#102	1	1	yes	characteristic
41	C₄×C₂₄₁	D₁₆	1	1	yes	characteristic
42	C₄×C₂₄₁	SD₃₂	1	1	yes	characteristic
43	C₂×C₂₄₁	#331	1	1	yes	characteristic
44	C₂×C₂₄₁	#357	1	1	yes	characteristic
45	C₂×C₂₄₁	#361	1	1	yes	characteristic
46	D₂₄₁	—	16	2	no	—
47	C₂₄₁	#1361	1	1	yes	characteristic, complemented, Sylow
48	#1361	—	241	1	no	maximal, Sylow
49	#493	—	241	1	no	—
50	C₄⋊C₁₆	—	241	1	no	—
51	#335	D₂₄₁	1	1	yes	characteristic, complemented
52	C₂×D₈	—	482	1	no	—
53	C₂×D₈	—	241	2	no	—
54	#127	—	482	1	no	—
55	C₂×C₁₆	—	482	1	no	—
56	C₄⋊C₈	—	2	1	no	—
57	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
58	C₂×D₄	—	964	1	no	—
59	C₂×D₄	—	964	1	no	—
60	C₂×D₄	—	482	2	no	—
61	D₈	—	964	2	no	—
62	D₈	—	964	1	no	—
63	D₈	—	964	1	no	—
64	C₂×C₈	—	4	1	no	—
65	C₂×C₈	C₄×D₂₄₁	1	1	yes	characteristic
66	C₂×C₈	D₉₆₄	1	1	yes	characteristic
67	C₄²	C₂²⋊D₂₄₁	1	1	yes	characteristic
68	C₁₆	—	964	1	no	—
69	C₂³	—	964	2	no	—
70	D₄	—	1928	2	no	—
71	D₄	—	1928	1	no	—
72	D₄	—	1928	1	no	—
73	D₄	—	964	2	no	—
74	D₄	—	964	2	no	—
75	C₂×C₄	#16838747	1	1	yes	characteristic
76	C₂×C₄	#16838755	1	1	yes	characteristic
77	C₂×C₄	#16838757	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	8	1	no	—
80	C₈	D₁₉₂₈	1	1	yes	characteristic
81	C₈	#16838759	1	1	yes	characteristic
82	C₂²	—	1928	2	no	—
83	C₂²	—	1928	2	no	—
84	C₂²	—	1928	2	no	—
85	C₂²	#21440562	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	#21440558	1	1	yes	characteristic
88	C₄	#21440564	1	1	yes	characteristic
89	C₄	#21440583	1	1	yes	characteristic
90	C₄	#21440585	1	1	yes	characteristic
91	C₂	—	3856	2	no	—
92	C₂	#29507460	1	1	yes	characteristic
93	C₂	#29507517	1	1	yes	characteristic
94	C₂	#29507529	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#21440562
commutator	C₂×C₈×C₂₄₁	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₄₁
Fitting	#335×C₂₄₁	C₂
socle	C₂²×C₂₄₁	#102
prime radical	#29508094	C₂
cosocle	C₄×C₈×C₂₄₁	C₂²
hypercenter	#335	D₂₄₁
hypocenter	C₂₄₁	#1361
LCS	G ▷ C₂×C₈×C₂₄₁ ▷ C₂×C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
2. C₄⋊#16838745	C₂	semidirect
3. #335×C₂₄₁	C₂	semidirect
47. C₂₄₁	#1361	semidirect
51. #335	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
C₄⋊#16838745	2
#335×C₂₄₁	2
#1361	241