Subgroups — #44509702

Order 30848.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21440585	C₂	1	4	yes	maximal, complemented
2	#29508094	C₂	1	1	yes	maximal, characteristic
3	C₄×#16838745	C₂	1	1	yes	maximal, characteristic, complemented
4	#494×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₉₂₈	—	2	1	no	—
6	C₂×D₁₉₂₈	C₂²	1	2	yes	—
7	#21440639	—	2	1	no	—
8	#21440585	—	2	8	no	—
9	C₂×#16838745	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₂₄₁	—	2	1	no	—
11	C₂×Q₁₆×C₂₄₁	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₂₄₁	—	2	1	no	—
13	C₄×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
14	C₂×D₉₆₄	—	2	2	no	—
15	C₂×D₉₆₄	—	4	2	no	—
16	D₁₉₂₈	—	2	4	no	—
17	D₁₉₂₈	—	4	2	no	—
18	#16838745	D₄	1	4	yes	complemented
19	C₂×Q₈×C₂₄₁	—	2	2	no	—
20	Q₁₆×C₂₄₁	—	2	4	no	—
21	Q₁₆×C₂₄₁	—	4	2	no	—
22	C₂×C₈×C₂₄₁	D₄	1	1	yes	characteristic
23	C₂×C₈×C₂₄₁	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₂₄₁	—	4	2	no	—
25	C₄²×C₂₄₁	D₄	1	1	yes	characteristic
26	C₂²×D₂₄₁	—	4	2	no	—
27	D₉₆₄	—	4	2	no	—
28	D₉₆₄	—	4	2	no	—
29	D₉₆₄	—	8	4	no	—
30	Q₈×C₂₄₁	—	4	2	no	—
31	Q₈×C₂₄₁	—	4	2	no	—
32	C₂×C₄×C₂₄₁	—	4	2	no	—
33	C₂×C₄×C₂₄₁	D₈	1	2	yes	—
34	C₂×C₄×C₂₄₁	C₂×D₄	1	1	yes	characteristic
35	C₈×C₂₄₁	D₈	1	2	yes	—
36	C₈×C₂₄₁	C₂×D₄	1	2	yes	—
37	C₂²×C₂₄₁	C₂×D₈	1	1	yes	characteristic
38	C₂×D₂₄₁	—	8	2	no	—
39	C₂×D₂₄₁	—	8	4	no	—
40	C₄×C₂₄₁	—	8	2	no	—
41	C₄×C₂₄₁	SD₃₂	1	4	yes	complemented
42	C₄×C₂₄₁	#127	1	1	yes	characteristic
43	C₄×C₂₄₁	C₂×D₈	1	1	yes	characteristic
44	C₂×C₂₄₁	#493	1	1	yes	characteristic
45	C₂×C₂₄₁	C₂×SD₃₂	1	2	yes	—
46	D₂₄₁	—	16	2	no	—
47	C₂₄₁	#2248	1	1	yes	characteristic, complemented, Sylow
48	#2248	—	241	1	no	maximal, Sylow
49	C₂×SD₃₂	—	241	4	no	—
50	#494	D₂₄₁	1	1	yes	characteristic, complemented
51	#493	—	241	1	no	—
52	C₄×C₁₆	—	241	1	no	—
53	C₂×Q₁₆	—	2	1	no	—
54	C₂×Q₁₆	C₂×D₂₄₁	1	2	yes	—
55	C₂×D₈	—	482	1	no	—
56	C₂×D₈	—	241	2	no	—
57	C₄⋊Q₈	—	2	1	no	—
58	#127	—	482	1	no	—
59	SD₃₂	—	482	8	no	—
60	C₂×C₁₆	—	241	2	no	—
61	C₄×C₈	C₂×D₂₄₁	1	1	yes	characteristic
62	C₂×Q₈	—	2	2	no	—
63	C₂×D₄	—	964	2	no	—
64	C₂×D₄	—	482	2	no	—
65	Q₁₆	—	2	4	no	—
66	Q₁₆	—	4	2	no	—
67	D₈	—	964	2	no	—
68	D₈	—	482	4	no	—
69	C₂×C₈	C₂²⋊D₂₄₁	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₂₄₁	1	1	yes	characteristic
71	C₄⋊C₄	—	4	2	no	—
72	C₄²	C₂²⋊D₂₄₁	1	1	yes	characteristic
73	C₁₆	—	241	4	no	—
74	C₂³	—	964	2	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	4	2	no	—
77	D₄	—	1928	4	no	—
78	D₄	—	964	2	no	—
79	D₄	—	964	2	no	—
80	C₂×C₄	—	4	2	no	—
81	C₂×C₄	#16838755	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₂₄₁	1	1	yes	characteristic
83	C₈	#16838755	1	2	yes	—
84	C₈	D₄×D₂₄₁	1	2	yes	—
85	C₂²	—	1928	4	no	—
86	C₂²	—	1928	2	no	—
87	C₂²	C₂×#16838755	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	#21440585	1	4	yes	complemented
90	C₄	#21440638	1	1	yes	characteristic
91	C₄	C₂×#16838755	1	1	yes	characteristic
92	C₂	—	3856	2	no	—
93	C₂	#29508093	1	1	yes	characteristic
94	C₂	C₂×#21440585	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#16838755
commutator, cosocle	C₂×C₈×C₂₄₁	C₂³
Frattini	C₂×C₈	C₂²×D₂₄₁
Fitting	#494×C₂₄₁	C₂
socle	C₂²×C₂₄₁	C₂×D₈
prime radical	#29508094	C₂
hypercenter	#494	D₂₄₁
hypocenter	C₂₄₁	#2248
LCS	G ▷ C₂×C₈×C₂₄₁ ▷ C₄×C₂₄₁ ▷ C₂×C₂₄₁ ▷ C₂₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
1. C₂×#21440585	C₂	semidirect
3. C₄×#16838745	C₂	semidirect
4. #494×C₂₄₁	C₂	semidirect
18. #16838745	D₄	semidirect
41. C₄×C₂₄₁	SD₃₂	semidirect
47. C₂₄₁	#2248	semidirect
50. #494	D₂₄₁	semidirect
89. C₄	#21440585	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21440585	2
#29508094	2
C₄×#16838745	2
#494×C₂₄₁	2
#2248	241