Subgroups — #28412333

Order 14656.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301045	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×#11745021)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#20300963	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11745021	—	2	1	no	—
5	C₂×#14270087	—	2	1	no	—
6	C₂×D₉₁₆	—	2	1	no	—
7	C₂×D₉₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₂₂₉	C₂²	1	1	yes	characteristic
9	#16814643	—	2	1	no	—
10	C₄⋊C₄×C₂₂₉	C₄	1	1	yes	characteristic, complemented
11	C₂×#11745021	—	2	2	no	—
12	C₂×#11745021	—	4	1	no	—
13	C₂×#11745021	—	4	1	no	—
14	#14270087	—	4	1	no	—
15	C₂²×D₂₂₉	—	2	1	no	—
16	C₂²×D₂₂₉	D₄	1	1	yes	characteristic
17	D₉₁₆	—	4	1	no	—
18	D₉₁₆	—	4	1	no	—
19	D₉₁₆	—	4	1	no	—
20	C₂×Dic₂₂₉	D₄	1	1	yes	characteristic
21	C₄×D₂₂₉	—	4	1	no	—
22	C₂×C₄×C₂₂₉	—	2	1	no	—
23	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₂₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₂₂₉	—	2	1	no	—
26	C₂×D₂₂₉	—	2	1	no	—
27	C₂×D₂₂₉	—	4	1	no	—
28	C₂×D₂₂₉	—	4	1	no	—
29	C₂×D₂₂₉	—	4	1	no	—
30	C₂×D₂₂₉	D₈	1	1	yes	characteristic
31	C₂×D₂₂₉	SD₁₆	1	1	yes	characteristic
32	#11745021	—	4	2	no	—
33	C₄×C₂₂₉	—	2	1	no	—
34	C₄×C₂₂₉	—	4	1	no	—
35	Dic₂₂₉	—	2	1	no	—
36	C₂×C₂₂₉	#99	1	1	yes	characteristic
37	C₂×C₂₂₉	#102	1	1	yes	characteristic
38	C₂×C₂₂₉	#104	1	1	yes	characteristic
39	D₂₂₉	—	2	1	no	—
40	D₂₂₉	—	2	1	no	—
41	D₂₂₉	—	8	1	no	—
42	C₂₂₉	#327	1	1	yes	characteristic, complemented, Sylow
43	#327	—	229	1	no	maximal, Sylow
44	#121	—	229	1	no	—
45	C₂²⋊C₈	—	229	1	no	—
46	#95	—	229	1	no	—
47	C₂×D₄	—	458	1	no	—
48	C₂×D₄	—	229	1	no	—
49	C₂²×C₄	—	458	1	no	—
50	C₂²×C₄	—	229	1	no	—
51	C₂×C₈	—	458	1	no	—
52	C₄⋊C₄	#11745021	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	458	1	no	—
54	C₂³	—	458	1	no	—
55	C₂³	—	229	1	no	—
56	D₄	—	916	1	no	—
57	D₄	—	916	1	no	—
58	D₄	—	916	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	916	1	no	—
61	C₂×C₄	—	916	1	no	—
62	C₂×C₄	—	916	1	no	—
63	C₂×C₄	—	458	2	no	—
64	C₂×C₄	—	229	1	no	—
65	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
66	C₈	—	916	1	no	—
67	C₂²	—	916	1	no	—
68	C₂²	—	916	1	no	—
69	C₂²	—	916	1	no	—
70	C₂²	—	458	1	no	—
71	C₂²	—	458	1	no	—
72	C₂²	—	229	1	no	—
73	C₂²	—	229	1	no	—
74	C₂²	C₂²⋊#11745021	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	916	2	no	—
78	C₄	—	458	1	no	—
79	C₂	—	1832	1	no	—
80	C₂	—	458	1	no	—
81	C₂	—	458	1	no	—
82	C₂	#20301047	1	1	yes	characteristic
83	C₂	#20301050	1	1	yes	characteristic
84	C₂	#20301053	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#11745021
commutator	C₂×C₄×C₂₂₉	C₂×C₄
Frattini	C₂×C₄	C₂×#11745021
Fitting	C₄⋊C₄×C₂₂₉	C₄
socle	C₂²×C₂₂₉	C₂²⋊C₄
prime radical	#20300963	C₂
cosocle	C₂×C₄×D₂₂₉	C₂²
hypercenter	C₄⋊C₄	#11745021
hypocenter	C₂₂₉	#327
LCS	G ▷ C₂×C₄×C₂₂₉ ▷ C₂²×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #20301045	C₂	semidirect
2. (C₂×#11745021)⋊C₄	C₂	semidirect
7. C₂×D₉₁₆	C₄	semidirect
10. C₄⋊C₄×C₂₂₉	C₄	semidirect
42. C₂₂₉	#327	semidirect
52. C₄⋊C₄	#11745021	semidirect

Maximal subgroups

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

subgroup	index
#20301045	2
(C₂×#11745021)⋊C₄	2
#20300963	2
#327	229