Subgroups — #28377991

Order 13952.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295915	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295887	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295108	C₂	1	1	yes	maximal, characteristic
4	C₂×#13182032	—	2	1	no	—
5	C₄⋊#11724786	—	2	1	no	—
6	C₂×D₈₇₂	C₄	1	1	yes	characteristic
7	#16812661	—	2	1	no	—
8	#16812619	—	2	1	no	—
9	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic
10	#107×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂×#11724786	—	4	1	no	—
12	#13182032	—	2	2	no	—
13	C₂×D₄₃₆	—	2	1	no	—
14	C₂×C₄×D₁₀₉	—	4	1	no	—
15	D₈₇₂	—	2	1	no	—
16	D₈₇₂	C₈	1	2	yes	complemented
17	C₂×#11724784	D₄	1	1	yes	characteristic
18	#13182006	—	4	1	no	—
19	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₀₉	—	2	1	no	—
22	C₂²×D₁₀₉	—	4	1	no	—
23	C₂×C₄×C₁₀₉	—	4	1	no	—
24	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₁₀₉	D₈	1	1	yes	characteristic
26	C₂×Dic₁₀₉	SD₁₆	1	1	yes	characteristic
27	D₄₃₆	—	2	2	no	—
28	D₄₃₆	—	4	1	no	—
29	C₄×D₁₀₉	—	8	2	no	—
30	#11724786	—	8	1	no	—
31	C₈×C₁₀₉	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₀₉	M₁₆	1	1	yes	characteristic
33	#11724784	—	2	1	no	—
34	C₂²×C₁₀₉	#102	1	1	yes	characteristic
35	C₂×D₁₀₉	—	4	2	no	—
36	C₂×D₁₀₉	—	8	1	no	—
37	C₂×D₁₀₉	—	8	1	no	—
38	C₄×C₁₀₉	—	8	1	no	—
39	C₄×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₁₀₉	#104	1	1	yes	characteristic
41	Dic₁₀₉	—	2	1	no	—
42	Dic₁₀₉	—	2	1	no	—
43	C₂×C₁₀₉	D₄⋊C₈	1	1	yes	characteristic
44	C₂×C₁₀₉	#360	1	1	yes	characteristic
45	C₂×C₁₀₉	#361	1	1	yes	characteristic
46	D₁₀₉	—	8	2	no	—
47	#1333	—	109	1	no	maximal, Sylow
48	C₁₀₉	#1333	1	1	yes	characteristic, complemented, Sylow
49	C₄×D₈	—	109	1	no	—
50	#346	—	109	1	no	—
51	#334	—	109	1	no	—
52	C₂×D₈	—	109	1	no	—
53	C₄×D₄	—	218	1	no	—
54	C₂×C₁₆	—	218	1	no	—
55	#107	#89137	1	1	yes	characteristic
56	C₄⋊C₈	—	218	1	no	—
57	#102	—	218	1	no	—
58	C₄×C₈	—	109	1	no	—
59	C₂×D₄	—	218	1	no	—
60	C₂²×C₄	—	436	1	no	—
61	D₈	—	109	2	no	—
62	D₈	—	218	1	no	—
63	C₂×C₈	—	109	1	no	—
64	C₂×C₈	—	436	1	no	—
65	C₂×C₈	C₂×#89137	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₂²⋊C₄	—	436	1	no	—
68	C₄²	—	109	1	no	—
69	C₁₆	—	218	2	no	—
70	C₂³	—	436	1	no	—
71	D₄	—	436	1	no	—
72	D₄	—	218	2	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	872	2	no	—
75	C₂×C₄	—	109	1	no	—
76	C₂×C₄	—	109	1	no	—
77	C₂×C₄	C₂²⋊#89137	1	1	yes	characteristic
78	C₈	—	872	1	no	—
79	C₈	—	218	1	no	—
80	C₈	D₁₀₉⋊C₈	1	1	yes	characteristic
81	C₈	#13182039	1	1	yes	characteristic
82	C₂²	—	872	1	no	—
83	C₂²	—	872	1	no	—
84	C₂²	—	436	2	no	—
85	C₂²	#16812761	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	—	218	1	no	—
88	C₄	—	218	1	no	—
89	C₄	#16812756	1	1	yes	characteristic
90	C₄	#16812764	1	1	yes	characteristic
91	C₂	—	872	2	no	—
92	C₂	#20295874	1	1	yes	characteristic
93	C₂	#20295943	1	1	yes	characteristic
94	C₂	#20295944	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812761
commutator	C₈×C₁₀₉	C₂×C₈
Frattini	C₂×C₈	C₂×#89137
Fitting	#107×C₁₀₉	C₄
socle	C₂²×C₁₀₉	#102
prime radical	C₂×D₈₇₂	C₄
cosocle	C₈×Dic₁₀₉	C₂²
hypercenter	#107	#89137
hypocenter	C₁₀₉	#1333
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
1. #20295915	C₂	semidirect
2. #20295887	C₂	semidirect
16. D₈₇₂	C₈	semidirect
48. C₁₀₉	#1333	semidirect

Maximal subgroups

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

subgroup	index
#20295915	2
#20295887	2
#20295108	2
#1333	109