Subgroups — #20295878

Order 6976.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812756	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂×#89137)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812674	C₂	1	1	yes	maximal, characteristic
4	C₂²×#89137	—	2	1	no	—
5	C₂×#11724786	—	2	1	no	—
6	C₂×D₄₃₆	—	2	1	no	—
7	C₂×D₄₃₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
9	#13182006	—	2	1	no	—
10	C₄⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic, complemented
11	C₂²×D₁₀₉	—	2	1	no	—
12	C₂²×D₁₀₉	D₄	1	1	yes	characteristic
13	C₂×#89137	—	2	2	no	—
14	C₂×#89137	—	4	1	no	—
15	C₂×#89137	—	4	1	no	—
16	C₂×C₄×C₁₀₉	—	2	1	no	—
17	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
19	D₄₃₆	—	4	1	no	—
20	D₄₃₆	—	4	1	no	—
21	D₄₃₆	—	4	1	no	—
22	C₄×D₁₀₉	—	4	1	no	—
23	#11724786	—	4	1	no	—
24	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×D₁₀₉	—	2	1	no	—
26	C₂×D₁₀₉	—	2	1	no	—
27	C₂×D₁₀₉	—	4	1	no	—
28	C₂×D₁₀₉	—	4	1	no	—
29	C₂×D₁₀₉	—	4	1	no	—
30	C₂×D₁₀₉	D₈	1	1	yes	characteristic
31	C₂×D₁₀₉	SD₁₆	1	1	yes	characteristic
32	#89137	—	4	2	no	—
33	C₄×C₁₀₉	—	2	1	no	—
34	C₄×C₁₀₉	—	4	1	no	—
35	Dic₁₀₉	—	2	1	no	—
36	C₂×C₁₀₉	#99	1	1	yes	characteristic
37	C₂×C₁₀₉	#102	1	1	yes	characteristic
38	C₂×C₁₀₉	#104	1	1	yes	characteristic
39	D₁₀₉	—	2	1	no	—
40	D₁₀₉	—	2	1	no	—
41	D₁₀₉	—	8	1	no	—
42	C₁₀₉	#327	1	1	yes	characteristic, complemented, Sylow
43	#327	—	109	1	no	maximal, Sylow
44	#121	—	109	1	no	—
45	C₂²⋊C₈	—	109	1	no	—
46	#95	—	109	1	no	—
47	C₂×D₄	—	109	1	no	—
48	C₂×D₄	—	218	1	no	—
49	C₂²×C₄	—	109	1	no	—
50	C₂²×C₄	—	218	1	no	—
51	C₂×C₈	—	218	1	no	—
52	C₄⋊C₄	#89137	1	1	yes	characteristic, complemented
53	C₂²⋊C₄	—	218	1	no	—
54	C₂³	—	109	1	no	—
55	C₂³	—	218	1	no	—
56	D₄	—	436	1	no	—
57	D₄	—	436	1	no	—
58	D₄	—	436	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	109	1	no	—
61	C₂×C₄	—	436	1	no	—
62	C₂×C₄	—	436	1	no	—
63	C₂×C₄	—	436	1	no	—
64	C₂×C₄	—	218	2	no	—
65	C₂×C₄	C₂×#89137	1	1	yes	characteristic
66	C₈	—	436	1	no	—
67	C₂²	—	109	1	no	—
68	C₂²	—	109	1	no	—
69	C₂²	—	436	1	no	—
70	C₂²	—	436	1	no	—
71	C₂²	—	436	1	no	—
72	C₂²	—	218	1	no	—
73	C₂²	—	218	1	no	—
74	C₂²	C₂²⋊#89137	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	436	2	no	—
78	C₄	—	218	1	no	—
79	C₂	—	872	1	no	—
80	C₂	—	218	1	no	—
81	C₂	—	218	1	no	—
82	C₂	#16812758	1	1	yes	characteristic
83	C₂	#16812761	1	1	yes	characteristic
84	C₂	#16812764	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#89137
commutator	C₂×C₄×C₁₀₉	C₂×C₄
Frattini	C₂×C₄	C₂×#89137
Fitting	C₄⋊C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²⋊C₄
hypercenter	C₄⋊C₄	#89137
hypocenter	C₁₀₉	#327
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #16812756	C₂	semidirect
2. (C₂×#89137)⋊C₄	C₂	semidirect
7. C₂×D₄₃₆	C₄	semidirect
10. C₄⋊C₄×C₁₀₉	C₄	semidirect
42. C₁₀₉	#327	semidirect
52. C₄⋊C₄	#89137	semidirect