Subgroups — #20295010

Order 6976.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182013	C₂	1	2	yes	maximal, complemented
2	#16812618	C₂	1	2	yes	maximal, complemented
3	#16812616	C₂	1	2	yes	maximal, complemented
4	C₂×#41×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	#13182013	—	2	2	no	—
6	#13182013	C₂²	1	4	yes	—
7	C₂×#11724784	—	2	2	no	—
8	#41×C₁₀₉	—	2	2	no	—
9	#41×C₁₀₉	—	2	2	no	—
10	C₂×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₁₀₉	C₄	1	2	yes	—
12	C₂×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₁₀₉	C₄	1	2	yes	—
14	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
15	C₂³×C₁₀₉	C₂×C₄	1	2	yes	—
16	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	Q₈×C₁₀₉	—	2	2	no	—
18	D₄×C₁₀₉	—	2	4	no	—
19	D₄×C₁₀₉	—	2	2	no	—
20	C₂×C₄×C₁₀₉	—	2	2	no	—
21	C₂×C₄×C₁₀₉	—	2	2	no	—
22	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
25	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
26	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
27	#11724784	—	2	4	no	—
28	C₂²×C₁₀₉	—	2	2	no	—
29	C₂²×C₁₀₉	—	4	1	no	—
30	C₂²×C₁₀₉	—	4	2	no	—
31	C₂²×C₁₀₉	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₁₀₉	—	2	2	no	—
34	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₄×C₁₀₉	C₂×D₄	1	2	yes	—
37	C₂×C₁₀₉	—	2	1	no	—
38	C₂×C₁₀₉	—	2	2	no	—
39	C₂×C₁₀₉	—	4	2	no	—
40	C₂×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₁₀₉	#413	1	1	yes	characteristic, complemented, Sylow
42	#413	—	109	1	no	maximal, Sylow
43	C₂×#41	D₁₀₉	1	1	yes	characteristic
44	C₂×M₁₆	—	109	2	no	—
45	#101	—	109	2	no	—
46	#100	—	109	2	no	—
47	#41	—	2	2	no	—
48	#41	—	2	2	no	—
49	C₂×Q₈	C₂×D₁₀₉	1	1	yes	characteristic
50	C₂×D₄	Dic₁₀₉	1	2	yes	—
51	C₂×D₄	C₂×D₁₀₉	1	1	yes	characteristic
52	C₂²×C₄	Dic₁₀₉	1	2	yes	—
53	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
54	M₁₆	—	109	4	no	—
55	M₁₆	—	218	2	no	—
56	C₂×C₈	—	218	2	no	—
57	C₂³	C₂×Dic₁₀₉	1	2	yes	—
58	C₂³	C₂×Dic₁₀₉	1	1	yes	characteristic
59	Q₈	—	2	2	no	—
60	D₄	—	2	4	no	—
61	D₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	C₂×Dic₁₀₉	1	2	yes	—
65	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
66	C₂×C₄	C₂²⋊D₁₀₉	1	2	yes	—
67	C₂×C₄	C₂²⋊D₁₀₉	1	2	yes	—
68	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
69	C₈	—	218	4	no	—
70	C₂²	—	2	2	no	—
71	C₂²	—	4	1	no	—
72	C₂²	—	4	2	no	—
73	C₂²	C₂²⋊Dic₁₀₉	1	2	yes	—
74	C₂²	C₂²×Dic₁₀₉	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
77	C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
78	C₄	C₂×C₂²⋊D₁₀₉	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	2	2	no	—
81	C₂	—	4	2	no	—
82	C₂	C₂×C₂²⋊Dic₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊Dic₁₀₉
commutator	C₂²×C₁₀₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂×#41×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂×C₂²⋊C₄
hypercenter	C₂×#41	D₁₀₉
hypocenter	C₁₀₉	#413
LCS	G ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#13182013	C₂	semidirect
2. #16812618	C₂	semidirect
3. #16812616	C₂	semidirect
41. C₁₀₉	#413	semidirect