Subgroups — #20294992

Order 6976.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182029	C₂	1	1	yes	maximal, characteristic
2	C₂×#13182013	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812611	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#13182029	—	2	2	no	—
6	#13182029	—	2	2	no	—
7	C₂×Dic₂₁₈	C₄	1	1	yes	characteristic
8	C₂×D₄₃₆	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₁₀₉	C₄	1	2	yes	—
10	C₂×C₄×D₁₀₉	C₂²	1	2	yes	—
11	#13182013	—	2	2	no	—
12	C₂×#11724784	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₀₉	—	2	2	no	—
15	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
16	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×D₁₀₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
20	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
21	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
22	C₂²⋊D₁₀₉	—	2	4	no	—
23	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
24	D₄₃₆	—	2	2	no	—
25	C₄×D₁₀₉	—	2	2	no	—
26	C₄×D₁₀₉	—	2	2	no	—
27	Dic₂₁₈	—	2	2	no	—
28	C₈×C₁₀₉	—	2	2	no	—
29	#11724784	—	2	2	no	—
30	C₂²×C₁₀₉	—	2	2	no	—
31	C₂²×C₁₀₉	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₁₀₉	—	2	2	no	—
34	C₂×D₁₀₉	—	2	4	no	—
35	C₄×C₁₀₉	C₂²⋊C₄	1	2	yes	—
36	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
38	Dic₁₀₉	—	2	2	no	—
39	C₂×C₁₀₉	—	2	2	no	—
40	C₂×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₁₀₉	#131	1	2	yes	—
42	D₁₀₉	—	4	2	no	—
43	C₁₀₉	#408	1	1	yes	characteristic, complemented, Sylow
44	#408	—	109	1	no	maximal, Sylow
45	C₂×#41	—	109	1	no	—
46	C₂×M₁₆	—	109	1	no	—
47	C₂²×C₈	D₁₀₉	1	1	yes	characteristic, complemented
48	C₂²⋊C₈	—	109	4	no	—
49	#41	—	218	2	no	—
50	#41	—	218	2	no	—
51	C₂×Q₈	—	109	1	no	—
52	C₂×D₄	—	109	2	no	—
53	C₂×D₄	—	109	1	no	—
54	C₂²×C₄	—	109	2	no	—
55	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
56	M₁₆	—	218	2	no	—
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	109	2	no	—
59	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
60	C₂³	—	109	2	no	—
61	C₂³	C₄×D₁₀₉	1	1	yes	characteristic
62	Q₈	—	218	2	no	—
63	D₄	—	218	4	no	—
64	D₄	—	218	2	no	—
65	C₂×C₄	—	109	2	no	—
66	C₂×C₄	—	218	2	no	—
67	C₂×C₄	—	218	2	no	—
68	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
69	C₂×C₄	D₄₃₆	1	2	yes	—
70	C₂×C₄	C₂²⋊D₁₀₉	1	2	yes	—
71	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₈	—	218	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	218	2	no	—
76	C₂²	—	218	4	no	—
77	C₂²	#13182006	1	2	yes	—
78	C₂²	C₂×C₄×D₁₀₉	1	1	yes	characteristic
79	C₄	—	218	2	no	—
80	C₄	#13182006	1	2	yes	—
81	C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
82	C₄	C₂×D₄₃₆	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	436	2	no	—
85	C₂	C₂×#13182006	1	1	yes	characteristic
86	C₂	#16812705	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₀₉
commutator, socle	C₂²×C₁₀₉	C₂²×C₄
Fitting	C₂²×C₈×C₁₀₉	C₂
hypercenter	C₂²×C₈	D₁₀₉
hypocenter	C₁₀₉	#408
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#13182013	C₂	semidirect
3. #16812611	C₂	semidirect
4. C₂²×C₈×C₁₀₉	C₂	semidirect
43. C₁₀₉	#408	semidirect
47. C₂²×C₈	D₁₀₉	semidirect