Subgroups — #20295991

Order 6976.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182039	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₀₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#16812754	C₂	1	2	yes	maximal, complemented
4	C₄×#11724786	C₂	1	2	yes	maximal, complemented
5	#16812657	C₂	1	1	yes	maximal, characteristic
6	#13182039	C₄	1	4	yes	complemented
7	D₁₀₉⋊C₈	C₄	1	4	yes	complemented
8	C₂×#11724786	C₂²	1	1	yes	characteristic
9	C₂×#11724786	C₂²	1	2	yes	—
10	C₂×#11724786	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₉	C₄	1	1	yes	characteristic
13	#13182006	C₄	1	2	yes	—
14	C₄×Dic₁₀₉	C₂²	1	2	yes	—
15	C₄⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic
16	C₂²×D₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
20	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
21	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
22	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
23	#11724786	C₂×C₄	1	2	yes	—
24	#11724786	C₂×C₄	1	2	yes	—
25	#11724786	C₂×C₄	1	4	yes	—
26	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₀₉	—	2	1	no	—
28	C₂×D₁₀₉	—	2	1	no	—
29	C₂×D₁₀₉	C₄²	1	2	yes	—
30	C₄×C₁₀₉	—	2	2	no	—
31	C₄×C₁₀₉	C₄²	1	2	yes	—
32	Dic₁₀₉	—	2	2	no	—
33	Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
34	Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₁₀₉	#131	1	1	yes	characteristic
37	C₂×C₁₀₉	#131	1	1	yes	characteristic
38	D₁₀₉	—	2	2	no	—
39	C₁₀₉	#405	1	1	yes	characteristic, complemented, Sylow
40	#405	—	109	1	no	maximal, Sylow
41	C₂×M₁₆	—	109	1	no	—
42	C₂²×C₈	—	109	1	no	—
43	#117	—	109	1	no	—
44	#97	—	109	2	no	—
45	C₄×C₈	—	109	2	no	—
46	C₂²×C₄	—	109	1	no	—
47	M₁₆	—	109	4	no	—
48	C₂×C₈	—	109	1	no	—
49	C₂×C₈	—	109	2	no	—
50	C₂×C₈	—	109	1	no	—
51	C₂×C₈	—	109	4	no	—
52	C₄⋊C₄	—	109	1	no	—
53	C₄⋊C₄	#89137	1	1	yes	characteristic
54	C₂²⋊C₄	—	109	2	no	—
55	C₄²	—	109	2	no	—
56	C₂³	—	109	1	no	—
57	C₂×C₄	—	109	1	no	—
58	C₂×C₄	—	109	2	no	—
59	C₂×C₄	—	109	2	no	—
60	C₂×C₄	—	109	2	no	—
61	C₂×C₄	C₂×#89137	1	2	yes	—
62	C₂×C₄	C₂×#89137	1	1	yes	characteristic
63	C₈	—	109	2	no	—
64	C₈	—	109	2	no	—
65	C₈	—	109	4	no	—
66	C₂²	—	109	2	no	—
67	C₂²	—	218	1	no	—
68	C₂²	—	218	1	no	—
69	C₂²	C₂²×#89137	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	109	1	no	—
72	C₄	—	109	1	no	—
73	C₄	—	218	2	no	—
74	C₄	C₄×#89137	1	2	yes	—
75	C₂	—	218	2	no	—
76	C₂	C₂×C₄×#89137	1	1	yes	characteristic
77	C₂	#16812786	1	1	yes	characteristic
78	C₂	#16812787	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#89137
commutator	C₂×C₁₀₉	C₂×C₄²
Fitting	C₄⋊C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²×C₄
hypercenter	C₄⋊C₄	#89137
hypocenter	C₁₀₉	#405
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #16812754	C₂	semidirect
4. C₄×#11724786	C₂	semidirect
6. #13182039	C₄	semidirect
7. D₁₀₉⋊C₈	C₄	semidirect
39. C₁₀₉	#405	semidirect