Subgroups — #20295990

Order 6976.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182038	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11724786	C₂	1	1	yes	maximal, characteristic
3	#16812754	C₂	1	2	yes	maximal, complemented
4	C₄×#11724786	C₂	1	2	yes	maximal, complemented
5	#16812655	C₂	1	1	yes	maximal, characteristic
6	#13182038	C₄	1	4	yes	complemented
7	C₂×#11724786	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	C₂²×Dic₁₀₉	C₂²	1	1	yes	characteristic
12	#13182008	C₄	1	2	yes	—
13	C₂²⋊Dic₁₀₉	C₄	1	1	yes	characteristic
14	C₄×Dic₁₀₉	C₂²	1	2	yes	—
15	C₂²⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic
16	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
19	C₂×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
21	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
22	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
23	#11724786	C₂×C₄	1	2	yes	—
24	#11724786	C₂×C₄	1	2	yes	—
25	#11724786	C₂×C₄	1	4	yes	—
26	C₂²×C₁₀₉	—	2	2	no	—
27	C₂²×C₁₀₉	C₄²	1	2	yes	—
28	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₀₉	—	2	2	no	—
30	Dic₁₀₉	—	2	2	no	—
31	Dic₁₀₉	C₄²	1	2	yes	—
32	Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
33	Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₁₀₉	—	2	2	no	—
35	C₂×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₁₀₉	#131	1	2	yes	—
37	C₁₀₉	#405	1	1	yes	characteristic, complemented, Sylow
38	#405	—	109	1	no	maximal, Sylow
39	C₂×M₁₆	—	109	1	no	—
40	C₂²×C₈	—	109	1	no	—
41	#117	—	109	1	no	—
42	#97	—	109	2	no	—
43	C₄×C₈	—	109	2	no	—
44	C₂²×C₄	—	109	1	no	—
45	M₁₆	—	109	4	no	—
46	C₂×C₈	—	109	4	no	—
47	C₂×C₈	—	109	1	no	—
48	C₂×C₈	—	109	2	no	—
49	C₂×C₈	—	109	1	no	—
50	C₄⋊C₄	—	109	2	no	—
51	C₂²⋊C₄	—	109	1	no	—
52	C₂²⋊C₄	#89137	1	1	yes	characteristic
53	C₄²	—	109	2	no	—
54	C₂³	C₂×#89137	1	1	yes	characteristic
55	C₂×C₄	—	109	2	no	—
56	C₂×C₄	—	109	2	no	—
57	C₂×C₄	—	109	1	no	—
58	C₂×C₄	—	109	1	no	—
59	C₂×C₄	—	109	2	no	—
60	C₂×C₄	C₂×#89137	1	2	yes	—
61	C₈	—	109	2	no	—
62	C₈	—	109	2	no	—
63	C₈	—	109	4	no	—
64	C₂²	—	2	2	no	—
65	C₂²	C₄×#89137	1	2	yes	—
66	C₂²	C₂²×#89137	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	109	1	no	—
69	C₄	—	109	1	no	—
70	C₄	—	109	2	no	—
71	C₄	—	218	2	no	—
72	C₂	—	2	2	no	—
73	C₂	C₂×C₄×#89137	1	1	yes	characteristic
74	C₂	#16812786	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#89137
commutator	C₂×C₁₀₉	C₂×C₄²
Fitting	C₂²⋊C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²×C₄
hypercenter	C₂²⋊C₄	#89137
hypocenter	C₁₀₉	#405
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊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. #13182038	C₄	semidirect
7. C₂×#11724786	C₄	semidirect
37. C₁₀₉	#405	semidirect