Subgroups — D₁₀₉⋊M₃₂ #20296082

Order 6976.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812774	C₂	1	2	yes	maximal, complemented
2	#16812773	C₂	1	2	yes	maximal, complemented
3	D₁₀₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
5	#13182032	C₂²	1	4	yes	complemented
6	C₂×C₄×D₁₀₉	C₄	1	1	yes	characteristic
7	C₂×#11724784	C₂²	1	1	yes	characteristic
8	C₈×D₁₀₉	C₄	1	1	yes	characteristic
9	C₈×D₁₀₉	C₄	1	1	yes	characteristic
10	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
11	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
13	C₂²×D₁₀₉	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
16	C₄×D₁₀₉	C₈	1	1	yes	characteristic
17	C₄×D₁₀₉	C₈	1	1	yes	characteristic
18	C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
22	#11724784	C₂×C₄	1	1	yes	characteristic
23	#11724784	C₂³	1	1	yes	characteristic
24	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
25	C₂×D₁₀₉	—	2	2	no	—
26	C₂×D₁₀₉	C₂×C₈	1	1	yes	characteristic
27	C₂×D₁₀₉	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₀₉	C₂×C₈	1	1	yes	characteristic
31	Dic₁₀₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₁₀₉	—	2	1	no	—
33	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
34	D₁₀₉	—	2	1	no	—
35	D₁₀₉	M₃₂	1	2	yes	complemented
36	C₁₀₉	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×M₃₂	—	109	1	no	maximal, Sylow
38	C₂²×C₈	—	109	1	no	—
39	M₃₂	—	109	2	no	—
40	M₃₂	—	109	2	no	—
41	C₂×C₁₆	—	109	2	no	—
42	C₂²×C₄	—	109	1	no	—
43	C₂×C₈	—	109	1	no	—
44	C₂×C₈	—	109	1	no	—
45	C₂×C₈	—	109	1	no	—
46	C₂×C₈	—	109	1	no	—
47	C₂×C₈	—	109	1	no	—
48	C₂×C₈	#89137	1	1	yes	characteristic
49	C₁₆	—	109	4	no	—
50	C₂³	—	109	1	no	—
51	C₂×C₄	—	109	1	no	—
52	C₂×C₄	—	109	1	no	—
53	C₂×C₄	—	109	1	no	—
54	C₂×C₄	—	109	1	no	—
55	C₂×C₄	—	109	1	no	—
56	C₂×C₄	C₂×#89137	1	1	yes	characteristic
57	C₈	—	109	1	no	—
58	C₈	—	109	1	no	—
59	C₈	C₂×#89137	1	1	yes	characteristic
60	C₈	C₂×#89137	1	1	yes	characteristic
61	C₂²	—	109	1	no	—
62	C₂²	—	109	1	no	—
63	C₂²	—	218	2	no	—
64	C₂²	D₁₀₉⋊C₈	1	1	yes	characteristic
65	C₄	—	109	1	no	—
66	C₄	—	109	1	no	—
67	C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
68	C₄	C₂²×#89137	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	109	2	no	—
71	C₂	—	218	1	no	—
72	C₂	C₂×D₁₀₉⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#89137
commutator, socle	C₂×C₁₀₉	C₂²×C₈
Frattini	C₄	C₂²×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	C₂×M₃₂
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #16812774	C₂	semidirect
2. #16812773	C₂	semidirect
3. D₁₀₉⋊C₁₆	C₂	semidirect
5. #13182032	C₂²	semidirect
35. D₁₀₉	M₃₂	semidirect
36. C₁₀₉	C₂×M₃₂	semidirect

Subgroups — D109⋊M32 #20296082

Conjugacy classes of subgroups

Complements

Subgroups — D₁₀₉⋊M₃₂ #20296082