Subgroups — #20295153

Order 6976.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₂₁₈	C₂	1	1	yes	maximal, characteristic
2	#16812628	C₂	1	2	yes	maximal
3	#16812609	C₂	1	2	yes	maximal
4	C₄×#11724784	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₁₈	C₄	1	1	yes	characteristic
7	C₂×#11724784	C₂²	1	1	yes	characteristic
8	C₂×#11724784	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₀₉	C₄	1	1	yes	characteristic
10	#13182008	C₄	1	2	yes	—
11	C₄×Dic₁₀₉	C₂²	1	2	yes	—
12	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
13	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
19	Dic₂₁₈	—	2	2	no	—
20	C₈×C₁₀₉	—	2	2	no	—
21	#11724784	—	2	1	no	—
22	#11724784	Q₈	1	2	yes	complemented
23	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₀₉	—	2	1	no	—
25	C₄×C₁₀₉	M₁₆	1	2	yes	—
26	C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₁₀₉	#41	1	1	yes	characteristic
28	Dic₁₀₉	—	2	2	no	—
29	Dic₁₀₉	—	2	2	no	—
30	C₂×C₁₀₉	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₁₀₉	#131	1	1	yes	characteristic
33	C₁₀₉	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	109	1	no	maximal, Sylow
35	C₄×Q₈	—	109	1	no	—
36	C₄⋊C₈	—	109	2	no	—
37	C₄⋊C₈	D₁₀₉	1	1	yes	characteristic
38	#97	—	109	2	no	—
39	C₄×C₈	—	109	1	no	—
40	C₂×Q₈	—	109	1	no	—
41	C₂×C₈	—	109	1	no	—
42	C₂×C₈	—	109	1	no	—
43	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
44	C₄⋊C₄	—	109	2	no	—
45	C₄⋊C₄	—	109	1	no	—
46	C₄²	—	109	2	no	—
47	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
48	Q₈	—	218	2	no	—
49	C₂×C₄	—	109	2	no	—
50	C₂×C₄	—	109	2	no	—
51	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
52	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	109	2	no	—
56	C₈	—	218	1	no	—
57	C₂²	C₂×C₄×D₁₀₉	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	218	2	no	—
60	C₄	—	218	2	no	—
61	C₄	#13182012	1	2	yes	—
62	C₄	Q₈×D₁₀₉	1	1	yes	characteristic
63	C₄	#13182028	1	1	yes	characteristic
64	C₂	#16812664	1	1	yes	characteristic
65	C₂	C₂×#13182012	1	1	yes	characteristic
66	C₂	#16812707	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₀₉
commutator, socle	C₂²×C₁₀₉	C₂²×C₄
Fitting	C₄⋊C₈×C₁₀₉	C₂
hypercenter	C₄⋊C₈	D₁₀₉
hypocenter	C₁₀₉	#446
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
22. #11724784	Q₈	semidirect
33. C₁₀₉	#446	semidirect