Subgroups — #20296076

Order 6976.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11724786	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11724786	C₂	1	2	yes	maximal
3	#16812754	C₂	1	2	yes	maximal
4	C₄×#11724786	C₂	1	1	yes	maximal, characteristic
5	#16812664	C₂	1	1	yes	maximal, characteristic
6	C₂×#11724786	C₂²	1	1	yes	characteristic
7	C₂×#11724786	C₂²	1	2	yes	—
8	C₂×#11724786	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₁₈	C₄	1	1	yes	characteristic
10	#13182008	C₄	1	2	yes	—
11	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₀₉	C₂²	1	2	yes	—
13	C₄⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
19	Dic₂₁₈	—	2	2	no	—
20	#11724786	—	2	1	no	—
21	#11724786	—	2	2	no	—
22	#11724786	Q₈	1	2	yes	complemented
23	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₀₉	—	2	2	no	—
25	C₄×C₁₀₉	M₁₆	1	2	yes	—
26	Dic₁₀₉	—	2	2	no	—
27	Dic₁₀₉	—	2	1	no	—
28	Dic₁₀₉	C₂×Q₈	1	1	yes	characteristic
29	Dic₁₀₉	#41	1	1	yes	characteristic
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	1	no	—
37	C₄⋊C₈	—	109	2	no	—
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	—	109	2	no	—
44	C₄⋊C₄	—	109	2	no	—
45	C₄⋊C₄	#89137	1	1	yes	characteristic
46	C₄²	—	109	1	no	—
47	C₄²	—	109	2	no	—
48	Q₈	—	218	2	no	—
49	C₂×C₄	—	109	1	no	—
50	C₂×C₄	—	109	1	no	—
51	C₂×C₄	—	109	2	no	—
52	C₂×C₄	C₂×#89137	1	2	yes	—
53	C₂×C₄	C₂×#89137	1	1	yes	characteristic
54	C₈	—	109	2	no	—
55	C₈	—	218	1	no	—
56	C₈	—	218	2	no	—
57	C₂²	C₂²×#89137	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	109	1	no	—
60	C₄	—	109	1	no	—
61	C₄	—	218	2	no	—
62	C₄	—	218	1	no	—
63	C₄	#13182039	1	2	yes	—
64	C₂	Q₈×#89137	1	1	yes	characteristic
65	C₂	C₂×#13182039	1	1	yes	characteristic
66	C₂	#16812786	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#89137
commutator, socle	C₂²×C₁₀₉	C₂²×C₄
Fitting	C₄⋊C₄×C₁₀₉	C₄
hypercenter	C₄⋊C₄	#89137
hypocenter	C₁₀₉	#446
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
22. #11724786	Q₈	semidirect
33. C₁₀₉	#446	semidirect