Subgroups — C₂×C₄⋊#11724786 #20296026

Order 6976.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11724786	C₂	1	2	yes	maximal
2	C₄⋊#11724786	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724786	—	2	4	no	—
5	C₂×#11724786	C₂²	1	4	yes	—
6	C₂²×Dic₁₀₉	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₀₉	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₀₉	C₄	1	2	yes	—
9	C₄×Dic₁₀₉	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₀₉	C₈	1	4	yes	complemented
13	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
14	C₂×Dic₁₀₉	—	2	2	no	—
15	C₂×Dic₁₀₉	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₀₉	D₄	1	2	yes	—
18	C₂×Dic₁₀₉	Q₈	1	2	yes	—
19	C₂×Dic₁₀₉	C₂³	1	1	yes	characteristic
20	#11724786	—	2	4	no	—
21	C₂²×C₁₀₉	C₄⋊C₄	1	2	yes	—
22	C₂²×C₁₀₉	C₂×C₈	1	2	yes	—
23	C₂²×C₁₀₉	M₁₆	1	2	yes	—
24	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₁₀₉	C₂×C₈	1	4	yes	complemented
26	Dic₁₀₉	—	2	2	no	—
27	Dic₁₀₉	C₄⋊C₄	1	2	yes	—
28	Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
29	Dic₁₀₉	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₁₀₉	C₄⋊C₈	1	4	yes	complemented
31	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₁₀₉	C₂×M₁₆	1	1	yes	characteristic
34	C₁₀₉	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₄⋊C₈	—	109	1	no	maximal, Sylow
36	C₂²×C₈	—	109	2	no	—
37	C₂×C₄²	—	109	1	no	—
38	C₄⋊C₈	—	109	4	no	—
39	C₂²×C₄	—	109	1	no	—
40	C₂²×C₄	—	109	1	no	—
41	C₂²×C₄	#89137	1	1	yes	characteristic
42	C₂×C₈	—	109	4	no	—
43	C₂×C₈	—	218	4	no	—
44	C₄²	—	109	2	no	—
45	C₄²	—	109	2	no	—
46	C₂³	C₂×#89137	1	1	yes	characteristic
47	C₂×C₄	—	109	2	no	—
48	C₂×C₄	—	109	2	no	—
49	C₂×C₄	—	109	1	no	—
50	C₂×C₄	—	109	1	no	—
51	C₂×C₄	—	109	2	no	—
52	C₂×C₄	—	218	2	no	—
53	C₂×C₄	#11724786	1	4	yes	complemented
54	C₂×C₄	C₂×#89137	1	2	yes	—
55	C₈	—	218	4	no	—
56	C₂²	C₄⋊#89137	1	2	yes	—
57	C₂²	C₂×#11724786	1	2	yes	—
58	C₂²	#13182039	1	2	yes	—
59	C₂²	C₂²×#89137	1	1	yes	characteristic
60	C₄	—	109	1	no	—
61	C₄	—	109	2	no	—
62	C₄	—	109	1	no	—
63	C₄	—	218	2	no	—
64	C₄	C₂×#11724786	1	4	yes	complemented
65	C₂	C₄⋊#11724786	1	4	yes	direct product factor
66	C₂	C₂×C₄⋊#89137	1	1	yes	characteristic
67	C₂	C₂²×#11724786	1	1	yes	characteristic
68	C₂	C₂×#13182039	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#89137
commutator	C₂×C₁₀₉	C₂²×C₈
Frattini	C₂²	C₂²×#89137
Fitting	C₂²×C₄×C₁₀₉	C₄
socle	C₂³×C₁₀₉	C₂×C₄
hypercenter	C₂²×C₄	#89137
hypocenter	C₁₀₉	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊#11724786	C₂	direct (N × H)
12. C₂×C₄×C₁₀₉	C₈	semidirect
25. C₄×C₁₀₉	C₂×C₈	semidirect
30. C₂×C₁₀₉	C₄⋊C₈	semidirect
34. C₁₀₉	C₂×C₄⋊C₈	semidirect
53. C₂×C₄	#11724786	semidirect
64. C₄	C₂×#11724786	semidirect
65. C₂	C₄⋊#11724786	direct (N × H)

Subgroups — C2×C4⋊#11724786 #20296026

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄⋊#11724786 #20296026