Subgroups — (C₂×#89137)⋊C₄ #16812750

Order 3488.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#89137	C₂	1	2	yes	maximal
2	C₂×C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×D₁₀₉	C₂²	1	1	yes	characteristic
4	C₂×#89137	—	2	2	no	—
5	C₂×#89137	—	2	2	no	—
6	C₂×#89137	C₄	1	4	yes	complemented
7	C₂×C₄×C₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂×Dic₁₀₉	C₄	1	1	yes	characteristic, complemented
9	C₄×D₁₀₉	—	2	2	no	—
10	C₂²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₀₉	C₂×C₄	1	2	yes	—
12	C₂×D₁₀₉	D₄	1	1	yes	characteristic
13	C₂×D₁₀₉	D₄	1	2	yes	—
14	C₂×D₁₀₉	Q₈	1	1	yes	characteristic
15	#89137	—	2	4	no	—
16	C₄×C₁₀₉	—	2	1	no	—
17	Dic₁₀₉	—	2	1	no	—
18	C₂×C₁₀₉	C₄²	1	1	yes	characteristic
19	C₂×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
21	D₁₀₉	C₂²⋊C₄	1	2	yes	—
22	D₁₀₉	C₄⋊C₄	1	2	yes	—
23	C₁₀₉	#95	1	1	yes	characteristic, complemented, Sylow
24	#95	—	109	1	no	maximal, Sylow
25	C₂²×C₄	—	109	2	no	—
26	C₂²×C₄	—	109	1	no	—
27	C₂³	—	109	1	no	—
28	C₂×C₄	—	109	4	no	—
29	C₂×C₄	—	109	1	no	—
30	C₂×C₄	—	218	2	no	—
31	C₂×C₄	—	218	2	no	—
32	C₂×C₄	—	218	2	no	—
33	C₂×C₄	#89137	1	1	yes	characteristic, complemented
34	C₂²	—	109	2	no	—
35	C₂²	—	109	2	no	—
36	C₂²	—	109	1	no	—
37	C₂²	—	109	1	no	—
38	C₂²	C₂×#89137	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	218	4	no	—
41	C₄	—	218	1	no	—
42	C₂	—	109	2	no	—
43	C₂	—	109	2	no	—
44	C₂	C₄×#89137	1	1	yes	characteristic
45	C₂	C₂²⋊#89137	1	1	yes	characteristic
46	C₂	C₄⋊#89137	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#89137
commutator	C₂×C₁₀₉	C₄²
Fitting	C₂×C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂×C₄
prime radical, cosocle	C₂²×D₁₀₉	C₂²
hypercenter	C₂×C₄	#89137
hypocenter	C₁₀₉	#95
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
6. C₂×#89137	C₄	semidirect
7. C₂×C₄×C₁₀₉	C₄	semidirect
8. C₂×Dic₁₀₉	C₄	semidirect
23. C₁₀₉	#95	semidirect
33. C₂×C₄	#89137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#89137	2
C₂×C₄×D₁₀₉	2
#95	109

Subgroups — (C2×#89137)⋊C4 #16812750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#89137)⋊C₄ #16812750