Subgroups — C₂×C₂²⋊#89137 #16812776

Order 3488.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#89137	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#89137	C₂	1	4	yes	maximal, direct product factor
3	C₂³×D₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₁₀₉	C₄	1	1	yes	characteristic, complemented
5	C₂²×D₁₀₉	—	2	4	no	—
6	C₂²×D₁₀₉	C₄	1	2	yes	complemented
7	C₂²×D₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂²×D₁₀₉	C₂²	1	2	yes	—
9	C₂²×D₁₀₉	C₂²	1	1	yes	characteristic
10	C₂×#89137	—	2	4	no	—
11	C₂×#89137	C₂²	1	4	yes	complemented
12	C₂²×C₁₀₉	—	2	2	no	—
13	C₂²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₁₀₉	C₂×C₄	1	2	yes	complemented
15	C₂×D₁₀₉	—	2	2	no	—
16	C₂×D₁₀₉	—	2	4	no	—
17	C₂×D₁₀₉	—	2	4	no	—
18	C₂×D₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₂×D₁₀₉	C₂×C₄	1	2	yes	complemented
20	C₂×D₁₀₉	D₄	1	4	yes	—
21	C₂×D₁₀₉	C₂³	1	1	yes	characteristic
22	#89137	—	2	4	no	—
23	C₂×C₁₀₉	—	2	2	no	—
24	C₂×C₁₀₉	C₂²⋊C₄	1	2	yes	complemented
25	C₂×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
26	D₁₀₉	—	2	2	no	—
27	D₁₀₉	C₂²⋊C₄	1	2	yes	complemented
28	D₁₀₉	C₂×D₄	1	2	yes	—
29	C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₂²⋊C₄	—	109	1	no	maximal, Sylow
31	C₂⁴	—	109	1	no	—
32	C₂²×C₄	—	109	2	no	—
33	C₂²⋊C₄	—	109	4	no	—
34	C₂³	—	109	1	no	—
35	C₂³	—	109	1	no	—
36	C₂³	—	109	2	no	—
37	C₂³	—	109	2	no	—
38	C₂³	—	218	4	no	—
39	C₂³	#89137	1	1	yes	characteristic, complemented
40	C₂×C₄	—	109	4	no	—
41	C₂×C₄	—	218	4	no	—
42	C₂²	—	2	2	no	—
43	C₂²	—	109	4	no	—
44	C₂²	—	109	1	no	—
45	C₂²	—	109	1	no	—
46	C₂²	—	109	2	no	—
47	C₂²	—	218	4	no	—
48	C₂²	—	218	4	no	—
49	C₂²	—	218	2	no	—
50	C₂²	C₂×#89137	1	1	yes	characteristic
51	C₂²	C₂×#89137	1	2	yes	complemented
52	C₄	—	218	4	no	—
53	C₂	—	2	2	no	—
54	C₂	—	109	2	no	—
55	C₂	—	109	2	no	—
56	C₂	—	218	2	no	—
57	C₂	C₂²⋊#89137	1	2	yes	direct product factor
58	C₂	C₂²×#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#89137
commutator	C₂×C₁₀₉	C₂²×C₄
Frattini	C₂	C₂²×#89137
Fitting	C₂³×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂×C₄
prime radical	C₂³×D₁₀₉	C₂
cosocle	C₂×D₁₀₉	C₂³
hypercenter	C₂³	#89137
hypocenter	C₁₀₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂²×#89137	C₂	semidirect
2. C₂²⋊#89137	C₂	direct (N × H)
4. C₂³×C₁₀₉	C₄	semidirect
6. C₂²×D₁₀₉	C₄	semidirect
7. C₂²×D₁₀₉	C₄	semidirect
11. C₂×#89137	C₂²	semidirect
14. C₂²×C₁₀₉	C₂×C₄	semidirect
19. C₂×D₁₀₉	C₂×C₄	semidirect
24. C₂×C₁₀₉	C₂²⋊C₄	semidirect
27. D₁₀₉	C₂²⋊C₄	semidirect
29. C₁₀₉	C₂×C₂²⋊C₄	semidirect
39. C₂³	#89137	semidirect
51. C₂²	C₂×#89137	semidirect
57. C₂	C₂²⋊#89137	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#89137	2
C₂²⋊#89137	2
C₂³×D₁₀₉	2
C₂×C₂²⋊C₄	109

Subgroups — C2×C22⋊#89137 #16812776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊#89137 #16812776