Subgroups — C₂²⋊#90770 #14272057

Order 1856.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6597	C₂	1	1	yes	maximal, characteristic
2	C₂×#90770	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₂₉	C₄	1	1	yes	characteristic
4	C₂×#6597	—	2	2	no	—
5	C₂×#6597	C₄	1	1	yes	characteristic
6	C₂×#6597	C₂²	1	1	yes	characteristic
7	#90770	—	2	2	no	—
8	C₂³×C₂₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₂₉	—	2	1	no	—
10	C₂×C₄×C₂₉	—	2	1	no	—
11	C₂×C₄×C₂₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#6597	—	2	1	no	—
14	#6597	D₄	1	2	yes	—
15	C₂²×C₂₉	—	2	1	no	—
16	C₂²×C₂₉	—	2	1	no	—
17	C₂²×C₂₉	C₁₆	1	2	yes	complemented
18	C₂²×C₂₉	C₂×C₈	1	1	yes	characteristic
19	C₄×C₂₉	—	2	1	no	—
20	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₂₉	M₁₆	1	1	yes	characteristic
22	C₂²⋊C₁₆	—	29	1	no	maximal, Sylow
23	C₂×C₂₉	—	2	2	no	—
24	C₂×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
25	C₂×C₂₉	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₂₉	M₃₂	1	1	yes	characteristic
27	C₂²×C₈	—	29	1	no	—
28	C₂×C₁₆	—	29	2	no	—
29	C₂₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₄	#1181	1	1	yes	characteristic
31	C₂×C₈	—	29	1	no	—
32	C₂×C₈	—	29	1	no	—
33	C₂×C₈	—	58	2	no	—
34	C₁₆	—	58	2	no	—
35	C₂³	#6599	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#6599	1	1	yes	characteristic
39	C₂×C₄	C₂×#1181	1	1	yes	characteristic
40	C₈	—	29	2	no	—
41	C₈	—	58	1	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#90770	1	2	yes	complemented
45	C₂²	C₂×#6599	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	#90800	1	1	yes	characteristic
48	C₄	C₂²⋊#1181	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂×#90770	1	1	yes	characteristic
51	C₂	#11745214	1	1	yes	characteristic
52	C₂	C₂²⋊#6599	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#1181
commutator	C₂×C₂₉	C₂×C₁₆
Fitting	C₂²×C₄×C₂₉	C₄
socle	C₂²×C₂₉	C₂×C₈
prime radical	C₂³×C₂₉	C₈
cosocle	C₂×#6597	C₂²
hypercenter	C₂²×C₄	#1181
hypocenter	C₂₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#90770	C₂	semidirect
17. C₂²×C₂₉	C₁₆	semidirect
29. C₂₉	C₂²⋊C₁₆	semidirect
44. C₂²	#90770	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6597	2
C₂×#90770	2
C₂²⋊C₁₆	29

Subgroups — C22⋊#90770 #14272057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#90770 #14272057