Subgroups — C₂²⋊#20297739 #43272901

Order 28736.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20297739	C₂	1	2	yes	maximal, complemented
2	C₂²×#16813311	C₂	1	1	yes	maximal, characteristic
3	#20297739	—	2	2	no	—
4	C₂×#16813311	—	2	2	no	—
5	C₂×#16813311	C₄	1	1	yes	characteristic
6	C₂×#16813311	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₄₄₉	C₄	1	1	yes	characteristic
8	#16813311	—	2	1	no	—
9	#16813311	D₄	1	2	yes	—
10	C₂³×C₄₄₉	C₈	1	1	yes	characteristic
11	C₂×C₄×C₄₄₉	—	2	1	no	—
12	C₂×C₄×C₄₄₉	—	2	1	no	—
13	C₂×C₄×C₄₄₉	C₈	1	1	yes	characteristic
14	C₂×C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄₄₉	—	2	1	no	—
16	C₂²×C₄₄₉	—	2	1	no	—
17	C₂²×C₄₄₉	C₁₆	1	2	yes	complemented
18	C₂²×C₄₄₉	C₂×C₈	1	1	yes	characteristic
19	C₄×C₄₄₉	—	2	1	no	—
20	C₄×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₄₉	M₁₆	1	1	yes	characteristic
22	C₂×C₄₄₉	—	2	2	no	—
23	C₂×C₄₄₉	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₄₄₉	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₄₄₉	M₃₂	1	1	yes	characteristic
26	C₄₄₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	449	1	no	maximal, Sylow
28	C₂²×C₈	—	449	1	no	—
29	C₂×C₁₆	—	449	2	no	—
30	C₂²×C₄	#14267798	1	1	yes	characteristic
31	C₂×C₈	—	898	2	no	—
32	C₂×C₈	—	449	1	no	—
33	C₂×C₈	—	449	1	no	—
34	C₁₆	—	898	2	no	—
35	C₂³	#16813318	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#16813318	1	1	yes	characteristic
39	C₂×C₄	C₂×#14267798	1	1	yes	characteristic
40	C₈	—	898	1	no	—
41	C₈	—	449	2	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#20297739	1	2	yes	complemented
45	C₂²	C₂×#16813318	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊#14267798	1	1	yes	characteristic
48	C₄	#20297745	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊#16813318	1	1	yes	characteristic
51	C₂	C₂×#20297739	1	1	yes	characteristic
52	C₂	#28385414	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#14267798
commutator	C₂×C₄₄₉	C₂×C₁₆
Fitting	C₂²×C₄×C₄₄₉	C₄
socle	C₂²×C₄₄₉	C₂×C₈
prime radical	C₂³×C₄₄₉	C₈
cosocle	C₂×#16813311	C₂²
hypercenter	C₂²×C₄	#14267798
hypocenter	C₄₄₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄₄₉ ▷ C₄₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#20297739	C₂	semidirect
17. C₂²×C₄₄₉	C₁₆	semidirect
26. C₄₄₉	C₂²⋊C₁₆	semidirect
44. C₂²	#20297739	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20297739	2
C₂²×#16813311	2
C₂²⋊C₁₆	449

Subgroups — C22⋊#20297739 #43272901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#20297739 #43272901