Subgroups — C₂²⋊#63216 #11763703

Order 1088.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3622	C₂	1	1	yes	maximal, characteristic
2	C₂×#63216	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₁₇	C₄	1	1	yes	characteristic
4	C₂×#3622	—	2	2	no	—
5	C₂×#3622	C₄	1	1	yes	characteristic
6	C₂×#3622	C₂²	1	1	yes	characteristic
7	#63216	—	2	2	no	—
8	C₂³×C₁₇	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₇	—	2	1	no	—
10	C₂×C₄×C₁₇	—	2	1	no	—
11	C₂×C₄×C₁₇	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
13	#3622	—	2	1	no	—
14	#3622	D₄	1	2	yes	—
15	C₂²×C₁₇	—	2	1	no	—
16	C₂²×C₁₇	—	2	1	no	—
17	C₂²×C₁₇	C₁₆	1	2	yes	complemented
18	C₂²×C₁₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₁₇	—	2	1	no	—
20	C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₇	M₁₆	1	1	yes	characteristic
22	C₂²⋊C₁₆	—	17	1	no	maximal, Sylow
23	C₂×C₁₇	—	2	2	no	—
24	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
25	C₂×C₁₇	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₁₇	M₃₂	1	1	yes	characteristic
27	C₂²×C₈	—	17	1	no	—
28	C₂×C₁₆	—	17	2	no	—
29	C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₄	#595	1	1	yes	characteristic
31	C₂×C₈	—	17	1	no	—
32	C₂×C₈	—	17	1	no	—
33	C₂×C₈	—	34	2	no	—
34	C₁₆	—	34	2	no	—
35	C₂³	#3624	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#3624	1	1	yes	characteristic
39	C₂×C₄	C₂×#595	1	1	yes	characteristic
40	C₈	—	17	2	no	—
41	C₈	—	34	1	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#63216	1	2	yes	complemented
45	C₂²	C₂×#3624	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	#63247	1	1	yes	characteristic
48	C₄	C₂²⋊#595	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂×#63216	1	1	yes	characteristic
51	C₂	#10587538	1	1	yes	characteristic
52	C₂	C₂²⋊#3624	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#595
commutator	C₂×C₁₇	C₂×C₁₆
Fitting	C₂²×C₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₈
prime radical	C₂³×C₁₇	C₈
cosocle	C₂×#3622	C₂²
hypercenter	C₂²×C₄	#595
hypocenter	C₁₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#63216	C₂	semidirect
17. C₂²×C₁₇	C₁₆	semidirect
29. C₁₇	C₂²⋊C₁₆	semidirect
44. C₂²	#63216	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#3622	2
C₂×#63216	2
C₂²⋊C₁₆	17

Subgroups — C22⋊#63216 #11763703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#63216 #11763703