Subgroups — D₄⋊#3624 #11763656

Order 1088.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#3624	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₁₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₁₇	—	2	1	no	—
6	C₂×#3624	—	2	1	no	—
7	C₂×#3624	—	2	1	no	—
8	C₂²⋊Dic₁₇	—	2	1	no	—
9	C₄⋊Dic₁₇	C₄	1	1	yes	characteristic
10	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂³×C₁₇	—	2	1	no	—
12	D₄×C₁₇	—	2	1	no	—
13	D₄×C₁₇	C₈	1	2	yes	complemented
14	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₇	—	2	1	no	—
16	C₂×Dic₁₇	—	4	1	no	—
17	C₂×Dic₁₇	—	4	1	no	—
18	C₂×Dic₁₇	D₄	1	1	yes	characteristic
19	C₂×Dic₁₇	D₄	1	1	yes	characteristic
20	#3624	—	2	2	no	—
21	#3624	—	4	1	no	—
22	C₂²×C₁₇	—	2	2	no	—
23	C₂²×C₁₇	—	4	1	no	—
24	C₂²×C₁₇	—	4	1	no	—
25	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₄×C₁₇	M₁₆	1	1	yes	characteristic
28	Dic₁₇	—	2	1	no	—
29	Dic₁₇	—	4	1	no	—
30	Dic₁₇	D₈	1	1	yes	characteristic
31	Dic₁₇	SD₁₆	1	1	yes	characteristic
32	D₄⋊C₈	—	17	1	no	maximal, Sylow
33	C₂×C₁₇	—	4	2	no	—
34	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
35	C₂×C₁₇	#102	1	1	yes	characteristic
36	C₂×C₁₇	#104	1	1	yes	characteristic
37	C₄×D₄	—	17	1	no	—
38	C₄⋊C₈	—	17	1	no	—
39	C₄×C₈	—	17	1	no	—
40	C₁₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂×D₄	#595	1	1	yes	characteristic
42	C₂²×C₄	—	34	1	no	—
43	C₂×C₈	—	34	1	no	—
44	C₂×C₈	—	34	1	no	—
45	C₄⋊C₄	—	17	1	no	—
46	C₂²⋊C₄	—	34	1	no	—
47	C₄²	—	17	1	no	—
48	C₂³	—	2	1	no	—
49	D₄	—	2	1	no	—
50	D₄	#3624	1	2	yes	complemented
51	C₂×C₄	—	17	1	no	—
52	C₂×C₄	—	17	1	no	—
53	C₂×C₄	—	34	1	no	—
54	C₂×C₄	—	68	1	no	—
55	C₂×C₄	—	68	1	no	—
56	C₂×C₄	C₂×#595	1	1	yes	characteristic
57	C₈	—	34	2	no	—
58	C₈	—	68	1	no	—
59	C₂²	—	2	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₂²⋊#595	1	1	yes	characteristic
63	C₄	—	17	1	no	—
64	C₄	—	17	1	no	—
65	C₄	—	34	1	no	—
66	C₄	—	68	1	no	—
67	C₄	C₂×#3624	1	1	yes	characteristic
68	C₄	#63247	1	1	yes	characteristic
69	C₂	—	4	2	no	—
70	C₂	#10587547	1	1	yes	characteristic
71	C₂	#10587548	1	1	yes	characteristic
72	C₂	C₂²⋊#3624	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₈
Frattini	C₂×C₄	C₂×#595
Fitting, prime radical	C₂×D₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₄
cosocle	C₄×Dic₁₇	C₂²
hypercenter	C₂×D₄	#595
hypocenter	C₁₇	D₄⋊C₈
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊#3624	C₂	semidirect
3. C₄×#3624	C₂	semidirect
13. D₄×C₁₇	C₈	semidirect
40. C₁₇	D₄⋊C₈	semidirect
50. D₄	#3624	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₁₇	2
C₄⋊#3624	2
C₄×#3624	2
D₄⋊C₈	17

Subgroups — D4⋊#3624 #11763656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊#3624 #11763656