Subgroups — (C₂²⋊D₄₇)⋊C₄ #13093984

Order 1504.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×D₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²⋊D₄₇	C₄	1	4	yes	complemented
13	C₂×Dic₄₇	—	2	2	no	—
14	C₂×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇	C₂²	1	1	yes	characteristic
17	C₄×D₄₇	—	2	2	no	—
18	C₂²×C₄₇	—	2	1	no	—
19	C₂²×C₄₇	—	2	1	no	—
20	C₂²×C₄₇	C₂×C₄	1	2	yes	complemented
21	C₂²×C₄₇	C₂³	1	1	yes	characteristic
22	C₂×D₄₇	—	2	1	no	—
23	C₂×D₄₇	—	2	1	no	—
24	C₂×D₄₇	C₂×C₄	1	2	yes	complemented
25	C₄×C₄₇	—	2	1	no	—
26	C₄×C₄₇	—	2	1	no	—
27	Dic₄₇	—	2	1	no	—
28	Dic₄₇	C₂×C₄	1	2	yes	complemented
29	Dic₄₇	D₄	1	2	yes	complemented
30	C₂×C₄₇	—	2	2	no	—
31	C₂×C₄₇	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄₇	#41	1	1	yes	characteristic
34	D₄₇	—	2	2	no	—
35	C₄₇	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
36	C₄×D₄	—	47	1	no	maximal, Sylow
37	C₂×D₄	—	47	1	no	—
38	C₂²×C₄	—	47	1	no	—
39	C₂²×C₄	—	47	1	no	—
40	C₄⋊C₄	—	47	1	no	—
41	C₂²⋊C₄	—	47	1	no	—
42	C₂²⋊C₄	D₄₇	1	1	yes	characteristic, complemented
43	C₄²	—	47	1	no	—
44	C₂³	—	47	1	no	—
45	C₂³	C₂×D₄₇	1	1	yes	characteristic
46	D₄	—	47	4	no	—
47	C₂×C₄	—	47	1	no	—
48	C₂×C₄	—	47	1	no	—
49	C₂×C₄	—	47	1	no	—
50	C₂×C₄	—	94	2	no	—
51	C₂×C₄	—	94	2	no	—
52	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
53	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
54	C₂²	—	2	1	no	—
55	C₂²	—	2	1	no	—
56	C₂²	—	47	2	no	—
57	C₂²	—	94	1	no	—
58	C₂²	—	94	1	no	—
59	C₂²	C₄×D₄₇	1	2	yes	complemented
60	C₂²	C₂²×D₄₇	1	1	yes	characteristic
61	C₄	—	2	1	no	—
62	C₄	—	2	1	no	—
63	C₄	—	47	2	no	—
64	C₄	—	47	2	no	—
65	C₄	—	94	1	no	—
66	C₂	—	2	2	no	—
67	C₂	—	94	2	no	—
68	C₂	C₂×C₄×D₄₇	1	1	yes	characteristic
69	C₂	D₄×D₄₇	1	1	yes	characteristic
70	C₂	#10625352	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₄₇
commutator	C₂×C₄₇	C₂²×C₄
Fitting	C₂²⋊C₄×C₄₇	C₂
socle, cosocle	C₂²×C₄₇	C₂³
prime radical	C₂×C₂²⋊D₄₇	C₂
hypercenter	C₂²⋊C₄	D₄₇
hypocenter	C₄₇	C₄×D₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₄₇	C₂	semidirect
3. C₂×C₄×D₄₇	C₂	semidirect
4. C₂²⋊C₄×C₄₇	C₂	semidirect
5. (C₂×D₄₇)⋊C₄	C₂	semidirect
6. Dic₄₇⋊C₄	C₂	semidirect
7. C₄×Dic₄₇	C₂	semidirect
12. C₂²⋊D₄₇	C₄	semidirect
20. C₂²×C₄₇	C₂×C₄	semidirect
24. C₂×D₄₇	C₂×C₄	semidirect
28. Dic₄₇	C₂×C₄	semidirect
29. Dic₄₇	D₄	semidirect
35. C₄₇	C₄×D₄	semidirect
42. C₂²⋊C₄	D₄₇	semidirect
59. C₂²	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊D₄₇	2
C₂²×Dic₄₇	2
C₂×C₄×D₄₇	2
C₂²⋊C₄×C₄₇	2
(C₂×D₄₇)⋊C₄	2
Dic₄₇⋊C₄	2
C₄×Dic₄₇	2
C₄×D₄	47

Subgroups — (C22⋊D47)⋊C4 #13093984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂²⋊D₄₇)⋊C₄ #13093984