Subgroups — #13094004

Order 1504.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₄₇)⋊C₄	C₂	1	2	yes	maximal
5	C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
6	C₂²×D₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₄₇	C₂²	1	2	yes	—
8	C₂×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₄₇	C₂²	1	2	yes	—
11	C₄×D₄₇	—	2	2	no	—
12	Dic₉₄	—	2	2	no	—
13	C₂²×C₄₇	C₂³	1	1	yes	characteristic
14	C₂×D₄₇	—	2	1	no	—
15	C₂×D₄₇	—	2	1	no	—
16	C₂×D₄₇	Q₈	1	2	yes	complemented
17	C₄×C₄₇	—	2	2	no	—
18	C₄×C₄₇	D₄	1	2	yes	—
19	Dic₄₇	—	2	2	no	—
20	Dic₄₇	—	2	1	no	—
21	C₂×C₄₇	C₂×D₄	1	1	yes	characteristic
22	C₂×C₄₇	C₂×Q₈	1	1	yes	characteristic
23	C₂×C₄₇	#41	1	1	yes	characteristic
24	D₄₇	—	2	2	no	—
25	C₄₇	C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₂²⋊Q₈	—	47	1	no	maximal, Sylow
27	C₂×Q₈	—	47	1	no	—
28	C₂²×C₄	—	47	1	no	—
29	C₄⋊C₄	—	47	2	no	—
30	C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
31	C₂²⋊C₄	—	47	2	no	—
32	C₂³	—	47	1	no	—
33	Q₈	—	94	2	no	—
34	C₂×C₄	—	47	2	no	—
35	C₂×C₄	—	47	1	no	—
36	C₂×C₄	—	94	2	no	—
37	C₂×C₄	C₂×D₄₇	1	2	yes	—
38	C₂×C₄	C₂×D₄₇	1	1	yes	characteristic
39	C₂²	—	47	2	no	—
40	C₂²	—	94	1	no	—
41	C₂²	—	94	1	no	—
42	C₂²	C₂²×D₄₇	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	94	1	no	—
45	C₄	—	94	2	no	—
46	C₄	D₁₈₈	1	2	yes	—
47	C₂	—	94	2	no	—
48	C₂	C₂×D₁₈₈	1	1	yes	characteristic
49	C₂	#10625352	1	1	yes	characteristic
50	C₂	Q₈×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂³
Fitting	C₄⋊C₄×C₄₇	C₂
prime radical	C₂²×D₄₇	C₂²
hypercenter	C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂²⋊Q₈
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₉₄	C₂	semidirect
3. C₄⋊C₄×C₄₇	C₂	semidirect
5. C₄⋊Dic₄₇	C₂	semidirect
16. C₂×D₄₇	Q₈	semidirect
25. C₄₇	C₂²⋊Q₈	semidirect
30. C₄⋊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×C₄×D₄₇	2
C₂×Dic₉₄	2
C₄⋊C₄×C₄₇	2
(C₂×D₄₇)⋊C₄	2
C₄⋊Dic₄₇	2
C₂²⋊Q₈	47