Subgroups — #15689217

Order 3008.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#13093989	C₂	1	2	yes	maximal
3	#13093947	C₂	1	2	yes	maximal
4	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#107×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₄	C₂²	1	2	yes	—
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
9	Dic₄₇⋊C₄	—	2	2	no	—
10	C₄×Dic₄₇	—	2	2	no	—
11	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	Dic₁₈₈	C₄	1	4	yes	complemented
14	C₂×C₄×C₄₇	—	2	2	no	—
15	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₇	—	2	2	no	—
17	C₂×Dic₄₇	D₄	1	1	yes	characteristic
18	C₂×Dic₄₇	D₄	1	1	yes	characteristic
19	Dic₉₄	—	2	2	no	—
20	Dic₉₄	C₂×C₄	1	4	yes	—
21	C₈×C₄₇	C₂×C₄	1	2	yes	—
22	C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₇	—	4	2	no	—
25	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
26	C₄×C₄₇	#41	1	1	yes	characteristic
27	Dic₄₇	—	2	4	no	—
28	Dic₄₇	—	2	1	no	—
29	Dic₄₇	Q₁₆	1	2	yes	complemented
30	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
31	C₂×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₄₇	#135	1	1	yes	characteristic
33	C₄×Q₁₆	—	47	1	no	maximal, Sylow
34	C₄₇	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	47	1	no	—
36	C₄×Q₈	—	47	2	no	—
37	#107	D₄₇	1	1	yes	characteristic
38	#103	—	47	2	no	—
39	C₄×C₈	—	47	1	no	—
40	C₂×Q₈	—	47	2	no	—
41	Q₁₆	—	47	4	no	—
42	C₂×C₈	—	47	1	no	—
43	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
44	C₄⋊C₄	—	94	2	no	—
45	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
46	C₄²	—	47	1	no	—
47	C₄²	—	94	2	no	—
48	Q₈	—	47	4	no	—
49	Q₈	—	94	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	47	1	no	—
52	C₂×C₄	—	47	1	no	—
53	C₂×C₄	—	94	2	no	—
54	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
55	C₈	—	94	1	no	—
56	C₈	C₄×D₄₇	1	2	yes	—
57	C₂²	D₄×D₄₇	1	1	yes	characteristic
58	C₄	—	4	2	no	—
59	C₄	—	47	2	no	—
60	C₄	—	94	4	no	—
61	C₄	—	94	1	no	—
62	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
63	C₄	#10625354	1	1	yes	characteristic
64	C₂	#13093986	1	1	yes	characteristic
65	C₂	Q₁₆×D₄₇	1	1	yes	characteristic
66	C₂	#13094043	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#107×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	#107	D₄₇
hypocenter	C₄₇	C₄×Q₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
13. Dic₁₈₈	C₄	semidirect
29. Dic₄₇	Q₁₆	semidirect
34. C₄₇	C₄×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₈₈	2
#13093989	2
#13093947	2
C₈×Dic₄₇	2
#107×C₄₇	2
C₄×Q₁₆	47