Subgroups — #15689461

Order 3008.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093983	C₂	1	1	yes	maximal, characteristic
2	#13093957	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093955	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093948	C₂	1	1	yes	maximal, characteristic, complemented
5	#13093948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₇	—	2	1	no	—
11	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²⋊C₄×C₄₇	—	2	1	no	—
13	C₂²⋊Dic₄₇	—	2	1	no	—
14	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	C₄×Dic₄₇	—	2	1	no	—
17	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇	D₄	1	1	yes	characteristic
20	Q₈×C₄₇	—	2	1	no	—
21	Q₈×C₄₇	—	2	1	no	—
22	C₂×C₄×C₄₇	—	2	1	no	—
23	C₂×C₄×C₄₇	—	2	1	no	—
24	C₂×C₄×C₄₇	—	2	1	no	—
25	C₂×C₄×C₄₇	—	2	1	no	—
26	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₄₇	—	2	1	no	—
29	C₂×Dic₄₇	—	2	1	no	—
30	C₄₇⋊C₈	—	2	1	no	—
31	C₄₇⋊C₈	—	2	1	no	—
32	C₂²×C₄₇	—	2	1	no	—
33	C₂²×C₄₇	—	2	1	no	—
34	C₂²×C₄₇	—	2	1	no	—
35	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₇	—	2	1	no	—
37	C₄×C₄₇	—	4	1	no	—
38	C₄×C₄₇	—	4	1	no	—
39	C₄×C₄₇	#41	1	1	yes	characteristic
40	C₄×C₄₇	#41	1	1	yes	characteristic
41	Dic₄₇	—	4	1	no	—
42	Dic₄₇	—	4	1	no	—
43	C₂×C₄₇	—	4	1	no	—
44	C₂×C₄₇	#123	1	1	yes	characteristic
45	C₂×C₄₇	#135	1	1	yes	characteristic
46	C₂×C₄₇	#137	1	1	yes	characteristic
47	#485	—	47	1	no	maximal, Sylow
48	C₄₇	#485	1	1	yes	characteristic, complemented, Sylow
49	C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
50	#117	—	47	1	no	—
51	#107	—	47	1	no	—
52	#106	—	47	1	no	—
53	#103	—	47	1	no	—
54	#103	—	47	1	no	—
55	C₂²⋊C₈	—	47	1	no	—
56	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
57	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
58	C₂×C₈	—	47	1	no	—
59	C₂×C₈	—	47	1	no	—
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	47	1	no	—
62	C₄⋊C₄	—	47	1	no	—
63	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
64	C₂²⋊C₄	—	2	1	no	—
65	C₂²⋊C₄	—	94	1	no	—
66	C₄²	—	94	1	no	—
67	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
68	Q₈	—	2	1	no	—
69	Q₈	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	94	1	no	—
75	C₂×C₄	—	94	1	no	—
76	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
77	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
78	C₈	—	94	1	no	—
79	C₈	—	94	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	188	1	no	—
88	C₄	—	188	1	no	—
89	C₄	#10625352	1	1	yes	characteristic
90	C₄	#10625352	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	#13094005	1	1	yes	characteristic
93	C₂	#13094044	1	1	yes	characteristic
94	C₂	#13094055	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂²⋊Q₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂³×C₄₇	D₄
hypercenter	C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#485
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #13093957	C₂	semidirect
3. #13093955	C₂	semidirect
4. #13093948	C₂	semidirect
5. #13093948	C₂	semidirect
48. C₄₇	#485	semidirect

Maximal subgroups

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

subgroup	index
#13093983	2
#13093957	2
#13093955	2
#13093948	2
C₂²⋊(C₄₇⋊C₈)	2
C₂²⋊Q₈×C₄₇	2
#485	47