Subgroups — #15689401

Order 3008.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094023	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093958	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093957	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#13093945	C₂	1	1	yes	maximal, characteristic
7	#102×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇	—	2	1	no	—
10	C₂×Dic₉₄	—	2	1	no	—
11	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₄₇	—	2	1	no	—
14	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
16	Dic₄₇⋊C₄	—	2	1	no	—
17	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇	—	2	1	no	—
20	D₄×C₄₇	—	2	1	no	—
21	D₄×C₄₇	Q₈	1	2	yes	complemented
22	C₂×C₄×C₄₇	—	2	1	no	—
23	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂×Dic₄₇	—	2	1	no	—
25	C₂×Dic₄₇	—	2	1	no	—
26	C₂×Dic₄₇	—	4	2	no	—
27	C₂×Dic₄₇	D₄	1	1	yes	characteristic
28	C₂×Dic₄₇	D₄	1	1	yes	characteristic
29	Dic₉₄	—	4	2	no	—
30	C₈×C₄₇	—	2	1	no	—
31	C₄₇⋊C₈	—	2	1	no	—
32	C₂²×C₄₇	—	2	2	no	—
33	C₂²×C₄₇	—	4	1	no	—
34	C₂²×C₄₇	—	4	1	no	—
35	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
36	C₄×C₄₇	—	4	1	no	—
37	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₄₇	#41	1	1	yes	characteristic
39	Dic₄₇	—	2	1	no	—
40	Dic₄₇	—	4	1	no	—
41	Dic₄₇	—	4	1	no	—
42	Dic₄₇	D₈	1	2	yes	—
43	C₂×C₄₇	—	4	2	no	—
44	C₂×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
46	C₂×C₄₇	#137	1	1	yes	characteristic
47	#474	—	47	1	no	maximal, Sylow
48	C₄₇	#474	1	1	yes	characteristic, complemented, Sylow
49	C₄⋊Q₈	—	47	1	no	—
50	C₄×D₄	—	47	1	no	—
51	#107	—	47	1	no	—
52	#107	—	47	1	no	—
53	C₄⋊C₈	—	47	1	no	—
54	#102	—	47	1	no	—
55	#102	D₄₇	1	1	yes	characteristic
56	C₂×Q₈	—	94	1	no	—
57	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
58	C₂²×C₄	—	94	1	no	—
59	C₂×C₈	—	47	1	no	—
60	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
61	C₄⋊C₄	—	47	1	no	—
62	C₄⋊C₄	—	47	1	no	—
63	C₄⋊C₄	—	94	1	no	—
64	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
65	C₂²⋊C₄	—	94	1	no	—
66	C₄²	—	47	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	188	2	no	—
69	D₄	—	2	1	no	—
70	D₄	Dic₉₄	1	2	yes	complemented
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	47	1	no	—
73	C₂×C₄	—	47	1	no	—
74	C₂×C₄	—	94	1	no	—
75	C₂×C₄	—	94	1	no	—
76	C₂×C₄	—	188	2	no	—
77	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	94	1	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₄₇	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	47	2	no	—
86	C₄	—	94	1	no	—
87	C₄	—	188	1	no	—
88	C₄	—	188	1	no	—
89	C₄	C₂×Dic₉₄	1	1	yes	characteristic
90	C₄	#10625352	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	#13094001	1	1	yes	characteristic
93	C₂	D₈×D₄₇	1	1	yes	characteristic
94	C₂	#13094053	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#102×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂×D₄×C₄₇	C₂²
hypercenter	#102	D₄₇
hypocenter	C₄₇	#474
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
1. #13094023	C₂	semidirect
3. #13093958	C₂	semidirect
4. #13093957	C₂	semidirect
5. Dic₄₇⋊C₈	C₂	semidirect
21. D₄×C₄₇	Q₈	semidirect
48. C₄₇	#474	semidirect
70. D₄	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
#13094023	2
D₄×Dic₄₇	2
#13093958	2
#13093957	2
Dic₄₇⋊C₈	2
#13093945	2
#102×C₄₇	2
#474	47