Subgroups — C₂²×#10625335 #15689896

Order 3008.

298 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10625335	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×C₄₇	—	2	1	no	—
6	C₂×D₄×C₄₇	—	2	3	no	—
7	C₂×D₄×C₄₇	C₂²	1	6	yes	—
8	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₄₇	—	2	1	no	—
10	C₂×Dic₉₄	—	2	3	no	—
11	C₂×Dic₉₄	C₂²	1	6	yes	complemented
12	#10625335	C₂²	1	16	yes	direct product factor
13	C₂×C₄₇⋊C₈	C₂²	1	6	yes	complemented
14	C₂³×C₄₇	—	2	6	no	—
15	C₂³×C₄₇	—	4	4	no	—
16	C₂³×C₄₇	D₄	1	1	yes	characteristic
17	D₄×C₄₇	—	2	6	no	—
18	D₄×C₄₇	C₂³	1	4	yes	—
19	C₂×C₄×C₄₇	D₄	1	3	yes	—
20	C₂×C₄×C₄₇	C₂³	1	3	yes	—
21	C₂×Dic₄₇	—	2	6	no	—
22	Dic₉₄	—	2	6	no	—
23	Dic₉₄	C₂³	1	4	yes	complemented
24	C₄₇⋊C₈	C₂³	1	4	yes	complemented
25	C₂²×C₄₇	—	2	4	no	—
26	C₂²×C₄₇	—	4	12	no	—
27	C₂²×C₄₇	SD₁₆	1	4	yes	complemented
28	C₂²×C₄₇	C₂×D₄	1	3	yes	—
29	C₄×C₄₇	C₂×D₄	1	3	yes	—
30	C₄×C₄₇	C₂⁴	1	1	yes	characteristic
31	Dic₄₇	—	2	4	no	—
32	C₂×C₄₇	—	4	4	no	—
33	C₂×C₄₇	C₂×SD₁₆	1	6	yes	complemented
34	C₂×C₄₇	C₂²×D₄	1	1	yes	characteristic
35	C₂²×SD₁₆	—	47	1	no	maximal, Sylow
36	C₄₇	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
37	C₂²×Q₈	—	47	1	no	—
38	C₂²×D₄	D₄₇	1	1	yes	characteristic
39	C₂×SD₁₆	—	47	12	no	—
40	C₂²×C₈	—	47	1	no	—
41	C₂⁴	—	2	1	no	—
42	C₂×Q₈	—	47	6	no	—
43	C₂×Q₈	—	94	3	no	—
44	C₂×D₄	—	2	3	no	—
45	C₂×D₄	C₂×D₄₇	1	6	yes	—
46	C₂²×C₄	—	94	1	no	—
47	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
48	SD₁₆	—	47	16	no	—
49	C₂×C₈	—	47	6	no	—
50	C₂³	—	2	6	no	—
51	C₂³	—	4	4	no	—
52	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
53	Q₈	—	47	4	no	—
54	Q₈	—	94	6	no	—
55	D₄	—	2	6	no	—
56	D₄	C₂²×D₄₇	1	4	yes	—
57	C₂×C₄	—	94	6	no	—
58	C₂×C₄	C₂²⋊D₄₇	1	3	yes	—
59	C₂×C₄	C₂²×D₄₇	1	3	yes	—
60	C₈	—	47	4	no	—
61	C₂²	—	2	4	no	—
62	C₂²	—	4	12	no	—
63	C₂²	#10625335	1	4	yes	direct product factor
64	C₂²	C₂×C₂²⋊D₄₇	1	3	yes	—
65	C₄	—	94	4	no	—
66	C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
67	C₄	C₂³×D₄₇	1	1	yes	characteristic
68	C₂	—	4	4	no	—
69	C₂	C₂×#10625335	1	6	yes	direct product factor
70	C₂	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₄₇
commutator, cosocle	C₄×C₄₇	C₂⁴
Frattini	C₄	C₂³×D₄₇
Fitting, prime radical	C₂²×D₄×C₄₇	C₂
socle	C₂³×C₄₇	D₄
hypercenter	C₂²×D₄	D₄₇
hypocenter	C₄₇	C₂²×SD₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₉₄	C₂	semidirect
2. C₂×#10625335	C₂	direct (N × H)
3. C₂²×C₄₇⋊C₈	C₂	semidirect
11. C₂×Dic₉₄	C₂²	semidirect
12. #10625335	C₂²	direct (N × H)
13. C₂×C₄₇⋊C₈	C₂²	semidirect
23. Dic₉₄	C₂³	semidirect
24. C₄₇⋊C₈	C₂³	semidirect
27. C₂²×C₄₇	SD₁₆	semidirect
33. C₂×C₄₇	C₂×SD₁₆	semidirect
36. C₄₇	C₂²×SD₁₆	semidirect
63. C₂²	#10625335	direct (N × H)
69. C₂	C₂×#10625335	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₉₄	2
C₂×#10625335	2
C₂²×C₄₇⋊C₈	2
C₂²×D₄×C₄₇	2
C₂²×SD₁₆	47

Subgroups — C22×#10625335 #15689896

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10625335 #15689896