Subgroups — #20241554

Order 6016.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689497	C₂	1	1	yes	maximal, characteristic
2	#15688922	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#356	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625336	—	2	1	no	—
5	C₂×#10625336	—	2	1	no	—
6	#13094021	C₄	1	1	yes	characteristic
7	#13093943	—	2	1	no	—
8	C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	#101×C₄₇	—	2	1	no	—
11	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
13	C₂×D₁₈₈	—	2	1	no	—
14	C₂×D₁₈₈	—	4	1	no	—
15	M₁₆×C₄₇	—	4	1	no	—
16	C₄⋊C₄×C₄₇	—	4	1	no	—
17	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
18	#10625336	—	4	2	no	—
19	#10625336	—	4	2	no	—
20	#10625329	—	4	1	no	—
21	C₂×C₄₇⋊C₈	—	2	1	no	—
22	C₂²×D₄₇	—	4	1	no	—
23	Q₈×C₄₇	—	4	1	no	—
24	Q₈×C₄₇	—	4	1	no	—
25	C₂×C₄×C₄₇	—	2	1	no	—
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
29	D₁₈₈	—	4	1	no	—
30	D₁₈₈	—	4	1	no	—
31	D₁₈₈	—	8	2	no	—
32	C₈×C₄₇	—	8	1	no	—
33	C₄₇⋊C₈	—	2	2	no	—
34	C₄₇⋊C₈	—	8	1	no	—
35	C₂²×C₄₇	#99	1	1	yes	characteristic
36	C₂×D₄₇	—	8	2	no	—
37	C₂×D₄₇	—	8	1	no	—
38	C₄×C₄₇	—	2	2	no	—
39	C₄×C₄₇	—	2	1	no	—
40	C₄×C₄₇	—	4	1	no	—
41	C₄×C₄₇	—	4	1	no	—
42	#1410	—	47	1	no	maximal, Sylow
43	C₂×C₄₇	—	2	1	no	—
44	C₂×C₄₇	#353	1	1	yes	characteristic
45	D₄₇	—	16	1	no	—
46	#492	—	47	1	no	—
47	#356	—	47	1	no	—
48	#356	D₄₇	1	1	yes	characteristic, complemented
49	C₄₇	#1410	1	1	yes	characteristic, complemented, Sylow
50	C₂×SD₁₆	—	94	1	no	—
51	C₂×SD₁₆	—	94	1	no	—
52	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
53	#127	—	47	1	no	—
54	#101	—	2	1	no	—
55	#101	—	94	1	no	—
56	C₄×C₈	—	47	1	no	—
57	C₂×Q₈	D₁₈₈	1	1	yes	characteristic
58	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
59	C₂×D₄	—	94	1	no	—
60	C₂×D₄	—	188	1	no	—
61	SD₁₆	—	188	2	no	—
62	SD₁₆	—	188	2	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	188	1	no	—
65	C₂×C₈	—	94	1	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄²	C₄×D₄₇	1	1	yes	characteristic
68	C₂³	—	188	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	D₄	—	376	2	no	—
72	D₄	—	188	1	no	—
73	D₄	—	188	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
78	C₈	—	8	1	no	—
79	C₈	—	94	2	no	—
80	C₈	—	376	1	no	—
81	C₂²	—	376	2	no	—
82	C₂²	—	376	1	no	—
83	C₂²	#13093938	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	—	2	1	no	—
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	752	1	no	—
90	C₂	#15688915	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688915
commutator	C₄²×C₄₇	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₄₇
Fitting	C₄₇×#356	C₂
socle	C₂×C₄₇	#353
hypercenter	#356	D₄₇
hypocenter	C₄₇	#1410
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
2. #15688922	C₂	semidirect
3. C₄₇×#356	C₂	semidirect
48. #356	D₄₇	semidirect
49. C₄₇	#1410	semidirect