Subgroups — #20241544

Order 6016.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689513	C₂	1	1	yes	maximal, characteristic
2	#15688920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625336	—	2	1	no	—
5	C₂×#10625334	—	2	1	no	—
6	#13094021	C₄	1	1	yes	characteristic, complemented
7	#13093943	—	2	1	no	—
8	#13093935	C₄	1	1	yes	characteristic, complemented
9	#124×C₄₇	C₂²	1	1	yes	characteristic
10	#99×C₄₇	—	2	1	no	—
11	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
12	C₂×D₄×C₄₇	D₄	1	1	yes	characteristic
13	C₂×D₁₈₈	—	2	1	no	—
14	C₂×D₁₈₈	—	4	1	no	—
15	C₂²⋊C₄×C₄₇	—	4	1	no	—
16	C₂²⋊C₄×C₄₇	—	4	1	no	—
17	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
18	#10625336	—	4	2	no	—
19	#10625334	—	4	2	no	—
20	#10625329	—	4	1	no	—
21	C₂×C₄₇⋊C₈	—	2	1	no	—
22	C₂³×C₄₇	—	2	1	no	—
23	C₂²×D₄₇	—	4	1	no	—
24	Q₈×C₄₇	—	4	1	no	—
25	D₄×C₄₇	—	4	1	no	—
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	8	1	no	—
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	D₁₈₈	—	4	1	no	—
31	D₁₈₈	—	4	1	no	—
32	D₁₈₈	—	8	2	no	—
33	C₄₇⋊C₈	—	2	2	no	—
34	C₄₇⋊C₈	—	8	1	no	—
35	C₂²×C₄₇	—	4	1	no	—
36	C₂²×C₄₇	—	8	1	no	—
37	C₂²×C₄₇	#99	1	1	yes	characteristic
38	C₂×D₄₇	—	8	2	no	—
39	C₂×D₄₇	—	8	1	no	—
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	—	4	1	no	—
42	C₄×C₄₇	—	4	1	no	—
43	C₄×C₄₇	—	16	1	no	—
44	#1406	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	—	2	1	no	—
46	C₂×C₄₇	—	8	1	no	—
47	C₂×C₄₇	#353	1	1	yes	characteristic
48	D₄₇	—	16	1	no	—
49	#496	—	47	1	no	—
50	#355	—	47	1	no	—
51	#354	D₄₇	1	1	yes	characteristic, complemented
52	C₄₇	#1406	1	1	yes	characteristic, complemented, Sylow
53	C₂×SD₁₆	—	94	1	no	—
54	C₂×D₈	—	94	1	no	—
55	#127	—	47	1	no	—
56	#124	C₂×D₄₇	1	1	yes	characteristic
57	#101	—	94	1	no	—
58	#99	—	2	1	no	—
59	#97	—	47	1	no	—
60	C₂×Q₈	D₁₈₈	1	1	yes	characteristic
61	C₂×D₄	—	94	1	no	—
62	C₂×D₄	—	188	1	no	—
63	C₂×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
64	SD₁₆	—	188	2	no	—
65	D₈	—	188	2	no	—
66	M₁₆	—	188	1	no	—
67	C₂×C₈	—	94	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₄×D₄₇	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	188	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	376	2	no	—
76	D₄	—	188	1	no	—
77	D₄	—	188	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
82	C₈	—	94	2	no	—
83	C₈	—	376	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	376	2	no	—
87	C₂²	—	376	1	no	—
88	C₂²	#13093938	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	752	1	no	—
96	C₂	#15688915	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688915
commutator	C₄²×C₄₇	C₂×C₄
Frattini	#124	C₂×D₄₇
Fitting	C₄₇×#354	C₂
socle	C₂×C₄₇	#353
hypercenter	#354	D₄₇
hypocenter	C₄₇	#1406
LCS	G ▷ C₄²×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
2. #15688920	C₂	semidirect
3. C₄₇×#354	C₂	semidirect
6. #13094021	C₄	semidirect
8. #13093935	C₄	semidirect
51. #354	D₄₇	semidirect
52. C₄₇	#1406	semidirect