Subgroups — C₂×#15688865 #20241972

Order 6016.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093935	C₂	1	2	yes	maximal
2	#15688865	C₂	1	4	yes	maximal, direct product factor
3	C₂×#125×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	—	2	2	no	—
5	#13093935	—	2	2	no	—
6	#13093935	C₂²	1	4	yes	—
7	#125×C₄₇	—	2	2	no	—
8	#125×C₄₇	C₄	1	2	yes	—
9	#125×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
11	C₂×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₄₇	—	2	2	no	—
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	D₄	1	2	yes	—
16	C₄⋊C₄×C₄₇	—	2	4	no	—
17	C₄⋊C₄×C₄₇	—	2	2	no	—
18	C₄⋊C₄×C₄₇	—	2	4	no	—
19	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
20	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₇	D₄	1	2	yes	—
22	C₄²×C₄₇	C₂³	1	1	yes	characteristic
23	C₂×C₄₇⋊C₈	—	2	8	no	—
24	C₂×C₄₇⋊C₈	—	2	4	no	—
25	C₂³×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇	—	2	2	no	—
27	C₂×C₄×C₄₇	—	2	4	no	—
28	C₂×C₄×C₄₇	—	2	4	no	—
29	C₂×C₄×C₄₇	—	4	4	no	—
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
34	C₄₇⋊C₈	—	2	8	no	—
35	C₂²×C₄₇	#101	1	2	yes	—
36	C₂²×C₄₇	#104	1	4	yes	—
37	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₄×C₄₇	—	2	1	no	—
39	C₄×C₄₇	—	2	1	no	—
40	C₄×C₄₇	—	2	2	no	—
41	C₄×C₄₇	—	2	2	no	—
42	C₄×C₄₇	—	4	4	no	—
43	C₂×#330	—	47	1	no	maximal, Sylow
44	C₂×C₄₇	#330	1	4	yes	complemented
45	C₂×C₄₇	C₂×#101	1	1	yes	characteristic
46	C₂×C₄₇	C₂×#104	1	2	yes	—
47	C₂×#125	D₄₇	1	1	yes	characteristic
48	C₂×#97	—	47	2	no	—
49	#330	—	47	4	no	—
50	C₄₇	C₂×#330	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₈	—	94	2	no	—
52	#125	—	2	2	no	—
53	#125	Dic₄₇	1	2	yes	—
54	#125	C₂×D₄₇	1	2	yes	—
55	C₂×C₄⋊C₄	—	2	2	no	—
56	C₂×C₄⋊C₄	Dic₄₇	1	2	yes	—
57	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
58	#97	—	47	4	no	—
59	#97	—	94	2	no	—
60	C₂²×C₄	—	2	2	no	—
61	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
62	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
63	C₂×C₈	—	94	8	no	—
64	C₂×C₈	—	94	4	no	—
65	C₄⋊C₄	—	2	4	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
69	C₄²	C₂×Dic₄₇	1	1	yes	characteristic
70	C₄²	C₂²⋊D₄₇	1	2	yes	—
71	C₄²	C₂²×D₄₇	1	1	yes	characteristic
72	C₂³	C₂²⋊Dic₄₇	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	4	no	—
77	C₂×C₄	C₂²⋊Dic₄₇	1	2	yes	—
78	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
79	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
80	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
81	C₈	—	94	8	no	—
82	C₂²	#13093943	1	2	yes	—
83	C₂²	#13093951	1	4	yes	—
84	C₂²	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₂	#15688865	1	4	yes	direct product factor
91	C₂	C₂×#13093943	1	1	yes	characteristic
92	C₂	C₂×#13093951	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₂×#125×C₄₇	C₂
socle	C₂³×C₄₇	C₂²⋊C₄
hypercenter	C₂×#125	D₄₇
hypocenter	C₄₇	C₂×#330
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
2. #15688865	C₂	direct (N × H)
44. C₂×C₄₇	#330	semidirect
50. C₄₇	C₂×#330	semidirect
90. C₂	#15688865	direct (N × H)

Subgroups — C2×#15688865 #20241972

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688865 #20241972