Subgroups — #28405787

Order 14464.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299614	C₂	1	2	yes	maximal
2	#20299440	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11744753	C₄	1	4	yes	—
5	C₂²⋊#11744753	C₄	1	4	yes	—
6	C₄×#11744753	C₂²	1	4	yes	—
7	C₂²×#11744751	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
9	C₈×Dic₁₁₃	C₄	1	2	yes	—
10	C₈×Dic₁₁₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₁₃	C₄	1	1	yes	characteristic
12	C₂×#11744753	C₂×C₄	1	8	yes	—
13	C₂²×Dic₁₁₃	C₂×C₄	1	2	yes	—
14	C₂×#11744751	—	2	2	no	—
15	C₂×#11744751	C₂×C₄	1	2	yes	—
16	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₁₁₃	C₂×C₄	1	2	yes	—
18	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₁₃	—	2	2	no	—
21	C₂×C₈×C₁₁₃	C₂×C₄	1	2	yes	—
22	C₂³×C₁₁₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₁₃	M₁₆	1	2	yes	—
25	C₂×C₄×C₁₁₃	M₁₆	1	2	yes	—
26	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×Dic₁₁₃	—	2	4	no	—
28	C₂×Dic₁₁₃	C₄²	1	2	yes	—
29	C₂×Dic₁₁₃	C₂²×C₄	1	2	yes	—
30	#11744753	—	2	8	no	—
31	C₈×C₁₁₃	—	2	2	no	—
32	#11744751	—	2	2	no	—
33	C₂²×C₁₁₃	—	2	2	no	—
34	C₂²×C₁₁₃	#97	1	2	yes	—
35	C₂²×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₁₁₃	#97	1	2	yes	—
37	C₄×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
38	C₄×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
39	Dic₁₁₃	—	2	2	no	—
40	Dic₁₁₃	#131	1	4	yes	—
41	C₂×C₁₁₃	—	2	2	no	—
42	C₂×C₁₁₃	C₂×#97	1	1	yes	characteristic
43	C₂×C₁₁₃	#405	1	2	yes	—
44	#1452	—	113	1	no	maximal, Sylow
45	C₁₁₃	#1452	1	1	yes	characteristic, complemented, Sylow
46	#431	—	113	2	no	—
47	C₂×C₄×C₈	—	113	1	no	—
48	#322	—	113	4	no	—
49	C₂²×C₈	—	113	1	no	—
50	C₂²×C₈	#90673	1	1	yes	characteristic
51	C₂×C₄²	—	113	1	no	—
52	C₄⋊C₈	—	113	4	no	—
53	C₂²⋊C₈	—	113	4	no	—
54	C₄×C₈	—	113	4	no	—
55	C₄×C₈	—	113	2	no	—
56	C₄×C₈	—	113	2	no	—
57	C₂²×C₄	—	113	2	no	—
58	C₂²×C₄	C₂×#90673	1	1	yes	characteristic
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	—	113	8	no	—
61	C₂×C₈	—	113	2	no	—
62	C₂×C₈	—	226	2	no	—
63	C₂×C₈	C₂×#90673	1	2	yes	—
64	C₄²	—	113	2	no	—
65	C₄²	—	113	1	no	—
66	C₄²	—	113	1	no	—
67	C₂³	C₄×#90673	1	1	yes	characteristic
68	C₂×C₄	—	113	2	no	—
69	C₂×C₄	—	113	2	no	—
70	C₂×C₄	—	226	4	no	—
71	C₂×C₄	C₄×#90673	1	1	yes	characteristic
72	C₂×C₄	#14268656	1	2	yes	—
73	C₂×C₄	#14268657	1	2	yes	—
74	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	226	8	no	—
77	C₈	—	226	2	no	—
78	C₂²	—	2	2	no	—
79	C₂²	#16813677	1	2	yes	—
80	C₂²	C₂×C₄×#90673	1	1	yes	characteristic
81	C₄	—	113	4	no	—
82	C₄	—	226	2	no	—
83	C₄	#16813677	1	2	yes	—
84	C₄	C₂×#14268656	1	1	yes	characteristic
85	C₄	C₂×#14268657	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₂×#16813677	1	1	yes	characteristic
88	C₂	#20299561	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#90673
commutator, socle	C₂²×C₁₁₃	C₂×C₄²
Fitting	C₂²×C₈×C₁₁₃	C₄
prime radical	C₂³×C₁₁₃	C₄²
cosocle	C₄×Dic₁₁₃	C₂³
hypercenter	C₂²×C₈	#90673
hypocenter	C₁₁₃	#1452
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #20299440	C₂	semidirect
45. C₁₁₃	#1452	semidirect

Maximal subgroups

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

subgroup	index
#20299614	2
#20299440	2
C₂×C₈×Dic₁₁₃	2
#1452	113