Subgroups — #28405618

Order 14464.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813696	C₂	1	2	yes	maximal
2	C₂×C₄×#11744751	C₂	1	1	yes	maximal, characteristic
3	#16813696	—	2	2	no	—
4	#16813696	C₄	1	4	yes	complemented
5	C₂×#14268650	—	2	2	no	—
6	C₂²×#11744751	C₄	1	1	yes	characteristic
7	C₂²×#11744751	C₂²	1	1	yes	characteristic
8	C₄×#11744751	—	2	2	no	—
9	C₂×C₄²×C₁₁₃	C₄	1	1	yes	characteristic
10	#14268650	—	2	4	no	—
11	C₂×#11744751	—	2	1	no	—
12	C₂×#11744751	—	2	1	no	—
13	C₂×#11744751	C₈	1	2	yes	—
14	C₂×#11744751	C₂×C₄	1	2	yes	—
15	C₂×#11744751	D₄	1	1	yes	characteristic
16	C₂×#11744751	D₄	1	2	yes	—
17	C₂×#11744751	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₁₁₃	—	2	1	no	—
19	C₂²×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₁₃	—	2	1	no	—
21	C₄²×C₁₁₃	C₈	1	2	yes	—
22	C₂³×C₁₁₃	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	—	2	4	no	—
24	C₂×C₄×C₁₁₃	—	2	2	no	—
25	C₂×C₄×C₁₁₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
31	#11744751	—	2	2	no	—
32	#11744751	C₂²⋊C₄	1	2	yes	—
33	#11744751	C₄⋊C₄	1	2	yes	—
34	C₂²×C₁₁₃	—	2	2	no	—
35	C₂²×C₁₁₃	#97	1	1	yes	characteristic
36	C₂²×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₁₃	—	2	4	no	—
39	C₄×C₁₁₃	#95	1	1	yes	characteristic
40	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
41	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₁₁₃	—	2	1	no	—
44	C₂×C₁₁₃	—	2	1	no	—
45	C₂×C₁₁₃	#336	1	1	yes	characteristic
46	C₂×C₁₁₃	#364	1	2	yes	—
47	#1376	—	113	1	no	maximal, Sylow
48	C₁₁₃	#1376	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₃₂	—	113	2	no	—
50	C₂×C₄×C₈	—	113	1	no	—
51	C₂²×C₈	—	113	1	no	—
52	C₂²×C₈	—	113	1	no	—
53	C₂×C₄²	#90673	1	1	yes	characteristic
54	M₃₂	—	113	4	no	—
55	M₃₂	—	226	2	no	—
56	C₂×C₁₆	—	226	2	no	—
57	C₄×C₈	—	226	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×#90673	1	1	yes	characteristic
60	C₂×C₈	—	113	2	no	—
61	C₂×C₈	—	113	2	no	—
62	C₂×C₈	—	113	1	no	—
63	C₂×C₈	—	113	1	no	—
64	C₂×C₈	—	113	2	no	—
65	C₂×C₈	—	226	1	no	—
66	C₂×C₈	—	226	1	no	—
67	C₄²	—	2	1	no	—
68	C₄²	#11744753	1	2	yes	—
69	C₁₆	—	226	4	no	—
70	C₂³	#14268656	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₄×#90673	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#90673	1	1	yes	characteristic
76	C₂×C₄	C₂×#11744753	1	1	yes	characteristic
77	C₂×C₄	#14268655	1	1	yes	characteristic
78	C₂×C₄	#14268657	1	1	yes	characteristic
79	C₈	—	113	2	no	—
80	C₈	—	113	2	no	—
81	C₈	—	226	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#16813677	1	1	yes	characteristic
84	C₂²	C₂²⋊#11744753	1	1	yes	characteristic
85	C₂²	#16813689	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	(C₂×#90673)⋊C₄	1	1	yes	characteristic
88	C₄	C₄×#11744753	1	1	yes	characteristic
89	C₄	#16813679	1	1	yes	characteristic
90	C₄	C₄⋊#11744753	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#20299464	1	1	yes	characteristic
94	C₂	#20299521	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄⋊#90673
commutator	C₄×C₁₁₃	C₄×C₈
Frattini	C₂²×C₄	C₂×#90673
Fitting	C₂×C₄²×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₄⋊C₈
prime radical	C₂³×C₁₁₃	M₁₆
cosocle	C₂²×#11744751	C₂²
hypercenter	C₂×C₄²	#90673
hypocenter	C₁₁₃	#1376
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #16813696	C₄	semidirect
48. C₁₁₃	#1376	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813696	2
C₂×C₄×#11744751	2
#1376	113