Subgroups — #28406917

Order 14464.

152 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	#20299521	C₂	1	4	yes	maximal, complemented
3	#20298554	C₂	1	1	yes	maximal, characteristic
4	#16813696	—	2	2	no	—
5	#16813696	C₂²	1	4	yes	—
6	C₂×#14268650	—	2	2	no	—
7	C₂×#14268631	C₄	1	1	yes	characteristic
8	C₂²×#11744751	C₂²	1	1	yes	characteristic
9	#16813533	C₄	1	2	yes	—
10	C₄×#11744751	C₂²	1	2	yes	—
11	#117×C₁₁₃	C₄	1	1	yes	characteristic
12	#14268650	—	2	4	no	—
13	#14268631	C₈	1	4	yes	—
14	C₂×#11744751	C₂×C₄	1	1	yes	characteristic
15	C₂×#11744751	C₂×C₄	1	2	yes	—
16	C₂×#11744751	D₄	1	2	yes	—
17	C₂×#11744751	Q₈	1	2	yes	—
18	C₂×#11744751	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₁₁₃	—	2	1	no	—
21	C₂²⋊C₄×C₁₁₃	—	2	1	no	—
22	C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
23	C₂³×C₁₁₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₁₃	—	2	2	no	—
25	C₂×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₁₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
29	#11744751	C₄⋊C₄	1	2	yes	—
30	#11744751	C₂×C₈	1	4	yes	—
31	#11744751	C₂×D₄	1	1	yes	characteristic
32	#11744751	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₁₁₃	—	4	1	no	—
34	C₂²×C₁₁₃	C₄⋊C₈	1	2	yes	—
35	C₂²×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₁₁₃	—	4	2	no	—
37	C₄×C₁₁₃	C₄⋊C₈	1	2	yes	—
38	C₄×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₁₁₃	—	2	1	no	—
41	C₂×C₁₁₃	—	2	2	no	—
42	C₂×C₁₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
43	#2153	—	113	1	no	maximal, Sylow
44	C₁₁₃	#2153	1	1	yes	characteristic, complemented, Sylow
45	C₂×M₃₂	—	113	2	no	—
46	#405	—	113	1	no	—
47	#364	—	113	4	no	—
48	C₂×M₁₆	—	113	1	no	—
49	C₂²×C₈	—	113	1	no	—
50	#117	#90673	1	1	yes	characteristic
51	M₃₂	—	113	4	no	—
52	M₃₂	—	226	2	no	—
53	C₂×C₁₆	—	226	2	no	—
54	#97	—	113	2	no	—
55	C₄×C₈	—	113	2	no	—
56	C₂²×C₄	C₂×#90673	1	1	yes	characteristic
57	M₁₆	—	113	4	no	—
58	C₂×C₈	—	113	2	no	—
59	C₂×C₈	—	113	2	no	—
60	C₂×C₈	—	113	1	no	—
61	C₂×C₈	—	113	2	no	—
62	C₂×C₈	—	113	1	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×#90673	1	2	yes	—
66	C₁₆	—	226	4	no	—
67	C₂³	#14268656	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₄⋊#90673	1	2	yes	—
70	C₂×C₄	#14268655	1	2	yes	—
71	C₂×C₄	#14268656	1	1	yes	characteristic
72	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
73	C₈	—	113	1	no	—
74	C₈	—	113	2	no	—
75	C₈	—	113	1	no	—
76	C₈	—	113	4	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#16813689	1	2	yes	—
79	C₂²	C₂×#14268656	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#16813689	1	2	yes	—
82	C₄	C₂×C₄⋊#90673	1	1	yes	characteristic
83	C₄	C₂×#14268655	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#16813689	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#90673
commutator	C₄×C₁₁₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×#90673
Fitting	#117×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁₃	M₁₆
cosocle	C₂×#11744751	C₂³
hypercenter	#117	#90673
hypocenter	C₁₁₃	#2153
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #20299521	C₂	semidirect
44. C₁₁₃	#2153	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
#20299521	2
#20298554	2
#2153	113