Subgroups — #28388614

Order 14464.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298971	C₂	1	1	yes	maximal, characteristic
2	#20298419	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14268636	—	2	1	no	—
5	C₂×#14268636	—	2	1	no	—
6	#16813622	C₄	1	1	yes	characteristic
7	#16813619	C₄	1	1	yes	characteristic
8	#16813562	—	2	1	no	—
9	M₃₂×C₁₁₃	—	2	1	no	—
10	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₂₆	—	2	1	no	—
12	C₂×D₄₅₂	—	2	1	no	—
13	C₂×D₄₅₂	—	4	1	no	—
14	#14268636	—	4	1	no	—
15	#14268636	—	4	1	no	—
16	#14268636	—	4	1	no	—
17	#14268636	—	4	1	no	—
18	C₄⋊Dic₁₁₃	—	4	1	no	—
19	#14268622	—	4	1	no	—
20	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
22	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₁₁₃	—	4	1	no	—
24	C₂²×D₁₁₃	—	4	1	no	—
25	C₂×C₄×C₁₁₃	—	2	1	no	—
26	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₁₃	—	4	1	no	—
28	D₄₅₂	—	4	1	no	—
29	D₄₅₂	—	4	1	no	—
30	D₄₅₂	—	8	2	no	—
31	Dic₂₂₆	—	4	1	no	—
32	Dic₂₂₆	—	4	1	no	—
33	C₈×C₁₁₃	D₈	1	1	yes	characteristic
34	C₈×C₁₁₃	D₈	1	1	yes	characteristic
35	C₈×C₁₁₃	SD₁₆	1	1	yes	characteristic
36	C₈×C₁₁₃	SD₁₆	1	1	yes	characteristic
37	C₂²×C₁₁₃	#100	1	1	yes	characteristic
38	C₂×D₁₁₃	—	8	2	no	—
39	C₂×D₁₁₃	—	8	1	no	—
40	C₄×C₁₁₃	—	2	2	no	—
41	C₄×C₁₁₃	#102	1	1	yes	characteristic
42	C₄×C₁₁₃	#102	1	1	yes	characteristic
43	Dic₁₁₃	—	8	1	no	—
44	C₂×C₁₁₃	—	2	1	no	—
45	C₂×C₁₁₃	#331	1	1	yes	characteristic
46	D₁₁₃	—	16	1	no	—
47	#1359	—	113	1	no	maximal, Sylow
48	C₁₁₃	#1359	1	1	yes	characteristic, complemented, Sylow
49	#492	—	113	1	no	—
50	#364	—	113	1	no	—
51	#364	D₁₁₃	1	1	yes	characteristic, complemented
52	C₂×SD₁₆	—	226	1	no	—
53	C₂×SD₁₆	—	226	1	no	—
54	C₄⋊Q₈	—	113	1	no	—
55	#127	—	113	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	226	1	no	—
58	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
59	C₂×Q₈	—	226	1	no	—
60	C₂×D₄	—	452	1	no	—
61	C₂×D₄	—	226	1	no	—
62	SD₁₆	—	452	1	no	—
63	SD₁₆	—	452	1	no	—
64	SD₁₆	—	452	1	no	—
65	SD₁₆	—	452	1	no	—
66	C₂×C₈	D₄₅₂	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
68	C₄⋊C₄	—	452	1	no	—
69	C₄²	C₄×D₁₁₃	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	452	1	no	—
72	C₂³	—	452	1	no	—
73	Q₈	—	452	1	no	—
74	Q₈	—	452	1	no	—
75	D₄	—	904	2	no	—
76	D₄	—	452	1	no	—
77	D₄	—	452	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	452	1	no	—
80	C₂×C₄	#14268624	1	1	yes	characteristic
81	C₈	#14268632	1	1	yes	characteristic
82	C₈	D₉₀₄	1	1	yes	characteristic
83	C₈	#14268634	1	1	yes	characteristic
84	C₈	#14268636	1	1	yes	characteristic
85	C₂²	—	904	2	no	—
86	C₂²	—	904	1	no	—
87	C₂²	#16813538	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	904	1	no	—
90	C₄	#16813542	1	1	yes	characteristic
91	C₄	#16813544	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	1808	1	no	—
94	C₂	#20298341	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20298341
commutator	C₄²×C₁₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₁₃
Fitting	#364×C₁₁₃	C₂
socle	C₂×C₁₁₃	#331
prime radical	#16813619	C₄
cosocle	C₄×C₈×C₁₁₃	C₂²
hypercenter	#364	D₁₁₃
hypocenter	C₁₁₃	#1359
LCS	G ▷ C₄²×C₁₁₃ ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #20298419	C₂	semidirect
3. #364×C₁₁₃	C₂	semidirect
48. C₁₁₃	#1359	semidirect
51. #364	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20298971	2
#20298419	2
#364×C₁₁₃	2
#1359	113