Subgroups — #13129963

Order 1664.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11718735	C₂	1	1	yes	maximal, characteristic
2	#11718228	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#127	C₄	1	1	yes	characteristic, complemented
5	C₂×#6105	—	2	1	no	—
6	C₂×#6104	—	2	1	no	—
7	#88129	C₂²	1	1	yes	characteristic
8	#88113	—	2	1	no	—
9	#88107	—	2	1	no	—
10	#88043	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₁₃	—	2	1	no	—
12	C₂×D₄×C₁₃	—	4	1	no	—
13	C₂×D₅₂	D₄	1	1	yes	characteristic
14	C₂×Dic₂₆	D₄	1	1	yes	characteristic
15	C₂²⋊#261	—	4	1	no	—
16	#6122	—	4	1	no	—
17	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	#6105	—	4	2	no	—
19	#6104	—	4	2	no	—
20	#6103	—	4	1	no	—
21	C₂×#1055	—	2	1	no	—
22	#1406	—	13	1	no	maximal, Sylow
23	C₂³×C₁₃	—	4	1	no	—
24	C₂²×D₁₃	—	2	1	no	—
25	C₂×#261	—	8	1	no	—
26	D₄×C₁₃	—	4	1	no	—
27	D₄×C₁₃	—	4	1	no	—
28	D₄×C₁₃	—	8	2	no	—
29	C₂×C₄×C₁₃	—	2	1	no	—
30	C₂×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×Dic₁₃	—	2	1	no	—
32	D₅₂	—	4	1	no	—
33	Dic₂₆	—	4	1	no	—
34	#1057	—	8	1	no	—
35	#1055	—	2	2	no	—
36	#496	—	13	1	no	—
37	#355	—	13	1	no	—
38	#354	—	13	1	no	—
39	C₂²×C₁₃	—	8	2	no	—
40	C₂²×C₁₃	—	8	1	no	—
41	C₂²×C₁₃	#99	1	1	yes	characteristic
42	C₂×D₁₃	—	4	1	no	—
43	C₂×D₁₃	—	8	1	no	—
44	#261	—	16	1	no	—
45	C₄×C₁₃	—	2	1	no	—
46	C₄×C₁₃	—	4	1	no	—
47	Dic₁₃	—	4	1	no	—
48	C₂×SD₁₆	—	26	1	no	—
49	C₂×D₈	—	26	1	no	—
50	#127	#261	1	1	yes	characteristic, complemented
51	#124	—	13	1	no	—
52	#101	—	26	1	no	—
53	#99	—	26	1	no	—
54	#97	—	13	1	no	—
55	C₂×C₁₃	—	2	1	no	—
56	C₂×C₁₃	—	16	1	no	—
57	C₂×C₁₃	#353	1	1	yes	characteristic
58	D₁₃	—	8	1	no	—
59	C₂×Q₈	—	13	1	no	—
60	C₂×D₄	—	2	1	no	—
61	C₂×D₄	—	4	1	no	—
62	C₂×D₄	—	13	1	no	—
63	SD₁₆	—	52	2	no	—
64	D₈	—	52	2	no	—
65	M₁₆	—	52	1	no	—
66	C₂×C₈	—	26	1	no	—
67	C₂²⋊C₄	—	52	1	no	—
68	C₂²⋊C₄	—	52	1	no	—
69	C₄²	C₂×#261	1	1	yes	characteristic
70	C₁₃	#1406	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	4	1	no	—
72	C₂³	—	26	1	no	—
73	Q₈	—	52	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	2	no	—
77	D₄	—	52	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	26	1	no	—
80	C₂×C₄	—	104	1	no	—
81	C₂×C₄	C₂²⋊#261	1	1	yes	characteristic
82	C₈	—	26	2	no	—
83	C₈	—	104	1	no	—
84	C₂²	—	8	2	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	52	1	no	—
87	C₂²	—	104	1	no	—
88	C₂²	#88119	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	52	1	no	—
92	C₄	—	208	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	16	1	no	—
95	C₂	—	104	1	no	—
96	C₂	#11718294	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11718294
commutator	C₄²×C₁₃	C₂×C₄
Frattini	C₄²	C₂×#261
Fitting	C₁₃×#127	C₄
socle	C₂×C₁₃	#353
prime radical	#11718735	C₂
cosocle	#88129	C₂²
hypercenter	#127	#261
hypocenter	C₁₃	#1406
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
2. #11718228	C₂	semidirect
3. #11718226	C₂	semidirect
4. C₁₃×#127	C₄	semidirect
10. #88043	C₄	semidirect
50. #127	#261	semidirect
70. C₁₃	#1406	semidirect

Maximal subgroups

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

subgroup	index
#11718735	2
#11718228	2
#11718226	2
#1406	13