Subgroups — #14668487

Order 2816.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070868	C₂	1	4	yes	maximal
2	#13068234	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1713	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#500	—	2	2	no	—
6	C₁₁×#494	C₂²	1	2	yes	—
7	C₂×#66893	—	2	8	no	—
8	#10622312	C₂²	1	2	yes	—
9	#10622295	—	2	2	no	—
10	C₈²×C₁₁	C₂²	1	1	yes	characteristic
11	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
12	C₂×C₁₁×Q₁₆	—	2	4	no	—
13	C₁₁×C₄⋊Q₈	—	2	2	no	—
14	C₂×Dic₄₄	—	2	4	no	—
15	#66922	—	2	2	no	—
16	C₁₁×#107	—	4	4	no	—
17	C₄×C₈×C₁₁	D₄	1	2	yes	—
18	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	#66893	—	4	16	no	—
20	#66882	—	4	4	no	—
21	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	—
22	#12516	—	11	1	no	maximal, Sylow
23	C₂×Q₈×C₁₁	—	4	2	no	—
24	C₂×Dic₂₂	—	4	2	no	—
25	C₁₁×Q₁₆	—	4	8	no	—
26	C₂×C₈×C₁₁	D₈	1	4	yes	—
27	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
28	C₁₁×C₄⋊C₄	—	4	4	no	—
29	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₄⋊Dic₁₁	—	4	4	no	—
31	Dic₄₄	—	4	8	no	—
32	C₁₁⋊C₁₆	D₈	1	8	yes	—
33	#2247	—	11	4	no	—
34	#1713	—	11	1	no	—
35	#1713	D₁₁	1	1	yes	characteristic
36	C₈×C₁₆	—	11	1	no	—
37	Q₈×C₁₁	—	8	4	no	—
38	C₂×C₄×C₁₁	—	8	2	no	—
39	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
40	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
41	C₂×Dic₁₁	—	8	2	no	—
42	Dic₂₂	—	8	4	no	—
43	C₈×C₁₁	Q₃₂	1	8	yes	complemented
44	C₈×C₁₁	C₂×D₈	1	4	yes	—
45	C₂×Q₃₂	—	22	8	no	—
46	#500	—	2	2	no	—
47	#500	—	22	2	no	—
48	#494	—	11	2	no	—
49	#494	C₂×D₁₁	1	2	yes	—
50	C₄×C₁₆	—	11	2	no	—
51	C₈²	C₂×D₁₁	1	1	yes	characteristic
52	C₂²×C₁₁	#493	1	1	yes	characteristic
53	C₄×C₁₁	—	16	2	no	—
54	C₄×C₁₁	#493	1	2	yes	—
55	C₄×C₁₁	C₂×Q₃₂	1	4	yes	—
56	Dic₁₁	—	16	2	no	—
57	C₂×Q₁₆	—	2	4	no	—
58	C₂×Q₁₆	—	22	4	no	—
59	C₄⋊Q₈	—	2	2	no	—
60	C₄⋊Q₈	—	22	2	no	—
61	Q₃₂	—	44	16	no	—
62	C₂×C₁₆	—	11	4	no	—
63	#107	—	4	4	no	—
64	#107	—	44	4	no	—
65	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
66	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
67	C₂×C₁₁	#1712	1	1	yes	characteristic
68	C₂×C₁₁	#2247	1	2	yes	—
69	C₂×Q₈	—	4	2	no	—
70	C₂×Q₈	—	44	2	no	—
71	Q₁₆	—	4	8	no	—
72	Q₁₆	—	44	8	no	—
73	C₂×C₈	#4323	1	4	yes	—
74	C₂×C₈	D₄×D₁₁	1	2	yes	—
75	C₄⋊C₄	—	4	4	no	—
76	C₄⋊C₄	—	44	4	no	—
77	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
78	C₁₆	—	11	8	no	—
79	C₁₁	#12516	1	1	yes	characteristic, complemented, Sylow
80	Q₈	—	8	4	no	—
81	Q₈	—	88	4	no	—
82	C₂×C₄	—	8	2	no	—
83	C₂×C₄	—	88	2	no	—
84	C₂×C₄	C₂×#4323	1	2	yes	—
85	C₂×C₄	#66993	1	1	yes	characteristic
86	C₈	#66893	1	8	yes	complemented
87	C₈	D₈×D₁₁	1	4	yes	—
88	C₂²	#10622686	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	176	2	no	—
91	C₄	#10622764	1	2	yes	—
92	C₄	C₂×#66893	1	4	yes	—
93	C₂	#13068230	1	1	yes	characteristic
94	C₂	#13070868	1	2	yes	—

	subgroup	G/H
center	C₂²	#10622686
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1713	C₂
socle, prime radical	C₂²×C₁₁	#493
hypercenter	#1713	D₁₁
hypocenter	C₁₁	#12516
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1713

Complements

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

N	H ≅ G/N	type
43. C₈×C₁₁	Q₃₂	semidirect
79. C₁₁	#12516	semidirect
86. C₈	#66893	semidirect

Maximal subgroups

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

subgroup	index
#13070868	2
#13068234	2
C₈×C₁₁⋊C₁₆	2
C₁₁×#1713	2
#12516	11