Subgroups — #14665337

Order 2816.

220 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622101	C₂	1	1	yes	maximal, characteristic
2	C₄×#66876	C₂	1	1	yes	maximal, characteristic
3	#13066683	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×M₃₂	—	2	1	no	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#66876	—	2	1	no	—
8	C₂×#66876	C₄	1	1	yes	characteristic
9	C₂×#66876	C₄	1	1	yes	characteristic
10	C₁₁×#364	—	2	1	no	—
11	C₁₁×#364	C₂²	1	2	yes	—
12	#10622101	—	2	1	no	—
13	#10622101	C₂²	1	2	yes	—
14	#10622099	C₂²	1	2	yes	—
15	C₄×C₁₁⋊C₁₆	C₄	1	2	yes	—
16	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
19	C₁₁×M₃₂	—	2	2	no	—
20	C₁₁×M₃₂	—	4	1	no	—
21	C₂×C₁₁×C₁₆	—	4	1	no	—
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	#66876	—	2	1	no	—
27	#66876	—	2	1	no	—
28	#66876	—	2	2	no	—
29	#66876	—	4	1	no	—
30	#66876	C₈	1	2	yes	—
31	#66876	C₈	1	2	yes	—
32	C₂×C₁₁⋊C₁₆	—	4	1	no	—
33	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
34	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
35	#12002	—	11	1	no	maximal, Sylow
36	C₂²×C₄×C₁₁	—	2	1	no	—
37	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
43	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₄²×C₁₁	—	2	1	no	—
51	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
53	C₁₁×C₁₆	—	4	2	no	—
54	C₁₁⋊C₁₆	—	2	2	no	—
55	C₁₁⋊C₁₆	—	4	2	no	—
56	C₁₁⋊C₁₆	C₂×C₈	1	4	yes	—
57	C₂×#364	—	11	1	no	—
58	C₂×#364	D₁₁	1	1	yes	characteristic
59	C₄×M₃₂	—	11	1	no	—
60	#1369	—	11	4	no	—
61	C₂³×C₁₁	#108	1	1	yes	characteristic
62	C₂×C₄×C₁₁	—	2	1	no	—
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	4	2	no	—
65	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
72	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
73	C₈×C₁₁	#106	1	1	yes	characteristic
74	C₈×C₁₁	#106	1	1	yes	characteristic
75	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
76	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
77	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
78	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×M₃₂	—	2	1	no	—
80	C₂×M₃₂	—	11	1	no	—
81	C₂×M₃₂	—	11	1	no	—
82	C₂×M₃₂	—	22	1	no	—
83	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
84	#364	—	2	1	no	—
85	#364	—	11	2	no	—
86	#364	—	22	1	no	—
87	#364	C₂×D₁₁	1	2	yes	—
88	#346	—	11	2	no	—
89	C₄×C₁₆	—	11	2	no	—
90	C₂²×C₁₁	—	4	1	no	—
91	C₂²×C₁₁	#334	1	1	yes	characteristic
92	C₂²×C₁₁	#334	1	1	yes	characteristic
93	C₂²×C₁₁	C₂×#108	1	1	yes	characteristic
94	C₄×C₁₁	—	2	2	no	—
95	C₄×C₁₁	—	4	1	no	—
96	C₄×C₁₁	#334	1	1	yes	characteristic
97	C₄×C₁₁	#334	1	1	yes	characteristic
98	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
99	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
100	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
101	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
102	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
103	M₃₂	—	2	2	no	—
104	M₃₂	—	4	1	no	—
105	M₃₂	—	11	2	no	—
106	M₃₂	—	11	2	no	—
107	M₃₂	—	22	1	no	—
108	M₃₂	—	22	1	no	—
109	M₃₂	—	22	2	no	—
110	M₃₂	—	44	1	no	—
111	C₂×C₁₆	—	4	1	no	—
112	C₂×C₁₆	—	11	2	no	—
113	C₂×C₁₆	—	11	2	no	—
114	C₂×C₁₆	—	44	1	no	—
115	C₄×C₈	Dic₂₂	1	1	yes	characteristic
116	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
117	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
119	C₂×C₁₁	—	2	1	no	—
120	C₂×C₁₁	—	2	1	no	—
121	C₂×C₁₁	—	2	1	no	—
122	C₂×C₁₁	C₂×#334	1	1	yes	characteristic
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
126	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
127	C₂×C₈	#4313	1	1	yes	characteristic
128	C₂×C₈	#4313	1	1	yes	characteristic
129	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
130	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
131	C₂×C₈	#4324	1	1	yes	characteristic
132	C₂×C₈	#4324	1	1	yes	characteristic
133	C₂×C₈	#4325	1	1	yes	characteristic
134	C₂×C₈	#4325	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
136	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
137	C₄²	—	2	1	no	—
138	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
139	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
140	C₁₆	—	4	2	no	—
141	C₁₆	—	11	4	no	—
142	C₁₆	—	22	2	no	—
143	C₁₆	—	44	2	no	—
144	C₁₁	#12002	1	1	yes	characteristic, complemented, Sylow
145	C₂³	#66886	1	1	yes	characteristic
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	#66872	1	1	yes	characteristic
150	C₂×C₄	#66872	1	1	yes	characteristic
151	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
152	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
153	C₂×C₄	#66886	1	1	yes	characteristic
154	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
155	C₈	#66872	1	1	yes	characteristic
156	C₈	#66872	1	1	yes	characteristic
157	C₈	Dic₁₁⋊C₈	1	1	yes	characteristic
158	C₈	Dic₁₁⋊C₈	1	1	yes	characteristic
159	C₈	C₂×C₈×D₁₁	1	1	yes	characteristic
160	C₈	C₂×#4313	1	1	yes	characteristic
161	C₈	C₂×#4324	1	1	yes	characteristic
162	C₈	C₂×#4325	1	1	yes	characteristic
163	C₂²	—	4	1	no	—
164	C₂²	#10622118	1	1	yes	characteristic
165	C₂²	#10622118	1	1	yes	characteristic
166	C₂²	C₂×#66886	1	1	yes	characteristic
167	C₄	—	2	2	no	—
168	C₄	—	4	1	no	—
169	C₄	#10622118	1	1	yes	characteristic
170	C₄	#10622118	1	1	yes	characteristic
171	C₄	C₂×#66872	1	1	yes	characteristic
172	C₄	C₂×Dic₁₁⋊C₈	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	—	2	1	no	—
176	C₂	C₂×#10622118	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66872
commutator	C₈×C₁₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#364	C₂
socle	C₂×C₁₁	C₂×#334
prime radical	C₂³×C₁₁	#108
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×#364	D₁₁
hypocenter	C₁₁	#12002
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
3. #13066683	C₂	semidirect
144. C₁₁	#12002	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622101	2
C₄×#66876	2
#13066683	2
C₂×C₁₁×#364	2
#12002	11