Subgroups — #14647520

Order 2816.

418 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068733	C₂	1	1	yes	maximal, characteristic
2	C₄×#66867	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622117	C₂	1	2	yes	maximal
4	C₂×#10622118	C₂	1	2	yes	maximal
5	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
7	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
8	C₄³×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#66867	C₄	1	1	yes	characteristic
12	C₂×#66867	C₄	1	2	yes	—
13	C₂×#66867	C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
15	#10622162	—	2	2	no	—
16	#10622118	—	2	4	no	—
17	#10622117	—	2	4	no	—
18	C₂²×C₈×C₁₁	—	2	2	no	—
19	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	D₄	1	2	yes	—
22	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₂²×C₁₁⋊C₈	—	2	1	no	—
25	C₂²×C₁₁⋊C₈	—	2	1	no	—
26	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
27	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
28	C₁₁×C₄⋊C₈	—	2	2	no	—
29	C₁₁×C₄⋊C₈	—	2	2	no	—
30	C₁₁×C₄⋊C₈	—	4	4	no	—
31	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
33	#66867	—	2	2	no	—
34	#66867	—	2	4	no	—
35	#66867	C₈	1	4	yes	complemented
36	C₄×C₁₁⋊C₈	D₄	1	4	yes	—
37	C₄×C₁₁⋊C₈	Q₈	1	4	yes	—
38	#8808	—	11	1	no	maximal, Sylow
39	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₈×C₁₁	—	4	2	no	—
45	C₂×C₈×C₁₁	—	4	4	no	—
46	C₄²×C₁₁	—	2	2	no	—
47	C₄²×C₁₁	—	2	2	no	—
48	C₄²×C₁₁	—	2	2	no	—
49	C₄²×C₁₁	—	4	2	no	—
50	C₄²×C₁₁	C₂×C₈	1	2	yes	—
51	C₄²×C₁₁	M₁₆	1	2	yes	—
52	C₄²×C₁₁	C₂×D₄	1	2	yes	—
53	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
54	C₂×C₁₁⋊C₈	—	2	2	no	—
55	C₂×C₁₁⋊C₈	—	2	2	no	—
56	C₂×C₁₁⋊C₈	—	4	1	no	—
57	C₂×C₁₁⋊C₈	—	4	1	no	—
58	C₂×C₁₁⋊C₈	—	4	2	no	—
59	C₂×C₁₁⋊C₈	—	4	2	no	—
60	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
61	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
62	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
63	C₂×C₁₁⋊C₈	M₁₆	1	4	yes	—
64	#1842	D₁₁	1	1	yes	characteristic
65	#1831	—	11	1	no	—
66	C₄×#97	—	11	1	no	—
67	C₂×#335	—	11	2	no	—
68	C₂×#334	—	11	2	no	—
69	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
77	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
78	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
80	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
84	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
85	C₂×C₄×C₁₁	#137	1	2	yes	—
86	C₈×C₁₁	—	8	2	no	—
87	C₁₁⋊C₈	—	2	4	no	—
88	C₁₁⋊C₈	—	8	1	no	—
89	C₁₁⋊C₈	—	8	1	no	—
90	C₁₁⋊C₈	C₄⋊C₈	1	8	yes	complemented
91	C₂×C₄⋊C₈	—	2	2	no	—
92	C₂×C₄⋊C₈	—	11	1	no	—
93	C₂×C₄⋊C₈	—	11	1	no	—
94	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
95	C₂×#97	—	11	1	no	—
96	C₂×#97	—	11	2	no	—
97	C₂×#97	—	11	1	no	—
98	C₂×C₄×C₈	—	11	2	no	—
99	C₄³	C₂×D₁₁	1	1	yes	characteristic
100	#336	—	22	2	no	—
101	#335	—	22	4	no	—
102	#334	—	22	4	no	—
103	C₂²×C₁₁	#384	1	1	yes	characteristic
104	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
105	C₂²×C₁₁	#423	1	1	yes	characteristic
106	C₂²×C₁₁	#428	1	2	yes	—
107	C₂²×C₁₁	#430	1	2	yes	—
108	C₄×C₁₁	—	2	4	no	—
109	C₄×C₁₁	—	2	2	no	—
110	C₄×C₁₁	—	4	2	no	—
111	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
112	C₄×C₁₁	#423	1	2	yes	—
113	C₄×C₁₁	#496	1	1	yes	characteristic
114	C₄×C₁₁	#497	1	1	yes	characteristic
115	C₄×C₁₁	#501	1	2	yes	—
116	C₂²×C₈	—	2	2	no	—
117	C₂²×C₈	—	11	2	no	—
118	C₂²×C₈	—	11	2	no	—
119	C₂²×C₈	—	22	1	no	—
120	C₂²×C₈	—	22	1	no	—
121	C₂×C₄²	Dic₂₂	1	2	yes	—
122	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
123	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
124	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
125	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
126	C₄⋊C₈	—	2	2	no	—
127	C₄⋊C₈	—	2	2	no	—
128	C₄⋊C₈	—	4	4	no	—
129	C₄⋊C₈	—	22	2	no	—
130	C₄⋊C₈	—	22	2	no	—
131	#97	—	11	4	no	—
132	#97	—	22	4	no	—
133	#97	—	22	2	no	—
134	C₄×C₈	—	11	4	no	—
135	C₄×C₈	—	11	4	no	—
136	C₂×C₁₁	#1565	1	2	yes	—
137	C₂×C₁₁	#1569	1	2	yes	—
138	C₂×C₁₁	#1842	1	1	yes	characteristic
139	C₂×C₁₁	#1847	1	1	yes	characteristic
140	C₂×C₁₁	#1849	1	1	yes	characteristic
141	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
142	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
143	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
144	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
145	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
146	C₂×C₈	—	4	4	no	—
147	C₂×C₈	—	4	2	no	—
148	C₂×C₈	—	11	4	no	—
149	C₂×C₈	—	11	4	no	—
150	C₂×C₈	—	11	4	no	—
151	C₂×C₈	—	11	4	no	—
152	C₂×C₈	—	22	2	no	—
153	C₂×C₈	—	22	2	no	—
154	C₂×C₈	—	44	2	no	—
155	C₂×C₈	—	44	1	no	—
156	C₂×C₈	—	44	1	no	—
157	C₂×C₈	—	44	2	no	—
158	C₄²	—	2	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	4	2	no	—
162	C₄²	C₈×D₁₁	1	2	yes	—
163	C₄²	#4313	1	2	yes	—
164	C₄²	D₄×D₁₁	1	2	yes	—
165	C₄²	Q₈×D₁₁	1	2	yes	—
166	C₁₁	#8808	1	1	yes	characteristic, complemented, Sylow
167	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
175	C₂×C₄	#66941	1	2	yes	—
176	C₂×C₄	C₄⋊C₄×D₁₁	1	2	yes	—
177	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
178	C₂×C₄	C₂×#4313	1	1	yes	characteristic
179	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
180	C₂×C₄	#66985	1	2	yes	—
181	C₂×C₄	#66993	1	1	yes	characteristic
182	C₂×C₄	#66995	1	2	yes	—
183	C₂×C₄	#66997	1	1	yes	characteristic
184	C₈	—	8	2	no	—
185	C₈	—	11	8	no	—
186	C₈	—	22	4	no	—
187	C₈	—	88	1	no	—
188	C₈	—	88	1	no	—
189	C₂²	#10622577	1	2	yes	—
190	C₂²	#10622589	1	1	yes	characteristic
191	C₂²	C₂×Dic₁₁⋊C₈	1	1	yes	characteristic
192	C₂²	#10622731	1	1	yes	characteristic
193	C₂²	#10622737	1	2	yes	—
194	C₄	—	2	4	no	—
195	C₄	—	2	2	no	—
196	C₄	—	4	2	no	—
197	C₄	D₁₁×C₄⋊C₈	1	2	yes	—
198	C₄	#10622450	1	2	yes	—
199	C₄	#10622687	1	1	yes	characteristic
200	C₄	#10622693	1	2	yes	—
201	C₄	#10622699	1	1	yes	characteristic
202	C₂	#13067366	1	2	yes	—
203	C₂	#13067381	1	2	yes	—
204	C₂	#13068767	1	1	yes	characteristic
205	C₂	#13068782	1	1	yes	characteristic
206	C₂	#13068790	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1842	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1842	D₁₁
hypocenter	C₁₁	#8808
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
35. #66867	C₈	semidirect
90. C₁₁⋊C₈	C₄⋊C₈	semidirect
166. C₁₁	#8808	semidirect

Maximal subgroups

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

subgroup	index
#13068733	2
C₄×#66867	2
C₂×#10622117	2
C₂×#10622118	2
C₁₁×#1842	2
#8808	11