Subgroups — #14643178

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	2	yes	maximal
2	#13066445	C₂	1	4	yes	maximal, complemented
3	C₄×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#117	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₄×C₁₁×C₄⋊C₄	—	2	2	no	—
7	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
8	C₁₁×#376	C₂²	1	2	yes	—
9	C₄³×C₁₁	C₄	1	2	yes	—
10	#10622820	—	2	2	no	—
11	#10622539	—	2	2	no	—
12	#10622539	—	2	2	no	—
13	#10622538	C₄	1	4	yes	complemented
14	#10622538	C₂²	1	4	yes	—
15	#10622537	—	2	2	no	—
16	C₄×#4318	C₄	1	4	yes	complemented
17	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₁	D₄	1	2	yes	—
19	C₁₁×#117	—	2	8	no	—
20	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
21	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
22	C₂×C₄²×C₁₁	—	2	4	no	—
23	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₁	D₄	1	2	yes	—
30	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₂×#4318	—	2	4	no	—
34	C₁₁×#95	—	2	4	no	—
35	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
36	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
37	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
38	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
39	#66867	—	2	4	no	—
40	C₄×C₁₁⋊C₈	C₂×C₄	1	8	yes	—
41	#7856	—	11	1	no	maximal, Sylow
42	C₂⁴×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	—	2	4	no	—
44	C₂²×C₄×C₁₁	—	2	4	no	—
45	C₂²×C₄×C₁₁	—	4	4	no	—
46	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
58	C₁₁×C₄⋊C₄	—	2	8	no	—
59	C₁₁×C₂²⋊C₄	—	2	8	no	—
60	C₄²×C₁₁	—	2	4	no	—
61	C₄²×C₁₁	—	4	8	no	—
62	C₄²×C₁₁	C₄²	1	2	yes	—
63	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
66	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₁	M₁₆	1	8	yes	complemented
70	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
71	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
73	#4318	—	4	8	no	—
74	C₂×C₁₁⋊C₈	—	2	8	no	—
75	#2920	—	11	2	no	—
76	C₄×#117	D₁₁	1	1	yes	characteristic
77	#1274	—	11	4	no	—
78	C₂³×C₁₁	—	2	2	no	—
79	C₂³×C₁₁	—	4	2	no	—
80	C₂³×C₁₁	#95	1	1	yes	characteristic
81	C₂³×C₁₁	#95	1	1	yes	characteristic
82	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	2	4	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	8	no	—
92	C₂×C₄×C₁₁	—	4	2	no	—
93	C₂×C₄×C₁₁	—	4	2	no	—
94	C₂×C₄×C₁₁	—	4	2	no	—
95	C₂×C₄×C₁₁	—	4	8	no	—
96	C₂×C₄×C₁₁	#95	1	2	yes	—
97	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
99	C₂×C₄×C₁₁	#95	1	2	yes	—
100	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
103	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
105	C₁₁⋊C₈	—	4	8	no	—
106	C₂×#117	Dic₁₁	1	2	yes	—
107	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
108	#432	—	22	2	no	—
109	#432	—	22	2	no	—
110	#431	—	11	4	no	—
111	#431	—	11	4	no	—
112	#423	—	22	2	no	—
113	#407	—	22	2	no	—
114	C₄×M₁₆	—	11	4	no	—
115	C₄×C₄⋊C₄	—	2	2	no	—
116	C₄×C₂²⋊C₄	—	2	2	no	—
117	#376	C₂×D₁₁	1	2	yes	—
118	C₄³	Dic₁₁	1	2	yes	—
119	C₂²×C₁₁	—	2	2	no	—
120	C₂²×C₁₁	—	2	1	no	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	2	no	—
123	C₂²×C₁₁	—	2	2	no	—
124	C₂²×C₁₁	—	4	4	no	—
125	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
126	C₂²×C₁₁	#407	1	2	yes	—
127	C₄×C₁₁	—	2	1	no	—
128	C₄×C₁₁	—	2	1	no	—
129	C₄×C₁₁	—	2	2	no	—
130	C₄×C₁₁	—	2	2	no	—
131	C₄×C₁₁	—	2	2	no	—
132	C₄×C₁₁	—	4	8	no	—
133	C₄×C₁₁	H(3,ℤ/4)	1	4	yes	—
134	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
135	C₄×C₁₁	#423	1	2	yes	—
136	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
137	C₂³×C₄	C₂²⋊D₁₁	1	2	yes	—
138	C₂×M₁₆	—	22	4	no	—
139	#117	—	2	8	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₂²⋊C₄	—	2	2	no	—
142	C₂×C₄²	—	2	4	no	—
143	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
144	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
145	C₂×C₄²	C₄×D₁₁	1	2	yes	—
146	C₂×C₄²	C₄×D₁₁	1	2	yes	—
147	C₂×C₄²	D₄₄	1	1	yes	characteristic
148	C₂×C₄²	D₄₄	1	1	yes	characteristic
149	C₂×C₄²	C₂×Dic₁₁	1	4	yes	—
150	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
151	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
152	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
153	C₄⋊C₈	—	22	4	no	—
154	C₄⋊C₈	—	22	4	no	—
155	C₂²⋊C₈	—	22	4	no	—
156	C₂²⋊C₈	—	22	4	no	—
157	#97	—	22	4	no	—
158	C₄×C₈	—	11	8	no	—
159	#95	—	2	4	no	—
160	C₂×C₁₁	—	2	2	no	—
161	C₂×C₁₁	—	4	1	no	—
162	C₂×C₁₁	—	4	1	no	—
163	C₂×C₁₁	#1728	1	1	yes	characteristic
164	C₂×C₁₁	C₂×H(3,ℤ/4)	1	2	yes	—
165	C₂⁴	C₂²⋊Dic₁₁	1	1	yes	characteristic
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	4	4	no	—
169	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
171	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
172	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
173	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
174	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
175	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
176	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
177	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
178	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
179	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₁₁	1	2	yes	—
181	M₁₆	—	44	8	no	—
182	C₂×C₈	—	22	8	no	—
183	C₄⋊C₄	—	2	8	no	—
184	C₂²⋊C₄	—	2	8	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	4	8	no	—
187	C₄²	#4318	1	8	yes	complemented
188	C₄²	C₄×Dic₁₁	1	2	yes	—
189	C₄²	Dic₁₁⋊C₄	1	2	yes	—
190	C₄²	Dic₁₁⋊C₄	1	2	yes	—
191	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
192	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
193	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
194	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
195	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
196	C₄²	C₂×C₄×D₁₁	1	2	yes	—
197	C₄²	C₂×D₄₄	1	1	yes	characteristic
198	C₁₁	#7856	1	1	yes	characteristic, complemented, Sylow
199	C₂³	—	2	2	no	—
200	C₂³	—	4	2	no	—
201	C₂³	C₁₁⋊#95	1	1	yes	characteristic
202	C₂³	C₁₁⋊#95	1	1	yes	characteristic
203	C₂³	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	2	8	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	8	no	—
217	C₂×C₄	C₁₁⋊#95	1	2	yes	—
218	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
219	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
220	C₂×C₄	C₁₁⋊#95	1	2	yes	—
221	C₂×C₄	C₂×#4318	1	4	yes	—
222	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
223	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
224	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
225	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	2	yes	—
226	C₈	—	44	8	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	2	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	4	4	no	—
233	C₂²	#10622820	1	2	yes	—
234	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	2	2	no	—
240	C₄	—	4	8	no	—
241	C₄	#10622169	1	4	yes	—
242	C₄	C₄×#4318	1	2	yes	—
243	C₄	#10622537	1	2	yes	—
244	C₂	—	2	2	no	—
245	C₂	—	4	1	no	—
246	C₂	—	4	1	no	—
247	C₂	#13068310	1	1	yes	characteristic
248	C₂	C₂×#10622169	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₁
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₄×C₁₁×#117	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄×#117	D₁₁
hypocenter	C₁₁	#7856
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
2. #13066445	C₂	semidirect
13. #10622538	C₄	semidirect
16. C₄×#4318	C₄	semidirect
69. C₄²×C₁₁	M₁₆	semidirect
187. C₄²	#4318	semidirect
198. C₁₁	#7856	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
#13066445	2
C₄×C₁₁×#117	2
#7856	11