Subgroups — #14907186

Order 2816.

652 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622809	C₂	1	2	yes	maximal, complemented
2	#13070502	C₂	1	4	yes	maximal, complemented
3	#13070497	C₂	1	4	yes	maximal, complemented
4	#13070411	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070344	C₂	1	2	yes	maximal, complemented
6	M₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#3414	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×#135	C₂²	1	2	yes	—
9	C₂×#67001	—	2	2	no	—
10	C₁₁×#510	C₄	1	4	yes	complemented
11	C₁₁×#509	C₄	1	4	yes	complemented
12	C₁₁×#508	C₂²	1	4	yes	—
13	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
14	C₂×#66901	—	2	2	no	—
15	#10622809	—	2	2	no	—
16	#10622809	—	2	2	no	—
17	#10622809	C₂²	1	4	yes	complemented
18	#10622809	C₂²	1	4	yes	complemented
19	C₂×#66883	C₂²	1	2	yes	—
20	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
21	C₂×#66876	C₂²	1	1	yes	characteristic
22	#10622205	C₂²	1	8	yes	complemented
23	#10622144	C₂²	1	4	yes	complemented
24	#10622140	C₂²	1	2	yes	complemented
25	C₁₆×Dic₁₁	C₂²	1	2	yes	complemented
26	C₂×C₁₁×#41	—	2	2	no	—
27	C₁₁×#135	—	2	2	no	—
28	C₁₁×#135	—	2	2	no	—
29	C₁₁×#135	C₂×C₄	1	4	yes	—
30	C₁₁×#135	C₂³	1	4	yes	—
31	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
32	C₂×C₁₁×SD₁₆	—	2	2	no	—
33	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
35	#67001	—	2	4	no	—
36	#67001	—	2	4	no	—
37	#67001	—	4	2	no	—
38	#67001	—	4	2	no	—
39	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
40	C₂×#4318	—	2	2	no	—
41	C₂×#4318	—	4	2	no	—
42	C₂²×C₁₁⋊C₈	—	4	2	no	—
43	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
44	C₁₁×Q₃₂	C₂×C₄	1	4	yes	complemented
45	C₁₁×SD₃₂	C₂×C₄	1	8	yes	complemented
46	C₁₁×D₁₆	C₂×C₄	1	4	yes	complemented
47	C₁₁×M₃₂	C₂×C₄	1	4	yes	—
48	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
49	#66901	—	2	4	no	—
50	#66901	—	2	4	no	—
51	#66883	—	2	2	no	—
52	#66883	C₂³	1	4	yes	—
53	C₈×Dic₁₁	D₄	1	1	yes	characteristic
54	C₈×Dic₁₁	D₄	1	1	yes	characteristic
55	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
56	C₈×Dic₁₁	C₂³	1	1	yes	characteristic
57	#66876	—	2	2	no	—
58	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
59	#33463	—	11	1	no	maximal, Sylow
60	C₁₁×#41	—	2	4	no	—
61	C₁₁×#41	—	2	4	no	—
62	C₁₁×#41	—	4	2	no	—
63	C₁₁×#41	—	4	2	no	—
64	C₂×Q₈×C₁₁	—	2	2	no	—
65	C₂×D₄×C₁₁	—	2	2	no	—
66	C₂×D₄×C₁₁	—	4	2	no	—
67	C₂²×C₄×C₁₁	—	4	2	no	—
68	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₁₁	—	2	1	no	—
70	C₁₁×Q₁₆	—	2	2	no	—
71	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	—
72	C₁₁×SD₁₆	—	2	4	no	—
73	C₁₁×SD₁₆	—	2	4	no	—
74	C₁₁×D₈	—	2	2	no	—
75	C₁₁×D₈	C₂²×C₄	1	4	yes	—
76	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₈×C₁₁	#41	1	2	yes	—
79	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
80	C₄×Dic₁₁	—	2	1	no	—
81	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
82	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
83	#4318	—	2	4	no	—
84	#4318	—	4	4	no	—
85	#4318	—	4	4	no	—
86	#4318	—	4	2	no	—
87	C₂×C₁₁⋊C₈	—	4	4	no	—
88	C₂×C₁₁⋊C₈	—	4	4	no	—
89	C₂×C₁₁⋊C₈	—	4	2	no	—
90	C₂×C₁₁⋊C₈	D₈	1	2	yes	—
91	C₂×C₁₁⋊C₈	D₈	1	2	yes	—
92	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
93	C₂×C₁₁⋊C₈	C₂×D₄	1	1	yes	characteristic
94	C₁₁×C₁₆	C₂²×C₄	1	4	yes	—
95	C₁₁⋊C₁₆	—	2	2	no	—
96	#3414	D₁₁	1	1	yes	characteristic
97	C₂×#443	—	11	2	no	—
98	#2179	—	11	4	no	—
99	#2178	—	11	4	no	—
100	#2161	—	11	1	no	—
101	#2143	—	11	2	no	—
102	C₄×M₃₂	—	11	1	no	—
103	C₂³×C₁₁	—	4	2	no	—
104	C₂³×C₁₁	#135	1	1	yes	characteristic
105	Q₈×C₁₁	—	2	4	no	—
106	Q₈×C₁₁	—	4	2	no	—
107	D₄×C₁₁	—	2	4	no	—
108	D₄×C₁₁	—	4	4	no	—
109	D₄×C₁₁	—	4	4	no	—
110	D₄×C₁₁	—	4	2	no	—
111	C₂×C₄×C₁₁	—	4	2	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	—	4	4	no	—
114	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
115	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
116	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
118	C₂×Dic₁₁	—	2	1	no	—
119	C₂×Dic₁₁	—	2	1	no	—
120	C₂×Dic₁₁	—	4	2	no	—
121	C₈×C₁₁	C₄×D₄	1	2	yes	—
122	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
123	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
124	C₁₁⋊C₈	—	4	4	no	—
125	C₁₁⋊C₈	C₂×D₈	1	1	yes	characteristic
126	C₁₁⋊C₈	C₂×D₈	1	2	yes	—
127	C₁₁⋊C₈	C₂×D₈	1	1	yes	characteristic
128	C₂×#135	C₂×D₁₁	1	2	yes	—
129	C₂×#131	—	22	2	no	—
130	#510	Dic₁₁	1	4	yes	complemented
131	#509	Dic₁₁	1	4	yes	complemented
132	#508	C₂×D₁₁	1	4	yes	—
133	C₂×M₃₂	—	11	1	no	—
134	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
135	#443	—	11	4	no	—
136	#443	—	11	4	no	—
137	#443	—	22	2	no	—
138	#443	—	22	2	no	—
139	C₂×#108	—	11	2	no	—
140	C₂×#104	—	22	2	no	—
141	C₂×C₄×C₈	—	11	1	no	—
142	#368	—	11	4	no	—
143	#359	—	11	8	no	—
144	#346	—	11	2	no	—
145	C₄×C₁₆	—	11	2	no	—
146	C₂²×C₁₁	—	4	1	no	—
147	C₂²×C₁₁	—	4	4	no	—
148	C₂²×C₁₁	—	8	4	no	—
149	C₂²×C₁₁	C₄×D₈	1	2	yes	—
150	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
151	C₄×C₁₁	—	4	4	no	—
152	C₄×C₁₁	C₄×D₈	1	2	yes	—
153	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
154	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
155	Dic₁₁	—	2	2	no	—
156	Dic₁₁	—	4	1	no	—
157	C₂×#41	—	2	2	no	—
158	#135	—	2	2	no	—
159	#135	—	2	2	no	—
160	#135	C₂×Dic₁₁	1	4	yes	—
161	#135	C₂²×D₁₁	1	4	yes	—
162	C₂×Q₁₆	C₂×Dic₁₁	1	2	yes	—
163	C₂×SD₁₆	—	2	2	no	—
164	C₂×D₈	C₂×Dic₁₁	1	2	yes	—
165	#131	—	22	4	no	—
166	#131	—	22	4	no	—
167	#131	—	44	2	no	—
168	#131	—	44	2	no	—
169	C₂×M₁₆	—	22	2	no	—
170	C₂×M₁₆	—	44	2	no	—
171	C₂²×C₈	—	11	1	no	—
172	C₂²×C₈	—	44	2	no	—
173	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
174	C₂×C₄²	—	11	1	no	—
175	Q₃₂	C₂×Dic₁₁	1	4	yes	complemented
176	SD₃₂	C₂×Dic₁₁	1	8	yes	complemented
177	D₁₆	C₂×Dic₁₁	1	4	yes	complemented
178	M₃₂	—	22	2	no	—
179	M₃₂	C₂×Dic₁₁	1	4	yes	—
180	C₂×C₁₆	—	11	2	no	—
181	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
182	#108	—	11	4	no	—
183	#108	—	22	2	no	—
184	#104	—	22	4	no	—
185	#104	—	22	4	no	—
186	C₄×C₈	—	11	1	no	—
187	C₄×C₈	—	11	1	no	—
188	C₄×C₈	—	11	1	no	—
189	C₄×C₈	—	11	1	no	—
190	C₂×C₁₁	—	2	1	no	—
191	C₂×C₁₁	—	2	2	no	—
192	C₂×C₁₁	—	8	4	no	—
193	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
194	#41	—	2	4	no	—
195	#41	—	2	4	no	—
196	#41	—	4	2	no	—
197	#41	—	4	2	no	—
198	C₂×Q₈	—	2	2	no	—
199	C₂×D₄	—	2	2	no	—
200	C₂×D₄	—	4	2	no	—
201	C₂²×C₄	—	4	2	no	—
202	C₂²×C₄	—	22	1	no	—
203	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
204	Q₁₆	—	2	2	no	—
205	Q₁₆	C₂²×Dic₁₁	1	4	yes	—
206	SD₁₆	—	2	4	no	—
207	SD₁₆	—	2	4	no	—
208	D₈	—	2	2	no	—
209	D₈	C₂²×Dic₁₁	1	4	yes	—
210	M₁₆	—	22	4	no	—
211	M₁₆	—	44	4	no	—
212	M₁₆	—	44	4	no	—
213	M₁₆	—	44	2	no	—
214	C₂×C₈	—	11	2	no	—
215	C₂×C₈	—	11	2	no	—
216	C₂×C₈	—	11	1	no	—
217	C₂×C₈	—	11	1	no	—
218	C₂×C₈	—	44	4	no	—
219	C₂×C₈	—	44	4	no	—
220	C₂×C₈	—	44	2	no	—
221	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
222	C₂×C₈	#4341	1	2	yes	—
223	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
224	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
225	C₄²	—	11	1	no	—
226	C₄²	—	11	1	no	—
227	C₄²	—	22	1	no	—
228	C₁₆	—	22	2	no	—
229	C₁₆	C₂²×Dic₁₁	1	4	yes	—
230	C₁₁	#33463	1	1	yes	characteristic, complemented, Sylow
231	C₂³	—	4	2	no	—
232	C₂³	#66965	1	1	yes	characteristic
233	Q₈	—	2	4	no	—
234	Q₈	—	4	2	no	—
235	D₄	—	2	4	no	—
236	D₄	—	4	4	no	—
237	D₄	—	4	4	no	—
238	D₄	—	4	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	4	4	no	—
241	C₂×C₄	—	4	4	no	—
242	C₂×C₄	—	22	1	no	—
243	C₂×C₄	—	22	1	no	—
244	C₂×C₄	—	44	2	no	—
245	C₂×C₄	D₈×D₁₁	1	2	yes	—
246	C₂×C₄	#66965	1	1	yes	characteristic
247	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
248	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
249	C₈	—	11	1	no	—
250	C₈	—	11	2	no	—
251	C₈	—	11	1	no	—
252	C₈	—	44	4	no	—
253	C₈	D₄×Dic₁₁	1	2	yes	—
254	C₈	C₂×#4341	1	1	yes	characteristic
255	C₈	C₂³×Dic₁₁	1	1	yes	characteristic
256	C₂²	—	4	1	no	—
257	C₂²	—	4	4	no	—
258	C₂²	—	8	4	no	—
259	C₂²	D₈×Dic₁₁	1	2	yes	—
260	C₂²	C₂×#66965	1	1	yes	characteristic
261	C₄	—	4	4	no	—
262	C₄	—	22	2	no	—
263	C₄	—	44	1	no	—
264	C₄	D₈×Dic₁₁	1	2	yes	—
265	C₄	C₂×D₈×D₁₁	1	1	yes	characteristic
266	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
267	C₂	—	2	1	no	—
268	C₂	—	2	2	no	—
269	C₂	—	8	4	no	—
270	C₂	C₂×D₈×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₁₁
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting, prime radical	C₁₁×#3414	C₂
socle	C₂×C₁₁	C₂×C₄×D₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#3414	D₁₁
hypocenter	C₁₁	#33463
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #3414

Complements

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

N	H ≅ G/N	type
1. C₂×#10622809	C₂	semidirect
2. #13070502	C₂	semidirect
3. #13070497	C₂	semidirect
4. #13070411	C₂	semidirect
5. #13070344	C₂	semidirect
6. M₃₂×Dic₁₁	C₂	semidirect
10. C₁₁×#510	C₄	semidirect
11. C₁₁×#509	C₄	semidirect
17. #10622809	C₂²	semidirect
18. #10622809	C₂²	semidirect
22. #10622205	C₂²	semidirect
23. #10622144	C₂²	semidirect
24. #10622140	C₂²	semidirect
25. C₁₆×Dic₁₁	C₂²	semidirect
44. C₁₁×Q₃₂	C₂×C₄	semidirect
45. C₁₁×SD₃₂	C₂×C₄	semidirect
46. C₁₁×D₁₆	C₂×C₄	semidirect
130. #510	Dic₁₁	semidirect
131. #509	Dic₁₁	semidirect
175. Q₃₂	C₂×Dic₁₁	semidirect
176. SD₃₂	C₂×Dic₁₁	semidirect
177. D₁₆	C₂×Dic₁₁	semidirect
230. C₁₁	#33463	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622809	2
#13070502	2
#13070497	2
#13070411	2
#13070344	2
M₃₂×Dic₁₁	2
C₁₁×#3414	2
#33463	11