Subgroups — #14722917

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622538	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622537	C₂	1	1	yes	maximal, characteristic
3	#13067388	C₂	1	4	yes	maximal, complemented
4	#13067386	C₂	1	4	yes	maximal, complemented
5	#13067371	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×M₁₆	—	2	1	no	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²×#4318	—	2	1	no	—
10	C₁₁×#423	—	2	1	no	—
11	C₁₁×#423	—	2	1	no	—
12	C₁₁×#423	C₂²	1	2	yes	—
13	C₁₁×#423	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
17	#10622538	C₄	1	2	yes	—
18	#10622538	C₄	1	2	yes	—
19	#10622538	C₂²	1	2	yes	—
20	#10622538	C₂²	1	2	yes	—
21	#10622537	—	2	1	no	—
22	#10622537	—	2	1	no	—
23	#10622537	C₂²	1	2	yes	—
24	#10622537	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
26	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
27	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
28	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
29	#10622118	C₂²	1	16	yes	complemented
30	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
33	C₂×C₁₁×M₁₆	—	2	2	no	—
34	C₂×C₁₁×M₁₆	—	2	2	no	—
35	C₂×C₁₁×M₁₆	—	4	4	no	—
36	C₂²×C₈×C₁₁	—	2	2	no	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	C₂×#4318	—	2	2	no	—
50	C₂×#4318	—	2	2	no	—
51	C₂×#4318	—	4	4	no	—
52	C₂²×C₁₁⋊C₈	—	2	2	no	—
53	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
54	C₁₁×C₄⋊C₈	—	2	2	no	—
55	C₁₁×C₄⋊C₈	—	2	2	no	—
56	C₁₁×C₄⋊C₈	—	2	2	no	—
57	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
58	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
59	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
60	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
61	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
62	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
63	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
64	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
65	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
66	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
67	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
68	#17813	—	11	1	no	maximal, Sylow
69	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	—	4	2	no	—
71	C₂²×C₄×C₁₁	—	4	2	no	—
72	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	SD₁₆	1	4	yes	—
82	C₂²×C₄×C₁₁	SD₁₆	1	4	yes	—
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
92	C₁₁×M₁₆	—	4	4	no	—
93	C₁₁×M₁₆	—	4	4	no	—
94	C₂×C₈×C₁₁	—	2	4	no	—
95	C₂×C₈×C₁₁	—	4	4	no	—
96	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
109	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
110	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
112	#4318	—	4	4	no	—
113	#4318	—	4	4	no	—
114	C₂×C₁₁⋊C₈	—	2	4	no	—
115	C₂×C₁₁⋊C₈	—	4	4	no	—
116	C₂×C₁₁⋊C₈	—	4	4	no	—
117	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
118	C₂×#431	—	11	1	no	—
119	C₂×#423	—	11	1	no	—
120	C₂×#423	D₁₁	1	1	yes	characteristic
121	#1570	—	11	4	no	—
122	#1570	—	11	4	no	—
123	#1566	—	11	4	no	—
124	C₂³×C₁₁	—	4	1	no	—
125	C₂³×C₁₁	—	4	1	no	—
126	C₂³×C₁₁	#106	1	4	yes	—
127	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	4	1	no	—
137	C₂×C₄×C₁₁	—	4	1	no	—
138	C₂×C₄×C₁₁	—	4	1	no	—
139	C₂×C₄×C₁₁	—	4	1	no	—
140	C₂×C₄×C₁₁	—	4	1	no	—
141	C₂×C₄×C₁₁	—	4	1	no	—
142	C₂×C₄×C₁₁	#106	1	4	yes	—
143	C₂×C₄×C₁₁	#106	1	4	yes	—
144	C₂×C₄×C₁₁	#106	1	4	yes	—
145	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
155	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
156	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
163	C₈×C₁₁	—	4	4	no	—
164	C₁₁⋊C₈	—	2	8	no	—
165	C₁₁⋊C₈	—	4	4	no	—
166	C₂²×M₁₆	—	2	1	no	—
167	C₂²×M₁₆	—	22	1	no	—
168	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
169	#431	—	11	2	no	—
170	#431	—	11	2	no	—
171	#431	—	11	2	no	—
172	#431	—	11	2	no	—
173	#423	—	2	1	no	—
174	#423	—	2	1	no	—
175	#423	—	11	2	no	—
176	#423	—	11	2	no	—
177	#423	—	22	1	no	—
178	#423	—	22	1	no	—
179	#423	C₂×D₁₁	1	2	yes	—
180	#423	C₂×D₁₁	1	2	yes	—
181	C₂×C₄⋊C₈	—	2	1	no	—
182	C₂×C₄⋊C₈	—	11	2	no	—
183	C₂×C₄⋊C₈	—	11	2	no	—
184	C₂×C₄⋊C₈	—	22	1	no	—
185	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
186	C₂×C₂²⋊C₈	—	11	2	no	—
187	C₂×C₄×C₈	—	11	2	no	—
188	#334	—	11	16	no	—
189	C₂²×C₁₁	—	2	1	no	—
190	C₂²×C₁₁	—	2	1	no	—
191	C₂²×C₁₁	—	2	1	no	—
192	C₂²×C₁₁	—	2	1	no	—
193	C₂²×C₁₁	—	2	1	no	—
194	C₂²×C₁₁	—	2	1	no	—
195	C₂²×C₁₁	—	4	4	no	—
196	C₂²×C₁₁	C₂×#106	1	2	yes	—
197	C₂²×C₁₁	C₂×#106	1	2	yes	—
198	C₂²×C₁₁	C₂×#106	1	2	yes	—
199	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₄×C₁₁	—	2	1	no	—
201	C₄×C₁₁	—	2	1	no	—
202	C₄×C₁₁	—	2	1	no	—
203	C₄×C₁₁	—	2	1	no	—
204	C₄×C₁₁	—	2	1	no	—
205	C₄×C₁₁	—	2	1	no	—
206	C₄×C₁₁	C₂×#106	1	2	yes	—
207	C₄×C₁₁	C₂×#106	1	2	yes	—
208	C₄×C₁₁	C₂×#106	1	2	yes	—
209	C₄×C₁₁	#430	1	2	yes	—
210	C₄×C₁₁	#568	1	2	yes	—
211	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
212	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
213	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
214	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	4	4	no	—
219	C₂×M₁₆	—	22	2	no	—
220	C₂×M₁₆	—	22	2	no	—
221	C₂×M₁₆	—	44	4	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	11	4	no	—
224	C₂²×C₈	—	22	2	no	—
225	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
226	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
227	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
229	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	11	4	no	—
241	C₄⋊C₈	—	11	4	no	—
242	C₄⋊C₈	—	11	4	no	—
243	C₄⋊C₈	—	22	2	no	—
244	C₄⋊C₈	—	22	2	no	—
245	C₄⋊C₈	—	22	2	no	—
246	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
247	C₂²⋊C₈	—	11	4	no	—
248	C₂²⋊C₈	—	11	4	no	—
249	C₄×C₈	—	11	4	no	—
250	C₄×C₈	—	11	4	no	—
251	C₂×C₁₁	—	2	2	no	—
252	C₂×C₁₁	—	2	2	no	—
253	C₂×C₁₁	—	2	2	no	—
254	C₂×C₁₁	#2905	1	1	yes	characteristic
255	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
256	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
257	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	#4324	1	4	yes	—
270	C₂²×C₄	#4325	1	4	yes	—
271	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
273	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
280	M₁₆	—	4	4	no	—
281	M₁₆	—	4	4	no	—
282	M₁₆	—	44	4	no	—
283	M₁₆	—	44	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	—	11	8	no	—
287	C₂×C₈	—	22	4	no	—
288	C₂×C₈	—	44	4	no	—
289	C₂×C₈	—	44	4	no	—
290	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
296	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
297	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
298	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
299	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
305	C₄²	C₂³×D₁₁	1	1	yes	characteristic
306	C₁₁	#17813	1	1	yes	characteristic, complemented, Sylow
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	#66872	1	4	yes	—
310	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
311	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
312	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	#66872	1	4	yes	—
326	C₂×C₄	#66872	1	4	yes	—
327	C₂×C₄	#66872	1	4	yes	—
328	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×#4324	1	2	yes	—
338	C₂×C₄	C₂×#4324	1	2	yes	—
339	C₂×C₄	C₂×#4324	1	2	yes	—
340	C₂×C₄	C₂×#4325	1	2	yes	—
341	C₂×C₄	C₂×#4325	1	2	yes	—
342	C₂×C₄	C₂×#4325	1	2	yes	—
343	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	22	8	no	—
348	C₈	—	44	4	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	C₂×#66872	1	2	yes	—
357	C₂²	C₂×#66872	1	2	yes	—
358	C₂²	C₂×#66872	1	2	yes	—
359	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	C₂×#66872	1	2	yes	—
367	C₄	C₂×#66872	1	2	yes	—
368	C₄	C₂×#66872	1	2	yes	—
369	C₄	#10622737	1	2	yes	—
370	C₄	#10623276	1	2	yes	—
371	C₄	C₂²×#4324	1	1	yes	characteristic
372	C₄	C₂²×#4325	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	#13077179	1	1	yes	characteristic
377	C₂	C₂²×#66872	1	1	yes	characteristic
378	C₂	C₂×#10622737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#423	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#423	D₁₁
hypocenter	C₁₁	#17813
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #13067388	C₂	semidirect
4. #13067386	C₂	semidirect
5. #13067371	C₂	semidirect
29. #10622118	C₂²	semidirect
306. C₁₁	#17813	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622538	2
C₂×#10622537	2
#13067388	2
#13067386	2
#13067371	2
C₂×C₁₁×#423	2
#17813	11