Subgroups — C₂×#13070442 #14906930

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66876	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#13070442	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10622099	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
12	C₈×D₄×C₁₁	C₄	1	4	yes	—
13	C₈×D₄×C₁₁	C₂²	1	4	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
15	C₂×C₁₁×C₂²⋊C₈	C₄	1	1	yes	characteristic
16	C₂×C₁₁×C₂²⋊C₈	C₄	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×#66876	—	2	4	no	—
19	C₂×#66876	C₂²	1	4	yes	complemented
20	C₂²×C₁₁⋊C₁₆	—	2	4	no	—
21	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	complemented
26	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	complemented
27	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	complemented
28	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	complemented
29	#10622099	C₂²	1	4	yes	complemented
30	C₂²×D₄×C₁₁	C₈	1	1	yes	characteristic
31	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	—	2	2	no	—
34	C₂²×C₈×C₁₁	—	2	2	no	—
35	C₂²×C₈×C₁₁	—	2	2	no	—
36	C₂²×C₈×C₁₁	—	2	2	no	—
37	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₄×D₄×C₁₁	C₈	1	4	yes	—
46	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	—
47	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
48	C₂×C₁₁×C₂²⋊C₄	C₈	1	1	yes	characteristic
49	C₂×C₁₁×C₂²⋊C₄	C₈	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
52	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
53	C₁₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
54	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
55	C₄×C₈×C₁₁	C₂³	1	2	yes	—
56	#66876	—	2	8	no	—
57	C₂×C₁₁⋊C₁₆	—	2	2	no	—
58	C₂×C₁₁⋊C₁₆	—	2	2	no	—
59	C₂×C₁₁⋊C₁₆	—	2	2	no	—
60	C₂×C₁₁⋊C₁₆	—	2	8	no	—
61	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	complemented
62	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
63	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
66	C₂×#2168	—	11	1	no	maximal, Sylow
67	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
68	C₂⁴×C₁₁	C₂×C₈	1	1	yes	characteristic
69	C₂×D₄×C₁₁	—	2	4	no	—
70	C₂×D₄×C₁₁	C₂×C₈	1	4	yes	—
71	C₂²×C₄×C₁₁	—	2	2	no	—
72	C₂²×C₄×C₁₁	—	2	2	no	—
73	C₂²×C₄×C₁₁	—	2	2	no	—
74	C₂²×C₄×C₁₁	—	2	2	no	—
75	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	—	2	4	no	—
85	C₂×C₈×C₁₁	—	2	4	no	—
86	C₂×C₈×C₁₁	—	2	2	no	—
87	C₂×C₈×C₁₁	—	2	2	no	—
88	C₂×C₈×C₁₁	—	2	2	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₁₁	#41	1	2	yes	—
99	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
100	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
101	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
102	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
103	C₄²×C₁₁	C₂×C₈	1	2	yes	—
104	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
105	C₁₁⋊C₁₆	—	2	2	no	—
106	C₁₁⋊C₁₆	—	2	2	no	—
107	C₁₁⋊C₁₆	—	2	2	no	—
108	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	complemented
109	C₂²×M₃₂	—	11	1	no	—
110	C₂³×C₁₆	—	11	1	no	—
111	C₂×C₈×D₄	D₁₁	1	1	yes	characteristic
112	#2168	—	11	8	no	—
113	C₂×C₄⋊C₁₆	—	11	1	no	—
114	C₂×C₂²⋊C₁₆	—	11	1	no	—
115	C₂×C₂²⋊C₁₆	—	11	1	no	—
116	C₂×#346	—	11	1	no	—
117	C₂³×C₁₁	—	2	2	no	—
118	C₂³×C₁₁	—	2	2	no	—
119	C₂³×C₁₁	—	2	2	no	—
120	C₂³×C₁₁	—	2	2	no	—
121	C₂³×C₁₁	—	2	2	no	—
122	C₂³×C₁₁	M₃₂	1	4	yes	complemented
123	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
124	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
125	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
126	D₄×C₁₁	—	2	8	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
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	4	no	—
136	C₂×C₄×C₁₁	—	2	4	no	—
137	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
140	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₁	#131	1	2	yes	—
144	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
145	C₈×C₁₁	—	2	2	no	—
146	C₈×C₁₁	—	2	2	no	—
147	C₈×C₁₁	—	2	2	no	—
148	C₈×C₁₁	C₄×D₄	1	2	yes	—
149	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
151	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
152	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
153	C₂×C₄×D₄	Dic₁₁	1	1	yes	characteristic
154	C₂×M₃₂	—	11	4	no	—
155	C₂×M₃₂	—	22	4	no	—
156	C₂²×C₁₆	—	11	1	no	—
157	C₂²×C₁₆	—	11	4	no	—
158	C₂²×C₁₆	—	11	1	no	—
159	C₂²×C₁₆	—	11	1	no	—
160	C₂²×C₁₆	—	11	1	no	—
161	C₂²×C₁₆	—	22	4	no	—
162	C₈×D₄	Dic₁₁	1	4	yes	—
163	C₈×D₄	C₂×D₁₁	1	4	yes	—
164	C₂×C₄⋊C₈	Dic₁₁	1	1	yes	characteristic
165	C₂×C₂²⋊C₈	Dic₁₁	1	1	yes	characteristic
166	C₂×C₂²⋊C₈	Dic₁₁	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
168	C₄⋊C₁₆	—	11	4	no	—
169	C₂²⋊C₁₆	—	11	4	no	—
170	C₂²⋊C₁₆	—	11	4	no	—
171	#346	—	11	4	no	—
172	C₂²×C₁₁	—	2	2	no	—
173	C₂²×C₁₁	—	2	2	no	—
174	C₂²×C₁₁	—	2	8	no	—
175	C₂²×C₁₁	—	2	2	no	—
176	C₂²×C₁₁	—	2	2	no	—
177	C₂²×C₁₁	—	2	2	no	—
178	C₂²×C₁₁	—	4	4	no	—
179	C₂²×C₁₁	C₈×D₄	1	2	yes	—
180	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
181	C₂²×C₁₁	C₂×M₃₂	1	4	yes	complemented
182	C₂²×C₁₁	#504	1	2	yes	—
183	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
184	C₄×C₁₁	—	2	2	no	—
185	C₄×C₁₁	—	2	2	no	—
186	C₄×C₁₁	—	2	2	no	—
187	C₄×C₁₁	—	2	2	no	—
188	C₄×C₁₁	C₈×D₄	1	2	yes	—
189	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
190	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
191	C₂²×D₄	C₁₁⋊C₈	1	1	yes	characteristic
192	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
193	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	—	2	2	no	—
196	C₂²×C₈	—	2	2	no	—
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
199	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
200	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
201	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
202	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
203	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
204	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
205	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
206	C₄×D₄	C₁₁⋊C₈	1	4	yes	—
207	C₄×D₄	C₂×Dic₁₁	1	4	yes	—
208	C₂×C₄⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
209	C₂×C₂²⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
211	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
212	M₃₂	—	22	8	no	—
213	C₂×C₁₆	—	11	4	no	—
214	C₂×C₁₆	—	11	2	no	—
215	C₂×C₁₆	—	11	2	no	—
216	C₂×C₁₆	—	11	2	no	—
217	C₂×C₁₆	—	11	2	no	—
218	C₂×C₁₆	—	22	8	no	—
219	C₂×C₁₆	—	22	2	no	—
220	C₂×C₁₆	—	22	2	no	—
221	C₂×C₁₆	—	22	2	no	—
222	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
223	C₂²⋊C₈	C₂×Dic₁₁	1	4	yes	—
224	C₂²⋊C₈	C₂×Dic₁₁	1	4	yes	—
225	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
226	C₄×C₈	C₂²×D₁₁	1	2	yes	—
227	C₂×C₁₁	—	2	4	no	—
228	C₂×C₁₁	—	4	2	no	—
229	C₂×C₁₁	#2168	1	4	yes	complemented
230	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
231	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
232	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
233	C₂⁴	C₂×C₁₁⋊C₈	1	1	yes	characteristic
234	C₂⁴	C₂×C₁₁⋊C₈	1	1	yes	characteristic
235	C₂×D₄	—	2	4	no	—
236	C₂×D₄	C₂×C₁₁⋊C₈	1	4	yes	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
246	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
247	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
248	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
249	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	4	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	D₄×D₁₁	1	2	yes	—
260	C₂×C₈	#4341	1	2	yes	—
261	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
262	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
263	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
264	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
265	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
266	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
267	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
268	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
269	C₄²	C₂×C₁₁⋊C₈	1	2	yes	—
270	C₄²	C₂²×Dic₁₁	1	2	yes	—
271	C₁₆	—	11	4	no	—
272	C₁₆	—	22	2	no	—
273	C₁₆	—	22	2	no	—
274	C₁₆	—	22	2	no	—
275	C₁₁	C₂×#2168	1	1	yes	characteristic, complemented, Sylow
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	#66876	1	4	yes	complemented
282	C₂³	C₂²×C₁₁⋊C₈	1	2	yes	—
283	C₂³	C₂²×C₁₁⋊C₈	1	2	yes	—
284	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
285	D₄	—	2	8	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
297	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
298	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
299	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
300	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
301	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
302	C₂×C₄	#67001	1	2	yes	—
303	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
304	C₈	—	2	2	no	—
305	C₈	—	2	2	no	—
306	C₈	—	2	2	no	—
307	C₈	D₄×Dic₁₁	1	2	yes	—
308	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
309	C₈	C₂×#4341	1	1	yes	characteristic
310	C₂²	—	2	2	no	—
311	C₂²	—	2	8	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	4	no	—
317	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
318	C₂²	C₂×#66876	1	2	yes	—
319	C₂²	C₂×#66876	1	4	yes	complemented
320	C₂²	#10622753	1	2	yes	—
321	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
327	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
328	C₄	C₂×#67001	1	1	yes	characteristic
329	C₂	—	2	4	no	—
330	C₂	—	4	2	no	—
331	C₂	#13070442	1	4	yes	direct product factor
332	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic
333	C₂	C₂²×#66876	1	1	yes	characteristic
334	C₂	C₂×#10622753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₈×D₄×C₁₁	C₂
socle	C₂³×C₁₁	C₂²×C₈
prime radical	C₂²×D₄×C₁₁	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₈×D₄	D₁₁
hypocenter	C₁₁	C₂×#2168
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#66876	C₂	semidirect
2. C₂³×C₁₁⋊C₁₆	C₂	semidirect
3. #13070442	C₂	direct (N × H)
4. C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	semidirect
5. C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	semidirect
6. C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	semidirect
7. C₂×#10622099	C₂	semidirect
19. C₂×#66876	C₂²	semidirect
25. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
26. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
27. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
28. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
29. #10622099	C₂²	semidirect
61. C₂×C₁₁⋊C₁₆	D₄	semidirect
108. C₁₁⋊C₁₆	C₂×D₄	semidirect
122. C₂³×C₁₁	M₃₂	semidirect
181. C₂²×C₁₁	C₂×M₃₂	semidirect
229. C₂×C₁₁	#2168	semidirect
275. C₁₁	C₂×#2168	semidirect
281. C₂³	#66876	semidirect
319. C₂²	C₂×#66876	semidirect
331. C₂	#13070442	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#66876	2
C₂³×C₁₁⋊C₁₆	2
#13070442	2
C₂×C₄⋊(C₁₁⋊C₁₆)	2
C₂×C₂²⋊(C₁₁⋊C₁₆)	2
C₂×#10622099	2
C₂×C₈×D₄×C₁₁	2
C₂×#2168	11

Subgroups — C2×#13070442 #14906930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070442 #14906930