Subgroups — #2358×C₂₁₁ #41009978

Order 27008.

928 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#120×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₂₁₁	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊C₄×C₂₁₁	C₂	1	2	yes	maximal, complemented
4	#390×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#388×C₂₁₁	C₂	1	2	yes	maximal, complemented
6	#386×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#386×C₂₁₁	C₂	1	2	yes	maximal, complemented
8	#385×C₂₁₁	C₂	1	2	yes	maximal, complemented
9	C₄×C₂²⋊C₄×C₂₁₁	C₂	1	2	yes	maximal, complemented
10	C₂⁵×C₂₁₁	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₂₁₁	C₂²	1	2	yes	—
12	C₂²×D₄×C₂₁₁	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₂₁₁	C₂²	1	2	yes	—
14	C₂³×C₄×C₂₁₁	C₂²	1	2	yes	—
15	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic, complemented
16	#120×C₂₁₁	C₄	1	8	yes	complemented
17	C₄×D₄×C₂₁₁	—	2	8	no	—
18	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	2	yes	complemented
19	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₂²⋊C₄×C₂₁₁	—	2	8	no	—
21	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄²×C₂₁₁	C₂²	1	2	yes	complemented
30	C₂×C₄²×C₂₁₁	C₂²	1	1	yes	characteristic, complemented
31	#95×C₂₁₁	C₂²	1	2	yes	complemented
32	#95×C₂₁₁	C₂²	1	2	yes	complemented
33	#95×C₂₁₁	C₂²	1	2	yes	complemented
34	C₂⁴×C₂₁₁	—	2	4	no	—
35	C₂⁴×C₂₁₁	—	2	4	no	—
36	C₂⁴×C₂₁₁	—	4	1	no	—
37	C₂⁴×C₂₁₁	—	4	1	no	—
38	C₂⁴×C₂₁₁	C₂×C₄	1	4	yes	complemented
39	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
40	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
41	C₂⁴×C₂₁₁	C₂³	1	2	yes	—
42	C₂×D₄×C₂₁₁	—	2	4	no	—
43	C₂×D₄×C₂₁₁	—	2	4	no	—
44	C₂×D₄×C₂₁₁	—	4	1	no	—
45	C₂×D₄×C₂₁₁	—	4	1	no	—
46	C₂×D₄×C₂₁₁	C₂×C₄	1	8	yes	complemented
47	C₂×D₄×C₂₁₁	C₂×C₄	1	4	yes	complemented
48	C₂²×C₄×C₂₁₁	—	2	4	no	—
49	C₂²×C₄×C₂₁₁	—	2	4	no	—
50	C₂²×C₄×C₂₁₁	—	2	4	no	—
51	C₂²×C₄×C₂₁₁	—	2	4	no	—
52	C₂²×C₄×C₂₁₁	—	2	4	no	—
53	C₂²×C₄×C₂₁₁	—	4	2	no	—
54	C₂²×C₄×C₂₁₁	—	4	2	no	—
55	C₂²×C₄×C₂₁₁	—	4	1	no	—
56	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
57	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
58	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
59	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
61	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
62	C₄⋊C₄×C₂₁₁	—	2	4	no	—
63	C₄⋊C₄×C₂₁₁	—	4	1	no	—
64	C₂²⋊C₄×C₂₁₁	—	2	4	no	—
65	C₂²⋊C₄×C₂₁₁	—	2	4	no	—
66	C₂²⋊C₄×C₂₁₁	—	2	4	no	—
67	C₂²⋊C₄×C₂₁₁	—	2	4	no	—
68	C₂²⋊C₄×C₂₁₁	—	4	1	no	—
69	C₂²⋊C₄×C₂₁₁	C₂×C₄	1	4	yes	complemented
70	C₂²⋊C₄×C₂₁₁	C₂×C₄	1	8	yes	complemented
71	C₂²⋊C₄×C₂₁₁	D₄	1	8	yes	complemented
72	C₄²×C₂₁₁	—	2	4	no	—
73	C₄²×C₂₁₁	—	4	1	no	—
74	C₂³×C₂₁₁	—	2	2	no	—
75	C₂³×C₂₁₁	—	2	2	no	—
76	C₂³×C₂₁₁	—	2	2	no	—
77	C₂³×C₂₁₁	—	2	2	no	—
78	C₂³×C₂₁₁	—	2	16	no	—
79	C₂³×C₂₁₁	—	2	2	no	—
80	C₂³×C₂₁₁	—	2	2	no	—
81	C₂³×C₂₁₁	—	2	2	no	—
82	C₂³×C₂₁₁	—	2	2	no	—
83	C₂³×C₂₁₁	—	2	1	no	—
84	C₂³×C₂₁₁	—	2	1	no	—
85	C₂³×C₂₁₁	—	2	1	no	—
86	C₂³×C₂₁₁	—	2	1	no	—
87	C₂³×C₂₁₁	—	4	4	no	—
88	C₂³×C₂₁₁	—	4	4	no	—
89	C₂³×C₂₁₁	—	4	8	no	—
90	C₂³×C₂₁₁	—	4	4	no	—
91	C₂³×C₂₁₁	C₂²×C₄	1	2	yes	—
92	C₂³×C₂₁₁	C₂²×C₄	1	2	yes	—
93	C₂³×C₂₁₁	C₂²×C₄	1	4	yes	—
94	C₂³×C₂₁₁	C₂×D₄	1	4	yes	—
95	C₂³×C₂₁₁	#41	1	4	yes	—
96	C₂³×C₂₁₁	C₂⁴	1	1	yes	characteristic
97	D₄×C₂₁₁	—	2	16	no	—
98	D₄×C₂₁₁	—	4	4	no	—
99	C₂×C₄×C₂₁₁	—	2	2	no	—
100	C₂×C₄×C₂₁₁	—	2	2	no	—
101	C₂×C₄×C₂₁₁	—	2	2	no	—
102	C₂×C₄×C₂₁₁	—	2	2	no	—
103	C₂×C₄×C₂₁₁	—	2	2	no	—
104	C₂×C₄×C₂₁₁	—	2	1	no	—
105	C₂×C₄×C₂₁₁	—	2	1	no	—
106	C₂×C₄×C₂₁₁	—	2	2	no	—
107	C₂×C₄×C₂₁₁	—	2	2	no	—
108	C₂×C₄×C₂₁₁	—	2	2	no	—
109	C₂×C₄×C₂₁₁	—	2	2	no	—
110	C₂×C₄×C₂₁₁	—	2	2	no	—
111	C₂×C₄×C₂₁₁	—	2	2	no	—
112	C₂×C₄×C₂₁₁	—	2	2	no	—
113	C₂×C₄×C₂₁₁	—	4	4	no	—
114	C₂×C₄×C₂₁₁	—	4	8	no	—
115	C₂×C₄×C₂₁₁	—	4	8	no	—
116	C₂×C₄×C₂₁₁	C₂²×C₄	1	4	yes	—
117	C₂×C₄×C₂₁₁	C₂²×C₄	1	2	yes	—
118	C₂×C₄×C₂₁₁	C₂×D₄	1	4	yes	—
119	C₂×C₄×C₂₁₁	C₂×D₄	1	4	yes	—
120	C₂²×C₂₁₁	—	2	4	no	—
121	C₂²×C₂₁₁	—	2	4	no	—
122	C₂²×C₂₁₁	—	2	4	no	—
123	C₂²×C₂₁₁	—	2	4	no	—
124	C₂²×C₂₁₁	—	2	4	no	—
125	C₂²×C₂₁₁	—	2	4	no	—
126	C₂²×C₂₁₁	—	2	4	no	—
127	C₂²×C₂₁₁	—	2	4	no	—
128	C₂²×C₂₁₁	—	2	2	no	—
129	C₂²×C₂₁₁	—	2	2	no	—
130	C₂²×C₂₁₁	—	4	16	no	—
131	C₂²×C₂₁₁	—	4	1	no	—
132	C₂²×C₂₁₁	—	4	1	no	—
133	C₂²×C₂₁₁	—	4	2	no	—
134	C₂²×C₂₁₁	—	4	2	no	—
135	C₂²×C₂₁₁	—	4	1	no	—
136	C₂²×C₂₁₁	—	4	1	no	—
137	C₂²×C₂₁₁	C₄×D₄	1	8	yes	complemented
138	C₂²×C₂₁₁	C₂³×C₄	1	1	yes	characteristic
139	C₂²×C₂₁₁	C₂²×D₄	1	2	yes	—
140	C₂²×C₂₁₁	C₂×#41	1	2	yes	—
141	C₂²×C₂₁₁	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂²×C₂₁₁	H(5,𝔽₂)	1	1	yes	characteristic
143	C₄×C₂₁₁	—	2	4	no	—
144	C₄×C₂₁₁	—	2	2	no	—
145	C₄×C₂₁₁	—	2	4	no	—
146	C₄×C₂₁₁	—	2	4	no	—
147	C₄×C₂₁₁	—	4	2	no	—
148	C₄×C₂₁₁	—	4	2	no	—
149	C₂×C₂₁₁	—	2	8	no	—
150	C₂×C₂₁₁	—	4	2	no	—
151	C₂×C₂₁₁	—	4	2	no	—
152	C₂×C₂₁₁	C₂×C₄×D₄	1	2	yes	—
153	C₂×C₂₁₁	#518	1	1	yes	characteristic
154	C₂×C₂₁₁	D₄²	1	1	yes	characteristic
155	C₂×C₂₁₁	#546	1	2	yes	—
156	C₂×C₂₁₁	#551	1	1	yes	characteristic
157	C₂₁₁	#2358	1	1	yes	characteristic, direct product factor, Sylow
158	#2358	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂×#120	C₂×C₂₁₁	1	1	yes	characteristic
160	C₂×C₄×D₄	C₂×C₂₁₁	1	2	yes	complemented
161	C₂²×C₂²⋊C₄	C₂×C₂₁₁	1	2	yes	complemented
162	#390	C₂×C₂₁₁	1	1	yes	characteristic, complemented
163	#388	C₂×C₂₁₁	1	2	yes	complemented
164	#386	C₂×C₂₁₁	1	1	yes	characteristic, complemented
165	#386	C₂×C₂₁₁	1	2	yes	complemented
166	#385	C₂×C₂₁₁	1	2	yes	complemented
167	C₄×C₂²⋊C₄	C₂×C₂₁₁	1	2	yes	complemented
168	C₂⁵	C₂²×C₂₁₁	1	1	yes	characteristic
169	C₂²×D₄	C₂²×C₂₁₁	1	2	yes	—
170	C₂²×D₄	C₂²×C₂₁₁	1	1	yes	characteristic
171	C₂³×C₄	C₂²×C₂₁₁	1	2	yes	—
172	C₂³×C₄	C₂²×C₂₁₁	1	2	yes	—
173	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic, complemented
174	#120	C₄×C₂₁₁	1	8	yes	complemented
175	C₄×D₄	—	2	8	no	—
176	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	2	yes	complemented
177	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic, complemented
178	C₂×C₂²⋊C₄	—	2	8	no	—
179	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
180	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
181	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
182	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
183	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
184	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
185	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	complemented
186	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic, complemented
187	C₂×C₄²	C₂²×C₂₁₁	1	2	yes	complemented
188	C₂×C₄²	C₂²×C₂₁₁	1	1	yes	characteristic, complemented
189	#95	C₂²×C₂₁₁	1	2	yes	complemented
190	#95	C₂²×C₂₁₁	1	2	yes	complemented
191	#95	C₂²×C₂₁₁	1	2	yes	complemented
192	C₂⁴	—	2	4	no	—
193	C₂⁴	—	2	4	no	—
194	C₂⁴	—	4	1	no	—
195	C₂⁴	—	4	1	no	—
196	C₂⁴	C₂×C₄×C₂₁₁	1	4	yes	complemented
197	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
198	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
199	C₂⁴	C₂³×C₂₁₁	1	2	yes	—
200	C₂×D₄	—	2	4	no	—
201	C₂×D₄	—	2	4	no	—
202	C₂×D₄	—	4	1	no	—
203	C₂×D₄	—	4	1	no	—
204	C₂×D₄	C₂×C₄×C₂₁₁	1	8	yes	complemented
205	C₂×D₄	C₂×C₄×C₂₁₁	1	4	yes	complemented
206	C₂²×C₄	—	2	4	no	—
207	C₂²×C₄	—	2	4	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	4	no	—
210	C₂²×C₄	—	2	4	no	—
211	C₂²×C₄	—	4	2	no	—
212	C₂²×C₄	—	4	2	no	—
213	C₂²×C₄	—	4	1	no	—
214	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
215	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
216	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
217	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
218	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
219	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
220	C₄⋊C₄	—	2	4	no	—
221	C₄⋊C₄	—	4	1	no	—
222	C₂²⋊C₄	—	2	4	no	—
223	C₂²⋊C₄	—	2	4	no	—
224	C₂²⋊C₄	—	2	4	no	—
225	C₂²⋊C₄	—	2	4	no	—
226	C₂²⋊C₄	—	4	1	no	—
227	C₂²⋊C₄	C₂×C₄×C₂₁₁	1	4	yes	complemented
228	C₂²⋊C₄	C₂×C₄×C₂₁₁	1	8	yes	complemented
229	C₂²⋊C₄	D₄×C₂₁₁	1	8	yes	complemented
230	C₄²	—	2	4	no	—
231	C₄²	—	4	1	no	—
232	C₂³	—	2	2	no	—
233	C₂³	—	2	2	no	—
234	C₂³	—	2	2	no	—
235	C₂³	—	2	2	no	—
236	C₂³	—	2	16	no	—
237	C₂³	—	2	2	no	—
238	C₂³	—	2	2	no	—
239	C₂³	—	2	2	no	—
240	C₂³	—	2	2	no	—
241	C₂³	—	2	1	no	—
242	C₂³	—	2	1	no	—
243	C₂³	—	2	1	no	—
244	C₂³	—	2	1	no	—
245	C₂³	—	4	4	no	—
246	C₂³	—	4	4	no	—
247	C₂³	—	4	8	no	—
248	C₂³	—	4	4	no	—
249	C₂³	C₂²×C₄×C₂₁₁	1	2	yes	—
250	C₂³	C₂²×C₄×C₂₁₁	1	2	yes	—
251	C₂³	C₂²×C₄×C₂₁₁	1	4	yes	—
252	C₂³	C₂×D₄×C₂₁₁	1	4	yes	—
253	C₂³	#41×C₂₁₁	1	4	yes	—
254	C₂³	C₂⁴×C₂₁₁	1	1	yes	characteristic
255	D₄	—	2	16	no	—
256	D₄	—	4	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	2	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	2	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	2	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	4	4	no	—
272	C₂×C₄	—	4	8	no	—
273	C₂×C₄	—	4	8	no	—
274	C₂×C₄	C₂²×C₄×C₂₁₁	1	4	yes	—
275	C₂×C₄	C₂²×C₄×C₂₁₁	1	2	yes	—
276	C₂×C₄	C₂×D₄×C₂₁₁	1	4	yes	—
277	C₂×C₄	C₂×D₄×C₂₁₁	1	4	yes	—
278	C₂²	—	2	4	no	—
279	C₂²	—	2	4	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	2	4	no	—
282	C₂²	—	2	4	no	—
283	C₂²	—	2	4	no	—
284	C₂²	—	2	4	no	—
285	C₂²	—	2	4	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	2	2	no	—
288	C₂²	—	4	16	no	—
289	C₂²	—	4	1	no	—
290	C₂²	—	4	1	no	—
291	C₂²	—	4	2	no	—
292	C₂²	—	4	2	no	—
293	C₂²	—	4	1	no	—
294	C₂²	—	4	1	no	—
295	C₂²	C₄×D₄×C₂₁₁	1	8	yes	complemented
296	C₂²	C₂³×C₄×C₂₁₁	1	1	yes	characteristic
297	C₂²	C₂²×D₄×C₂₁₁	1	2	yes	—
298	C₂²	C₂×#41×C₂₁₁	1	2	yes	—
299	C₂²	H(5,𝔽₂)×C₂₁₁	1	1	yes	characteristic
300	C₂²	H(5,𝔽₂)×C₂₁₁	1	1	yes	characteristic
301	C₄	—	2	4	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	4	no	—
304	C₄	—	2	2	no	—
305	C₄	—	4	2	no	—
306	C₄	—	4	2	no	—
307	C₂	—	2	8	no	—
308	C₂	—	4	2	no	—
309	C₂	—	4	2	no	—
310	C₂	C₂×C₄×D₄×C₂₁₁	1	2	yes	—
311	C₂	#518×C₂₁₁	1	1	yes	characteristic
312	C₂	D₄²×C₂₁₁	1	1	yes	characteristic
313	C₂	#546×C₂₁₁	1	2	yes	—
314	C₂	#551×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₁₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₁₁
Frattini, cosocle	C₂³	C₂⁴×C₂₁₁
prime radical	C₂×#120×C₂₁₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×C₂₁₁	C₂	semidirect
3. C₂²×C₂²⋊C₄×C₂₁₁	C₂	semidirect
4. #390×C₂₁₁	C₂	semidirect
5. #388×C₂₁₁	C₂	semidirect
6. #386×C₂₁₁	C₂	semidirect
7. #386×C₂₁₁	C₂	semidirect
8. #385×C₂₁₁	C₂	semidirect
9. C₄×C₂²⋊C₄×C₂₁₁	C₂	semidirect
15. C₂³×C₄×C₂₁₁	C₂²	semidirect
16. #120×C₂₁₁	C₄	semidirect
18. C₂×C₄⋊C₄×C₂₁₁	C₂²	semidirect
19. C₂×C₄⋊C₄×C₂₁₁	C₂²	semidirect
27. C₂×C₂²⋊C₄×C₂₁₁	C₂²	semidirect
28. C₂×C₂²⋊C₄×C₂₁₁	C₂²	semidirect
29. C₂×C₄²×C₂₁₁	C₂²	semidirect
30. C₂×C₄²×C₂₁₁	C₂²	semidirect
31. #95×C₂₁₁	C₂²	semidirect
32. #95×C₂₁₁	C₂²	semidirect
33. #95×C₂₁₁	C₂²	semidirect
38. C₂⁴×C₂₁₁	C₂×C₄	semidirect
46. C₂×D₄×C₂₁₁	C₂×C₄	semidirect
47. C₂×D₄×C₂₁₁	C₂×C₄	semidirect
69. C₂²⋊C₄×C₂₁₁	C₂×C₄	semidirect
70. C₂²⋊C₄×C₂₁₁	C₂×C₄	semidirect
71. C₂²⋊C₄×C₂₁₁	D₄	semidirect
137. C₂²×C₂₁₁	C₄×D₄	semidirect
157. C₂₁₁	#2358	direct (N × H)
158. #2358	C₂₁₁	direct (N × H)
160. C₂×C₄×D₄	C₂×C₂₁₁	semidirect
161. C₂²×C₂²⋊C₄	C₂×C₂₁₁	semidirect
162. #390	C₂×C₂₁₁	semidirect
163. #388	C₂×C₂₁₁	semidirect
164. #386	C₂×C₂₁₁	semidirect
165. #386	C₂×C₂₁₁	semidirect
166. #385	C₂×C₂₁₁	semidirect
167. C₄×C₂²⋊C₄	C₂×C₂₁₁	semidirect
173. C₂³×C₄	C₂²×C₂₁₁	semidirect
174. #120	C₄×C₂₁₁	semidirect
176. C₂×C₄⋊C₄	C₂²×C₂₁₁	semidirect
177. C₂×C₄⋊C₄	C₂²×C₂₁₁	semidirect
185. C₂×C₂²⋊C₄	C₂²×C₂₁₁	semidirect
186. C₂×C₂²⋊C₄	C₂²×C₂₁₁	semidirect
187. C₂×C₄²	C₂²×C₂₁₁	semidirect
188. C₂×C₄²	C₂²×C₂₁₁	semidirect
189. #95	C₂²×C₂₁₁	semidirect
190. #95	C₂²×C₂₁₁	semidirect
191. #95	C₂²×C₂₁₁	semidirect
196. C₂⁴	C₂×C₄×C₂₁₁	semidirect
204. C₂×D₄	C₂×C₄×C₂₁₁	semidirect
205. C₂×D₄	C₂×C₄×C₂₁₁	semidirect
227. C₂²⋊C₄	C₂×C₄×C₂₁₁	semidirect
228. C₂²⋊C₄	C₂×C₄×C₂₁₁	semidirect
229. C₂²⋊C₄	D₄×C₂₁₁	semidirect
295. C₂²	C₄×D₄×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#120×C₂₁₁	2
C₂×C₄×D₄×C₂₁₁	2
C₂²×C₂²⋊C₄×C₂₁₁	2
#390×C₂₁₁	2
#388×C₂₁₁	2
#386×C₂₁₁	2
#385×C₂₁₁	2
C₄×C₂²⋊C₄×C₂₁₁	2
#2358	211

Subgroups — #2358×C211 #41009978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2358×C₂₁₁ #41009978