Subgroups — #2352×C₂₁₁ #41009972

Order 27008.

660 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#117×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊C₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#388×C₂₁₁	C₂	1	2	yes	maximal, complemented
5	#387×C₂₁₁	C₂	1	2	yes	maximal, complemented
6	#386×C₂₁₁	C₂	1	2	yes	maximal
7	#382×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#380×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#380×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₄⋊C₄×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₄×C₂₁₁	C₂	1	2	yes	maximal, complemented
12	C₂²×D₄×C₂₁₁	C₂²	1	1	yes	characteristic
13	C₂³×C₄×C₂₁₁	C₂²	1	2	yes	—
14	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₂₁₁	C₂²	1	1	yes	characteristic
16	C₄×D₄×C₂₁₁	C₄	1	8	yes	complemented
17	#117×C₂₁₁	—	2	4	no	—
18	C₂×C₄⋊C₄×C₂₁₁	—	2	4	no	—
19	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	2	yes	—
23	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₂₁₁	C₂²	1	2	yes	—
31	C₂×C₄²×C₂₁₁	C₂²	1	2	yes	—
32	C₂×C₄²×C₂₁₁	C₂²	1	1	yes	characteristic
33	#95×C₂₁₁	C₂²	1	2	yes	—
34	#95×C₂₁₁	C₂²	1	2	yes	—
35	#95×C₂₁₁	C₂²	1	2	yes	—
36	#95×C₂₁₁	C₂²	1	2	yes	—
37	#95×C₂₁₁	C₂²	1	2	yes	—
38	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
39	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
40	C₂×D₄×C₂₁₁	—	2	2	no	—
41	C₂×D₄×C₂₁₁	—	2	2	no	—
42	C₂×D₄×C₂₁₁	C₂×C₄	1	4	yes	—
43	C₂²×C₄×C₂₁₁	—	2	2	no	—
44	C₂²×C₄×C₂₁₁	—	2	2	no	—
45	C₂²×C₄×C₂₁₁	—	2	2	no	—
46	C₂²×C₄×C₂₁₁	—	2	2	no	—
47	C₂²×C₄×C₂₁₁	—	2	4	no	—
48	C₂²×C₄×C₂₁₁	—	2	4	no	—
49	C₂²×C₄×C₂₁₁	—	4	2	no	—
50	C₂²×C₄×C₂₁₁	C₂×C₄	1	4	yes	—
51	C₂²×C₄×C₂₁₁	C₂×C₄	1	4	yes	complemented
52	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
53	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
54	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
55	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₂₁₁	C₂³	1	2	yes	—
60	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
61	C₄⋊C₄×C₂₁₁	—	2	4	no	—
62	C₄⋊C₄×C₂₁₁	—	2	2	no	—
63	C₄⋊C₄×C₂₁₁	—	2	2	no	—
64	C₄⋊C₄×C₂₁₁	—	2	2	no	—
65	C₄⋊C₄×C₂₁₁	C₂×C₄	1	4	yes	complemented
66	C₄⋊C₄×C₂₁₁	D₄	1	4	yes	complemented
67	C₂²⋊C₄×C₂₁₁	—	2	4	no	—
68	C₂²⋊C₄×C₂₁₁	—	2	4	no	—
69	C₂²⋊C₄×C₂₁₁	—	4	2	no	—
70	C₂²⋊C₄×C₂₁₁	C₂×C₄	1	4	yes	—
71	C₂²⋊C₄×C₂₁₁	C₂×C₄	1	4	yes	complemented
72	C₄²×C₂₁₁	—	2	4	no	—
73	C₄²×C₂₁₁	—	4	2	no	—
74	C₄²×C₂₁₁	C₂×C₄	1	4	yes	complemented
75	C₂³×C₂₁₁	—	2	1	no	—
76	C₂³×C₂₁₁	—	2	1	no	—
77	C₂³×C₂₁₁	—	2	1	no	—
78	C₂³×C₂₁₁	—	2	1	no	—
79	C₂³×C₂₁₁	—	2	1	no	—
80	C₂³×C₂₁₁	—	2	1	no	—
81	C₂³×C₂₁₁	—	2	1	no	—
82	C₂³×C₂₁₁	—	2	1	no	—
83	C₂³×C₂₁₁	—	2	1	no	—
84	C₂³×C₂₁₁	—	2	1	no	—
85	C₂³×C₂₁₁	C₂²×C₄	1	2	yes	—
86	C₂³×C₂₁₁	C₂²×C₄	1	2	yes	—
87	C₂³×C₂₁₁	#41	1	2	yes	—
88	C₂³×C₂₁₁	#41	1	2	yes	—
89	C₂³×C₂₁₁	C₂⁴	1	1	yes	characteristic
90	D₄×C₂₁₁	—	2	8	no	—
91	C₂×C₄×C₂₁₁	—	2	1	no	—
92	C₂×C₄×C₂₁₁	—	2	1	no	—
93	C₂×C₄×C₂₁₁	—	2	1	no	—
94	C₂×C₄×C₂₁₁	—	2	1	no	—
95	C₂×C₄×C₂₁₁	—	2	2	no	—
96	C₂×C₄×C₂₁₁	—	2	1	no	—
97	C₂×C₄×C₂₁₁	—	2	1	no	—
98	C₂×C₄×C₂₁₁	—	2	1	no	—
99	C₂×C₄×C₂₁₁	—	2	2	no	—
100	C₂×C₄×C₂₁₁	—	2	1	no	—
101	C₂×C₄×C₂₁₁	—	2	8	no	—
102	C₂×C₄×C₂₁₁	—	2	8	no	—
103	C₂×C₄×C₂₁₁	—	2	2	no	—
104	C₂×C₄×C₂₁₁	—	2	2	no	—
105	C₂×C₄×C₂₁₁	—	2	2	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	—	4	8	no	—
113	C₂×C₄×C₂₁₁	C₂²×C₄	1	2	yes	—
114	C₂×C₄×C₂₁₁	C₂²×C₄	1	2	yes	—
115	C₂×C₄×C₂₁₁	C₂²×C₄	1	2	yes	—
116	C₂×C₄×C₂₁₁	C₂²×C₄	1	2	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	2	yes	—
120	C₂×C₄×C₂₁₁	#41	1	2	yes	—
121	C₂²×C₂₁₁	—	2	2	no	—
122	C₂²×C₂₁₁	—	2	2	no	—
123	C₂²×C₂₁₁	—	2	2	no	—
124	C₂²×C₂₁₁	—	2	2	no	—
125	C₂²×C₂₁₁	—	2	2	no	—
126	C₂²×C₂₁₁	—	2	2	no	—
127	C₂²×C₂₁₁	—	2	2	no	—
128	C₂²×C₂₁₁	—	2	2	no	—
129	C₂²×C₂₁₁	—	2	2	no	—
130	C₂²×C₂₁₁	—	4	1	no	—
131	C₂²×C₂₁₁	—	4	1	no	—
132	C₂²×C₂₁₁	—	4	1	no	—
133	C₂²×C₂₁₁	—	4	1	no	—
134	C₂²×C₂₁₁	#117	1	4	yes	complemented
135	C₂²×C₂₁₁	C₂³×C₄	1	1	yes	characteristic
136	C₂²×C₂₁₁	C₂²×D₄	1	1	yes	characteristic
137	C₂²×C₂₁₁	C₂×#41	1	1	yes	characteristic
138	C₂²×C₂₁₁	C₂×#41	1	1	yes	characteristic
139	C₂²×C₂₁₁	C₂×#41	1	1	yes	characteristic
140	C₂²×C₂₁₁	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂²×C₂₁₁	2₋¹⁺⁴	1	1	yes	characteristic
142	C₄×C₂₁₁	—	2	2	no	—
143	C₄×C₂₁₁	—	2	2	no	—
144	C₄×C₂₁₁	—	2	2	no	—
145	C₄×C₂₁₁	—	2	2	no	—
146	C₄×C₂₁₁	—	2	4	no	—
147	C₄×C₂₁₁	—	4	2	no	—
148	C₄×C₂₁₁	—	4	2	no	—
149	C₄×C₂₁₁	—	4	2	no	—
150	C₄×C₂₁₁	C₄×D₄	1	4	yes	—
151	C₂×C₂₁₁	—	2	4	no	—
152	C₂×C₂₁₁	—	4	2	no	—
153	C₂×C₂₁₁	C₂×#117	1	1	yes	characteristic
154	C₂×C₂₁₁	C₂×C₄×D₄	1	1	yes	characteristic
155	C₂×C₂₁₁	#520	1	1	yes	characteristic
156	C₂×C₂₁₁	#546	1	1	yes	characteristic
157	C₂×C₂₁₁	#548	1	1	yes	characteristic
158	C₂×C₂₁₁	#552	1	1	yes	characteristic
159	C₂×C₂₁₁	#553	1	1	yes	characteristic
160	C₂₁₁	#2352	1	1	yes	characteristic, direct product factor, Sylow
161	#2352	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂×C₄×D₄	C₂×C₂₁₁	1	1	yes	characteristic
163	C₂×#117	C₂×C₂₁₁	1	1	yes	characteristic, complemented
164	C₂²×C₄⋊C₄	C₂×C₂₁₁	1	1	yes	characteristic, complemented
165	#388	C₂×C₂₁₁	1	2	yes	complemented
166	#387	C₂×C₂₁₁	1	2	yes	complemented
167	#386	C₂×C₂₁₁	1	2	yes	—
168	#382	C₂×C₂₁₁	1	1	yes	characteristic, complemented
169	#380	C₂×C₂₁₁	1	1	yes	characteristic, complemented
170	#380	C₂×C₂₁₁	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄	C₂×C₂₁₁	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊C₄	C₂×C₂₁₁	1	2	yes	complemented
173	C₂²×D₄	C₂²×C₂₁₁	1	1	yes	characteristic
174	C₂³×C₄	C₂²×C₂₁₁	1	2	yes	—
175	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic
176	C₂³×C₄	C₂²×C₂₁₁	1	1	yes	characteristic
177	C₄×D₄	C₄×C₂₁₁	1	8	yes	complemented
178	#117	—	2	4	no	—
179	C₂×C₄⋊C₄	—	2	4	no	—
180	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	2	yes	—
182	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
184	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
190	C₂×C₂²⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
191	C₂×C₄²	C₂²×C₂₁₁	1	2	yes	—
192	C₂×C₄²	C₂²×C₂₁₁	1	2	yes	—
193	C₂×C₄²	C₂²×C₂₁₁	1	1	yes	characteristic
194	#95	C₂²×C₂₁₁	1	2	yes	—
195	#95	C₂²×C₂₁₁	1	2	yes	—
196	#95	C₂²×C₂₁₁	1	2	yes	—
197	#95	C₂²×C₂₁₁	1	2	yes	—
198	#95	C₂²×C₂₁₁	1	2	yes	—
199	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
200	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
201	C₂×D₄	—	2	2	no	—
202	C₂×D₄	—	2	2	no	—
203	C₂×D₄	C₂×C₄×C₂₁₁	1	4	yes	—
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	2	no	—
206	C₂²×C₄	—	2	2	no	—
207	C₂²×C₄	—	2	2	no	—
208	C₂²×C₄	—	2	4	no	—
209	C₂²×C₄	—	2	4	no	—
210	C₂²×C₄	—	4	2	no	—
211	C₂²×C₄	C₂×C₄×C₂₁₁	1	4	yes	—
212	C₂²×C₄	C₂×C₄×C₂₁₁	1	4	yes	complemented
213	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
214	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
215	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
216	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
217	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
218	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
219	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
220	C₂²×C₄	C₂³×C₂₁₁	1	2	yes	—
221	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
222	C₄⋊C₄	—	2	4	no	—
223	C₄⋊C₄	—	2	2	no	—
224	C₄⋊C₄	—	2	2	no	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	C₂×C₄×C₂₁₁	1	4	yes	complemented
227	C₄⋊C₄	D₄×C₂₁₁	1	4	yes	complemented
228	C₂²⋊C₄	—	2	4	no	—
229	C₂²⋊C₄	—	2	4	no	—
230	C₂²⋊C₄	—	4	2	no	—
231	C₂²⋊C₄	C₂×C₄×C₂₁₁	1	4	yes	—
232	C₂²⋊C₄	C₂×C₄×C₂₁₁	1	4	yes	complemented
233	C₄²	—	2	4	no	—
234	C₄²	—	4	2	no	—
235	C₄²	C₂×C₄×C₂₁₁	1	4	yes	complemented
236	C₂³	—	2	1	no	—
237	C₂³	—	2	1	no	—
238	C₂³	—	2	1	no	—
239	C₂³	—	2	1	no	—
240	C₂³	—	2	1	no	—
241	C₂³	—	2	1	no	—
242	C₂³	—	2	1	no	—
243	C₂³	—	2	1	no	—
244	C₂³	—	2	1	no	—
245	C₂³	—	2	1	no	—
246	C₂³	C₂²×C₄×C₂₁₁	1	2	yes	—
247	C₂³	C₂²×C₄×C₂₁₁	1	2	yes	—
248	C₂³	#41×C₂₁₁	1	2	yes	—
249	C₂³	#41×C₂₁₁	1	2	yes	—
250	C₂³	C₂⁴×C₂₁₁	1	1	yes	characteristic
251	D₄	—	2	8	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	1	no	—
257	C₂×C₄	—	2	1	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	2	1	no	—
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	2	8	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	—	2	2	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	4	8	no	—
274	C₂×C₄	C₂²×C₄×C₂₁₁	1	2	yes	—
275	C₂×C₄	C₂²×C₄×C₂₁₁	1	2	yes	—
276	C₂×C₄	C₂²×C₄×C₂₁₁	1	2	yes	—
277	C₂×C₄	C₂²×C₄×C₂₁₁	1	2	yes	—
278	C₂×C₄	C₂²×C₄×C₂₁₁	1	2	yes	—
279	C₂×C₄	C₂×D₄×C₂₁₁	1	4	yes	—
280	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
281	C₂×C₄	#41×C₂₁₁	1	2	yes	—
282	C₂²	—	2	2	no	—
283	C₂²	—	2	2	no	—
284	C₂²	—	2	2	no	—
285	C₂²	—	2	2	no	—
286	C₂²	—	2	2	no	—
287	C₂²	—	2	2	no	—
288	C₂²	—	2	2	no	—
289	C₂²	—	2	2	no	—
290	C₂²	—	2	2	no	—
291	C₂²	—	4	1	no	—
292	C₂²	—	4	1	no	—
293	C₂²	—	4	1	no	—
294	C₂²	—	4	1	no	—
295	C₂²	#117×C₂₁₁	1	4	yes	complemented
296	C₂²	C₂³×C₄×C₂₁₁	1	1	yes	characteristic
297	C₂²	C₂²×D₄×C₂₁₁	1	1	yes	characteristic
298	C₂²	C₂×#41×C₂₁₁	1	1	yes	characteristic
299	C₂²	C₂×#41×C₂₁₁	1	1	yes	characteristic
300	C₂²	C₂×#41×C₂₁₁	1	1	yes	characteristic
301	C₂²	H(5,𝔽₂)×C₂₁₁	1	1	yes	characteristic
302	C₂²	2₋¹⁺⁴×C₂₁₁	1	1	yes	characteristic
303	C₄	—	2	4	no	—
304	C₄	—	2	2	no	—
305	C₄	—	2	2	no	—
306	C₄	—	2	2	no	—
307	C₄	—	2	2	no	—
308	C₄	—	4	2	no	—
309	C₄	—	4	2	no	—
310	C₄	—	4	2	no	—
311	C₄	C₄×D₄×C₂₁₁	1	4	yes	—
312	C₂	—	2	4	no	—
313	C₂	—	4	2	no	—
314	C₂	C₂×#117×C₂₁₁	1	1	yes	characteristic
315	C₂	C₂×C₄×D₄×C₂₁₁	1	1	yes	characteristic
316	C₂	#520×C₂₁₁	1	1	yes	characteristic
317	C₂	#546×C₂₁₁	1	1	yes	characteristic
318	C₂	#548×C₂₁₁	1	1	yes	characteristic
319	C₂	#552×C₂₁₁	1	1	yes	characteristic
320	C₂	#553×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	C₂²×D₄×C₂₁₁	C₂²
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×#117×C₂₁₁	C₂	semidirect
3. C₂²×C₄⋊C₄×C₂₁₁	C₂	semidirect
4. #388×C₂₁₁	C₂	semidirect
5. #387×C₂₁₁	C₂	semidirect
7. #382×C₂₁₁	C₂	semidirect
8. #380×C₂₁₁	C₂	semidirect
9. #380×C₂₁₁	C₂	semidirect
10. C₄×C₄⋊C₄×C₂₁₁	C₂	semidirect
11. C₄×C₂²⋊C₄×C₂₁₁	C₂	semidirect
16. C₄×D₄×C₂₁₁	C₄	semidirect
51. C₂²×C₄×C₂₁₁	C₂×C₄	semidirect
65. C₄⋊C₄×C₂₁₁	C₂×C₄	semidirect
66. C₄⋊C₄×C₂₁₁	D₄	semidirect
71. C₂²⋊C₄×C₂₁₁	C₂×C₄	semidirect
74. C₄²×C₂₁₁	C₂×C₄	semidirect
134. C₂²×C₂₁₁	#117	semidirect
160. C₂₁₁	#2352	direct (N × H)
161. #2352	C₂₁₁	direct (N × H)
163. C₂×#117	C₂×C₂₁₁	semidirect
164. C₂²×C₄⋊C₄	C₂×C₂₁₁	semidirect
165. #388	C₂×C₂₁₁	semidirect
166. #387	C₂×C₂₁₁	semidirect
168. #382	C₂×C₂₁₁	semidirect
169. #380	C₂×C₂₁₁	semidirect
170. #380	C₂×C₂₁₁	semidirect
171. C₄×C₄⋊C₄	C₂×C₂₁₁	semidirect
172. C₄×C₂²⋊C₄	C₂×C₂₁₁	semidirect
177. C₄×D₄	C₄×C₂₁₁	semidirect
212. C₂²×C₄	C₂×C₄×C₂₁₁	semidirect
226. C₄⋊C₄	C₂×C₄×C₂₁₁	semidirect
227. C₄⋊C₄	D₄×C₂₁₁	semidirect
232. C₂²⋊C₄	C₂×C₄×C₂₁₁	semidirect
235. C₄²	C₂×C₄×C₂₁₁	semidirect
295. C₂²	#117×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄×C₂₁₁	2
C₂×#117×C₂₁₁	2
C₂²×C₄⋊C₄×C₂₁₁	2
#388×C₂₁₁	2
#387×C₂₁₁	2
#386×C₂₁₁	2
#382×C₂₁₁	2
#380×C₂₁₁	2
C₄×C₄⋊C₄×C₂₁₁	2
C₄×C₂²⋊C₄×C₂₁₁	2
#2352	211

Subgroups — #2352×C211 #41009972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2352×C₂₁₁ #41009972