Subgroups — C₂²×C₈×D₄×C₁₁ #14637323

Order 2816.

3694 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₄×C₁₁	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₁×C₂²⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₁₁	C₄	1	1	yes	characteristic
8	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
9	C₂³×C₈×C₁₁	—	2	16	no	—
10	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	24	yes	complemented
14	C₂×C₄×D₄×C₁₁	C₄	1	12	yes	—
15	C₂×C₄×D₄×C₁₁	C₂²	1	12	yes	—
16	C₂²×C₁₁×C₄⋊C₄	C₄	1	1	yes	characteristic
17	C₂²×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
18	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₁₁	C₂²	1	64	yes	direct product factor
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	12	yes	complemented
21	C₂×C₁₁×C₂²⋊C₈	C₂²	1	24	yes	complemented
22	C₂×C₄×C₈×C₁₁	C₂²	1	12	yes	complemented
23	C₂⁵×C₁₁	C₂×C₄	1	2	yes	—
24	C₂²×D₄×C₁₁	C₈	1	16	yes	direct product factor
25	C₂²×D₄×C₁₁	C₂×C₄	1	12	yes	—
26	C₂³×C₄×C₁₁	—	2	8	no	—
27	C₂³×C₄×C₁₁	—	2	8	no	—
28	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₁	C₂×C₄	1	12	yes	—
31	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
33	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
34	C₂²×C₈×C₁₁	—	2	8	no	—
35	C₂²×C₈×C₁₁	—	2	4	no	—
36	C₂²×C₈×C₁₁	—	2	96	no	—
37	C₂²×C₈×C₁₁	D₄	1	8	yes	direct product factor
38	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	32	yes	complemented
42	C₄×D₄×C₁₁	C₂×C₄	1	48	yes	—
43	C₄×D₄×C₁₁	C₂³	1	16	yes	—
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	12	yes	—
45	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	24	yes	—
46	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
47	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
48	C₁₁×C₄⋊C₈	C₂³	1	16	yes	complemented
49	C₁₁×C₂²⋊C₈	C₂³	1	32	yes	complemented
50	C₄×C₈×C₁₁	C₂³	1	16	yes	complemented
51	C₂²×C₈×D₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂⁴×C₁₁	—	2	8	no	—
53	C₂⁴×C₁₁	—	2	8	no	—
54	C₂⁴×C₁₁	C₂×C₈	1	16	yes	complemented
55	C₂⁴×C₁₁	C₂²×C₄	1	12	yes	—
56	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×D₄×C₁₁	C₂×C₈	1	96	yes	direct product factor
58	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
59	C₂²×C₄×C₁₁	—	2	8	no	—
60	C₂²×C₄×C₁₁	—	2	4	no	—
61	C₂²×C₄×C₁₁	—	2	48	no	—
62	C₂²×C₄×C₁₁	—	2	24	no	—
63	C₂²×C₄×C₁₁	—	2	24	no	—
64	C₂²×C₄×C₁₁	C₂×C₈	1	8	yes	complemented
65	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
66	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
67	C₂²×C₄×C₁₁	C₂²×C₄	1	24	yes	—
68	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
69	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
70	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
71	C₂²×C₄×C₁₁	#41	1	4	yes	—
72	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
73	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
74	C₂×C₈×C₁₁	—	2	64	no	—
75	C₂×C₈×C₁₁	—	2	24	no	—
76	C₂×C₈×C₁₁	—	2	12	no	—
77	C₂×C₈×C₁₁	C₂×D₄	1	24	yes	direct product factor
78	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
79	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
80	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
81	C₁₁×C₄⋊C₄	C₂²×C₄	1	16	yes	—
82	C₁₁×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
83	C₄²×C₁₁	C₂²×C₄	1	12	yes	—
84	C₄²×C₁₁	C₂⁴	1	4	yes	—
85	C₂⁴×C₈	C₂×C₁₁	1	2	yes	complemented
86	C₂²×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic
87	C₂×C₈×D₄	C₂×C₁₁	1	24	yes	direct product factor
88	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
89	C₂²×C₂²⋊C₈	C₂×C₁₁	1	2	yes	complemented
90	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
91	C₂³×C₁₁	—	2	24	no	—
92	C₂³×C₁₁	—	2	24	no	—
93	C₂³×C₁₁	—	2	64	no	—
94	C₂³×C₁₁	C₄×D₄	1	4	yes	—
95	C₂³×C₁₁	C₂²×C₈	1	4	yes	—
96	C₂³×C₁₁	C₂²×C₈	1	48	yes	complemented
97	C₂³×C₁₁	#131	1	4	yes	—
98	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
99	C₂³×C₁₁	C₂³×C₄	1	3	yes	—
100	D₄×C₁₁	C₂²×C₈	1	64	yes	direct product factor
101	C₂×C₄×C₁₁	—	2	24	no	—
102	C₂×C₄×C₁₁	—	2	12	no	—
103	C₂×C₄×C₁₁	—	2	48	no	—
104	C₂×C₄×C₁₁	—	2	8	no	—
105	C₂×C₄×C₁₁	—	2	8	no	—
106	C₂×C₄×C₁₁	C₄×D₄	1	12	yes	—
107	C₂×C₄×C₁₁	C₂²×C₈	1	24	yes	complemented
108	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
109	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
110	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
111	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
112	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
113	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
114	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
115	C₈×C₁₁	—	2	8	no	—
116	C₈×C₁₁	—	2	4	no	—
117	C₈×C₁₁	C₂²×D₄	1	8	yes	direct product factor
118	C₂³×D₄	C₄×C₁₁	1	1	yes	characteristic
119	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
120	C₂³×C₈	—	2	16	no	—
121	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
122	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
123	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
124	C₂³×C₈	C₂²×C₁₁	1	24	yes	complemented
125	C₂×C₄×D₄	C₄×C₁₁	1	12	yes	—
126	C₂×C₄×D₄	C₂²×C₁₁	1	12	yes	—
127	C₂²×C₄⋊C₄	C₄×C₁₁	1	1	yes	characteristic
128	C₂²×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
129	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
130	C₈×D₄	C₂²×C₁₁	1	64	yes	direct product factor
131	C₂×C₄⋊C₈	C₂²×C₁₁	1	12	yes	complemented
132	C₂×C₂²⋊C₈	C₂²×C₁₁	1	24	yes	complemented
133	C₂×C₄×C₈	C₂²×C₁₁	1	12	yes	complemented
134	C₂²×C₁₁	—	2	8	no	—
135	C₂²×C₁₁	—	2	96	no	—
136	C₂²×C₁₁	—	2	8	no	—
137	C₂²×C₁₁	C₈×D₄	1	16	yes	direct product factor
138	C₂²×C₁₁	C₂×C₄×D₄	1	6	yes	—
139	C₂²×C₁₁	C₂³×C₈	1	6	yes	—
140	C₂²×C₁₁	C₂³×C₈	1	16	yes	complemented
141	C₂²×C₁₁	C₂×#131	1	6	yes	—
142	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
143	C₄×C₁₁	—	2	8	no	—
144	C₄×C₁₁	—	2	4	no	—
145	C₄×C₁₁	C₂×C₄×D₄	1	6	yes	—
146	C₄×C₁₁	C₂³×C₈	1	8	yes	complemented
147	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
148	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
149	C₂⁵	C₂×C₄×C₁₁	1	2	yes	—
150	C₂²×D₄	C₈×C₁₁	1	16	yes	direct product factor
151	C₂²×D₄	C₂×C₄×C₁₁	1	12	yes	—
152	C₂³×C₄	—	2	8	no	—
153	C₂³×C₄	—	2	8	no	—
154	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
155	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
156	C₂³×C₄	C₂×C₄×C₁₁	1	12	yes	—
157	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
158	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
159	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
160	C₂²×C₈	—	2	8	no	—
161	C₂²×C₈	—	2	4	no	—
162	C₂²×C₈	—	2	96	no	—
163	C₂²×C₈	D₄×C₁₁	1	8	yes	direct product factor
164	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
165	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
166	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
167	C₂²×C₈	C₂³×C₁₁	1	32	yes	complemented
168	C₄×D₄	C₂×C₄×C₁₁	1	48	yes	—
169	C₄×D₄	C₂³×C₁₁	1	16	yes	—
170	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	12	yes	—
171	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	24	yes	—
172	C₂×C₄²	C₂×C₄×C₁₁	1	6	yes	—
173	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
174	C₄⋊C₈	C₂³×C₁₁	1	16	yes	complemented
175	C₂²⋊C₈	C₂³×C₁₁	1	32	yes	complemented
176	C₄×C₈	C₂³×C₁₁	1	16	yes	complemented
177	C₂×C₁₁	—	2	16	no	—
178	C₂×C₁₁	C₂×C₈×D₄	1	12	yes	direct product factor
179	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
180	C₂×C₁₁	C₂⁴×C₈	1	1	yes	characteristic
181	C₂×C₁₁	C₂²×#131	1	1	yes	characteristic
182	C₂⁴	—	2	8	no	—
183	C₂⁴	—	2	8	no	—
184	C₂⁴	C₂×C₈×C₁₁	1	16	yes	complemented
185	C₂⁴	C₂²×C₄×C₁₁	1	12	yes	—
186	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
187	C₂×D₄	C₂×C₈×C₁₁	1	96	yes	direct product factor
188	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
189	C₂²×C₄	—	2	8	no	—
190	C₂²×C₄	—	2	4	no	—
191	C₂²×C₄	—	2	48	no	—
192	C₂²×C₄	—	2	24	no	—
193	C₂²×C₄	—	2	24	no	—
194	C₂²×C₄	C₂×C₈×C₁₁	1	8	yes	complemented
195	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
196	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
197	C₂²×C₄	C₂²×C₄×C₁₁	1	24	yes	—
198	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
199	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
200	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
201	C₂²×C₄	C₁₁×#41	1	4	yes	—
202	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
203	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
204	C₂×C₈	—	2	24	no	—
205	C₂×C₈	—	2	12	no	—
206	C₂×C₈	—	2	64	no	—
207	C₂×C₈	C₂×D₄×C₁₁	1	24	yes	direct product factor
208	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
209	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
210	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
211	C₄⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
212	C₂²⋊C₄	C₂²×C₄×C₁₁	1	32	yes	—
213	C₄²	C₂²×C₄×C₁₁	1	12	yes	—
214	C₄²	C₂⁴×C₁₁	1	4	yes	—
215	C₁₁	C₂²×C₈×D₄	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³	—	2	24	no	—
217	C₂³	—	2	24	no	—
218	C₂³	—	2	64	no	—
219	C₂³	C₄×D₄×C₁₁	1	4	yes	—
220	C₂³	C₂²×C₈×C₁₁	1	4	yes	—
221	C₂³	C₂²×C₈×C₁₁	1	48	yes	complemented
222	C₂³	C₁₁×#131	1	4	yes	—
223	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
224	C₂³	C₂³×C₄×C₁₁	1	3	yes	—
225	D₄	C₂²×C₈×C₁₁	1	64	yes	direct product factor
226	C₂×C₄	—	2	24	no	—
227	C₂×C₄	—	2	12	no	—
228	C₂×C₄	—	2	48	no	—
229	C₂×C₄	—	2	8	no	—
230	C₂×C₄	—	2	8	no	—
231	C₂×C₄	C₄×D₄×C₁₁	1	12	yes	—
232	C₂×C₄	C₂²×C₈×C₁₁	1	24	yes	complemented
233	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
234	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
235	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
236	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
237	C₂×C₄	C₂²×D₄×C₁₁	1	6	yes	—
238	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
239	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
240	C₈	—	2	8	no	—
241	C₈	—	2	4	no	—
242	C₈	C₂²×D₄×C₁₁	1	8	yes	direct product factor
243	C₂²	—	2	8	no	—
244	C₂²	—	2	96	no	—
245	C₂²	—	2	8	no	—
246	C₂²	C₈×D₄×C₁₁	1	16	yes	direct product factor
247	C₂²	C₂×C₄×D₄×C₁₁	1	6	yes	—
248	C₂²	C₂³×C₈×C₁₁	1	6	yes	—
249	C₂²	C₂³×C₈×C₁₁	1	16	yes	complemented
250	C₂²	C₂×C₁₁×#131	1	6	yes	—
251	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
252	C₄	—	2	8	no	—
253	C₄	—	2	4	no	—
254	C₄	C₂×C₄×D₄×C₁₁	1	6	yes	—
255	C₄	C₂³×C₈×C₁₁	1	8	yes	complemented
256	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
257	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
258	C₂	—	2	16	no	—
259	C₂	C₂×C₈×D₄×C₁₁	1	12	yes	direct product factor
260	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
261	C₂	C₂⁴×C₈×C₁₁	1	1	yes	characteristic
262	C₂	C₂²×C₁₁×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₈×C₁₁	C₂²
commutator	C₂	C₂⁴×C₈×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂⁴×C₁₁	C₂²×C₄
prime radical	C₂³×D₄×C₁₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₈×C₁₁	C₂	semidirect
3. C₂×C₈×D₄×C₁₁	C₂	direct (N × H)
4. C₂²×C₁₁×C₄⋊C₈	C₂	semidirect
5. C₂²×C₁₁×C₂²⋊C₈	C₂	semidirect
6. C₂²×C₄×C₈×C₁₁	C₂	semidirect
13. C₂³×C₈×C₁₁	C₂²	semidirect
19. C₈×D₄×C₁₁	C₂²	direct (N × H)
20. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
21. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
22. C₂×C₄×C₈×C₁₁	C₂²	semidirect
24. C₂²×D₄×C₁₁	C₈	direct (N × H)
37. C₂²×C₈×C₁₁	D₄	direct (N × H)
41. C₂²×C₈×C₁₁	C₂³	semidirect
48. C₁₁×C₄⋊C₈	C₂³	semidirect
49. C₁₁×C₂²⋊C₈	C₂³	semidirect
50. C₄×C₈×C₁₁	C₂³	semidirect
51. C₂²×C₈×D₄	C₁₁	direct (N × H)
54. C₂⁴×C₁₁	C₂×C₈	semidirect
57. C₂×D₄×C₁₁	C₂×C₈	direct (N × H)
64. C₂²×C₄×C₁₁	C₂×C₈	semidirect
77. C₂×C₈×C₁₁	C₂×D₄	direct (N × H)
85. C₂⁴×C₈	C₂×C₁₁	semidirect
87. C₂×C₈×D₄	C₂×C₁₁	direct (N × H)
88. C₂²×C₄⋊C₈	C₂×C₁₁	semidirect
89. C₂²×C₂²⋊C₈	C₂×C₁₁	semidirect
90. C₂²×C₄×C₈	C₂×C₁₁	semidirect
96. C₂³×C₁₁	C₂²×C₈	semidirect
100. D₄×C₁₁	C₂²×C₈	direct (N × H)
107. C₂×C₄×C₁₁	C₂²×C₈	semidirect
117. C₈×C₁₁	C₂²×D₄	direct (N × H)
124. C₂³×C₈	C₂²×C₁₁	semidirect
130. C₈×D₄	C₂²×C₁₁	direct (N × H)
131. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
132. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
133. C₂×C₄×C₈	C₂²×C₁₁	semidirect
137. C₂²×C₁₁	C₈×D₄	direct (N × H)
140. C₂²×C₁₁	C₂³×C₈	semidirect
146. C₄×C₁₁	C₂³×C₈	semidirect
150. C₂²×D₄	C₈×C₁₁	direct (N × H)
163. C₂²×C₈	D₄×C₁₁	direct (N × H)
167. C₂²×C₈	C₂³×C₁₁	semidirect
174. C₄⋊C₈	C₂³×C₁₁	semidirect
175. C₂²⋊C₈	C₂³×C₁₁	semidirect
176. C₄×C₈	C₂³×C₁₁	semidirect
178. C₂×C₁₁	C₂×C₈×D₄	direct (N × H)
184. C₂⁴	C₂×C₈×C₁₁	semidirect
187. C₂×D₄	C₂×C₈×C₁₁	direct (N × H)
194. C₂²×C₄	C₂×C₈×C₁₁	semidirect
207. C₂×C₈	C₂×D₄×C₁₁	direct (N × H)
215. C₁₁	C₂²×C₈×D₄	direct (N × H)
221. C₂³	C₂²×C₈×C₁₁	semidirect
225. D₄	C₂²×C₈×C₁₁	direct (N × H)
232. C₂×C₄	C₂²×C₈×C₁₁	semidirect
242. C₈	C₂²×D₄×C₁₁	direct (N × H)
246. C₂²	C₈×D₄×C₁₁	direct (N × H)
249. C₂²	C₂³×C₈×C₁₁	semidirect
255. C₄	C₂³×C₈×C₁₁	semidirect
259. C₂	C₂×C₈×D₄×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₈×C₁₁	2
C₂²×C₄×D₄×C₁₁	2
C₂×C₈×D₄×C₁₁	2
C₂²×C₁₁×C₄⋊C₈	2
C₂²×C₁₁×C₂²⋊C₈	2
C₂²×C₄×C₈×C₁₁	2
C₂²×C₈×D₄	11

Subgroups — C22×C8×D4×C11 #14637323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₈×D₄×C₁₁ #14637323