Subgroups — C₄×C₁₁×AGL(1,ℤ/8) #13065782

Order 1408.

548 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#442	C₂	1	2	yes	maximal, complemented
5	C₁₁×#440	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
7	C₄×C₁₁×D₈	C₂	1	2	yes	maximal, complemented
8	C₁₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₁₁	—	2	1	no	—
15	C₁₁×AGL(1,ℤ/8)	C₄	1	8	yes	direct product factor
16	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
17	C₂×C₁₁×D₈	C₂²	1	2	yes	—
18	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
21	C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
22	C₄×D₄×C₁₁	—	2	1	no	—
23	C₄×D₄×C₁₁	—	2	1	no	—
24	C₄×D₄×C₁₁	—	2	1	no	—
25	C₄×D₄×C₁₁	—	2	1	no	—
26	C₄×D₄×C₁₁	C₂²	1	2	yes	—
27	C₄×D₄×C₁₁	C₂²	1	2	yes	—
28	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#117	—	2	1	no	—
31	C₁₁×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
34	C₂×C₄²×C₁₁	—	2	1	no	—
35	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
36	C₁₁×#107	C₂²	1	2	yes	complemented
37	C₁₁×#106	C₂²	1	2	yes	complemented
38	C₁₁×#103	C₂²	1	2	yes	complemented
39	C₁₁×#102	C₂²	1	2	yes	—
40	C₁₁×#102	C₂²	1	2	yes	—
41	C₁₁×#102	C₂²	1	2	yes	complemented
42	C₁₁×#97	C₂²	1	2	yes	complemented
43	C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
44	C₂⁴×C₁₁	—	2	1	no	—
45	C₁₁×#41	—	2	2	no	—
46	C₁₁×#41	C₂×C₄	1	4	yes	complemented
47	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×D₄×C₁₁	—	2	1	no	—
49	C₂×D₄×C₁₁	—	2	1	no	—
50	C₂×D₄×C₁₁	—	2	2	no	—
51	C₂×D₄×C₁₁	C₂×C₄	1	4	yes	complemented
52	C₂×D₄×C₁₁	C₂³	1	2	yes	—
53	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	—	2	1	no	—
55	C₂²×C₄×C₁₁	—	2	1	no	—
56	C₂²×C₄×C₁₁	—	2	1	no	—
57	C₂²×C₄×C₁₁	—	2	2	no	—
58	C₂²×C₄×C₁₁	—	2	1	no	—
59	C₂²×C₄×C₁₁	—	2	2	no	—
60	C₂²×C₄×C₁₁	—	4	4	no	—
61	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
65	C₁₁×D₈	C₂×C₄	1	8	yes	complemented
66	C₁₁×M₁₆	—	2	2	no	—
67	C₁₁×M₁₆	C₂×C₄	1	4	yes	complemented
68	C₂×C₈×C₁₁	C₂³	1	2	yes	—
69	C₂×C₈×C₁₁	C₂³	1	2	yes	—
70	C₁₁×C₄⋊C₄	—	2	1	no	—
71	C₁₁×C₄⋊C₄	—	2	1	no	—
72	C₁₁×C₄⋊C₄	—	2	1	no	—
73	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
76	C₁₁×C₂²⋊C₄	—	2	1	no	—
77	C₁₁×C₂²⋊C₄	—	2	2	no	—
78	C₁₁×C₂²⋊C₄	—	2	2	no	—
79	C₁₁×C₂²⋊C₄	—	2	1	no	—
80	C₁₁×C₂²⋊C₄	—	2	1	no	—
81	C₄²×C₁₁	—	2	1	no	—
82	C₄²×C₁₁	—	2	1	no	—
83	C₄²×C₁₁	—	2	1	no	—
84	C₄²×C₁₁	D₄	1	1	yes	characteristic
85	C₄²×C₁₁	D₄	1	1	yes	characteristic
86	C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₄×AGL(1,ℤ/8)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂³×C₁₁	—	2	4	no	—
90	C₂³×C₁₁	—	2	1	no	—
91	C₂³×C₁₁	—	2	2	no	—
92	C₂³×C₁₁	—	4	2	no	—
93	C₂³×C₁₁	—	4	2	no	—
94	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
95	Q₈×C₁₁	—	2	1	no	—
96	Q₈×C₁₁	C₂²×C₄	1	2	yes	complemented
97	D₄×C₁₁	—	2	4	no	—
98	D₄×C₁₁	—	2	4	no	—
99	D₄×C₁₁	—	2	2	no	—
100	D₄×C₁₁	—	2	1	no	—
101	D₄×C₁₁	C₂²×C₄	1	4	yes	—
102	D₄×C₁₁	C₂²×C₄	1	2	yes	complemented
103	C₂×C₄×C₁₁	—	2	1	no	—
104	C₂×C₄×C₁₁	—	2	4	no	—
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	—	2	1	no	—
107	C₂×C₄×C₁₁	—	2	1	no	—
108	C₂×C₄×C₁₁	—	2	2	no	—
109	C₂×C₄×C₁₁	—	4	1	no	—
110	C₂×C₄×C₁₁	—	4	2	no	—
111	C₂×C₄×C₁₁	—	4	4	no	—
112	C₂×C₄×C₁₁	—	4	2	no	—
113	C₂×C₄×C₁₁	—	4	2	no	—
114	C₂×C₄×C₁₁	—	4	4	no	—
115	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	#41	1	2	yes	—
122	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
123	C₈×C₁₁	—	2	2	no	—
124	C₈×C₁₁	C₂²×C₄	1	4	yes	complemented
125	C₂×AGL(1,ℤ/8)	C₂×C₁₁	1	1	yes	characteristic
126	C₄×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
127	C₂×C₄×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
128	#442	C₂×C₁₁	1	2	yes	complemented
129	#440	C₂×C₁₁	1	2	yes	complemented
130	C₄×SD₁₆	C₂×C₁₁	1	2	yes	complemented
131	C₄×D₈	C₂×C₁₁	1	2	yes	complemented
132	#428	C₂×C₁₁	1	1	yes	characteristic, complemented
133	#418	C₂×C₁₁	1	1	yes	characteristic, complemented
134	#417	C₂×C₁₁	1	1	yes	characteristic, complemented
135	C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
136	C₂²×C₁₁	—	2	1	no	—
137	C₂²×C₁₁	—	2	1	no	—
138	C₂²×C₁₁	—	2	2	no	—
139	C₂²×C₁₁	—	2	4	no	—
140	C₂²×C₁₁	—	4	8	no	—
141	C₂²×C₁₁	—	4	2	no	—
142	C₂²×C₁₁	—	4	1	no	—
143	C₂²×C₁₁	—	4	1	no	—
144	C₂²×C₁₁	—	4	2	no	—
145	C₂²×C₁₁	C₄×D₄	1	2	yes	—
146	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
147	C₄×C₁₁	—	2	2	no	—
148	C₄×C₁₁	—	2	1	no	—
149	C₄×C₁₁	—	2	1	no	—
150	C₄×C₁₁	—	2	1	no	—
151	C₄×C₁₁	—	4	1	no	—
152	C₄×C₁₁	—	4	2	no	—
153	C₄×C₁₁	—	4	1	no	—
154	C₄×C₁₁	C₄×D₄	1	2	yes	—
155	C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	direct product factor
156	C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
157	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
158	C₂×#41	C₂²×C₁₁	1	1	yes	characteristic
159	C₂²×D₄	C₂²×C₁₁	1	1	yes	characteristic
160	C₂³×C₄	—	2	1	no	—
161	AGL(1,ℤ/8)	C₄×C₁₁	1	8	yes	direct product factor
162	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
163	C₂×D₈	C₂²×C₁₁	1	2	yes	—
164	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
165	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
166	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
167	C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
168	C₄×D₄	—	2	1	no	—
169	C₄×D₄	—	2	1	no	—
170	C₄×D₄	—	2	1	no	—
171	C₄×D₄	—	2	1	no	—
172	C₄×D₄	C₂²×C₁₁	1	2	yes	—
173	C₄×D₄	C₂²×C₁₁	1	2	yes	—
174	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
175	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
176	#117	—	2	1	no	—
177	#117	C₂²×C₁₁	1	1	yes	characteristic
178	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
179	C₂×C₂²⋊C₄	—	2	1	no	—
180	C₂×C₄²	—	2	1	no	—
181	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
182	#107	C₂²×C₁₁	1	2	yes	complemented
183	#106	C₂²×C₁₁	1	2	yes	complemented
184	#103	C₂²×C₁₁	1	2	yes	complemented
185	#102	C₂²×C₁₁	1	2	yes	—
186	#102	C₂²×C₁₁	1	2	yes	—
187	#102	C₂²×C₁₁	1	2	yes	complemented
188	#97	C₂²×C₁₁	1	2	yes	complemented
189	C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
190	C₂×C₁₁	—	2	2	no	—
191	C₂×C₁₁	—	4	2	no	—
192	C₂×C₁₁	—	4	4	no	—
193	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×C₁₁	#575	1	1	yes	characteristic
196	C₂⁴	—	2	1	no	—
197	#41	—	2	2	no	—
198	#41	C₂×C₄×C₁₁	1	4	yes	complemented
199	C₂×Q₈	C₂³×C₁₁	1	1	yes	characteristic
200	C₂×D₄	—	2	1	no	—
201	C₂×D₄	—	2	1	no	—
202	C₂×D₄	—	2	2	no	—
203	C₂×D₄	C₂×C₄×C₁₁	1	4	yes	complemented
204	C₂×D₄	C₂³×C₁₁	1	2	yes	—
205	C₂×D₄	C₂³×C₁₁	1	1	yes	characteristic
206	C₂²×C₄	—	2	1	no	—
207	C₂²×C₄	—	2	1	no	—
208	C₂²×C₄	—	2	1	no	—
209	C₂²×C₄	—	2	1	no	—
210	C₂²×C₄	—	2	2	no	—
211	C₂²×C₄	—	2	2	no	—
212	C₂²×C₄	—	4	4	no	—
213	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
214	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
215	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
216	SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
217	D₈	C₂×C₄×C₁₁	1	8	yes	complemented
218	M₁₆	—	2	2	no	—
219	M₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
220	C₂×C₈	C₂³×C₁₁	1	2	yes	—
221	C₂×C₈	C₂³×C₁₁	1	2	yes	—
222	C₄⋊C₄	—	2	1	no	—
223	C₄⋊C₄	—	2	1	no	—
224	C₄⋊C₄	—	2	1	no	—
225	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
226	C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
227	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
228	C₂²⋊C₄	—	2	1	no	—
229	C₂²⋊C₄	—	2	2	no	—
230	C₂²⋊C₄	—	2	2	no	—
231	C₂²⋊C₄	—	2	1	no	—
232	C₂²⋊C₄	—	2	1	no	—
233	C₄²	—	2	1	no	—
234	C₄²	—	2	1	no	—
235	C₄²	—	2	1	no	—
236	C₄²	D₄×C₁₁	1	1	yes	characteristic
237	C₄²	D₄×C₁₁	1	1	yes	characteristic
238	C₄²	C₂³×C₁₁	1	1	yes	characteristic
239	C₄²	C₂³×C₁₁	1	1	yes	characteristic
240	C₁₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
241	C₂³	—	2	4	no	—
242	C₂³	—	2	1	no	—
243	C₂³	—	2	2	no	—
244	C₂³	—	4	2	no	—
245	C₂³	—	4	2	no	—
246	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
247	Q₈	—	2	1	no	—
248	Q₈	C₂²×C₄×C₁₁	1	2	yes	complemented
249	D₄	—	2	4	no	—
250	D₄	—	2	4	no	—
251	D₄	—	2	2	no	—
252	D₄	—	2	1	no	—
253	D₄	C₂²×C₄×C₁₁	1	4	yes	—
254	D₄	C₂²×C₄×C₁₁	1	2	yes	complemented
255	C₂×C₄	—	2	1	no	—
256	C₂×C₄	—	2	4	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	2	1	no	—
259	C₂×C₄	—	2	1	no	—
260	C₂×C₄	—	2	2	no	—
261	C₂×C₄	—	4	1	no	—
262	C₂×C₄	—	4	2	no	—
263	C₂×C₄	—	4	4	no	—
264	C₂×C₄	—	4	2	no	—
265	C₂×C₄	—	4	2	no	—
266	C₂×C₄	—	4	4	no	—
267	C₂×C₄	C₂²×C₄×C₁₁	1	2	yes	—
268	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
269	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
270	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
271	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
272	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
273	C₂×C₄	C₁₁×#41	1	2	yes	—
274	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
275	C₈	—	2	2	no	—
276	C₈	C₂²×C₄×C₁₁	1	4	yes	complemented
277	C₂²	—	2	1	no	—
278	C₂²	—	2	1	no	—
279	C₂²	—	2	2	no	—
280	C₂²	—	2	4	no	—
281	C₂²	—	4	8	no	—
282	C₂²	—	4	2	no	—
283	C₂²	—	4	1	no	—
284	C₂²	—	4	1	no	—
285	C₂²	—	4	2	no	—
286	C₂²	C₄×D₄×C₁₁	1	2	yes	—
287	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
288	C₄	—	2	2	no	—
289	C₄	—	2	1	no	—
290	C₄	—	2	1	no	—
291	C₄	—	2	1	no	—
292	C₄	—	4	2	no	—
293	C₄	—	4	1	no	—
294	C₄	—	4	1	no	—
295	C₄	C₄×D₄×C₁₁	1	2	yes	—
296	C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	direct product factor
297	C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
298	C₄	C₂×C₁₁×#41	1	1	yes	characteristic
299	C₂	—	2	2	no	—
300	C₂	—	4	4	no	—
301	C₂	—	4	2	no	—
302	C₂	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
303	C₂	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₂	C₁₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×D₄
commutator	C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×D₄
prime radical	C₂×C₁₁×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₁×#41	C₂	semidirect
3. C₂×C₄×D₄×C₁₁	C₂	semidirect
4. C₁₁×#442	C₂	semidirect
5. C₁₁×#440	C₂	semidirect
6. C₄×C₁₁×SD₁₆	C₂	semidirect
7. C₄×C₁₁×D₈	C₂	semidirect
8. C₁₁×#428	C₂	semidirect
9. C₁₁×#418	C₂	semidirect
10. C₁₁×#417	C₂	semidirect
11. C₄×C₁₁×M₁₆	C₂	semidirect
15. C₁₁×AGL(1,ℤ/8)	C₄	direct (N × H)
20. C₄×Q₈×C₁₁	C₂²	semidirect
21. C₄×Q₈×C₁₁	C₂²	semidirect
28. C₄×D₄×C₁₁	C₂²	semidirect
29. C₄×D₄×C₁₁	C₂²	semidirect
36. C₁₁×#107	C₂²	semidirect
37. C₁₁×#106	C₂²	semidirect
38. C₁₁×#103	C₂²	semidirect
41. C₁₁×#102	C₂²	semidirect
42. C₁₁×#97	C₂²	semidirect
43. C₄×C₈×C₁₁	C₂²	semidirect
46. C₁₁×#41	C₂×C₄	semidirect
51. C₂×D₄×C₁₁	C₂×C₄	semidirect
64. C₁₁×SD₁₆	C₂×C₄	semidirect
65. C₁₁×D₈	C₂×C₄	semidirect
67. C₁₁×M₁₆	C₂×C₄	semidirect
88. C₄×AGL(1,ℤ/8)	C₁₁	direct (N × H)
96. Q₈×C₁₁	C₂²×C₄	semidirect
102. D₄×C₁₁	C₂²×C₄	semidirect
124. C₈×C₁₁	C₂²×C₄	semidirect
126. C₄×#41	C₂×C₁₁	semidirect
127. C₂×C₄×D₄	C₂×C₁₁	semidirect
128. #442	C₂×C₁₁	semidirect
129. #440	C₂×C₁₁	semidirect
130. C₄×SD₁₆	C₂×C₁₁	semidirect
131. C₄×D₈	C₂×C₁₁	semidirect
132. #428	C₂×C₁₁	semidirect
133. #418	C₂×C₁₁	semidirect
134. #417	C₂×C₁₁	semidirect
135. C₄×M₁₆	C₂×C₁₁	semidirect
155. C₄×C₁₁	AGL(1,ℤ/8)	direct (N × H)
161. AGL(1,ℤ/8)	C₄×C₁₁	direct (N × H)
166. C₄×Q₈	C₂²×C₁₁	semidirect
167. C₄×Q₈	C₂²×C₁₁	semidirect
174. C₄×D₄	C₂²×C₁₁	semidirect
175. C₄×D₄	C₂²×C₁₁	semidirect
182. #107	C₂²×C₁₁	semidirect
183. #106	C₂²×C₁₁	semidirect
184. #103	C₂²×C₁₁	semidirect
187. #102	C₂²×C₁₁	semidirect
188. #97	C₂²×C₁₁	semidirect
189. C₄×C₈	C₂²×C₁₁	semidirect
198. #41	C₂×C₄×C₁₁	semidirect
203. C₂×D₄	C₂×C₄×C₁₁	semidirect
216. SD₁₆	C₂×C₄×C₁₁	semidirect
217. D₈	C₂×C₄×C₁₁	semidirect
219. M₁₆	C₂×C₄×C₁₁	semidirect
240. C₁₁	C₄×AGL(1,ℤ/8)	direct (N × H)
248. Q₈	C₂²×C₄×C₁₁	semidirect
254. D₄	C₂²×C₄×C₁₁	semidirect
276. C₈	C₂²×C₄×C₁₁	semidirect
296. C₄	C₁₁×AGL(1,ℤ/8)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×AGL(1,ℤ/8)	2
C₄×C₁₁×#41	2
C₂×C₄×D₄×C₁₁	2
C₁₁×#442	2
C₁₁×#440	2
C₄×C₁₁×SD₁₆	2
C₄×C₁₁×D₈	2
C₁₁×#428	2
C₁₁×#418	2
C₁₁×#417	2
C₄×C₁₁×M₁₆	2
C₄×AGL(1,ℤ/8)	11

Subgroups — C4×C11×AGL(1,ℤ/8) #13065782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×AGL(1,ℤ/8) #13065782