Subgroups — C₂²×C₁₁×#548 #14639891

Order 2816.

12142 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#548	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₁₁×#124	C₂	1	3	yes	maximal, complemented
5	C₂²×C₁₁×C₂²⋊Q₈	C₂	1	3	yes	maximal, complemented
6	C₂²×C₁₁×#121	C₂	1	3	yes	maximal, complemented
7	C₂²×C₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₁₁	C₂	1	3	yes	maximal, complemented
9	C₂²×C₁₁×#41	—	2	16	no	—
10	C₂²×C₁₁×#41	C₂²	1	24	yes	complemented
11	C₂³×Q₈×C₁₁	—	2	16	no	—
12	C₂³×Q₈×C₁₁	C₂²	1	3	yes	—
13	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₁	C₂²	1	24	yes	complemented
15	C₂³×D₄×C₁₁	C₂²	1	3	yes	—
16	C₂³×D₄×C₁₁	C₂²	1	3	yes	—
17	C₂⁴×C₄×C₁₁	C₂²	1	3	yes	—
18	C₂⁴×C₄×C₁₁	C₂²	1	3	yes	—
19	C₁₁×#548	C₂²	1	256	yes	direct product factor
20	C₂×C₁₁×#124	C₂²	1	72	yes	complemented
21	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	72	yes	complemented
22	C₂×C₁₁×#121	C₂²	1	72	yes	complemented
23	C₂×C₄×Q₈×C₁₁	C₂²	1	24	yes	complemented
24	C₂×C₄×D₄×C₁₁	C₂²	1	72	yes	complemented
25	C₂²×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
26	C₂²×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
27	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	3	yes	—
29	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	6	yes	—
30	C₂²×C₄²×C₁₁	C₂²	1	3	yes	—
31	C₂⁵×C₁₁	C₂³	1	3	yes	—
32	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
33	C₂×C₁₁×#41	—	2	192	no	—
34	C₂×C₁₁×#41	C₂³	1	64	yes	complemented
35	C₂²×Q₈×C₁₁	—	2	192	no	—
36	C₂²×Q₈×C₁₁	—	2	24	no	—
37	C₂²×Q₈×C₁₁	D₄	1	16	yes	complemented
38	C₂²×Q₈×C₁₁	C₂³	1	36	yes	—
39	C₂²×Q₈×C₁₁	C₂³	1	12	yes	—
40	C₂²×Q₈×C₁₁	C₂³	1	64	yes	complemented
41	C₂²×D₄×C₁₁	—	2	24	no	—
42	C₂²×D₄×C₁₁	—	2	24	no	—
43	C₂²×D₄×C₁₁	C₂³	1	36	yes	—
44	C₂²×D₄×C₁₁	C₂³	1	36	yes	—
45	C₂³×C₄×C₁₁	—	2	24	no	—
46	C₂³×C₄×C₁₁	—	2	24	no	—
47	C₂³×C₄×C₁₁	C₂³	1	36	yes	—
48	C₂³×C₄×C₁₁	C₂³	1	36	yes	—
49	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
51	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
52	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₁	C₂³	1	3	yes	—
54	C₁₁×#124	C₂³	1	192	yes	complemented
55	C₁₁×C₂²⋊Q₈	C₂³	1	192	yes	complemented
56	C₁₁×#121	C₂³	1	192	yes	complemented
57	C₄×Q₈×C₁₁	C₂³	1	64	yes	complemented
58	C₄×D₄×C₁₁	C₂³	1	192	yes	complemented
59	C₂×C₁₁×C₄⋊C₄	C₂³	1	36	yes	—
60	C₂×C₁₁×C₄⋊C₄	C₂³	1	36	yes	—
61	C₂×C₁₁×C₂²⋊C₄	C₂³	1	12	yes	—
62	C₂×C₁₁×C₂²⋊C₄	C₂³	1	36	yes	—
63	C₂×C₁₁×C₂²⋊C₄	C₂³	1	72	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	36	yes	—
65	C₂²×#548	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₁	—	2	4	no	—
67	C₂⁴×C₁₁	—	2	4	no	—
68	C₂⁴×C₁₁	—	2	12	no	—
69	C₂⁴×C₁₁	—	2	12	no	—
70	C₂⁴×C₁₁	—	2	12	no	—
71	C₂⁴×C₁₁	#41	1	8	yes	complemented
72	C₂⁴×C₁₁	C₂⁴	1	18	yes	—
73	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
74	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
75	C₁₁×#41	—	2	256	no	—
76	C₂×Q₈×C₁₁	—	2	256	no	—
77	C₂×Q₈×C₁₁	—	2	144	no	—
78	C₂×Q₈×C₁₁	C₂×D₄	1	96	yes	complemented
79	C₂×Q₈×C₁₁	C₂⁴	1	48	yes	—
80	C₂×Q₈×C₁₁	C₂⁴	1	16	yes	—
81	C₂×D₄×C₁₁	—	2	144	no	—
82	C₂×D₄×C₁₁	—	2	144	no	—
83	C₂×D₄×C₁₁	C₂⁴	1	48	yes	—
84	C₂×D₄×C₁₁	C₂⁴	1	48	yes	—
85	C₂²×C₄×C₁₁	—	2	4	no	—
86	C₂²×C₄×C₁₁	—	2	12	no	—
87	C₂²×C₄×C₁₁	—	2	12	no	—
88	C₂²×C₄×C₁₁	—	2	4	no	—
89	C₂²×C₄×C₁₁	—	2	144	no	—
90	C₂²×C₄×C₁₁	—	2	144	no	—
91	C₂²×C₄×C₁₁	C₂×D₄	1	24	yes	—
92	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₁₁	C₂⁴	1	18	yes	—
94	C₂²×C₄×C₁₁	C₂⁴	1	18	yes	—
95	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₁₁	C₂⁴	1	48	yes	—
97	C₂²×C₄×C₁₁	C₂⁴	1	48	yes	—
98	C₂²×C₄×C₁₁	C₂⁴	1	18	yes	—
99	C₁₁×C₄⋊C₄	C₂⁴	1	48	yes	—
100	C₁₁×C₄⋊C₄	C₂⁴	1	48	yes	—
101	C₁₁×C₂²⋊C₄	C₂⁴	1	16	yes	—
102	C₁₁×C₂²⋊C₄	C₂⁴	1	48	yes	—
103	C₁₁×C₂²⋊C₄	C₂⁴	1	96	yes	—
104	C₄²×C₁₁	C₂⁴	1	48	yes	—
105	C₂³×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
106	C₂⁴×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
107	C₂×#548	C₂×C₁₁	1	48	yes	direct product factor
108	C₂²×#124	C₂×C₁₁	1	3	yes	complemented
109	C₂²×C₂²⋊Q₈	C₂×C₁₁	1	3	yes	complemented
110	C₂²×#121	C₂×C₁₁	1	3	yes	complemented
111	C₂²×C₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
112	C₂²×C₄×D₄	C₂×C₁₁	1	3	yes	complemented
113	C₂³×C₁₁	—	2	32	no	—
114	C₂³×C₁₁	—	2	12	no	—
115	C₂³×C₁₁	—	2	12	no	—
116	C₂³×C₁₁	—	2	36	no	—
117	C₂³×C₁₁	—	2	36	no	—
118	C₂³×C₁₁	—	2	36	no	—
119	C₂³×C₁₁	—	4	48	no	—
120	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
121	C₂³×C₁₁	C₂×#41	1	4	yes	—
122	C₂³×C₁₁	C₂×#41	1	24	yes	complemented
123	C₂³×C₁₁	2₋¹⁺⁴	1	4	yes	—
124	C₂³×C₁₁	C₂⁵	1	12	yes	—
125	C₂³×C₁₁	C₂⁵	1	4	yes	—
126	C₂³×C₁₁	C₂⁵	1	3	yes	—
127	Q₈×C₁₁	—	2	96	no	—
128	Q₈×C₁₁	C₂²×D₄	1	64	yes	complemented
129	D₄×C₁₁	—	2	96	no	—
130	D₄×C₁₁	—	2	96	no	—
131	C₂×C₄×C₁₁	—	2	12	no	—
132	C₂×C₄×C₁₁	—	2	36	no	—
133	C₂×C₄×C₁₁	—	2	36	no	—
134	C₂×C₄×C₁₁	—	2	12	no	—
135	C₂×C₄×C₁₁	—	2	96	no	—
136	C₂×C₄×C₁₁	—	2	96	no	—
137	C₂×C₄×C₁₁	C₂²×D₄	1	72	yes	—
138	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
139	C₂×C₄×C₁₁	C₂⁵	1	12	yes	—
140	C₂×C₄×C₁₁	C₂⁵	1	12	yes	—
141	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
142	C₂×C₄×C₁₁	C₂⁵	1	12	yes	—
143	C₂²×#41	—	2	16	no	—
144	C₂²×#41	C₂²×C₁₁	1	24	yes	complemented
145	C₂³×Q₈	—	2	16	no	—
146	C₂³×Q₈	C₂²×C₁₁	1	3	yes	—
147	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
148	C₂³×Q₈	C₂²×C₁₁	1	24	yes	complemented
149	C₂³×D₄	C₂²×C₁₁	1	3	yes	—
150	C₂³×D₄	C₂²×C₁₁	1	3	yes	—
151	C₂⁴×C₄	C₂²×C₁₁	1	3	yes	—
152	C₂⁴×C₄	C₂²×C₁₁	1	3	yes	—
153	#548	C₂²×C₁₁	1	256	yes	direct product factor
154	C₂×#124	C₂²×C₁₁	1	72	yes	complemented
155	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	72	yes	complemented
156	C₂×#121	C₂²×C₁₁	1	72	yes	complemented
157	C₂×C₄×Q₈	C₂²×C₁₁	1	24	yes	complemented
158	C₂×C₄×D₄	C₂²×C₁₁	1	72	yes	complemented
159	C₂²×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
160	C₂²×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
161	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
162	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	3	yes	—
163	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	6	yes	—
164	C₂²×C₄²	C₂²×C₁₁	1	3	yes	—
165	C₂²×C₁₁	—	2	4	no	—
166	C₂²×C₁₁	—	2	4	no	—
167	C₂²×C₁₁	—	2	48	no	—
168	C₂²×C₁₁	—	2	12	no	—
169	C₂²×C₁₁	—	2	12	no	—
170	C₂²×C₁₁	—	2	12	no	—
171	C₂²×C₁₁	—	4	72	no	—
172	C₂²×C₁₁	#548	1	16	yes	direct product factor
173	C₂²×C₁₁	C₂³×D₄	1	6	yes	—
174	C₂²×C₁₁	C₂²×#41	1	6	yes	—
175	C₂²×C₁₁	C₂²×#41	1	8	yes	complemented
176	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	6	yes	—
177	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
178	C₄×C₁₁	—	2	4	no	—
179	C₄×C₁₁	—	2	12	no	—
180	C₄×C₁₁	—	2	12	no	—
181	C₄×C₁₁	—	2	4	no	—
182	C₄×C₁₁	C₂³×D₄	1	24	yes	—
183	C₂⁵	C₂³×C₁₁	1	3	yes	—
184	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
185	C₂×#41	—	2	192	no	—
186	C₂×#41	C₂³×C₁₁	1	64	yes	complemented
187	C₂²×Q₈	—	2	192	no	—
188	C₂²×Q₈	—	2	24	no	—
189	C₂²×Q₈	D₄×C₁₁	1	16	yes	complemented
190	C₂²×Q₈	C₂³×C₁₁	1	36	yes	—
191	C₂²×Q₈	C₂³×C₁₁	1	12	yes	—
192	C₂²×Q₈	C₂³×C₁₁	1	64	yes	complemented
193	C₂²×D₄	—	2	24	no	—
194	C₂²×D₄	—	2	24	no	—
195	C₂²×D₄	C₂³×C₁₁	1	36	yes	—
196	C₂²×D₄	C₂³×C₁₁	1	36	yes	—
197	C₂³×C₄	—	2	24	no	—
198	C₂³×C₄	—	2	24	no	—
199	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
200	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
201	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
202	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₁₁	1	36	yes	—
204	C₂³×C₄	C₂³×C₁₁	1	36	yes	—
205	C₂³×C₄	C₂³×C₁₁	1	3	yes	—
206	#124	C₂³×C₁₁	1	192	yes	complemented
207	C₂²⋊Q₈	C₂³×C₁₁	1	192	yes	complemented
208	#121	C₂³×C₁₁	1	192	yes	complemented
209	C₄×Q₈	C₂³×C₁₁	1	64	yes	complemented
210	C₄×D₄	C₂³×C₁₁	1	192	yes	complemented
211	C₂×C₄⋊C₄	C₂³×C₁₁	1	36	yes	—
212	C₂×C₄⋊C₄	C₂³×C₁₁	1	36	yes	—
213	C₂×C₂²⋊C₄	C₂³×C₁₁	1	12	yes	—
214	C₂×C₂²⋊C₄	C₂³×C₁₁	1	36	yes	—
215	C₂×C₂²⋊C₄	C₂³×C₁₁	1	72	yes	—
216	C₂×C₄²	C₂³×C₁₁	1	36	yes	—
217	C₂×C₁₁	—	2	8	no	—
218	C₂×C₁₁	—	4	12	no	—
219	C₂×C₁₁	C₂×#548	1	12	yes	direct product factor
220	C₂×C₁₁	C₂⁴×D₄	1	1	yes	characteristic
221	C₂×C₁₁	C₂³×#41	1	1	yes	characteristic
222	C₂×C₁₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂⁴	—	2	4	no	—
224	C₂⁴	—	2	4	no	—
225	C₂⁴	—	2	12	no	—
226	C₂⁴	—	2	12	no	—
227	C₂⁴	—	2	12	no	—
228	C₂⁴	C₁₁×#41	1	8	yes	complemented
229	C₂⁴	C₂⁴×C₁₁	1	18	yes	—
230	C₂⁴	C₂⁴×C₁₁	1	6	yes	—
231	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
232	#41	—	2	256	no	—
233	C₂×Q₈	—	2	256	no	—
234	C₂×Q₈	—	2	144	no	—
235	C₂×Q₈	C₂×D₄×C₁₁	1	96	yes	complemented
236	C₂×Q₈	C₂⁴×C₁₁	1	48	yes	—
237	C₂×Q₈	C₂⁴×C₁₁	1	16	yes	—
238	C₂×D₄	—	2	144	no	—
239	C₂×D₄	—	2	144	no	—
240	C₂×D₄	C₂⁴×C₁₁	1	48	yes	—
241	C₂×D₄	C₂⁴×C₁₁	1	48	yes	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	12	no	—
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	4	no	—
246	C₂²×C₄	—	2	144	no	—
247	C₂²×C₄	—	2	144	no	—
248	C₂²×C₄	C₂×D₄×C₁₁	1	24	yes	—
249	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
250	C₂²×C₄	C₂⁴×C₁₁	1	18	yes	—
251	C₂²×C₄	C₂⁴×C₁₁	1	18	yes	—
252	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
253	C₂²×C₄	C₂⁴×C₁₁	1	48	yes	—
254	C₂²×C₄	C₂⁴×C₁₁	1	48	yes	—
255	C₂²×C₄	C₂⁴×C₁₁	1	18	yes	—
256	C₄⋊C₄	C₂⁴×C₁₁	1	48	yes	—
257	C₄⋊C₄	C₂⁴×C₁₁	1	48	yes	—
258	C₂²⋊C₄	C₂⁴×C₁₁	1	16	yes	—
259	C₂²⋊C₄	C₂⁴×C₁₁	1	48	yes	—
260	C₂²⋊C₄	C₂⁴×C₁₁	1	96	yes	—
261	C₄²	C₂⁴×C₁₁	1	48	yes	—
262	C₁₁	C₂²×#548	1	1	yes	characteristic, direct product factor, Sylow
263	C₂³	—	2	32	no	—
264	C₂³	—	2	12	no	—
265	C₂³	—	2	12	no	—
266	C₂³	—	2	36	no	—
267	C₂³	—	2	36	no	—
268	C₂³	—	2	36	no	—
269	C₂³	—	4	48	no	—
270	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
271	C₂³	C₂×C₁₁×#41	1	4	yes	—
272	C₂³	C₂×C₁₁×#41	1	24	yes	complemented
273	C₂³	C₁₁×2₋¹⁺⁴	1	4	yes	—
274	C₂³	C₂⁵×C₁₁	1	12	yes	—
275	C₂³	C₂⁵×C₁₁	1	4	yes	—
276	C₂³	C₂⁵×C₁₁	1	3	yes	—
277	Q₈	—	2	96	no	—
278	Q₈	C₂²×D₄×C₁₁	1	64	yes	complemented
279	D₄	—	2	96	no	—
280	D₄	—	2	96	no	—
281	C₂×C₄	—	2	12	no	—
282	C₂×C₄	—	2	36	no	—
283	C₂×C₄	—	2	36	no	—
284	C₂×C₄	—	2	12	no	—
285	C₂×C₄	—	2	96	no	—
286	C₂×C₄	—	2	96	no	—
287	C₂×C₄	C₂²×D₄×C₁₁	1	72	yes	—
288	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
289	C₂×C₄	C₂⁵×C₁₁	1	12	yes	—
290	C₂×C₄	C₂⁵×C₁₁	1	12	yes	—
291	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
292	C₂×C₄	C₂⁵×C₁₁	1	12	yes	—
293	C₂²	—	2	48	no	—
294	C₂²	—	2	4	no	—
295	C₂²	—	2	4	no	—
296	C₂²	—	2	12	no	—
297	C₂²	—	2	12	no	—
298	C₂²	—	2	12	no	—
299	C₂²	—	4	72	no	—
300	C₂²	C₁₁×#548	1	16	yes	direct product factor
301	C₂²	C₂³×D₄×C₁₁	1	6	yes	—
302	C₂²	C₂²×C₁₁×#41	1	6	yes	—
303	C₂²	C₂²×C₁₁×#41	1	8	yes	complemented
304	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	6	yes	—
305	C₂²	C₂⁶×C₁₁	1	1	yes	characteristic
306	C₄	—	2	4	no	—
307	C₄	—	2	12	no	—
308	C₄	—	2	12	no	—
309	C₄	—	2	4	no	—
310	C₄	C₂³×D₄×C₁₁	1	24	yes	—
311	C₂	—	2	8	no	—
312	C₂	—	4	12	no	—
313	C₂	C₂×C₁₁×#548	1	12	yes	direct product factor
314	C₂	C₂⁴×D₄×C₁₁	1	1	yes	characteristic
315	C₂	C₂³×C₁₁×#41	1	1	yes	characteristic
316	C₂	C₂²×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×#41	C₂	semidirect
2. C₂⁴×Q₈×C₁₁	C₂	semidirect
3. C₂×C₁₁×#548	C₂	direct (N × H)
4. C₂²×C₁₁×#124	C₂	semidirect
5. C₂²×C₁₁×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₁₁×#121	C₂	semidirect
7. C₂²×C₄×Q₈×C₁₁	C₂	semidirect
8. C₂²×C₄×D₄×C₁₁	C₂	semidirect
10. C₂²×C₁₁×#41	C₂²	semidirect
14. C₂³×Q₈×C₁₁	C₂²	semidirect
19. C₁₁×#548	C₂²	direct (N × H)
20. C₂×C₁₁×#124	C₂²	semidirect
21. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
22. C₂×C₁₁×#121	C₂²	semidirect
23. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
24. C₂×C₄×D₄×C₁₁	C₂²	semidirect
34. C₂×C₁₁×#41	C₂³	semidirect
37. C₂²×Q₈×C₁₁	D₄	semidirect
40. C₂²×Q₈×C₁₁	C₂³	semidirect
54. C₁₁×#124	C₂³	semidirect
55. C₁₁×C₂²⋊Q₈	C₂³	semidirect
56. C₁₁×#121	C₂³	semidirect
57. C₄×Q₈×C₁₁	C₂³	semidirect
58. C₄×D₄×C₁₁	C₂³	semidirect
65. C₂²×#548	C₁₁	direct (N × H)
71. C₂⁴×C₁₁	#41	semidirect
78. C₂×Q₈×C₁₁	C₂×D₄	semidirect
105. C₂³×#41	C₂×C₁₁	semidirect
106. C₂⁴×Q₈	C₂×C₁₁	semidirect
107. C₂×#548	C₂×C₁₁	direct (N × H)
108. C₂²×#124	C₂×C₁₁	semidirect
109. C₂²×C₂²⋊Q₈	C₂×C₁₁	semidirect
110. C₂²×#121	C₂×C₁₁	semidirect
111. C₂²×C₄×Q₈	C₂×C₁₁	semidirect
112. C₂²×C₄×D₄	C₂×C₁₁	semidirect
122. C₂³×C₁₁	C₂×#41	semidirect
128. Q₈×C₁₁	C₂²×D₄	semidirect
144. C₂²×#41	C₂²×C₁₁	semidirect
148. C₂³×Q₈	C₂²×C₁₁	semidirect
153. #548	C₂²×C₁₁	direct (N × H)
154. C₂×#124	C₂²×C₁₁	semidirect
155. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
156. C₂×#121	C₂²×C₁₁	semidirect
157. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
158. C₂×C₄×D₄	C₂²×C₁₁	semidirect
172. C₂²×C₁₁	#548	direct (N × H)
175. C₂²×C₁₁	C₂²×#41	semidirect
186. C₂×#41	C₂³×C₁₁	semidirect
189. C₂²×Q₈	D₄×C₁₁	semidirect
192. C₂²×Q₈	C₂³×C₁₁	semidirect
206. #124	C₂³×C₁₁	semidirect
207. C₂²⋊Q₈	C₂³×C₁₁	semidirect
208. #121	C₂³×C₁₁	semidirect
209. C₄×Q₈	C₂³×C₁₁	semidirect
210. C₄×D₄	C₂³×C₁₁	semidirect
219. C₂×C₁₁	C₂×#548	direct (N × H)
228. C₂⁴	C₁₁×#41	semidirect
235. C₂×Q₈	C₂×D₄×C₁₁	semidirect
262. C₁₁	C₂²×#548	direct (N × H)
272. C₂³	C₂×C₁₁×#41	semidirect
278. Q₈	C₂²×D₄×C₁₁	semidirect
300. C₂²	C₁₁×#548	direct (N × H)
303. C₂²	C₂²×C₁₁×#41	semidirect
313. C₂	C₂×C₁₁×#548	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×#41	2
C₂⁴×Q₈×C₁₁	2
C₂×C₁₁×#548	2
C₂²×C₁₁×#124	2
C₂²×C₁₁×C₂²⋊Q₈	2
C₂²×C₁₁×#121	2
C₂²×C₄×Q₈×C₁₁	2
C₂²×C₄×D₄×C₁₁	2
C₂²×#548	11

Subgroups — C22×C11×#548 #14639891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#548 #14639891