Subgroups — Q₈×C₁₁×#104 #14599721

Order 2816.

1096 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1994	C₂	1	3	yes	maximal, complemented
5	C₁₁×#1986	C₂	1	3	yes	maximal, complemented
6	C₁₁×#1806	C₂	1	3	yes	maximal
7	C₄×C₁₁×#104	C₂	1	3	yes	maximal
8	Q₈²×C₁₁	C₄	1	1	yes	characteristic, complemented
9	C₁₁×#557	C₄	1	3	yes	complemented
10	C₁₁×#554	—	2	3	no	—
11	C₁₁×#554	C₄	1	3	yes	complemented
12	D₄×Q₈×C₁₁	—	2	1	no	—
13	D₄×Q₈×C₁₁	C₄	1	1	yes	characteristic, complemented
14	C₁₁×#533	—	2	3	no	—
15	C₁₁×#533	C₂²	1	3	yes	—
16	C₄×C₁₁×#41	C₂²	1	3	yes	—
17	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
19	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₁₁×#446	—	2	3	no	—
21	C₈×Q₈×C₁₁	—	2	1	no	—
22	C₁₁×#423	C₂²	1	3	yes	—
23	C₂×C₁₁×#104	C₂²	1	3	yes	—
24	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
25	C₄×C₁₁×M₁₆	C₂²	1	3	yes	—
26	C₄×C₁₁×C₄⋊C₄	—	2	3	no	—
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
28	C₄³×C₁₁	C₂²	1	3	yes	—
29	C₁₁×#339	C₂²	1	3	yes	—
30	C₁₁×#339	C₂²	1	6	yes	—
31	C₁₁×#339	C₂²	1	3	yes	—
32	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
33	C₂²×Q₈×C₁₁	—	2	1	no	—
34	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
36	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
37	C₁₁×C₄⋊Q₈	—	2	3	no	—
38	C₁₁×C₄⋊Q₈	—	2	3	no	—
39	C₁₁×C₄⋊Q₈	C₂×C₄	1	3	yes	—
40	C₁₁×C₄⋊Q₈	C₂×C₄	1	3	yes	—
41	C₁₁×#125	—	2	6	no	—
42	C₁₁×#125	C₂×C₄	1	6	yes	—
43	C₁₁×C₂²⋊Q₈	—	2	3	no	—
44	C₁₁×C₂²⋊Q₈	—	2	3	no	—
45	C₁₁×C₂²⋊Q₈	—	2	3	no	—
46	C₁₁×C₂²⋊Q₈	—	2	3	no	—
47	C₁₁×C₂²⋊Q₈	—	2	6	no	—
48	C₄×Q₈×C₁₁	—	2	8	no	—
49	C₄×Q₈×C₁₁	—	2	1	no	—
50	C₄×Q₈×C₁₁	—	2	3	no	—
51	C₄×Q₈×C₁₁	—	2	3	no	—
52	C₄×Q₈×C₁₁	—	2	3	no	—
53	C₄×Q₈×C₁₁	C₂×C₄	1	3	yes	—
54	C₄×Q₈×C₁₁	C₂×C₄	1	3	yes	—
55	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₄×Q₈×C₁₁	C₂×C₄	1	3	yes	—
57	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
58	C₄×Q₈×C₁₁	D₄	1	3	yes	—
59	C₄×D₄×C₁₁	—	2	3	no	—
60	C₄×D₄×C₁₁	—	2	3	no	—
61	C₄×D₄×C₁₁	C₂×C₄	1	3	yes	—
62	C₄×D₄×C₁₁	C₂×C₄	1	3	yes	—
63	C₁₁×#117	—	2	3	no	—
64	C₁₁×#117	C₂³	1	3	yes	—
65	C₂×C₁₁×C₄⋊C₄	—	2	3	no	—
66	C₂×C₁₁×C₄⋊C₄	—	2	3	no	—
67	C₂×C₁₁×C₄⋊C₄	D₄	1	3	yes	—
68	C₂×C₄²×C₁₁	—	2	3	no	—
69	C₂×C₄²×C₁₁	—	2	3	no	—
70	C₂×C₄²×C₁₁	—	2	3	no	—
71	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
72	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
74	C₁₁×C₄⋊C₈	—	2	3	no	—
75	C₁₁×C₄⋊C₈	—	2	3	no	—
76	C₁₁×#104	—	2	6	no	—
77	C₁₁×#104	Q₈	1	4	yes	direct product factor
78	C₁₁×#97	—	2	3	no	—
79	C₄×C₈×C₁₁	—	2	3	no	—
80	C₁₁×#95	—	2	3	no	—
81	Q₈×#104	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₁₁×#41	—	2	1	no	—
83	C₁₁×#41	—	2	1	no	—
84	C₁₁×#41	C₂×Q₈	1	2	yes	—
85	C₁₁×#41	#41	1	2	yes	—
86	C₂×Q₈×C₁₁	—	2	4	no	—
87	C₂×Q₈×C₁₁	—	2	3	no	—
88	C₂×Q₈×C₁₁	—	2	3	no	—
89	C₂×Q₈×C₁₁	—	4	4	no	—
90	C₂×Q₈×C₁₁	C₂²⋊C₄	1	3	yes	—
91	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×D₄×C₁₁	—	2	1	no	—
94	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	—	2	1	no	—
96	C₂²×C₄×C₁₁	—	2	1	no	—
97	C₂²×C₄×C₁₁	—	2	3	no	—
98	C₂²×C₄×C₁₁	—	2	3	no	—
99	C₂²×C₄×C₁₁	—	2	3	no	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
101	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
102	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₁₁×M₁₆	—	2	3	no	—
104	C₁₁×M₁₆	—	2	1	no	—
105	C₁₁×M₁₆	—	2	3	no	—
106	C₁₁×M₁₆	C₂×Q₈	1	2	yes	complemented
107	C₂×C₈×C₁₁	—	2	1	no	—
108	C₂×C₈×C₁₁	—	2	3	no	—
109	C₁₁×C₄⋊C₄	—	2	12	no	—
110	C₁₁×C₄⋊C₄	—	2	6	no	—
111	C₁₁×C₄⋊C₄	—	2	3	no	—
112	C₁₁×C₄⋊C₄	—	2	3	no	—
113	C₁₁×C₄⋊C₄	—	2	3	no	—
114	C₁₁×C₄⋊C₄	—	2	3	no	—
115	C₁₁×C₄⋊C₄	—	2	6	no	—
116	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
117	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
118	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	3	yes	—
119	C₁₁×C₄⋊C₄	C₂²×C₄	1	3	yes	—
120	C₁₁×C₄⋊C₄	C₂²×C₄	1	3	yes	—
121	C₁₁×C₂²⋊C₄	—	2	3	no	—
122	C₁₁×C₂²⋊C₄	—	2	3	no	—
123	C₁₁×C₂²⋊C₄	—	2	3	no	—
124	C₄²×C₁₁	—	2	12	no	—
125	C₄²×C₁₁	—	2	3	no	—
126	C₄²×C₁₁	—	2	3	no	—
127	C₄²×C₁₁	—	2	3	no	—
128	C₄²×C₁₁	—	2	1	no	—
129	C₄²×C₁₁	—	2	3	no	—
130	C₄²×C₁₁	—	2	3	no	—
131	C₄²×C₁₁	—	4	6	no	—
132	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
133	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
134	C₄²×C₁₁	C₂×D₄	1	3	yes	—
135	C₄²×C₁₁	C₂×D₄	1	3	yes	—
136	C₄²×C₁₁	C₂×Q₈	1	2	yes	complemented
137	Q₈×#41	C₂×C₁₁	1	1	yes	characteristic
138	Q₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
139	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
140	#1994	C₂×C₁₁	1	3	yes	complemented
141	#1986	C₂×C₁₁	1	3	yes	complemented
142	#1806	C₂×C₁₁	1	3	yes	—
143	C₄×#104	C₂×C₁₁	1	3	yes	—
144	C₂³×C₁₁	—	2	1	no	—
145	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₁	—	2	1	no	—
147	Q₈×C₁₁	—	2	6	no	—
148	Q₈×C₁₁	—	4	6	no	—
149	Q₈×C₁₁	—	8	3	no	—
150	Q₈×C₁₁	#104	1	4	yes	direct product factor
151	Q₈×C₁₁	C₄×Q₈	1	2	yes	complemented
152	D₄×C₁₁	—	2	2	no	—
153	D₄×C₁₁	—	2	2	no	—
154	D₄×C₁₁	—	2	1	no	—
155	D₄×C₁₁	C₄×Q₈	1	2	yes	complemented
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	6	no	—
163	C₂×C₄×C₁₁	—	2	6	no	—
164	C₂×C₄×C₁₁	—	2	3	no	—
165	C₂×C₄×C₁₁	—	2	3	no	—
166	C₂×C₄×C₁₁	—	4	3	no	—
167	C₂×C₄×C₁₁	—	4	3	no	—
168	C₂×C₄×C₁₁	—	4	3	no	—
169	C₂×C₄×C₁₁	—	4	6	no	—
170	C₂×C₄×C₁₁	—	8	3	no	—
171	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
172	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
173	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
174	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
175	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
181	C₈×C₁₁	—	2	2	no	—
182	C₈×C₁₁	—	4	3	no	—
183	Q₈²	C₄×C₁₁	1	1	yes	characteristic, complemented
184	#557	C₄×C₁₁	1	3	yes	complemented
185	#554	—	2	3	no	—
186	#554	C₄×C₁₁	1	3	yes	complemented
187	D₄×Q₈	—	2	1	no	—
188	D₄×Q₈	C₄×C₁₁	1	1	yes	characteristic, complemented
189	#533	—	2	3	no	—
190	#533	C₂²×C₁₁	1	3	yes	—
191	C₄×#41	C₂²×C₁₁	1	3	yes	—
192	C₂×C₄×Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
195	#446	—	2	3	no	—
196	C₈×Q₈	—	2	1	no	—
197	#423	C₂²×C₁₁	1	3	yes	—
198	C₂×#104	C₂²×C₁₁	1	3	yes	—
199	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
200	C₄×M₁₆	C₂²×C₁₁	1	3	yes	—
201	C₄×C₄⋊C₄	—	2	3	no	—
202	C₄×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
203	C₄³	C₂²×C₁₁	1	3	yes	—
204	#339	C₂²×C₁₁	1	6	yes	—
205	#339	C₂²×C₁₁	1	3	yes	—
206	#339	C₂²×C₁₁	1	3	yes	—
207	C₂²×C₁₁	—	2	1	no	—
208	C₂²×C₁₁	—	2	1	no	—
209	C₂²×C₁₁	—	2	2	no	—
210	C₂²×C₁₁	—	4	1	no	—
211	C₂²×C₁₁	—	4	1	no	—
212	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₁₁	#548	1	1	yes	characteristic
214	C₂²×C₁₁	D₄×Q₈	1	1	yes	characteristic
215	C₄×C₁₁	—	2	4	no	—
216	C₄×C₁₁	—	2	2	no	—
217	C₄×C₁₁	—	2	3	no	—
218	C₄×C₁₁	—	2	3	no	—
219	C₄×C₁₁	—	2	3	no	—
220	C₄×C₁₁	—	4	6	no	—
221	C₄×C₁₁	—	4	3	no	—
222	C₄×C₁₁	—	4	3	no	—
223	C₄×C₁₁	C₂×#104	1	6	yes	—
224	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
225	C₄×C₁₁	#519	1	1	yes	characteristic
226	C₄×C₁₁	#548	1	1	yes	characteristic
227	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
228	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
231	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
232	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
233	C₄⋊Q₈	—	2	3	no	—
234	C₄⋊Q₈	—	2	3	no	—
235	C₄⋊Q₈	C₂×C₄×C₁₁	1	3	yes	—
236	C₄⋊Q₈	C₂×C₄×C₁₁	1	3	yes	—
237	#125	—	2	6	no	—
238	#125	C₂×C₄×C₁₁	1	6	yes	—
239	C₂²⋊Q₈	—	2	3	no	—
240	C₂²⋊Q₈	—	2	3	no	—
241	C₂²⋊Q₈	—	2	3	no	—
242	C₂²⋊Q₈	—	2	3	no	—
243	C₂²⋊Q₈	—	2	6	no	—
244	C₄×Q₈	—	2	8	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	3	no	—
247	C₄×Q₈	—	2	3	no	—
248	C₄×Q₈	—	2	3	no	—
249	C₄×Q₈	C₂×C₄×C₁₁	1	3	yes	—
250	C₄×Q₈	C₂×C₄×C₁₁	1	3	yes	—
251	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
252	C₄×Q₈	C₂×C₄×C₁₁	1	3	yes	—
253	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
254	C₄×Q₈	D₄×C₁₁	1	3	yes	—
255	C₄×D₄	—	2	3	no	—
256	C₄×D₄	—	2	3	no	—
257	C₄×D₄	C₂×C₄×C₁₁	1	3	yes	—
258	C₄×D₄	C₂×C₄×C₁₁	1	3	yes	—
259	#117	—	2	3	no	—
260	#117	C₂³×C₁₁	1	3	yes	—
261	C₂×C₄⋊C₄	—	2	3	no	—
262	C₂×C₄⋊C₄	—	2	3	no	—
263	C₂×C₄⋊C₄	D₄×C₁₁	1	3	yes	—
264	C₂×C₄²	—	2	3	no	—
265	C₂×C₄²	—	2	3	no	—
266	C₂×C₄²	—	2	3	no	—
267	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
268	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
270	C₄⋊C₈	—	2	3	no	—
271	C₄⋊C₈	—	2	3	no	—
272	#104	—	2	6	no	—
273	#104	Q₈×C₁₁	1	4	yes	direct product factor
274	#97	—	2	3	no	—
275	C₄×C₈	—	2	3	no	—
276	#95	—	2	3	no	—
277	C₂×C₁₁	—	2	1	no	—
278	C₂×C₁₁	—	2	1	no	—
279	C₂×C₁₁	—	4	2	no	—
280	C₂×C₁₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
281	C₂×C₁₁	C₂²×#104	1	1	yes	characteristic
282	C₂×C₁₁	#2901	1	1	yes	characteristic
283	#41	—	2	1	no	—
284	#41	—	2	1	no	—
285	#41	C₂×Q₈×C₁₁	1	2	yes	—
286	#41	C₁₁×#41	1	2	yes	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	3	no	—
289	C₂×Q₈	—	2	3	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	C₁₁×C₂²⋊C₄	1	3	yes	—
292	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	3	no	—
299	C₂²×C₄	—	2	3	no	—
300	C₂²×C₄	—	2	3	no	—
301	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
302	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
303	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
304	M₁₆	—	2	1	no	—
305	M₁₆	—	2	3	no	—
306	M₁₆	—	2	3	no	—
307	M₁₆	C₂×Q₈×C₁₁	1	2	yes	complemented
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	3	no	—
310	C₄⋊C₄	—	2	12	no	—
311	C₄⋊C₄	—	2	6	no	—
312	C₄⋊C₄	—	2	3	no	—
313	C₄⋊C₄	—	2	3	no	—
314	C₄⋊C₄	—	2	3	no	—
315	C₄⋊C₄	—	2	3	no	—
316	C₄⋊C₄	—	2	6	no	—
317	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	3	yes	—
318	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	6	yes	—
319	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	3	yes	—
320	C₄⋊C₄	C₂²×C₄×C₁₁	1	3	yes	—
321	C₄⋊C₄	C₂²×C₄×C₁₁	1	3	yes	—
322	C₂²⋊C₄	—	2	3	no	—
323	C₂²⋊C₄	—	2	3	no	—
324	C₂²⋊C₄	—	2	3	no	—
325	C₄²	—	2	12	no	—
326	C₄²	—	2	3	no	—
327	C₄²	—	2	3	no	—
328	C₄²	—	2	3	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	3	no	—
331	C₄²	—	2	3	no	—
332	C₄²	—	4	6	no	—
333	C₄²	C₂²×C₄×C₁₁	1	3	yes	—
334	C₄²	C₂²×C₄×C₁₁	1	3	yes	—
335	C₄²	C₂×D₄×C₁₁	1	3	yes	—
336	C₄²	C₂×D₄×C₁₁	1	3	yes	—
337	C₄²	C₂×Q₈×C₁₁	1	2	yes	complemented
338	C₁₁	Q₈×#104	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	1	no	—
340	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
341	Q₈	—	2	1	no	—
342	Q₈	—	2	6	no	—
343	Q₈	—	4	6	no	—
344	Q₈	—	8	3	no	—
345	Q₈	C₁₁×#104	1	4	yes	direct product factor
346	Q₈	C₄×Q₈×C₁₁	1	2	yes	complemented
347	D₄	—	2	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	1	no	—
350	D₄	C₄×Q₈×C₁₁	1	2	yes	complemented
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	6	no	—
359	C₂×C₄	—	2	3	no	—
360	C₂×C₄	—	2	3	no	—
361	C₂×C₄	—	4	3	no	—
362	C₂×C₄	—	4	3	no	—
363	C₂×C₄	—	4	3	no	—
364	C₂×C₄	—	4	6	no	—
365	C₂×C₄	—	8	3	no	—
366	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
367	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
368	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
369	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
370	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
374	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	4	3	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²	C₁₁×#548	1	1	yes	characteristic
385	C₂²	D₄×Q₈×C₁₁	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	2	3	no	—
388	C₄	—	2	3	no	—
389	C₄	—	2	3	no	—
390	C₄	—	2	2	no	—
391	C₄	—	4	6	no	—
392	C₄	—	4	3	no	—
393	C₄	—	4	3	no	—
394	C₄	C₂×C₁₁×#104	1	6	yes	—
395	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
396	C₄	C₁₁×#519	1	1	yes	characteristic
397	C₄	C₁₁×#548	1	1	yes	characteristic
398	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	4	2	no	—
402	C₂	Q₈×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
403	C₂	C₂²×C₁₁×#104	1	1	yes	characteristic
404	C₂	C₁₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₁₁×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₁×M₁₆	C₂	semidirect
3. C₄²×Q₈×C₁₁	C₂	semidirect
4. C₁₁×#1994	C₂	semidirect
5. C₁₁×#1986	C₂	semidirect
8. Q₈²×C₁₁	C₄	semidirect
9. C₁₁×#557	C₄	semidirect
11. C₁₁×#554	C₄	semidirect
13. D₄×Q₈×C₁₁	C₄	semidirect
77. C₁₁×#104	Q₈	direct (N × H)
81. Q₈×#104	C₁₁	direct (N × H)
106. C₁₁×M₁₆	C₂×Q₈	semidirect
136. C₄²×C₁₁	C₂×Q₈	semidirect
138. Q₈×M₁₆	C₂×C₁₁	semidirect
139. C₄²×Q₈	C₂×C₁₁	semidirect
140. #1994	C₂×C₁₁	semidirect
141. #1986	C₂×C₁₁	semidirect
150. Q₈×C₁₁	#104	direct (N × H)
151. Q₈×C₁₁	C₄×Q₈	semidirect
155. D₄×C₁₁	C₄×Q₈	semidirect
183. Q₈²	C₄×C₁₁	semidirect
184. #557	C₄×C₁₁	semidirect
186. #554	C₄×C₁₁	semidirect
188. D₄×Q₈	C₄×C₁₁	semidirect
273. #104	Q₈×C₁₁	direct (N × H)
307. M₁₆	C₂×Q₈×C₁₁	semidirect
337. C₄²	C₂×Q₈×C₁₁	semidirect
338. C₁₁	Q₈×#104	direct (N × H)
345. Q₈	C₁₁×#104	direct (N × H)
346. Q₈	C₄×Q₈×C₁₁	semidirect
350. D₄	C₄×Q₈×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₁₁×#41	2
Q₈×C₁₁×M₁₆	2
C₄²×Q₈×C₁₁	2
C₁₁×#1994	2
C₁₁×#1986	2
C₁₁×#1806	2
C₄×C₁₁×#104	2
Q₈×#104	11

Subgroups — Q8×C11×#104 #14599721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×#104 #14599721