Subgroups — D₄×#66876 #14906987

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66876	C₂	1	2	yes	maximal, complemented
2	#13070448	C₂	1	2	yes	maximal, complemented
3	#13070442	C₂	1	4	yes	maximal, complemented
4	D₄×C₁₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	#13070372	C₂	1	1	yes	maximal, characteristic, complemented
6	#13070227	C₂	1	2	yes	maximal, complemented
7	C₄×#66876	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
11	C₈×D₄×C₁₁	C₄	1	2	yes	—
12	C₈×D₄×C₁₁	C₄	1	1	yes	characteristic
13	C₈×D₄×C₁₁	C₄	1	1	yes	characteristic
14	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₈×D₄×C₁₁	C₂²	1	2	yes	—
16	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
18	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×#66876	—	2	8	no	—
21	C₂×#66876	C₂²	1	2	yes	—
22	C₂×#66876	C₂²	1	1	yes	characteristic
23	C₂×#66876	C₂²	1	1	yes	characteristic
24	C₂×#66876	C₂²	1	4	yes	complemented
25	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	complemented
26	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	complemented
27	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	complemented
28	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
29	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	complemented
30	#10622099	C₂²	1	2	yes	complemented
31	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	complemented
32	C₂²×D₄×C₁₁	C₈	1	1	yes	characteristic
33	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	—	2	4	no	—
35	C₂²×C₈×C₁₁	—	2	4	no	—
36	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₁₁	C₈	1	2	yes	—
44	C₄×D₄×C₁₁	C₈	1	1	yes	characteristic
45	C₄×D₄×C₁₁	C₈	1	1	yes	characteristic
46	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
50	C₂×C₁₁×C₂²⋊C₄	C₈	1	2	yes	—
51	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
54	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
56	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
58	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
59	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	#66876	—	2	4	no	—
64	#66876	—	2	2	no	—
65	#66876	—	2	8	no	—
66	#66876	D₄	1	4	yes	direct product factor
67	C₂×C₁₁⋊C₁₆	—	2	8	no	—
68	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
69	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
70	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
71	D₄×M₃₂	—	11	1	no	maximal, Sylow
72	C₂⁴×C₁₁	C₂×C₈	1	2	yes	—
73	C₂×D₄×C₁₁	—	2	4	no	—
74	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
75	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
76	C₂×D₄×C₁₁	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	—	2	4	no	—
78	C₂²×C₄×C₁₁	—	2	4	no	—
79	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
83	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₁₁	—	2	4	no	—
88	C₂×C₈×C₁₁	—	2	4	no	—
89	C₂×C₈×C₁₁	—	2	2	no	—
90	C₂×C₈×C₁₁	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	4	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₁	#41	1	2	yes	—
102	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
104	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
105	C₁₁×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
106	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
107	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
108	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
109	C₁₁×C₂²⋊C₄	C₂×C₈	1	2	yes	—
110	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
111	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
112	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₁₁⋊C₁₆	—	2	4	no	—
115	C₁₁⋊C₁₆	—	2	2	no	—
116	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	complemented
117	C₂²×M₃₂	—	11	2	no	—
118	C₂×C₈×D₄	D₁₁	1	1	yes	characteristic
119	#2169	—	11	2	no	—
120	#2168	—	11	4	no	—
121	D₄×C₁₆	—	11	2	no	—
122	#2150	—	11	1	no	—
123	#2112	—	11	2	no	—
124	C₄×M₃₂	—	11	1	no	—
125	C₂³×C₁₁	—	2	4	no	—
126	C₂³×C₁₁	—	2	4	no	—
127	C₂³×C₁₁	—	4	2	no	—
128	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
129	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
130	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
131	D₄×C₁₁	—	2	4	no	—
132	D₄×C₁₁	—	2	2	no	—
133	D₄×C₁₁	M₃₂	1	4	yes	complemented
134	C₂×C₄×C₁₁	—	2	4	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	2	2	no	—
139	C₂×C₄×C₁₁	—	2	4	no	—
140	C₂×C₄×C₁₁	—	2	4	no	—
141	C₂×C₄×C₁₁	—	2	2	no	—
142	C₂×C₄×C₁₁	—	4	1	no	—
143	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
148	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₁	#131	1	2	yes	—
152	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
153	C₈×C₁₁	—	2	2	no	—
154	C₈×C₁₁	—	2	2	no	—
155	C₈×C₁₁	—	2	1	no	—
156	C₈×C₁₁	—	2	1	no	—
157	C₈×C₁₁	C₄×D₄	1	2	yes	—
158	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
160	C₂³×C₈	C₂×D₁₁	1	2	yes	—
161	C₂×C₄×D₄	Dic₁₁	1	1	yes	characteristic
162	C₂×M₃₂	—	11	1	no	—
163	C₂×M₃₂	—	11	1	no	—
164	C₂×M₃₂	—	11	2	no	—
165	C₂×M₃₂	—	11	4	no	—
166	C₂×M₃₂	—	22	8	no	—
167	C₂²×C₁₆	—	11	4	no	—
168	C₈×D₄	Dic₁₁	1	2	yes	—
169	C₈×D₄	Dic₁₁	1	1	yes	characteristic
170	C₈×D₄	Dic₁₁	1	1	yes	characteristic
171	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
172	C₈×D₄	C₂×D₁₁	1	2	yes	—
173	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
174	C₂×C₄⋊C₈	Dic₁₁	1	1	yes	characteristic
175	C₂×C₂²⋊C₈	Dic₁₁	1	2	yes	—
176	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
177	C₄⋊C₁₆	—	11	2	no	—
178	C₄⋊C₁₆	—	11	2	no	—
179	C₂²⋊C₁₆	—	11	4	no	—
180	C₂²⋊C₁₆	—	11	4	no	—
181	#346	—	11	2	no	—
182	C₄×C₁₆	—	11	2	no	—
183	C₂²×C₁₁	—	2	1	no	—
184	C₂²×C₁₁	—	2	1	no	—
185	C₂²×C₁₁	—	2	2	no	—
186	C₂²×C₁₁	—	2	2	no	—
187	C₂²×C₁₁	—	2	2	no	—
188	C₂²×C₁₁	—	2	2	no	—
189	C₂²×C₁₁	—	2	2	no	—
190	C₂²×C₁₁	—	4	8	no	—
191	C₂²×C₁₁	C₈×D₄	1	2	yes	—
192	C₂²×C₁₁	C₂×M₃₂	1	4	yes	complemented
193	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
194	C₄×C₁₁	—	2	1	no	—
195	C₄×C₁₁	—	2	1	no	—
196	C₄×C₁₁	—	2	1	no	—
197	C₄×C₁₁	—	2	2	no	—
198	C₄×C₁₁	—	2	2	no	—
199	C₄×C₁₁	C₈×D₄	1	2	yes	—
200	C₄×C₁₁	C₂×M₃₂	1	2	yes	complemented
201	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
203	C₂²×D₄	C₁₁⋊C₈	1	1	yes	characteristic
204	C₂³×C₄	C₂×Dic₁₁	1	2	yes	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	—	2	4	no	—
207	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
208	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
209	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
210	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
211	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
212	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
213	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
214	C₄×D₄	C₁₁⋊C₈	1	2	yes	—
215	C₄×D₄	C₁₁⋊C₈	1	1	yes	characteristic
216	C₄×D₄	C₁₁⋊C₈	1	1	yes	characteristic
217	C₄×D₄	C₂×Dic₁₁	1	2	yes	—
218	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
219	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₁₁⋊C₈	1	2	yes	—
222	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
223	M₃₂	—	11	4	no	—
224	M₃₂	—	22	8	no	—
225	M₃₂	—	22	4	no	—
226	M₃₂	—	22	2	no	—
227	C₂×C₁₆	—	11	2	no	—
228	C₂×C₁₆	—	11	2	no	—
229	C₂×C₁₆	—	11	4	no	—
230	C₂×C₁₆	—	22	8	no	—
231	C₄⋊C₈	C₂×Dic₁₁	1	1	yes	characteristic
232	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
233	C₄⋊C₈	C₂×Dic₁₁	1	1	yes	characteristic
234	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
235	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
236	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
237	C₂²⋊C₈	C₂×Dic₁₁	1	2	yes	—
238	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
239	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
240	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
241	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
242	C₂×C₁₁	—	2	2	no	—
243	C₂×C₁₁	—	2	4	no	—
244	C₂×C₁₁	—	4	2	no	—
245	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
246	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
247	C₂×C₁₁	#3407	1	1	yes	characteristic
248	C₂⁴	C₂×C₁₁⋊C₈	1	2	yes	—
249	C₂×D₄	—	2	4	no	—
250	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
251	C₂×D₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
252	C₂×D₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
257	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
258	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
259	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
260	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
261	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
262	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
263	C₂×C₈	—	2	4	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	D₄×D₁₁	1	2	yes	—
272	C₂×C₈	#4341	1	2	yes	—
273	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
274	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
275	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
276	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
277	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
278	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
279	C₄⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
280	C₄⋊C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
281	C₄⋊C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
282	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
283	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
284	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
285	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
286	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
287	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
288	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
289	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
290	C₁₆	—	11	4	no	—
291	C₁₆	—	22	4	no	—
292	C₁₆	—	22	2	no	—
293	C₁₁	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	2	no	—
297	C₂³	C₂²×C₁₁⋊C₈	1	2	yes	—
298	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
299	C₂³	C₂²×C₁₁⋊C₈	1	2	yes	—
300	D₄	—	2	4	no	—
301	D₄	—	2	2	no	—
302	D₄	#66876	1	4	yes	direct product factor
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
313	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
316	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
317	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
318	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
319	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
320	C₂×C₄	#67001	1	2	yes	—
321	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	2	1	no	—
325	C₈	—	2	1	no	—
326	C₈	D₄×Dic₁₁	1	2	yes	—
327	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
328	C₈	C₂×#4341	1	1	yes	characteristic
329	C₂²	—	2	2	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
338	C₂²	C₂×#66876	1	4	yes	complemented
339	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
346	C₄	C₂×#66876	1	2	yes	complemented
347	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
348	C₄	C₂×#67001	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	2	4	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic
353	C₂	C₂²×#66876	1	1	yes	characteristic
354	C₂	#13081719	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₂×C₈×D₄×C₁₁	C₂
prime radical	C₂²×D₄×C₁₁	C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₈×D₄	D₁₁
hypocenter	C₁₁	D₄×M₃₂
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#66876	C₂	semidirect
2. #13070448	C₂	semidirect
3. #13070442	C₂	semidirect
4. D₄×C₁₁⋊C₁₆	C₂	semidirect
5. #13070372	C₂	semidirect
6. #13070227	C₂	semidirect
7. C₄×#66876	C₂	semidirect
24. C₂×#66876	C₂²	semidirect
25. C₂²×C₁₁⋊C₁₆	C₂²	semidirect
26. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
27. C₂²⋊(C₁₁⋊C₁₆)	C₂²	semidirect
28. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
29. C₄⋊(C₁₁⋊C₁₆)	C₂²	semidirect
30. #10622099	C₂²	semidirect
31. C₄×C₁₁⋊C₁₆	C₂²	semidirect
66. #66876	D₄	direct (N × H)
116. C₁₁⋊C₁₆	C₂×D₄	semidirect
133. D₄×C₁₁	M₃₂	semidirect
192. C₂²×C₁₁	C₂×M₃₂	semidirect
200. C₄×C₁₁	C₂×M₃₂	semidirect
293. C₁₁	D₄×M₃₂	semidirect
302. D₄	#66876	direct (N × H)
338. C₂²	C₂×#66876	semidirect
346. C₄	C₂×#66876	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66876	2
#13070448	2
#13070442	2
D₄×C₁₁⋊C₁₆	2
#13070372	2
#13070227	2
C₄×#66876	2
C₂×C₈×D₄×C₁₁	2
D₄×M₃₂	11

Subgroups — D4×#66876 #14906987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#66876 #14906987