Subgroups — C₂×C₈×#4325 #14723136

Order 2816.

822 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#4325	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄₄	C₂	1	1	yes	maximal, characteristic
3	C₈×#4325	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622118	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10622121	C₂	1	1	yes	maximal, characteristic
7	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂²×#4325	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₁₁	—	2	1	no	—
12	C₂×C₄×D₄₄	C₂²	1	1	yes	characteristic
13	C₈×Q₈×C₁₁	—	2	2	no	—
14	C₈×Q₈×C₁₁	C₂²	1	4	yes	complemented
15	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₁	—	2	1	no	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
19	C₂×#66899	C₄	1	1	yes	characteristic
20	C₂×(C₂×D₁₁)⋊C₈	—	2	1	no	—
21	C₄×#4325	C₄	1	4	yes	—
22	C₄×#4325	C₂²	1	4	yes	—
23	C₂×#66873	C₄	1	1	yes	characteristic
24	C₂×#66872	C₄	1	1	yes	characteristic
25	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×D₄₄	—	2	2	no	—
29	C₈×D₄₄	C₂²	1	4	yes	—
30	Q₈⋊(C₁₁⋊C₈)	C₂²	1	4	yes	complemented
31	#10622121	C₂²	1	4	yes	—
32	#10622118	C₂²	1	4	yes	complemented
33	C₈×C₁₁⋊C₈	C₂²	1	4	yes	complemented
34	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄₄	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₁	—	2	1	no	—
37	C₂²×C₈×C₁₁	—	2	1	no	—
38	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
40	C₄×Q₈×C₁₁	—	2	1	no	—
41	C₄×Q₈×C₁₁	—	2	1	no	—
42	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
43	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
44	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
45	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	—	2	1	no	—
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×#4325	C₈	1	8	yes	direct product factor
49	C₂×#4325	C₂×C₄	1	4	yes	—
50	C₂×(C₂×D₁₁)⋊C₄	—	2	1	no	—
51	C₂×C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₁₁⋊C₈	—	2	1	no	—
53	C₂²×C₁₁⋊C₈	—	2	1	no	—
54	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₁	—	2	4	no	—
57	C₂×C₈×D₁₁	—	4	4	no	—
58	C₄×D₄₄	—	2	1	no	—
59	C₄×D₄₄	—	2	1	no	—
60	C₄×D₄₄	C₂×C₄	1	2	yes	—
61	C₄×D₄₄	C₂³	1	2	yes	—
62	C₁₁×C₄⋊C₈	—	2	4	no	—
63	C₁₁×C₄⋊C₈	—	2	1	no	—
64	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
65	C₄×C₈×C₁₁	—	2	4	no	—
66	C₄×C₈×C₁₁	D₄	1	2	yes	—
67	C₄×C₈×C₁₁	C₂³	1	2	yes	—
68	#66899	C₂×C₄	1	4	yes	—
69	(C₂×D₁₁)⋊C₈	—	2	4	no	—
70	#66873	C₂×C₄	1	4	yes	—
71	#66872	C₂×C₄	1	4	yes	—
72	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
73	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
74	C₄×C₁₁⋊C₈	—	2	1	no	—
75	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
76	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
77	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
78	C₂×C₈×SD₁₆	—	11	1	no	maximal, Sylow
79	C₂³×D₁₁	—	2	1	no	—
80	C₂×Q₈×C₁₁	—	2	1	no	—
81	C₂×Q₈×C₁₁	—	2	2	no	—
82	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	complemented
83	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₁	—	2	1	no	—
85	C₂²×C₄×C₁₁	—	2	1	no	—
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
89	C₂²×Dic₁₁	—	2	1	no	—
90	C₂×D₄₄	—	2	1	no	—
91	C₂×D₄₄	—	2	2	no	—
92	C₂×D₄₄	C₂×C₈	1	4	yes	—
93	C₂×D₄₄	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₁₁	—	2	2	no	—
95	C₂×C₄×D₁₁	—	2	2	no	—
96	C₂×C₄×D₁₁	—	4	2	no	—
97	C₂×C₄×D₁₁	—	4	2	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	4	2	no	—
101	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
102	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
104	C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₁₁×C₄⋊C₄	—	2	1	no	—
106	C₁₁×C₄⋊C₄	—	2	2	no	—
107	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₁	#41	1	1	yes	characteristic
113	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
114	#4325	C₂×C₈	1	16	yes	direct product factor
115	(C₂×D₁₁)⋊C₄	—	2	2	no	—
116	(C₂×D₁₁)⋊C₄	—	2	2	no	—
117	C₄⋊Dic₁₁	—	2	1	no	—
118	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
119	C₂×C₁₁⋊C₈	—	2	4	no	—
120	C₂×C₁₁⋊C₈	—	2	2	no	—
121	C₂×C₁₁⋊C₈	—	2	2	no	—
122	C₂×C₁₁⋊C₈	—	2	2	no	—
123	C₂×C₁₁⋊C₈	—	4	2	no	—
124	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	complemented
125	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
127	C₈×D₁₁	—	4	8	no	—
128	C₂×C₈×Q₈	D₁₁	1	1	yes	characteristic, complemented
129	C₂×C₄×SD₁₆	—	11	1	no	—
130	C₂×C₈×D₄	—	11	1	no	—
131	C₈×SD₁₆	—	11	8	no	—
132	C₂×#334	—	11	1	no	—
133	C₂×Q₈⋊C₈	—	11	1	no	—
134	C₂×D₄⋊C₈	—	11	1	no	—
135	C₂×C₈²	—	11	1	no	—
136	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
137	C₂²×D₁₁	—	2	2	no	—
138	C₂²×D₁₁	—	2	4	no	—
139	C₂²×D₁₁	—	4	2	no	—
140	C₂²×D₁₁	—	4	2	no	—
141	Q₈×C₁₁	—	2	2	no	—
142	Q₈×C₁₁	—	2	4	no	—
143	Q₈×C₁₁	C₂²×C₈	1	4	yes	complemented
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	4	no	—
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	4	2	no	—
149	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₁₁	#131	1	2	yes	—
154	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
155	C₂×C₄×C₁₁	#135	1	2	yes	—
156	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
159	C₂×Dic₁₁	—	2	2	no	—
160	C₂×Dic₁₁	—	4	2	no	—
161	D₄₄	—	2	2	no	—
162	D₄₄	—	2	4	no	—
163	D₄₄	C₂²×C₈	1	4	yes	—
164	C₄×D₁₁	—	4	2	no	—
165	C₄×D₁₁	—	4	2	no	—
166	C₄×D₁₁	—	4	4	no	—
167	C₈×C₁₁	—	2	2	no	—
168	C₈×C₁₁	—	4	2	no	—
169	C₈×C₁₁	C₂×SD₁₆	1	4	yes	complemented
170	C₁₁⋊C₈	—	2	4	no	—
171	C₁₁⋊C₈	—	2	2	no	—
172	C₁₁⋊C₈	—	4	2	no	—
173	C₁₁⋊C₈	C₂²×C₈	1	4	yes	complemented
174	C₂²×SD₁₆	—	11	1	no	—
175	C₂³×C₈	—	22	1	no	—
176	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
177	C₂×C₄×D₄	—	11	1	no	—
178	C₈×Q₈	—	2	2	no	—
179	C₈×Q₈	C₂×D₁₁	1	4	yes	complemented
180	C₄×SD₁₆	—	11	4	no	—
181	C₄×SD₁₆	—	11	4	no	—
182	C₈×D₄	—	11	4	no	—
183	C₈×D₄	—	22	2	no	—
184	C₂×#106	—	11	1	no	—
185	C₂×C₄⋊C₈	—	2	1	no	—
186	C₂×C₄⋊C₈	—	11	1	no	—
187	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
188	C₂×#103	—	11	1	no	—
189	C₂×#102	—	11	1	no	—
190	C₂×C₂²⋊C₈	—	22	1	no	—
191	C₂×C₄×C₈	—	2	1	no	—
192	C₂×C₄×C₈	—	11	1	no	—
193	C₂×C₄×C₈	—	11	1	no	—
194	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
195	#334	—	11	4	no	—
196	Q₈⋊C₈	—	11	4	no	—
197	D₄⋊C₈	—	11	4	no	—
198	C₈²	—	11	4	no	—
199	C₂²×C₁₁	C₈×D₄	1	2	yes	—
200	C₂²×C₁₁	C₄×SD₁₆	1	2	yes	—
201	C₂²×C₁₁	#443	1	2	yes	—
202	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₁₁	—	2	4	no	—
204	C₂×D₁₁	—	4	8	no	—
205	C₂×D₁₁	—	4	2	no	—
206	C₂×D₁₁	—	4	2	no	—
207	C₄×C₁₁	—	2	4	no	—
208	C₄×C₁₁	—	2	1	no	—
209	C₄×C₁₁	—	2	1	no	—
210	C₄×C₁₁	—	4	2	no	—
211	C₄×C₁₁	C₈×D₄	1	2	yes	—
212	C₄×C₁₁	C₄×SD₁₆	1	2	yes	—
213	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
214	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
215	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
216	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
217	Dic₁₁	—	4	2	no	—
218	C₂²×Q₈	C₄×D₁₁	1	1	yes	characteristic
219	C₂²×D₄	—	11	1	no	—
220	C₂³×C₄	—	22	1	no	—
221	C₂×SD₁₆	—	11	8	no	—
222	C₂×SD₁₆	—	11	4	no	—
223	C₂²×C₈	—	2	1	no	—
224	C₂²×C₈	—	11	1	no	—
225	C₂²×C₈	—	11	1	no	—
226	C₂²×C₈	—	22	1	no	—
227	C₂²×C₈	—	22	1	no	—
228	C₂²×C₈	—	22	4	no	—
229	C₂²×C₈	—	44	4	no	—
230	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
231	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
232	C₄×Q₈	—	2	1	no	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	C₄×D₁₁	1	2	yes	—
235	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
236	C₄×D₄	—	11	2	no	—
237	C₄×D₄	—	11	2	no	—
238	C₄×D₄	—	22	1	no	—
239	C₄×D₄	—	22	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	11	1	no	—
242	C₂×C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
243	C₂×C₂²⋊C₄	—	22	1	no	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
246	#106	—	11	4	no	—
247	C₄⋊C₈	—	2	4	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	11	2	no	—
250	C₄⋊C₈	—	22	1	no	—
251	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
252	#103	—	11	4	no	—
253	#102	—	11	4	no	—
254	C₂²⋊C₈	—	22	4	no	—
255	C₄×C₈	—	2	4	no	—
256	C₄×C₈	—	11	2	no	—
257	C₄×C₈	—	11	2	no	—
258	C₄×C₈	—	11	2	no	—
259	C₄×C₈	—	22	1	no	—
260	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
261	C₄×C₈	C₂²×D₁₁	1	2	yes	—
262	C₂×C₁₁	C₈×SD₁₆	1	4	yes	complemented
263	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
264	C₂×C₁₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
265	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
266	D₁₁	—	4	4	no	—
267	C₂⁴	—	22	1	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	C₈×D₁₁	1	4	yes	complemented
271	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
272	C₂×D₄	—	11	4	no	—
273	C₂×D₄	—	11	2	no	—
274	C₂×D₄	—	22	2	no	—
275	C₂×D₄	—	22	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	22	1	no	—
279	C₂²×C₄	—	22	2	no	—
280	C₂²×C₄	—	22	2	no	—
281	C₂²×C₄	—	44	2	no	—
282	C₂²×C₄	—	44	2	no	—
283	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
284	C₂²×C₄	#4339	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
286	SD₁₆	—	11	16	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	11	4	no	—
291	C₂×C₈	—	11	2	no	—
292	C₂×C₈	—	11	2	no	—
293	C₂×C₈	—	22	4	no	—
294	C₂×C₈	—	22	2	no	—
295	C₂×C₈	—	22	2	no	—
296	C₂×C₈	—	22	2	no	—
297	C₂×C₈	—	44	2	no	—
298	C₂×C₈	—	44	8	no	—
299	C₂×C₈	#4325	1	4	yes	direct product factor
300	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
301	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	11	2	no	—
306	C₄⋊C₄	—	22	1	no	—
307	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
308	C₂²⋊C₄	—	22	2	no	—
309	C₂²⋊C₄	—	22	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
313	C₄²	#4339	1	1	yes	characteristic
314	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
315	C₄²	C₂³×D₁₁	1	1	yes	characteristic
316	C₁₁	C₂×C₈×SD₁₆	1	1	yes	characteristic, complemented, Sylow
317	C₂³	—	22	4	no	—
318	C₂³	—	22	2	no	—
319	C₂³	—	44	2	no	—
320	C₂³	—	44	2	no	—
321	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	2	no	—
324	Q₈	C₂×C₈×D₁₁	1	4	yes	complemented
325	D₄	—	11	4	no	—
326	D₄	—	22	4	no	—
327	D₄	—	22	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	22	2	no	—
334	C₂×C₄	—	44	2	no	—
335	C₂×C₄	—	44	2	no	—
336	C₂×C₄	—	44	2	no	—
337	C₂×C₄	—	44	4	no	—
338	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
339	C₂×C₄	#66954	1	2	yes	—
340	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
341	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
342	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
343	C₂×C₄	C₂×#4325	1	2	yes	—
344	C₂×C₄	#67003	1	2	yes	—
345	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
346	C₂×C₄	C₂×#4339	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	11	4	no	—
351	C₈	—	22	4	no	—
352	C₈	—	22	2	no	—
353	C₈	—	44	2	no	—
354	C₈	C₂×#4325	1	4	yes	direct product factor
355	C₂²	—	22	4	no	—
356	C₂²	—	44	2	no	—
357	C₂²	—	44	2	no	—
358	C₂²	—	44	8	no	—
359	C₂²	C₄×#4325	1	2	yes	—
360	C₂²	C₈×C₂²⋊D₁₁	1	2	yes	—
361	C₂²	#10622757	1	2	yes	—
362	C₂²	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	44	2	no	—
368	C₄	C₄×#4325	1	2	yes	—
369	C₄	C₈×C₂²⋊D₁₁	1	2	yes	—
370	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
371	C₄	C₂×#66954	1	1	yes	characteristic
372	C₄	C₂²×#4325	1	1	yes	characteristic
373	C₄	C₂×#67003	1	1	yes	characteristic
374	C₂	—	44	4	no	—
375	C₂	C₈×#4325	1	4	yes	direct product factor
376	C₂	C₂×C₈×C₂²⋊D₁₁	1	1	yes	characteristic
377	C₂	C₂×C₄×#4325	1	1	yes	characteristic
378	C₂	C₂×#10622757	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₈×Q₈×C₁₁	C₂
socle	C₂³×C₁₁	C₄×D₄
prime radical	C₂²×D₄₄	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×C₈×Q₈	D₁₁
hypocenter	C₁₁	C₂×C₈×SD₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
3. C₈×#4325	C₂	direct (N × H)
4. C₂×#10622118	C₂	semidirect
5. C₂×Q₈⋊(C₁₁⋊C₈)	C₂	semidirect
7. C₂×C₈×C₁₁⋊C₈	C₂	semidirect
8. C₂×C₈×Q₈×C₁₁	C₂	semidirect
14. C₈×Q₈×C₁₁	C₂²	semidirect
30. Q₈⋊(C₁₁⋊C₈)	C₂²	semidirect
32. #10622118	C₂²	semidirect
33. C₈×C₁₁⋊C₈	C₂²	semidirect
48. C₂×#4325	C₈	direct (N × H)
82. C₂×Q₈×C₁₁	C₂×C₈	semidirect
101. C₂×C₈×C₁₁	SD₁₆	semidirect
114. #4325	C₂×C₈	direct (N × H)
124. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
128. C₂×C₈×Q₈	D₁₁	semidirect
143. Q₈×C₁₁	C₂²×C₈	semidirect
169. C₈×C₁₁	C₂×SD₁₆	semidirect
173. C₁₁⋊C₈	C₂²×C₈	semidirect
179. C₈×Q₈	C₂×D₁₁	semidirect
262. C₂×C₁₁	C₈×SD₁₆	semidirect
270. C₂×Q₈	C₈×D₁₁	semidirect
299. C₂×C₈	#4325	direct (N × H)
316. C₁₁	C₂×C₈×SD₁₆	semidirect
324. Q₈	C₂×C₈×D₁₁	semidirect
354. C₈	C₂×#4325	direct (N × H)
375. C₂	C₈×#4325	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×C₄×#4325	2
C₂×C₈×D₄₄	2
C₈×#4325	2
C₂×#10622118	2
C₂×Q₈⋊(C₁₁⋊C₈)	2
C₂×#10622121	2
C₂×C₈×C₁₁⋊C₈	2
C₂×C₈×Q₈×C₁₁	2
C₂×C₈×SD₁₆	11

Subgroups — C2×C8×#4325 #14723136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×#4325 #14723136