Subgroups — C₂×#13069392 #14757294

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66883	C₂	1	2	yes	maximal
2	C₂×#10622537	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#4318	C₂	1	1	yes	maximal, characteristic
4	#13069392	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10622190	C₂	1	2	yes	maximal
6	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²×#4318	C₂²	1	2	yes	—
10	C₂²×#4318	C₂²	1	1	yes	characteristic
11	C₂²×#4318	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₄	1	4	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
16	C₂×#66883	—	2	8	no	—
17	C₂×#66883	C₂²	1	8	yes	—
18	#10622537	—	2	2	no	—
19	#10622537	C₂²	1	4	yes	—
20	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
21	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
22	C₄×#4318	—	2	2	no	—
23	C₄×#4318	C₂²	1	4	yes	—
24	C₂×#66867	—	2	1	no	—
25	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
26	#10622190	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	4	no	—
31	C₂²×C₈×C₁₁	—	2	4	no	—
32	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	2	yes	—
41	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
42	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
43	C₂×#4318	—	2	1	no	—
44	C₂×#4318	—	2	1	no	—
45	C₂×#4318	—	2	2	no	—
46	C₂×#4318	—	2	2	no	—
47	C₂×#4318	—	2	2	no	—
48	C₂×#4318	—	2	4	no	—
49	C₂×#4318	—	2	4	no	—
50	C₂×#4318	D₄	1	4	yes	—
51	C₂×#4318	Q₈	1	4	yes	—
52	C₂×#4318	C₂³	1	4	yes	—
53	C₂×#4318	C₂³	1	2	yes	—
54	C₂×#4318	C₂³	1	2	yes	—
55	C₂²×C₁₁⋊C₈	—	2	1	no	—
56	C₂²×C₁₁⋊C₈	—	2	1	no	—
57	C₂²×C₁₁⋊C₈	—	2	2	no	—
58	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
59	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
60	#66883	—	2	16	no	—
61	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
62	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
63	#66867	—	2	4	no	—
64	C₄×C₁₁⋊C₈	—	2	4	no	—
65	C₂×#1950	—	11	1	no	maximal, Sylow
66	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	—	2	4	no	—
68	C₂²×C₄×C₁₁	—	4	2	no	—
69	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₁₁	#41	1	2	yes	—
85	C₂²×C₄×C₁₁	#41	1	2	yes	—
86	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₁₁	—	2	8	no	—
88	C₂×C₈×C₁₁	—	2	8	no	—
89	C₂×C₈×C₁₁	—	2	4	no	—
90	C₂×C₈×C₁₁	—	2	4	no	—
91	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
92	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
93	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
94	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
95	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
96	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
97	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
98	C₄²×C₁₁	C₂×D₄	1	2	yes	—
99	C₄²×C₁₁	C₂×D₄	1	2	yes	—
100	#4318	—	2	4	no	—
101	#4318	—	2	4	no	—
102	#4318	—	2	4	no	—
103	#4318	—	2	2	no	—
104	#4318	—	2	2	no	—
105	#4318	—	2	4	no	—
106	#4318	—	4	4	no	—
107	#4318	C₂×D₄	1	4	yes	—
108	#4318	C₂×Q₈	1	4	yes	—
109	C₂×C₁₁⋊C₈	—	2	4	no	—
110	C₂×C₁₁⋊C₈	—	2	4	no	—
111	C₂×C₁₁⋊C₈	—	2	2	no	—
112	C₂×C₁₁⋊C₈	—	2	2	no	—
113	C₂×C₁₁⋊C₈	—	2	4	no	—
114	C₂×C₁₁⋊C₈	—	4	4	no	—
115	C₂²×#108	—	11	2	no	—
116	C₂×#423	—	11	1	no	—
117	C₂²×C₄⋊C₈	D₁₁	1	1	yes	characteristic
118	C₂×C₄×M₁₆	—	11	1	no	—
119	#1950	—	11	8	no	—
120	C₂×#341	—	11	2	no	—
121	C₂³×C₁₁	—	2	2	no	—
122	C₂³×C₁₁	—	2	2	no	—
123	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₁	#125	1	2	yes	—
126	C₂³×C₁₁	C₄⋊Q₈	1	2	yes	—
127	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	4	no	—
132	C₂×C₄×C₁₁	—	2	4	no	—
133	C₂×C₄×C₁₁	—	4	2	no	—
134	C₂×C₄×C₁₁	—	4	2	no	—
135	C₂×C₄×C₁₁	#108	1	4	yes	complemented
136	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
146	C₂×C₄×C₁₁	#121	1	2	yes	—
147	C₂×C₄×C₁₁	#121	1	2	yes	—
148	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₁₁	#125	1	2	yes	—
151	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₁	—	2	8	no	—
159	C₁₁⋊C₈	—	2	4	no	—
160	C₁₁⋊C₈	—	2	4	no	—
161	C₁₁⋊C₈	—	4	4	no	—
162	C₂²×M₁₆	—	11	1	no	—
163	C₂²×M₁₆	—	11	1	no	—
164	C₂²×M₁₆	—	11	2	no	—
165	C₂³×C₈	C₂×D₁₁	1	2	yes	—
166	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
167	C₂×#108	—	11	8	no	—
168	C₂×#108	—	22	8	no	—
169	#423	—	11	4	no	—
170	#423	—	22	2	no	—
171	C₂×C₄⋊C₈	—	22	1	no	—
172	C₂×C₄⋊C₈	—	22	1	no	—
173	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
174	C₂×C₄⋊C₈	Dic₁₁	1	4	yes	—
175	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
176	C₂×C₄⋊C₈	C₂×D₁₁	1	4	yes	—
177	C₄×M₁₆	—	11	4	no	—
178	C₄×M₁₆	—	22	2	no	—
179	C₂×#97	—	22	1	no	—
180	C₂×C₄×C₈	—	22	1	no	—
181	#341	—	11	8	no	—
182	C₂²×C₁₁	—	2	1	no	—
183	C₂²×C₁₁	—	2	1	no	—
184	C₂²×C₁₁	—	2	1	no	—
185	C₂²×C₁₁	—	2	1	no	—
186	C₂²×C₁₁	—	2	4	no	—
187	C₂²×C₁₁	—	2	4	no	—
188	C₂²×C₁₁	#389	1	2	yes	—
189	C₂²×C₁₁	#389	1	2	yes	—
190	C₂²×C₁₁	C₂×#108	1	2	yes	—
191	C₂²×C₁₁	#430	1	2	yes	—
192	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₁₁	C₂×#125	1	1	yes	characteristic
194	C₂²×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
195	C₄×C₁₁	—	2	2	no	—
196	C₄×C₁₁	—	2	2	no	—
197	C₄×C₁₁	—	2	2	no	—
198	C₄×C₁₁	#389	1	2	yes	—
199	C₄×C₁₁	#389	1	2	yes	—
200	C₄×C₁₁	C₂×#108	1	4	yes	complemented
201	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
203	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
204	C₄×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
206	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
207	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
208	C₂×M₁₆	—	11	4	no	—
209	C₂×M₁₆	—	11	4	no	—
210	C₂×M₁₆	—	11	2	no	—
211	C₂×M₁₆	—	11	2	no	—
212	C₂×M₁₆	—	11	4	no	—
213	C₂×M₁₆	—	22	1	no	—
214	C₂×M₁₆	—	22	1	no	—
215	C₂×M₁₆	—	22	2	no	—
216	C₂×M₁₆	—	22	2	no	—
217	C₂×M₁₆	—	22	2	no	—
218	C₂×M₁₆	—	22	4	no	—
219	C₂×M₁₆	—	22	4	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	—	22	1	no	—
223	C₂²×C₈	—	22	1	no	—
224	C₂²×C₈	—	22	2	no	—
225	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
226	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
227	C₂²×C₈	C₂²×D₁₁	1	4	yes	—
228	C₂×C₄²	Dic₂₂	1	2	yes	—
229	C₂×C₄²	D₄₄	1	2	yes	—
230	C₂×C₄²	D₄₄	1	1	yes	characteristic
231	C₂×C₄²	D₄₄	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
234	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
236	#108	—	22	16	no	—
237	C₄⋊C₈	—	22	4	no	—
238	C₄⋊C₈	—	22	4	no	—
239	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
240	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
241	#97	—	22	4	no	—
242	C₄×C₈	—	22	4	no	—
243	C₂×C₁₁	—	2	1	no	—
244	C₂×C₁₁	—	2	1	no	—
245	C₂×C₁₁	—	2	2	no	—
246	C₂×C₁₁	#1950	1	4	yes	complemented
247	C₂×C₁₁	C₂×#389	1	1	yes	characteristic
248	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
249	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
250	C₂⁴	C₂×Dic₂₂	1	1	yes	characteristic
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
254	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
257	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
258	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
259	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
260	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
261	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
264	C₂²×C₄	D₄×D₁₁	1	2	yes	—
265	C₂²×C₄	#4341	1	2	yes	—
266	C₂²×C₄	Q₈×D₁₁	1	2	yes	—
267	C₂²×C₄	#4343	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
270	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
271	M₁₆	—	11	4	no	—
272	M₁₆	—	11	4	no	—
273	M₁₆	—	22	4	no	—
274	M₁₆	—	22	4	no	—
275	M₁₆	—	22	2	no	—
276	M₁₆	—	22	2	no	—
277	M₁₆	—	22	4	no	—
278	M₁₆	—	22	4	no	—
279	M₁₆	—	44	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	22	4	no	—
285	C₂×C₈	—	22	4	no	—
286	C₂×C₈	—	22	2	no	—
287	C₂×C₈	—	22	2	no	—
288	C₂×C₈	—	22	4	no	—
289	C₂×C₈	—	44	4	no	—
290	C₂×C₈	C₂²×Dic₁₁	1	8	yes	—
291	C₄²	C₄⋊Dic₁₁	1	2	yes	—
292	C₄²	C₄⋊Dic₁₁	1	2	yes	—
293	C₄²	C₄⋊Dic₁₁	1	2	yes	—
294	C₄²	C₄⋊Dic₁₁	1	2	yes	—
295	C₄²	C₂×D₄₄	1	2	yes	—
296	C₄²	C₂×D₄₄	1	2	yes	—
297	C₄²	C₂²×Dic₁₁	1	2	yes	—
298	C₄²	C₂²×Dic₁₁	1	2	yes	—
299	C₁₁	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	#66941	1	2	yes	—
303	C₂³	#66943	1	2	yes	—
304	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
305	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
306	C₂³	C₂²×Dic₂₂	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	#66883	1	4	yes	complemented
315	C₂×C₄	#66941	1	2	yes	—
316	C₂×C₄	#66943	1	2	yes	—
317	C₂×C₄	#66948	1	2	yes	—
318	C₂×C₄	#66948	1	2	yes	—
319	C₂×C₄	#66950	1	2	yes	—
320	C₂×C₄	#66950	1	2	yes	—
321	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
323	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
324	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
325	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
327	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
328	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
329	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
330	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
331	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
332	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
333	C₂×C₄	C₂×#4341	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
335	C₂×C₄	C₂×#4343	1	1	yes	characteristic
336	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	22	4	no	—
339	C₈	—	22	4	no	—
340	C₈	—	44	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	#10622598	1	2	yes	—
348	C₂²	#10622598	1	2	yes	—
349	C₂²	C₂×#66883	1	2	yes	—
350	C₂²	#10622738	1	2	yes	—
351	C₂²	C₂×#66941	1	1	yes	characteristic
352	C₂²	C₂×#66943	1	1	yes	characteristic
353	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	#10622598	1	2	yes	—
358	C₄	#10622598	1	2	yes	—
359	C₄	C₂×#66883	1	4	yes	complemented
360	C₄	C₂×#66948	1	1	yes	characteristic
361	C₄	C₂×#66950	1	1	yes	characteristic
362	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
363	C₄	C₂×Q₈×Dic₁₁	1	1	yes	characteristic
364	C₂	—	2	1	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	2	no	—
367	C₂	#13069392	1	4	yes	direct product factor
368	C₂	C₂×#10622598	1	1	yes	characteristic
369	C₂	C₂²×#66883	1	1	yes	characteristic
370	C₂	C₂×#10622738	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₂²×C₁₁×C₄⋊C₈	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₁₁
hypocenter	C₁₁	C₂×#1950
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #13069392	C₂	direct (N × H)
135. C₂×C₄×C₁₁	#108	semidirect
200. C₄×C₁₁	C₂×#108	semidirect
246. C₂×C₁₁	#1950	semidirect
299. C₁₁	C₂×#1950	semidirect
314. C₂×C₄	#66883	semidirect
359. C₄	C₂×#66883	semidirect
367. C₂	#13069392	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#66883	2
C₂×#10622537	2
C₂×C₄×#4318	2
#13069392	2
C₂×#10622190	2
C₂²×C₁₁×C₄⋊C₈	2
C₂×#1950	11

Subgroups — C2×#13069392 #14757294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13069392 #14757294