Subgroups — #14775844

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077565	C₂	1	1	yes	maximal, characteristic, complemented
2	#13077184	C₂	1	1	yes	maximal, characteristic
3	#13069594	C₂	1	1	yes	maximal, characteristic, complemented
4	#13069392	C₂	1	1	yes	maximal, characteristic, complemented
5	#13069365	C₂	1	2	yes	maximal, complemented
6	#13069217	C₂	1	2	yes	maximal, complemented
7	#13068893	C₂	1	2	yes	maximal
8	C₄⋊C₈×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#13068456	C₂	1	2	yes	maximal
10	C₄×#66901	C₂	1	1	yes	maximal, characteristic
11	C₁₁×#3076	C₂	1	1	yes	maximal, characteristic
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂×#67001	C₂²	1	2	yes	—
15	C₁₁×#479	C₄	1	2	yes	complemented
16	C₁₁×#478	C₄	1	2	yes	complemented
17	C₁₁×#477	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#476	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#475	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#474	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#427	C₂²	1	2	yes	—
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₁₁×#416	C₂²	1	2	yes	—
24	C₂×#66901	C₂²	1	1	yes	characteristic
25	C₂×#66901	C₂²	1	1	yes	characteristic
26	C₂×#66883	C₂²	1	2	yes	—
27	C₂×C₈×Dic₁₁	C₂²	1	2	yes	—
28	#10622637	—	2	1	no	—
29	#10622637	—	2	2	no	—
30	Q₈×C₁₁⋊C₈	—	2	1	no	—
31	#10622612	—	2	2	no	—
32	#10622612	C₂²	1	2	yes	—
33	#10622612	C₂²	1	2	yes	—
34	#10622610	C₂²	1	2	yes	—
35	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
36	#10622537	—	2	1	no	—
37	#10622537	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
39	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
40	C₄×#4318	C₂²	1	1	yes	characteristic
41	#10622190	C₂²	1	2	yes	—
42	#10622188	C₂²	1	2	yes	—
43	#10622170	C₂²	1	2	yes	—
44	#10622170	C₂²	1	2	yes	—
45	#10622170	C₂²	1	1	yes	characteristic
46	#10622170	C₂²	1	1	yes	characteristic
47	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
51	C₁₁×#125	C₂×C₄	1	2	yes	—
52	C₁₁×C₂²⋊Q₈	—	2	1	no	—
53	C₁₁×C₂²⋊Q₈	—	2	1	no	—
54	C₄×Q₈×C₁₁	—	2	1	no	—
55	C₄×Q₈×C₁₁	—	2	1	no	—
56	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
58	C₄×D₄×C₁₁	—	2	1	no	—
59	C₄×D₄×C₁₁	—	2	1	no	—
60	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₁₁×#117	—	2	1	no	—
63	C₁₁×#117	C₂³	1	2	yes	—
64	C₁₁×#117	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	—	2	1	no	—
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	#67001	—	2	4	no	—
68	#67001	—	4	2	no	—
69	C₂×C₄×Dic₁₁	—	2	1	no	—
70	C₂×C₄×Dic₁₁	—	2	1	no	—
71	C₂×C₄×Dic₁₁	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₁₁	C₂³	1	1	yes	characteristic
73	C₂×#4318	—	2	2	no	—
74	C₂×#4318	C₂³	1	1	yes	characteristic
75	C₂×#4318	C₂³	1	2	yes	—
76	C₂×#4318	C₂³	1	1	yes	characteristic
77	C₂²×C₁₁⋊C₈	—	2	2	no	—
78	C₂²×C₁₁⋊C₈	C₂³	1	2	yes	—
79	C₁₁×#107	C₂×C₄	1	2	yes	—
80	C₁₁×#107	C₂×C₄	1	2	yes	—
81	C₁₁×#106	C₂×C₄	1	2	yes	—
82	C₁₁×#106	C₂×C₄	1	2	yes	—
83	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
85	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
86	C₁₁×#103	C₂×C₄	1	2	yes	—
87	C₁₁×#103	C₂×C₄	1	2	yes	—
88	C₁₁×#102	C₂×C₄	1	2	yes	—
89	C₁₁×#102	C₂×C₄	1	2	yes	—
90	#66901	—	2	2	no	—
91	#66901	Q₈	1	4	yes	complemented
92	#66883	—	4	2	no	—
93	C₈×Dic₁₁	—	4	2	no	—
94	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
95	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
96	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
97	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
98	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
99	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
100	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
101	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
102	C₄⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
103	#66867	—	2	1	no	—
104	#66867	—	2	2	no	—
105	C₄×C₁₁⋊C₈	—	2	1	no	—
106	C₄×C₁₁⋊C₈	—	2	2	no	—
107	#22982	—	11	1	no	maximal, Sylow
108	C₁₁×#41	—	2	1	no	—
109	C₁₁×#41	—	2	1	no	—
110	C₁₁×#41	C₂×Q₈	1	2	yes	—
111	C₁₁×#41	#41	1	2	yes	—
112	C₂×Q₈×C₁₁	—	2	1	no	—
113	C₂×Q₈×C₁₁	—	2	1	no	—
114	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₁	—	2	1	no	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
123	C₂²×Dic₁₁	—	2	1	no	—
124	C₂²×Dic₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	2	no	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
129	C₁₁×C₄⋊C₄	—	2	1	no	—
130	C₁₁×C₄⋊C₄	—	2	1	no	—
131	C₁₁×C₄⋊C₄	—	2	2	no	—
132	C₁₁×C₄⋊C₄	—	2	2	no	—
133	C₁₁×C₄⋊C₄	—	2	1	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
136	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
138	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
139	C₁₁×C₂²⋊C₄	—	2	1	no	—
140	C₁₁×C₂²⋊C₄	—	2	2	no	—
141	C₁₁×C₂²⋊C₄	—	2	1	no	—
142	C₁₁×C₂²⋊C₄	—	2	1	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	2	1	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	1	no	—
147	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₁₁	—	2	4	no	—
152	C₄×Dic₁₁	—	2	1	no	—
153	C₄×Dic₁₁	—	2	1	no	—
154	C₄×Dic₁₁	—	2	1	no	—
155	C₄×Dic₁₁	—	4	2	no	—
156	C₄×Dic₁₁	C₂×Q₈	1	2	yes	—
157	#4318	—	2	1	no	—
158	#4318	—	2	2	no	—
159	#4318	—	2	1	no	—
160	#4318	—	2	2	no	—
161	#4318	—	2	1	no	—
162	#4318	—	4	4	no	—
163	#4318	C₂×Q₈	1	2	yes	—
164	C₂×C₁₁⋊C₈	—	2	1	no	—
165	C₂×C₁₁⋊C₈	—	2	1	no	—
166	C₂×C₁₁⋊C₈	—	2	2	no	—
167	C₂×C₁₁⋊C₈	—	2	2	no	—
168	C₂×C₁₁⋊C₈	—	2	2	no	—
169	C₂×C₁₁⋊C₈	—	4	4	no	—
170	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
171	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
172	#3076	D₁₁	1	1	yes	characteristic
173	#2962	—	11	1	no	—
174	#2906	—	11	1	no	—
175	#1994	—	11	1	no	—
176	#1950	—	11	1	no	—
177	#1945	—	11	2	no	—
178	#1922	—	11	2	no	—
179	#1866	—	11	2	no	—
180	C₄×C₄⋊C₈	—	11	1	no	—
181	#1764	—	11	2	no	—
182	C₄×#104	—	11	1	no	—
183	C₂³×C₁₁	—	2	1	no	—
184	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
185	Q₈×C₁₁	—	2	1	no	—
186	Q₈×C₁₁	—	4	2	no	—
187	Q₈×C₁₁	—	8	1	no	—
188	Q₈×C₁₁	C₄×Q₈	1	2	yes	—
189	D₄×C₁₁	—	2	2	no	—
190	D₄×C₁₁	—	2	2	no	—
191	D₄×C₁₁	—	2	1	no	—
192	D₄×C₁₁	C₄×Q₈	1	2	yes	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	4	1	no	—
202	C₂×C₄×C₁₁	—	4	2	no	—
203	C₂×C₄×C₁₁	—	8	1	no	—
204	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
214	C₂×Dic₁₁	—	2	2	no	—
215	C₂×Dic₁₁	—	2	2	no	—
216	C₂×Dic₁₁	—	2	2	no	—
217	C₂×Dic₁₁	—	2	2	no	—
218	C₂×Dic₁₁	—	4	1	no	—
219	C₂×Dic₁₁	—	4	1	no	—
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	2	2	no	—
222	C₁₁⋊C₈	—	2	2	no	—
223	C₁₁⋊C₈	—	2	2	no	—
224	C₁₁⋊C₈	—	2	2	no	—
225	C₁₁⋊C₈	—	4	2	no	—
226	C₁₁⋊C₈	—	4	1	no	—
227	C₂×#131	—	11	2	no	—
228	#533	C₂×D₁₁	1	1	yes	characteristic
229	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
230	#479	Dic₁₁	1	2	yes	complemented
231	#478	Dic₁₁	1	2	yes	complemented
232	#477	Dic₁₁	1	1	yes	characteristic, complemented
233	#476	Dic₁₁	1	1	yes	characteristic, complemented
234	#475	Dic₁₁	1	1	yes	characteristic, complemented
235	#474	Dic₁₁	1	1	yes	characteristic, complemented
236	#446	—	22	2	no	—
237	#446	—	22	1	no	—
238	C₈×Q₈	—	22	1	no	—
239	C₂×#108	—	11	2	no	—
240	#427	C₂×D₁₁	1	2	yes	—
241	#424	—	11	2	no	—
242	#424	—	11	2	no	—
243	#424	—	22	2	no	—
244	#423	—	11	1	no	—
245	#423	—	22	1	no	—
246	C₂×C₄⋊C₈	—	11	1	no	—
247	C₂×C₄⋊C₈	—	22	1	no	—
248	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
249	C₂×#104	—	11	1	no	—
250	C₂×#104	—	11	1	no	—
251	#416	C₂×D₁₁	1	2	yes	—
252	#405	—	11	2	no	—
253	C₄×M₁₆	—	11	1	no	—
254	C₂×C₄×C₈	—	11	2	no	—
255	C₄³	—	11	1	no	—
256	#341	—	11	2	no	—
257	#339	—	11	2	no	—
258	#339	—	11	1	no	—
259	#339	—	11	1	no	—
260	#339	—	11	2	no	—
261	#336	—	11	2	no	—
262	C₂²×C₁₁	—	2	1	no	—
263	C₂²×C₁₁	—	2	1	no	—
264	C₂²×C₁₁	—	2	2	no	—
265	C₂²×C₁₁	—	4	1	no	—
266	C₂²×C₁₁	—	4	1	no	—
267	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂²×C₁₁	#552	1	1	yes	characteristic
269	C₂²×C₁₁	#554	1	1	yes	characteristic
270	C₄×C₁₁	—	2	2	no	—
271	C₄×C₁₁	—	2	1	no	—
272	C₄×C₁₁	—	2	1	no	—
273	C₄×C₁₁	—	2	1	no	—
274	C₄×C₁₁	—	4	1	no	—
275	C₄×C₁₁	—	4	2	no	—
276	C₄×C₁₁	—	4	1	no	—
277	C₄×C₁₁	—	4	2	no	—
278	C₄×C₁₁	#443	1	2	yes	—
279	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
280	C₄×C₁₁	#520	1	1	yes	characteristic
281	C₄×C₁₁	#546	1	1	yes	characteristic
282	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
283	Dic₁₁	—	2	4	no	—
284	Dic₁₁	—	4	2	no	—
285	C₂×#41	C₂²×D₁₁	1	1	yes	characteristic
286	#131	—	22	4	no	—
287	#131	—	44	2	no	—
288	C₂×M₁₆	—	11	1	no	—
289	C₂×M₁₆	—	11	2	no	—
290	C₂×M₁₆	—	11	1	no	—
291	C₂×M₁₆	—	22	2	no	—
292	C₂²×C₈	—	11	2	no	—
293	C₂²×C₈	—	22	2	no	—
294	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
295	C₄⋊Q₈	C₂×Dic₁₁	1	1	yes	characteristic
296	C₄⋊Q₈	C₂×Dic₁₁	1	1	yes	characteristic
297	#125	C₂×Dic₁₁	1	2	yes	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
303	C₄×Q₈	C₂×Dic₁₁	1	1	yes	characteristic
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
307	C₄×D₄	C₂×Dic₁₁	1	1	yes	characteristic
308	#117	—	2	1	no	—
309	#117	C₂²×D₁₁	1	1	yes	characteristic
310	#117	C₂²×D₁₁	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	11	1	no	—
313	C₂×C₄²	—	11	1	no	—
314	C₂×C₄²	—	22	1	no	—
315	C₂×C₄²	—	22	1	no	—
316	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
317	#108	—	44	2	no	—
318	#107	C₂×Dic₁₁	1	2	yes	—
319	#107	C₂×Dic₁₁	1	2	yes	—
320	#106	C₂×Dic₁₁	1	2	yes	—
321	#106	C₂×Dic₁₁	1	2	yes	—
322	C₄⋊C₈	—	11	1	no	—
323	C₄⋊C₈	—	11	1	no	—
324	C₄⋊C₈	—	11	2	no	—
325	C₄⋊C₈	—	22	2	no	—
326	C₄⋊C₈	—	22	2	no	—
327	C₄⋊C₈	—	22	2	no	—
328	C₄⋊C₈	—	22	2	no	—
329	C₄⋊C₈	—	22	1	no	—
330	C₄⋊C₈	—	22	1	no	—
331	C₄⋊C₈	C₂×Dic₁₁	1	1	yes	characteristic
332	C₄⋊C₈	C₂×Dic₁₁	1	1	yes	characteristic
333	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
334	#104	—	11	4	no	—
335	#104	—	22	2	no	—
336	#103	C₂×Dic₁₁	1	2	yes	—
337	#103	C₂×Dic₁₁	1	2	yes	—
338	#102	C₂×Dic₁₁	1	2	yes	—
339	#102	C₂×Dic₁₁	1	2	yes	—
340	#97	—	22	2	no	—
341	#97	—	22	1	no	—
342	C₄×C₈	—	22	2	no	—
343	C₄×C₈	—	22	1	no	—
344	C₄×C₈	—	44	2	no	—
345	C₂×C₁₁	—	2	1	no	—
346	C₂×C₁₁	—	2	1	no	—
347	C₂×C₁₁	—	4	2	no	—
348	C₂×C₁₁	#2360	1	1	yes	characteristic
349	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
350	C₂×C₁₁	#2956	1	1	yes	characteristic
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	#41	Q₈×D₁₁	1	2	yes	—
354	#41	#4343	1	2	yes	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	C₂²×Dic₁₁	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₂²×Dic₁₁	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	22	1	no	—
364	C₂²×C₄	—	22	1	no	—
365	C₂²×C₄	#4341	1	1	yes	characteristic
366	C₂²×C₄	#4341	1	1	yes	characteristic
367	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
368	M₁₆	—	11	2	no	—
369	M₁₆	—	22	1	no	—
370	M₁₆	—	22	1	no	—
371	M₁₆	—	22	2	no	—
372	M₁₆	—	22	1	no	—
373	M₁₆	—	22	2	no	—
374	M₁₆	—	44	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	11	2	no	—
378	C₂×C₈	—	11	2	no	—
379	C₂×C₈	—	22	1	no	—
380	C₂×C₈	—	22	2	no	—
381	C₂×C₈	—	22	2	no	—
382	C₂×C₈	—	22	1	no	—
383	C₂×C₈	—	22	2	no	—
384	C₂×C₈	—	44	4	no	—
385	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
386	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
394	C₄⋊C₄	C₂²×Dic₁₁	1	2	yes	—
395	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×Dic₁₁	1	1	yes	characteristic
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	11	2	no	—
406	C₄²	—	22	4	no	—
407	C₄²	—	22	1	no	—
408	C₄²	—	22	1	no	—
409	C₄²	—	22	1	no	—
410	C₄²	—	44	2	no	—
411	C₄²	D₄×D₁₁	1	1	yes	characteristic
412	C₄²	D₄×D₁₁	1	1	yes	characteristic
413	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
414	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
415	C₁₁	#22982	1	1	yes	characteristic, complemented, Sylow
416	C₂³	—	2	1	no	—
417	C₂³	C₂×#4341	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	8	1	no	—
421	Q₈	Q₈×Dic₁₁	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	Q₈×Dic₁₁	1	2	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	22	2	no	—
438	C₂×C₄	—	22	2	no	—
439	C₂×C₄	—	22	2	no	—
440	C₂×C₄	—	22	2	no	—
441	C₂×C₄	—	44	1	no	—
442	C₂×C₄	—	44	1	no	—
443	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
445	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
446	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
448	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
449	C₂×C₄	C₂×#4343	1	1	yes	characteristic
450	C₂×C₄	#67042	1	1	yes	characteristic
451	C₂×C₄	#67043	1	1	yes	characteristic
452	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	22	2	no	—
456	C₈	—	22	2	no	—
457	C₈	—	22	2	no	—
458	C₈	—	44	2	no	—
459	C₈	—	44	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	#10623166	1	1	yes	characteristic
466	C₂²	#10623173	1	1	yes	characteristic
467	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	22	4	no	—
477	C₄	—	44	2	no	—
478	C₄	#10622809	1	2	yes	—
479	C₄	#10623161	1	1	yes	characteristic
480	C₄	#10623163	1	1	yes	characteristic
481	C₄	C₂×Q₈×Dic₁₁	1	1	yes	characteristic
482	C₄	#10623358	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	#13071625	1	1	yes	characteristic
487	C₂	C₂×#10622809	1	1	yes	characteristic
488	C₂	#13077526	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₁₁×#3076	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×C₁₁×#41	C₂³
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	#3076	D₁₁
hypocenter	C₁₁	#22982
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #13077565	C₂	semidirect
3. #13069594	C₂	semidirect
4. #13069392	C₂	semidirect
5. #13069365	C₂	semidirect
6. #13069217	C₂	semidirect
8. C₄⋊C₈×Dic₁₁	C₂	semidirect
15. C₁₁×#479	C₄	semidirect
16. C₁₁×#478	C₄	semidirect
17. C₁₁×#477	C₄	semidirect
18. C₁₁×#476	C₄	semidirect
19. C₁₁×#475	C₄	semidirect
20. C₁₁×#474	C₄	semidirect
91. #66901	Q₈	semidirect
230. #479	Dic₁₁	semidirect
231. #478	Dic₁₁	semidirect
232. #477	Dic₁₁	semidirect
233. #476	Dic₁₁	semidirect
234. #475	Dic₁₁	semidirect
235. #474	Dic₁₁	semidirect
415. C₁₁	#22982	semidirect

Maximal subgroups

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

subgroup	index
#13077565	2
#13077184	2
#13069594	2
#13069392	2
#13069365	2
#13069217	2
#13068893	2
C₄⋊C₈×Dic₁₁	2
#13068456	2
C₄×#66901	2
C₁₁×#3076	2
#22982	11