Subgroups — #14736210

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079195	C₂	1	1	yes	maximal, characteristic, complemented
2	#13078071	C₂	1	2	yes	maximal, complemented
3	#13068060	C₂	1	2	yes	maximal, complemented
4	#13068053	C₂	1	2	yes	maximal, complemented
5	#13068010	C₂	1	1	yes	maximal, characteristic, complemented
6	#13068005	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067976	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10622096	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067263	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂×#67003	—	2	2	no	—
14	#10623008	C₂²	1	2	yes	—
15	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₁	—	2	1	no	—
18	C₈×D₄×C₁₁	—	2	1	no	—
19	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
20	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#431	—	2	1	no	—
22	C₁₁×#431	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₁	—	2	1	no	—
24	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
25	#10622728	—	2	1	no	—
26	#10622728	—	2	1	no	—
27	#10622644	C₂²	1	2	yes	—
28	#10622641	—	2	2	no	—
29	#10622640	C₂²	1	2	yes	—
30	#10622632	C₂²	1	2	yes	—
31	#10622629	—	2	2	no	—
32	#10622628	C₂²	1	2	yes	—
33	#10622615	—	2	2	no	—
34	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
35	#10622308	C₂²	1	1	yes	characteristic
36	#10622307	C₂²	1	2	yes	—
37	C₄×D₈₈	—	2	1	no	—
38	C₄×D₈₈	—	2	1	no	—
39	#10622295	C₂²	1	1	yes	characteristic
40	#10622124	C₂²	1	2	yes	—
41	#10622124	C₂²	1	2	yes	—
42	#10622123	C₂²	1	2	yes	—
43	#10622123	C₂²	1	2	yes	—
44	#10622096	C₂²	1	2	yes	—
45	#10622096	C₂²	1	1	yes	characteristic
46	#10622096	C₂²	1	1	yes	characteristic
47	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
48	C₂×#4339	—	2	2	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂²×C₈×C₁₁	—	2	1	no	—
51	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₁	—	2	1	no	—
56	C₄×D₄×C₁₁	—	2	1	no	—
57	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
58	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×#117	—	2	1	no	—
60	C₁₁×#117	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	—	2	1	no	—
62	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	#67003	—	4	8	no	—
64	C₂×#4326	—	2	2	no	—
65	C₂×#4325	—	2	2	no	—
66	C₂×#4324	—	2	2	no	—
67	C₂×#4323	—	2	2	no	—
68	#66983	—	2	2	no	—
69	#66983	—	2	2	no	—
70	C₂²×C₁₁⋊C₈	—	2	2	no	—
71	C₂×D₈₈	—	2	1	no	—
72	C₂×D₈₈	—	2	1	no	—
73	#66928	—	2	2	no	—
74	#66927	C₂³	1	2	yes	—
75	C₄×D₄₄	—	2	2	no	—
76	C₄×D₄₄	—	2	2	no	—
77	#66922	C₂³	1	2	yes	—
78	C₁₁×C₄⋊C₈	—	2	1	no	—
79	C₁₁×C₄⋊C₈	—	2	1	no	—
80	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₁₁×C₂²⋊C₈	—	2	1	no	—
83	C₁₁×C₂²⋊C₈	—	2	1	no	—
84	C₁₁×C₂²⋊C₈	—	2	1	no	—
85	C₄×C₈×C₁₁	—	2	1	no	—
86	C₄×C₈×C₁₁	—	2	1	no	—
87	C₄×C₈×C₁₁	—	2	1	no	—
88	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	#66885	—	2	2	no	—
93	#66885	—	2	2	no	—
94	#66882	—	2	1	no	—
95	#66882	—	2	1	no	—
96	#66874	—	2	2	no	—
97	#66874	—	2	2	no	—
98	#66873	—	2	2	no	—
99	#66873	—	2	2	no	—
100	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
101	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
102	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
103	#19125	—	11	1	no	maximal, Sylow
104	C₁₁×#41	—	2	2	no	—
105	C₁₁×#41	D₈	1	4	yes	complemented
106	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₂×D₄×C₁₁	—	2	1	no	—
108	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	1	no	—
112	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₁	—	4	2	no	—
116	#4339	—	4	4	no	—
117	#4339	—	4	4	no	—
118	C₂×D₄₄	—	2	2	no	—
119	C₂×D₄₄	—	2	2	no	—
120	C₂×D₄₄	—	2	2	no	—
121	C₂×C₄×D₁₁	—	4	2	no	—
122	C₂×Dic₂₂	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	4	1	no	—
127	C₂×C₈×C₁₁	—	4	2	no	—
128	C₂×C₈×C₁₁	—	4	2	no	—
129	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₁₁×C₄⋊C₄	—	2	1	no	—
134	C₁₁×C₄⋊C₄	—	2	1	no	—
135	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
136	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
137	C₁₁×C₂²⋊C₄	—	2	1	no	—
138	C₁₁×C₂²⋊C₄	—	2	1	no	—
139	C₁₁×C₂²⋊C₄	—	2	1	no	—
140	C₄²×C₁₁	—	2	1	no	—
141	C₄²×C₁₁	—	2	1	no	—
142	C₄²×C₁₁	—	2	1	no	—
143	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₁₁	#41	1	1	yes	characteristic
146	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
147	#4326	—	4	4	no	—
148	#4325	—	4	4	no	—
149	#4324	—	4	4	no	—
150	#4323	—	4	4	no	—
151	(C₂×D₁₁)⋊C₄	—	4	2	no	—
152	(C₂×D₁₁)⋊C₄	—	4	2	no	—
153	C₄⋊Dic₁₁	—	2	2	no	—
154	C₄⋊Dic₁₁	—	2	2	no	—
155	C₂×C₁₁⋊C₈	—	2	2	no	—
156	C₂×C₁₁⋊C₈	—	2	2	no	—
157	C₂×C₁₁⋊C₈	—	4	4	no	—
158	D₈₈	—	4	2	no	—
159	D₈₈	—	4	2	no	—
160	#3169	—	11	1	no	—
161	#3035	—	11	2	no	—
162	C₈×#41	D₁₁	1	1	yes	characteristic, complemented
163	#1682	—	11	2	no	—
164	#1681	—	11	2	no	—
165	#1674	—	11	1	no	—
166	#1673	—	11	1	no	—
167	#1668	—	11	1	no	—
168	#1667	—	11	1	no	—
169	C₂×#335	—	11	1	no	—
170	#1540	—	11	2	no	—
171	C₂³×C₁₁	—	2	1	no	—
172	C₂³×C₁₁	#121	1	1	yes	characteristic
173	C₂²×D₁₁	—	4	2	no	—
174	Q₈×C₁₁	—	2	1	no	—
175	Q₈×C₁₁	C₂×D₈	1	2	yes	—
176	D₄×C₁₁	—	2	4	no	—
177	D₄×C₁₁	—	2	1	no	—
178	D₄×C₁₁	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	2	4	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	4	1	no	—
186	C₂×C₄×C₁₁	—	4	2	no	—
187	C₂×C₄×C₁₁	—	4	1	no	—
188	C₂×C₄×C₁₁	—	4	1	no	—
189	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
191	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₁₁	#135	1	2	yes	—
194	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
197	C₂²⋊D₁₁	—	8	4	no	—
198	C₂×Dic₁₁	—	4	2	no	—
199	D₄₄	—	4	2	no	—
200	D₄₄	—	4	2	no	—
201	D₄₄	—	4	2	no	—
202	D₄₄	—	4	2	no	—
203	D₄₄	—	8	2	no	—
204	C₄×D₁₁	—	8	4	no	—
205	Dic₂₂	—	4	2	no	—
206	Dic₂₂	—	4	2	no	—
207	C₈×C₁₁	—	2	1	no	—
208	C₈×C₁₁	—	2	1	no	—
209	C₈×C₁₁	—	2	1	no	—
210	C₈×C₁₁	—	4	1	no	—
211	C₈×C₁₁	—	4	1	no	—
212	C₈×C₁₁	#135	1	2	yes	complemented
213	C₁₁⋊C₈	—	4	2	no	—
214	C₁₁⋊C₈	—	4	2	no	—
215	C₂×#135	—	22	2	no	—
216	#532	—	11	2	no	—
217	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
218	#500	—	11	1	no	—
219	#493	—	11	1	no	—
220	#486	—	11	2	no	—
221	#466	—	22	1	no	—
222	#466	—	22	1	no	—
223	#464	—	22	2	no	—
224	#463	—	22	2	no	—
225	#462	—	11	2	no	—
226	#461	—	11	2	no	—
227	#460	—	11	2	no	—
228	#459	—	11	2	no	—
229	C₈×Q₈	C₂×D₁₁	1	1	yes	characteristic
230	C₈×Q₈	C₂×D₁₁	1	1	yes	characteristic
231	C₄×D₈	—	22	1	no	—
232	C₄×D₈	—	22	1	no	—
233	C₈×D₄	—	2	1	no	—
234	C₈×D₄	—	2	1	no	—
235	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
236	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic
237	#431	—	2	1	no	—
238	#431	C₂×D₁₁	1	1	yes	characteristic
239	C₂×C₄⋊C₈	—	11	2	no	—
240	#416	—	22	2	no	—
241	C₂×C₄×C₈	—	2	1	no	—
242	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
243	#335	—	11	1	no	—
244	#335	—	11	1	no	—
245	#335	—	11	2	no	—
246	#332	—	11	2	no	—
247	#332	—	11	2	no	—
248	#331	—	11	2	no	—
249	#331	—	11	2	no	—
250	C₂²×C₁₁	—	2	1	no	—
251	C₂²×C₁₁	—	2	1	no	—
252	C₂²×C₁₁	—	2	2	no	—
253	C₂²×C₁₁	—	4	1	no	—
254	C₂²×C₁₁	—	4	1	no	—
255	C₂²×C₁₁	#466	1	2	yes	—
256	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
257	C₂×D₁₁	—	8	2	no	—
258	C₂×D₁₁	—	8	2	no	—
259	C₂×D₁₁	—	8	2	no	—
260	C₄×C₁₁	—	2	1	no	—
261	C₄×C₁₁	—	2	2	no	—
262	C₄×C₁₁	—	2	1	no	—
263	C₄×C₁₁	—	2	1	no	—
264	C₄×C₁₁	—	4	1	no	—
265	C₄×C₁₁	—	4	1	no	—
266	C₄×C₁₁	#466	1	2	yes	—
267	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
268	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
269	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
270	C₄×C₁₁	#575	1	1	yes	characteristic
271	Dic₁₁	—	8	2	no	—
272	C₂×#41	—	22	2	no	—
273	C₂×#41	D₄₄	1	1	yes	characteristic
274	#135	—	44	8	no	—
275	C₂×Q₁₆	—	22	2	no	—
276	C₂×SD₁₆	—	22	2	no	—
277	C₂×SD₁₆	—	22	2	no	—
278	C₂×D₈	—	22	2	no	—
279	C₂×D₈	—	22	1	no	—
280	C₂×D₈	—	22	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	22	2	no	—
284	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
285	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
286	C₄⋊Q₈	—	11	2	no	—
287	#127	—	11	2	no	—
288	#124	—	22	2	no	—
289	#121	—	22	2	no	—
290	#121	—	22	2	no	—
291	C₄×Q₈	D₄₄	1	1	yes	characteristic
292	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	22	2	no	—
296	C₄×D₄	—	22	2	no	—
297	C₄×D₄	D₄₄	1	1	yes	characteristic
298	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
299	#117	—	2	1	no	—
300	#117	D₄₄	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
303	#107	—	22	1	no	—
304	#107	—	22	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	11	2	no	—
308	C₄⋊C₈	—	11	2	no	—
309	C₄⋊C₈	—	22	2	no	—
310	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
312	#103	—	22	2	no	—
313	#103	—	22	2	no	—
314	#102	—	22	2	no	—
315	#102	—	22	2	no	—
316	#102	—	22	2	no	—
317	#102	—	22	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
325	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
328	C₂×C₁₁	—	2	2	no	—
329	C₂×C₁₁	—	4	2	no	—
330	C₂×C₁₁	#3035	1	1	yes	characteristic
331	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
332	C₂×C₁₁	#3067	1	1	yes	characteristic
333	D₁₁	—	16	2	no	—
334	#41	—	2	2	no	—
335	#41	—	44	4	no	—
336	#41	—	44	4	no	—
337	#41	D₈₈	1	4	yes	complemented
338	C₂×Q₈	—	22	2	no	—
339	C₂×Q₈	C₂×D₄₄	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	22	2	no	—
342	C₂×D₄	—	22	2	no	—
343	C₂×D₄	—	22	2	no	—
344	C₂×D₄	—	44	2	no	—
345	C₂×D₄	C₂×D₄₄	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	44	2	no	—
350	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
351	C₂²×C₄	#4339	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
353	Q₁₆	—	44	4	no	—
354	SD₁₆	—	44	4	no	—
355	SD₁₆	—	44	4	no	—
356	D₈	—	44	2	no	—
357	D₈	—	44	4	no	—
358	D₈	—	44	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	22	2	no	—
366	C₂×C₈	—	22	2	no	—
367	C₂×C₈	—	44	4	no	—
368	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
369	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
371	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	22	2	no	—
375	C₄⋊C₄	—	22	2	no	—
376	C₄⋊C₄	C₂×D₄₄	1	1	yes	characteristic
377	C₄⋊C₄	C₂×D₄₄	1	1	yes	characteristic
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	2	1	no	—
381	C₂²⋊C₄	—	44	2	no	—
382	C₂²⋊C₄	—	44	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	C₂×D₄₄	1	1	yes	characteristic
387	C₄²	#4339	1	1	yes	characteristic
388	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
389	C₄²	C₂³×D₁₁	1	1	yes	characteristic
390	C₁₁	#19125	1	1	yes	characteristic, complemented, Sylow
391	C₂³	—	2	1	no	—
392	C₂³	—	44	2	no	—
393	C₂³	#66983	1	1	yes	characteristic
394	Q₈	—	2	1	no	—
395	Q₈	—	44	2	no	—
396	Q₈	—	44	2	no	—
397	Q₈	C₂×D₈₈	1	2	yes	—
398	D₄	—	2	4	no	—
399	D₄	—	2	1	no	—
400	D₄	—	44	2	no	—
401	D₄	—	44	2	no	—
402	D₄	—	44	2	no	—
403	D₄	—	44	2	no	—
404	D₄	—	88	2	no	—
405	D₄	—	88	4	no	—
406	D₄	C₂×D₈₈	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	44	2	no	—
418	C₂×C₄	—	88	4	no	—
419	C₂×C₄	C₂×D₈₈	1	2	yes	—
420	C₂×C₄	#66957	1	2	yes	—
421	C₂×C₄	#66983	1	1	yes	characteristic
422	C₂×C₄	#66983	1	1	yes	characteristic
423	C₂×C₄	#66983	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
425	C₂×C₄	C₂×#4339	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₈	—	44	2	no	—
433	C₈	—	44	2	no	—
434	C₈	#67003	1	2	yes	complemented
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	88	2	no	—
441	C₂²	—	88	2	no	—
442	C₂²	—	88	2	no	—
443	C₂²	#10622728	1	2	yes	—
444	C₂²	C₂×#66983	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	88	2	no	—
452	C₄	#10622728	1	2	yes	—
453	C₄	C₂²×D₈₈	1	1	yes	characteristic
454	C₄	C₂×#66957	1	1	yes	characteristic
455	C₄	C₂×#67003	1	1	yes	characteristic
456	C₄	#10623353	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	4	2	no	—
459	C₂	—	176	2	no	—
460	C₂	#13078071	1	1	yes	characteristic
461	C₂	C₂×#10622728	1	1	yes	characteristic
462	C₂	#13078336	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#66983
commutator, cosocle	C₄²×C₁₁	C₂⁴
Frattini	C₄²	C₂³×D₁₁
Fitting	C₈×C₁₁×#41	C₂
socle	C₂²×C₁₁	C₂×#121
hypercenter	C₈×#41	D₁₁
hypocenter	C₁₁	#19125
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #13079195	C₂	semidirect
2. #13078071	C₂	semidirect
3. #13068060	C₂	semidirect
4. #13068053	C₂	semidirect
5. #13068010	C₂	semidirect
6. #13068005	C₂	semidirect
7. #13067976	C₂	semidirect
8. #13067971	C₂	semidirect
9. C₂×#10622096	C₂	semidirect
10. #13067263	C₂	semidirect
11. C₈×C₁₁×#41	C₂	semidirect
105. C₁₁×#41	D₈	semidirect
162. C₈×#41	D₁₁	semidirect
212. C₈×C₁₁	#135	semidirect
337. #41	D₈₈	semidirect
390. C₁₁	#19125	semidirect
434. C₈	#67003	semidirect

Maximal subgroups

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

subgroup	index
#13079195	2
#13078071	2
#13068060	2
#13068053	2
#13068010	2
#13068005	2
#13067976	2
#13067971	2
C₂×#10622096	2
#13067263	2
C₈×C₁₁×#41	2
#19125	11