Subgroups — #28404681

Order 14464.

1030 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299330	C₂	1	2	yes	maximal, complemented
2	#20299330	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299323	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299314	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299310	C₂	1	2	yes	maximal, complemented
6	#20299300	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299299	C₂	1	2	yes	maximal, complemented
8	#20299290	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299284	C₂	1	2	yes	maximal, complemented
10	#20299266	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299258	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299256	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299218	C₂	1	2	yes	maximal, complemented
14	#20299200	C₂	1	2	yes	maximal, complemented
15	#20299199	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299135	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299134	C₂	1	2	yes	maximal, complemented
18	#20299126	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299125	C₂	1	2	yes	maximal, complemented
20	#20299078	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14268646	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268647	C₂²	1	1	yes	characteristic
25	C₂×#14268646	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
27	#16813620	C₂²	1	2	yes	—
28	#16813618	C₂²	1	1	yes	characteristic
29	#16813618	C₂²	1	2	yes	—
30	#16813617	C₂²	1	2	yes	—
31	#16813617	C₂²	1	2	yes	—
32	#16813617	C₂²	1	1	yes	characteristic
33	#16813615	C₂²	1	2	yes	—
34	#16813615	C₂²	1	1	yes	characteristic
35	#16813613	C₂²	1	2	yes	—
36	#16813613	C₂²	1	1	yes	characteristic
37	#16813613	C₂²	1	1	yes	characteristic
38	#16813612	C₂²	1	1	yes	characteristic
39	#16813612	C₂²	1	2	yes	—
40	#16813612	C₂²	1	2	yes	—
41	#16813611	C₂²	1	2	yes	—
42	#16813611	C₂²	1	2	yes	—
43	#16813611	C₂²	1	1	yes	characteristic
44	#16813608	C₂²	1	1	yes	characteristic
45	#16813608	C₂²	1	2	yes	—
46	#16813608	C₂²	1	2	yes	—
47	#16813608	C₂²	1	2	yes	—
48	#16813607	C₂²	1	1	yes	characteristic
49	#16813607	C₂²	1	2	yes	—
50	#16813606	C₂²	1	2	yes	—
51	#16813606	C₂²	1	2	yes	—
52	#16813606	C₂²	1	2	yes	—
53	#16813605	C₂²	1	2	yes	—
54	#16813604	C₂²	1	2	yes	—
55	#16813604	C₂²	1	2	yes	—
56	#16813604	C₂²	1	1	yes	characteristic
57	#16813600	C₂²	1	2	yes	—
58	#16813600	C₂²	1	1	yes	characteristic
59	#16813599	C₂²	1	2	yes	—
60	#16813598	C₂²	1	1	yes	characteristic
61	#16813597	C₂²	1	1	yes	characteristic
62	#16813597	C₂²	1	2	yes	—
63	#16813597	C₂²	1	1	yes	characteristic
64	#16813596	C₂²	1	2	yes	—
65	#16813595	C₂²	1	2	yes	—
66	#16813595	C₂²	1	2	yes	—
67	#16813595	C₂²	1	2	yes	—
68	#16813595	C₂²	1	2	yes	—
69	#16813595	C₂²	1	1	yes	characteristic
70	#16813594	C₂²	1	2	yes	—
71	#16813594	C₂²	1	2	yes	—
72	#16813593	C₂²	1	1	yes	characteristic
73	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
74	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
75	C₄×Dic₂₂₆	C₂²	1	2	yes	—
76	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
77	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
79	#16813587	C₂²	1	1	yes	characteristic
80	#16813587	C₂²	1	1	yes	characteristic
81	#16813587	C₂²	1	2	yes	—
82	C₄×D₄₅₂	C₂²	1	2	yes	—
83	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
84	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
85	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
86	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
87	D₄×Dic₁₁₃	C₂²	1	2	yes	—
88	#16813584	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
92	#16813582	C₂²	1	2	yes	—
93	#16813582	C₂²	1	2	yes	—
94	#16813582	C₂²	1	2	yes	—
95	#16813582	C₂²	1	2	yes	—
96	#16813582	C₂²	1	2	yes	—
97	#16813582	C₂²	1	2	yes	—
98	#16813580	C₂²	1	2	yes	—
99	#16813580	C₂²	1	1	yes	characteristic
100	#16813580	C₂²	1	1	yes	characteristic
101	#16813580	C₂²	1	2	yes	—
102	#16813580	C₂²	1	2	yes	—
103	#16813579	C₂²	1	2	yes	—
104	#16813579	C₂²	1	2	yes	—
105	#16813579	C₂²	1	1	yes	characteristic
106	#16813578	C₂²	1	2	yes	—
107	#16813578	C₂²	1	2	yes	—
108	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
113	#126×C₁₁₃	C₂²	1	2	yes	—
114	#124×C₁₁₃	C₂²	1	2	yes	—
115	#124×C₁₁₃	C₂²	1	1	yes	characteristic
116	#123×C₁₁₃	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
119	#121×C₁₁₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
122	#117×C₁₁₃	C₂²	1	1	yes	characteristic
123	#14268647	—	2	4	no	—
124	#14268646	—	2	4	no	—
125	C₂×Dic₂₂₆	C₂³	1	2	yes	—
126	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
128	Q₈×D₁₁₃	—	2	4	no	—
129	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
130	C₂×D₄₅₂	C₂³	1	2	yes	—
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
143	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
151	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
152	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
156	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
157	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
159	#14268626	C₂³	1	2	yes	—
160	#14268626	C₂³	1	2	yes	—
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	2	yes	—
163	#14268626	C₂³	1	2	yes	—
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	1	yes	characteristic
166	#14268626	C₂³	1	1	yes	characteristic
167	#14268626	C₂³	1	2	yes	—
168	#14268626	C₂³	1	1	yes	characteristic
169	#14268626	C₂³	1	1	yes	characteristic
170	#14268626	C₂³	1	1	yes	characteristic
171	#14268626	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
176	#14268624	C₂³	1	1	yes	characteristic
177	#14268624	C₂³	1	2	yes	—
178	#14268624	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	2	yes	—
180	#14268624	C₂³	1	2	yes	—
181	#14268624	C₂³	1	2	yes	—
182	#14268624	C₂³	1	2	yes	—
183	#14268624	C₂³	1	2	yes	—
184	#14268624	C₂³	1	2	yes	—
185	#14268624	C₂³	1	1	yes	characteristic
186	#14268624	C₂³	1	2	yes	—
187	#14268624	C₂³	1	1	yes	characteristic
188	#14268624	C₂³	1	1	yes	characteristic
189	#14268624	C₂³	1	2	yes	—
190	#14268624	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₁₃	C₂³	1	2	yes	—
195	C₄×Dic₁₁₃	C₂³	1	2	yes	—
196	C₄×Dic₁₁₃	C₂³	1	2	yes	—
197	C₄×Dic₁₁₃	C₂³	1	2	yes	—
198	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₁₃	C₂³	1	2	yes	—
200	C₄×Dic₁₁₃	C₂³	1	2	yes	—
201	C₄×Dic₁₁₃	C₂³	1	2	yes	—
202	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
204	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
206	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
222	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₄²×C₁₁₃	C₂³	1	2	yes	—
224	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
225	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
226	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
229	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
230	Q₈×C₁₁₃	—	2	2	no	—
231	Q₈×C₁₁₃	—	4	2	no	—
232	D₄×C₁₁₃	—	2	2	no	—
233	D₄×C₁₁₃	—	4	2	no	—
234	C₂×C₄×C₁₁₃	—	2	2	no	—
235	C₂×C₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₁₁₃	—	2	4	no	—
246	C₂²⋊D₁₁₃	—	2	4	no	—
247	C₂²⋊D₁₁₃	—	4	1	no	—
248	C₂²⋊D₁₁₃	—	4	2	no	—
249	C₂²⋊D₁₁₃	—	4	2	no	—
250	C₂²⋊D₁₁₃	—	4	2	no	—
251	C₂²⋊D₁₁₃	—	4	1	no	—
252	C₂×Dic₁₁₃	—	2	4	no	—
253	C₂×Dic₁₁₃	—	4	2	no	—
254	C₂×Dic₁₁₃	—	4	2	no	—
255	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
258	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
264	D₄₅₂	—	2	2	no	—
265	D₄₅₂	—	4	1	no	—
266	D₄₅₂	—	4	2	no	—
267	D₄₅₂	—	4	2	no	—
268	C₄×D₁₁₃	—	2	2	no	—
269	C₄×D₁₁₃	—	2	2	no	—
270	C₄×D₁₁₃	—	2	4	no	—
271	C₄×D₁₁₃	—	2	4	no	—
272	C₄×D₁₁₃	—	4	1	no	—
273	C₄×D₁₁₃	—	4	1	no	—
274	C₄×D₁₁₃	—	4	2	no	—
275	C₄×D₁₁₃	—	4	2	no	—
276	Dic₂₂₆	—	2	4	no	—
277	Dic₂₂₆	—	4	1	no	—
278	Dic₂₂₆	#41	1	4	yes	—
279	C₂²×C₁₁₃	—	2	2	no	—
280	C₂²×C₁₁₃	—	2	1	no	—
281	C₂²×C₁₁₃	—	2	1	no	—
282	C₂²×C₁₁₃	—	2	2	no	—
283	C₂²×C₁₁₃	—	2	2	no	—
284	C₂²×C₁₁₃	—	2	1	no	—
285	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₁₃	—	2	1	no	—
287	C₂×D₁₁₃	—	2	2	no	—
288	C₂×D₁₁₃	—	2	1	no	—
289	C₂×D₁₁₃	—	2	2	no	—
290	C₂×D₁₁₃	—	2	1	no	—
291	C₂×D₁₁₃	—	2	1	no	—
292	C₂×D₁₁₃	—	2	1	no	—
293	C₂×D₁₁₃	—	2	2	no	—
294	C₂×D₁₁₃	—	2	1	no	—
295	C₄×C₁₁₃	—	2	2	no	—
296	C₄×C₁₁₃	—	2	1	no	—
297	C₄×C₁₁₃	—	2	1	no	—
298	C₄×C₁₁₃	—	2	1	no	—
299	C₄×C₁₁₃	—	2	1	no	—
300	C₄×C₁₁₃	—	2	1	no	—
301	C₄×C₁₁₃	—	2	2	no	—
302	C₄×C₁₁₃	—	2	2	no	—
303	C₄×C₁₁₃	C₂×#41	1	2	yes	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	—	2	1	no	—
306	Dic₁₁₃	—	2	1	no	—
307	Dic₁₁₃	—	2	1	no	—
308	Dic₁₁₃	—	2	1	no	—
309	Dic₁₁₃	—	2	2	no	—
310	Dic₁₁₃	—	2	2	no	—
311	Dic₁₁₃	—	2	1	no	—
312	Dic₁₁₃	C₂×#41	1	4	yes	—
313	C₂×C₁₁₃	—	4	2	no	—
314	C₂×C₁₁₃	—	4	1	no	—
315	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
316	C₂×C₁₁₃	#585	1	1	yes	characteristic
317	C₂×C₁₁₃	#585	1	1	yes	characteristic
318	D₁₁₃	—	4	1	no	—
319	D₁₁₃	—	4	2	no	—
320	D₁₁₃	—	4	1	no	—
321	#3524	—	113	1	no	maximal, Sylow
322	C₁₁₃	#3524	1	1	yes	characteristic, complemented, Sylow
323	#559	—	113	1	no	—
324	#559	—	113	2	no	—
325	#557	—	113	1	no	—
326	#555	—	113	1	no	—
327	#555	—	113	2	no	—
328	#553	—	113	2	no	—
329	#553	—	113	1	no	—
330	#552	—	113	2	no	—
331	#552	—	113	1	no	—
332	#550	—	113	1	no	—
333	#548	—	113	1	no	—
334	#548	—	113	1	no	—
335	#542	—	113	2	no	—
336	#542	D₁₁₃	1	1	yes	characteristic, complemented
337	#540	—	113	2	no	—
338	#540	—	113	1	no	—
339	#529	—	113	2	no	—
340	#529	—	113	2	no	—
341	#529	—	113	1	no	—
342	#529	—	113	1	no	—
343	#520	—	113	1	no	—
344	#519	—	113	1	no	—
345	C₄×#41	—	113	1	no	—
346	C₂×#41	—	113	1	no	—
347	C₂×#41	—	113	1	no	—
348	C₂²×Q₈	—	113	1	no	—
349	C₄⋊Q₈	—	113	2	no	—
350	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
351	#127	—	113	1	no	—
352	#127	—	113	2	no	—
353	#126	—	113	1	no	—
354	#126	—	113	2	no	—
355	#126	—	113	2	no	—
356	#126	—	113	1	no	—
357	#126	—	113	2	no	—
358	#126	C₂×D₁₁₃	1	2	yes	—
359	#125	—	113	1	no	—
360	#125	—	113	2	no	—
361	#125	—	113	2	no	—
362	#125	—	113	1	no	—
363	#125	—	113	2	no	—
364	#125	—	113	1	no	—
365	#124	—	113	1	no	—
366	#124	—	113	2	no	—
367	#124	—	113	2	no	—
368	#124	—	113	2	no	—
369	#124	—	113	1	no	—
370	#124	—	113	2	no	—
371	#124	—	113	2	no	—
372	#124	C₂×D₁₁₃	1	1	yes	characteristic
373	#124	C₂×D₁₁₃	1	2	yes	—
374	#123	—	113	2	no	—
375	#123	—	113	2	no	—
376	#123	—	113	1	no	—
377	#123	—	113	1	no	—
378	#123	—	113	2	no	—
379	#123	—	113	2	no	—
380	#123	—	113	2	no	—
381	#123	—	113	2	no	—
382	#123	—	113	2	no	—
383	#123	C₂×D₁₁₃	1	2	yes	—
384	C₂²⋊Q₈	—	113	1	no	—
385	C₂²⋊Q₈	—	113	1	no	—
386	C₂²⋊Q₈	—	113	2	no	—
387	C₂²⋊Q₈	—	113	2	no	—
388	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
389	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
390	#121	—	113	2	no	—
391	#121	—	113	1	no	—
392	#121	—	113	2	no	—
393	#121	—	113	2	no	—
394	#121	—	113	1	no	—
395	#121	—	113	1	no	—
396	#121	—	113	2	no	—
397	#121	—	113	1	no	—
398	#121	—	113	2	no	—
399	#121	—	113	2	no	—
400	#121	—	113	2	no	—
401	#121	—	113	2	no	—
402	#121	C₂×D₁₁₃	1	1	yes	characteristic
403	C₄×Q₈	—	113	1	no	—
404	C₄×Q₈	—	113	2	no	—
405	C₄×Q₈	—	113	1	no	—
406	C₄×Q₈	—	113	2	no	—
407	C₄×Q₈	—	113	1	no	—
408	C₄×Q₈	—	113	1	no	—
409	C₄×Q₈	—	113	2	no	—
410	C₄×Q₈	—	113	1	no	—
411	C₄×Q₈	—	113	1	no	—
412	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
413	C₄×D₄	—	113	1	no	—
414	C₄×D₄	—	113	2	no	—
415	C₄×D₄	—	113	2	no	—
416	C₄×D₄	—	113	1	no	—
417	C₄×D₄	—	113	1	no	—
418	C₄×D₄	—	113	2	no	—
419	C₄×D₄	—	113	2	no	—
420	C₄×D₄	—	113	2	no	—
421	C₄×D₄	—	113	2	no	—
422	C₄×D₄	—	113	2	no	—
423	C₄×D₄	—	113	2	no	—
424	C₄×D₄	—	113	2	no	—
425	C₄×D₄	—	113	1	no	—
426	C₄×D₄	—	113	1	no	—
427	C₄×D₄	—	113	1	no	—
428	C₄×D₄	—	113	2	no	—
429	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
430	#117	—	113	1	no	—
431	#117	—	113	2	no	—
432	#117	—	113	1	no	—
433	#117	—	113	2	no	—
434	#117	—	113	2	no	—
435	#117	—	113	2	no	—
436	#117	—	113	2	no	—
437	#117	—	113	1	no	—
438	#117	—	113	2	no	—
439	#117	—	113	2	no	—
440	#117	C₂×D₁₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	—	113	1	no	—
442	C₂×C₄⋊C₄	—	113	2	no	—
443	C₂×C₄²	—	113	2	no	—
444	C₂×C₄²	—	113	1	no	—
445	#41	—	226	4	no	—
446	#41	—	226	4	no	—
447	C₂×Q₈	—	113	1	no	—
448	C₂×Q₈	—	113	1	no	—
449	C₂×Q₈	—	113	2	no	—
450	C₂×Q₈	—	226	4	no	—
451	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
453	C₂×D₄	—	113	2	no	—
454	C₂×D₄	—	113	1	no	—
455	C₂×D₄	—	113	2	no	—
456	C₂×D₄	—	113	1	no	—
457	C₂×D₄	—	113	2	no	—
458	C₂×D₄	—	113	2	no	—
459	C₂×D₄	—	113	2	no	—
460	C₂×D₄	—	113	1	no	—
461	C₂×D₄	—	113	2	no	—
462	C₂×D₄	—	113	2	no	—
463	C₂×D₄	—	113	1	no	—
464	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
465	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
466	C₂²×C₄	—	113	2	no	—
467	C₂²×C₄	—	113	2	no	—
468	C₂²×C₄	—	113	2	no	—
469	C₂²×C₄	—	113	1	no	—
470	C₂²×C₄	—	113	1	no	—
471	C₂²×C₄	—	113	2	no	—
472	C₂²×C₄	—	113	2	no	—
473	C₂²×C₄	—	113	1	no	—
474	C₂²×C₄	—	113	2	no	—
475	C₂²×C₄	—	113	2	no	—
476	C₂²×C₄	—	113	1	no	—
477	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
479	C₄⋊C₄	—	113	2	no	—
480	C₄⋊C₄	—	113	2	no	—
481	C₄⋊C₄	—	113	1	no	—
482	C₄⋊C₄	—	113	2	no	—
483	C₄⋊C₄	—	113	1	no	—
484	C₄⋊C₄	—	113	2	no	—
485	C₄⋊C₄	—	113	1	no	—
486	C₄⋊C₄	—	113	2	no	—
487	C₄⋊C₄	—	113	2	no	—
488	C₄⋊C₄	—	113	1	no	—
489	C₄⋊C₄	—	113	1	no	—
490	C₄⋊C₄	—	113	2	no	—
491	C₄⋊C₄	—	113	2	no	—
492	C₄⋊C₄	—	113	2	no	—
493	C₄⋊C₄	—	113	1	no	—
494	C₄⋊C₄	—	113	1	no	—
495	C₄⋊C₄	—	113	2	no	—
496	C₄⋊C₄	—	113	1	no	—
497	C₄⋊C₄	—	113	1	no	—
498	C₄⋊C₄	—	113	1	no	—
499	C₄⋊C₄	—	113	2	no	—
500	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
507	C₂²⋊C₄	—	113	1	no	—
508	C₂²⋊C₄	—	113	2	no	—
509	C₂²⋊C₄	—	113	1	no	—
510	C₂²⋊C₄	—	113	2	no	—
511	C₂²⋊C₄	—	113	1	no	—
512	C₂²⋊C₄	—	113	2	no	—
513	C₂²⋊C₄	—	113	1	no	—
514	C₂²⋊C₄	—	113	2	no	—
515	C₂²⋊C₄	—	113	2	no	—
516	C₂²⋊C₄	—	113	2	no	—
517	C₂²⋊C₄	—	113	2	no	—
518	C₂²⋊C₄	—	113	2	no	—
519	C₂²⋊C₄	—	113	2	no	—
520	C₂²⋊C₄	—	113	1	no	—
521	C₂²⋊C₄	—	113	2	no	—
522	C₂²⋊C₄	—	113	1	no	—
523	C₂²⋊C₄	—	113	1	no	—
524	C₂²⋊C₄	—	113	2	no	—
525	C₂²⋊C₄	—	113	1	no	—
526	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
529	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
533	C₄²	—	113	1	no	—
534	C₄²	—	113	2	no	—
535	C₄²	—	113	1	no	—
536	C₄²	—	113	2	no	—
537	C₄²	—	113	2	no	—
538	C₄²	—	113	1	no	—
539	C₄²	—	113	2	no	—
540	C₄²	—	113	2	no	—
541	C₄²	—	113	2	no	—
542	C₄²	—	113	2	no	—
543	C₄²	—	113	1	no	—
544	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
545	C₄²	C₂²×D₁₁₃	1	2	yes	—
546	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
547	C₂³	—	113	1	no	—
548	C₂³	—	113	1	no	—
549	C₂³	—	113	2	no	—
550	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
551	C₂³	C₂³×D₁₁₃	1	2	yes	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	2	no	—
554	Q₈	—	113	4	no	—
555	Q₈	—	452	1	no	—
556	Q₈	—	226	4	no	—
557	D₄	—	2	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	452	2	no	—
560	D₄	—	452	2	no	—
561	D₄	—	452	1	no	—
562	D₄	—	452	1	no	—
563	D₄	—	452	2	no	—
564	D₄	—	452	2	no	—
565	D₄	—	452	1	no	—
566	D₄	—	452	2	no	—
567	D₄	—	226	4	no	—
568	D₄	—	226	4	no	—
569	D₄	—	226	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	113	2	no	—
573	C₂×C₄	—	113	1	no	—
574	C₂×C₄	—	113	1	no	—
575	C₂×C₄	—	113	2	no	—
576	C₂×C₄	—	113	1	no	—
577	C₂×C₄	—	113	1	no	—
578	C₂×C₄	—	113	1	no	—
579	C₂×C₄	—	113	1	no	—
580	C₂×C₄	—	113	2	no	—
581	C₂×C₄	—	452	1	no	—
582	C₂×C₄	—	452	1	no	—
583	C₂×C₄	—	452	2	no	—
584	C₂×C₄	—	452	2	no	—
585	C₂×C₄	—	452	2	no	—
586	C₂×C₄	—	452	2	no	—
587	C₂×C₄	—	226	4	no	—
588	C₂×C₄	—	226	4	no	—
589	C₂×C₄	—	226	4	no	—
590	C₂×C₄	—	226	2	no	—
591	C₂×C₄	—	226	2	no	—
592	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
595	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
596	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
598	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
601	C₂²	—	2	1	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	226	1	no	—
608	C₂²	—	226	2	no	—
609	C₂²	—	226	1	no	—
610	C₂²	—	226	1	no	—
611	C₂²	—	226	1	no	—
612	C₂²	—	226	2	no	—
613	C₂²	—	226	2	no	—
614	C₂²	—	226	1	no	—
615	C₂²	—	226	1	no	—
616	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	113	4	no	—
626	C₄	—	226	1	no	—
627	C₄	—	226	1	no	—
628	C₄	—	226	1	no	—
629	C₄	—	226	1	no	—
630	C₄	—	226	1	no	—
631	C₄	—	226	2	no	—
632	C₄	—	226	2	no	—
633	C₄	—	226	1	no	—
634	C₄	#41×D₁₁₃	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	2	no	—
637	C₂	—	452	1	no	—
638	C₂	—	452	1	no	—
639	C₂	—	452	2	no	—
640	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
641	C₂	#20299433	1	1	yes	characteristic
642	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#542×C₁₁₃	C₂
hypercenter	#542	D₁₁₃
hypocenter	C₁₁₃	#3524
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #20299330	C₂	semidirect
2. #20299330	C₂	semidirect
3. #20299323	C₂	semidirect
4. #20299314	C₂	semidirect
5. #20299310	C₂	semidirect
6. #20299300	C₂	semidirect
7. #20299299	C₂	semidirect
8. #20299290	C₂	semidirect
9. #20299284	C₂	semidirect
10. #20299266	C₂	semidirect
11. #20299258	C₂	semidirect
12. #20299256	C₂	semidirect
13. #20299218	C₂	semidirect
14. #20299200	C₂	semidirect
15. #20299199	C₂	semidirect
16. #20299135	C₂	semidirect
17. #20299134	C₂	semidirect
18. #20299126	C₂	semidirect
19. #20299125	C₂	semidirect
20. #20299078	C₂	semidirect
21. #20299074	C₂	semidirect
22. C₄×#14268646	C₂	semidirect
23. #542×C₁₁₃	C₂	semidirect
322. C₁₁₃	#3524	semidirect
336. #542	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299330	2
#20299323	2
#20299314	2
#20299310	2
#20299300	2
#20299299	2
#20299290	2
#20299284	2
#20299266	2
#20299258	2
#20299256	2
#20299218	2
#20299200	2
#20299199	2
#20299135	2
#20299134	2
#20299126	2
#20299125	2
#20299078	2
#20299074	2
C₄×#14268646	2
#542×C₁₁₃	2
#3524	113