Subgroups — #28404463

Order 14464.

1040 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299332	C₂	1	2	yes	maximal, complemented
2	#20299331	C₂	1	2	yes	maximal, complemented
3	#20299316	C₂	1	2	yes	maximal, complemented
4	#20299315	C₂	1	2	yes	maximal, complemented
5	#20299277	C₂	1	2	yes	maximal, complemented
6	#20299276	C₂	1	2	yes	maximal, complemented
7	#20299273	C₂	1	2	yes	maximal, complemented
8	#20299272	C₂	1	2	yes	maximal, complemented
9	#20299221	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299220	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299215	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299213	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299171	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299164	C₂	1	1	yes	maximal, characteristic
15	#20299154	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299133	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299132	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299127	C₂	1	1	yes	maximal, characteristic, complemented
19	#124×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299074	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268647	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
27	#16813621	C₂²	1	2	yes	complemented
28	#16813621	C₂²	1	1	yes	characteristic, complemented
29	#16813621	C₂²	1	1	yes	characteristic, complemented
30	#16813618	C₂²	1	2	yes	—
31	#16813617	C₂²	1	2	yes	complemented
32	#16813617	C₂²	1	2	yes	complemented
33	#16813616	C₂²	1	2	yes	complemented
34	#16813616	C₂²	1	2	yes	complemented
35	#16813615	C₂²	1	2	yes	complemented
36	#16813615	C₂²	1	2	yes	complemented
37	#16813615	C₂²	1	2	yes	complemented
38	#16813614	C₂²	1	1	yes	characteristic, complemented
39	#16813611	C₂²	1	1	yes	characteristic
40	#16813610	C₂²	1	1	yes	characteristic
41	#16813610	C₂²	1	2	yes	complemented
42	#16813609	C₂²	1	1	yes	characteristic
43	#16813609	C₂²	1	2	yes	complemented
44	#16813608	C₂²	1	2	yes	—
45	#16813608	C₂²	1	2	yes	—
46	#16813608	C₂²	1	2	yes	—
47	#16813608	C₂²	1	2	yes	complemented
48	#16813608	C₂²	1	2	yes	complemented
49	#16813608	C₂²	1	2	yes	complemented
50	#16813607	C₂²	1	2	yes	—
51	#16813607	C₂²	1	2	yes	complemented
52	#16813607	C₂²	1	2	yes	complemented
53	#16813605	C₂²	1	2	yes	complemented
54	#16813605	C₂²	1	2	yes	complemented
55	#16813604	C₂²	1	2	yes	—
56	#16813604	C₂²	1	2	yes	complemented
57	#16813604	C₂²	1	2	yes	complemented
58	#16813603	C₂²	1	2	yes	complemented
59	#16813602	C₂²	1	2	yes	complemented
60	#16813602	C₂²	1	1	yes	characteristic, complemented
61	#16813601	C₂²	1	2	yes	complemented
62	#16813601	C₂²	1	1	yes	characteristic, complemented
63	#16813600	C₂²	1	2	yes	—
64	#16813600	C₂²	1	2	yes	—
65	#16813600	C₂²	1	2	yes	complemented
66	#16813599	C₂²	1	2	yes	complemented
67	#16813598	C₂²	1	1	yes	characteristic, complemented
68	#16813597	C₂²	1	1	yes	characteristic
69	#16813596	C₂²	1	1	yes	characteristic
70	#16813593	C₂²	1	1	yes	characteristic
71	#16813592	C₂²	1	2	yes	—
72	#16813590	C₂²	1	2	yes	—
73	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
75	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
77	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
78	#16813587	C₂²	1	2	yes	complemented
79	#16813587	C₂²	1	2	yes	complemented
80	#16813587	C₂²	1	2	yes	complemented
81	#16813587	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
83	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
84	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
85	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
86	#16813584	C₂²	1	1	yes	characteristic
87	#16813584	C₂²	1	2	yes	complemented
88	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
94	#16813582	C₂²	1	2	yes	—
95	#16813582	C₂²	1	2	yes	complemented
96	#16813581	C₂²	1	1	yes	characteristic, complemented
97	#16813580	C₂²	1	2	yes	—
98	#16813580	C₂²	1	1	yes	characteristic
99	#16813580	C₂²	1	1	yes	characteristic
100	#16813580	C₂²	1	2	yes	complemented
101	#16813579	C₂²	1	2	yes	—
102	#16813579	C₂²	1	1	yes	characteristic
103	#16813579	C₂²	1	2	yes	complemented
104	#16813579	C₂²	1	1	yes	characteristic, complemented
105	#16813578	C₂²	1	2	yes	complemented
106	C₂×#14268624	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
110	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	#126×C₁₁₃	C₂²	1	2	yes	complemented
113	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
114	#124×C₁₁₃	C₂²	1	1	yes	characteristic
115	#123×C₁₁₃	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₁₃	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
121	#117×C₁₁₃	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁₃	C₂³	1	2	yes	—
124	#14268647	—	2	4	no	—
125	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₂₆	C₂³	1	2	yes	—
127	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₂₆	C₂³	1	2	yes	—
129	C₂×Dic₂₂₆	C₂³	1	2	yes	—
130	Q₈×D₁₁₃	—	2	4	no	—
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
133	C₂×D₄₅₂	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
139	D₄×D₁₁₃	—	2	4	no	—
140	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
143	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
153	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
154	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	2	yes	—
158	#14268626	C₂³	1	1	yes	characteristic
159	#14268626	C₂³	1	1	yes	characteristic
160	#14268626	C₂³	1	2	yes	—
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	1	yes	characteristic
163	#14268626	C₂³	1	1	yes	characteristic
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	2	yes	—
166	#14268626	C₂³	1	2	yes	—
167	#14268626	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
175	#14268624	C₂³	1	1	yes	characteristic
176	#14268624	C₂³	1	2	yes	—
177	#14268624	C₂³	1	2	yes	—
178	#14268624	C₂³	1	2	yes	—
179	#14268624	C₂³	1	2	yes	—
180	#14268624	C₂³	1	2	yes	—
181	#14268624	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
187	#14268624	C₂³	1	2	yes	—
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	2	yes	—
190	#14268624	C₂³	1	2	yes	—
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	1	yes	characteristic
195	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
196	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₁₃	C₂³	1	2	yes	—
198	C₄×Dic₁₁₃	C₂³	1	2	yes	—
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×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
204	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
205	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
207	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂²×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	2	yes	—
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	2	yes	—
218	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
220	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
221	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₄²×C₁₁₃	C₂³	1	2	yes	—
223	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
228	C₂²×D₁₁₃	—	4	2	no	—
229	C₂²×D₁₁₃	—	4	2	no	—
230	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₁₃	—	2	2	no	—
234	D₄×C₁₁₃	—	2	2	no	—
235	D₄×C₁₁₃	—	4	2	no	—
236	C₂×C₄×C₁₁₃	—	2	2	no	—
237	C₂×C₄×C₁₁₃	—	4	2	no	—
238	C₂×C₄×C₁₁₃	—	4	1	no	—
239	C₂×C₄×C₁₁₃	—	4	1	no	—
240	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₁₃	—	2	2	no	—
250	C₂²⋊D₁₁₃	—	2	4	no	—
251	C₂²⋊D₁₁₃	—	2	2	no	—
252	C₂²⋊D₁₁₃	—	4	2	no	—
253	C₂²⋊D₁₁₃	—	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	2	yes	—
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	1	yes	characteristic
264	D₄₅₂	—	2	2	no	—
265	D₄₅₂	—	2	2	no	—
266	D₄₅₂	—	4	2	no	—
267	C₄×D₁₁₃	—	2	4	no	—
268	C₄×D₁₁₃	—	2	2	no	—
269	C₄×D₁₁₃	—	4	1	no	—
270	C₄×D₁₁₃	—	4	1	no	—
271	C₄×D₁₁₃	—	4	2	no	—
272	C₄×D₁₁₃	—	4	2	no	—
273	C₄×D₁₁₃	—	4	1	no	—
274	C₄×D₁₁₃	—	4	1	no	—
275	C₄×D₁₁₃	#41	1	4	yes	—
276	Dic₂₂₆	—	2	2	no	—
277	Dic₂₂₆	—	2	4	no	—
278	Dic₂₂₆	—	2	2	no	—
279	Dic₂₂₆	—	4	2	no	—
280	Dic₂₂₆	—	4	2	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	—	2	2	no	—
286	C₂²×C₁₁₃	—	2	1	no	—
287	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
288	C₂×D₁₁₃	—	2	1	no	—
289	C₂×D₁₁₃	—	2	1	no	—
290	C₂×D₁₁₃	—	2	1	no	—
291	C₂×D₁₁₃	—	2	2	no	—
292	C₂×D₁₁₃	—	2	1	no	—
293	C₂×D₁₁₃	—	2	2	no	—
294	C₂×D₁₁₃	—	2	1	no	—
295	C₂×D₁₁₃	—	2	2	no	—
296	C₂×D₁₁₃	—	8	4	no	—
297	C₂×D₁₁₃	C₂×#41	1	2	yes	—
298	C₄×C₁₁₃	—	2	2	no	—
299	C₄×C₁₁₃	—	2	1	no	—
300	C₄×C₁₁₃	—	2	2	no	—
301	C₄×C₁₁₃	—	2	2	no	—
302	C₄×C₁₁₃	—	2	1	no	—
303	C₄×C₁₁₃	—	2	1	no	—
304	C₄×C₁₁₃	—	2	1	no	—
305	C₄×C₁₁₃	—	2	1	no	—
306	C₄×C₁₁₃	C₂×#41	1	2	yes	—
307	Dic₁₁₃	—	2	2	no	—
308	Dic₁₁₃	—	2	1	no	—
309	Dic₁₁₃	—	2	1	no	—
310	Dic₁₁₃	—	2	1	no	—
311	Dic₁₁₃	—	2	2	no	—
312	Dic₁₁₃	—	2	2	no	—
313	Dic₁₁₃	—	2	1	no	—
314	Dic₁₁₃	—	2	1	no	—
315	Dic₁₁₃	C₂×#41	1	2	yes	—
316	C₂×C₁₁₃	—	4	2	no	—
317	C₂×C₁₁₃	—	4	1	no	—
318	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
319	C₂×C₁₁₃	#585	1	1	yes	characteristic
320	C₂×C₁₁₃	#585	1	1	yes	characteristic
321	D₁₁₃	—	2	2	no	—
322	D₁₁₃	—	4	1	no	—
323	D₁₁₃	—	4	2	no	—
324	#3510	—	113	1	no	maximal, Sylow
325	C₁₁₃	#3510	1	1	yes	characteristic, complemented, Sylow
326	#559	—	113	2	no	—
327	#559	—	113	2	no	—
328	#556	—	113	2	no	—
329	#556	—	113	2	no	—
330	#551	—	113	2	no	—
331	#551	—	113	2	no	—
332	#551	—	113	2	no	—
333	#551	—	113	2	no	—
334	#542	—	113	1	no	—
335	#542	—	113	1	no	—
336	#542	—	113	1	no	—
337	#542	—	113	1	no	—
338	#536	—	113	1	no	—
339	#535	—	113	1	no	—
340	#533	—	113	1	no	—
341	#529	—	113	1	no	—
342	#529	—	113	1	no	—
343	#529	—	113	1	no	—
344	#529	D₁₁₃	1	1	yes	characteristic, complemented
345	C₂×#124	—	113	1	no	—
346	#519	—	113	1	no	—
347	#518	—	113	1	no	—
348	C₄×#41	—	113	1	no	—
349	C₂×#41	—	113	1	no	—
350	C₂²×Q₈	—	113	1	no	—
351	C₂²×D₄	—	113	1	no	—
352	C₄⋊Q₈	—	113	1	no	—
353	C₄⋊Q₈	—	113	1	no	—
354	C₄⋊Q₈	—	113	2	no	—
355	#127	—	113	2	no	—
356	#126	—	113	2	no	—
357	#126	—	113	2	no	—
358	#126	—	113	2	no	—
359	#126	—	113	2	no	—
360	#126	—	113	2	no	—
361	#126	—	113	2	no	—
362	#126	—	113	2	no	—
363	#126	C₂×D₁₁₃	1	2	yes	complemented
364	#125	—	113	1	no	—
365	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
366	#124	—	113	1	no	—
367	#124	—	113	1	no	—
368	#124	—	113	2	no	—
369	#124	—	113	2	no	—
370	#124	—	113	2	no	—
371	#124	—	113	2	no	—
372	#124	—	113	2	no	—
373	#124	—	113	2	no	—
374	#124	—	113	2	no	—
375	#124	—	113	1	no	—
376	#124	—	113	2	no	—
377	#124	C₂×D₁₁₃	1	1	yes	characteristic
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	—	113	2	no	—
384	#123	—	113	2	no	—
385	#123	—	113	2	no	—
386	#123	—	113	2	no	—
387	#123	C₂×D₁₁₃	1	2	yes	complemented
388	C₂²⋊Q₈	—	113	1	no	—
389	C₂²⋊Q₈	—	113	1	no	—
390	C₂²⋊Q₈	—	113	2	no	—
391	C₂²⋊Q₈	—	113	1	no	—
392	C₂²⋊Q₈	—	113	2	no	—
393	C₂²⋊Q₈	—	113	2	no	—
394	C₂²⋊Q₈	—	113	2	no	—
395	C₂²⋊Q₈	—	113	2	no	—
396	C₂²⋊Q₈	—	113	2	no	—
397	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
398	#121	—	113	1	no	—
399	#121	—	113	1	no	—
400	#121	—	113	1	no	—
401	#121	C₂×D₁₁₃	1	1	yes	characteristic
402	#120	—	113	2	no	—
403	#120	—	113	2	no	—
404	C₄×Q₈	—	113	1	no	—
405	C₄×Q₈	—	113	1	no	—
406	C₄×Q₈	—	113	2	no	—
407	C₄×Q₈	—	113	2	no	—
408	C₄×Q₈	—	113	2	no	—
409	C₄×Q₈	—	113	1	no	—
410	C₄×Q₈	—	113	1	no	—
411	C₄×Q₈	—	113	1	no	—
412	C₄×Q₈	—	113	2	no	—
413	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
414	C₄×D₄	—	113	1	no	—
415	C₄×D₄	—	113	1	no	—
416	C₄×D₄	—	113	1	no	—
417	C₄×D₄	—	113	1	no	—
418	C₄×D₄	—	113	1	no	—
419	C₄×D₄	—	113	2	no	—
420	C₄×D₄	—	113	2	no	—
421	C₄×D₄	—	113	1	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	C₂×D₁₁₃	1	1	yes	characteristic
429	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
430	#117	—	113	1	no	—
431	#117	—	113	1	no	—
432	#117	—	113	1	no	—
433	#117	—	113	2	no	—
434	#117	—	113	2	no	—
435	#117	—	113	2	no	—
436	#117	—	113	1	no	—
437	#117	—	113	1	no	—
438	#117	—	113	2	no	—
439	#117	—	113	2	no	—
440	#117	C₂×D₁₁₃	1	2	yes	complemented
441	C₂×C₂²⋊C₄	—	113	2	no	—
442	C₂×C₂²⋊C₄	—	113	2	no	—
443	C₂×C₂²⋊C₄	—	113	2	no	—
444	C₂×C₂²⋊C₄	—	113	2	no	—
445	C₂×C₄²	—	113	1	no	—
446	C₂×C₄²	—	113	1	no	—
447	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic, complemented
448	C₂⁴	—	113	2	no	—
449	#41	—	226	4	no	—
450	C₂×Q₈	—	113	2	no	—
451	C₂×Q₈	—	113	2	no	—
452	C₂×Q₈	—	113	1	no	—
453	C₂×Q₈	—	113	2	no	—
454	C₂×Q₈	—	113	1	no	—
455	C₂×Q₈	—	226	4	no	—
456	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
457	C₂×D₄	—	113	2	no	—
458	C₂×D₄	—	113	2	no	—
459	C₂×D₄	—	113	1	no	—
460	C₂×D₄	—	113	2	no	—
461	C₂×D₄	—	113	1	no	—
462	C₂×D₄	—	113	2	no	—
463	C₂×D₄	—	113	1	no	—
464	C₂×D₄	—	113	1	no	—
465	C₂×D₄	—	226	4	no	—
466	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
467	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
468	C₂²×C₄	—	113	1	no	—
469	C₂²×C₄	—	113	2	no	—
470	C₂²×C₄	—	113	1	no	—
471	C₂²×C₄	—	113	1	no	—
472	C₂²×C₄	—	113	1	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	—	113	2	no	—
478	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
480	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
481	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
482	C₄⋊C₄	—	113	2	no	—
483	C₄⋊C₄	—	113	1	no	—
484	C₄⋊C₄	—	113	1	no	—
485	C₄⋊C₄	—	113	1	no	—
486	C₄⋊C₄	—	113	1	no	—
487	C₄⋊C₄	—	113	1	no	—
488	C₄⋊C₄	—	113	1	no	—
489	C₄⋊C₄	—	113	1	no	—
490	C₄⋊C₄	—	113	1	no	—
491	C₄⋊C₄	—	113	2	no	—
492	C₄⋊C₄	—	113	2	no	—
493	C₄⋊C₄	—	113	2	no	—
494	C₄⋊C₄	—	113	2	no	—
495	C₄⋊C₄	—	113	2	no	—
496	C₄⋊C₄	—	113	2	no	—
497	C₄⋊C₄	—	113	2	no	—
498	C₄⋊C₄	—	113	2	no	—
499	C₄⋊C₄	—	113	2	no	—
500	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
506	C₂²⋊C₄	—	113	2	no	—
507	C₂²⋊C₄	—	113	2	no	—
508	C₂²⋊C₄	—	113	2	no	—
509	C₂²⋊C₄	—	113	1	no	—
510	C₂²⋊C₄	—	113	1	no	—
511	C₂²⋊C₄	—	113	2	no	—
512	C₂²⋊C₄	—	113	2	no	—
513	C₂²⋊C₄	—	113	1	no	—
514	C₂²⋊C₄	—	113	1	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	2	no	—
521	C₂²⋊C₄	—	113	2	no	—
522	C₂²⋊C₄	—	113	2	no	—
523	C₂²⋊C₄	—	113	1	no	—
524	C₂²⋊C₄	—	113	1	no	—
525	C₂²⋊C₄	—	113	2	no	—
526	C₂²⋊C₄	—	113	2	no	—
527	C₂²⋊C₄	—	113	2	no	—
528	C₂²⋊C₄	—	113	2	no	—
529	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
534	C₄²	—	113	1	no	—
535	C₄²	—	113	1	no	—
536	C₄²	—	113	1	no	—
537	C₄²	—	113	1	no	—
538	C₄²	—	113	1	no	—
539	C₄²	—	113	1	no	—
540	C₄²	—	113	2	no	—
541	C₄²	—	113	2	no	—
542	C₄²	—	113	2	no	—
543	C₄²	—	113	2	no	—
544	C₄²	—	113	2	no	—
545	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
546	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
547	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
548	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
549	C₄²	C₂²×D₁₁₃	1	2	yes	—
550	C₂³	—	113	1	no	—
551	C₂³	—	113	2	no	—
552	C₂³	—	113	1	no	—
553	C₂³	—	452	2	no	—
554	C₂³	—	452	2	no	—
555	C₂³	—	226	4	no	—
556	C₂³	C₂³×D₁₁₃	1	2	yes	—
557	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
558	Q₈	—	2	2	no	—
559	Q₈	—	452	2	no	—
560	Q₈	—	452	2	no	—
561	Q₈	—	226	4	no	—
562	Q₈	—	226	2	no	—
563	Q₈	—	226	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	452	2	no	—
567	D₄	—	452	2	no	—
568	D₄	—	452	2	no	—
569	D₄	—	226	2	no	—
570	D₄	—	226	4	no	—
571	D₄	—	226	2	no	—
572	D₄	—	226	2	no	—
573	D₄	—	226	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	113	1	no	—
579	C₂×C₄	—	113	4	no	—
580	C₂×C₄	—	113	1	no	—
581	C₂×C₄	—	113	1	no	—
582	C₂×C₄	—	113	2	no	—
583	C₂×C₄	—	113	2	no	—
584	C₂×C₄	—	113	1	no	—
585	C₂×C₄	—	113	1	no	—
586	C₂×C₄	—	113	1	no	—
587	C₂×C₄	—	113	2	no	—
588	C₂×C₄	—	452	1	no	—
589	C₂×C₄	—	452	1	no	—
590	C₂×C₄	—	452	2	no	—
591	C₂×C₄	—	452	1	no	—
592	C₂×C₄	—	452	1	no	—
593	C₂×C₄	—	452	2	no	—
594	C₂×C₄	—	452	2	no	—
595	C₂×C₄	—	226	4	no	—
596	C₂×C₄	—	226	2	no	—
597	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
601	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
602	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
603	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	113	2	no	—
613	C₂²	—	904	4	no	—
614	C₂²	—	226	1	no	—
615	C₂²	—	226	2	no	—
616	C₂²	—	226	1	no	—
617	C₂²	—	226	1	no	—
618	C₂²	—	226	2	no	—
619	C₂²	—	226	2	no	—
620	C₂²	—	226	1	no	—
621	C₂²	—	226	1	no	—
622	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	113	2	no	—
632	C₄	—	226	1	no	—
633	C₄	—	226	2	no	—
634	C₄	—	226	1	no	—
635	C₄	—	226	1	no	—
636	C₄	—	226	2	no	—
637	C₄	—	226	1	no	—
638	C₄	—	226	1	no	—
639	C₄	—	226	2	no	—
640	C₄	#41×D₁₁₃	1	2	yes	—
641	C₂	—	4	2	no	—
642	C₂	—	4	1	no	—
643	C₂	—	452	2	no	—
644	C₂	—	452	1	no	—
645	C₂	—	226	2	no	—
646	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
647	C₂	#20299434	1	1	yes	characteristic
648	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#529×C₁₁₃	C₂
prime radical	#20299164	C₂
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3510
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #20299332	C₂	semidirect
2. #20299331	C₂	semidirect
3. #20299316	C₂	semidirect
4. #20299315	C₂	semidirect
5. #20299277	C₂	semidirect
6. #20299276	C₂	semidirect
7. #20299273	C₂	semidirect
8. #20299272	C₂	semidirect
9. #20299221	C₂	semidirect
10. #20299220	C₂	semidirect
11. #20299215	C₂	semidirect
12. #20299213	C₂	semidirect
13. #20299171	C₂	semidirect
15. #20299154	C₂	semidirect
16. #20299133	C₂	semidirect
17. #20299132	C₂	semidirect
18. #20299127	C₂	semidirect
19. #124×D₁₁₃	C₂	semidirect
20. #20299074	C₂	semidirect
21. #20299070	C₂	semidirect
22. C₄×#14268647	C₂	semidirect
23. #529×C₁₁₃	C₂	semidirect
27. #16813621	C₂²	semidirect
28. #16813621	C₂²	semidirect
29. #16813621	C₂²	semidirect
31. #16813617	C₂²	semidirect
32. #16813617	C₂²	semidirect
33. #16813616	C₂²	semidirect
34. #16813616	C₂²	semidirect
35. #16813615	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813615	C₂²	semidirect
38. #16813614	C₂²	semidirect
41. #16813610	C₂²	semidirect
43. #16813609	C₂²	semidirect
47. #16813608	C₂²	semidirect
48. #16813608	C₂²	semidirect
49. #16813608	C₂²	semidirect
51. #16813607	C₂²	semidirect
52. #16813607	C₂²	semidirect
53. #16813605	C₂²	semidirect
54. #16813605	C₂²	semidirect
56. #16813604	C₂²	semidirect
57. #16813604	C₂²	semidirect
58. #16813603	C₂²	semidirect
59. #16813602	C₂²	semidirect
60. #16813602	C₂²	semidirect
61. #16813601	C₂²	semidirect
62. #16813601	C₂²	semidirect
65. #16813600	C₂²	semidirect
66. #16813599	C₂²	semidirect
67. #16813598	C₂²	semidirect
73. Q₈×Dic₁₁₃	C₂²	semidirect
74. C₄×Dic₂₂₆	C₂²	semidirect
75. C₄×Dic₂₂₆	C₂²	semidirect
76. C₄×Dic₂₂₆	C₂²	semidirect
77. C₄×Dic₂₂₆	C₂²	semidirect
78. #16813587	C₂²	semidirect
79. #16813587	C₂²	semidirect
80. #16813587	C₂²	semidirect
81. #16813587	C₂²	semidirect
87. #16813584	C₂²	semidirect
91. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
92. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
93. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
95. #16813582	C₂²	semidirect
96. #16813581	C₂²	semidirect
100. #16813580	C₂²	semidirect
103. #16813579	C₂²	semidirect
104. #16813579	C₂²	semidirect
105. #16813578	C₂²	semidirect
111. C₄²×D₁₁₃	C₂²	semidirect
112. #126×C₁₁₃	C₂²	semidirect
113. #125×C₁₁₃	C₂²	semidirect
115. #123×C₁₁₃	C₂²	semidirect
116. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
118. C₄×Q₈×C₁₁₃	C₂²	semidirect
120. C₄×D₄×C₁₁₃	C₂²	semidirect
121. #117×C₁₁₃	C₂²	semidirect
122. C₂×C₄²×C₁₁₃	C₂²	semidirect
325. C₁₁₃	#3510	semidirect
344. #529	D₁₁₃	semidirect
363. #126	C₂×D₁₁₃	semidirect
365. #125	C₂×D₁₁₃	semidirect
387. #123	C₂×D₁₁₃	semidirect
397. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
413. C₄×Q₈	C₂×D₁₁₃	semidirect
429. C₄×D₄	C₂×D₁₁₃	semidirect
440. #117	C₂×D₁₁₃	semidirect
447. C₂×C₄²	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299332	2
#20299331	2
#20299316	2
#20299315	2
#20299277	2
#20299276	2
#20299273	2
#20299272	2
#20299221	2
#20299220	2
#20299215	2
#20299213	2
#20299171	2
#20299164	2
#20299154	2
#20299133	2
#20299132	2
#20299127	2
#124×D₁₁₃	2
#20299074	2
#20299070	2
C₄×#14268647	2
#529×C₁₁₃	2
#3510	113