Subgroups — #28404314

Order 14464.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299315	C₂	1	2	yes	maximal, complemented
2	#20299307	C₂	1	2	yes	maximal, complemented
3	#20299287	C₂	1	2	yes	maximal, complemented
4	#20299285	C₂	1	2	yes	maximal, complemented
5	#20299284	C₂	1	2	yes	maximal, complemented
6	#20299281	C₂	1	2	yes	maximal, complemented
7	#20299277	C₂	1	2	yes	maximal, complemented
8	#20299271	C₂	1	2	yes	maximal, complemented
9	#20299228	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299217	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299213	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299211	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299206	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299168	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299155	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299150	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299129	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299108	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299077	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16813579	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268646	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
27	#16813622	C₂²	1	1	yes	characteristic, complemented
28	#16813622	C₂²	1	1	yes	characteristic, complemented
29	#16813621	C₂²	1	2	yes	complemented
30	#16813621	C₂²	1	1	yes	characteristic, complemented
31	#16813620	C₂²	1	1	yes	characteristic, complemented
32	#16813617	C₂²	1	2	yes	—
33	#16813617	C₂²	1	2	yes	—
34	#16813617	C₂²	1	2	yes	—
35	#16813616	C₂²	1	2	yes	—
36	#16813615	C₂²	1	2	yes	complemented
37	#16813615	C₂²	1	2	yes	complemented
38	#16813615	C₂²	1	2	yes	complemented
39	#16813614	C₂²	1	2	yes	complemented
40	#16813614	C₂²	1	2	yes	complemented
41	#16813613	C₂²	1	2	yes	complemented
42	#16813613	C₂²	1	2	yes	complemented
43	#16813613	C₂²	1	1	yes	characteristic, complemented
44	#16813612	C₂²	1	2	yes	complemented
45	#16813612	C₂²	1	2	yes	complemented
46	#16813612	C₂²	1	2	yes	complemented
47	#16813609	C₂²	1	1	yes	characteristic, complemented
48	#16813608	C₂²	1	2	yes	—
49	#16813608	C₂²	1	2	yes	—
50	#16813606	C₂²	1	2	yes	—
51	#16813605	C₂²	1	2	yes	—
52	#16813604	C₂²	1	2	yes	—
53	#16813604	C₂²	1	2	yes	—
54	#16813604	C₂²	1	2	yes	—
55	#16813603	C₂²	1	2	yes	—
56	#16813602	C₂²	1	2	yes	—
57	#16813602	C₂²	1	1	yes	characteristic
58	#16813602	C₂²	1	1	yes	characteristic
59	#16813601	C₂²	1	2	yes	—
60	#16813601	C₂²	1	1	yes	characteristic
61	#16813601	C₂²	1	1	yes	characteristic
62	#16813601	C₂²	1	2	yes	complemented
63	#16813600	C₂²	1	2	yes	—
64	#16813600	C₂²	1	2	yes	—
65	#16813599	C₂²	1	2	yes	—
66	#16813599	C₂²	1	2	yes	—
67	#16813599	C₂²	1	2	yes	complemented
68	#16813599	C₂²	1	2	yes	complemented
69	#16813599	C₂²	1	2	yes	complemented
70	#16813598	C₂²	1	1	yes	characteristic
71	#16813593	C₂²	1	1	yes	characteristic
72	#16813590	C₂²	1	2	yes	—
73	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
74	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
75	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
76	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
81	#16813587	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₁₁₃	C₂²	1	2	yes	—
83	D₄×Dic₁₁₃	C₂²	1	2	yes	—
84	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
86	#16813582	C₂²	1	2	yes	—
87	#16813582	C₂²	1	2	yes	—
88	#16813581	C₂²	1	2	yes	—
89	#16813580	C₂²	1	2	yes	—
90	#16813580	C₂²	1	1	yes	characteristic
91	#16813579	C₂²	1	2	yes	—
92	#16813579	C₂²	1	1	yes	characteristic
93	#16813579	C₂²	1	1	yes	characteristic
94	#16813579	C₂²	1	1	yes	characteristic
95	#16813579	C₂²	1	1	yes	characteristic
96	#16813579	C₂²	1	1	yes	characteristic
97	#16813579	C₂²	1	1	yes	characteristic
98	#16813579	C₂²	1	1	yes	characteristic
99	#16813579	C₂²	1	1	yes	characteristic
100	#16813578	C₂²	1	2	yes	—
101	#16813578	C₂²	1	2	yes	complemented
102	#16813578	C₂²	1	2	yes	complemented
103	C₂×#14268626	C₂²	1	1	yes	characteristic
104	C₂×#14268626	C₂²	1	1	yes	characteristic
105	C₂×#14268626	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
108	C₂×#14268624	C₂²	1	1	yes	characteristic
109	C₂×#14268624	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
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, complemented
115	#123×C₁₁₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
117	#121×C₁₁₃	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
120	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₁₃	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
123	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
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	C₂×Dic₂₂₆	C₂³	1	2	yes	—
129	C₂×Dic₂₂₆	C₂³	1	2	yes	—
130	Q₈×D₁₁₃	—	2	4	no	—
131	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
133	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
138	C₂×C₄×D₁₁₃	—	2	4	no	—
139	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
144	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
147	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
149	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
150	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
151	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
152	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
153	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
154	#14268626	C₂³	1	2	yes	—
155	#14268626	C₂³	1	2	yes	—
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	1	yes	characteristic
158	#14268626	C₂³	1	1	yes	characteristic
159	#14268626	C₂³	1	1	yes	characteristic
160	#14268626	C₂³	1	1	yes	characteristic
161	#14268626	C₂³	1	1	yes	characteristic
162	#14268626	C₂³	1	1	yes	characteristic
163	#14268626	C₂³	1	1	yes	characteristic
164	#14268626	C₂³	1	1	yes	characteristic
165	#14268626	C₂³	1	2	yes	—
166	#14268626	C₂³	1	2	yes	—
167	#14268626	C₂³	1	2	yes	—
168	#14268626	C₂³	1	2	yes	—
169	#14268626	C₂³	1	2	yes	—
170	#14268626	C₂³	1	2	yes	—
171	#14268626	C₂³	1	2	yes	—
172	#14268626	C₂³	1	2	yes	—
173	#14268626	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
180	#14268624	C₂³	1	2	yes	—
181	#14268624	C₂³	1	2	yes	—
182	#14268624	C₂³	1	1	yes	characteristic
183	#14268624	C₂³	1	1	yes	characteristic
184	#14268624	C₂³	1	1	yes	characteristic
185	#14268624	C₂³	1	1	yes	characteristic
186	#14268624	C₂³	1	1	yes	characteristic
187	#14268624	C₂³	1	1	yes	characteristic
188	#14268624	C₂³	1	1	yes	characteristic
189	#14268624	C₂³	1	1	yes	characteristic
190	#14268624	C₂³	1	2	yes	—
191	#14268624	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
204	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
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	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	1	yes	characteristic
223	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
224	C₄²×C₁₁₃	C₂³	1	2	yes	—
225	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
226	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₁₃	—	2	2	no	—
228	C₂²×D₁₁₃	—	2	2	no	—
229	C₂²×D₁₁₃	—	4	1	no	—
230	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
232	Q₈×C₁₁₃	—	2	2	no	—
233	D₄×C₁₁₃	—	2	4	no	—
234	D₄×C₁₁₃	—	2	2	no	—
235	C₂×C₄×C₁₁₃	—	2	2	no	—
236	C₂×C₄×C₁₁₃	—	2	2	no	—
237	C₂×C₄×C₁₁₃	—	4	1	no	—
238	C₂×C₄×C₁₁₃	—	4	2	no	—
239	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
245	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₁₁₃	—	2	4	no	—
249	C₂²⋊D₁₁₃	—	4	2	no	—
250	C₂×Dic₁₁₃	—	2	2	no	—
251	C₂×Dic₁₁₃	—	2	2	no	—
252	C₂×Dic₁₁₃	—	2	4	no	—
253	C₂×Dic₁₁₃	—	4	1	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	2	yes	—
261	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
262	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
265	C₄×D₁₁₃	—	2	2	no	—
266	C₄×D₁₁₃	—	2	4	no	—
267	C₄×D₁₁₃	—	2	2	no	—
268	C₄×D₁₁₃	—	2	2	no	—
269	C₄×D₁₁₃	—	4	2	no	—
270	C₄×D₁₁₃	#41	1	4	yes	—
271	Dic₂₂₆	—	2	2	no	—
272	Dic₂₂₆	—	2	2	no	—
273	Dic₂₂₆	—	2	4	no	—
274	Dic₂₂₆	—	4	2	no	—
275	Dic₂₂₆	—	4	2	no	—
276	C₂²×C₁₁₃	—	2	1	no	—
277	C₂²×C₁₁₃	—	2	1	no	—
278	C₂²×C₁₁₃	—	2	2	no	—
279	C₂²×C₁₁₃	—	2	2	no	—
280	C₂²×C₁₁₃	—	2	2	no	—
281	C₂²×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
282	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
283	C₂×D₁₁₃	—	2	1	no	—
284	C₂×D₁₁₃	—	2	1	no	—
285	C₂×D₁₁₃	—	2	1	no	—
286	C₂×D₁₁₃	—	2	1	no	—
287	C₂×D₁₁₃	—	2	1	no	—
288	C₂×D₁₁₃	—	4	4	no	—
289	C₂×D₁₁₃	C₂×#41	1	2	yes	—
290	C₄×C₁₁₃	—	2	2	no	—
291	C₄×C₁₁₃	—	2	1	no	—
292	C₄×C₁₁₃	—	2	1	no	—
293	C₄×C₁₁₃	—	2	1	no	—
294	C₄×C₁₁₃	—	2	2	no	—
295	C₄×C₁₁₃	—	2	1	no	—
296	C₄×C₁₁₃	—	2	2	no	—
297	C₄×C₁₁₃	—	2	1	no	—
298	C₄×C₁₁₃	C₂×#41	1	2	yes	—
299	Dic₁₁₃	—	2	2	no	—
300	Dic₁₁₃	—	2	2	no	—
301	Dic₁₁₃	—	2	1	no	—
302	Dic₁₁₃	—	2	1	no	—
303	Dic₁₁₃	—	2	1	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	—	2	2	no	—
306	Dic₁₁₃	—	2	2	no	—
307	Dic₁₁₃	—	2	1	no	—
308	Dic₁₁₃	C₂×#41	1	2	yes	—
309	C₂×C₁₁₃	—	2	2	no	—
310	C₂×C₁₁₃	—	4	2	no	—
311	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
312	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
313	C₂×C₁₁₃	#585	1	1	yes	characteristic
314	D₁₁₃	—	2	2	no	—
315	D₁₁₃	—	4	1	no	—
316	#3495	—	113	1	no	maximal, Sylow
317	C₁₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
318	#556	—	113	2	no	—
319	#554	—	113	2	no	—
320	#552	—	113	2	no	—
321	#552	—	113	2	no	—
322	#552	—	113	2	no	—
323	#552	—	113	2	no	—
324	#551	—	113	2	no	—
325	#551	—	113	2	no	—
326	#544	—	113	1	no	—
327	#542	—	113	1	no	—
328	#542	—	113	1	no	—
329	#541	—	113	1	no	—
330	#541	—	113	1	no	—
331	#536	—	113	1	no	—
332	#533	—	113	1	no	—
333	#533	—	113	1	no	—
334	#529	—	113	1	no	—
335	#529	D₁₁₃	1	1	yes	characteristic, complemented
336	#525	—	113	1	no	—
337	C₂×C₂²⋊Q₈	—	113	1	no	—
338	#520	—	113	1	no	—
339	#519	—	113	1	no	—
340	C₂×#117	—	113	1	no	—
341	C₂×#41	—	113	1	no	—
342	C₂²×Q₈	—	113	1	no	—
343	C₂³×C₄	—	113	1	no	—
344	C₄⋊Q₈	—	113	1	no	—
345	C₄⋊Q₈	—	113	1	no	—
346	C₄⋊Q₈	—	113	2	no	—
347	C₄⋊Q₈	—	113	1	no	—
348	C₄⋊Q₈	—	113	1	no	—
349	#126	—	113	2	no	—
350	#126	—	113	2	no	—
351	#126	—	113	2	no	—
352	#126	—	113	2	no	—
353	#126	—	113	2	no	—
354	#126	—	113	2	no	—
355	#126	—	113	2	no	—
356	#126	C₂×D₁₁₃	1	2	yes	complemented
357	#125	—	113	1	no	—
358	#125	—	113	2	no	—
359	#125	—	113	2	no	—
360	#125	—	113	2	no	—
361	#125	—	113	2	no	—
362	#125	—	113	2	no	—
363	#125	—	113	2	no	—
364	#125	—	113	2	no	—
365	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
366	#124	—	113	1	no	—
367	#124	—	113	2	no	—
368	#124	—	113	2	no	—
369	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
370	#123	—	113	2	no	—
371	#123	—	113	2	no	—
372	#123	—	113	2	no	—
373	#123	—	113	2	no	—
374	#123	—	113	2	no	—
375	#123	—	113	2	no	—
376	#123	C₂×D₁₁₃	1	2	yes	—
377	C₂²⋊Q₈	—	113	1	no	—
378	C₂²⋊Q₈	—	113	1	no	—
379	C₂²⋊Q₈	—	113	1	no	—
380	C₂²⋊Q₈	—	113	2	no	—
381	C₂²⋊Q₈	—	113	2	no	—
382	C₂²⋊Q₈	—	113	1	no	—
383	C₂²⋊Q₈	—	113	2	no	—
384	C₂²⋊Q₈	—	113	1	no	—
385	C₂²⋊Q₈	—	113	2	no	—
386	C₂²⋊Q₈	—	113	2	no	—
387	C₂²⋊Q₈	—	113	2	no	—
388	C₂²⋊Q₈	—	113	2	no	—
389	C₂²⋊Q₈	—	113	2	no	—
390	C₂²⋊Q₈	—	113	2	no	—
391	C₂²⋊Q₈	—	113	2	no	—
392	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
393	#121	—	113	1	no	—
394	#121	C₂×D₁₁₃	1	1	yes	characteristic
395	#120	—	113	2	no	—
396	C₄×Q₈	—	113	1	no	—
397	C₄×Q₈	—	113	1	no	—
398	C₄×Q₈	—	113	2	no	—
399	C₄×Q₈	—	113	1	no	—
400	C₄×Q₈	—	113	2	no	—
401	C₄×Q₈	—	113	1	no	—
402	C₄×Q₈	—	113	2	no	—
403	C₄×Q₈	—	113	1	no	—
404	C₄×Q₈	—	113	2	no	—
405	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
406	C₄×D₄	—	113	1	no	—
407	C₄×D₄	—	113	2	no	—
408	C₄×D₄	—	113	2	no	—
409	C₄×D₄	—	113	2	no	—
410	C₄×D₄	—	113	2	no	—
411	C₄×D₄	—	113	2	no	—
412	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
413	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
414	#117	—	113	2	no	—
415	#117	—	113	1	no	—
416	#117	—	113	2	no	—
417	#117	—	113	2	no	—
418	#117	—	113	2	no	—
419	#117	—	113	2	no	—
420	#117	—	113	1	no	—
421	#117	—	113	1	no	—
422	#117	—	113	1	no	—
423	#117	—	113	1	no	—
424	#117	—	113	1	no	—
425	#117	—	113	1	no	—
426	#117	—	113	1	no	—
427	#117	—	113	1	no	—
428	#117	—	113	2	no	—
429	#117	C₂×D₁₁₃	1	2	yes	complemented
430	C₂×C₄⋊C₄	—	113	1	no	—
431	C₂×C₄⋊C₄	—	113	1	no	—
432	C₂×C₄⋊C₄	—	113	2	no	—
433	C₂×C₄⋊C₄	—	113	1	no	—
434	C₂×C₄⋊C₄	—	113	2	no	—
435	C₂×C₂²⋊C₄	—	113	1	no	—
436	C₂×C₂²⋊C₄	—	113	1	no	—
437	C₂×C₂²⋊C₄	—	113	2	no	—
438	C₂×C₄²	—	113	1	no	—
439	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
440	C₂⁴	—	113	1	no	—
441	#41	—	226	4	no	—
442	C₂×Q₈	—	113	2	no	—
443	C₂×Q₈	—	113	2	no	—
444	C₂×Q₈	—	113	2	no	—
445	C₂×Q₈	—	113	1	no	—
446	C₂×Q₈	—	113	1	no	—
447	C₂×Q₈	—	226	4	no	—
448	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
449	C₂×D₄	—	113	2	no	—
450	C₂×D₄	—	113	2	no	—
451	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
452	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
453	C₂²×C₄	—	113	1	no	—
454	C₂²×C₄	—	113	1	no	—
455	C₂²×C₄	—	113	2	no	—
456	C₂²×C₄	—	113	1	no	—
457	C₂²×C₄	—	113	1	no	—
458	C₂²×C₄	—	113	2	no	—
459	C₂²×C₄	—	113	2	no	—
460	C₂²×C₄	—	113	2	no	—
461	C₂²×C₄	—	113	1	no	—
462	C₂²×C₄	—	113	1	no	—
463	C₂²×C₄	—	113	1	no	—
464	C₂²×C₄	—	226	4	no	—
465	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
469	C₄⋊C₄	—	113	1	no	—
470	C₄⋊C₄	—	113	2	no	—
471	C₄⋊C₄	—	113	1	no	—
472	C₄⋊C₄	—	113	1	no	—
473	C₄⋊C₄	—	113	1	no	—
474	C₄⋊C₄	—	113	1	no	—
475	C₄⋊C₄	—	113	1	no	—
476	C₄⋊C₄	—	113	1	no	—
477	C₄⋊C₄	—	113	1	no	—
478	C₄⋊C₄	—	113	2	no	—
479	C₄⋊C₄	—	113	1	no	—
480	C₄⋊C₄	—	113	2	no	—
481	C₄⋊C₄	—	113	2	no	—
482	C₄⋊C₄	—	113	2	no	—
483	C₄⋊C₄	—	113	2	no	—
484	C₄⋊C₄	—	113	1	no	—
485	C₄⋊C₄	—	113	2	no	—
486	C₄⋊C₄	—	113	2	no	—
487	C₄⋊C₄	—	113	2	no	—
488	C₄⋊C₄	—	113	2	no	—
489	C₄⋊C₄	—	113	2	no	—
490	C₄⋊C₄	—	113	2	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	C₂²×D₁₁₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
504	C₂²⋊C₄	—	113	2	no	—
505	C₂²⋊C₄	—	113	2	no	—
506	C₂²⋊C₄	—	113	2	no	—
507	C₂²⋊C₄	—	113	2	no	—
508	C₂²⋊C₄	—	113	2	no	—
509	C₂²⋊C₄	—	113	2	no	—
510	C₂²⋊C₄	—	113	1	no	—
511	C₂²⋊C₄	—	113	1	no	—
512	C₂²⋊C₄	—	113	1	no	—
513	C₂²⋊C₄	—	113	1	no	—
514	C₂²⋊C₄	—	113	1	no	—
515	C₂²⋊C₄	—	113	1	no	—
516	C₂²⋊C₄	—	113	1	no	—
517	C₂²⋊C₄	—	113	1	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	C₂²×D₁₁₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
527	C₄²	—	113	1	no	—
528	C₄²	—	113	1	no	—
529	C₄²	—	113	1	no	—
530	C₄²	—	113	1	no	—
531	C₄²	—	113	2	no	—
532	C₄²	—	113	2	no	—
533	C₄²	—	113	2	no	—
534	C₄²	—	113	2	no	—
535	C₄²	—	113	2	no	—
536	C₄²	—	113	2	no	—
537	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
538	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
539	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
540	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
541	C₄²	C₂²×D₁₁₃	1	2	yes	—
542	C₂³	—	113	1	no	—
543	C₂³	—	113	1	no	—
544	C₂³	—	452	1	no	—
545	C₂³	—	226	2	no	—
546	C₂³	—	226	2	no	—
547	C₂³	C₂³×D₁₁₃	1	2	yes	—
548	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	452	2	no	—
551	Q₈	—	452	2	no	—
552	Q₈	—	226	4	no	—
553	Q₈	—	226	2	no	—
554	Q₈	—	226	2	no	—
555	D₄	—	2	4	no	—
556	D₄	—	2	2	no	—
557	D₄	—	452	2	no	—
558	D₄	—	226	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	113	1	no	—
564	C₂×C₄	—	113	4	no	—
565	C₂×C₄	—	113	1	no	—
566	C₂×C₄	—	113	1	no	—
567	C₂×C₄	—	113	2	no	—
568	C₂×C₄	—	113	1	no	—
569	C₂×C₄	—	113	2	no	—
570	C₂×C₄	—	113	1	no	—
571	C₂×C₄	—	113	2	no	—
572	C₂×C₄	—	113	2	no	—
573	C₂×C₄	—	113	1	no	—
574	C₂×C₄	—	452	2	no	—
575	C₂×C₄	—	452	2	no	—
576	C₂×C₄	—	452	1	no	—
577	C₂×C₄	—	226	2	no	—
578	C₂×C₄	—	226	2	no	—
579	C₂×C₄	—	226	4	no	—
580	C₂×C₄	—	226	2	no	—
581	C₂×C₄	—	226	4	no	—
582	C₂×C₄	—	226	2	no	—
583	C₂×C₄	—	226	2	no	—
584	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
587	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
588	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
589	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	113	2	no	—
599	C₂²	—	452	4	no	—
600	C₂²	—	226	1	no	—
601	C₂²	—	226	1	no	—
602	C₂²	—	226	1	no	—
603	C₂²	—	226	1	no	—
604	C₂²	—	226	1	no	—
605	C₂²	#16813669	1	2	yes	—
606	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	113	2	no	—
616	C₄	—	226	1	no	—
617	C₄	—	226	2	no	—
618	C₄	—	226	2	no	—
619	C₄	—	226	1	no	—
620	C₄	—	226	1	no	—
621	C₄	—	226	1	no	—
622	C₄	—	226	2	no	—
623	C₄	—	226	1	no	—
624	C₄	—	226	2	no	—
625	C₄	#41×D₁₁₃	1	2	yes	—
626	C₂	—	2	2	no	—
627	C₂	—	4	2	no	—
628	C₂	—	452	1	no	—
629	C₂	—	226	2	no	—
630	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
631	C₂	C₂×#16813669	1	1	yes	characteristic
632	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	#20299108	C₂
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3495
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. #20299315	C₂	semidirect
2. #20299307	C₂	semidirect
3. #20299287	C₂	semidirect
4. #20299285	C₂	semidirect
5. #20299284	C₂	semidirect
6. #20299281	C₂	semidirect
7. #20299277	C₂	semidirect
8. #20299271	C₂	semidirect
9. #20299228	C₂	semidirect
10. #20299217	C₂	semidirect
11. #20299213	C₂	semidirect
12. #20299211	C₂	semidirect
13. #20299206	C₂	semidirect
14. #20299168	C₂	semidirect
15. #20299155	C₂	semidirect
16. #20299150	C₂	semidirect
17. #20299129	C₂	semidirect
19. C₂²⋊Q₈×D₁₁₃	C₂	semidirect
20. #20299077	C₂	semidirect
21. #20299074	C₂	semidirect
22. C₂×#16813579	C₂	semidirect
23. #529×C₁₁₃	C₂	semidirect
27. #16813622	C₂²	semidirect
28. #16813622	C₂²	semidirect
29. #16813621	C₂²	semidirect
30. #16813621	C₂²	semidirect
31. #16813620	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813615	C₂²	semidirect
38. #16813615	C₂²	semidirect
39. #16813614	C₂²	semidirect
40. #16813614	C₂²	semidirect
41. #16813613	C₂²	semidirect
42. #16813613	C₂²	semidirect
43. #16813613	C₂²	semidirect
44. #16813612	C₂²	semidirect
45. #16813612	C₂²	semidirect
46. #16813612	C₂²	semidirect
47. #16813609	C₂²	semidirect
62. #16813601	C₂²	semidirect
67. #16813599	C₂²	semidirect
68. #16813599	C₂²	semidirect
69. #16813599	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
84. D₄×Dic₁₁₃	C₂²	semidirect
101. #16813578	C₂²	semidirect
102. #16813578	C₂²	semidirect
105. C₂×#14268626	C₂²	semidirect
112. #126×C₁₁₃	C₂²	semidirect
113. #125×C₁₁₃	C₂²	semidirect
114. #124×C₁₁₃	C₂²	semidirect
118. C₄×Q₈×C₁₁₃	C₂²	semidirect
120. C₄×D₄×C₁₁₃	C₂²	semidirect
121. #117×C₁₁₃	C₂²	semidirect
317. C₁₁₃	#3495	semidirect
335. #529	D₁₁₃	semidirect
356. #126	C₂×D₁₁₃	semidirect
365. #125	C₂×D₁₁₃	semidirect
369. #124	C₂×D₁₁₃	semidirect
405. C₄×Q₈	C₂×D₁₁₃	semidirect
413. C₄×D₄	C₂×D₁₁₃	semidirect
429. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299315	2
#20299307	2
#20299287	2
#20299285	2
#20299284	2
#20299281	2
#20299277	2
#20299271	2
#20299228	2
#20299217	2
#20299213	2
#20299211	2
#20299206	2
#20299168	2
#20299155	2
#20299150	2
#20299129	2
#20299108	2
C₂²⋊Q₈×D₁₁₃	2
#20299077	2
#20299074	2
C₂×#16813579	2
#529×C₁₁₃	2
#3495	113