Subgroups — #28404562

Order 14464.

1012 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299326	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299315	C₂	1	2	yes	maximal, complemented
3	#20299308	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299302	C₂	1	2	yes	maximal, complemented
5	#20299299	C₂	1	2	yes	maximal, complemented
6	#20299298	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299289	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299281	C₂	1	2	yes	maximal, complemented
9	#20299263	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299256	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299256	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299218	C₂	1	2	yes	maximal, complemented
13	#20299217	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299209	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299205	C₂	1	2	yes	maximal, complemented
16	#20299135	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299131	C₂	1	2	yes	maximal, complemented
18	#20299127	C₂	1	1	yes	maximal, characteristic, complemented
19	#20299126	C₂	1	2	yes	maximal, complemented
20	#20299077	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×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	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
27	#16813622	C₂²	1	1	yes	characteristic
28	#16813621	C₂²	1	2	yes	—
29	#16813620	C₂²	1	2	yes	—
30	#16813617	C₂²	1	1	yes	characteristic
31	#16813617	C₂²	1	2	yes	—
32	#16813617	C₂²	1	1	yes	characteristic
33	#16813617	C₂²	1	2	yes	—
34	#16813616	C₂²	1	2	yes	—
35	#16813615	C₂²	1	2	yes	—
36	#16813615	C₂²	1	2	yes	—
37	#16813615	C₂²	1	2	yes	—
38	#16813614	C₂²	1	2	yes	—
39	#16813614	C₂²	1	1	yes	characteristic
40	#16813614	C₂²	1	1	yes	characteristic
41	#16813613	C₂²	1	1	yes	characteristic
42	#16813612	C₂²	1	2	yes	—
43	#16813612	C₂²	1	2	yes	—
44	#16813612	C₂²	1	2	yes	—
45	#16813612	C₂²	1	2	yes	—
46	#16813612	C₂²	1	2	yes	—
47	#16813611	C₂²	1	1	yes	characteristic
48	#16813608	C₂²	1	2	yes	—
49	#16813608	C₂²	1	2	yes	—
50	#16813608	C₂²	1	2	yes	—
51	#16813607	C₂²	1	2	yes	—
52	#16813607	C₂²	1	1	yes	characteristic
53	#16813607	C₂²	1	1	yes	characteristic
54	#16813606	C₂²	1	2	yes	—
55	#16813605	C₂²	1	2	yes	—
56	#16813604	C₂²	1	2	yes	—
57	#16813600	C₂²	1	2	yes	—
58	#16813600	C₂²	1	2	yes	—
59	#16813600	C₂²	1	2	yes	—
60	#16813600	C₂²	1	2	yes	—
61	#16813599	C₂²	1	2	yes	—
62	#16813599	C₂²	1	2	yes	—
63	#16813599	C₂²	1	2	yes	—
64	#16813598	C₂²	1	1	yes	characteristic
65	#16813598	C₂²	1	1	yes	characteristic
66	#16813598	C₂²	1	1	yes	characteristic
67	#16813598	C₂²	1	1	yes	characteristic
68	#16813598	C₂²	1	1	yes	characteristic
69	#16813597	C₂²	1	1	yes	characteristic
70	#16813595	C₂²	1	2	yes	—
71	#16813595	C₂²	1	2	yes	—
72	#16813595	C₂²	1	2	yes	—
73	#16813593	C₂²	1	1	yes	characteristic
74	#16813593	C₂²	1	1	yes	characteristic
75	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
76	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
77	C₄×Dic₂₂₆	C₂²	1	2	yes	—
78	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
79	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
80	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
81	C₄×Dic₂₂₆	C₂²	1	2	yes	—
82	#16813587	C₂²	1	2	yes	—
83	#16813587	C₂²	1	2	yes	—
84	#16813587	C₂²	1	1	yes	characteristic
85	#16813587	C₂²	1	2	yes	—
86	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
87	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
88	C₄×D₄₅₂	C₂²	1	2	yes	—
89	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
90	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
91	#16813584	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
93	C₄×C₂²⋊D₁₁₃	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	1	yes	characteristic
99	#16813580	C₂²	1	2	yes	—
100	#16813579	C₂²	1	2	yes	—
101	#16813579	C₂²	1	2	yes	—
102	#16813579	C₂²	1	1	yes	characteristic
103	#16813579	C₂²	1	1	yes	characteristic
104	#16813578	C₂²	1	2	yes	—
105	#16813578	C₂²	1	2	yes	—
106	C₂×#14268626	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
110	C₄²×D₁₁₃	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	#126×C₁₁₃	C₂²	1	2	yes	—
115	#124×C₁₁₃	C₂²	1	1	yes	characteristic
116	#124×C₁₁₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
118	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
119	C₄×Q₈×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	2	yes	—
123	#14268646	—	2	4	no	—
124	C₂×Dic₂₂₆	C₂³	1	2	yes	—
125	C₂×Dic₂₂₆	C₂³	1	2	yes	—
126	C₂×Dic₂₂₆	C₂³	1	2	yes	—
127	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
128	Q₈×D₁₁₃	—	2	4	no	—
129	Q₈×D₁₁₃	—	2	4	no	—
130	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
137	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
138	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
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	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	2	yes	—
146	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
147	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
150	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
155	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	2	yes	—
158	#14268626	C₂³	1	2	yes	—
159	#14268626	C₂³	1	2	yes	—
160	#14268626	C₂³	1	1	yes	characteristic
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	1	yes	characteristic
163	#14268626	C₂³	1	2	yes	—
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	1	yes	characteristic
166	#14268626	C₂³	1	2	yes	—
167	#14268626	C₂³	1	1	yes	characteristic
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	#14268624	C₂³	1	1	yes	characteristic
178	#14268624	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	2	yes	—
180	#14268624	C₂³	1	1	yes	characteristic
181	#14268624	C₂³	1	1	yes	characteristic
182	#14268624	C₂³	1	1	yes	characteristic
183	#14268624	C₂³	1	2	yes	—
184	#14268624	C₂³	1	1	yes	characteristic
185	#14268624	C₂³	1	1	yes	characteristic
186	#14268624	C₂³	1	2	yes	—
187	#14268624	C₂³	1	1	yes	characteristic
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	2	yes	—
190	#14268624	C₂³	1	1	yes	characteristic
191	#14268624	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₁₃	C₂³	1	2	yes	—
194	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₁₃	C₂³	1	2	yes	—
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×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
207	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
229	Q₈×C₁₁₃	—	2	2	no	—
230	Q₈×C₁₁₃	—	2	2	no	—
231	Q₈×C₁₁₃	—	4	1	no	—
232	D₄×C₁₁₃	—	2	2	no	—
233	C₂×C₄×C₁₁₃	—	4	2	no	—
234	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₁₃	—	2	4	no	—
245	C₂²⋊D₁₁₃	—	2	4	no	—
246	C₂²⋊D₁₁₃	—	4	2	no	—
247	C₂×Dic₁₁₃	—	2	4	no	—
248	C₂×Dic₁₁₃	—	4	2	no	—
249	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
255	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
256	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
258	D₄₅₂	—	2	2	no	—
259	D₄₅₂	—	2	2	no	—
260	D₄₅₂	—	4	1	no	—
261	C₄×D₁₁₃	—	2	2	no	—
262	C₄×D₁₁₃	—	2	2	no	—
263	C₄×D₁₁₃	—	2	2	no	—
264	C₄×D₁₁₃	—	2	2	no	—
265	C₄×D₁₁₃	—	2	4	no	—
266	C₄×D₁₁₃	—	2	4	no	—
267	C₄×D₁₁₃	—	4	2	no	—
268	C₄×D₁₁₃	—	4	2	no	—
269	C₄×D₁₁₃	—	4	1	no	—
270	Dic₂₂₆	—	2	4	no	—
271	Dic₂₂₆	—	2	4	no	—
272	Dic₂₂₆	—	4	2	no	—
273	Dic₂₂₆	#41	1	4	yes	—
274	C₂²×C₁₁₃	—	2	2	no	—
275	C₂²×C₁₁₃	—	2	2	no	—
276	C₂²×C₁₁₃	—	2	2	no	—
277	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
278	C₂×D₁₁₃	—	2	1	no	—
279	C₂×D₁₁₃	—	2	1	no	—
280	C₂×D₁₁₃	—	2	1	no	—
281	C₂×D₁₁₃	—	2	1	no	—
282	C₂×D₁₁₃	—	2	1	no	—
283	C₂×D₁₁₃	—	2	1	no	—
284	C₂×D₁₁₃	—	2	1	no	—
285	C₂×D₁₁₃	—	2	1	no	—
286	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
287	C₄×C₁₁₃	—	2	2	no	—
288	C₄×C₁₁₃	—	2	2	no	—
289	C₄×C₁₁₃	—	2	1	no	—
290	C₄×C₁₁₃	—	2	1	no	—
291	C₄×C₁₁₃	—	2	1	no	—
292	C₄×C₁₁₃	—	2	1	no	—
293	C₄×C₁₁₃	—	2	2	no	—
294	C₄×C₁₁₃	—	2	1	no	—
295	C₄×C₁₁₃	—	2	1	no	—
296	C₄×C₁₁₃	C₂×#41	1	2	yes	—
297	Dic₁₁₃	—	2	1	no	—
298	Dic₁₁₃	—	2	1	no	—
299	Dic₁₁₃	—	2	1	no	—
300	Dic₁₁₃	—	2	1	no	—
301	Dic₁₁₃	—	2	2	no	—
302	Dic₁₁₃	—	2	2	no	—
303	Dic₁₁₃	—	2	2	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	C₂×#41	1	4	yes	—
306	C₂×C₁₁₃	—	4	2	no	—
307	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
308	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂×C₁₁₃	#585	1	1	yes	characteristic
310	D₁₁₃	—	2	2	no	—
311	D₁₁₃	—	4	1	no	—
312	D₁₁₃	—	4	1	no	—
313	#3516	—	113	1	no	maximal, Sylow
314	C₁₁₃	#3516	1	1	yes	characteristic, complemented, Sylow
315	#557	—	113	1	no	—
316	#556	—	113	2	no	—
317	#556	D₁₁₃	1	1	yes	characteristic, complemented
318	#554	—	113	2	no	—
319	#554	—	113	1	no	—
320	#553	—	113	2	no	—
321	#553	—	113	1	no	—
322	#552	—	113	1	no	—
323	#552	—	113	2	no	—
324	D₄×Q₈	—	113	1	no	—
325	#548	—	113	1	no	—
326	#548	—	113	1	no	—
327	#542	—	113	1	no	—
328	#542	—	113	2	no	—
329	#541	—	113	1	no	—
330	#541	—	113	2	no	—
331	#529	—	113	2	no	—
332	#529	—	113	1	no	—
333	#529	—	113	1	no	—
334	#529	—	113	2	no	—
335	#520	—	113	1	no	—
336	#519	—	113	1	no	—
337	C₂×C₄×Q₈	—	113	1	no	—
338	C₂×#41	—	113	1	no	—
339	C₂²×Q₈	—	113	1	no	—
340	C₂²×Q₈	—	113	1	no	—
341	C₄⋊Q₈	—	113	2	no	—
342	C₄⋊Q₈	—	113	2	no	—
343	C₄⋊Q₈	—	113	1	no	—
344	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
345	#126	—	113	2	no	—
346	#126	—	113	1	no	—
347	#126	—	113	1	no	—
348	#126	—	113	2	no	—
349	#126	—	113	2	no	—
350	#126	—	113	2	no	—
351	#126	—	113	2	no	—
352	#126	—	113	2	no	—
353	#126	C₂×D₁₁₃	1	2	yes	—
354	#126	C₂×D₁₁₃	1	2	yes	—
355	#125	—	113	2	no	—
356	#125	—	113	1	no	—
357	#125	—	113	2	no	—
358	#125	—	113	2	no	—
359	#125	—	113	2	no	—
360	#125	—	113	2	no	—
361	#125	—	113	1	no	—
362	#125	—	113	2	no	—
363	#125	—	113	1	no	—
364	#124	—	113	1	no	—
365	#124	—	113	2	no	—
366	#124	—	113	2	no	—
367	#124	—	113	2	no	—
368	#124	C₂×D₁₁₃	1	1	yes	characteristic
369	#124	C₂×D₁₁₃	1	1	yes	characteristic
370	#123	—	113	2	no	—
371	#123	—	113	1	no	—
372	#123	—	113	1	no	—
373	#123	—	113	2	no	—
374	#123	—	113	2	no	—
375	#123	—	113	2	no	—
376	C₂²⋊Q₈	—	113	1	no	—
377	C₂²⋊Q₈	—	113	1	no	—
378	C₂²⋊Q₈	—	113	1	no	—
379	C₂²⋊Q₈	—	113	1	no	—
380	C₂²⋊Q₈	—	113	1	no	—
381	C₂²⋊Q₈	—	113	2	no	—
382	C₂²⋊Q₈	—	113	2	no	—
383	C₂²⋊Q₈	—	113	2	no	—
384	C₂²⋊Q₈	—	113	2	no	—
385	C₂²⋊Q₈	—	113	2	no	—
386	C₂²⋊Q₈	—	113	2	no	—
387	C₂²⋊Q₈	—	113	2	no	—
388	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
389	#121	—	113	1	no	—
390	#121	—	113	1	no	—
391	#121	—	113	1	no	—
392	#121	—	113	2	no	—
393	#121	—	113	2	no	—
394	#121	—	113	2	no	—
395	C₄×Q₈	—	113	1	no	—
396	C₄×Q₈	—	113	1	no	—
397	C₄×Q₈	—	113	1	no	—
398	C₄×Q₈	—	113	2	no	—
399	C₄×Q₈	—	113	2	no	—
400	C₄×Q₈	—	113	2	no	—
401	C₄×Q₈	—	113	1	no	—
402	C₄×Q₈	—	113	2	no	—
403	C₄×Q₈	—	113	2	no	—
404	C₄×Q₈	—	113	1	no	—
405	C₄×Q₈	—	113	1	no	—
406	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
408	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
409	C₄×D₄	—	113	1	no	—
410	C₄×D₄	—	113	2	no	—
411	C₄×D₄	—	113	2	no	—
412	C₄×D₄	—	113	2	no	—
413	C₄×D₄	—	113	2	no	—
414	C₄×D₄	—	113	2	no	—
415	C₄×D₄	—	113	2	no	—
416	C₄×D₄	—	113	2	no	—
417	C₄×D₄	—	113	1	no	—
418	C₄×D₄	—	113	1	no	—
419	C₄×D₄	—	113	1	no	—
420	C₄×D₄	—	113	2	no	—
421	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
422	#117	—	113	2	no	—
423	#117	—	113	1	no	—
424	#117	—	113	2	no	—
425	#117	—	113	2	no	—
426	#117	—	113	1	no	—
427	#117	—	113	2	no	—
428	#117	—	113	1	no	—
429	#117	—	113	2	no	—
430	#117	C₂×D₁₁₃	1	2	yes	—
431	C₂×C₄⋊C₄	—	113	2	no	—
432	C₂×C₄⋊C₄	—	113	2	no	—
433	C₂×C₄⋊C₄	—	113	1	no	—
434	C₂×C₄⋊C₄	—	113	1	no	—
435	C₂×C₄²	—	113	1	no	—
436	C₂×C₄²	—	113	2	no	—
437	#41	—	226	4	no	—
438	C₂×Q₈	—	113	1	no	—
439	C₂×Q₈	—	113	2	no	—
440	C₂×Q₈	—	113	2	no	—
441	C₂×Q₈	—	113	2	no	—
442	C₂×Q₈	—	226	4	no	—
443	C₂×Q₈	—	226	4	no	—
444	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
445	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
446	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
447	C₂×D₄	—	113	2	no	—
448	C₂×D₄	—	113	2	no	—
449	C₂×D₄	—	113	2	no	—
450	C₂×D₄	—	113	1	no	—
451	C₂×D₄	—	113	1	no	—
452	C₂×D₄	—	113	1	no	—
453	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
454	C₂²×C₄	—	113	2	no	—
455	C₂²×C₄	—	113	2	no	—
456	C₂²×C₄	—	113	1	no	—
457	C₂²×C₄	—	113	2	no	—
458	C₂²×C₄	—	113	2	no	—
459	C₂²×C₄	—	113	1	no	—
460	C₂²×C₄	—	113	2	no	—
461	C₂²×C₄	—	113	1	no	—
462	C₂²×C₄	—	113	1	no	—
463	C₂²×C₄	—	113	2	no	—
464	C₂²×C₄	—	113	1	no	—
465	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
466	C₄⋊C₄	—	113	2	no	—
467	C₄⋊C₄	—	113	1	no	—
468	C₄⋊C₄	—	113	2	no	—
469	C₄⋊C₄	—	113	2	no	—
470	C₄⋊C₄	—	113	1	no	—
471	C₄⋊C₄	—	113	2	no	—
472	C₄⋊C₄	—	113	1	no	—
473	C₄⋊C₄	—	113	2	no	—
474	C₄⋊C₄	—	113	2	no	—
475	C₄⋊C₄	—	113	1	no	—
476	C₄⋊C₄	—	113	2	no	—
477	C₄⋊C₄	—	113	2	no	—
478	C₄⋊C₄	—	113	1	no	—
479	C₄⋊C₄	—	113	1	no	—
480	C₄⋊C₄	—	113	1	no	—
481	C₄⋊C₄	—	113	2	no	—
482	C₄⋊C₄	—	113	2	no	—
483	C₄⋊C₄	—	113	2	no	—
484	C₄⋊C₄	—	113	2	no	—
485	C₄⋊C₄	—	113	1	no	—
486	C₄⋊C₄	—	113	2	no	—
487	C₄⋊C₄	—	113	1	no	—
488	C₄⋊C₄	—	113	2	no	—
489	C₄⋊C₄	—	113	2	no	—
490	C₄⋊C₄	—	113	2	no	—
491	C₄⋊C₄	—	113	1	no	—
492	C₄⋊C₄	—	113	2	no	—
493	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
495	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
496	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	C₂²⋊C₄	—	113	2	no	—
502	C₂²⋊C₄	—	113	2	no	—
503	C₂²⋊C₄	—	113	2	no	—
504	C₂²⋊C₄	—	113	1	no	—
505	C₂²⋊C₄	—	113	2	no	—
506	C₂²⋊C₄	—	113	1	no	—
507	C₂²⋊C₄	—	113	1	no	—
508	C₂²⋊C₄	—	113	1	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	1	no	—
515	C₂²⋊C₄	—	113	2	no	—
516	C₂²⋊C₄	—	113	1	no	—
517	C₂²⋊C₄	—	113	2	no	—
518	C₂²⋊C₄	—	113	1	no	—
519	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
524	C₄²	—	113	2	no	—
525	C₄²	—	113	1	no	—
526	C₄²	—	113	1	no	—
527	C₄²	—	113	2	no	—
528	C₄²	—	113	1	no	—
529	C₄²	—	113	2	no	—
530	C₄²	—	113	2	no	—
531	C₄²	—	113	2	no	—
532	C₄²	—	113	2	no	—
533	C₄²	—	113	2	no	—
534	C₄²	C₂²×D₁₁₃	1	2	yes	—
535	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
536	C₄²	C₂²×D₁₁₃	1	2	yes	—
537	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
538	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
539	C₂³	—	113	1	no	—
540	C₂³	—	113	1	no	—
541	C₂³	—	113	1	no	—
542	C₂³	C₂³×D₁₁₃	1	2	yes	—
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	113	4	no	—
547	Q₈	—	452	2	no	—
548	Q₈	—	226	4	no	—
549	Q₈	—	226	4	no	—
550	D₄	—	2	2	no	—
551	D₄	—	452	1	no	—
552	D₄	—	452	2	no	—
553	D₄	—	226	2	no	—
554	D₄	—	226	2	no	—
555	D₄	—	226	4	no	—
556	D₄	—	226	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	113	2	no	—
559	C₂×C₄	—	113	1	no	—
560	C₂×C₄	—	113	1	no	—
561	C₂×C₄	—	113	2	no	—
562	C₂×C₄	—	113	1	no	—
563	C₂×C₄	—	113	1	no	—
564	C₂×C₄	—	113	2	no	—
565	C₂×C₄	—	113	2	no	—
566	C₂×C₄	—	113	1	no	—
567	C₂×C₄	—	452	2	no	—
568	C₂×C₄	—	452	2	no	—
569	C₂×C₄	—	452	1	no	—
570	C₂×C₄	—	452	2	no	—
571	C₂×C₄	—	226	4	no	—
572	C₂×C₄	—	226	4	no	—
573	C₂×C₄	—	226	2	no	—
574	C₂×C₄	—	226	4	no	—
575	C₂×C₄	—	226	2	no	—
576	C₂×C₄	—	226	2	no	—
577	C₂×C₄	—	226	2	no	—
578	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
580	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
583	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
584	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	113	2	no	—
592	C₂²	—	226	1	no	—
593	C₂²	—	226	1	no	—
594	C₂²	—	226	1	no	—
595	C₂²	—	226	1	no	—
596	C₂²	—	226	1	no	—
597	C₂²	—	226	1	no	—
598	C₂²	—	226	1	no	—
599	C₂²	—	226	1	no	—
600	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	113	4	no	—
611	C₄	—	226	1	no	—
612	C₄	—	226	1	no	—
613	C₄	—	226	1	no	—
614	C₄	—	226	1	no	—
615	C₄	—	226	2	no	—
616	C₄	—	226	1	no	—
617	C₄	—	226	2	no	—
618	C₄	—	226	2	no	—
619	C₄	#41×D₁₁₃	1	2	yes	—
620	C₂	—	4	2	no	—
621	C₂	—	452	1	no	—
622	C₂	—	452	1	no	—
623	C₂	—	226	2	no	—
624	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
625	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic
626	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#556×C₁₁₃	C₂
hypercenter	#556	D₁₁₃
hypocenter	C₁₁₃	#3516
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #20299326	C₂	semidirect
2. #20299315	C₂	semidirect
3. #20299308	C₂	semidirect
4. #20299302	C₂	semidirect
5. #20299299	C₂	semidirect
6. #20299298	C₂	semidirect
7. #20299289	C₂	semidirect
8. #20299281	C₂	semidirect
9. #20299263	C₂	semidirect
10. #20299256	C₂	semidirect
11. #20299256	C₂	semidirect
12. #20299218	C₂	semidirect
13. #20299217	C₂	semidirect
14. #20299209	C₂	semidirect
15. #20299205	C₂	semidirect
16. #20299135	C₂	semidirect
17. #20299131	C₂	semidirect
18. #20299127	C₂	semidirect
19. #20299126	C₂	semidirect
20. #20299077	C₂	semidirect
21. #20299074	C₂	semidirect
22. C₄×Q₈×D₁₁₃	C₂	semidirect
23. #556×C₁₁₃	C₂	semidirect
314. C₁₁₃	#3516	semidirect
317. #556	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299326	2
#20299315	2
#20299308	2
#20299302	2
#20299299	2
#20299298	2
#20299289	2
#20299281	2
#20299263	2
#20299256	2
#20299218	2
#20299217	2
#20299209	2
#20299205	2
#20299135	2
#20299131	2
#20299127	2
#20299126	2
#20299077	2
#20299074	2
C₄×Q₈×D₁₁₃	2
#556×C₁₁₃	2
#3516	113