Subgroups — #28404435

Order 14464.

1012 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299331	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299330	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299326	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299323	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299321	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299320	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299317	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299315	C₂	1	2	yes	maximal, complemented
9	#20299302	C₂	1	2	yes	maximal, complemented
10	#20299284	C₂	1	2	yes	maximal, complemented
11	#20299281	C₂	1	2	yes	maximal, complemented
12	#20299194	C₂	1	2	yes	maximal, complemented
13	#20299189	C₂	1	2	yes	maximal, complemented
14	#20299173	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299168	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299147	C₂	1	1	yes	maximal, characteristic
18	#20299131	C₂	1	2	yes	maximal, complemented
19	#20299126	C₂	1	2	yes	maximal, complemented
20	#20299080	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299077	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×#14268648	C₂²	1	1	yes	characteristic
25	C₂×#14268646	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	1	yes	characteristic
29	#16813620	C₂²	1	1	yes	characteristic
30	#16813620	C₂²	1	1	yes	characteristic
31	#16813620	C₂²	1	1	yes	characteristic
32	#16813620	C₂²	1	1	yes	characteristic
33	#16813618	C₂²	1	1	yes	characteristic
34	#16813617	C₂²	1	2	yes	—
35	#16813617	C₂²	1	2	yes	—
36	#16813617	C₂²	1	2	yes	—
37	#16813616	C₂²	1	2	yes	—
38	#16813615	C₂²	1	2	yes	—
39	#16813615	C₂²	1	2	yes	—
40	#16813614	C₂²	1	2	yes	—
41	#16813613	C₂²	1	2	yes	—
42	#16813612	C₂²	1	1	yes	characteristic
43	#16813612	C₂²	1	2	yes	—
44	#16813612	C₂²	1	1	yes	characteristic
45	#16813612	C₂²	1	2	yes	—
46	#16813612	C₂²	1	2	yes	—
47	#16813612	C₂²	1	2	yes	—
48	#16813611	C₂²	1	1	yes	characteristic
49	#16813610	C₂²	1	1	yes	characteristic
50	#16813610	C₂²	1	1	yes	characteristic
51	#16813609	C₂²	1	1	yes	characteristic
52	#16813608	C₂²	1	2	yes	—
53	#16813608	C₂²	1	2	yes	—
54	#16813607	C₂²	1	2	yes	—
55	#16813607	C₂²	1	2	yes	—
56	#16813606	C₂²	1	2	yes	—
57	#16813605	C₂²	1	2	yes	—
58	#16813604	C₂²	1	2	yes	—
59	#16813604	C₂²	1	2	yes	—
60	#16813604	C₂²	1	2	yes	—
61	#16813604	C₂²	1	2	yes	—
62	#16813602	C₂²	1	1	yes	characteristic
63	#16813600	C₂²	1	2	yes	—
64	#16813600	C₂²	1	2	yes	—
65	#16813600	C₂²	1	2	yes	—
66	#16813600	C₂²	1	1	yes	characteristic
67	#16813600	C₂²	1	1	yes	characteristic
68	#16813599	C₂²	1	2	yes	—
69	#16813599	C₂²	1	2	yes	—
70	#16813599	C₂²	1	2	yes	—
71	#16813598	C₂²	1	2	yes	—
72	#16813598	C₂²	1	1	yes	characteristic
73	#16813595	C₂²	1	2	yes	—
74	#16813595	C₂²	1	2	yes	—
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	2	yes	—
79	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
80	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
81	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
82	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
83	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
84	#16813587	C₂²	1	2	yes	—
85	#16813587	C₂²	1	2	yes	—
86	#16813587	C₂²	1	1	yes	characteristic
87	#16813587	C₂²	1	1	yes	characteristic
88	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
89	C₄×D₄₅₂	C₂²	1	2	yes	—
90	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
91	#16813584	C₂²	1	1	yes	characteristic
92	#16813584	C₂²	1	2	yes	—
93	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
95	#16813582	C₂²	1	2	yes	—
96	#16813582	C₂²	1	2	yes	—
97	#16813582	C₂²	1	2	yes	—
98	#16813582	C₂²	1	2	yes	—
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	2	yes	—
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	#14268648	—	2	4	no	—
124	#14268646	—	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	1	yes	characteristic
129	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
131	Q₈×D₁₁₃	—	2	4	no	—
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
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	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁₃	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	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	1	yes	characteristic
152	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
153	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
155	#14268626	C₂³	1	2	yes	—
156	#14268626	C₂³	1	1	yes	characteristic
157	#14268626	C₂³	1	2	yes	—
158	#14268626	C₂³	1	2	yes	—
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	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	2	yes	—
170	#14268626	C₂³	1	2	yes	—
171	#14268626	C₂³	1	1	yes	characteristic
172	#14268626	C₂³	1	2	yes	—
173	#14268626	C₂³	1	1	yes	characteristic
174	#14268626	C₂³	1	1	yes	characteristic
175	#14268626	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	#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	2	yes	—
186	#14268624	C₂³	1	2	yes	—
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	2	yes	—
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	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	1	yes	characteristic
201	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
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	2	yes	—
227	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
228	Q₈×C₁₁₃	—	2	2	no	—
229	Q₈×C₁₁₃	—	2	2	no	—
230	Q₈×C₁₁₃	—	4	1	no	—
231	D₄×C₁₁₃	—	2	2	no	—
232	C₂×C₄×C₁₁₃	—	4	2	no	—
233	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₁₃	—	2	4	no	—
244	C₂²⋊D₁₁₃	—	2	4	no	—
245	C₂²⋊D₁₁₃	—	4	2	no	—
246	C₂×Dic₁₁₃	—	2	4	no	—
247	C₂×Dic₁₁₃	—	4	2	no	—
248	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
253	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
258	D₄₅₂	—	2	4	no	—
259	D₄₅₂	—	2	2	no	—
260	C₄×D₁₁₃	—	2	4	no	—
261	C₄×D₁₁₃	—	2	4	no	—
262	C₄×D₁₁₃	—	2	2	no	—
263	C₄×D₁₁₃	—	4	2	no	—
264	C₄×D₁₁₃	—	4	2	no	—
265	C₄×D₁₁₃	—	4	2	no	—
266	C₄×D₁₁₃	—	4	1	no	—
267	C₄×D₁₁₃	#41	1	4	yes	—
268	Dic₂₂₆	—	2	2	no	—
269	Dic₂₂₆	—	2	2	no	—
270	Dic₂₂₆	—	2	4	no	—
271	Dic₂₂₆	—	2	2	no	—
272	Dic₂₂₆	—	2	2	no	—
273	Dic₂₂₆	—	4	1	no	—
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	2	no	—
281	C₂×D₁₁₃	—	2	2	no	—
282	C₂×D₁₁₃	—	2	2	no	—
283	C₂×D₁₁₃	C₂×#41	1	2	yes	—
284	C₄×C₁₁₃	—	2	2	no	—
285	C₄×C₁₁₃	—	2	2	no	—
286	C₄×C₁₁₃	—	2	1	no	—
287	C₄×C₁₁₃	—	2	1	no	—
288	C₄×C₁₁₃	—	2	1	no	—
289	C₄×C₁₁₃	—	2	1	no	—
290	C₄×C₁₁₃	—	2	2	no	—
291	C₄×C₁₁₃	—	2	1	no	—
292	C₄×C₁₁₃	—	2	1	no	—
293	C₄×C₁₁₃	C₂×#41	1	2	yes	—
294	Dic₁₁₃	—	2	2	no	—
295	Dic₁₁₃	—	2	2	no	—
296	Dic₁₁₃	—	2	1	no	—
297	Dic₁₁₃	—	2	1	no	—
298	Dic₁₁₃	—	2	1	no	—
299	Dic₁₁₃	—	2	1	no	—
300	Dic₁₁₃	—	2	2	no	—
301	Dic₁₁₃	—	2	1	no	—
302	Dic₁₁₃	C₂×#41	1	2	yes	—
303	Dic₁₁₃	2₋¹⁺⁴	1	2	yes	—
304	C₂×C₁₁₃	—	4	2	no	—
305	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
306	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₂×C₁₁₃	#585	1	1	yes	characteristic
308	D₁₁₃	—	2	2	no	—
309	D₁₁₃	—	4	2	no	—
310	#3507	—	113	1	no	maximal, Sylow
311	C₁₁₃	#3507	1	1	yes	characteristic, complemented, Sylow
312	#559	—	113	1	no	—
313	#559	—	113	1	no	—
314	#557	—	113	1	no	—
315	#557	—	113	1	no	—
316	#556	—	113	2	no	—
317	#556	—	113	1	no	—
318	#556	—	113	1	no	—
319	#556	—	113	1	no	—
320	#556	D₁₁₃	1	1	yes	characteristic, complemented
321	#554	—	113	2	no	—
322	#552	—	113	2	no	—
323	#552	—	113	2	no	—
324	#539	—	113	2	no	—
325	#539	—	113	2	no	—
326	#536	—	113	1	no	—
327	#536	—	113	1	no	—
328	#533	—	113	1	no	—
329	#532	—	113	1	no	—
330	#529	—	113	2	no	—
331	#529	—	113	2	no	—
332	#520	—	113	1	no	—
333	#520	—	113	1	no	—
334	C₂×C₄×Q₈	—	113	1	no	—
335	C₂×#41	—	113	1	no	—
336	C₂×#41	—	113	1	no	—
337	C₂²×Q₈	—	113	1	no	—
338	C₄⋊Q₈	—	113	1	no	—
339	C₄⋊Q₈	—	113	1	no	—
340	C₄⋊Q₈	—	113	1	no	—
341	C₄⋊Q₈	—	113	1	no	—
342	C₄⋊Q₈	—	113	1	no	—
343	C₄⋊Q₈	—	113	1	no	—
344	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
345	#127	—	113	1	no	—
346	#126	—	113	2	no	—
347	#126	—	113	2	no	—
348	#126	—	113	2	no	—
349	#126	—	113	2	no	—
350	#126	—	113	2	no	—
351	#126	—	113	2	no	—
352	#126	C₂×D₁₁₃	1	2	yes	—
353	#126	C₂×D₁₁₃	1	2	yes	—
354	#125	—	113	2	no	—
355	#125	—	113	2	no	—
356	#125	—	113	1	no	—
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	#124	—	113	1	no	—
363	#124	—	113	1	no	—
364	#124	—	113	2	no	—
365	#124	—	113	2	no	—
366	#124	—	113	1	no	—
367	#124	—	113	1	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	2	no	—
372	#123	—	113	2	no	—
373	#123	—	113	2	no	—
374	#123	—	113	2	no	—
375	#123	—	113	2	no	—
376	#123	—	113	2	no	—
377	#123	—	113	2	no	—
378	C₂²⋊Q₈	—	113	1	no	—
379	C₂²⋊Q₈	—	113	2	no	—
380	C₂²⋊Q₈	—	113	1	no	—
381	C₂²⋊Q₈	—	113	1	no	—
382	C₂²⋊Q₈	—	113	1	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	—	113	2	no	—
389	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
390	#121	—	113	2	no	—
391	#121	—	113	2	no	—
392	C₄×Q₈	—	113	1	no	—
393	C₄×Q₈	—	113	1	no	—
394	C₄×Q₈	—	113	2	no	—
395	C₄×Q₈	—	113	1	no	—
396	C₄×Q₈	—	113	1	no	—
397	C₄×Q₈	—	113	2	no	—
398	C₄×Q₈	—	113	2	no	—
399	C₄×Q₈	—	113	1	no	—
400	C₄×Q₈	—	113	1	no	—
401	C₄×Q₈	—	113	2	no	—
402	C₄×Q₈	—	113	1	no	—
403	C₄×Q₈	—	113	1	no	—
404	C₄×Q₈	—	113	1	no	—
405	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
406	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
408	C₄×D₄	—	113	1	no	—
409	C₄×D₄	—	113	2	no	—
410	C₄×D₄	—	113	2	no	—
411	C₄×D₄	—	113	2	no	—
412	C₄×D₄	—	113	1	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	2	no	—
418	C₄×D₄	—	113	1	no	—
419	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
420	#117	—	113	2	no	—
421	#117	—	113	2	no	—
422	#117	—	113	2	no	—
423	#117	—	113	1	no	—
424	#117	—	113	1	no	—
425	#117	—	113	2	no	—
426	#117	—	113	2	no	—
427	#117	C₂×D₁₁₃	1	2	yes	—
428	C₂×C₄⋊C₄	—	113	2	no	—
429	C₂×C₄⋊C₄	—	113	1	no	—
430	C₂×C₄⋊C₄	—	113	2	no	—
431	C₂×C₄⋊C₄	—	113	2	no	—
432	C₂×C₄²	—	113	2	no	—
433	C₂×C₄²	—	113	1	no	—
434	#41	—	226	4	no	—
435	#41	—	226	4	no	—
436	C₂×Q₈	—	113	1	no	—
437	C₂×Q₈	—	113	1	no	—
438	C₂×Q₈	—	113	1	no	—
439	C₂×Q₈	—	113	2	no	—
440	C₂×Q₈	—	113	1	no	—
441	C₂×Q₈	—	113	1	no	—
442	C₂×Q₈	—	226	4	no	—
443	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
444	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
445	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
446	C₂×D₄	—	113	2	no	—
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	C₂²×D₁₁₃	1	1	yes	characteristic
452	C₂²×C₄	—	113	1	no	—
453	C₂²×C₄	—	113	2	no	—
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	2	no	—
462	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
463	C₄⋊C₄	—	113	2	no	—
464	C₄⋊C₄	—	113	1	no	—
465	C₄⋊C₄	—	113	1	no	—
466	C₄⋊C₄	—	113	1	no	—
467	C₄⋊C₄	—	113	2	no	—
468	C₄⋊C₄	—	113	2	no	—
469	C₄⋊C₄	—	113	2	no	—
470	C₄⋊C₄	—	113	2	no	—
471	C₄⋊C₄	—	113	2	no	—
472	C₄⋊C₄	—	113	2	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	2	no	—
478	C₄⋊C₄	—	113	2	no	—
479	C₄⋊C₄	—	113	2	no	—
480	C₄⋊C₄	—	113	1	no	—
481	C₄⋊C₄	—	113	1	no	—
482	C₄⋊C₄	—	113	2	no	—
483	C₄⋊C₄	—	113	2	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	2	no	—
489	C₄⋊C₄	—	113	2	no	—
490	C₄⋊C₄	—	113	2	no	—
491	C₄⋊C₄	—	113	1	no	—
492	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
494	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
495	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	113	2	no	—
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	1	no	—
506	C₂²⋊C₄	—	113	1	no	—
507	C₂²⋊C₄	—	113	1	no	—
508	C₂²⋊C₄	—	113	2	no	—
509	C₂²⋊C₄	—	113	2	no	—
510	C₂²⋊C₄	—	113	2	no	—
511	C₂²⋊C₄	—	113	2	no	—
512	C₂²⋊C₄	—	113	2	no	—
513	C₂²⋊C₄	—	113	2	no	—
514	C₂²⋊C₄	—	113	2	no	—
515	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
519	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
520	C₄²	—	113	2	no	—
521	C₄²	—	113	1	no	—
522	C₄²	—	113	1	no	—
523	C₄²	—	113	2	no	—
524	C₄²	—	113	2	no	—
525	C₄²	—	113	1	no	—
526	C₄²	—	113	2	no	—
527	C₄²	—	113	2	no	—
528	C₄²	—	113	2	no	—
529	C₄²	—	113	1	no	—
530	C₄²	—	113	1	no	—
531	C₄²	C₂²×D₁₁₃	1	2	yes	—
532	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
533	C₄²	C₂²×D₁₁₃	1	2	yes	—
534	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
535	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
536	C₂³	—	113	1	no	—
537	C₂³	—	113	2	no	—
538	C₂³	C₂³×D₁₁₃	1	2	yes	—
539	Q₈	—	2	2	no	—
540	Q₈	—	2	2	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	452	1	no	—
543	Q₈	—	226	4	no	—
544	Q₈	—	226	2	no	—
545	Q₈	—	226	2	no	—
546	Q₈	—	226	2	no	—
547	Q₈	—	226	2	no	—
548	D₄	—	2	2	no	—
549	D₄	—	452	2	no	—
550	D₄	—	226	4	no	—
551	D₄	—	226	4	no	—
552	D₄	—	226	4	no	—
553	D₄	—	226	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	113	1	no	—
556	C₂×C₄	—	113	1	no	—
557	C₂×C₄	—	113	4	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	2	no	—
563	C₂×C₄	—	113	1	no	—
564	C₂×C₄	—	113	1	no	—
565	C₂×C₄	—	113	1	no	—
566	C₂×C₄	—	452	2	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	2	no	—
573	C₂×C₄	—	226	4	no	—
574	C₂×C₄	—	226	4	no	—
575	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
576	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
577	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
578	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
579	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
581	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	113	2	no	—
589	C₂²	—	226	2	no	—
590	C₂²	—	226	2	no	—
591	C₂²	—	226	2	no	—
592	C₂²	—	226	1	no	—
593	C₂²	—	226	1	no	—
594	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	113	2	no	—
605	C₄	—	113	2	no	—
606	C₄	—	226	2	no	—
607	C₄	—	226	2	no	—
608	C₄	—	226	1	no	—
609	C₄	—	226	1	no	—
610	C₄	—	226	2	no	—
611	C₄	—	226	1	no	—
612	C₄	—	226	1	no	—
613	C₄	—	226	1	no	—
614	C₄	#41×D₁₁₃	1	2	yes	—
615	C₂	—	4	2	no	—
616	C₂	—	452	2	no	—
617	C₂	—	226	2	no	—
618	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
619	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic
620	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#556×C₁₁₃	C₂
prime radical	#20299147	C₂
hypercenter	#556	D₁₁₃
hypocenter	C₁₁₃	#3507
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. #20299331	C₂	semidirect
2. #20299330	C₂	semidirect
3. #20299326	C₂	semidirect
4. #20299323	C₂	semidirect
5. #20299321	C₂	semidirect
6. #20299320	C₂	semidirect
7. #20299317	C₂	semidirect
8. #20299315	C₂	semidirect
9. #20299302	C₂	semidirect
10. #20299284	C₂	semidirect
11. #20299281	C₂	semidirect
12. #20299194	C₂	semidirect
13. #20299189	C₂	semidirect
14. #20299173	C₂	semidirect
15. #20299168	C₂	semidirect
16. #20299152	C₂	semidirect
18. #20299131	C₂	semidirect
19. #20299126	C₂	semidirect
20. #20299080	C₂	semidirect
21. #20299077	C₂	semidirect
22. C₄×Q₈×D₁₁₃	C₂	semidirect
23. #556×C₁₁₃	C₂	semidirect
311. C₁₁₃	#3507	semidirect
320. #556	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299331	2
#20299330	2
#20299326	2
#20299323	2
#20299321	2
#20299320	2
#20299317	2
#20299315	2
#20299302	2
#20299284	2
#20299281	2
#20299194	2
#20299189	2
#20299173	2
#20299168	2
#20299152	2
#20299147	2
#20299131	2
#20299126	2
#20299080	2
#20299077	2
C₄×Q₈×D₁₁₃	2
#556×C₁₁₃	2
#3507	113