Subgroups — #28404488

Order 14464.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299301	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299301	C₂	1	2	yes	maximal, complemented
3	#20299299	C₂	1	2	yes	maximal, complemented
4	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299294	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299293	C₂	1	2	yes	maximal, complemented
7	#20299292	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299292	C₂	1	2	yes	maximal, complemented
9	#20299290	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299289	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299282	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299207	C₂	1	2	yes	maximal, complemented
13	#20299200	C₂	1	2	yes	maximal, complemented
14	#20299178	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299178	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299145	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299131	C₂	1	2	yes	maximal, complemented
18	#20299126	C₂	1	2	yes	maximal, complemented
19	#125×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299078	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14268648	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268648	C₂²	1	1	yes	characteristic
25	C₂×#14268647	C₂²	1	1	yes	characteristic
26	C₂×#14268647	C₂²	1	1	yes	characteristic
27	#16813621	C₂²	1	1	yes	characteristic
28	#16813618	C₂²	1	1	yes	characteristic
29	#16813617	C₂²	1	2	yes	—
30	#16813617	C₂²	1	2	yes	—
31	#16813617	C₂²	1	2	yes	—
32	#16813617	C₂²	1	2	yes	—
33	#16813616	C₂²	1	2	yes	—
34	#16813616	C₂²	1	2	yes	—
35	#16813615	C₂²	1	2	yes	—
36	#16813614	C₂²	1	1	yes	characteristic
37	#16813613	C₂²	1	1	yes	characteristic
38	#16813613	C₂²	1	2	yes	—
39	#16813613	C₂²	1	1	yes	characteristic
40	#16813612	C₂²	1	2	yes	—
41	#16813612	C₂²	1	2	yes	—
42	#16813612	C₂²	1	2	yes	—
43	#16813612	C₂²	1	2	yes	—
44	#16813608	C₂²	1	1	yes	characteristic
45	#16813608	C₂²	1	1	yes	characteristic
46	#16813607	C₂²	1	2	yes	—
47	#16813607	C₂²	1	2	yes	—
48	#16813607	C₂²	1	2	yes	—
49	#16813606	C₂²	1	2	yes	—
50	#16813604	C₂²	1	2	yes	—
51	#16813604	C₂²	1	2	yes	—
52	#16813604	C₂²	1	2	yes	—
53	#16813600	C₂²	1	2	yes	—
54	#16813600	C₂²	1	2	yes	—
55	#16813598	C₂²	1	1	yes	characteristic
56	#16813598	C₂²	1	1	yes	characteristic
57	#16813597	C₂²	1	1	yes	characteristic
58	#16813597	C₂²	1	2	yes	—
59	#16813597	C₂²	1	1	yes	characteristic
60	#16813597	C₂²	1	2	yes	—
61	#16813597	C₂²	1	1	yes	characteristic
62	#16813597	C₂²	1	2	yes	—
63	#16813596	C₂²	1	1	yes	characteristic
64	#16813596	C₂²	1	2	yes	—
65	#16813596	C₂²	1	1	yes	characteristic
66	#16813595	C₂²	1	1	yes	characteristic
67	#16813595	C₂²	1	2	yes	—
68	#16813595	C₂²	1	2	yes	—
69	#16813595	C₂²	1	2	yes	—
70	#16813595	C₂²	1	1	yes	characteristic
71	#16813595	C₂²	1	2	yes	—
72	#16813595	C₂²	1	2	yes	—
73	#16813594	C₂²	1	2	yes	—
74	#16813593	C₂²	1	1	yes	characteristic
75	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
76	C₄×Dic₂₂₆	C₂²	1	2	yes	—
77	#16813587	C₂²	1	2	yes	—
78	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
79	C₄×D₄₅₂	C₂²	1	2	yes	—
80	C₄×D₄₅₂	C₂²	1	2	yes	—
81	C₄×D₄₅₂	C₂²	1	2	yes	—
82	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
83	#16813584	C₂²	1	1	yes	characteristic
84	#16813584	C₂²	1	2	yes	—
85	#16813584	C₂²	1	2	yes	—
86	#16813584	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
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	#16813581	C₂²	1	1	yes	characteristic
96	#16813580	C₂²	1	2	yes	—
97	#16813580	C₂²	1	1	yes	characteristic
98	#16813580	C₂²	1	1	yes	characteristic
99	#16813580	C₂²	1	1	yes	characteristic
100	#16813580	C₂²	1	2	yes	—
101	#16813579	C₂²	1	2	yes	—
102	#16813578	C₂²	1	2	yes	—
103	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
104	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
105	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₁₁₃	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	1	yes	characteristic
110	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
111	C₄²×D₁₁₃	C₂²	1	2	yes	—
112	#126×C₁₁₃	C₂²	1	2	yes	—
113	#125×C₁₁₃	C₂²	1	1	yes	characteristic
114	#125×C₁₁₃	C₂²	1	2	yes	—
115	#123×C₁₁₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
120	#117×C₁₁₃	C₂²	1	1	yes	characteristic
121	#117×C₁₁₃	C₂²	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
123	#14268648	—	2	4	no	—
124	#14268647	—	2	4	no	—
125	#14268647	—	2	4	no	—
126	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
128	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
129	C₂×D₄₅₂	C₂³	1	2	yes	—
130	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×D₄₅₂	C₂³	1	2	yes	—
134	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
144	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
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	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
152	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
160	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
161	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
162	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
163	C₄⋊Dic₁₁₃	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	#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	#14268626	C₂³	1	1	yes	characteristic
175	#14268626	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	1	yes	characteristic
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	2	yes	—
186	#14268624	C₂³	1	2	yes	—
187	#14268624	C₂³	1	2	yes	—
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	1	yes	characteristic
190	#14268624	C₂³	1	2	yes	—
191	#14268624	C₂³	1	1	yes	characteristic
192	#14268624	C₂³	1	2	yes	—
193	#14268624	C₂³	1	2	yes	—
194	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
195	C₄×Dic₁₁₃	C₂³	1	2	yes	—
196	C₄×Dic₁₁₃	C₂³	1	2	yes	—
197	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
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×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×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	1	yes	characteristic
209	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
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	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×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	2	yes	—
225	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
226	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
228	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
231	Q₈×C₁₁₃	—	2	2	no	—
232	D₄×C₁₁₃	—	4	1	no	—
233	C₂×C₄×C₁₁₃	—	2	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	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	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	2	yes	—
244	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₁₁₃	—	2	2	no	—
246	C₂²⋊D₁₁₃	—	2	2	no	—
247	C₂²⋊D₁₁₃	—	2	2	no	—
248	C₂²⋊D₁₁₃	—	2	2	no	—
249	C₂²⋊D₁₁₃	—	4	2	no	—
250	C₂²⋊D₁₁₃	—	4	2	no	—
251	C₂²⋊D₁₁₃	—	4	1	no	—
252	C₂²⋊D₁₁₃	—	4	1	no	—
253	C₂×Dic₁₁₃	—	4	2	no	—
254	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
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	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
260	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
262	D₄₅₂	—	2	2	no	—
263	D₄₅₂	—	2	2	no	—
264	D₄₅₂	—	2	4	no	—
265	D₄₅₂	—	2	2	no	—
266	D₄₅₂	—	4	2	no	—
267	D₄₅₂	—	4	2	no	—
268	D₄₅₂	—	4	1	no	—
269	C₄×D₁₁₃	—	2	2	no	—
270	C₄×D₁₁₃	—	2	2	no	—
271	C₄×D₁₁₃	—	2	4	no	—
272	C₄×D₁₁₃	—	4	2	no	—
273	C₄×D₁₁₃	—	4	1	no	—
274	C₄×D₁₁₃	—	4	2	no	—
275	C₄×D₁₁₃	—	4	2	no	—
276	C₄×D₁₁₃	—	4	2	no	—
277	C₄×D₁₁₃	—	4	2	no	—
278	C₄×D₁₁₃	—	4	2	no	—
279	C₄×D₁₁₃	—	4	1	no	—
280	C₄×D₁₁₃	#41	1	4	yes	—
281	Dic₂₂₆	—	2	2	no	—
282	Dic₂₂₆	—	2	2	no	—
283	C₂²×C₁₁₃	—	2	1	no	—
284	C₂²×C₁₁₃	—	2	1	no	—
285	C₂²×C₁₁₃	—	2	1	no	—
286	C₂²×C₁₁₃	—	2	1	no	—
287	C₂²×C₁₁₃	—	2	1	no	—
288	C₂²×C₁₁₃	—	2	1	no	—
289	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
290	C₂×D₁₁₃	—	2	1	no	—
291	C₂×D₁₁₃	—	2	1	no	—
292	C₂×D₁₁₃	—	2	2	no	—
293	C₂×D₁₁₃	—	2	1	no	—
294	C₂×D₁₁₃	—	2	1	no	—
295	C₂×D₁₁₃	—	2	1	no	—
296	C₂×D₁₁₃	—	2	1	no	—
297	C₂×D₁₁₃	—	2	2	no	—
298	C₂×D₁₁₃	—	2	2	no	—
299	C₂×D₁₁₃	—	2	1	no	—
300	C₂×D₁₁₃	—	2	1	no	—
301	C₂×D₁₁₃	C₂×#41	1	2	yes	—
302	C₄×C₁₁₃	—	2	1	no	—
303	C₄×C₁₁₃	—	2	1	no	—
304	C₄×C₁₁₃	—	2	2	no	—
305	C₄×C₁₁₃	—	2	1	no	—
306	C₄×C₁₁₃	—	2	2	no	—
307	C₄×C₁₁₃	—	2	2	no	—
308	C₄×C₁₁₃	—	2	2	no	—
309	C₄×C₁₁₃	—	2	1	no	—
310	C₄×C₁₁₃	C₂×#41	1	2	yes	—
311	Dic₁₁₃	—	2	1	no	—
312	Dic₁₁₃	—	2	1	no	—
313	Dic₁₁₃	—	2	1	no	—
314	Dic₁₁₃	—	2	2	no	—
315	Dic₁₁₃	—	2	2	no	—
316	Dic₁₁₃	—	2	2	no	—
317	Dic₁₁₃	—	2	1	no	—
318	Dic₁₁₃	C₂×#41	1	2	yes	—
319	C₂×C₁₁₃	—	4	1	no	—
320	C₂×C₁₁₃	—	4	1	no	—
321	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
322	C₂×C₁₁₃	#585	1	1	yes	characteristic
323	C₂×C₁₁₃	#585	1	1	yes	characteristic
324	D₁₁₃	—	2	2	no	—
325	D₁₁₃	—	4	2	no	—
326	D₁₁₃	—	4	1	no	—
327	D₁₁₃	—	4	1	no	—
328	#3512	—	113	1	no	maximal, Sylow
329	C₁₁₃	#3512	1	1	yes	characteristic, complemented, Sylow
330	#553	—	113	2	no	—
331	#553	—	113	1	no	—
332	#553	—	113	2	no	—
333	#553	—	113	2	no	—
334	#553	—	113	1	no	—
335	#553	—	113	1	no	—
336	#553	—	113	2	no	—
337	#553	—	113	1	no	—
338	#552	—	113	1	no	—
339	#552	—	113	1	no	—
340	#552	—	113	1	no	—
341	#552	D₁₁₃	1	1	yes	characteristic, complemented
342	#541	—	113	2	no	—
343	#540	—	113	2	no	—
344	#537	—	113	1	no	—
345	#537	—	113	1	no	—
346	#532	—	113	1	no	—
347	#529	—	113	2	no	—
348	#529	—	113	2	no	—
349	C₂×#125	—	113	1	no	—
350	#520	—	113	1	no	—
351	#520	—	113	1	no	—
352	C₄×#41	—	113	1	no	—
353	C₂×#41	—	113	1	no	—
354	C₂×#41	—	113	1	no	—
355	C₂×#41	—	113	1	no	—
356	C₄⋊Q₈	—	113	1	no	—
357	#127	—	113	1	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	—	113	2	no	—
364	#126	—	113	2	no	—
365	#126	C₂×D₁₁₃	1	2	yes	—
366	#125	—	113	2	no	—
367	#125	—	113	2	no	—
368	#125	—	113	1	no	—
369	#125	—	113	1	no	—
370	#125	—	113	2	no	—
371	#125	—	113	2	no	—
372	#125	—	113	2	no	—
373	#125	—	113	1	no	—
374	#125	C₂×D₁₁₃	1	1	yes	characteristic
375	#125	C₂×D₁₁₃	1	2	yes	—
376	#124	—	113	1	no	—
377	#124	—	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	—	113	2	no	—
384	#123	—	113	2	no	—
385	#123	C₂×D₁₁₃	1	2	yes	—
386	C₂²⋊Q₈	—	113	1	no	—
387	C₂²⋊Q₈	—	113	1	no	—
388	C₂²⋊Q₈	—	113	2	no	—
389	C₂²⋊Q₈	—	113	2	no	—
390	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
392	#121	—	113	1	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	1	no	—
401	#121	—	113	1	no	—
402	#121	—	113	2	no	—
403	#121	—	113	2	no	—
404	#121	—	113	2	no	—
405	#121	—	113	1	no	—
406	#121	—	113	1	no	—
407	#121	—	113	2	no	—
408	#121	—	113	2	no	—
409	#121	—	113	2	no	—
410	C₄×Q₈	—	113	1	no	—
411	C₄×Q₈	—	113	2	no	—
412	C₄×Q₈	—	113	2	no	—
413	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
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	2	no	—
420	C₄×D₄	—	113	1	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	2	no	—
426	C₄×D₄	—	113	2	no	—
427	C₄×D₄	—	113	1	no	—
428	C₄×D₄	—	113	2	no	—
429	C₄×D₄	—	113	2	no	—
430	C₄×D₄	—	113	1	no	—
431	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
432	#117	—	113	1	no	—
433	#117	—	113	1	no	—
434	#117	—	113	2	no	—
435	#117	—	113	1	no	—
436	#117	—	113	1	no	—
437	#117	—	113	2	no	—
438	#117	—	113	2	no	—
439	#117	—	113	2	no	—
440	#117	C₂×D₁₁₃	1	1	yes	characteristic
441	#117	C₂×D₁₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	—	113	1	no	—
443	C₂×C₄⋊C₄	—	113	1	no	—
444	C₂×C₄⋊C₄	—	113	1	no	—
445	C₂×C₄⋊C₄	—	113	1	no	—
446	C₂×C₄⋊C₄	—	113	1	no	—
447	C₂×C₄⋊C₄	—	113	2	no	—
448	C₂×C₄⋊C₄	—	113	2	no	—
449	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
450	C₂×C₄²	—	113	1	no	—
451	C₂×C₄²	—	113	2	no	—
452	#41	—	226	4	no	—
453	#41	—	226	4	no	—
454	#41	—	226	4	no	—
455	C₂×Q₈	—	113	1	no	—
456	C₂×Q₈	—	113	1	no	—
457	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
458	C₂×D₄	—	113	2	no	—
459	C₂×D₄	—	113	2	no	—
460	C₂×D₄	—	113	1	no	—
461	C₂×D₄	—	113	1	no	—
462	C₂×D₄	—	113	1	no	—
463	C₂×D₄	—	113	1	no	—
464	C₂×D₄	—	113	1	no	—
465	C₂×D₄	—	113	1	no	—
466	C₂×D₄	—	113	2	no	—
467	C₂×D₄	—	113	2	no	—
468	C₂×D₄	—	113	1	no	—
469	C₂×D₄	—	113	1	no	—
470	C₂×D₄	—	113	2	no	—
471	C₂×D₄	—	113	1	no	—
472	C₂×D₄	—	113	1	no	—
473	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
474	C₂²×C₄	—	113	1	no	—
475	C₂²×C₄	—	113	2	no	—
476	C₂²×C₄	—	113	1	no	—
477	C₂²×C₄	—	113	1	no	—
478	C₂²×C₄	—	113	2	no	—
479	C₂²×C₄	—	113	2	no	—
480	C₂²×C₄	—	113	2	no	—
481	C₂²×C₄	—	113	2	no	—
482	C₂²×C₄	—	113	2	no	—
483	C₂²×C₄	—	113	2	no	—
484	C₂²×C₄	—	113	2	no	—
485	C₂²×C₄	—	113	1	no	—
486	C₂²×C₄	—	113	1	no	—
487	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
490	C₄⋊C₄	—	113	1	no	—
491	C₄⋊C₄	—	113	1	no	—
492	C₄⋊C₄	—	113	1	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	—	113	2	no	—
501	C₄⋊C₄	—	113	2	no	—
502	C₄⋊C₄	—	113	2	no	—
503	C₄⋊C₄	—	113	2	no	—
504	C₄⋊C₄	—	113	2	no	—
505	C₄⋊C₄	—	113	2	no	—
506	C₄⋊C₄	—	113	2	no	—
507	C₄⋊C₄	—	113	1	no	—
508	C₄⋊C₄	—	113	1	no	—
509	C₄⋊C₄	—	113	1	no	—
510	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
517	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
518	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
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	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	—	113	2	no	—
530	C₂²⋊C₄	—	113	2	no	—
531	C₂²⋊C₄	—	113	2	no	—
532	C₂²⋊C₄	—	113	1	no	—
533	C₂²⋊C₄	—	113	1	no	—
534	C₂²⋊C₄	—	113	2	no	—
535	C₂²⋊C₄	—	113	2	no	—
536	C₂²⋊C₄	—	113	2	no	—
537	C₂²⋊C₄	—	113	2	no	—
538	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
540	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
543	C₄²	—	113	1	no	—
544	C₄²	—	113	2	no	—
545	C₄²	—	113	2	no	—
546	C₄²	—	113	1	no	—
547	C₄²	—	113	1	no	—
548	C₄²	—	113	2	no	—
549	C₄²	—	113	2	no	—
550	C₄²	—	113	2	no	—
551	C₄²	C₂²×D₁₁₃	1	2	yes	—
552	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
553	C₄²	C₂²×D₁₁₃	1	2	yes	—
554	C₂³	—	113	1	no	—
555	C₂³	—	113	1	no	—
556	C₂³	—	113	2	no	—
557	C₂³	—	113	1	no	—
558	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
559	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
560	Q₈	—	2	2	no	—
561	Q₈	—	226	2	no	—
562	Q₈	—	226	2	no	—
563	D₄	—	4	1	no	—
564	D₄	—	452	2	no	—
565	D₄	—	452	1	no	—
566	D₄	—	452	2	no	—
567	D₄	—	452	2	no	—
568	D₄	—	452	2	no	—
569	D₄	—	452	1	no	—
570	D₄	—	452	1	no	—
571	D₄	—	226	2	no	—
572	D₄	—	226	2	no	—
573	D₄	—	226	4	no	—
574	D₄	—	226	2	no	—
575	D₄	—	226	2	no	—
576	D₄	—	226	2	no	—
577	D₄	—	226	2	no	—
578	D₄	—	226	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	113	1	no	—
583	C₂×C₄	—	113	4	no	—
584	C₂×C₄	—	113	1	no	—
585	C₂×C₄	—	113	2	no	—
586	C₂×C₄	—	113	1	no	—
587	C₂×C₄	—	113	1	no	—
588	C₂×C₄	—	113	1	no	—
589	C₂×C₄	—	113	2	no	—
590	C₂×C₄	—	113	2	no	—
591	C₂×C₄	—	452	2	no	—
592	C₂×C₄	—	452	2	no	—
593	C₂×C₄	—	452	2	no	—
594	C₂×C₄	—	452	1	no	—
595	C₂×C₄	—	452	2	no	—
596	C₂×C₄	—	452	1	no	—
597	C₂×C₄	—	452	2	no	—
598	C₂×C₄	—	452	2	no	—
599	C₂×C₄	—	452	2	no	—
600	C₂×C₄	—	226	4	no	—
601	C₂×C₄	—	226	2	no	—
602	C₂×C₄	—	226	2	no	—
603	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
604	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
607	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
609	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
611	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	113	2	no	—
619	C₂²	—	226	2	no	—
620	C₂²	—	226	1	no	—
621	C₂²	—	226	1	no	—
622	C₂²	—	226	1	no	—
623	C₂²	—	226	2	no	—
624	C₂²	—	226	1	no	—
625	C₂²	—	226	1	no	—
626	C₂²	—	226	2	no	—
627	C₂²	—	226	1	no	—
628	C₂²	—	226	1	no	—
629	C₂²	—	226	1	no	—
630	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	113	2	no	—
640	C₄	—	226	1	no	—
641	C₄	—	226	1	no	—
642	C₄	—	226	1	no	—
643	C₄	—	226	2	no	—
644	C₄	—	226	2	no	—
645	C₄	—	226	2	no	—
646	C₄	—	226	1	no	—
647	C₄	#41×D₁₁₃	1	2	yes	—
648	C₂	—	4	1	no	—
649	C₂	—	4	1	no	—
650	C₂	—	452	1	no	—
651	C₂	—	452	2	no	—
652	C₂	—	452	1	no	—
653	C₂	—	226	2	no	—
654	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
655	C₂	#20299434	1	1	yes	characteristic
656	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#552×C₁₁₃	C₂
hypercenter	#552	D₁₁₃
hypocenter	C₁₁₃	#3512
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #20299301	C₂	semidirect
2. #20299301	C₂	semidirect
3. #20299299	C₂	semidirect
4. #20299296	C₂	semidirect
5. #20299294	C₂	semidirect
6. #20299293	C₂	semidirect
7. #20299292	C₂	semidirect
8. #20299292	C₂	semidirect
9. #20299290	C₂	semidirect
10. #20299289	C₂	semidirect
11. #20299282	C₂	semidirect
12. #20299207	C₂	semidirect
13. #20299200	C₂	semidirect
14. #20299178	C₂	semidirect
15. #20299178	C₂	semidirect
16. #20299145	C₂	semidirect
17. #20299131	C₂	semidirect
18. #20299126	C₂	semidirect
19. #125×D₁₁₃	C₂	semidirect
20. #20299079	C₂	semidirect
21. #20299078	C₂	semidirect
22. C₄×#14268648	C₂	semidirect
23. #552×C₁₁₃	C₂	semidirect
329. C₁₁₃	#3512	semidirect
341. #552	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299301	2
#20299299	2
#20299296	2
#20299294	2
#20299293	2
#20299292	2
#20299290	2
#20299289	2
#20299282	2
#20299207	2
#20299200	2
#20299178	2
#20299145	2
#20299131	2
#20299126	2
#125×D₁₁₃	2
#20299079	2
#20299078	2
C₄×#14268648	2
#552×C₁₁₃	2
#3512	113