Subgroups — #28404187

Order 14464.

1094 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299325	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299317	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299315	C₂	1	2	yes	maximal, complemented
4	#20299290	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299286	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299285	C₂	1	2	yes	maximal, complemented
7	#20299284	C₂	1	2	yes	maximal, complemented
8	#20299261	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299256	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299254	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299248	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299246	C₂	1	2	yes	maximal, complemented
13	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299151	C₂	1	2	yes	maximal, complemented
15	#20299130	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299128	C₂	1	2	yes	maximal, complemented
17	#20299126	C₂	1	2	yes	maximal, complemented
18	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14268646	C₂	1	2	yes	maximal, complemented
20	C₄×#14268646	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₁₃	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×#14268646	C₂²	1	2	yes	—
26	C₂×#14268646	C₂²	1	1	yes	characteristic
27	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
29	#16813621	C₂²	1	2	yes	—
30	#16813621	C₂²	1	2	yes	—
31	#16813621	C₂²	1	1	yes	characteristic
32	#16813620	C₂²	1	1	yes	characteristic
33	#16813617	C₂²	1	2	yes	—
34	#16813617	C₂²	1	2	yes	—
35	#16813615	C₂²	1	2	yes	—
36	#16813615	C₂²	1	2	yes	—
37	#16813615	C₂²	1	2	yes	—
38	#16813613	C₂²	1	2	yes	—
39	#16813613	C₂²	1	2	yes	—
40	#16813613	C₂²	1	1	yes	characteristic
41	#16813612	C₂²	1	2	yes	—
42	#16813612	C₂²	1	2	yes	—
43	#16813612	C₂²	1	2	yes	—
44	#16813609	C₂²	1	1	yes	characteristic
45	#16813608	C₂²	1	2	yes	—
46	#16813608	C₂²	1	2	yes	—
47	#16813607	C₂²	1	2	yes	—
48	#16813606	C₂²	1	2	yes	—
49	#16813604	C₂²	1	2	yes	—
50	#16813604	C₂²	1	2	yes	—
51	#16813603	C₂²	1	2	yes	—
52	#16813602	C₂²	1	1	yes	characteristic
53	#16813602	C₂²	1	1	yes	characteristic
54	#16813600	C₂²	1	2	yes	—
55	#16813600	C₂²	1	2	yes	—
56	#16813599	C₂²	1	2	yes	—
57	#16813599	C₂²	1	2	yes	—
58	#16813599	C₂²	1	2	yes	—
59	#16813599	C₂²	1	2	yes	—
60	#16813599	C₂²	1	2	yes	—
61	#16813598	C₂²	1	1	yes	characteristic
62	#16813595	C₂²	1	2	yes	—
63	#16813594	C₂²	1	2	yes	—
64	#16813593	C₂²	1	1	yes	characteristic
65	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
66	C₄×Dic₂₂₆	C₂²	1	2	yes	—
67	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
68	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
69	C₄×Dic₂₂₆	C₂²	1	2	yes	—
70	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
71	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
72	C₄×Dic₂₂₆	C₂²	1	2	yes	—
73	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
74	C₄×Dic₂₂₆	C₂²	1	2	yes	—
75	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
76	#16813587	C₂²	1	2	yes	—
77	#16813587	C₂²	1	2	yes	—
78	#16813587	C₂²	1	1	yes	characteristic
79	#16813587	C₂²	1	1	yes	characteristic
80	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
81	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
82	D₄×Dic₁₁₃	C₂²	1	2	yes	—
83	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
84	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
90	#16813582	C₂²	1	2	yes	—
91	#16813582	C₂²	1	2	yes	—
92	#16813582	C₂²	1	2	yes	—
93	#16813581	C₂²	1	1	yes	characteristic
94	#16813581	C₂²	1	2	yes	—
95	#16813580	C₂²	1	2	yes	—
96	#16813580	C₂²	1	1	yes	characteristic
97	#16813579	C₂²	1	1	yes	characteristic
98	#16813579	C₂²	1	1	yes	characteristic
99	#16813579	C₂²	1	2	yes	—
100	#16813578	C₂²	1	2	yes	—
101	#16813578	C₂²	1	2	yes	—
102	#16813578	C₂²	1	2	yes	—
103	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
104	C₂×#14268626	C₂²	1	2	yes	—
105	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
107	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
108	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
109	C₄²×D₁₁₃	C₂²	1	2	yes	—
110	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
112	#126×C₁₁₃	C₂²	1	2	yes	—
113	#125×C₁₁₃	C₂²	1	1	yes	characteristic
114	#124×C₁₁₃	C₂²	1	1	yes	characteristic
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
119	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
120	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
121	#117×C₁₁₃	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
123	#14268647	—	2	4	no	—
124	#14268646	—	2	8	no	—
125	#14268646	—	2	4	no	—
126	C₂×Dic₂₂₆	—	2	4	no	—
127	C₂×Dic₂₂₆	C₂³	1	2	yes	—
128	C₂×Dic₂₂₆	C₂³	1	2	yes	—
129	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₂₆	C₂³	1	2	yes	—
131	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
132	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
133	Q₈×D₁₁₃	—	2	4	no	—
134	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
139	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
140	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
141	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₁₃	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	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₁₃	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	1	yes	characteristic
154	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
155	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
156	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
159	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
160	#14268626	C₂³	1	2	yes	—
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	2	yes	—
163	#14268626	C₂³	1	2	yes	—
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	2	yes	—
166	#14268626	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
172	#14268626	C₂³	1	1	yes	characteristic
173	#14268626	C₂³	1	1	yes	characteristic
174	#14268626	C₂³	1	2	yes	—
175	#14268626	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁₃	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	2	yes	—
187	#14268624	C₂³	1	2	yes	—
188	#14268624	C₂³	1	2	yes	—
189	#14268624	C₂³	1	2	yes	—
190	C₄×Dic₁₁₃	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	2	yes	—
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	1	yes	characteristic
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	C₄×Dic₁₁₃	C₂³	1	2	yes	—
203	C₄×Dic₁₁₃	C₂³	1	2	yes	—
204	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
207	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₄⋊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	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
222	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₄²×C₁₁₃	C₂³	1	2	yes	—
224	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
225	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
226	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
227	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
228	C₂³×C₁₁₃	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	—	2	4	no	—
233	D₄×C₁₁₃	—	2	2	no	—
234	C₂×C₄×C₁₁₃	—	2	2	no	—
235	C₂×C₄×C₁₁₃	—	2	2	no	—
236	C₂×C₄×C₁₁₃	—	2	2	no	—
237	C₂×C₄×C₁₁₃	—	2	4	no	—
238	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
243	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₁₁₃	—	2	2	no	—
248	C₂²⋊D₁₁₃	—	2	4	no	—
249	C₂²⋊D₁₁₃	—	2	4	no	—
250	C₂²⋊D₁₁₃	#41	1	4	yes	complemented
251	C₂×Dic₁₁₃	—	2	4	no	—
252	C₂×Dic₁₁₃	—	2	4	no	—
253	C₂×Dic₁₁₃	—	2	4	no	—
254	C₂×Dic₁₁₃	—	2	4	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	2	yes	—
262	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
265	D₄₅₂	—	2	2	no	—
266	C₄×D₁₁₃	—	2	4	no	—
267	C₄×D₁₁₃	—	2	2	no	—
268	C₄×D₁₁₃	—	2	2	no	—
269	C₄×D₁₁₃	—	2	2	no	—
270	C₄×D₁₁₃	—	2	2	no	—
271	C₄×D₁₁₃	—	2	2	no	—
272	C₄×D₁₁₃	—	2	4	no	—
273	C₄×D₁₁₃	—	2	2	no	—
274	Dic₂₂₆	—	2	2	no	—
275	Dic₂₂₆	—	2	4	no	—
276	Dic₂₂₆	—	2	4	no	—
277	Dic₂₂₆	—	2	4	no	—
278	Dic₂₂₆	—	2	2	no	—
279	Dic₂₂₆	#41	1	4	yes	complemented
280	C₂²×C₁₁₃	—	2	1	no	—
281	C₂²×C₁₁₃	—	2	1	no	—
282	C₂²×C₁₁₃	—	2	2	no	—
283	C₂²×C₁₁₃	—	2	2	no	—
284	C₂²×C₁₁₃	—	2	2	no	—
285	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
286	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
287	C₂×D₁₁₃	—	2	1	no	—
288	C₂×D₁₁₃	—	2	1	no	—
289	C₂×D₁₁₃	—	2	1	no	—
290	C₂×D₁₁₃	—	2	1	no	—
291	C₂×D₁₁₃	—	2	1	no	—
292	C₂×D₁₁₃	C₂×#41	1	2	yes	—
293	C₄×C₁₁₃	—	2	1	no	—
294	C₄×C₁₁₃	—	2	2	no	—
295	C₄×C₁₁₃	—	2	2	no	—
296	C₄×C₁₁₃	—	2	1	no	—
297	C₄×C₁₁₃	—	2	1	no	—
298	C₄×C₁₁₃	—	2	1	no	—
299	C₄×C₁₁₃	—	2	2	no	—
300	C₄×C₁₁₃	C₂×#41	1	2	yes	—
301	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
302	Dic₁₁₃	—	2	1	no	—
303	Dic₁₁₃	—	2	2	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	—	2	2	no	—
306	Dic₁₁₃	—	2	2	no	—
307	Dic₁₁₃	—	2	1	no	—
308	Dic₁₁₃	—	2	1	no	—
309	Dic₁₁₃	—	2	1	no	—
310	Dic₁₁₃	C₂×#41	1	2	yes	—
311	Dic₁₁₃	C₂×#41	1	4	yes	—
312	C₂×C₁₁₃	—	2	2	no	—
313	C₂×C₁₁₃	—	4	2	no	—
314	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
315	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
316	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	D₁₁₃	—	2	2	no	—
318	D₁₁₃	—	4	1	no	—
319	#3482	—	113	1	no	maximal, Sylow
320	C₁₁₃	#3482	1	1	yes	characteristic, complemented, Sylow
321	#557	—	113	1	no	—
322	#556	—	113	2	no	—
323	#556	—	113	1	no	—
324	#552	—	113	2	no	—
325	#552	—	113	1	no	—
326	#552	—	113	2	no	—
327	#552	—	113	1	no	—
328	D₄×Q₈	—	113	1	no	—
329	#548	—	113	1	no	—
330	#548	—	113	1	no	—
331	#547	—	113	2	no	—
332	#547	—	113	1	no	—
333	#533	—	113	1	no	—
334	#533	—	113	2	no	—
335	#529	—	113	2	no	—
336	#529	—	113	1	no	—
337	#529	—	113	2	no	—
338	#529	D₁₁₃	1	1	yes	characteristic, complemented
339	C₄×#41	—	113	2	no	—
340	C₄×#41	—	113	1	no	—
341	C₄×#41	—	113	1	no	—
342	C₂×C₄×Q₈	—	113	1	no	—
343	C₂×C₄×Q₈	—	113	1	no	—
344	C₂×#41	—	113	2	no	—
345	C₂×#41	—	113	1	no	—
346	C₂×#41	—	113	1	no	—
347	C₂²×Q₈	—	113	1	no	—
348	C₂²×Q₈	—	113	1	no	—
349	C₄⋊Q₈	—	113	1	no	—
350	C₄⋊Q₈	—	113	2	no	—
351	C₄⋊Q₈	—	113	1	no	—
352	C₄⋊Q₈	—	113	2	no	—
353	#126	—	113	2	no	—
354	#126	—	113	2	no	—
355	#126	—	113	2	no	—
356	#126	—	113	2	no	—
357	#126	—	113	2	no	—
358	#126	C₂×D₁₁₃	1	2	yes	—
359	#125	—	113	2	no	—
360	#125	—	113	2	no	—
361	#125	—	113	1	no	—
362	#125	—	113	2	no	—
363	#125	—	113	2	no	—
364	#125	—	113	2	no	—
365	#125	C₂×D₁₁₃	1	1	yes	characteristic
366	#124	—	113	1	no	—
367	#124	—	113	2	no	—
368	#124	—	113	2	no	—
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	C₂×D₁₁₃	1	2	yes	—
376	C₂²⋊Q₈	—	113	1	no	—
377	C₂²⋊Q₈	—	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	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	C₂×D₁₁₃	1	1	yes	characteristic
387	#121	—	113	1	no	—
388	#121	—	113	2	no	—
389	#121	—	113	2	no	—
390	#121	C₂×D₁₁₃	1	1	yes	characteristic
391	C₄×Q₈	—	113	1	no	—
392	C₄×Q₈	—	113	1	no	—
393	C₄×Q₈	—	113	2	no	—
394	C₄×Q₈	—	113	1	no	—
395	C₄×Q₈	—	113	2	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	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×D₄	—	113	1	no	—
408	C₄×D₄	—	113	2	no	—
409	C₄×D₄	—	113	1	no	—
410	C₄×D₄	—	113	2	no	—
411	C₄×D₄	—	113	1	no	—
412	C₄×D₄	—	113	2	no	—
413	C₄×D₄	—	113	1	no	—
414	C₄×D₄	—	113	1	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	—	113	1	no	—
420	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
421	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
422	#117	—	113	1	no	—
423	#117	—	113	2	no	—
424	#117	—	113	1	no	—
425	#117	—	113	2	no	—
426	#117	—	113	2	no	—
427	#117	—	113	2	no	—
428	#117	—	113	2	no	—
429	#117	—	113	1	no	—
430	#117	—	113	1	no	—
431	#117	—	113	2	no	—
432	#117	C₂×D₁₁₃	1	2	yes	—
433	C₂×C₄⋊C₄	—	113	2	no	—
434	C₂×C₄⋊C₄	—	113	1	no	—
435	C₂×C₄⋊C₄	—	113	2	no	—
436	C₂×C₄⋊C₄	—	113	1	no	—
437	C₂×C₄²	—	113	2	no	—
438	C₂×C₄²	—	113	2	no	—
439	C₂×C₄²	—	113	2	no	—
440	C₂×C₄²	—	113	1	no	—
441	C₂×C₄²	—	113	1	no	—
442	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
443	#41	—	226	4	no	—
444	#41	—	226	8	no	—
445	#41	—	226	4	no	—
446	C₂×Q₈	—	113	1	no	—
447	C₂×Q₈	—	113	2	no	—
448	C₂×Q₈	—	113	2	no	—
449	C₂×Q₈	—	113	1	no	—
450	C₂×Q₈	—	113	2	no	—
451	C₂×Q₈	—	113	1	no	—
452	C₂×Q₈	—	226	4	no	—
453	C₂×Q₈	—	226	4	no	—
454	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
455	C₂×D₄	—	113	1	no	—
456	C₂×D₄	—	113	2	no	—
457	C₂×D₄	—	113	1	no	—
458	C₂×D₄	—	113	2	no	—
459	C₂×D₄	—	113	1	no	—
460	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
461	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
462	C₂²×C₄	—	113	2	no	—
463	C₂²×C₄	—	113	2	no	—
464	C₂²×C₄	—	113	2	no	—
465	C₂²×C₄	—	113	2	no	—
466	C₂²×C₄	—	113	2	no	—
467	C₂²×C₄	—	113	1	no	—
468	C₂²×C₄	—	113	2	no	—
469	C₂²×C₄	—	113	1	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	C₂²×D₁₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
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	1	no	—
483	C₄⋊C₄	—	113	2	no	—
484	C₄⋊C₄	—	113	2	no	—
485	C₄⋊C₄	—	113	2	no	—
486	C₄⋊C₄	—	113	2	no	—
487	C₄⋊C₄	—	113	2	no	—
488	C₄⋊C₄	—	113	1	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	—	113	1	no	—
494	C₄⋊C₄	—	113	2	no	—
495	C₄⋊C₄	—	113	1	no	—
496	C₄⋊C₄	—	113	2	no	—
497	C₄⋊C₄	—	113	1	no	—
498	C₄⋊C₄	—	113	1	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	C₂²×D₁₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	2	no	—
514	C₂²⋊C₄	—	113	2	no	—
515	C₂²⋊C₄	—	113	1	no	—
516	C₂²⋊C₄	—	113	1	no	—
517	C₂²⋊C₄	—	113	2	no	—
518	C₂²⋊C₄	—	113	2	no	—
519	C₂²⋊C₄	—	113	1	no	—
520	C₂²⋊C₄	—	113	1	no	—
521	C₂²⋊C₄	—	113	2	no	—
522	C₂²⋊C₄	—	113	2	no	—
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	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
528	C₄²	—	113	2	no	—
529	C₄²	—	113	1	no	—
530	C₄²	—	113	2	no	—
531	C₄²	—	113	1	no	—
532	C₄²	—	113	2	no	—
533	C₄²	—	113	2	no	—
534	C₄²	—	113	1	no	—
535	C₄²	—	113	2	no	—
536	C₄²	—	113	2	no	—
537	C₄²	—	113	1	no	—
538	C₄²	—	113	2	no	—
539	C₄²	—	113	1	no	—
540	C₄²	—	113	2	no	—
541	C₄²	—	113	1	no	—
542	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
543	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
544	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
545	C₄²	C₂²×D₁₁₃	1	2	yes	—
546	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
547	C₂³	—	113	1	no	—
548	C₂³	—	113	1	no	—
549	C₂³	C₂³×D₁₁₃	1	2	yes	—
550	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
551	Q₈	—	2	2	no	—
552	Q₈	—	113	4	no	—
553	Q₈	—	226	4	no	—
554	Q₈	—	226	4	no	—
555	Q₈	—	226	2	no	—
556	Q₈	—	226	4	no	—
557	Q₈	—	226	2	no	—
558	D₄	—	2	4	no	—
559	D₄	—	2	2	no	—
560	D₄	—	113	4	no	—
561	D₄	—	226	2	no	—
562	D₄	—	226	4	no	—
563	D₄	—	226	4	no	—
564	D₄	—	226	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	113	1	no	—
570	C₂×C₄	—	113	2	no	—
571	C₂×C₄	—	113	1	no	—
572	C₂×C₄	—	113	1	no	—
573	C₂×C₄	—	113	2	no	—
574	C₂×C₄	—	113	1	no	—
575	C₂×C₄	—	113	1	no	—
576	C₂×C₄	—	113	2	no	—
577	C₂×C₄	—	113	1	no	—
578	C₂×C₄	—	113	2	no	—
579	C₂×C₄	—	226	4	no	—
580	C₂×C₄	—	226	2	no	—
581	C₂×C₄	—	226	2	no	—
582	C₂×C₄	—	226	4	no	—
583	C₂×C₄	—	226	4	no	—
584	C₂×C₄	—	226	4	no	—
585	C₂×C₄	—	226	4	no	—
586	C₂×C₄	—	226	4	no	—
587	C₂×C₄	—	226	2	no	—
588	C₂×C₄	—	226	2	no	—
589	C₂×C₄	—	226	2	no	—
590	C₂×C₄	—	226	2	no	—
591	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
594	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
595	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
596	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
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	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	113	2	no	—
606	C₂²	—	226	1	no	—
607	C₂²	—	226	1	no	—
608	C₂²	—	226	1	no	—
609	C₂²	—	226	1	no	—
610	C₂²	—	226	1	no	—
611	C₂²	#41×D₁₁₃	1	2	yes	—
612	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	113	2	no	—
621	C₄	—	113	4	no	—
622	C₄	—	226	2	no	—
623	C₄	—	226	1	no	—
624	C₄	—	226	1	no	—
625	C₄	—	226	2	no	—
626	C₄	—	226	2	no	—
627	C₄	—	226	1	no	—
628	C₄	—	226	1	no	—
629	C₄	—	226	1	no	—
630	C₄	#41×D₁₁₃	1	2	yes	—
631	C₄	#16813669	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	452	1	no	—
635	C₂	—	226	2	no	—
636	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
637	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
638	C₂	C₂×#16813669	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	#529×C₁₁₃	C₂
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3482
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #20299325	C₂	semidirect
2. #20299317	C₂	semidirect
3. #20299315	C₂	semidirect
4. #20299290	C₂	semidirect
5. #20299286	C₂	semidirect
6. #20299285	C₂	semidirect
7. #20299284	C₂	semidirect
8. #20299261	C₂	semidirect
9. #20299256	C₂	semidirect
10. #20299254	C₂	semidirect
11. #20299248	C₂	semidirect
12. #20299246	C₂	semidirect
13. #20299152	C₂	semidirect
14. #20299151	C₂	semidirect
15. #20299130	C₂	semidirect
16. #20299128	C₂	semidirect
17. #20299126	C₂	semidirect
18. C₄×#14268647	C₂	semidirect
19. C₄×#14268646	C₂	semidirect
20. C₄×#14268646	C₂	semidirect
21. C₂×C₄×Dic₂₂₆	C₂	semidirect
22. C₄×Q₈×D₁₁₃	C₂	semidirect
23. #529×C₁₁₃	C₂	semidirect
250. C₂²⋊D₁₁₃	#41	semidirect
279. Dic₂₂₆	#41	semidirect
320. C₁₁₃	#3482	semidirect
338. #529	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299325	2
#20299317	2
#20299315	2
#20299290	2
#20299286	2
#20299285	2
#20299284	2
#20299261	2
#20299256	2
#20299254	2
#20299248	2
#20299246	2
#20299152	2
#20299151	2
#20299130	2
#20299128	2
#20299126	2
C₄×#14268647	2
C₄×#14268646	2
C₂×C₄×Dic₂₂₆	2
C₄×Q₈×D₁₁₃	2
#529×C₁₁₃	2
#3482	113