Subgroups — #28404479

Order 14464.

1104 conjugacy classes of subgroups.

The subgroup lattice has 662 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	#20299310	C₂	1	2	yes	maximal, complemented
3	#20299302	C₂	1	2	yes	maximal, complemented
4	#20299299	C₂	1	2	yes	maximal, complemented
5	#20299293	C₂	1	2	yes	maximal, complemented
6	#20299258	C₂	1	2	yes	maximal, complemented
7	#20299256	C₂	1	2	yes	maximal, complemented
8	#20299246	C₂	1	2	yes	maximal, complemented
9	#20299222	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299219	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299217	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299178	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299177	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299150	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299147	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299145	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299143	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄⋊Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299080	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299077	C₂	1	1	yes	maximal, characteristic, complemented
22	#20299066	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×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	2	yes	—
27	C₂×#14268646	C₂²	1	1	yes	characteristic
28	C₂×#14268646	C₂²	1	2	yes	—
29	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
30	#16813622	C₂²	1	1	yes	characteristic
31	#16813621	C₂²	1	2	yes	—
32	#16813621	C₂²	1	1	yes	characteristic
33	#16813621	C₂²	1	1	yes	characteristic
34	#16813620	C₂²	1	2	yes	—
35	#16813620	C₂²	1	1	yes	characteristic
36	#16813618	C₂²	1	1	yes	characteristic
37	#16813617	C₂²	1	2	yes	—
38	#16813617	C₂²	1	2	yes	—
39	#16813615	C₂²	1	2	yes	—
40	#16813612	C₂²	1	2	yes	—
41	#16813612	C₂²	1	2	yes	—
42	#16813611	C₂²	1	2	yes	—
43	#16813610	C₂²	1	1	yes	characteristic
44	#16813608	C₂²	1	2	yes	—
45	#16813608	C₂²	1	2	yes	—
46	#16813608	C₂²	1	2	yes	—
47	#16813608	C₂²	1	2	yes	—
48	#16813607	C₂²	1	2	yes	—
49	#16813606	C₂²	1	2	yes	—
50	#16813604	C₂²	1	2	yes	—
51	#16813602	C₂²	1	1	yes	characteristic
52	#16813601	C₂²	1	1	yes	characteristic
53	#16813600	C₂²	1	2	yes	—
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	#16813598	C₂²	1	2	yes	—
60	#16813598	C₂²	1	1	yes	characteristic
61	#16813597	C₂²	1	2	yes	—
62	#16813597	C₂²	1	1	yes	characteristic
63	#16813596	C₂²	1	1	yes	characteristic
64	#16813595	C₂²	1	2	yes	—
65	#16813595	C₂²	1	2	yes	—
66	#16813595	C₂²	1	2	yes	—
67	#16813595	C₂²	1	2	yes	—
68	#16813595	C₂²	1	2	yes	—
69	#16813595	C₂²	1	2	yes	—
70	#16813594	C₂²	1	2	yes	—
71	#16813594	C₂²	1	2	yes	—
72	#16813593	C₂²	1	2	yes	—
73	#16813593	C₂²	1	1	yes	characteristic
74	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
75	C₄×Dic₂₂₆	C₂²	1	2	yes	—
76	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
77	#16813587	C₂²	1	1	yes	characteristic
78	#16813587	C₂²	1	1	yes	characteristic
79	#16813587	C₂²	1	2	yes	—
80	#16813587	C₂²	1	1	yes	characteristic
81	C₄×D₄₅₂	C₂²	1	2	yes	—
82	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
84	#16813584	C₂²	1	2	yes	—
85	#16813584	C₂²	1	1	yes	characteristic
86	#16813584	C₂²	1	1	yes	characteristic
87	#16813584	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
89	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
90	#16813582	C₂²	1	1	yes	characteristic
91	#16813582	C₂²	1	2	yes	—
92	#16813582	C₂²	1	2	yes	—
93	#16813582	C₂²	1	2	yes	—
94	#16813582	C₂²	1	1	yes	characteristic
95	#16813582	C₂²	1	2	yes	—
96	#16813582	C₂²	1	1	yes	characteristic
97	#16813582	C₂²	1	1	yes	characteristic
98	#16813579	C₂²	1	2	yes	—
99	#16813579	C₂²	1	2	yes	—
100	#16813579	C₂²	1	1	yes	characteristic
101	#16813579	C₂²	1	1	yes	characteristic
102	#16813578	C₂²	1	2	yes	—
103	#16813578	C₂²	1	2	yes	—
104	C₂×#14268626	C₂²	1	2	yes	—
105	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
109	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
110	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
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	#124×C₁₁₃	C₂²	1	2	yes	—
115	#124×C₁₁₃	C₂²	1	1	yes	characteristic
116	#123×C₁₁₃	C₂²	1	2	yes	—
117	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
119	#121×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	1	yes	characteristic
123	#14268648	—	2	4	no	—
124	#14268647	—	2	4	no	—
125	#14268647	—	4	4	no	—
126	#14268646	—	2	4	no	—
127	#14268646	—	4	4	no	—
128	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₂₆	C₂³	1	2	yes	—
131	C₂×Dic₂₂₆	C₂³	1	2	yes	—
132	C₂×Dic₂₂₆	C₂³	1	2	yes	—
133	Q₈×D₁₁₃	—	4	4	no	—
134	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
135	C₂×D₄₅₂	C₂³	1	2	yes	—
136	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
137	C₂×D₄₅₂	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
145	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
158	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
163	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
164	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
165	#14268626	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
173	#14268626	C₂³	1	2	yes	—
174	#14268626	C₂³	1	1	yes	characteristic
175	#14268626	C₂³	1	1	yes	characteristic
176	#14268626	C₂³	1	2	yes	—
177	#14268626	C₂³	1	2	yes	—
178	#14268626	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
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	#14268624	C₂³	1	2	yes	—
191	#14268624	C₂³	1	2	yes	—
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	1	yes	characteristic
196	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₁₃	C₂³	1	2	yes	—
203	C₄×Dic₁₁₃	C₂³	1	2	yes	—
204	C₄×Dic₁₁₃	C₂³	1	2	yes	—
205	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
207	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
216	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
217	C₄⋊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	1	yes	characteristic
221	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
225	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
226	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
227	C₄²×C₁₁₃	C₂³	1	2	yes	—
228	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
229	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₁₃	—	2	2	no	—
234	Q₈×C₁₁₃	—	4	2	no	—
235	D₄×C₁₁₃	—	2	2	no	—
236	D₄×C₁₁₃	—	4	2	no	—
237	C₂×C₄×C₁₁₃	—	2	2	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	2	yes	—
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	1	yes	characteristic
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	—	2	2	no	—
250	C₂²⋊D₁₁₃	—	2	2	no	—
251	C₂²⋊D₁₁₃	—	2	4	no	—
252	C₂²⋊D₁₁₃	—	2	4	no	—
253	C₂²⋊D₁₁₃	—	4	2	no	—
254	C₂²⋊D₁₁₃	—	4	2	no	—
255	C₂×Dic₁₁₃	—	2	4	no	—
256	C₂×Dic₁₁₃	—	2	2	no	—
257	C₂×Dic₁₁₃	—	2	2	no	—
258	C₂×Dic₁₁₃	—	4	2	no	—
259	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
264	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
265	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
268	D₄₅₂	—	2	2	no	—
269	D₄₅₂	—	2	4	no	—
270	D₄₅₂	—	2	2	no	—
271	D₄₅₂	—	4	2	no	—
272	C₄×D₁₁₃	—	2	2	no	—
273	C₄×D₁₁₃	—	2	4	no	—
274	C₄×D₁₁₃	—	2	2	no	—
275	C₄×D₁₁₃	—	2	2	no	—
276	C₄×D₁₁₃	—	2	2	no	—
277	C₄×D₁₁₃	—	2	2	no	—
278	C₄×D₁₁₃	—	4	2	no	—
279	C₄×D₁₁₃	—	4	2	no	—
280	C₄×D₁₁₃	—	4	2	no	—
281	C₄×D₁₁₃	—	4	2	no	—
282	C₄×D₁₁₃	#41	1	4	yes	complemented
283	Dic₂₂₆	—	2	2	no	—
284	Dic₂₂₆	—	2	2	no	—
285	Dic₂₂₆	—	2	4	no	—
286	Dic₂₂₆	—	2	4	no	—
287	Dic₂₂₆	—	4	2	no	—
288	C₂²×C₁₁₃	—	2	2	no	—
289	C₂²×C₁₁₃	—	2	1	no	—
290	C₂²×C₁₁₃	—	2	1	no	—
291	C₂²×C₁₁₃	—	2	2	no	—
292	C₂²×C₁₁₃	—	2	1	no	—
293	C₂²×C₁₁₃	—	2	2	no	—
294	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
295	C₂×D₁₁₃	—	2	1	no	—
296	C₂×D₁₁₃	—	2	1	no	—
297	C₂×D₁₁₃	—	2	2	no	—
298	C₂×D₁₁₃	—	2	1	no	—
299	C₂×D₁₁₃	—	2	1	no	—
300	C₂×D₁₁₃	—	2	2	no	—
301	C₂×D₁₁₃	—	2	1	no	—
302	C₂×D₁₁₃	—	2	2	no	—
303	C₂×D₁₁₃	C₂×#41	1	2	yes	—
304	C₄×C₁₁₃	—	2	1	no	—
305	C₄×C₁₁₃	—	2	2	no	—
306	C₄×C₁₁₃	—	2	2	no	—
307	C₄×C₁₁₃	—	2	2	no	—
308	C₄×C₁₁₃	—	2	1	no	—
309	C₄×C₁₁₃	—	2	1	no	—
310	C₄×C₁₁₃	—	2	1	no	—
311	C₄×C₁₁₃	—	2	1	no	—
312	C₄×C₁₁₃	C₂×#41	1	2	yes	—
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	—	2	1	no	—
319	Dic₁₁₃	C₂×#41	1	2	yes	—
320	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
321	Dic₁₁₃	2₋¹⁺⁴	1	2	yes	—
322	C₂×C₁₁₃	—	4	2	no	—
323	C₂×C₁₁₃	—	4	1	no	—
324	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
325	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
327	D₁₁₃	—	2	2	no	—
328	D₁₁₃	—	4	2	no	—
329	D₁₁₃	—	4	1	no	—
330	#3511	—	113	1	no	maximal, Sylow
331	C₁₁₃	#3511	1	1	yes	characteristic, complemented, Sylow
332	#556	—	113	2	no	—
333	#555	—	113	2	no	—
334	#554	—	113	2	no	—
335	#553	—	113	2	no	—
336	#553	—	113	2	no	—
337	#548	—	113	2	no	—
338	#548	—	113	2	no	—
339	#547	—	113	2	no	—
340	#542	—	113	1	no	—
341	#542	—	113	1	no	—
342	#542	—	113	1	no	—
343	#542	D₁₁₃	1	1	yes	characteristic, complemented
344	#537	—	113	1	no	—
345	#537	—	113	1	no	—
346	#533	—	113	1	no	—
347	#533	—	113	1	no	—
348	#532	—	113	1	no	—
349	#532	—	113	1	no	—
350	#532	—	113	1	no	—
351	C₂×C₄⋊Q₈	—	113	1	no	—
352	#520	—	113	1	no	—
353	#520	—	113	1	no	—
354	C₄×#41	—	113	1	no	—
355	C₂×#41	—	113	1	no	—
356	C₂×#41	—	113	2	no	—
357	C₂×#41	—	113	1	no	—
358	C₂×#41	—	113	2	no	—
359	C₂×#41	—	113	1	no	—
360	C₂²×Q₈	—	113	2	no	—
361	C₄⋊Q₈	—	113	2	no	—
362	C₄⋊Q₈	—	113	1	no	—
363	C₄⋊Q₈	—	113	1	no	—
364	C₄⋊Q₈	—	113	1	no	—
365	C₄⋊Q₈	—	113	2	no	—
366	C₄⋊Q₈	—	113	1	no	—
367	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
368	#127	—	113	1	no	—
369	#126	—	113	2	no	—
370	#126	—	113	2	no	—
371	#126	—	113	2	no	—
372	#126	C₂×D₁₁₃	1	2	yes	—
373	#125	—	113	2	no	—
374	#125	—	113	2	no	—
375	#124	—	113	2	no	—
376	#124	—	113	2	no	—
377	#124	—	113	2	no	—
378	#124	—	113	2	no	—
379	#124	—	113	2	no	—
380	#124	—	113	1	no	—
381	#124	C₂×D₁₁₃	1	1	yes	characteristic
382	#124	C₂×D₁₁₃	1	2	yes	—
383	#123	—	113	2	no	—
384	#123	—	113	2	no	—
385	#123	—	113	2	no	—
386	#123	C₂×D₁₁₃	1	2	yes	—
387	C₂²⋊Q₈	—	113	1	no	—
388	C₂²⋊Q₈	—	113	2	no	—
389	C₂²⋊Q₈	—	113	1	no	—
390	C₂²⋊Q₈	—	113	1	no	—
391	C₂²⋊Q₈	—	113	2	no	—
392	C₂²⋊Q₈	—	113	2	no	—
393	C₂²⋊Q₈	—	113	2	no	—
394	C₂²⋊Q₈	—	113	2	no	—
395	C₂²⋊Q₈	—	113	2	no	—
396	C₂²⋊Q₈	—	113	2	no	—
397	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
398	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
399	#121	—	113	1	no	—
400	#121	—	113	2	no	—
401	#121	—	113	2	no	—
402	#121	—	113	2	no	—
403	#121	—	113	1	no	—
404	#121	—	113	1	no	—
405	#121	—	113	2	no	—
406	#121	—	113	2	no	—
407	#121	—	113	2	no	—
408	#121	—	113	2	no	—
409	#121	—	113	2	no	—
410	#121	—	113	2	no	—
411	#121	—	113	2	no	—
412	#121	C₂×D₁₁₃	1	1	yes	characteristic
413	C₄×Q₈	—	113	1	no	—
414	C₄×Q₈	—	113	1	no	—
415	C₄×Q₈	—	113	1	no	—
416	C₄×Q₈	—	113	1	no	—
417	C₄×Q₈	—	113	2	no	—
418	C₄×Q₈	—	113	1	no	—
419	C₄×Q₈	—	113	2	no	—
420	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
421	C₄×D₄	—	113	1	no	—
422	C₄×D₄	—	113	2	no	—
423	C₄×D₄	—	113	2	no	—
424	C₄×D₄	—	113	1	no	—
425	C₄×D₄	—	113	1	no	—
426	C₄×D₄	—	113	1	no	—
427	C₄×D₄	—	113	2	no	—
428	C₄×D₄	—	113	1	no	—
429	C₄×D₄	—	113	1	no	—
430	C₄×D₄	—	113	1	no	—
431	C₄×D₄	—	113	1	no	—
432	C₄×D₄	—	113	2	no	—
433	C₄×D₄	—	113	2	no	—
434	C₄×D₄	—	113	2	no	—
435	C₄×D₄	—	113	2	no	—
436	C₄×D₄	—	113	1	no	—
437	C₄×D₄	—	113	2	no	—
438	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
439	#117	—	113	2	no	—
440	#117	—	113	2	no	—
441	#117	—	113	1	no	—
442	#117	—	113	1	no	—
443	#117	—	113	2	no	—
444	#117	—	113	2	no	—
445	#117	C₂×D₁₁₃	1	1	yes	characteristic
446	C₂×C₄⋊C₄	—	113	2	no	—
447	C₂×C₄⋊C₄	—	113	1	no	—
448	C₂×C₄⋊C₄	—	113	1	no	—
449	C₂×C₄⋊C₄	—	113	2	no	—
450	C₂×C₄⋊C₄	—	113	2	no	—
451	C₂×C₄²	—	113	1	no	—
452	C₂×C₄²	—	113	1	no	—
453	C₂×C₄²	—	113	1	no	—
454	#41	—	452	4	no	—
455	#41	—	452	4	no	—
456	#41	—	226	4	no	—
457	#41	—	226	4	no	—
458	#41	—	226	4	no	—
459	C₂×Q₈	—	113	2	no	—
460	C₂×Q₈	—	113	1	no	—
461	C₂×Q₈	—	113	1	no	—
462	C₂×Q₈	—	113	2	no	—
463	C₂×Q₈	—	113	2	no	—
464	C₂×Q₈	—	452	4	no	—
465	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
466	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
467	C₂×D₄	—	113	2	no	—
468	C₂×D₄	—	113	2	no	—
469	C₂×D₄	—	113	2	no	—
470	C₂×D₄	—	113	1	no	—
471	C₂×D₄	—	113	2	no	—
472	C₂×D₄	—	113	1	no	—
473	C₂×D₄	—	113	2	no	—
474	C₂×D₄	—	113	2	no	—
475	C₂×D₄	—	113	1	no	—
476	C₂×D₄	—	113	2	no	—
477	C₂×D₄	—	113	1	no	—
478	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
480	C₂²×C₄	—	113	1	no	—
481	C₂²×C₄	—	113	2	no	—
482	C₂²×C₄	—	113	1	no	—
483	C₂²×C₄	—	113	1	no	—
484	C₂²×C₄	—	113	2	no	—
485	C₂²×C₄	—	113	2	no	—
486	C₂²×C₄	—	113	2	no	—
487	C₂²×C₄	—	113	2	no	—
488	C₂²×C₄	—	113	2	no	—
489	C₂²×C₄	—	113	1	no	—
490	C₂²×C₄	—	113	1	no	—
491	C₂²×C₄	—	113	1	no	—
492	C₂²×C₄	—	113	1	no	—
493	C₂²×C₄	—	113	1	no	—
494	C₂²×C₄	—	113	2	no	—
495	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
497	C₄⋊C₄	—	113	1	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	1	no	—
503	C₄⋊C₄	—	113	1	no	—
504	C₄⋊C₄	—	113	2	no	—
505	C₄⋊C₄	—	113	2	no	—
506	C₄⋊C₄	—	113	2	no	—
507	C₄⋊C₄	—	113	2	no	—
508	C₄⋊C₄	—	113	1	no	—
509	C₄⋊C₄	—	113	2	no	—
510	C₄⋊C₄	—	113	1	no	—
511	C₄⋊C₄	—	113	1	no	—
512	C₄⋊C₄	—	113	2	no	—
513	C₄⋊C₄	—	113	2	no	—
514	C₄⋊C₄	—	113	2	no	—
515	C₄⋊C₄	—	113	2	no	—
516	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
518	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
523	C₂²⋊C₄	—	113	2	no	—
524	C₂²⋊C₄	—	113	2	no	—
525	C₂²⋊C₄	—	113	2	no	—
526	C₂²⋊C₄	—	113	1	no	—
527	C₂²⋊C₄	—	113	1	no	—
528	C₂²⋊C₄	—	113	2	no	—
529	C₂²⋊C₄	—	113	2	no	—
530	C₂²⋊C₄	—	113	1	no	—
531	C₂²⋊C₄	—	113	1	no	—
532	C₂²⋊C₄	—	113	2	no	—
533	C₂²⋊C₄	—	113	2	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	2	yes	—
540	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
545	C₄²	—	113	1	no	—
546	C₄²	—	113	1	no	—
547	C₄²	—	113	1	no	—
548	C₄²	—	113	1	no	—
549	C₄²	—	113	1	no	—
550	C₄²	—	113	1	no	—
551	C₄²	—	113	1	no	—
552	C₄²	—	113	1	no	—
553	C₄²	—	113	2	no	—
554	C₄²	—	113	2	no	—
555	C₄²	—	113	2	no	—
556	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
557	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
558	C₄²	C₂²×D₁₁₃	1	2	yes	—
559	C₂³	—	113	1	no	—
560	C₂³	—	113	2	no	—
561	C₂³	—	113	1	no	—
562	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
563	C₂³	C₂³×D₁₁₃	1	2	yes	—
564	Q₈	—	2	2	no	—
565	Q₈	—	4	2	no	—
566	Q₈	—	452	2	no	—
567	Q₈	—	226	4	no	—
568	Q₈	—	226	4	no	—
569	Q₈	—	226	2	no	—
570	Q₈	—	226	2	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	452	2	no	—
574	D₄	—	452	2	no	—
575	D₄	—	452	2	no	—
576	D₄	—	226	2	no	—
577	D₄	—	226	4	no	—
578	D₄	—	226	4	no	—
579	D₄	—	226	2	no	—
580	D₄	—	226	4	no	—
581	D₄	—	226	2	no	—
582	D₄	—	226	4	no	—
583	D₄	—	226	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	113	1	no	—
587	C₂×C₄	—	113	1	no	—
588	C₂×C₄	—	113	1	no	—
589	C₂×C₄	—	113	4	no	—
590	C₂×C₄	—	113	1	no	—
591	C₂×C₄	—	113	1	no	—
592	C₂×C₄	—	113	2	no	—
593	C₂×C₄	—	113	1	no	—
594	C₂×C₄	—	113	2	no	—
595	C₂×C₄	—	113	2	no	—
596	C₂×C₄	—	452	2	no	—
597	C₂×C₄	—	452	2	no	—
598	C₂×C₄	—	452	2	no	—
599	C₂×C₄	—	452	2	no	—
600	C₂×C₄	—	452	2	no	—
601	C₂×C₄	—	226	2	no	—
602	C₂×C₄	—	226	2	no	—
603	C₂×C₄	—	226	4	no	—
604	C₂×C₄	—	226	2	no	—
605	C₂×C₄	—	226	2	no	—
606	C₂×C₄	—	226	2	no	—
607	C₂×C₄	—	226	4	no	—
608	C₂×C₄	—	226	2	no	—
609	C₂×C₄	—	226	2	no	—
610	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
615	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
617	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
618	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	113	2	no	—
626	C₂²	—	226	2	no	—
627	C₂²	—	226	1	no	—
628	C₂²	—	226	2	no	—
629	C₂²	—	226	1	no	—
630	C₂²	—	226	1	no	—
631	C₂²	—	226	2	no	—
632	C₂²	—	226	1	no	—
633	C₂²	—	226	1	no	—
634	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	1	no	—
641	C₄	—	2	1	no	—
642	C₄	—	2	1	no	—
643	C₄	—	113	2	no	—
644	C₄	—	113	2	no	—
645	C₄	—	113	2	no	—
646	C₄	—	226	2	no	—
647	C₄	—	226	1	no	—
648	C₄	—	226	1	no	—
649	C₄	—	226	2	no	—
650	C₄	—	226	2	no	—
651	C₄	—	226	1	no	—
652	C₄	#41×D₁₁₃	1	2	yes	—
653	C₂	—	4	1	no	—
654	C₂	—	4	2	no	—
655	C₂	—	452	2	no	—
656	C₂	—	452	1	no	—
657	C₂	—	226	2	no	—
658	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
659	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
660	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#542×C₁₁₃	C₂
hypercenter	#542	D₁₁₃
hypocenter	C₁₁₃	#3511
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #20299315	C₂	semidirect
2. #20299310	C₂	semidirect
3. #20299302	C₂	semidirect
4. #20299299	C₂	semidirect
5. #20299293	C₂	semidirect
6. #20299258	C₂	semidirect
7. #20299256	C₂	semidirect
8. #20299246	C₂	semidirect
9. #20299222	C₂	semidirect
10. #20299219	C₂	semidirect
11. #20299217	C₂	semidirect
12. #20299178	C₂	semidirect
13. #20299177	C₂	semidirect
14. #20299152	C₂	semidirect
15. #20299150	C₂	semidirect
16. #20299147	C₂	semidirect
17. #20299145	C₂	semidirect
18. #20299143	C₂	semidirect
19. C₄⋊Q₈×D₁₁₃	C₂	semidirect
20. #20299080	C₂	semidirect
21. #20299077	C₂	semidirect
22. #20299066	C₂	semidirect
23. #542×C₁₁₃	C₂	semidirect
282. C₄×D₁₁₃	#41	semidirect
331. C₁₁₃	#3511	semidirect
343. #542	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
#20299310	2
#20299302	2
#20299299	2
#20299293	2
#20299258	2
#20299256	2
#20299246	2
#20299222	2
#20299219	2
#20299217	2
#20299178	2
#20299177	2
#20299152	2
#20299150	2
#20299147	2
#20299145	2
#20299143	2
C₄⋊Q₈×D₁₁₃	2
#20299080	2
#20299077	2
#20299066	2
#542×C₁₁₃	2
#3511	113