Subgroups — #28404486

Order 14464.

1104 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299320	C₂	1	2	yes	maximal, complemented
2	#20299311	C₂	1	2	yes	maximal, complemented
3	#20299304	C₂	1	2	yes	maximal, complemented
4	#20299301	C₂	1	2	yes	maximal, complemented
5	#20299292	C₂	1	2	yes	maximal, complemented
6	#20299260	C₂	1	2	yes	maximal, complemented
7	#20299258	C₂	1	2	yes	maximal, complemented
8	#20299250	C₂	1	2	yes	maximal, complemented
9	#20299221	C₂	1	2	yes	maximal, complemented
10	#20299220	C₂	1	2	yes	maximal, complemented
11	#20299178	C₂	1	2	yes	maximal, complemented
12	#20299153	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299149	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299149	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299148	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄⋊Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299080	C₂	1	2	yes	maximal, complemented
18	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
19	#533×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268648	C₂²	1	2	yes	—
21	C₂×#14268648	C₂²	1	2	yes	—
22	C₂×#14268647	C₂²	1	1	yes	characteristic
23	C₂×#14268647	C₂²	1	2	yes	—
24	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
25	#16813622	C₂²	1	1	yes	characteristic
26	#16813621	C₂²	1	2	yes	—
27	#16813621	C₂²	1	2	yes	—
28	#16813620	C₂²	1	2	yes	—
29	#16813619	C₂²	1	1	yes	characteristic
30	#16813617	C₂²	1	4	yes	—
31	#16813616	C₂²	1	4	yes	—
32	#16813613	C₂²	1	2	yes	—
33	#16813611	C₂²	1	2	yes	—
34	#16813611	C₂²	1	2	yes	—
35	#16813610	C₂²	1	4	yes	—
36	#16813610	C₂²	1	2	yes	—
37	#16813608	C₂²	1	4	yes	—
38	#16813607	C₂²	1	4	yes	—
39	#16813604	C₂²	1	4	yes	—
40	#16813602	C₂²	1	4	yes	—
41	#16813602	C₂²	1	2	yes	—
42	#16813600	C₂²	1	4	yes	—
43	#16813600	C₂²	1	4	yes	—
44	#16813598	C₂²	1	2	yes	—
45	#16813597	C₂²	1	2	yes	—
46	#16813597	C₂²	1	2	yes	—
47	#16813597	C₂²	1	4	yes	—
48	#16813597	C₂²	1	2	yes	—
49	#16813597	C₂²	1	2	yes	—
50	#16813596	C₂²	1	2	yes	—
51	#16813596	C₂²	1	2	yes	—
52	#16813595	C₂²	1	4	yes	—
53	#16813595	C₂²	1	4	yes	—
54	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
55	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
56	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
57	#16813587	C₂²	1	2	yes	—
58	C₄×D₄₅₂	C₂²	1	4	yes	—
59	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
60	C₄×D₄₅₂	C₂²	1	2	yes	—
61	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
62	C₄×D₄₅₂	C₂²	1	2	yes	—
63	#16813584	C₂²	1	2	yes	—
64	#16813584	C₂²	1	4	yes	—
65	#16813584	C₂²	1	2	yes	—
66	#16813584	C₂²	1	2	yes	—
67	#16813584	C₂²	1	2	yes	—
68	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
72	#16813581	C₂²	1	1	yes	characteristic
73	#16813580	C₂²	1	2	yes	—
74	#16813579	C₂²	1	4	yes	—
75	#16813579	C₂²	1	1	yes	characteristic
76	#16813579	C₂²	1	1	yes	characteristic
77	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
78	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
79	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
80	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
81	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
82	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
83	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
84	#125×C₁₁₃	C₂²	1	2	yes	—
85	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
86	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
87	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
88	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
89	#117×C₁₁₃	C₂²	1	2	yes	—
90	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
91	#14268648	—	2	8	no	—
92	#14268648	—	4	4	no	—
93	#14268647	—	2	4	no	—
94	#14268647	—	4	4	no	—
95	C₂×Dic₂₂₆	C₂³	1	2	yes	—
96	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
97	C₂×Dic₂₂₆	C₂³	1	4	yes	—
98	Q₈×D₁₁₃	—	4	4	no	—
99	C₂×D₄₅₂	C₂³	1	2	yes	—
100	C₂×D₄₅₂	C₂³	1	4	yes	—
101	C₂×D₄₅₂	C₂³	1	2	yes	—
102	C₂×D₄₅₂	C₂³	1	2	yes	—
103	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
104	C₂×D₄₅₂	C₂³	1	4	yes	—
105	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
108	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
114	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
115	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
116	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
117	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
118	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
119	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
120	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
121	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
123	#14268626	C₂³	1	1	yes	characteristic
124	#14268626	C₂³	1	4	yes	—
125	#14268626	C₂³	1	4	yes	—
126	#14268626	C₂³	1	1	yes	characteristic
127	#14268626	C₂³	1	1	yes	characteristic
128	#14268626	C₂³	1	1	yes	characteristic
129	#14268626	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
132	#14268624	C₂³	1	1	yes	characteristic
133	#14268624	C₂³	1	1	yes	characteristic
134	#14268624	C₂³	1	1	yes	characteristic
135	#14268624	C₂³	1	1	yes	characteristic
136	#14268624	C₂³	1	4	yes	—
137	#14268624	C₂³	1	4	yes	—
138	#14268624	C₂³	1	4	yes	—
139	#14268624	C₂³	1	4	yes	—
140	#14268624	C₂³	1	4	yes	—
141	#14268624	C₂³	1	4	yes	—
142	#14268624	C₂³	1	4	yes	—
143	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
144	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
145	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
146	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
147	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₁₁₃	C₂³	1	4	yes	—
150	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
151	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
153	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
156	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
157	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
158	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
160	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
161	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
162	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
163	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
164	C₄²×C₁₁₃	C₂³	1	4	yes	—
165	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
166	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
167	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
169	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
171	Q₈×C₁₁₃	—	2	4	no	—
172	Q₈×C₁₁₃	—	2	4	no	—
173	C₂×C₄×C₁₁₃	—	2	2	no	—
174	C₂×C₄×C₁₁₃	—	2	2	no	—
175	C₂×C₄×C₁₁₃	—	2	2	no	—
176	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
180	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
181	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²⋊D₁₁₃	—	2	2	no	—
185	C₂²⋊D₁₁₃	—	2	2	no	—
186	C₂²⋊D₁₁₃	—	4	4	no	—
187	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
190	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
193	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
194	D₄₅₂	—	2	2	no	—
195	D₄₅₂	—	2	8	no	—
196	D₄₅₂	—	2	4	no	—
197	D₄₅₂	—	2	4	no	—
198	D₄₅₂	—	2	4	no	—
199	D₄₅₂	—	4	4	no	—
200	C₄×D₁₁₃	—	2	2	no	—
201	C₄×D₁₁₃	—	2	2	no	—
202	C₄×D₁₁₃	—	2	2	no	—
203	C₄×D₁₁₃	—	2	2	no	—
204	C₄×D₁₁₃	—	2	2	no	—
205	C₄×D₁₁₃	—	2	8	no	—
206	C₄×D₁₁₃	—	4	4	no	—
207	C₄×D₁₁₃	—	4	4	no	—
208	C₄×D₁₁₃	—	4	4	no	—
209	C₄×D₁₁₃	#41	1	4	yes	complemented
210	Dic₂₂₆	—	2	4	no	—
211	Dic₂₂₆	—	2	2	no	—
212	Dic₂₂₆	—	4	4	no	—
213	C₂²×C₁₁₃	—	2	1	no	—
214	C₂²×C₁₁₃	—	2	1	no	—
215	C₂²×C₁₁₃	—	2	1	no	—
216	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
217	C₂×D₁₁₃	—	2	1	no	—
218	C₂×D₁₁₃	—	2	1	no	—
219	C₂×D₁₁₃	—	2	4	no	—
220	C₂×D₁₁₃	—	2	1	no	—
221	C₂×D₁₁₃	—	2	1	no	—
222	C₂×D₁₁₃	—	2	4	no	—
223	C₂×D₁₁₃	—	2	1	no	—
224	C₂×D₁₁₃	—	2	4	no	—
225	C₂×D₁₁₃	C₂×#41	1	2	yes	—
226	C₄×C₁₁₃	—	2	1	no	—
227	C₄×C₁₁₃	—	2	4	no	—
228	C₄×C₁₁₃	—	2	4	no	—
229	C₄×C₁₁₃	—	2	1	no	—
230	C₄×C₁₁₃	—	2	1	no	—
231	C₄×C₁₁₃	C₂×#41	1	2	yes	—
232	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
233	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
234	Dic₁₁₃	—	2	1	no	—
235	Dic₁₁₃	—	2	4	no	—
236	Dic₁₁₃	—	2	1	no	—
237	Dic₁₁₃	—	2	1	no	—
238	Dic₁₁₃	—	2	1	no	—
239	Dic₁₁₃	—	2	1	no	—
240	Dic₁₁₃	C₂×#41	1	2	yes	—
241	C₂×C₁₁₃	—	4	1	no	—
242	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
243	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
245	D₁₁₃	—	2	2	no	—
246	D₁₁₃	—	4	4	no	—
247	D₁₁₃	—	4	1	no	—
248	#3511	—	113	1	no	maximal, Sylow
249	C₁₁₃	#3511	1	1	yes	characteristic, complemented, Sylow
250	#556	—	113	2	no	—
251	#555	—	113	2	no	—
252	#554	—	113	2	no	—
253	#553	—	113	2	no	—
254	#553	—	113	2	no	—
255	#548	—	113	2	no	—
256	#548	—	113	2	no	—
257	#547	—	113	2	no	—
258	#542	—	113	2	no	—
259	#542	—	113	2	no	—
260	#537	—	113	2	no	—
261	#533	—	113	1	no	—
262	#533	D₁₁₃	1	1	yes	characteristic, complemented
263	#532	—	113	1	no	—
264	#532	—	113	1	no	—
265	#532	—	113	1	no	—
266	C₂×C₄⋊Q₈	—	113	1	no	—
267	#520	—	113	2	no	—
268	C₄×#41	—	113	1	no	—
269	C₂×#41	—	113	2	no	—
270	C₂×#41	—	113	2	no	—
271	C₂×#41	—	113	2	no	—
272	C₂×#41	—	113	1	no	—
273	C₂²×Q₈	—	113	2	no	—
274	C₄⋊Q₈	—	113	2	no	—
275	C₄⋊Q₈	—	113	2	no	—
276	C₄⋊Q₈	—	113	2	no	—
277	C₄⋊Q₈	—	113	1	no	—
278	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
279	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
280	#127	—	113	1	no	—
281	#126	—	113	4	no	—
282	#126	—	113	4	no	—
283	#125	—	113	2	no	—
284	#125	C₂×D₁₁₃	1	2	yes	—
285	#124	—	113	2	no	—
286	#124	—	113	2	no	—
287	#124	—	113	4	no	—
288	#124	—	113	2	no	—
289	#124	—	113	4	no	—
290	#123	—	113	4	no	—
291	#123	—	113	4	no	—
292	C₂²⋊Q₈	—	113	2	no	—
293	C₂²⋊Q₈	—	113	2	no	—
294	C₂²⋊Q₈	—	113	4	no	—
295	C₂²⋊Q₈	—	113	4	no	—
296	C₂²⋊Q₈	—	113	4	no	—
297	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
298	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
299	#121	—	113	2	no	—
300	#121	—	113	2	no	—
301	#121	—	113	2	no	—
302	#121	—	113	2	no	—
303	#121	—	113	2	no	—
304	#121	—	113	2	no	—
305	#121	—	113	4	no	—
306	#121	—	113	4	no	—
307	#121	—	113	4	no	—
308	C₄×Q₈	—	113	2	no	—
309	C₄×Q₈	—	113	2	no	—
310	C₄×Q₈	—	113	1	no	—
311	C₄×Q₈	—	113	1	no	—
312	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
313	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
314	C₄×D₄	—	113	1	no	—
315	C₄×D₄	—	113	1	no	—
316	C₄×D₄	—	113	1	no	—
317	C₄×D₄	—	113	1	no	—
318	C₄×D₄	—	113	2	no	—
319	C₄×D₄	—	113	4	no	—
320	C₄×D₄	—	113	2	no	—
321	C₄×D₄	—	113	2	no	—
322	C₄×D₄	—	113	2	no	—
323	C₄×D₄	—	113	1	no	—
324	C₄×D₄	—	113	1	no	—
325	C₄×D₄	—	113	2	no	—
326	C₄×D₄	—	113	4	no	—
327	C₄×D₄	—	113	2	no	—
328	#117	—	113	1	no	—
329	#117	—	113	2	no	—
330	#117	—	113	1	no	—
331	#117	—	113	1	no	—
332	#117	—	113	4	no	—
333	#117	C₂×D₁₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	—	113	2	no	—
335	C₂×C₄⋊C₄	—	113	4	no	—
336	C₂×C₄⋊C₄	—	113	2	no	—
337	C₂×C₄²	—	113	1	no	—
338	C₂×C₄²	—	113	1	no	—
339	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
340	#41	—	452	4	no	—
341	#41	—	452	4	no	—
342	#41	—	226	4	no	—
343	#41	—	226	8	no	—
344	C₂×Q₈	—	113	4	no	—
345	C₂×Q₈	—	113	1	no	—
346	C₂×Q₈	—	113	2	no	—
347	C₂×Q₈	—	452	4	no	—
348	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
349	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
350	C₂×D₄	—	113	4	no	—
351	C₂×D₄	—	113	1	no	—
352	C₂×D₄	—	113	1	no	—
353	C₂×D₄	—	113	4	no	—
354	C₂×D₄	—	113	2	no	—
355	C₂×D₄	—	113	4	no	—
356	C₂×D₄	—	113	1	no	—
357	C₂×D₄	—	113	2	no	—
358	C₂×D₄	—	113	2	no	—
359	C₂²×C₄	—	113	1	no	—
360	C₂²×C₄	—	113	4	no	—
361	C₂²×C₄	—	113	4	no	—
362	C₂²×C₄	—	113	4	no	—
363	C₂²×C₄	—	113	1	no	—
364	C₂²×C₄	—	113	1	no	—
365	C₂²×C₄	—	113	1	no	—
366	C₂²×C₄	—	113	1	no	—
367	C₂²×C₄	—	113	1	no	—
368	C₂²×C₄	—	113	4	no	—
369	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
372	C₄⋊C₄	—	113	1	no	—
373	C₄⋊C₄	—	113	4	no	—
374	C₄⋊C₄	—	113	2	no	—
375	C₄⋊C₄	—	113	2	no	—
376	C₄⋊C₄	—	113	4	no	—
377	C₄⋊C₄	—	113	4	no	—
378	C₄⋊C₄	—	113	1	no	—
379	C₄⋊C₄	—	113	1	no	—
380	C₄⋊C₄	—	113	1	no	—
381	C₄⋊C₄	—	113	1	no	—
382	C₄⋊C₄	—	113	1	no	—
383	C₄⋊C₄	—	113	4	no	—
384	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
385	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
386	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
387	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
388	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
389	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
390	C₂²⋊C₄	—	113	1	no	—
391	C₂²⋊C₄	—	113	1	no	—
392	C₂²⋊C₄	—	113	1	no	—
393	C₂²⋊C₄	—	113	1	no	—
394	C₂²⋊C₄	—	113	4	no	—
395	C₂²⋊C₄	—	113	4	no	—
396	C₂²⋊C₄	—	113	1	no	—
397	C₂²⋊C₄	—	113	1	no	—
398	C₂²⋊C₄	—	113	4	no	—
399	C₂²⋊C₄	—	113	4	no	—
400	C₂²⋊C₄	—	113	4	no	—
401	C₂²⋊C₄	—	113	4	no	—
402	C₂²⋊C₄	—	113	4	no	—
403	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
404	C₄²	—	113	1	no	—
405	C₄²	—	113	1	no	—
406	C₄²	—	113	1	no	—
407	C₄²	—	113	1	no	—
408	C₄²	—	113	1	no	—
409	C₄²	—	113	1	no	—
410	C₄²	—	113	4	no	—
411	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
412	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
413	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
414	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
415	C₄²	C₂²×D₁₁₃	1	4	yes	—
416	C₂³	—	113	1	no	—
417	C₂³	—	113	4	no	—
418	C₂³	—	113	1	no	—
419	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	452	4	no	—
423	Q₈	—	226	2	no	—
424	Q₈	—	226	4	no	—
425	D₄	—	452	4	no	—
426	D₄	—	452	4	no	—
427	D₄	—	226	2	no	—
428	D₄	—	226	8	no	—
429	D₄	—	226	2	no	—
430	D₄	—	226	2	no	—
431	D₄	—	226	4	no	—
432	D₄	—	226	4	no	—
433	D₄	—	226	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	113	1	no	—
438	C₂×C₄	—	113	4	no	—
439	C₂×C₄	—	113	1	no	—
440	C₂×C₄	—	113	1	no	—
441	C₂×C₄	—	113	1	no	—
442	C₂×C₄	—	113	1	no	—
443	C₂×C₄	—	113	1	no	—
444	C₂×C₄	—	113	4	no	—
445	C₂×C₄	—	452	4	no	—
446	C₂×C₄	—	452	4	no	—
447	C₂×C₄	—	452	4	no	—
448	C₂×C₄	—	226	8	no	—
449	C₂×C₄	—	226	2	no	—
450	C₂×C₄	—	226	2	no	—
451	C₂×C₄	—	226	2	no	—
452	C₂×C₄	—	226	2	no	—
453	C₂×C₄	—	226	2	no	—
454	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
455	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
459	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	113	2	no	—
466	C₂²	—	226	4	no	—
467	C₂²	—	226	1	no	—
468	C₂²	—	226	4	no	—
469	C₂²	—	226	1	no	—
470	C₂²	—	226	1	no	—
471	C₂²	—	226	4	no	—
472	C₂²	—	226	1	no	—
473	C₂²	—	226	1	no	—
474	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	1	no	—
480	C₄	—	113	2	no	—
481	C₄	—	226	1	no	—
482	C₄	—	226	1	no	—
483	C₄	—	226	4	no	—
484	C₄	—	226	1	no	—
485	C₄	—	226	1	no	—
486	C₄	—	226	1	no	—
487	C₄	#41×D₁₁₃	1	2	yes	—
488	C₄	#16813668	1	2	yes	—
489	C₄	#16813670	1	2	yes	—
490	C₂	—	4	1	no	—
491	C₂	—	452	4	no	—
492	C₂	—	452	1	no	—
493	C₂	—	226	2	no	—
494	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
495	C₂	C₂×#16813668	1	1	yes	characteristic
496	C₂	C₂×#16813670	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#533×C₁₁₃	C₂
hypercenter	#533	D₁₁₃
hypocenter	C₁₁₃	#3511
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #20299320	C₂	semidirect
2. #20299311	C₂	semidirect
3. #20299304	C₂	semidirect
4. #20299301	C₂	semidirect
5. #20299292	C₂	semidirect
6. #20299260	C₂	semidirect
7. #20299258	C₂	semidirect
8. #20299250	C₂	semidirect
9. #20299221	C₂	semidirect
10. #20299220	C₂	semidirect
11. #20299178	C₂	semidirect
12. #20299153	C₂	semidirect
13. #20299149	C₂	semidirect
14. #20299149	C₂	semidirect
15. #20299148	C₂	semidirect
16. C₄⋊Q₈×D₁₁₃	C₂	semidirect
17. #20299080	C₂	semidirect
18. C₄×#14268647	C₂	semidirect
19. #533×C₁₁₃	C₂	semidirect
209. C₄×D₁₁₃	#41	semidirect
249. C₁₁₃	#3511	semidirect
262. #533	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299320	2
#20299311	2
#20299304	2
#20299301	2
#20299292	2
#20299260	2
#20299258	2
#20299250	2
#20299221	2
#20299220	2
#20299178	2
#20299153	2
#20299149	2
#20299148	2
C₄⋊Q₈×D₁₁₃	2
#20299080	2
C₄×#14268647	2
#533×C₁₁₃	2
#3511	113