Subgroups — #28404005

Order 14464.

1012 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299225	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299222	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299221	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299218	C₂	1	2	yes	maximal, complemented
5	#20299209	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299208	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299207	C₂	1	2	yes	maximal, complemented
8	#20299196	C₂	1	2	yes	maximal, complemented
9	#20299194	C₂	1	2	yes	maximal, complemented
10	#20299178	C₂	1	1	yes	maximal, characteristic
11	#20299173	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299171	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299152	C₂	1	2	yes	maximal, complemented
15	#20299135	C₂	1	2	yes	maximal, complemented
16	#20299135	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299132	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299126	C₂	1	2	yes	maximal, complemented
19	#20299126	C₂	1	2	yes	maximal, complemented
20	C₄×#14268648	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#533×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×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
27	#16813621	C₂²	1	2	yes	—
28	#16813621	C₂²	1	1	yes	characteristic
29	#16813620	C₂²	1	1	yes	characteristic
30	#16813620	C₂²	1	2	yes	—
31	#16813617	C₂²	1	2	yes	—
32	#16813617	C₂²	1	2	yes	—
33	#16813617	C₂²	1	2	yes	—
34	#16813617	C₂²	1	2	yes	—
35	#16813617	C₂²	1	2	yes	—
36	#16813616	C₂²	1	2	yes	—
37	#16813615	C₂²	1	2	yes	—
38	#16813615	C₂²	1	2	yes	—
39	#16813614	C₂²	1	1	yes	characteristic
40	#16813613	C₂²	1	2	yes	—
41	#16813613	C₂²	1	1	yes	characteristic
42	#16813612	C₂²	1	2	yes	—
43	#16813612	C₂²	1	2	yes	—
44	#16813612	C₂²	1	2	yes	—
45	#16813612	C₂²	1	2	yes	—
46	#16813612	C₂²	1	2	yes	—
47	#16813611	C₂²	1	1	yes	characteristic
48	#16813611	C₂²	1	2	yes	—
49	#16813610	C₂²	1	1	yes	characteristic
50	#16813608	C₂²	1	2	yes	—
51	#16813608	C₂²	1	2	yes	—
52	#16813607	C₂²	1	2	yes	—
53	#16813607	C₂²	1	2	yes	—
54	#16813607	C₂²	1	2	yes	—
55	#16813607	C₂²	1	2	yes	—
56	#16813607	C₂²	1	2	yes	—
57	#16813605	C₂²	1	2	yes	—
58	#16813604	C₂²	1	2	yes	—
59	#16813604	C₂²	1	2	yes	—
60	#16813602	C₂²	1	1	yes	characteristic
61	#16813602	C₂²	1	2	yes	—
62	#16813601	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	2	yes	—
67	#16813600	C₂²	1	2	yes	—
68	#16813598	C₂²	1	1	yes	characteristic
69	#16813598	C₂²	1	2	yes	—
70	#16813598	C₂²	1	1	yes	characteristic
71	#16813598	C₂²	1	2	yes	—
72	#16813597	C₂²	1	2	yes	—
73	#16813597	C₂²	1	1	yes	characteristic
74	#16813596	C₂²	1	1	yes	characteristic
75	#16813595	C₂²	1	2	yes	—
76	#16813595	C₂²	1	2	yes	—
77	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
78	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
79	C₄×Dic₂₂₆	C₂²	1	2	yes	—
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	2	yes	—
84	#16813587	C₂²	1	2	yes	—
85	#16813587	C₂²	1	1	yes	characteristic
86	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
87	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
88	C₄×D₄₅₂	C₂²	1	2	yes	—
89	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
90	C₄×D₄₅₂	C₂²	1	2	yes	—
91	#16813584	C₂²	1	2	yes	—
92	#16813584	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
94	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
95	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
96	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
98	#16813581	C₂²	1	1	yes	characteristic
99	#16813580	C₂²	1	1	yes	characteristic
100	#16813580	C₂²	1	2	yes	—
101	#16813579	C₂²	1	1	yes	characteristic
102	#16813579	C₂²	1	1	yes	characteristic
103	#16813579	C₂²	1	2	yes	—
104	#16813579	C₂²	1	2	yes	—
105	#16813579	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
108	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
109	C₄²×D₁₁₃	C₂²	1	2	yes	—
110	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
111	C₄²×D₁₁₃	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
113	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
114	#125×C₁₁₃	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×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	2	yes	—
121	#117×C₁₁₃	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
123	#14268648	—	2	4	no	—
124	#14268647	—	2	4	no	—
125	C₂×Dic₂₂₆	C₂³	1	2	yes	—
126	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
128	C₂×Dic₂₂₆	C₂³	1	2	yes	—
129	Q₈×D₁₁₃	—	2	4	no	—
130	C₂×D₄₅₂	C₂³	1	2	yes	—
131	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
132	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
133	C₂×D₄₅₂	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₁₃	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	1	yes	characteristic
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	1	yes	characteristic
146	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
150	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
152	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
155	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	2	yes	—
158	#14268626	C₂³	1	2	yes	—
159	#14268626	C₂³	1	1	yes	characteristic
160	#14268626	C₂³	1	1	yes	characteristic
161	#14268626	C₂³	1	1	yes	characteristic
162	#14268626	C₂³	1	1	yes	characteristic
163	#14268626	C₂³	1	2	yes	—
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	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
175	#14268624	C₂³	1	1	yes	characteristic
176	#14268624	C₂³	1	1	yes	characteristic
177	#14268624	C₂³	1	1	yes	characteristic
178	#14268624	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	2	yes	—
180	#14268624	C₂³	1	2	yes	—
181	#14268624	C₂³	1	2	yes	—
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	2	yes	—
190	#14268624	C₂³	1	2	yes	—
191	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₁₃	C₂³	1	2	yes	—
193	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
205	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
210	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
211	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
217	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
219	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
220	C₄²×C₁₁₃	C₂³	1	2	yes	—
221	C₄²×C₁₁₃	C₂³	1	2	yes	—
222	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
223	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
224	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
225	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
227	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
229	Q₈×C₁₁₃	—	2	2	no	—
230	Q₈×C₁₁₃	—	2	2	no	—
231	Q₈×C₁₁₃	—	4	2	no	—
232	C₂×C₄×C₁₁₃	—	2	2	no	—
233	C₂×C₄×C₁₁₃	—	2	2	no	—
234	C₂×C₄×C₁₁₃	—	4	1	no	—
235	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
242	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₁₁₃	—	2	2	no	—
246	C₂²⋊D₁₁₃	—	2	2	no	—
247	C₂²⋊D₁₁₃	—	4	2	no	—
248	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
256	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
257	D₄₅₂	—	2	2	no	—
258	D₄₅₂	—	2	4	no	—
259	D₄₅₂	—	2	2	no	—
260	D₄₅₂	—	4	2	no	—
261	C₄×D₁₁₃	—	2	4	no	—
262	C₄×D₁₁₃	—	2	2	no	—
263	C₄×D₁₁₃	—	2	2	no	—
264	C₄×D₁₁₃	—	2	2	no	—
265	C₄×D₁₁₃	—	2	4	no	—
266	C₄×D₁₁₃	—	2	4	no	—
267	C₄×D₁₁₃	—	4	1	no	—
268	C₄×D₁₁₃	—	4	2	no	—
269	C₄×D₁₁₃	—	4	2	no	—
270	C₄×D₁₁₃	—	4	1	no	—
271	C₄×D₁₁₃	#41	1	4	yes	—
272	Dic₂₂₆	—	2	2	no	—
273	Dic₂₂₆	—	2	4	no	—
274	Dic₂₂₆	—	2	2	no	—
275	Dic₂₂₆	—	4	2	no	—
276	C₂²×C₁₁₃	—	2	1	no	—
277	C₂²×C₁₁₃	—	2	1	no	—
278	C₂²×C₁₁₃	—	2	1	no	—
279	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
280	C₂×D₁₁₃	—	2	1	no	—
281	C₂×D₁₁₃	—	2	1	no	—
282	C₂×D₁₁₃	—	2	2	no	—
283	C₂×D₁₁₃	—	2	1	no	—
284	C₂×D₁₁₃	—	2	2	no	—
285	C₂×D₁₁₃	—	2	1	no	—
286	C₂×D₁₁₃	—	2	1	no	—
287	C₂×D₁₁₃	—	2	2	no	—
288	C₂×D₁₁₃	C₂×#41	1	2	yes	—
289	C₄×C₁₁₃	—	2	2	no	—
290	C₄×C₁₁₃	—	2	1	no	—
291	C₄×C₁₁₃	—	2	2	no	—
292	C₄×C₁₁₃	—	2	1	no	—
293	C₄×C₁₁₃	—	2	2	no	—
294	C₄×C₁₁₃	—	2	1	no	—
295	C₄×C₁₁₃	—	2	2	no	—
296	C₄×C₁₁₃	—	2	1	no	—
297	C₄×C₁₁₃	C₂×#41	1	2	yes	—
298	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
299	Dic₁₁₃	—	2	2	no	—
300	Dic₁₁₃	—	2	1	no	—
301	Dic₁₁₃	—	2	1	no	—
302	Dic₁₁₃	—	2	1	no	—
303	Dic₁₁₃	—	2	2	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	—	2	2	no	—
306	Dic₁₁₃	—	2	1	no	—
307	Dic₁₁₃	C₂×#41	1	2	yes	—
308	C₂×C₁₁₃	—	4	1	no	—
309	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
310	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×C₁₁₃	#585	1	1	yes	characteristic
312	D₁₁₃	—	2	2	no	—
313	D₁₁₃	—	4	2	no	—
314	D₁₁₃	—	4	1	no	—
315	#3461	—	113	1	no	maximal, Sylow
316	C₁₁₃	#3461	1	1	yes	characteristic, complemented, Sylow
317	#544	—	113	1	no	—
318	#542	—	113	1	no	—
319	#542	—	113	2	no	—
320	#542	—	113	1	no	—
321	#541	—	113	1	no	—
322	#541	—	113	2	no	—
323	#541	—	113	1	no	—
324	#539	—	113	2	no	—
325	#539	—	113	2	no	—
326	#537	—	113	1	no	—
327	#536	—	113	1	no	—
328	#536	—	113	1	no	—
329	#533	—	113	2	no	—
330	#533	—	113	1	no	—
331	#533	D₁₁₃	1	1	yes	characteristic, complemented
332	#529	—	113	2	no	—
333	#529	—	113	1	no	—
334	#529	—	113	2	no	—
335	#529	—	113	2	no	—
336	#529	—	113	1	no	—
337	C₄×#41	—	113	1	no	—
338	C₄×#41	—	113	1	no	—
339	C₂×C₄×Q₈	—	113	1	no	—
340	C₂×#41	—	113	1	no	—
341	C₂×#41	—	113	1	no	—
342	C₂²×Q₈	—	113	1	no	—
343	C₄⋊Q₈	—	113	1	no	—
344	C₄⋊Q₈	—	113	2	no	—
345	C₄⋊Q₈	—	113	2	no	—
346	C₄⋊Q₈	—	113	1	no	—
347	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
348	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
349	#126	—	113	2	no	—
350	#126	—	113	2	no	—
351	#126	—	113	2	no	—
352	#126	—	113	2	no	—
353	#126	—	113	2	no	—
354	#126	—	113	2	no	—
355	#126	—	113	2	no	—
356	#126	—	113	2	no	—
357	#125	—	113	2	no	—
358	#125	—	113	2	no	—
359	#125	—	113	2	no	—
360	#125	—	113	1	no	—
361	#125	—	113	2	no	—
362	#125	—	113	2	no	—
363	#125	—	113	2	no	—
364	#125	—	113	1	no	—
365	#125	C₂×D₁₁₃	1	2	yes	—
366	#124	—	113	1	no	—
367	#124	—	113	2	no	—
368	#124	—	113	2	no	—
369	#124	—	113	2	no	—
370	#124	—	113	1	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	#123	—	113	2	no	—
379	C₂²⋊Q₈	—	113	1	no	—
380	C₂²⋊Q₈	—	113	2	no	—
381	C₂²⋊Q₈	—	113	1	no	—
382	C₂²⋊Q₈	—	113	2	no	—
383	C₂²⋊Q₈	—	113	1	no	—
384	C₂²⋊Q₈	—	113	2	no	—
385	C₂²⋊Q₈	—	113	2	no	—
386	C₂²⋊Q₈	—	113	2	no	—
387	C₂²⋊Q₈	—	113	1	no	—
388	C₂²⋊Q₈	—	113	2	no	—
389	C₂²⋊Q₈	—	113	2	no	—
390	C₂²⋊Q₈	—	113	2	no	—
391	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
393	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
394	#121	—	113	1	no	—
395	#121	—	113	2	no	—
396	#121	—	113	1	no	—
397	#121	—	113	2	no	—
398	#121	—	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	2	no	—
404	C₄×Q₈	—	113	1	no	—
405	C₄×Q₈	—	113	1	no	—
406	C₄×Q₈	—	113	1	no	—
407	C₄×Q₈	—	113	2	no	—
408	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
409	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
410	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
411	C₄×D₄	—	113	1	no	—
412	C₄×D₄	—	113	1	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	1	no	—
418	C₄×D₄	—	113	1	no	—
419	C₄×D₄	—	113	2	no	—
420	C₄×D₄	—	113	1	no	—
421	C₄×D₄	—	113	1	no	—
422	C₄×D₄	—	113	2	no	—
423	#117	—	113	1	no	—
424	#117	—	113	1	no	—
425	#117	—	113	2	no	—
426	#117	—	113	1	no	—
427	#117	—	113	1	no	—
428	#117	—	113	2	no	—
429	#117	—	113	2	no	—
430	#117	—	113	2	no	—
431	#117	C₂×D₁₁₃	1	2	yes	—
432	C₂×C₄⋊C₄	—	113	1	no	—
433	C₂×C₄⋊C₄	—	113	2	no	—
434	C₂×C₄²	—	113	1	no	—
435	C₂×C₄²	—	113	2	no	—
436	C₂×C₄²	—	113	2	no	—
437	C₂×C₄²	—	113	1	no	—
438	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
439	#41	—	226	4	no	—
440	#41	—	226	4	no	—
441	C₂×Q₈	—	113	2	no	—
442	C₂×Q₈	—	113	2	no	—
443	C₂×Q₈	—	113	1	no	—
444	C₂×Q₈	—	113	1	no	—
445	C₂×Q₈	—	226	4	no	—
446	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
449	C₂×D₄	—	113	2	no	—
450	C₂×D₄	—	113	1	no	—
451	C₂×D₄	—	113	1	no	—
452	C₂×D₄	—	113	2	no	—
453	C₂×D₄	—	113	2	no	—
454	C₂×D₄	—	113	1	no	—
455	C₂×D₄	—	113	1	no	—
456	C₂²×C₄	—	113	1	no	—
457	C₂²×C₄	—	113	1	no	—
458	C₂²×C₄	—	113	2	no	—
459	C₂²×C₄	—	113	2	no	—
460	C₂²×C₄	—	113	1	no	—
461	C₂²×C₄	—	113	2	no	—
462	C₂²×C₄	—	113	2	no	—
463	C₂²×C₄	—	113	1	no	—
464	C₂²×C₄	—	113	1	no	—
465	C₂²×C₄	—	113	1	no	—
466	C₂²×C₄	—	113	2	no	—
467	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
470	C₄⋊C₄	—	113	2	no	—
471	C₄⋊C₄	—	113	1	no	—
472	C₄⋊C₄	—	113	2	no	—
473	C₄⋊C₄	—	113	2	no	—
474	C₄⋊C₄	—	113	2	no	—
475	C₄⋊C₄	—	113	1	no	—
476	C₄⋊C₄	—	113	1	no	—
477	C₄⋊C₄	—	113	1	no	—
478	C₄⋊C₄	—	113	1	no	—
479	C₄⋊C₄	—	113	1	no	—
480	C₄⋊C₄	—	113	1	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	2	no	—
489	C₄⋊C₄	—	113	2	no	—
490	C₄⋊C₄	—	113	2	no	—
491	C₄⋊C₄	—	113	2	no	—
492	C₄⋊C₄	—	113	2	no	—
493	C₄⋊C₄	—	113	2	no	—
494	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
496	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
497	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
503	C₂²⋊C₄	—	113	1	no	—
504	C₂²⋊C₄	—	113	1	no	—
505	C₂²⋊C₄	—	113	2	no	—
506	C₂²⋊C₄	—	113	2	no	—
507	C₂²⋊C₄	—	113	1	no	—
508	C₂²⋊C₄	—	113	1	no	—
509	C₂²⋊C₄	—	113	1	no	—
510	C₂²⋊C₄	—	113	2	no	—
511	C₂²⋊C₄	—	113	2	no	—
512	C₂²⋊C₄	—	113	1	no	—
513	C₂²⋊C₄	—	113	2	no	—
514	C₂²⋊C₄	—	113	2	no	—
515	C₂²⋊C₄	—	113	2	no	—
516	C₂²⋊C₄	—	113	2	no	—
517	C₂²⋊C₄	—	113	2	no	—
518	C₂²⋊C₄	—	113	2	no	—
519	C₂²⋊C₄	—	113	2	no	—
520	C₂²⋊C₄	—	113	2	no	—
521	C₂²⋊C₄	—	113	2	no	—
522	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
524	C₄²	—	113	1	no	—
525	C₄²	—	113	1	no	—
526	C₄²	—	113	2	no	—
527	C₄²	—	113	1	no	—
528	C₄²	—	113	2	no	—
529	C₄²	—	113	1	no	—
530	C₄²	—	113	2	no	—
531	C₄²	—	113	2	no	—
532	C₄²	—	113	1	no	—
533	C₄²	—	113	2	no	—
534	C₄²	—	113	1	no	—
535	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
536	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
537	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
538	C₄²	C₂²×D₁₁₃	1	2	yes	—
539	C₄²	C₂²×D₁₁₃	1	2	yes	—
540	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
541	C₂³	—	113	1	no	—
542	C₂³	—	113	2	no	—
543	C₂³	—	113	1	no	—
544	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	452	2	no	—
549	Q₈	—	226	4	no	—
550	Q₈	—	226	2	no	—
551	Q₈	—	226	2	no	—
552	D₄	—	452	2	no	—
553	D₄	—	452	2	no	—
554	D₄	—	226	2	no	—
555	D₄	—	226	4	no	—
556	D₄	—	226	2	no	—
557	D₄	—	226	2	no	—
558	D₄	—	226	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	113	1	no	—
563	C₂×C₄	—	113	4	no	—
564	C₂×C₄	—	113	1	no	—
565	C₂×C₄	—	113	1	no	—
566	C₂×C₄	—	113	1	no	—
567	C₂×C₄	—	113	2	no	—
568	C₂×C₄	—	113	2	no	—
569	C₂×C₄	—	113	1	no	—
570	C₂×C₄	—	113	1	no	—
571	C₂×C₄	—	113	2	no	—
572	C₂×C₄	—	452	1	no	—
573	C₂×C₄	—	452	1	no	—
574	C₂×C₄	—	452	2	no	—
575	C₂×C₄	—	452	2	no	—
576	C₂×C₄	—	226	4	no	—
577	C₂×C₄	—	226	4	no	—
578	C₂×C₄	—	226	2	no	—
579	C₂×C₄	—	226	2	no	—
580	C₂×C₄	—	226	4	no	—
581	C₂×C₄	—	226	2	no	—
582	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
584	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
585	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
586	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
587	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	113	2	no	—
596	C₂²	—	226	2	no	—
597	C₂²	—	226	1	no	—
598	C₂²	—	226	2	no	—
599	C₂²	—	226	1	no	—
600	C₂²	—	226	1	no	—
601	C₂²	—	226	2	no	—
602	C₂²	—	226	1	no	—
603	C₂²	—	226	1	no	—
604	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	113	2	no	—
614	C₄	—	226	1	no	—
615	C₄	—	226	2	no	—
616	C₄	—	226	1	no	—
617	C₄	—	226	1	no	—
618	C₄	—	226	2	no	—
619	C₄	—	226	1	no	—
620	C₄	—	226	2	no	—
621	C₄	—	226	1	no	—
622	C₄	#41×D₁₁₃	1	2	yes	—
623	C₄	#16813670	1	2	yes	—
624	C₂	—	4	1	no	—
625	C₂	—	452	2	no	—
626	C₂	—	452	1	no	—
627	C₂	—	226	2	no	—
628	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
629	C₂	C₂×#16813670	1	1	yes	characteristic
630	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	#533×C₁₁₃	C₂
prime radical	#20299178	C₂
hypercenter	#533	D₁₁₃
hypocenter	C₁₁₃	#3461
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #533

Complements

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

N	H ≅ G/N	type
1. #20299225	C₂	semidirect
2. #20299222	C₂	semidirect
3. #20299221	C₂	semidirect
4. #20299218	C₂	semidirect
5. #20299209	C₂	semidirect
6. #20299208	C₂	semidirect
7. #20299207	C₂	semidirect
8. #20299196	C₂	semidirect
9. #20299194	C₂	semidirect
11. #20299173	C₂	semidirect
12. #20299171	C₂	semidirect
13. #20299152	C₂	semidirect
14. #20299152	C₂	semidirect
15. #20299135	C₂	semidirect
16. #20299135	C₂	semidirect
17. #20299132	C₂	semidirect
18. #20299126	C₂	semidirect
19. #20299126	C₂	semidirect
20. C₄×#14268648	C₂	semidirect
21. C₄×#14268647	C₂	semidirect
22. C₄×Q₈×D₁₁₃	C₂	semidirect
23. #533×C₁₁₃	C₂	semidirect
316. C₁₁₃	#3461	semidirect
331. #533	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299225	2
#20299222	2
#20299221	2
#20299218	2
#20299209	2
#20299208	2
#20299207	2
#20299196	2
#20299194	2
#20299178	2
#20299173	2
#20299171	2
#20299152	2
#20299135	2
#20299132	2
#20299126	2
C₄×#14268648	2
C₄×#14268647	2
C₄×Q₈×D₁₁₃	2
#533×C₁₁₃	2
#3461	113