Subgroups — #28404467

Order 14464.

1040 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	#20299334	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299331	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299330	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299321	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299320	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299318	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299317	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299278	C₂	1	2	yes	maximal, complemented
9	#20299277	C₂	1	2	yes	maximal, complemented
10	#20299276	C₂	1	2	yes	maximal, complemented
11	#20299271	C₂	1	2	yes	maximal, complemented
12	#20299216	C₂	1	2	yes	maximal, complemented
13	#20299212	C₂	1	2	yes	maximal, complemented
14	#20299168	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299161	C₂	1	1	yes	maximal, characteristic
16	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299128	C₂	1	2	yes	maximal, complemented
18	#20299125	C₂	1	2	yes	maximal, complemented
19	#124×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#20299074	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14268646	C₂	1	1	yes	maximal, characteristic, complemented
23	#559×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268646	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
27	#16813622	C₂²	1	1	yes	characteristic, complemented
28	#16813621	C₂²	1	1	yes	characteristic, complemented
29	#16813620	C₂²	1	1	yes	characteristic, complemented
30	#16813620	C₂²	1	1	yes	characteristic, complemented
31	#16813618	C₂²	1	1	yes	characteristic
32	#16813617	C₂²	1	2	yes	complemented
33	#16813617	C₂²	1	2	yes	complemented
34	#16813617	C₂²	1	2	yes	complemented
35	#16813616	C₂²	1	2	yes	complemented
36	#16813615	C₂²	1	2	yes	complemented
37	#16813615	C₂²	1	2	yes	complemented
38	#16813615	C₂²	1	2	yes	complemented
39	#16813615	C₂²	1	2	yes	complemented
40	#16813612	C₂²	1	1	yes	characteristic, complemented
41	#16813612	C₂²	1	1	yes	characteristic, complemented
42	#16813611	C₂²	1	1	yes	characteristic
43	#16813610	C₂²	1	1	yes	characteristic
44	#16813610	C₂²	1	1	yes	characteristic
45	#16813609	C₂²	1	1	yes	characteristic
46	#16813609	C₂²	1	1	yes	characteristic
47	#16813609	C₂²	1	2	yes	complemented
48	#16813609	C₂²	1	1	yes	characteristic, complemented
49	#16813608	C₂²	1	2	yes	—
50	#16813608	C₂²	1	2	yes	—
51	#16813608	C₂²	1	2	yes	complemented
52	#16813608	C₂²	1	2	yes	complemented
53	#16813606	C₂²	1	2	yes	complemented
54	#16813605	C₂²	1	2	yes	complemented
55	#16813604	C₂²	1	2	yes	—
56	#16813604	C₂²	1	2	yes	—
57	#16813604	C₂²	1	2	yes	complemented
58	#16813604	C₂²	1	2	yes	complemented
59	#16813603	C₂²	1	2	yes	complemented
60	#16813603	C₂²	1	2	yes	complemented
61	#16813602	C₂²	1	1	yes	characteristic
62	#16813601	C₂²	1	2	yes	complemented
63	#16813600	C₂²	1	1	yes	characteristic
64	#16813600	C₂²	1	1	yes	characteristic
65	#16813600	C₂²	1	2	yes	complemented
66	#16813599	C₂²	1	2	yes	complemented
67	#16813599	C₂²	1	2	yes	complemented
68	#16813599	C₂²	1	2	yes	complemented
69	#16813598	C₂²	1	1	yes	characteristic
70	#16813598	C₂²	1	2	yes	complemented
71	#16813594	C₂²	1	2	yes	—
72	#16813594	C₂²	1	2	yes	—
73	#16813590	C₂²	1	2	yes	—
74	#16813590	C₂²	1	2	yes	—
75	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
82	#16813587	C₂²	1	1	yes	characteristic, complemented
83	#16813587	C₂²	1	1	yes	characteristic, complemented
84	#16813587	C₂²	1	2	yes	complemented
85	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
86	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
87	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
88	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
89	#16813584	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
93	#16813582	C₂²	1	2	yes	—
94	#16813582	C₂²	1	2	yes	—
95	#16813582	C₂²	1	2	yes	complemented
96	#16813581	C₂²	1	2	yes	complemented
97	#16813580	C₂²	1	2	yes	—
98	#16813580	C₂²	1	1	yes	characteristic
99	#16813580	C₂²	1	2	yes	complemented
100	#16813579	C₂²	1	2	yes	—
101	#16813579	C₂²	1	1	yes	characteristic
102	#16813579	C₂²	1	1	yes	characteristic
103	#16813579	C₂²	1	2	yes	complemented
104	#16813578	C₂²	1	2	yes	complemented
105	#16813578	C₂²	1	2	yes	complemented
106	C₂×#14268624	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
112	#127×C₁₁₃	C₂²	1	1	yes	characteristic
113	#124×C₁₁₃	C₂²	1	1	yes	characteristic
114	#124×C₁₁₃	C₂²	1	2	yes	complemented
115	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
116	#123×C₁₁₃	C₂²	1	2	yes	complemented
117	#123×C₁₁₃	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁₃	C₂³	1	2	yes	—
124	#14268646	—	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	1	yes	characteristic
129	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
131	Q₈×D₁₁₃	—	2	4	no	—
132	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
137	D₄×D₁₁₃	—	2	4	no	—
138	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
139	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
140	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
142	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
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	#14268626	C₂³	1	1	yes	characteristic
155	#14268626	C₂³	1	2	yes	—
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	2	yes	—
158	#14268626	C₂³	1	1	yes	characteristic
159	#14268626	C₂³	1	1	yes	characteristic
160	#14268626	C₂³	1	1	yes	characteristic
161	#14268626	C₂³	1	2	yes	—
162	#14268626	C₂³	1	1	yes	characteristic
163	#14268626	C₂³	1	2	yes	—
164	#14268626	C₂³	1	1	yes	characteristic
165	#14268626	C₂³	1	2	yes	—
166	#14268626	C₂³	1	1	yes	characteristic
167	#14268626	C₂³	1	1	yes	characteristic
168	#14268626	C₂³	1	1	yes	characteristic
169	#14268626	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
185	#14268624	C₂³	1	2	yes	—
186	#14268624	C₂³	1	2	yes	—
187	#14268624	C₂³	1	1	yes	characteristic
188	#14268624	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
193	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₁₃	C₂³	1	2	yes	—
195	C₄×Dic₁₁₃	C₂³	1	2	yes	—
196	C₄×Dic₁₁₃	C₂³	1	2	yes	—
197	C₄×Dic₁₁₃	C₂³	1	2	yes	—
198	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
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×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
207	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
208	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
209	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
210	C₄⋊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	1	yes	characteristic
215	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₂²⋊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	C₄²×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	1	yes	characteristic
225	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
226	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
227	C₂²×D₁₁₃	—	2	4	no	—
228	C₂²×D₁₁₃	—	4	2	no	—
229	C₂²×D₁₁₃	—	4	2	no	—
230	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
232	Q₈×C₁₁₃	—	2	2	no	—
233	Q₈×C₁₁₃	—	4	1	no	—
234	D₄×C₁₁₃	—	2	2	no	—
235	D₄×C₁₁₃	—	2	2	no	—
236	D₄×C₁₁₃	—	4	2	no	—
237	D₄×C₁₁₃	—	4	2	no	—
238	C₂×C₄×C₁₁₃	—	4	2	no	—
239	C₂×C₄×C₁₁₃	—	4	2	no	—
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	1	yes	characteristic
245	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₁₃	—	2	4	no	—
250	C₂²⋊D₁₁₃	—	2	4	no	—
251	C₂²⋊D₁₁₃	—	4	2	no	—
252	C₂²⋊D₁₁₃	—	4	2	no	—
253	C₂×Dic₁₁₃	—	2	4	no	—
254	C₂×Dic₁₁₃	—	4	2	no	—
255	C₂×Dic₁₁₃	—	4	2	no	—
256	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
258	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
263	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
266	D₄₅₂	—	2	2	no	—
267	C₄×D₁₁₃	—	2	4	no	—
268	C₄×D₁₁₃	—	4	1	no	—
269	C₄×D₁₁₃	—	4	2	no	—
270	C₄×D₁₁₃	—	4	1	no	—
271	C₄×D₁₁₃	—	4	2	no	—
272	C₄×D₁₁₃	#41	1	4	yes	—
273	Dic₂₂₆	—	2	2	no	—
274	Dic₂₂₆	—	2	2	no	—
275	Dic₂₂₆	—	2	4	no	—
276	Dic₂₂₆	—	4	1	no	—
277	Dic₂₂₆	—	4	1	no	—
278	Dic₂₂₆	—	4	1	no	—
279	C₂²×C₁₁₃	—	2	2	no	—
280	C₂²×C₁₁₃	—	2	2	no	—
281	C₂²×C₁₁₃	—	2	2	no	—
282	C₂²×C₁₁₃	—	2	2	no	—
283	C₂²×C₁₁₃	—	2	2	no	—
284	C₂²×C₁₁₃	—	2	2	no	—
285	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
286	C₂×D₁₁₃	—	2	1	no	—
287	C₂×D₁₁₃	—	2	1	no	—
288	C₂×D₁₁₃	—	2	2	no	—
289	C₂×D₁₁₃	—	2	2	no	—
290	C₂×D₁₁₃	—	2	2	no	—
291	C₂×D₁₁₃	—	8	4	no	—
292	C₂×D₁₁₃	C₂×#41	1	2	yes	—
293	C₄×C₁₁₃	—	2	2	no	—
294	C₄×C₁₁₃	—	2	1	no	—
295	C₄×C₁₁₃	—	2	1	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	—	2	1	no	—
301	C₄×C₁₁₃	C₂×#41	1	2	yes	—
302	Dic₁₁₃	—	2	2	no	—
303	Dic₁₁₃	—	2	2	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	—	2	1	no	—
306	Dic₁₁₃	—	2	1	no	—
307	Dic₁₁₃	—	2	1	no	—
308	Dic₁₁₃	—	2	1	no	—
309	Dic₁₁₃	—	2	1	no	—
310	Dic₁₁₃	—	2	2	no	—
311	Dic₁₁₃	C₂×#41	1	2	yes	—
312	C₂×C₁₁₃	—	4	2	no	—
313	C₂×C₁₁₃	—	4	2	no	—
314	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
315	C₂×C₁₁₃	#585	1	1	yes	characteristic
316	C₂×C₁₁₃	#585	1	1	yes	characteristic
317	D₁₁₃	—	2	2	no	—
318	D₁₁₃	—	4	2	no	—
319	#3510	—	113	1	no	maximal, Sylow
320	C₁₁₃	#3510	1	1	yes	characteristic, complemented, Sylow
321	#559	—	113	1	no	—
322	#559	—	113	1	no	—
323	#559	—	113	1	no	—
324	#559	D₁₁₃	1	1	yes	characteristic, complemented
325	#556	—	113	1	no	—
326	#556	—	113	1	no	—
327	#556	—	113	1	no	—
328	#556	—	113	1	no	—
329	#551	—	113	2	no	—
330	#551	—	113	2	no	—
331	#551	—	113	2	no	—
332	#551	—	113	2	no	—
333	#542	—	113	2	no	—
334	#542	—	113	2	no	—
335	#536	—	113	1	no	—
336	#535	—	113	1	no	—
337	#533	—	113	1	no	—
338	#529	—	113	2	no	—
339	#529	—	113	2	no	—
340	C₂×#124	—	113	1	no	—
341	#519	—	113	1	no	—
342	#518	—	113	1	no	—
343	C₄×#41	—	113	1	no	—
344	C₂×#41	—	113	1	no	—
345	C₂²×Q₈	—	113	1	no	—
346	C₂²×D₄	—	113	1	no	—
347	C₄⋊Q₈	—	113	1	no	—
348	C₄⋊Q₈	—	113	1	no	—
349	C₄⋊Q₈	—	113	1	no	—
350	C₄⋊Q₈	—	113	1	no	—
351	#127	—	113	1	no	—
352	#127	C₂×D₁₁₃	1	1	yes	characteristic
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	—	113	2	no	—
359	#126	—	113	2	no	—
360	#126	—	113	2	no	—
361	#125	—	113	1	no	—
362	#125	—	113	1	no	—
363	#124	—	113	1	no	—
364	#124	—	113	1	no	—
365	#124	—	113	1	no	—
366	#124	—	113	1	no	—
367	#124	—	113	2	no	—
368	#124	—	113	2	no	—
369	#124	—	113	2	no	—
370	#124	—	113	2	no	—
371	#124	—	113	2	no	—
372	#124	—	113	1	no	—
373	#124	—	113	1	no	—
374	#124	C₂×D₁₁₃	1	1	yes	characteristic
375	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
376	#124	C₂×D₁₁₃	1	2	yes	complemented
377	#123	—	113	2	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	complemented
386	#123	C₂×D₁₁₃	1	2	yes	complemented
387	C₂²⋊Q₈	—	113	1	no	—
388	C₂²⋊Q₈	—	113	2	no	—
389	C₂²⋊Q₈	—	113	2	no	—
390	C₂²⋊Q₈	—	113	1	no	—
391	C₂²⋊Q₈	—	113	1	no	—
392	C₂²⋊Q₈	—	113	1	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	#121	—	113	2	no	—
398	#121	—	113	2	no	—
399	#120	—	113	2	no	—
400	#120	—	113	2	no	—
401	C₄×Q₈	—	113	1	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	2	no	—
407	C₄×Q₈	—	113	1	no	—
408	C₄×Q₈	—	113	1	no	—
409	C₄×Q₈	—	113	1	no	—
410	C₄×Q₈	—	113	1	no	—
411	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
412	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
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	2	no	—
419	C₄×D₄	—	113	1	no	—
420	C₄×D₄	—	113	2	no	—
421	C₄×D₄	—	113	2	no	—
422	C₄×D₄	—	113	2	no	—
423	C₄×D₄	—	113	1	no	—
424	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
425	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
426	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
427	#117	—	113	2	no	—
428	#117	—	113	1	no	—
429	#117	—	113	2	no	—
430	#117	—	113	2	no	—
431	#117	—	113	2	no	—
432	#117	—	113	2	no	—
433	#117	—	113	1	no	—
434	#117	—	113	1	no	—
435	#117	—	113	2	no	—
436	#117	—	113	2	no	—
437	C₂×C₂²⋊C₄	—	113	2	no	—
438	C₂×C₂²⋊C₄	—	113	2	no	—
439	C₂×C₂²⋊C₄	—	113	2	no	—
440	C₂×C₂²⋊C₄	—	113	2	no	—
441	C₂×C₄²	—	113	2	no	—
442	C₂×C₄²	—	113	1	no	—
443	C₂⁴	—	113	2	no	—
444	#41	—	226	4	no	—
445	C₂×Q₈	—	113	1	no	—
446	C₂×Q₈	—	113	1	no	—
447	C₂×Q₈	—	113	1	no	—
448	C₂×Q₈	—	113	2	no	—
449	C₂×Q₈	—	113	1	no	—
450	C₂×Q₈	—	113	1	no	—
451	C₂×Q₈	—	226	4	no	—
452	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
453	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
454	C₂×D₄	—	113	2	no	—
455	C₂×D₄	—	113	2	no	—
456	C₂×D₄	—	113	2	no	—
457	C₂×D₄	—	113	2	no	—
458	C₂×D₄	—	113	1	no	—
459	C₂×D₄	—	226	4	no	—
460	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
462	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
463	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
464	C₂²×C₄	—	113	1	no	—
465	C₂²×C₄	—	113	2	no	—
466	C₂²×C₄	—	113	2	no	—
467	C₂²×C₄	—	113	2	no	—
468	C₂²×C₄	—	113	1	no	—
469	C₂²×C₄	—	113	1	no	—
470	C₂²×C₄	—	113	2	no	—
471	C₂²×C₄	—	113	2	no	—
472	C₂²×C₄	—	113	2	no	—
473	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
474	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
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	2	no	—
483	C₄⋊C₄	—	113	1	no	—
484	C₄⋊C₄	—	113	1	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	1	no	—
493	C₄⋊C₄	—	113	1	no	—
494	C₄⋊C₄	—	113	1	no	—
495	C₄⋊C₄	—	113	1	no	—
496	C₄⋊C₄	—	113	1	no	—
497	C₄⋊C₄	—	113	1	no	—
498	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
503	C₂²⋊C₄	—	113	2	no	—
504	C₂²⋊C₄	—	113	2	no	—
505	C₂²⋊C₄	—	113	2	no	—
506	C₂²⋊C₄	—	113	2	no	—
507	C₂²⋊C₄	—	113	2	no	—
508	C₂²⋊C₄	—	113	2	no	—
509	C₂²⋊C₄	—	113	2	no	—
510	C₂²⋊C₄	—	113	2	no	—
511	C₂²⋊C₄	—	113	2	no	—
512	C₂²⋊C₄	—	113	1	no	—
513	C₂²⋊C₄	—	113	1	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	1	no	—
521	C₂²⋊C₄	—	113	1	no	—
522	C₂²⋊C₄	—	113	2	no	—
523	C₂²⋊C₄	—	113	2	no	—
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	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
530	C₄²	—	113	1	no	—
531	C₄²	—	113	2	no	—
532	C₄²	—	113	2	no	—
533	C₄²	—	113	2	no	—
534	C₄²	—	113	1	no	—
535	C₄²	—	113	1	no	—
536	C₄²	—	113	2	no	—
537	C₄²	—	113	2	no	—
538	C₄²	—	113	2	no	—
539	C₄²	—	113	1	no	—
540	C₄²	—	113	1	no	—
541	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
542	C₄²	C₂²×D₁₁₃	1	2	yes	—
543	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
544	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
545	C₂³	—	113	1	no	—
546	C₂³	—	113	2	no	—
547	C₂³	—	452	2	no	—
548	C₂³	—	452	2	no	—
549	C₂³	—	226	4	no	—
550	C₂³	C₂³×D₁₁₃	1	2	yes	—
551	C₂³	C₂³×D₁₁₃	1	2	yes	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	452	1	no	—
555	Q₈	—	452	1	no	—
556	Q₈	—	452	1	no	—
557	Q₈	—	226	4	no	—
558	Q₈	—	226	2	no	—
559	Q₈	—	226	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	452	2	no	—
565	D₄	—	452	2	no	—
566	D₄	—	226	4	no	—
567	D₄	—	226	4	no	—
568	D₄	—	226	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	113	1	no	—
572	C₂×C₄	—	113	4	no	—
573	C₂×C₄	—	113	1	no	—
574	C₂×C₄	—	113	2	no	—
575	C₂×C₄	—	113	1	no	—
576	C₂×C₄	—	113	1	no	—
577	C₂×C₄	—	113	2	no	—
578	C₂×C₄	—	113	1	no	—
579	C₂×C₄	—	113	2	no	—
580	C₂×C₄	—	113	1	no	—
581	C₂×C₄	—	113	1	no	—
582	C₂×C₄	—	452	2	no	—
583	C₂×C₄	—	452	1	no	—
584	C₂×C₄	—	452	2	no	—
585	C₂×C₄	—	452	1	no	—
586	C₂×C₄	—	452	2	no	—
587	C₂×C₄	—	452	2	no	—
588	C₂×C₄	—	226	4	no	—
589	C₂×C₄	—	226	4	no	—
590	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
592	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
594	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
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	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	113	2	no	—
606	C₂²	—	904	4	no	—
607	C₂²	—	226	2	no	—
608	C₂²	—	226	2	no	—
609	C₂²	—	226	2	no	—
610	C₂²	—	226	1	no	—
611	C₂²	—	226	1	no	—
612	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	113	2	no	—
622	C₄	—	226	2	no	—
623	C₄	—	226	2	no	—
624	C₄	—	226	1	no	—
625	C₄	—	226	1	no	—
626	C₄	—	226	1	no	—
627	C₄	—	226	1	no	—
628	C₄	—	226	2	no	—
629	C₄	—	226	1	no	—
630	C₄	—	226	1	no	—
631	C₄	#41×D₁₁₃	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	4	2	no	—
634	C₂	—	452	2	no	—
635	C₂	—	226	2	no	—
636	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
637	C₂	#20299433	1	1	yes	characteristic
638	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#559×C₁₁₃	C₂
prime radical	#20299161	C₂
hypercenter	#559	D₁₁₃
hypocenter	C₁₁₃	#3510
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #20299334	C₂	semidirect
2. #20299331	C₂	semidirect
3. #20299330	C₂	semidirect
4. #20299321	C₂	semidirect
5. #20299320	C₂	semidirect
6. #20299318	C₂	semidirect
7. #20299317	C₂	semidirect
8. #20299278	C₂	semidirect
9. #20299277	C₂	semidirect
10. #20299276	C₂	semidirect
11. #20299271	C₂	semidirect
12. #20299216	C₂	semidirect
13. #20299212	C₂	semidirect
14. #20299168	C₂	semidirect
16. #20299152	C₂	semidirect
17. #20299128	C₂	semidirect
18. #20299125	C₂	semidirect
19. #124×D₁₁₃	C₂	semidirect
20. #20299074	C₂	semidirect
21. #20299070	C₂	semidirect
22. C₄×#14268646	C₂	semidirect
23. #559×C₁₁₃	C₂	semidirect
27. #16813622	C₂²	semidirect
28. #16813621	C₂²	semidirect
29. #16813620	C₂²	semidirect
30. #16813620	C₂²	semidirect
32. #16813617	C₂²	semidirect
33. #16813617	C₂²	semidirect
34. #16813617	C₂²	semidirect
35. #16813616	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813615	C₂²	semidirect
38. #16813615	C₂²	semidirect
39. #16813615	C₂²	semidirect
40. #16813612	C₂²	semidirect
41. #16813612	C₂²	semidirect
47. #16813609	C₂²	semidirect
48. #16813609	C₂²	semidirect
51. #16813608	C₂²	semidirect
52. #16813608	C₂²	semidirect
53. #16813606	C₂²	semidirect
54. #16813605	C₂²	semidirect
57. #16813604	C₂²	semidirect
58. #16813604	C₂²	semidirect
59. #16813603	C₂²	semidirect
60. #16813603	C₂²	semidirect
62. #16813601	C₂²	semidirect
65. #16813600	C₂²	semidirect
66. #16813599	C₂²	semidirect
67. #16813599	C₂²	semidirect
68. #16813599	C₂²	semidirect
70. #16813598	C₂²	semidirect
75. Q₈×Dic₁₁₃	C₂²	semidirect
76. C₄×Dic₂₂₆	C₂²	semidirect
77. C₄×Dic₂₂₆	C₂²	semidirect
78. C₄×Dic₂₂₆	C₂²	semidirect
79. C₄×Dic₂₂₆	C₂²	semidirect
80. C₄×Dic₂₂₆	C₂²	semidirect
81. C₄×Dic₂₂₆	C₂²	semidirect
82. #16813587	C₂²	semidirect
83. #16813587	C₂²	semidirect
84. #16813587	C₂²	semidirect
87. D₄×Dic₁₁₃	C₂²	semidirect
88. D₄×Dic₁₁₃	C₂²	semidirect
92. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
95. #16813582	C₂²	semidirect
96. #16813581	C₂²	semidirect
99. #16813580	C₂²	semidirect
103. #16813579	C₂²	semidirect
104. #16813578	C₂²	semidirect
105. #16813578	C₂²	semidirect
110. C₂×C₄×Dic₁₁₃	C₂²	semidirect
114. #124×C₁₁₃	C₂²	semidirect
115. #124×C₁₁₃	C₂²	semidirect
116. #123×C₁₁₃	C₂²	semidirect
117. #123×C₁₁₃	C₂²	semidirect
118. C₄×Q₈×C₁₁₃	C₂²	semidirect
119. C₄×Q₈×C₁₁₃	C₂²	semidirect
121. C₄×D₄×C₁₁₃	C₂²	semidirect
122. C₄×D₄×C₁₁₃	C₂²	semidirect
320. C₁₁₃	#3510	semidirect
324. #559	D₁₁₃	semidirect
375. #124	C₂×D₁₁₃	semidirect
376. #124	C₂×D₁₁₃	semidirect
385. #123	C₂×D₁₁₃	semidirect
386. #123	C₂×D₁₁₃	semidirect
411. C₄×Q₈	C₂×D₁₁₃	semidirect
412. C₄×Q₈	C₂×D₁₁₃	semidirect
425. C₄×D₄	C₂×D₁₁₃	semidirect
426. C₄×D₄	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299334	2
#20299331	2
#20299330	2
#20299321	2
#20299320	2
#20299318	2
#20299317	2
#20299278	2
#20299277	2
#20299276	2
#20299271	2
#20299216	2
#20299212	2
#20299168	2
#20299161	2
#20299152	2
#20299128	2
#20299125	2
#124×D₁₁₃	2
#20299074	2
#20299070	2
C₄×#14268646	2
#559×C₁₁₃	2
#3510	113