Subgroups — #28404602

Order 14464.

1252 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299311	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299304	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299299	C₂	1	2	yes	maximal, complemented
4	#20299296	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299269	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299243	C₂	1	2	yes	maximal, complemented
7	#20299240	C₂	1	2	yes	maximal, complemented
8	#20299237	C₂	1	2	yes	maximal, complemented
9	D₄×D₄₅₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299232	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299232	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299204	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299201	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299187	C₂	1	2	yes	maximal, complemented
15	#20299184	C₂	1	2	yes	maximal, complemented
16	#20299143	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299128	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299107	C₂	1	2	yes	maximal, complemented
19	#121×D₁₁₃	C₂	1	2	yes	maximal, complemented
20	#20299072	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16813584	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268647	C₂²	1	2	yes	complemented
25	C₂×#14268646	C₂²	1	2	yes	complemented
26	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
27	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
30	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
31	C₂×D₄×D₁₁₃	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
33	#16813621	C₂²	1	1	yes	characteristic, complemented
34	#16813619	C₂²	1	1	yes	characteristic, complemented
35	#16813618	C₂²	1	1	yes	characteristic, complemented
36	#16813618	C₂²	1	1	yes	characteristic, complemented
37	#16813617	C₂²	1	2	yes	complemented
38	#16813617	C₂²	1	1	yes	characteristic, complemented
39	#16813615	C₂²	1	1	yes	characteristic, complemented
40	#16813613	C₂²	1	1	yes	characteristic, complemented
41	#16813612	C₂²	1	1	yes	characteristic, complemented
42	#16813610	C₂²	1	2	yes	complemented
43	#16813608	C₂²	1	2	yes	complemented
44	#16813608	C₂²	1	1	yes	characteristic, complemented
45	#16813608	C₂²	1	2	yes	complemented
46	#16813607	C₂²	1	2	yes	complemented
47	#16813607	C₂²	1	2	yes	complemented
48	#16813607	C₂²	1	2	yes	complemented
49	#16813606	C₂²	1	2	yes	complemented
50	#16813606	C₂²	1	1	yes	characteristic, complemented
51	#16813604	C₂²	1	2	yes	complemented
52	#16813603	C₂²	1	1	yes	characteristic, complemented
53	#16813602	C₂²	1	2	yes	complemented
54	#16813600	C₂²	1	2	yes	complemented
55	#16813600	C₂²	1	2	yes	complemented
56	#16813599	C₂²	1	1	yes	characteristic, complemented
57	#16813597	C₂²	1	1	yes	characteristic, complemented
58	#16813597	C₂²	1	2	yes	complemented
59	#16813597	C₂²	1	1	yes	characteristic, complemented
60	#16813597	C₂²	1	2	yes	complemented
61	#16813597	C₂²	1	2	yes	complemented
62	#16813596	C₂²	1	2	yes	complemented
63	#16813596	C₂²	1	2	yes	complemented
64	#16813596	C₂²	1	1	yes	characteristic, complemented
65	#16813596	C₂²	1	1	yes	characteristic, complemented
66	#16813595	C₂²	1	2	yes	complemented
67	#16813595	C₂²	1	2	yes	complemented
68	#16813595	C₂²	1	2	yes	complemented
69	#16813595	C₂²	1	2	yes	complemented
70	#16813595	C₂²	1	2	yes	complemented
71	#16813594	C₂²	1	1	yes	characteristic
72	#16813594	C₂²	1	2	yes	complemented
73	#16813594	C₂²	1	2	yes	complemented
74	#16813593	C₂²	1	2	yes	complemented
75	#16813592	C₂²	1	2	yes	complemented
76	#16813592	C₂²	1	2	yes	complemented
77	#16813592	C₂²	1	2	yes	complemented
78	#16813592	C₂²	1	2	yes	complemented
79	#16813590	C₂²	1	2	yes	complemented
80	#16813590	C₂²	1	2	yes	complemented
81	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
83	C₄×D₄₅₂	C₂²	1	2	yes	complemented
84	C₄×D₄₅₂	C₂²	1	2	yes	complemented
85	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
86	#16813584	C₂²	1	1	yes	characteristic
87	#16813584	C₂²	1	1	yes	characteristic
88	#16813584	C₂²	1	1	yes	characteristic
89	#16813584	C₂²	1	1	yes	characteristic, complemented
90	#16813584	C₂²	1	1	yes	characteristic, complemented
91	#16813584	C₂²	1	2	yes	complemented
92	#16813584	C₂²	1	2	yes	complemented
93	#16813584	C₂²	1	1	yes	characteristic, complemented
94	#16813584	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
99	#16813582	C₂²	1	2	yes	complemented
100	#16813582	C₂²	1	2	yes	complemented
101	#16813581	C₂²	1	1	yes	characteristic, complemented
102	#16813580	C₂²	1	1	yes	characteristic, complemented
103	#16813579	C₂²	1	2	yes	complemented
104	#16813579	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
106	C₂×#14268624	C₂²	1	2	yes	complemented
107	C₂×#14268624	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	#126×C₁₁₃	C₂²	1	2	yes	complemented
113	#125×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₁₃	C₂²	1	2	yes	complemented
115	#121×C₁₁₃	C₂²	1	2	yes	complemented
116	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₁₃	C₂³	1	2	yes	—
125	C₂³×D₁₁₃	C₂³	1	2	yes	—
126	#14268647	—	4	4	no	—
127	#14268646	—	4	4	no	—
128	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₂₆	C₂³	1	2	yes	—
130	C₂×D₄₅₂	—	2	4	no	—
131	C₂×D₄₅₂	—	2	4	no	—
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
134	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
135	C₂×D₄₅₂	C₂³	1	2	yes	—
136	C₂×D₄₅₂	C₂³	1	2	yes	—
137	C₂×D₄₅₂	C₂³	1	2	yes	—
138	C₂×D₄₅₂	C₂³	1	2	yes	—
139	C₂×D₄₅₂	C₂³	1	2	yes	—
140	C₂×D₄₅₂	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	1	yes	characteristic
145	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
150	D₄×D₁₁₃	—	2	4	no	—
151	D₄×D₁₁₃	—	4	4	no	—
152	D₄×D₁₁₃	—	4	4	no	—
153	D₄×D₁₁₃	—	4	4	no	—
154	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
155	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
156	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₁₃	—	4	4	no	—
158	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
163	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
164	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
165	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
167	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
168	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
177	#14268626	C₂³	1	2	yes	—
178	#14268626	C₂³	1	1	yes	characteristic
179	#14268626	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₁₁₃	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	1	yes	characteristic
192	#14268624	C₂³	1	2	yes	—
193	#14268624	C₂³	1	2	yes	—
194	#14268624	C₂³	1	2	yes	—
195	#14268624	C₂³	1	2	yes	—
196	#14268624	C₂³	1	2	yes	—
197	#14268624	C₂³	1	2	yes	—
198	#14268624	C₂³	1	2	yes	—
199	#14268624	C₂³	1	2	yes	—
200	#14268624	C₂³	1	1	yes	characteristic
201	#14268624	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
204	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
205	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₁₃	C₂³	1	2	yes	—
207	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
210	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
215	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
217	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
229	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
230	C₄²×C₁₁₃	C₂³	1	2	yes	—
231	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
233	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₁₃	—	2	4	no	—
235	C₂²×D₁₁₃	—	2	4	no	—
236	C₂²×D₁₁₃	—	2	4	no	—
237	C₂²×D₁₁₃	—	2	4	no	—
238	C₂²×D₁₁₃	—	4	2	no	—
239	C₂²×D₁₁₃	—	4	2	no	—
240	C₂²×D₁₁₃	—	4	2	no	—
241	C₂²×D₁₁₃	—	4	2	no	—
242	C₂²×D₁₁₃	—	4	2	no	—
243	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
245	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
246	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
247	D₄×C₁₁₃	—	2	2	no	—
248	D₄×C₁₁₃	—	2	4	no	—
249	D₄×C₁₁₃	—	2	2	no	—
250	D₄×C₁₁₃	—	4	2	no	—
251	C₂×C₄×C₁₁₃	—	2	2	no	—
252	C₂×C₄×C₁₁₃	—	2	2	no	—
253	C₂×C₄×C₁₁₃	—	4	2	no	—
254	C₂×C₄×C₁₁₃	—	4	2	no	—
255	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₁₁₃	—	2	2	no	—
264	C₂²⋊D₁₁₃	—	2	4	no	—
265	C₂²⋊D₁₁₃	—	2	4	no	—
266	C₂²⋊D₁₁₃	—	2	2	no	—
267	C₂²⋊D₁₁₃	—	2	4	no	—
268	C₂²⋊D₁₁₃	—	4	2	no	—
269	C₂²⋊D₁₁₃	—	4	2	no	—
270	C₂²⋊D₁₁₃	—	4	2	no	—
271	C₂²⋊D₁₁₃	—	4	2	no	—
272	C₂×Dic₁₁₃	—	2	2	no	—
273	C₂×Dic₁₁₃	—	2	2	no	—
274	C₂×Dic₁₁₃	—	4	2	no	—
275	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
280	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
283	D₄₅₂	—	2	4	no	—
284	D₄₅₂	—	2	4	no	—
285	D₄₅₂	—	2	2	no	—
286	D₄₅₂	—	2	2	no	—
287	D₄₅₂	—	4	2	no	—
288	D₄₅₂	—	4	2	no	—
289	D₄₅₂	—	4	2	no	—
290	D₄₅₂	—	4	2	no	—
291	D₄₅₂	#41	1	4	yes	complemented
292	C₄×D₁₁₃	—	2	2	no	—
293	C₄×D₁₁₃	—	2	4	no	—
294	C₄×D₁₁₃	—	2	4	no	—
295	C₄×D₁₁₃	—	4	2	no	—
296	C₄×D₁₁₃	—	4	2	no	—
297	C₄×D₁₁₃	—	4	2	no	—
298	C₄×D₁₁₃	—	4	2	no	—
299	C₄×D₁₁₃	—	4	2	no	—
300	C₄×D₁₁₃	—	4	2	no	—
301	Dic₂₂₆	—	2	2	no	—
302	Dic₂₂₆	—	4	2	no	—
303	C₂²×C₁₁₃	—	2	1	no	—
304	C₂²×C₁₁₃	—	2	1	no	—
305	C₂²×C₁₁₃	—	2	2	no	—
306	C₂²×C₁₁₃	—	2	1	no	—
307	C₂²×C₁₁₃	—	2	2	no	—
308	C₂²×C₁₁₃	—	2	2	no	—
309	C₂²×C₁₁₃	—	2	1	no	—
310	C₂²×C₁₁₃	—	2	1	no	—
311	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
313	C₂×D₁₁₃	—	2	2	no	—
314	C₂×D₁₁₃	—	2	2	no	—
315	C₂×D₁₁₃	—	2	1	no	—
316	C₂×D₁₁₃	—	2	2	no	—
317	C₂×D₁₁₃	—	2	2	no	—
318	C₂×D₁₁₃	—	2	2	no	—
319	C₂×D₁₁₃	—	2	2	no	—
320	C₂×D₁₁₃	—	2	2	no	—
321	C₂×D₁₁₃	—	2	1	no	—
322	C₂×D₁₁₃	—	2	1	no	—
323	C₂×D₁₁₃	—	2	2	no	—
324	C₂×D₁₁₃	—	4	8	no	—
325	C₂×D₁₁₃	—	8	4	no	—
326	C₂×D₁₁₃	—	8	4	no	—
327	C₂×D₁₁₃	C₂×#41	1	4	yes	—
328	C₄×C₁₁₃	—	2	1	no	—
329	C₄×C₁₁₃	—	2	1	no	—
330	C₄×C₁₁₃	—	2	1	no	—
331	C₄×C₁₁₃	—	2	2	no	—
332	C₄×C₁₁₃	—	2	2	no	—
333	C₄×C₁₁₃	—	2	2	no	—
334	C₄×C₁₁₃	—	2	1	no	—
335	C₄×C₁₁₃	C₂×#41	1	2	yes	—
336	Dic₁₁₃	—	2	1	no	—
337	Dic₁₁₃	—	2	1	no	—
338	Dic₁₁₃	—	2	1	no	—
339	Dic₁₁₃	—	2	2	no	—
340	Dic₁₁₃	—	2	1	no	—
341	Dic₁₁₃	—	2	1	no	—
342	Dic₁₁₃	—	2	1	no	—
343	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
344	C₂×C₁₁₃	—	2	2	no	—
345	C₂×C₁₁₃	—	4	1	no	—
346	C₂×C₁₁₃	—	4	2	no	—
347	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
348	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	D₁₁₃	—	2	4	no	—
351	D₁₁₃	—	4	2	no	—
352	D₁₁₃	—	4	2	no	—
353	D₁₁₃	—	4	1	no	—
354	#3519	—	113	1	no	maximal, Sylow
355	C₁₁₃	#3519	1	1	yes	characteristic, complemented, Sylow
356	#555	—	113	1	no	—
357	#554	—	113	1	no	—
358	#553	—	113	2	no	—
359	#553	—	113	1	no	—
360	#553	D₁₁₃	1	1	yes	characteristic, complemented
361	#550	—	113	1	no	—
362	#546	—	113	2	no	—
363	#546	—	113	2	no	—
364	#546	—	113	2	no	—
365	D₄²	—	113	1	no	—
366	D₄²	—	113	1	no	—
367	D₄²	—	113	1	no	—
368	#540	—	113	1	no	—
369	#540	—	113	1	no	—
370	#538	—	113	2	no	—
371	#538	—	113	2	no	—
372	#532	—	113	1	no	—
373	#529	—	113	1	no	—
374	#525	—	113	2	no	—
375	C₂×#121	—	113	2	no	—
376	#518	—	113	1	no	—
377	#518	—	113	1	no	—
378	C₂×C₄×D₄	—	113	1	no	—
379	C₂×#41	—	113	2	no	—
380	C₂×#41	—	113	2	no	—
381	C₂²×D₄	—	113	2	no	—
382	C₂²×D₄	—	113	2	no	—
383	C₂²×D₄	—	113	2	no	—
384	C₂²×D₄	—	113	1	no	—
385	C₂²×D₄	—	113	1	no	—
386	C₂²×D₄	—	113	1	no	—
387	C₂³×C₄	—	113	2	no	—
388	C₄⋊Q₈	—	113	1	no	—
389	#127	—	113	1	no	—
390	#127	—	113	1	no	—
391	#127	—	113	1	no	—
392	#126	—	113	1	no	—
393	#126	—	113	2	no	—
394	#126	—	113	1	no	—
395	#126	C₂×D₁₁₃	1	2	yes	complemented
396	#125	—	113	1	no	—
397	#125	—	113	1	no	—
398	#125	C₂×D₁₁₃	1	1	yes	characteristic, complemented
399	#124	—	113	1	no	—
400	#124	—	113	2	no	—
401	#124	—	113	2	no	—
402	#124	—	113	2	no	—
403	#123	—	113	1	no	—
404	#123	—	113	2	no	—
405	#123	—	113	2	no	—
406	#123	—	113	2	no	—
407	#123	—	113	2	no	—
408	#123	—	113	1	no	—
409	#123	—	113	2	no	—
410	#123	C₂×D₁₁₃	1	2	yes	complemented
411	C₂²⋊Q₈	—	113	2	no	—
412	C₂²⋊Q₈	—	113	2	no	—
413	C₂²⋊Q₈	—	113	2	no	—
414	C₂²⋊Q₈	—	113	1	no	—
415	#121	—	113	1	no	—
416	#121	—	113	2	no	—
417	#121	—	113	2	no	—
418	#121	—	113	2	no	—
419	#121	—	113	2	no	—
420	#121	—	113	1	no	—
421	#121	—	113	2	no	—
422	#121	—	113	1	no	—
423	#121	—	113	2	no	—
424	#121	—	113	2	no	—
425	#121	—	113	1	no	—
426	#121	—	113	1	no	—
427	#121	—	113	2	no	—
428	#121	—	113	2	no	—
429	#121	—	113	2	no	—
430	#121	—	113	2	no	—
431	#121	—	113	2	no	—
432	#121	—	113	2	no	—
433	#121	C₂×D₁₁₃	1	2	yes	complemented
434	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
435	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
436	#120	—	113	2	no	—
437	#120	—	113	2	no	—
438	#120	—	113	2	no	—
439	#120	—	113	2	no	—
440	#120	—	113	2	no	—
441	#120	—	113	2	no	—
442	C₄×Q₈	—	113	1	no	—
443	C₄×D₄	—	113	1	no	—
444	C₄×D₄	—	113	2	no	—
445	C₄×D₄	—	113	2	no	—
446	C₄×D₄	—	113	1	no	—
447	C₄×D₄	—	113	1	no	—
448	C₄×D₄	—	113	1	no	—
449	C₄×D₄	—	113	1	no	—
450	C₄×D₄	—	113	2	no	—
451	C₄×D₄	—	113	1	no	—
452	C₄×D₄	—	113	2	no	—
453	C₄×D₄	—	113	1	no	—
454	C₄×D₄	—	113	1	no	—
455	C₄×D₄	—	113	1	no	—
456	C₄×D₄	—	113	1	no	—
457	C₄×D₄	—	113	2	no	—
458	C₄×D₄	—	113	2	no	—
459	C₄×D₄	—	113	2	no	—
460	C₄×D₄	—	113	1	no	—
461	C₄×D₄	—	113	2	no	—
462	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
463	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
464	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
465	#117	—	113	1	no	—
466	#117	—	113	1	no	—
467	#117	—	113	1	no	—
468	#117	—	113	2	no	—
469	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
470	C₂×C₄⋊C₄	—	113	2	no	—
471	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
472	C₂×C₂²⋊C₄	—	113	2	no	—
473	C₂×C₂²⋊C₄	—	113	2	no	—
474	C₂×C₂²⋊C₄	—	113	2	no	—
475	C₂×C₂²⋊C₄	—	113	2	no	—
476	C₂×C₂²⋊C₄	—	113	2	no	—
477	C₂×C₄²	—	113	1	no	—
478	C₂⁴	—	113	2	no	—
479	C₂⁴	—	113	2	no	—
480	C₂⁴	—	113	2	no	—
481	#41	—	452	4	no	—
482	#41	—	452	4	no	—
483	C₂×Q₈	—	113	2	no	—
484	C₂×Q₈	—	113	1	no	—
485	C₂×D₄	—	113	2	no	—
486	C₂×D₄	—	113	2	no	—
487	C₂×D₄	—	113	2	no	—
488	C₂×D₄	—	113	2	no	—
489	C₂×D₄	—	113	2	no	—
490	C₂×D₄	—	113	2	no	—
491	C₂×D₄	—	113	1	no	—
492	C₂×D₄	—	113	1	no	—
493	C₂×D₄	—	113	2	no	—
494	C₂×D₄	—	113	1	no	—
495	C₂×D₄	—	113	2	no	—
496	C₂×D₄	—	113	2	no	—
497	C₂×D₄	—	113	2	no	—
498	C₂×D₄	—	113	2	no	—
499	C₂×D₄	—	113	2	no	—
500	C₂×D₄	—	113	2	no	—
501	C₂×D₄	—	113	1	no	—
502	C₂×D₄	—	113	1	no	—
503	C₂×D₄	—	452	4	no	—
504	C₂×D₄	—	452	4	no	—
505	C₂×D₄	—	452	4	no	—
506	C₂×D₄	—	226	4	no	—
507	C₂×D₄	—	226	4	no	—
508	C₂×D₄	—	226	4	no	—
509	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
510	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
511	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
512	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
513	C₂²×C₄	—	113	2	no	—
514	C₂²×C₄	—	113	1	no	—
515	C₂²×C₄	—	113	1	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	—	113	2	no	—
523	C₂²×C₄	—	113	1	no	—
524	C₂²×C₄	—	113	2	no	—
525	C₂²×C₄	—	452	4	no	—
526	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
529	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
530	C₄⋊C₄	—	113	1	no	—
531	C₄⋊C₄	—	113	2	no	—
532	C₄⋊C₄	—	113	2	no	—
533	C₄⋊C₄	—	113	1	no	—
534	C₄⋊C₄	—	113	1	no	—
535	C₄⋊C₄	—	113	1	no	—
536	C₄⋊C₄	—	113	1	no	—
537	C₄⋊C₄	—	113	1	no	—
538	C₄⋊C₄	—	113	1	no	—
539	C₄⋊C₄	—	113	1	no	—
540	C₄⋊C₄	—	113	2	no	—
541	C₄⋊C₄	—	113	1	no	—
542	C₄⋊C₄	—	113	1	no	—
543	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
544	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
550	C₂²⋊C₄	—	113	1	no	—
551	C₂²⋊C₄	—	113	1	no	—
552	C₂²⋊C₄	—	113	2	no	—
553	C₂²⋊C₄	—	113	1	no	—
554	C₂²⋊C₄	—	113	1	no	—
555	C₂²⋊C₄	—	113	2	no	—
556	C₂²⋊C₄	—	113	1	no	—
557	C₂²⋊C₄	—	113	1	no	—
558	C₂²⋊C₄	—	113	2	no	—
559	C₂²⋊C₄	—	113	2	no	—
560	C₂²⋊C₄	—	113	2	no	—
561	C₂²⋊C₄	—	113	2	no	—
562	C₂²⋊C₄	—	113	2	no	—
563	C₂²⋊C₄	—	113	2	no	—
564	C₂²⋊C₄	—	113	2	no	—
565	C₂²⋊C₄	—	113	2	no	—
566	C₂²⋊C₄	—	113	2	no	—
567	C₂²⋊C₄	—	113	2	no	—
568	C₂²⋊C₄	—	113	1	no	—
569	C₂²⋊C₄	—	113	1	no	—
570	C₂²⋊C₄	—	113	2	no	—
571	C₂²⋊C₄	—	113	2	no	—
572	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
577	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
578	C₄²	—	113	1	no	—
579	C₄²	—	113	1	no	—
580	C₄²	—	113	1	no	—
581	C₄²	—	113	1	no	—
582	C₄²	—	113	2	no	—
583	C₄²	—	113	1	no	—
584	C₄²	C₂²×D₁₁₃	1	2	yes	—
585	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
586	C₂³	—	113	2	no	—
587	C₂³	—	113	1	no	—
588	C₂³	—	113	2	no	—
589	C₂³	—	113	2	no	—
590	C₂³	—	452	2	no	—
591	C₂³	—	452	2	no	—
592	C₂³	—	452	2	no	—
593	C₂³	—	452	2	no	—
594	C₂³	—	452	2	no	—
595	C₂³	—	226	4	no	—
596	C₂³	—	226	4	no	—
597	C₂³	—	226	4	no	—
598	C₂³	—	226	4	no	—
599	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
600	C₂³	C₂³×D₁₁₃	1	2	yes	—
601	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
602	Q₈	—	452	2	no	—
603	Q₈	—	226	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	4	no	—
606	D₄	—	2	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	113	4	no	—
609	D₄	—	452	2	no	—
610	D₄	—	452	2	no	—
611	D₄	—	452	2	no	—
612	D₄	—	452	2	no	—
613	D₄	—	452	2	no	—
614	D₄	—	452	2	no	—
615	D₄	—	452	2	no	—
616	D₄	—	452	2	no	—
617	D₄	—	226	4	no	—
618	D₄	—	226	4	no	—
619	D₄	—	226	2	no	—
620	D₄	—	226	4	no	—
621	D₄	—	226	4	no	—
622	D₄	—	226	2	no	—
623	D₄	—	226	4	no	—
624	D₄	—	226	2	no	—
625	D₄	—	226	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	113	1	no	—
631	C₂×C₄	—	113	1	no	—
632	C₂×C₄	—	113	1	no	—
633	C₂×C₄	—	113	1	no	—
634	C₂×C₄	—	113	1	no	—
635	C₂×C₄	—	113	1	no	—
636	C₂×C₄	—	113	2	no	—
637	C₂×C₄	—	113	1	no	—
638	C₂×C₄	—	452	2	no	—
639	C₂×C₄	—	452	2	no	—
640	C₂×C₄	—	452	2	no	—
641	C₂×C₄	—	452	2	no	—
642	C₂×C₄	—	452	2	no	—
643	C₂×C₄	—	452	2	no	—
644	C₂×C₄	—	452	2	no	—
645	C₂×C₄	—	226	4	no	—
646	C₂×C₄	—	226	4	no	—
647	C₂×C₄	—	226	2	no	—
648	C₂×C₄	—	226	2	no	—
649	C₂×C₄	—	226	2	no	—
650	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
652	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
655	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
656	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
657	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	113	4	no	—
667	C₂²	—	904	4	no	—
668	C₂²	—	904	4	no	—
669	C₂²	—	452	8	no	—
670	C₂²	—	226	1	no	—
671	C₂²	—	226	2	no	—
672	C₂²	—	226	2	no	—
673	C₂²	—	226	2	no	—
674	C₂²	—	226	2	no	—
675	C₂²	—	226	1	no	—
676	C₂²	—	226	2	no	—
677	C₂²	—	226	2	no	—
678	C₂²	—	226	1	no	—
679	C₂²	—	226	2	no	—
680	C₂²	—	226	2	no	—
681	C₂²	#16813668	1	2	yes	—
682	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	2	no	—
690	C₄	—	113	2	no	—
691	C₄	—	226	1	no	—
692	C₄	—	226	1	no	—
693	C₄	—	226	1	no	—
694	C₄	—	226	1	no	—
695	C₄	—	226	1	no	—
696	C₄	—	226	2	no	—
697	C₄	—	226	1	no	—
698	C₄	#41×D₁₁₃	1	2	yes	—
699	C₂	—	2	2	no	—
700	C₂	—	4	1	no	—
701	C₂	—	4	2	no	—
702	C₂	—	452	1	no	—
703	C₂	—	452	2	no	—
704	C₂	—	452	2	no	—
705	C₂	—	226	4	no	—
706	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
707	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
708	C₂	C₂×#16813668	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#553×C₁₁₃	C₂
hypercenter	#553	D₁₁₃
hypocenter	C₁₁₃	#3519
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #20299311	C₂	semidirect
2. #20299304	C₂	semidirect
3. #20299299	C₂	semidirect
4. #20299296	C₂	semidirect
5. #20299269	C₂	semidirect
6. #20299243	C₂	semidirect
7. #20299240	C₂	semidirect
8. #20299237	C₂	semidirect
9. D₄×D₄₅₂	C₂	semidirect
10. #20299232	C₂	semidirect
11. #20299232	C₂	semidirect
12. #20299204	C₂	semidirect
13. #20299201	C₂	semidirect
14. #20299187	C₂	semidirect
15. #20299184	C₂	semidirect
16. #20299143	C₂	semidirect
17. #20299128	C₂	semidirect
18. #20299107	C₂	semidirect
19. #121×D₁₁₃	C₂	semidirect
20. #20299072	C₂	semidirect
21. #20299070	C₂	semidirect
22. C₂×#16813584	C₂	semidirect
23. #553×C₁₁₃	C₂	semidirect
24. C₂×#14268647	C₂²	semidirect
25. C₂×#14268646	C₂²	semidirect
29. C₂×D₄×D₁₁₃	C₂²	semidirect
30. C₂×D₄×D₁₁₃	C₂²	semidirect
31. C₂×D₄×D₁₁₃	C₂²	semidirect
32. C₂²×C₄×D₁₁₃	C₂²	semidirect
33. #16813621	C₂²	semidirect
34. #16813619	C₂²	semidirect
35. #16813618	C₂²	semidirect
36. #16813618	C₂²	semidirect
37. #16813617	C₂²	semidirect
38. #16813617	C₂²	semidirect
39. #16813615	C₂²	semidirect
40. #16813613	C₂²	semidirect
41. #16813612	C₂²	semidirect
42. #16813610	C₂²	semidirect
43. #16813608	C₂²	semidirect
44. #16813608	C₂²	semidirect
45. #16813608	C₂²	semidirect
46. #16813607	C₂²	semidirect
47. #16813607	C₂²	semidirect
48. #16813607	C₂²	semidirect
49. #16813606	C₂²	semidirect
50. #16813606	C₂²	semidirect
51. #16813604	C₂²	semidirect
52. #16813603	C₂²	semidirect
53. #16813602	C₂²	semidirect
54. #16813600	C₂²	semidirect
55. #16813600	C₂²	semidirect
56. #16813599	C₂²	semidirect
57. #16813597	C₂²	semidirect
58. #16813597	C₂²	semidirect
59. #16813597	C₂²	semidirect
60. #16813597	C₂²	semidirect
61. #16813597	C₂²	semidirect
62. #16813596	C₂²	semidirect
63. #16813596	C₂²	semidirect
64. #16813596	C₂²	semidirect
65. #16813596	C₂²	semidirect
66. #16813595	C₂²	semidirect
67. #16813595	C₂²	semidirect
68. #16813595	C₂²	semidirect
69. #16813595	C₂²	semidirect
70. #16813595	C₂²	semidirect
72. #16813594	C₂²	semidirect
73. #16813594	C₂²	semidirect
74. #16813593	C₂²	semidirect
75. #16813592	C₂²	semidirect
76. #16813592	C₂²	semidirect
77. #16813592	C₂²	semidirect
78. #16813592	C₂²	semidirect
79. #16813590	C₂²	semidirect
80. #16813590	C₂²	semidirect
81. C₄×Dic₂₂₆	C₂²	semidirect
83. C₄×D₄₅₂	C₂²	semidirect
84. C₄×D₄₅₂	C₂²	semidirect
85. D₄×Dic₁₁₃	C₂²	semidirect
89. #16813584	C₂²	semidirect
90. #16813584	C₂²	semidirect
91. #16813584	C₂²	semidirect
92. #16813584	C₂²	semidirect
93. #16813584	C₂²	semidirect
94. #16813584	C₂²	semidirect
95. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
96. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
97. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
98. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
99. #16813582	C₂²	semidirect
100. #16813582	C₂²	semidirect
101. #16813581	C₂²	semidirect
102. #16813580	C₂²	semidirect
103. #16813579	C₂²	semidirect
104. #16813579	C₂²	semidirect
105. C₄⋊C₄×D₁₁₃	C₂²	semidirect
106. C₂×#14268624	C₂²	semidirect
107. C₂×#14268624	C₂²	semidirect
108. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
109. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
110. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
111. C₂×C₄×Dic₁₁₃	C₂²	semidirect
112. #126×C₁₁₃	C₂²	semidirect
113. #125×C₁₁₃	C₂²	semidirect
114. #123×C₁₁₃	C₂²	semidirect
115. #121×C₁₁₃	C₂²	semidirect
116. #121×C₁₁₃	C₂²	semidirect
117. #121×C₁₁₃	C₂²	semidirect
118. C₄×D₄×C₁₁₃	C₂²	semidirect
119. C₄×D₄×C₁₁₃	C₂²	semidirect
120. C₄×D₄×C₁₁₃	C₂²	semidirect
121. #117×C₁₁₃	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
291. D₄₅₂	#41	semidirect
355. C₁₁₃	#3519	semidirect
360. #553	D₁₁₃	semidirect
395. #126	C₂×D₁₁₃	semidirect
398. #125	C₂×D₁₁₃	semidirect
410. #123	C₂×D₁₁₃	semidirect
433. #121	C₂×D₁₁₃	semidirect
434. #121	C₂×D₁₁₃	semidirect
435. #121	C₂×D₁₁₃	semidirect
462. C₄×D₄	C₂×D₁₁₃	semidirect
463. C₄×D₄	C₂×D₁₁₃	semidirect
464. C₄×D₄	C₂×D₁₁₃	semidirect
469. #117	C₂×D₁₁₃	semidirect
471. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299311	2
#20299304	2
#20299299	2
#20299296	2
#20299269	2
#20299243	2
#20299240	2
#20299237	2
D₄×D₄₅₂	2
#20299232	2
#20299204	2
#20299201	2
#20299187	2
#20299184	2
#20299143	2
#20299128	2
#20299107	2
#121×D₁₁₃	2
#20299072	2
#20299070	2
C₂×#16813584	2
#553×C₁₁₃	2
#3519	113