Subgroups — #28404533

Order 14464.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299330	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299319	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299314	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299312	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299276	C₂	1	2	yes	maximal, complemented
6	#20299275	C₂	1	2	yes	maximal, complemented
7	#20299263	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299258	C₂	1	2	yes	maximal, complemented
9	#20299241	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299240	C₂	1	2	yes	maximal, complemented
11	#20299239	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299232	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299220	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299187	C₂	1	2	yes	maximal, complemented
15	#20299182	C₂	1	2	yes	maximal, complemented
16	#20299145	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299131	C₂	1	2	yes	maximal, complemented
18	#20299126	C₂	1	1	yes	maximal, characteristic, complemented
19	#124×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	C₄×#14268648	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	2	yes	complemented
26	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	complemented
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	—
30	#16813621	C₂²	1	1	yes	characteristic, complemented
31	#16813621	C₂²	1	1	yes	characteristic, complemented
32	#16813618	C₂²	1	1	yes	characteristic
33	#16813617	C₂²	1	1	yes	characteristic, complemented
34	#16813617	C₂²	1	2	yes	complemented
35	#16813616	C₂²	1	2	yes	complemented
36	#16813615	C₂²	1	1	yes	characteristic, complemented
37	#16813615	C₂²	1	2	yes	complemented
38	#16813612	C₂²	1	1	yes	characteristic, complemented
39	#16813611	C₂²	1	2	yes	complemented
40	#16813611	C₂²	1	2	yes	complemented
41	#16813611	C₂²	1	1	yes	characteristic, complemented
42	#16813610	C₂²	1	2	yes	complemented
43	#16813609	C₂²	1	2	yes	complemented
44	#16813608	C₂²	1	2	yes	—
45	#16813608	C₂²	1	1	yes	characteristic
46	#16813608	C₂²	1	2	yes	complemented
47	#16813608	C₂²	1	2	yes	complemented
48	#16813608	C₂²	1	2	yes	complemented
49	#16813607	C₂²	1	2	yes	complemented
50	#16813607	C₂²	1	2	yes	complemented
51	#16813607	C₂²	1	1	yes	characteristic, complemented
52	#16813606	C₂²	1	2	yes	complemented
53	#16813604	C₂²	1	2	yes	complemented
54	#16813604	C₂²	1	2	yes	complemented
55	#16813604	C₂²	1	1	yes	characteristic, complemented
56	#16813600	C₂²	1	2	yes	complemented
57	#16813600	C₂²	1	2	yes	complemented
58	#16813600	C₂²	1	1	yes	characteristic, complemented
59	#16813600	C₂²	1	2	yes	complemented
60	#16813598	C₂²	1	2	yes	complemented
61	#16813598	C₂²	1	1	yes	characteristic, complemented
62	#16813597	C₂²	1	1	yes	characteristic
63	#16813597	C₂²	1	1	yes	characteristic, complemented
64	#16813597	C₂²	1	2	yes	complemented
65	#16813597	C₂²	1	2	yes	complemented
66	#16813595	C₂²	1	1	yes	characteristic
67	#16813595	C₂²	1	2	yes	—
68	#16813595	C₂²	1	2	yes	complemented
69	#16813595	C₂²	1	2	yes	complemented
70	#16813594	C₂²	1	2	yes	complemented
71	#16813593	C₂²	1	1	yes	characteristic, complemented
72	#16813592	C₂²	1	2	yes	—
73	#16813592	C₂²	1	2	yes	complemented
74	#16813592	C₂²	1	2	yes	complemented
75	#16813590	C₂²	1	2	yes	—
76	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
78	#16813587	C₂²	1	2	yes	complemented
79	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
80	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
81	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₄₅₂	C₂²	1	2	yes	complemented
84	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
89	#16813584	C₂²	1	2	yes	complemented
90	#16813584	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
95	#16813582	C₂²	1	2	yes	complemented
96	#16813582	C₂²	1	2	yes	complemented
97	#16813581	C₂²	1	1	yes	characteristic, complemented
98	#16813580	C₂²	1	2	yes	complemented
99	#16813580	C₂²	1	2	yes	complemented
100	#16813580	C₂²	1	1	yes	characteristic, complemented
101	#16813580	C₂²	1	1	yes	characteristic, complemented
102	#16813579	C₂²	1	1	yes	characteristic, complemented
103	#16813578	C₂²	1	2	yes	complemented
104	C₂×#14268624	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
110	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
111	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
113	#126×C₁₁₃	C₂²	1	2	yes	complemented
114	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
115	#124×C₁₁₃	C₂²	1	2	yes	complemented
116	#123×C₁₁₃	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₁₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
122	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₁₃	C₂³	1	2	yes	—
124	C₂³×D₁₁₃	C₂³	1	2	yes	—
125	#14268648	—	2	4	no	—
126	#14268647	—	4	4	no	—
127	C₂×Dic₂₂₆	C₂³	1	2	yes	—
128	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₂₆	C₂³	1	2	yes	—
130	Q₈×D₁₁₃	—	4	4	no	—
131	C₂×D₄₅₂	—	2	4	no	—
132	C₂×D₄₅₂	C₂³	1	2	yes	—
133	C₂×D₄₅₂	C₂³	1	2	yes	—
134	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
135	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
136	C₂×D₄₅₂	C₂³	1	2	yes	—
137	C₂×D₄₅₂	C₂³	1	2	yes	—
138	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
145	D₄×D₁₁₃	—	2	4	no	—
146	D₄×D₁₁₃	—	4	4	no	—
147	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
151	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
162	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
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	#14268626	C₂³	1	2	yes	—
171	#14268626	C₂³	1	2	yes	—
172	#14268626	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
178	#14268624	C₂³	1	1	yes	characteristic
179	#14268624	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	#14268624	C₂³	1	1	yes	characteristic
195	#14268624	C₂³	1	1	yes	characteristic
196	#14268624	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₁₃	C₂³	1	2	yes	—
199	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₁₃	C₂³	1	2	yes	—
201	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₁₃	C₂³	1	2	yes	—
203	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
212	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
219	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
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	2	yes	—
227	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
228	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
230	C₂²×D₁₁₃	—	2	4	no	—
231	C₂²×D₁₁₃	—	2	4	no	—
232	C₂²×D₁₁₃	—	4	2	no	—
233	C₂²×D₁₁₃	—	4	2	no	—
234	C₂²×D₁₁₃	—	4	2	no	—
235	C₂²×D₁₁₃	—	4	2	no	—
236	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
238	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
240	Q₈×C₁₁₃	—	2	2	no	—
241	Q₈×C₁₁₃	—	4	2	no	—
242	D₄×C₁₁₃	—	2	2	no	—
243	D₄×C₁₁₃	—	4	2	no	—
244	C₂×C₄×C₁₁₃	—	2	2	no	—
245	C₂×C₄×C₁₁₃	—	4	2	no	—
246	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₁₁₃	—	2	4	no	—
256	C₂²⋊D₁₁₃	—	2	2	no	—
257	C₂²⋊D₁₁₃	—	2	4	no	—
258	C₂²⋊D₁₁₃	—	4	2	no	—
259	C₂²⋊D₁₁₃	—	4	1	no	—
260	C₂²⋊D₁₁₃	—	4	2	no	—
261	C₂×Dic₁₁₃	—	4	2	no	—
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	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
269	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
270	D₄₅₂	—	2	4	no	—
271	D₄₅₂	—	2	4	no	—
272	D₄₅₂	—	2	2	no	—
273	D₄₅₂	—	4	2	no	—
274	D₄₅₂	—	4	1	no	—
275	D₄₅₂	—	4	2	no	—
276	D₄₅₂	#41	1	4	yes	complemented
277	C₄×D₁₁₃	—	2	4	no	—
278	C₄×D₁₁₃	—	2	2	no	—
279	C₄×D₁₁₃	—	2	2	no	—
280	C₄×D₁₁₃	—	2	4	no	—
281	C₄×D₁₁₃	—	2	2	no	—
282	C₄×D₁₁₃	—	4	2	no	—
283	C₄×D₁₁₃	—	4	2	no	—
284	C₄×D₁₁₃	—	4	1	no	—
285	C₄×D₁₁₃	—	4	2	no	—
286	C₄×D₁₁₃	—	4	2	no	—
287	C₄×D₁₁₃	—	4	2	no	—
288	Dic₂₂₆	—	2	2	no	—
289	Dic₂₂₆	—	2	4	no	—
290	Dic₂₂₆	—	4	2	no	—
291	C₂²×C₁₁₃	—	2	2	no	—
292	C₂²×C₁₁₃	—	2	1	no	—
293	C₂²×C₁₁₃	—	2	2	no	—
294	C₂²×C₁₁₃	—	2	1	no	—
295	C₂²×C₁₁₃	—	2	2	no	—
296	C₂²×C₁₁₃	—	2	1	no	—
297	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
298	C₂×D₁₁₃	—	2	2	no	—
299	C₂×D₁₁₃	—	2	2	no	—
300	C₂×D₁₁₃	—	2	1	no	—
301	C₂×D₁₁₃	—	2	1	no	—
302	C₂×D₁₁₃	—	2	2	no	—
303	C₂×D₁₁₃	—	2	1	no	—
304	C₂×D₁₁₃	—	2	2	no	—
305	C₂×D₁₁₃	—	2	1	no	—
306	C₂×D₁₁₃	—	2	1	no	—
307	C₂×D₁₁₃	—	2	2	no	—
308	C₂×D₁₁₃	—	2	1	no	—
309	C₂×D₁₁₃	—	8	4	no	—
310	C₂×D₁₁₃	—	8	4	no	—
311	C₂×D₁₁₃	C₂×#41	1	4	yes	—
312	C₄×C₁₁₃	—	2	2	no	—
313	C₄×C₁₁₃	—	2	1	no	—
314	C₄×C₁₁₃	—	2	1	no	—
315	C₄×C₁₁₃	—	2	2	no	—
316	C₄×C₁₁₃	—	2	2	no	—
317	C₄×C₁₁₃	—	2	1	no	—
318	C₄×C₁₁₃	—	2	1	no	—
319	C₄×C₁₁₃	—	2	1	no	—
320	C₄×C₁₁₃	C₂×#41	1	2	yes	—
321	Dic₁₁₃	—	2	1	no	—
322	Dic₁₁₃	—	2	1	no	—
323	Dic₁₁₃	—	2	1	no	—
324	Dic₁₁₃	—	2	2	no	—
325	Dic₁₁₃	—	2	2	no	—
326	Dic₁₁₃	—	2	1	no	—
327	Dic₁₁₃	—	2	1	no	—
328	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₁₁₃	—	4	1	no	—
330	C₂×C₁₁₃	—	4	2	no	—
331	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
332	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₁₁₃	#585	1	1	yes	characteristic
334	D₁₁₃	—	2	4	no	—
335	D₁₁₃	—	4	1	no	—
336	D₁₁₃	—	4	2	no	—
337	D₁₁₃	—	4	1	no	—
338	#3514	—	113	1	no	maximal, Sylow
339	C₁₁₃	#3514	1	1	yes	characteristic, complemented, Sylow
340	#559	—	113	1	no	—
341	#556	—	113	1	no	—
342	#555	—	113	1	no	—
343	#555	—	113	1	no	—
344	#551	—	113	2	no	—
345	#551	—	113	2	no	—
346	D₄×Q₈	—	113	1	no	—
347	#548	—	113	2	no	—
348	#546	—	113	1	no	—
349	#546	—	113	2	no	—
350	#546	—	113	1	no	—
351	D₄²	—	113	1	no	—
352	#542	—	113	1	no	—
353	#542	D₁₁₃	1	1	yes	characteristic, complemented
354	#538	—	113	2	no	—
355	#538	—	113	2	no	—
356	#532	—	113	1	no	—
357	#529	—	113	2	no	—
358	#529	—	113	1	no	—
359	C₂×#124	—	113	2	no	—
360	#518	—	113	1	no	—
361	#518	—	113	1	no	—
362	C₄×#41	—	113	1	no	—
363	C₂×#41	—	113	1	no	—
364	C₂×#41	—	113	2	no	—
365	C₂²×Q₈	—	113	2	no	—
366	C₂²×D₄	—	113	2	no	—
367	C₂²×D₄	—	113	1	no	—
368	C₂²×D₄	—	113	1	no	—
369	C₄⋊Q₈	—	113	1	no	—
370	C₄⋊Q₈	—	113	1	no	—
371	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
372	#127	—	113	1	no	—
373	#126	—	113	1	no	—
374	#126	—	113	2	no	—
375	#126	—	113	1	no	—
376	#126	—	113	2	no	—
377	#126	—	113	2	no	—
378	#126	C₂×D₁₁₃	1	2	yes	complemented
379	#125	—	113	1	no	—
380	#124	—	113	2	no	—
381	#124	—	113	2	no	—
382	#124	—	113	1	no	—
383	#124	—	113	2	no	—
384	#124	—	113	1	no	—
385	#124	—	113	2	no	—
386	#124	—	113	2	no	—
387	#124	—	113	2	no	—
388	#124	—	113	2	no	—
389	#124	—	113	2	no	—
390	#124	C₂×D₁₁₃	1	2	yes	complemented
391	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
392	#123	—	113	1	no	—
393	#123	—	113	2	no	—
394	#123	—	113	2	no	—
395	#123	—	113	1	no	—
396	#123	—	113	2	no	—
397	#123	—	113	2	no	—
398	#123	—	113	2	no	—
399	#123	C₂×D₁₁₃	1	2	yes	complemented
400	C₂²⋊Q₈	—	113	2	no	—
401	C₂²⋊Q₈	—	113	1	no	—
402	C₂²⋊Q₈	—	113	2	no	—
403	C₂²⋊Q₈	—	113	1	no	—
404	C₂²⋊Q₈	—	113	2	no	—
405	C₂²⋊Q₈	—	113	2	no	—
406	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
407	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
408	#121	—	113	1	no	—
409	#121	—	113	2	no	—
410	#121	—	113	1	no	—
411	#121	—	113	2	no	—
412	#121	—	113	2	no	—
413	#121	—	113	1	no	—
414	#121	—	113	2	no	—
415	#121	—	113	1	no	—
416	#121	—	113	2	no	—
417	#121	—	113	2	no	—
418	#121	C₂×D₁₁₃	1	1	yes	characteristic
419	#120	—	113	2	no	—
420	#120	—	113	2	no	—
421	#120	—	113	2	no	—
422	#120	—	113	2	no	—
423	C₄×Q₈	—	113	1	no	—
424	C₄×Q₈	—	113	2	no	—
425	C₄×Q₈	—	113	1	no	—
426	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
427	C₄×D₄	—	113	1	no	—
428	C₄×D₄	—	113	2	no	—
429	C₄×D₄	—	113	1	no	—
430	C₄×D₄	—	113	1	no	—
431	C₄×D₄	—	113	2	no	—
432	C₄×D₄	—	113	1	no	—
433	C₄×D₄	—	113	2	no	—
434	C₄×D₄	—	113	1	no	—
435	C₄×D₄	—	113	2	no	—
436	C₄×D₄	—	113	2	no	—
437	C₄×D₄	—	113	2	no	—
438	C₄×D₄	—	113	2	no	—
439	C₄×D₄	—	113	1	no	—
440	C₄×D₄	—	113	2	no	—
441	C₄×D₄	—	113	1	no	—
442	C₄×D₄	—	113	1	no	—
443	C₄×D₄	—	113	1	no	—
444	C₄×D₄	—	113	1	no	—
445	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
446	#117	—	113	1	no	—
447	#117	—	113	2	no	—
448	#117	—	113	1	no	—
449	#117	—	113	1	no	—
450	#117	—	113	2	no	—
451	#117	—	113	2	no	—
452	#117	—	113	1	no	—
453	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
454	C₂×C₂²⋊C₄	—	113	2	no	—
455	C₂×C₂²⋊C₄	—	113	2	no	—
456	C₂×C₂²⋊C₄	—	113	2	no	—
457	C₂×C₂²⋊C₄	—	113	2	no	—
458	C₂×C₂²⋊C₄	—	113	2	no	—
459	C₂×C₂²⋊C₄	—	113	2	no	—
460	C₂×C₄²	—	113	2	no	—
461	C₂×C₄²	—	113	1	no	—
462	C₂⁴	—	113	2	no	—
463	C₂⁴	—	113	2	no	—
464	#41	—	452	4	no	—
465	#41	—	226	4	no	—
466	C₂×Q₈	—	113	2	no	—
467	C₂×Q₈	—	113	1	no	—
468	C₂×Q₈	—	113	2	no	—
469	C₂×Q₈	—	452	4	no	—
470	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
472	C₂×D₄	—	113	1	no	—
473	C₂×D₄	—	113	2	no	—
474	C₂×D₄	—	113	2	no	—
475	C₂×D₄	—	113	2	no	—
476	C₂×D₄	—	113	1	no	—
477	C₂×D₄	—	113	2	no	—
478	C₂×D₄	—	113	1	no	—
479	C₂×D₄	—	113	1	no	—
480	C₂×D₄	—	113	2	no	—
481	C₂×D₄	—	113	2	no	—
482	C₂×D₄	—	113	2	no	—
483	C₂×D₄	—	113	2	no	—
484	C₂×D₄	—	113	1	no	—
485	C₂×D₄	—	452	4	no	—
486	C₂×D₄	—	226	4	no	—
487	C₂×D₄	—	226	4	no	—
488	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
490	C₂²×C₄	—	113	2	no	—
491	C₂²×C₄	—	113	2	no	—
492	C₂²×C₄	—	113	1	no	—
493	C₂²×C₄	—	113	2	no	—
494	C₂²×C₄	—	113	2	no	—
495	C₂²×C₄	—	113	2	no	—
496	C₂²×C₄	—	113	2	no	—
497	C₂²×C₄	—	113	2	no	—
498	C₂²×C₄	—	113	1	no	—
499	C₂²×C₄	—	113	2	no	—
500	C₂²×C₄	—	113	1	no	—
501	C₂²×C₄	—	113	1	no	—
502	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
504	C₄⋊C₄	—	113	1	no	—
505	C₄⋊C₄	—	113	1	no	—
506	C₄⋊C₄	—	113	1	no	—
507	C₄⋊C₄	—	113	1	no	—
508	C₄⋊C₄	—	113	1	no	—
509	C₄⋊C₄	—	113	1	no	—
510	C₄⋊C₄	—	113	2	no	—
511	C₄⋊C₄	—	113	2	no	—
512	C₄⋊C₄	—	113	1	no	—
513	C₄⋊C₄	—	113	1	no	—
514	C₄⋊C₄	—	113	2	no	—
515	C₄⋊C₄	—	113	2	no	—
516	C₄⋊C₄	—	113	1	no	—
517	C₄⋊C₄	—	113	1	no	—
518	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
522	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
525	C₂²⋊C₄	—	113	2	no	—
526	C₂²⋊C₄	—	113	1	no	—
527	C₂²⋊C₄	—	113	2	no	—
528	C₂²⋊C₄	—	113	2	no	—
529	C₂²⋊C₄	—	113	1	no	—
530	C₂²⋊C₄	—	113	2	no	—
531	C₂²⋊C₄	—	113	1	no	—
532	C₂²⋊C₄	—	113	2	no	—
533	C₂²⋊C₄	—	113	1	no	—
534	C₂²⋊C₄	—	113	1	no	—
535	C₂²⋊C₄	—	113	2	no	—
536	C₂²⋊C₄	—	113	2	no	—
537	C₂²⋊C₄	—	113	2	no	—
538	C₂²⋊C₄	—	113	2	no	—
539	C₂²⋊C₄	—	113	2	no	—
540	C₂²⋊C₄	—	113	2	no	—
541	C₂²⋊C₄	—	113	2	no	—
542	C₂²⋊C₄	—	113	2	no	—
543	C₂²⋊C₄	—	113	2	no	—
544	C₂²⋊C₄	—	113	2	no	—
545	C₂²⋊C₄	—	113	1	no	—
546	C₂²⋊C₄	—	113	2	no	—
547	C₂²⋊C₄	—	113	1	no	—
548	C₂²⋊C₄	—	113	1	no	—
549	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
556	C₄²	—	113	1	no	—
557	C₄²	—	113	2	no	—
558	C₄²	—	113	1	no	—
559	C₄²	—	113	2	no	—
560	C₄²	—	113	1	no	—
561	C₄²	—	113	2	no	—
562	C₄²	—	113	2	no	—
563	C₄²	—	113	1	no	—
564	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
565	C₄²	C₂²×D₁₁₃	1	2	yes	—
566	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
567	C₂³	—	113	2	no	—
568	C₂³	—	113	1	no	—
569	C₂³	—	113	2	no	—
570	C₂³	—	113	1	no	—
571	C₂³	—	452	2	no	—
572	C₂³	—	452	2	no	—
573	C₂³	—	452	2	no	—
574	C₂³	—	452	2	no	—
575	C₂³	—	226	4	no	—
576	C₂³	—	226	4	no	—
577	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
578	C₂³	C₂³×D₁₁₃	1	2	yes	—
579	Q₈	—	2	2	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	452	2	no	—
582	Q₈	—	226	2	no	—
583	Q₈	—	226	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	113	4	no	—
587	D₄	—	452	2	no	—
588	D₄	—	452	2	no	—
589	D₄	—	452	1	no	—
590	D₄	—	452	2	no	—
591	D₄	—	452	1	no	—
592	D₄	—	452	2	no	—
593	D₄	—	226	4	no	—
594	D₄	—	226	4	no	—
595	D₄	—	226	2	no	—
596	D₄	—	226	4	no	—
597	D₄	—	226	4	no	—
598	D₄	—	226	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	113	1	no	—
602	C₂×C₄	—	113	1	no	—
603	C₂×C₄	—	113	2	no	—
604	C₂×C₄	—	113	1	no	—
605	C₂×C₄	—	113	1	no	—
606	C₂×C₄	—	113	1	no	—
607	C₂×C₄	—	113	1	no	—
608	C₂×C₄	—	113	2	no	—
609	C₂×C₄	—	452	2	no	—
610	C₂×C₄	—	452	2	no	—
611	C₂×C₄	—	452	2	no	—
612	C₂×C₄	—	452	2	no	—
613	C₂×C₄	—	452	1	no	—
614	C₂×C₄	—	452	2	no	—
615	C₂×C₄	—	452	2	no	—
616	C₂×C₄	—	226	4	no	—
617	C₂×C₄	—	226	2	no	—
618	C₂×C₄	—	226	4	no	—
619	C₂×C₄	—	226	2	no	—
620	C₂×C₄	—	226	2	no	—
621	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
624	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
626	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
627	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	113	4	no	—
637	C₂²	—	904	4	no	—
638	C₂²	—	904	4	no	—
639	C₂²	—	226	1	no	—
640	C₂²	—	226	1	no	—
641	C₂²	—	226	2	no	—
642	C₂²	—	226	2	no	—
643	C₂²	—	226	1	no	—
644	C₂²	—	226	1	no	—
645	C₂²	—	226	1	no	—
646	C₂²	—	226	2	no	—
647	C₂²	—	226	1	no	—
648	C₂²	—	226	2	no	—
649	C₂²	—	226	2	no	—
650	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	113	2	no	—
660	C₄	—	226	1	no	—
661	C₄	—	226	1	no	—
662	C₄	—	226	2	no	—
663	C₄	—	226	1	no	—
664	C₄	—	226	2	no	—
665	C₄	—	226	1	no	—
666	C₄	—	226	1	no	—
667	C₄	#41×D₁₁₃	1	2	yes	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	—	452	1	no	—
671	C₂	—	452	2	no	—
672	C₂	—	452	1	no	—
673	C₂	—	226	4	no	—
674	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic
676	C₂	#20299435	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	#3514
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. #20299330	C₂	semidirect
2. #20299319	C₂	semidirect
3. #20299314	C₂	semidirect
4. #20299312	C₂	semidirect
5. #20299276	C₂	semidirect
6. #20299275	C₂	semidirect
7. #20299263	C₂	semidirect
8. #20299258	C₂	semidirect
9. #20299241	C₂	semidirect
10. #20299240	C₂	semidirect
11. #20299239	C₂	semidirect
12. #20299232	C₂	semidirect
13. #20299220	C₂	semidirect
14. #20299187	C₂	semidirect
15. #20299182	C₂	semidirect
16. #20299145	C₂	semidirect
17. #20299131	C₂	semidirect
18. #20299126	C₂	semidirect
19. #124×D₁₁₃	C₂	semidirect
20. #20299072	C₂	semidirect
21. #20299070	C₂	semidirect
22. C₄×#14268648	C₂	semidirect
23. #542×C₁₁₃	C₂	semidirect
25. C₂×#14268647	C₂²	semidirect
26. C₂×Q₈×D₁₁₃	C₂²	semidirect
30. #16813621	C₂²	semidirect
31. #16813621	C₂²	semidirect
33. #16813617	C₂²	semidirect
34. #16813617	C₂²	semidirect
35. #16813616	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813615	C₂²	semidirect
38. #16813612	C₂²	semidirect
39. #16813611	C₂²	semidirect
40. #16813611	C₂²	semidirect
41. #16813611	C₂²	semidirect
42. #16813610	C₂²	semidirect
43. #16813609	C₂²	semidirect
46. #16813608	C₂²	semidirect
47. #16813608	C₂²	semidirect
48. #16813608	C₂²	semidirect
49. #16813607	C₂²	semidirect
50. #16813607	C₂²	semidirect
51. #16813607	C₂²	semidirect
52. #16813606	C₂²	semidirect
53. #16813604	C₂²	semidirect
54. #16813604	C₂²	semidirect
55. #16813604	C₂²	semidirect
56. #16813600	C₂²	semidirect
57. #16813600	C₂²	semidirect
58. #16813600	C₂²	semidirect
59. #16813600	C₂²	semidirect
60. #16813598	C₂²	semidirect
61. #16813598	C₂²	semidirect
63. #16813597	C₂²	semidirect
64. #16813597	C₂²	semidirect
65. #16813597	C₂²	semidirect
68. #16813595	C₂²	semidirect
69. #16813595	C₂²	semidirect
70. #16813594	C₂²	semidirect
71. #16813593	C₂²	semidirect
73. #16813592	C₂²	semidirect
74. #16813592	C₂²	semidirect
76. Q₈×Dic₁₁₃	C₂²	semidirect
77. C₄×Dic₂₂₆	C₂²	semidirect
78. #16813587	C₂²	semidirect
81. C₄×D₄₅₂	C₂²	semidirect
82. C₄×D₄₅₂	C₂²	semidirect
83. C₄×D₄₅₂	C₂²	semidirect
84. C₄×D₄₅₂	C₂²	semidirect
85. D₄×Dic₁₁₃	C₂²	semidirect
88. #16813584	C₂²	semidirect
89. #16813584	C₂²	semidirect
90. #16813584	C₂²	semidirect
92. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
93. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
94. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
95. #16813582	C₂²	semidirect
96. #16813582	C₂²	semidirect
97. #16813581	C₂²	semidirect
98. #16813580	C₂²	semidirect
99. #16813580	C₂²	semidirect
100. #16813580	C₂²	semidirect
101. #16813580	C₂²	semidirect
102. #16813579	C₂²	semidirect
103. #16813578	C₂²	semidirect
104. C₂×#14268624	C₂²	semidirect
105. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
106. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
107. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
108. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
109. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
110. C₄²×D₁₁₃	C₂²	semidirect
111. C₄²×D₁₁₃	C₂²	semidirect
112. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
113. #126×C₁₁₃	C₂²	semidirect
114. #124×C₁₁₃	C₂²	semidirect
115. #124×C₁₁₃	C₂²	semidirect
116. #123×C₁₁₃	C₂²	semidirect
117. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
118. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
120. C₄×Q₈×C₁₁₃	C₂²	semidirect
121. C₄×D₄×C₁₁₃	C₂²	semidirect
122. #117×C₁₁₃	C₂²	semidirect
276. D₄₅₂	#41	semidirect
339. C₁₁₃	#3514	semidirect
353. #542	D₁₁₃	semidirect
371. C₄⋊Q₈	C₂×D₁₁₃	semidirect
378. #126	C₂×D₁₁₃	semidirect
390. #124	C₂×D₁₁₃	semidirect
391. #124	C₂×D₁₁₃	semidirect
399. #123	C₂×D₁₁₃	semidirect
406. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
407. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
426. C₄×Q₈	C₂×D₁₁₃	semidirect
445. C₄×D₄	C₂×D₁₁₃	semidirect
453. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299330	2
#20299319	2
#20299314	2
#20299312	2
#20299276	2
#20299275	2
#20299263	2
#20299258	2
#20299241	2
#20299240	2
#20299239	2
#20299232	2
#20299220	2
#20299187	2
#20299182	2
#20299145	2
#20299131	2
#20299126	2
#124×D₁₁₃	2
#20299072	2
#20299070	2
C₄×#14268648	2
#542×C₁₁₃	2
#3514	113