Subgroups — #28404627

Order 14464.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299318	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299317	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299305	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299300	C₂	1	2	yes	maximal, complemented
5	#20299295	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299285	C₂	1	2	yes	maximal, complemented
7	#20299282	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299279	C₂	1	2	yes	maximal, complemented
9	#20299274	C₂	1	2	yes	maximal, complemented
10	#20299247	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299242	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299217	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299208	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299193	C₂	1	2	yes	maximal, complemented
15	#20299183	C₂	1	2	yes	maximal, complemented
16	#20299129	C₂	1	1	yes	maximal, characteristic, complemented
17	#20299128	C₂	1	1	yes	maximal, characteristic, complemented
18	#20299125	C₂	1	2	yes	maximal, complemented
19	C₂×#16813615	C₂	1	2	yes	maximal, complemented
20	#20299077	C₂	1	1	yes	maximal, characteristic, complemented
21	#20299073	C₂	1	1	yes	maximal, characteristic, complemented
22	#41×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14268646	C₂²	1	1	yes	characteristic
25	#16813622	C₂²	1	1	yes	characteristic, complemented
26	#16813620	C₂²	1	1	yes	characteristic, complemented
27	#16813617	C₂²	1	1	yes	characteristic, complemented
28	#16813615	C₂²	1	2	yes	—
29	#16813615	C₂²	1	2	yes	—
30	#16813615	C₂²	1	2	yes	—
31	#16813615	C₂²	1	1	yes	characteristic
32	#16813615	C₂²	1	2	yes	—
33	#16813615	C₂²	1	2	yes	complemented
34	#16813615	C₂²	1	2	yes	complemented
35	#16813615	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	#16813613	C₂²	1	1	yes	characteristic, complemented
40	#16813613	C₂²	1	2	yes	complemented
41	#16813613	C₂²	1	1	yes	characteristic, complemented
42	#16813612	C₂²	1	2	yes	complemented
43	#16813612	C₂²	1	1	yes	characteristic, complemented
44	#16813612	C₂²	1	2	yes	complemented
45	#16813609	C₂²	1	2	yes	—
46	#16813609	C₂²	1	1	yes	characteristic
47	#16813608	C₂²	1	1	yes	characteristic
48	#16813608	C₂²	1	2	yes	complemented
49	#16813606	C₂²	1	2	yes	complemented
50	#16813606	C₂²	1	1	yes	characteristic, complemented
51	#16813605	C₂²	1	2	yes	complemented
52	#16813604	C₂²	1	2	yes	—
53	#16813603	C₂²	1	1	yes	characteristic
54	#16813603	C₂²	1	2	yes	—
55	#16813603	C₂²	1	2	yes	complemented
56	#16813603	C₂²	1	2	yes	complemented
57	#16813603	C₂²	1	2	yes	complemented
58	#16813601	C₂²	1	1	yes	characteristic
59	#16813601	C₂²	1	2	yes	complemented
60	#16813601	C₂²	1	1	yes	characteristic, complemented
61	#16813599	C₂²	1	2	yes	complemented
62	#16813599	C₂²	1	2	yes	complemented
63	#16813599	C₂²	1	2	yes	complemented
64	#16813599	C₂²	1	2	yes	complemented
65	#16813599	C₂²	1	1	yes	characteristic, complemented
66	#16813598	C₂²	1	1	yes	characteristic, complemented
67	#16813594	C₂²	1	2	yes	—
68	#16813594	C₂²	1	1	yes	characteristic
69	#16813594	C₂²	1	2	yes	complemented
70	#16813593	C₂²	1	1	yes	characteristic
71	#16813593	C₂²	1	2	yes	complemented
72	#16813591	C₂²	1	2	yes	—
73	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
74	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
77	#16813587	C₂²	1	2	yes	complemented
78	#16813587	C₂²	1	1	yes	characteristic, complemented
79	D₄×Dic₁₁₃	C₂²	1	2	yes	—
80	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
81	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
82	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
84	D₄×Dic₁₁₃	C₂²	1	2	yes	—
85	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
86	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
87	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
88	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
90	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
92	#16813582	C₂²	1	2	yes	complemented
93	#16813582	C₂²	1	2	yes	complemented
94	#16813581	C₂²	1	1	yes	characteristic
95	#16813581	C₂²	1	1	yes	characteristic
96	#16813581	C₂²	1	2	yes	complemented
97	#16813581	C₂²	1	1	yes	characteristic, complemented
98	#16813580	C₂²	1	2	yes	complemented
99	#16813579	C₂²	1	1	yes	characteristic, complemented
100	#16813578	C₂²	1	2	yes	complemented
101	#16813578	C₂²	1	2	yes	complemented
102	#16813578	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
104	C₂×#14268626	C₂²	1	2	yes	complemented
105	C₂×#14268626	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
108	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
109	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
110	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
114	#124×C₁₁₃	C₂²	1	1	yes	characteristic
115	#123×C₁₁₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
117	#121×C₁₁₃	C₂²	1	1	yes	characteristic
118	#121×C₁₁₃	C₂²	1	2	yes	—
119	#120×C₁₁₃	C₂²	1	2	yes	—
120	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
123	#14268646	—	2	4	no	—
124	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
125	C₂×Dic₂₂₆	C₂³	1	2	yes	—
126	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
133	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
134	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
137	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
138	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
141	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
144	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
145	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
146	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
151	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
152	#14268626	C₂³	1	2	yes	—
153	#14268626	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	2	yes	—
159	#14268626	C₂³	1	2	yes	—
160	#14268626	C₂³	1	1	yes	characteristic
161	#14268626	C₂³	1	1	yes	characteristic
162	#14268626	C₂³	1	2	yes	—
163	#14268626	C₂³	1	2	yes	—
164	#14268626	C₂³	1	2	yes	—
165	#14268626	C₂³	1	1	yes	characteristic
166	#14268626	C₂³	1	2	yes	—
167	#14268626	C₂³	1	1	yes	characteristic
168	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
184	#14268624	C₂³	1	1	yes	characteristic
185	#14268624	C₂³	1	1	yes	characteristic
186	#14268624	C₂³	1	1	yes	characteristic
187	#14268624	C₂³	1	2	yes	—
188	#14268624	C₂³	1	1	yes	characteristic
189	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
190	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₁₃	C₂³	1	2	yes	—
192	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₁₃	C₂³	1	2	yes	—
194	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
200	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
201	#41×C₁₁₃	—	2	4	no	—
202	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₁₁₃	—	2	4	no	—
204	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
206	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
207	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
208	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
224	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
225	C₂³×C₁₁₃	—	2	4	no	—
226	C₂³×C₁₁₃	—	4	2	no	—
227	C₂³×C₁₁₃	—	4	2	no	—
228	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
229	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
230	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
232	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₁₃	—	2	2	no	—
234	D₄×C₁₁₃	—	2	4	no	—
235	D₄×C₁₁₃	—	2	4	no	—
236	D₄×C₁₁₃	—	2	2	no	—
237	D₄×C₁₁₃	—	4	1	no	—
238	D₄×C₁₁₃	—	4	2	no	—
239	D₄×C₁₁₃	#41	1	4	yes	—
240	C₂×C₄×C₁₁₃	—	2	4	no	—
241	C₂×C₄×C₁₁₃	—	2	2	no	—
242	C₂×C₄×C₁₁₃	—	2	2	no	—
243	C₂×C₄×C₁₁₃	—	4	2	no	—
244	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
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	C₂²⋊D₁₁₃	—	2	4	no	—
252	C₂²⋊D₁₁₃	—	4	1	no	—
253	C₂²⋊D₁₁₃	—	4	2	no	—
254	C₂²⋊D₁₁₃	—	4	1	no	—
255	C₂×Dic₁₁₃	—	2	4	no	—
256	C₂×Dic₁₁₃	—	4	2	no	—
257	C₂×Dic₁₁₃	—	4	2	no	—
258	C₂×Dic₁₁₃	—	4	2	no	—
259	C₂×Dic₁₁₃	—	4	2	no	—
260	C₂×Dic₁₁₃	—	4	1	no	—
261	C₂×Dic₁₁₃	—	4	2	no	—
262	C₂×Dic₁₁₃	—	4	1	no	—
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	2	yes	—
267	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
268	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
270	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
274	C₄×D₁₁₃	—	2	2	no	—
275	C₄×D₁₁₃	—	4	2	no	—
276	Dic₂₂₆	—	2	2	no	—
277	Dic₂₂₆	—	4	2	no	—
278	Dic₂₂₆	—	4	1	no	—
279	C₂²×C₁₁₃	—	2	2	no	—
280	C₂²×C₁₁₃	—	2	2	no	—
281	C₂²×C₁₁₃	—	2	1	no	—
282	C₂²×C₁₁₃	—	2	1	no	—
283	C₂²×C₁₁₃	—	2	2	no	—
284	C₂²×C₁₁₃	—	2	1	no	—
285	C₂²×C₁₁₃	—	2	2	no	—
286	C₂²×C₁₁₃	—	2	1	no	—
287	C₂²×C₁₁₃	—	2	2	no	—
288	C₂²×C₁₁₃	—	2	1	no	—
289	C₂²×C₁₁₃	—	2	1	no	—
290	C₂²×C₁₁₃	—	8	4	no	—
291	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
292	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₁₃	—	2	1	no	—
294	C₂×D₁₁₃	—	2	1	no	—
295	C₂×D₁₁₃	—	2	1	no	—
296	C₄×C₁₁₃	—	2	1	no	—
297	C₄×C₁₁₃	—	2	1	no	—
298	C₄×C₁₁₃	—	2	2	no	—
299	C₄×C₁₁₃	—	2	1	no	—
300	C₄×C₁₁₃	—	2	1	no	—
301	C₄×C₁₁₃	—	2	2	no	—
302	C₄×C₁₁₃	C₂×#41	1	2	yes	—
303	Dic₁₁₃	—	2	2	no	—
304	Dic₁₁₃	—	2	1	no	—
305	Dic₁₁₃	—	2	1	no	—
306	Dic₁₁₃	—	2	2	no	—
307	Dic₁₁₃	—	2	1	no	—
308	Dic₁₁₃	—	2	2	no	—
309	Dic₁₁₃	—	2	2	no	—
310	Dic₁₁₃	—	2	1	no	—
311	Dic₁₁₃	—	2	1	no	—
312	Dic₁₁₃	—	2	1	no	—
313	Dic₁₁₃	—	2	1	no	—
314	C₂×C₁₁₃	—	2	4	no	—
315	C₂×C₁₁₃	—	4	1	no	—
316	C₂×C₁₁₃	—	4	2	no	—
317	C₂×C₁₁₃	—	4	1	no	—
318	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
319	C₂×C₁₁₃	#585	1	1	yes	characteristic
320	C₂×C₁₁₃	#585	1	1	yes	characteristic
321	D₁₁₃	—	4	1	no	—
322	#3521	—	113	1	no	maximal, Sylow
323	C₁₁₃	#3521	1	1	yes	characteristic, complemented, Sylow
324	#556	—	113	1	no	—
325	#556	—	113	1	no	—
326	#554	—	113	1	no	—
327	#553	—	113	1	no	—
328	#553	—	113	2	no	—
329	#552	—	113	2	no	—
330	#552	—	113	1	no	—
331	#551	—	113	2	no	—
332	#551	—	113	2	no	—
333	#547	—	113	1	no	—
334	#546	—	113	1	no	—
335	#546	D₁₁₃	1	1	yes	characteristic, complemented
336	#542	—	113	1	no	—
337	#541	—	113	1	no	—
338	#539	—	113	2	no	—
339	#538	—	113	2	no	—
340	#529	—	113	2	no	—
341	#529	—	113	1	no	—
342	#529	—	113	1	no	—
343	C₂×#126	—	113	2	no	—
344	#520	—	113	1	no	—
345	#518	—	113	1	no	—
346	C₄×#41	—	113	1	no	—
347	C₂×#41	—	113	1	no	—
348	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
349	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
350	C₄⋊Q₈	—	113	1	no	—
351	C₄⋊Q₈	—	113	1	no	—
352	#126	—	113	1	no	—
353	#126	—	113	1	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	#126	—	113	2	no	—
362	#126	—	113	2	no	—
363	#126	—	113	2	no	—
364	#125	—	113	2	no	—
365	#125	—	113	1	no	—
366	#125	—	113	1	no	—
367	#125	—	113	2	no	—
368	#125	—	113	2	no	—
369	#125	—	113	1	no	—
370	#124	—	113	1	no	—
371	#124	—	113	2	no	—
372	#124	—	113	2	no	—
373	#124	—	113	1	no	—
374	#124	C₂×D₁₁₃	1	1	yes	characteristic
375	#123	—	113	2	no	—
376	#123	—	113	1	no	—
377	#123	—	113	2	no	—
378	#123	—	113	2	no	—
379	#123	—	113	2	no	—
380	#123	—	113	2	no	—
381	#123	—	113	1	no	—
382	#123	—	113	2	no	—
383	#123	—	113	2	no	—
384	#123	C₂×D₁₁₃	1	2	yes	—
385	C₂²⋊Q₈	—	113	1	no	—
386	C₂²⋊Q₈	—	113	1	no	—
387	C₂²⋊Q₈	—	113	2	no	—
388	C₂²⋊Q₈	—	113	1	no	—
389	C₂²⋊Q₈	—	113	1	no	—
390	C₂²⋊Q₈	—	113	2	no	—
391	C₂²⋊Q₈	—	113	2	no	—
392	C₂²⋊Q₈	—	113	2	no	—
393	C₂²⋊Q₈	—	113	2	no	—
394	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
395	#121	—	113	1	no	—
396	#121	—	113	2	no	—
397	#121	—	113	1	no	—
398	#121	—	113	2	no	—
399	#121	—	113	2	no	—
400	#121	C₂×D₁₁₃	1	1	yes	characteristic
401	#121	C₂×D₁₁₃	1	2	yes	—
402	#120	—	113	2	no	—
403	#120	C₂×D₁₁₃	1	2	yes	—
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	—	113	1	no	—
409	C₄×Q₈	—	113	1	no	—
410	C₄×D₄	—	113	1	no	—
411	C₄×D₄	—	113	1	no	—
412	C₄×D₄	—	113	2	no	—
413	C₄×D₄	—	113	2	no	—
414	C₄×D₄	—	113	2	no	—
415	C₄×D₄	—	113	1	no	—
416	C₄×D₄	—	113	1	no	—
417	C₄×D₄	—	113	2	no	—
418	C₄×D₄	—	113	1	no	—
419	C₄×D₄	—	113	2	no	—
420	C₄×D₄	—	113	2	no	—
421	C₄×D₄	—	113	1	no	—
422	C₄×D₄	—	113	1	no	—
423	C₄×D₄	—	113	2	no	—
424	C₄×D₄	—	113	2	no	—
425	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
426	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
427	#117	—	113	2	no	—
428	#117	—	113	1	no	—
429	#117	—	113	1	no	—
430	#117	—	113	1	no	—
431	#117	—	113	2	no	—
432	#117	—	113	2	no	—
433	#117	—	113	2	no	—
434	#117	—	113	2	no	—
435	#117	—	113	1	no	—
436	C₂×C₄⋊C₄	—	113	2	no	—
437	C₂×C₄⋊C₄	—	113	2	no	—
438	C₂×C₄⋊C₄	—	113	2	no	—
439	C₂×C₄⋊C₄	—	113	1	no	—
440	C₂×C₂²⋊C₄	—	113	2	no	—
441	C₂×C₂²⋊C₄	—	113	2	no	—
442	C₂×C₂²⋊C₄	—	113	2	no	—
443	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	—
444	C₂×C₄²	—	113	2	no	—
445	C₂×C₄²	—	113	1	no	—
446	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
447	#41	—	2	4	no	—
448	#41	—	226	4	no	—
449	C₂×Q₈	—	113	1	no	—
450	C₂×Q₈	—	113	2	no	—
451	C₂×Q₈	—	113	1	no	—
452	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	113	1	no	—
455	C₂×D₄	—	113	2	no	—
456	C₂×D₄	—	113	1	no	—
457	C₂×D₄	—	113	2	no	—
458	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
459	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
460	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
461	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
462	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
463	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
464	C₂²×C₄	—	113	2	no	—
465	C₂²×C₄	—	113	2	no	—
466	C₂²×C₄	—	113	1	no	—
467	C₂²×C₄	—	113	1	no	—
468	C₂²×C₄	—	113	2	no	—
469	C₂²×C₄	—	113	2	no	—
470	C₂²×C₄	—	113	2	no	—
471	C₂²×C₄	—	113	2	no	—
472	C₂²×C₄	—	113	2	no	—
473	C₂²×C₄	—	113	1	no	—
474	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
478	C₄⋊C₄	—	113	1	no	—
479	C₄⋊C₄	—	113	2	no	—
480	C₄⋊C₄	—	113	1	no	—
481	C₄⋊C₄	—	113	1	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	1	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	2	no	—
498	C₄⋊C₄	—	113	2	no	—
499	C₄⋊C₄	—	113	2	no	—
500	C₄⋊C₄	—	113	2	no	—
501	C₄⋊C₄	—	113	2	no	—
502	C₄⋊C₄	—	113	1	no	—
503	C₄⋊C₄	—	113	1	no	—
504	C₄⋊C₄	—	113	2	no	—
505	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
508	C₂²⋊C₄	—	113	1	no	—
509	C₂²⋊C₄	—	113	2	no	—
510	C₂²⋊C₄	—	113	1	no	—
511	C₂²⋊C₄	—	113	1	no	—
512	C₂²⋊C₄	—	113	2	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	—	113	2	no	—
523	C₂²⋊C₄	—	113	1	no	—
524	C₂²⋊C₄	—	113	1	no	—
525	C₂²⋊C₄	—	113	1	no	—
526	C₂²⋊C₄	—	113	1	no	—
527	C₂²⋊C₄	—	113	2	no	—
528	C₂²⋊C₄	—	113	1	no	—
529	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
530	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
536	C₄²	—	113	1	no	—
537	C₄²	—	113	1	no	—
538	C₄²	—	113	1	no	—
539	C₄²	—	113	2	no	—
540	C₄²	—	113	2	no	—
541	C₄²	—	113	1	no	—
542	C₄²	—	113	2	no	—
543	C₄²	—	113	2	no	—
544	C₄²	—	113	2	no	—
545	C₄²	—	113	2	no	—
546	C₄²	—	113	1	no	—
547	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	—	113	1	no	—
552	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
553	C₂³	C₂³×D₁₁₃	1	2	yes	—
554	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
555	C₂³	C₂³×D₁₁₃	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	452	1	no	—
558	Q₈	—	452	2	no	—
559	Q₈	—	226	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	452	1	no	—
566	D₄	—	452	1	no	—
567	D₄	—	452	2	no	—
568	D₄	—	226	4	no	—
569	D₄	#14268646	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	113	1	no	—
575	C₂×C₄	—	113	2	no	—
576	C₂×C₄	—	113	1	no	—
577	C₂×C₄	—	113	1	no	—
578	C₂×C₄	—	113	2	no	—
579	C₂×C₄	—	113	1	no	—
580	C₂×C₄	—	113	2	no	—
581	C₂×C₄	—	113	1	no	—
582	C₂×C₄	—	113	2	no	—
583	C₂×C₄	—	113	1	no	—
584	C₂×C₄	—	113	1	no	—
585	C₂×C₄	—	452	2	no	—
586	C₂×C₄	—	452	2	no	—
587	C₂×C₄	—	452	2	no	—
588	C₂×C₄	—	452	1	no	—
589	C₂×C₄	—	452	1	no	—
590	C₂×C₄	—	452	2	no	—
591	C₂×C₄	—	452	2	no	—
592	C₂×C₄	—	452	2	no	—
593	C₂×C₄	—	226	4	no	—
594	C₂×C₄	—	226	2	no	—
595	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
598	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
600	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	8	4	no	—
614	C₂²	—	226	1	no	—
615	C₂²	—	226	1	no	—
616	C₂²	—	226	1	no	—
617	C₂²	C₂×#14268646	1	4	yes	—
618	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	226	1	no	—
626	C₄	—	226	2	no	—
627	C₄	—	226	2	no	—
628	C₄	—	226	1	no	—
629	C₄	—	226	1	no	—
630	C₄	—	226	1	no	—
631	C₄	—	226	1	no	—
632	C₄	—	226	1	no	—
633	C₄	—	226	1	no	—
634	C₄	—	226	2	no	—
635	C₄	—	226	2	no	—
636	C₄	C₂×#14268646	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	452	1	no	—
642	C₂	C₂²×#14268646	1	1	yes	characteristic
643	C₂	#20299433	1	1	yes	characteristic
644	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#546×C₁₁₃	C₂
hypercenter	#546	D₁₁₃
hypocenter	C₁₁₃	#3521
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #20299318	C₂	semidirect
2. #20299317	C₂	semidirect
3. #20299305	C₂	semidirect
4. #20299300	C₂	semidirect
5. #20299295	C₂	semidirect
6. #20299285	C₂	semidirect
7. #20299282	C₂	semidirect
8. #20299279	C₂	semidirect
9. #20299274	C₂	semidirect
10. #20299247	C₂	semidirect
11. #20299242	C₂	semidirect
12. #20299217	C₂	semidirect
13. #20299208	C₂	semidirect
14. #20299193	C₂	semidirect
15. #20299183	C₂	semidirect
16. #20299129	C₂	semidirect
17. #20299128	C₂	semidirect
18. #20299125	C₂	semidirect
19. C₂×#16813615	C₂	semidirect
20. #20299077	C₂	semidirect
21. #20299073	C₂	semidirect
22. #41×Dic₁₁₃	C₂	semidirect
23. #546×C₁₁₃	C₂	semidirect
25. #16813622	C₂²	semidirect
26. #16813620	C₂²	semidirect
27. #16813617	C₂²	semidirect
33. #16813615	C₂²	semidirect
34. #16813615	C₂²	semidirect
35. #16813615	C₂²	semidirect
36. #16813615	C₂²	semidirect
37. #16813615	C₂²	semidirect
38. #16813615	C₂²	semidirect
39. #16813613	C₂²	semidirect
40. #16813613	C₂²	semidirect
41. #16813613	C₂²	semidirect
42. #16813612	C₂²	semidirect
43. #16813612	C₂²	semidirect
44. #16813612	C₂²	semidirect
48. #16813608	C₂²	semidirect
49. #16813606	C₂²	semidirect
50. #16813606	C₂²	semidirect
51. #16813605	C₂²	semidirect
55. #16813603	C₂²	semidirect
56. #16813603	C₂²	semidirect
57. #16813603	C₂²	semidirect
59. #16813601	C₂²	semidirect
60. #16813601	C₂²	semidirect
61. #16813599	C₂²	semidirect
62. #16813599	C₂²	semidirect
63. #16813599	C₂²	semidirect
64. #16813599	C₂²	semidirect
65. #16813599	C₂²	semidirect
66. #16813598	C₂²	semidirect
69. #16813594	C₂²	semidirect
71. #16813593	C₂²	semidirect
73. Q₈×Dic₁₁₃	C₂²	semidirect
74. Q₈×Dic₁₁₃	C₂²	semidirect
75. C₄×Dic₂₂₆	C₂²	semidirect
76. C₄×Dic₂₂₆	C₂²	semidirect
77. #16813587	C₂²	semidirect
78. #16813587	C₂²	semidirect
86. D₄×Dic₁₁₃	C₂²	semidirect
87. D₄×Dic₁₁₃	C₂²	semidirect
88. D₄×Dic₁₁₃	C₂²	semidirect
90. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
91. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
92. #16813582	C₂²	semidirect
93. #16813582	C₂²	semidirect
96. #16813581	C₂²	semidirect
97. #16813581	C₂²	semidirect
98. #16813580	C₂²	semidirect
99. #16813579	C₂²	semidirect
100. #16813578	C₂²	semidirect
101. #16813578	C₂²	semidirect
102. #16813578	C₂²	semidirect
103. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
104. C₂×#14268626	C₂²	semidirect
105. C₂×#14268626	C₂²	semidirect
106. C₄⋊C₄×D₁₁₃	C₂²	semidirect
110. C₂×C₄×Dic₁₁₃	C₂²	semidirect
111. C₂×C₄×Dic₁₁₃	C₂²	semidirect
323. C₁₁₃	#3521	semidirect
335. #546	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299318	2
#20299317	2
#20299305	2
#20299300	2
#20299295	2
#20299285	2
#20299282	2
#20299279	2
#20299274	2
#20299247	2
#20299242	2
#20299217	2
#20299208	2
#20299193	2
#20299183	2
#20299129	2
#20299128	2
#20299125	2
C₂×#16813615	2
#20299077	2
#20299073	2
#41×Dic₁₁₃	2
#546×C₁₁₃	2
#3521	113