Subgroups — #28404177

Order 14464.

1242 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299332	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299302	C₂	1	2	yes	maximal, complemented
3	#20299299	C₂	1	2	yes	maximal, complemented
4	#20299297	C₂	1	2	yes	maximal, complemented
5	#20299278	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299272	C₂	1	2	yes	maximal, complemented
7	#20299240	C₂	1	2	yes	maximal, complemented
8	#20299238	C₂	1	2	yes	maximal, complemented
9	#20299230	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299147	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299131	C₂	1	2	yes	maximal, complemented
12	#20299125	C₂	1	2	yes	maximal, complemented
13	#20299111	C₂	1	2	yes	maximal, complemented
14	#20299106	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299104	C₂	1	1	yes	maximal, characteristic, complemented
16	#20299066	C₂	1	2	yes	maximal, complemented
17	C₂×#16813582	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₁₁₃	C₂	1	2	yes	maximal, complemented
19	#551×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268648	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14268647	C₂²	1	2	yes	—
22	C₂×#14268646	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
24	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
25	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
28	#16813620	C₂²	1	1	yes	characteristic, complemented
29	#16813618	C₂²	1	1	yes	characteristic
30	#16813617	C₂²	1	2	yes	complemented
31	#16813616	C₂²	1	2	yes	complemented
32	#16813615	C₂²	1	2	yes	complemented
33	#16813612	C₂²	1	2	yes	complemented
34	#16813612	C₂²	1	2	yes	complemented
35	#16813610	C₂²	1	1	yes	characteristic, complemented
36	#16813608	C₂²	1	2	yes	complemented
37	#16813608	C₂²	1	2	yes	complemented
38	#16813607	C₂²	1	2	yes	complemented
39	#16813607	C₂²	1	2	yes	complemented
40	#16813607	C₂²	1	2	yes	complemented
41	#16813606	C₂²	1	1	yes	characteristic, complemented
42	#16813605	C₂²	1	2	yes	complemented
43	#16813605	C₂²	1	1	yes	characteristic, complemented
44	#16813604	C₂²	1	2	yes	complemented
45	#16813603	C₂²	1	1	yes	characteristic, complemented
46	#16813600	C₂²	1	2	yes	complemented
47	#16813600	C₂²	1	2	yes	complemented
48	#16813599	C₂²	1	2	yes	complemented
49	#16813599	C₂²	1	2	yes	complemented
50	#16813598	C₂²	1	2	yes	complemented
51	#16813597	C₂²	1	2	yes	complemented
52	#16813596	C₂²	1	2	yes	complemented
53	#16813595	C₂²	1	2	yes	—
54	#16813595	C₂²	1	2	yes	complemented
55	#16813595	C₂²	1	2	yes	complemented
56	#16813595	C₂²	1	2	yes	complemented
57	#16813594	C₂²	1	2	yes	—
58	#16813594	C₂²	1	2	yes	complemented
59	#16813592	C₂²	1	2	yes	—
60	#16813592	C₂²	1	1	yes	characteristic, complemented
61	#16813592	C₂²	1	2	yes	complemented
62	#16813591	C₂²	1	1	yes	characteristic, complemented
63	#16813590	C₂²	1	1	yes	characteristic
64	#16813587	C₂²	1	2	yes	complemented
65	#16813587	C₂²	1	2	yes	complemented
66	C₄×D₄₅₂	C₂²	1	2	yes	complemented
67	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
68	#16813584	C₂²	1	2	yes	complemented
69	#16813584	C₂²	1	2	yes	complemented
70	#16813584	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
73	#16813582	C₂²	1	2	yes	—
74	#16813582	C₂²	1	2	yes	—
75	#16813582	C₂²	1	2	yes	—
76	#16813582	C₂²	1	2	yes	complemented
77	#16813582	C₂²	1	2	yes	complemented
78	#16813582	C₂²	1	2	yes	complemented
79	#16813582	C₂²	1	2	yes	complemented
80	#16813582	C₂²	1	2	yes	complemented
81	#16813582	C₂²	1	2	yes	complemented
82	#16813582	C₂²	1	2	yes	complemented
83	#16813582	C₂²	1	2	yes	complemented
84	#16813582	C₂²	1	2	yes	complemented
85	#16813580	C₂²	1	2	yes	complemented
86	#16813579	C₂²	1	2	yes	complemented
87	#16813579	C₂²	1	2	yes	complemented
88	#16813578	C₂²	1	1	yes	characteristic, complemented
89	#16813578	C₂²	1	1	yes	characteristic, complemented
90	C₂×#14268626	C₂²	1	2	yes	complemented
91	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
92	C₂×#14268624	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
95	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
96	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
97	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	#126×C₁₁₃	C₂²	1	2	yes	complemented
99	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
100	#123×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
101	#123×C₁₁₃	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
103	#120×C₁₁₃	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
105	#117×C₁₁₃	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
107	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
108	C₂³×D₁₁₃	C₂³	1	2	yes	—
109	#14268648	—	4	2	no	—
110	#14268647	—	2	8	no	—
111	#14268646	—	4	2	no	—
112	C₂×Dic₂₂₆	C₂³	1	2	yes	—
113	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
114	C₂×D₄₅₂	C₂³	1	2	yes	—
115	C₂×D₄₅₂	C₂³	1	2	yes	—
116	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
117	C₂×D₄₅₂	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
119	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊D₁₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
127	D₄×D₁₁₃	—	2	8	no	—
128	C₂²×Dic₁₁₃	—	4	2	no	—
129	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
130	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
132	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
134	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₁₃	—	4	2	no	—
136	C₂×C₄×D₁₁₃	—	4	4	no	—
137	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
138	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
143	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
144	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
146	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
147	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
148	#14268626	C₂³	1	2	yes	—
149	#14268626	C₂³	1	2	yes	—
150	#14268626	C₂³	1	2	yes	—
151	#14268626	C₂³	1	2	yes	—
152	#14268626	C₂³	1	2	yes	—
153	#14268626	C₂³	1	2	yes	—
154	#14268626	C₂³	1	2	yes	—
155	#14268626	C₂³	1	2	yes	—
156	#14268626	C₂³	1	2	yes	—
157	#14268626	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
161	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
162	#14268624	C₂³	1	2	yes	—
163	#14268624	C₂³	1	2	yes	—
164	#14268624	C₂³	1	2	yes	—
165	#14268624	C₂³	1	2	yes	—
166	#14268624	C₂³	1	2	yes	—
167	#14268624	C₂³	1	2	yes	—
168	#14268624	C₂³	1	2	yes	—
169	#14268624	C₂³	1	2	yes	—
170	#14268624	C₂³	1	2	yes	—
171	#14268624	C₂³	1	2	yes	—
172	#14268624	C₂³	1	2	yes	—
173	#14268624	C₂³	1	2	yes	—
174	C₄×Dic₁₁₃	C₂³	1	2	yes	—
175	C₄×Dic₁₁₃	C₂³	1	2	yes	—
176	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
177	C₄×Dic₁₁₃	C₂³	1	2	yes	—
178	C₄×Dic₁₁₃	C₂³	1	2	yes	—
179	C₄×Dic₁₁₃	C₂³	1	2	yes	—
180	C₄×Dic₁₁₃	C₂³	1	2	yes	—
181	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
182	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
184	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
186	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
187	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
191	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
196	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
200	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
201	C₄²×C₁₁₃	C₂³	1	2	yes	—
202	C₂³×C₁₁₃	—	2	4	no	—
203	C₂³×C₁₁₃	—	4	1	no	—
204	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
207	C₂²×D₁₁₃	—	2	4	no	—
208	C₂²×D₁₁₃	—	2	4	no	—
209	C₂²×D₁₁₃	—	2	4	no	—
210	C₂²×D₁₁₃	—	4	1	no	—
211	C₂²×D₁₁₃	—	4	2	no	—
212	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
213	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
215	Q₈×C₁₁₃	—	4	1	no	—
216	D₄×C₁₁₃	—	2	4	no	—
217	D₄×C₁₁₃	—	4	1	no	—
218	C₂×C₄×C₁₁₃	—	2	4	no	—
219	C₂×C₄×C₁₁₃	—	4	1	no	—
220	C₂×C₄×C₁₁₃	—	4	2	no	—
221	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
222	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
223	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
224	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
225	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
226	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
227	C₂²⋊D₁₁₃	—	2	4	no	—
228	C₂²⋊D₁₁₃	—	2	4	no	—
229	C₂²⋊D₁₁₃	—	2	4	no	—
230	C₂²⋊D₁₁₃	—	2	4	no	—
231	C₂²⋊D₁₁₃	—	2	4	no	—
232	C₂²⋊D₁₁₃	—	4	1	no	—
233	C₂²⋊D₁₁₃	—	4	1	no	—
234	C₂²⋊D₁₁₃	#41	1	8	yes	complemented
235	C₂×Dic₁₁₃	—	2	4	no	—
236	C₂×Dic₁₁₃	—	2	4	no	—
237	C₂×Dic₁₁₃	—	2	2	no	—
238	C₂×Dic₁₁₃	—	2	2	no	—
239	C₂×Dic₁₁₃	—	4	2	no	—
240	C₂×Dic₁₁₃	—	4	1	no	—
241	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
242	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
243	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
244	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
248	D₄₅₂	—	2	4	no	—
249	D₄₅₂	—	2	4	no	—
250	D₄₅₂	—	4	1	no	—
251	D₄₅₂	—	4	2	no	—
252	C₄×D₁₁₃	—	2	4	no	—
253	C₄×D₁₁₃	—	2	4	no	—
254	C₄×D₁₁₃	—	2	4	no	—
255	C₄×D₁₁₃	—	2	4	no	—
256	C₄×D₁₁₃	—	2	4	no	—
257	C₄×D₁₁₃	—	2	2	no	—
258	C₄×D₁₁₃	—	4	2	no	—
259	C₄×D₁₁₃	—	4	2	no	—
260	C₄×D₁₁₃	—	4	2	no	—
261	Dic₂₂₆	—	2	4	no	—
262	Dic₂₂₆	—	4	1	no	—
263	C₂²×C₁₁₃	—	2	2	no	—
264	C₂²×C₁₁₃	—	2	2	no	—
265	C₂²×C₁₁₃	—	2	2	no	—
266	C₂²×C₁₁₃	—	2	2	no	—
267	C₂²×C₁₁₃	—	2	1	no	—
268	C₂²×C₁₁₃	—	2	1	no	—
269	C₂²×C₁₁₃	—	4	4	no	—
270	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
271	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
272	C₂×D₁₁₃	—	2	2	no	—
273	C₂×D₁₁₃	—	2	2	no	—
274	C₂×D₁₁₃	—	2	2	no	—
275	C₂×D₁₁₃	—	2	2	no	—
276	C₂×D₁₁₃	—	2	2	no	—
277	C₂×D₁₁₃	—	2	2	no	—
278	C₂×D₁₁₃	—	2	1	no	—
279	C₂×D₁₁₃	—	4	4	no	—
280	C₂×D₁₁₃	—	4	8	no	—
281	C₂×D₁₁₃	C₂×#41	1	4	yes	—
282	C₄×C₁₁₃	—	2	2	no	—
283	C₄×C₁₁₃	—	2	2	no	—
284	C₄×C₁₁₃	—	2	2	no	—
285	C₄×C₁₁₃	—	2	1	no	—
286	C₄×C₁₁₃	—	2	2	no	—
287	C₄×C₁₁₃	—	2	2	no	—
288	Dic₁₁₃	—	2	2	no	—
289	Dic₁₁₃	—	2	2	no	—
290	Dic₁₁₃	—	2	1	no	—
291	Dic₁₁₃	—	2	1	no	—
292	Dic₁₁₃	—	2	2	no	—
293	Dic₁₁₃	C₂×#41	1	4	yes	—
294	Dic₁₁₃	H(5,𝔽₂)	1	2	yes	—
295	C₂×C₁₁₃	—	2	4	no	—
296	C₂×C₁₁₃	—	4	1	no	—
297	C₂×C₁₁₃	—	4	1	no	—
298	C₂×C₁₁₃	C₂²×#41	1	2	yes	—
299	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
300	D₁₁₃	—	2	4	no	—
301	D₁₁₃	—	4	1	no	—
302	D₁₁₃	—	4	2	no	—
303	#3481	—	113	1	no	maximal, Sylow
304	C₁₁₃	#3481	1	1	yes	characteristic, complemented, Sylow
305	#559	—	113	1	no	—
306	#554	—	113	2	no	—
307	#553	—	113	2	no	—
308	#553	—	113	2	no	—
309	#551	—	113	1	no	—
310	#551	—	113	2	no	—
311	#551	D₁₁₃	1	1	yes	characteristic, complemented
312	#546	—	113	2	no	—
313	#546	—	113	2	no	—
314	D₄²	—	113	1	no	—
315	#532	—	113	1	no	—
316	#529	—	113	2	no	—
317	#529	—	113	2	no	—
318	#525	—	113	1	no	—
319	#525	—	113	2	no	—
320	#525	—	113	1	no	—
321	C₄×#41	—	113	2	no	—
322	C₂×C₄×D₄	—	113	2	no	—
323	C₂×C₄×D₄	—	113	2	no	—
324	C₂×#41	—	113	1	no	—
325	C₂×#41	—	113	1	no	—
326	C₂×#41	—	113	2	no	—
327	C₂²×D₄	—	113	2	no	—
328	C₂²×D₄	—	113	2	no	—
329	C₂³×C₄	—	113	1	no	—
330	C₂³×C₄	—	113	2	no	—
331	C₂³×C₄	—	113	1	no	—
332	C₄⋊Q₈	—	113	1	no	—
333	#127	—	113	1	no	—
334	#126	—	113	2	no	—
335	#126	—	113	2	no	—
336	#126	—	113	2	no	—
337	#126	C₂×D₁₁₃	1	2	yes	complemented
338	#125	—	113	2	no	—
339	#125	—	113	2	no	—
340	#124	—	113	2	no	—
341	#124	—	113	2	no	—
342	#124	—	113	1	no	—
343	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
344	#123	—	113	1	no	—
345	#123	—	113	1	no	—
346	#123	—	113	2	no	—
347	#123	—	113	2	no	—
348	#123	—	113	2	no	—
349	#123	—	113	2	no	—
350	#123	—	113	1	no	—
351	#123	—	113	2	no	—
352	#123	C₂×D₁₁₃	1	1	yes	characteristic, complemented
353	#123	C₂×D₁₁₃	1	2	yes	complemented
354	C₂²⋊Q₈	—	113	2	no	—
355	C₂²⋊Q₈	—	113	2	no	—
356	C₂²⋊Q₈	—	113	2	no	—
357	C₂²⋊Q₈	—	113	2	no	—
358	C₂²⋊Q₈	—	113	2	no	—
359	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
360	#121	—	113	2	no	—
361	#121	—	113	2	no	—
362	#121	—	113	2	no	—
363	#121	—	113	2	no	—
364	#121	—	113	2	no	—
365	#121	—	113	2	no	—
366	#121	—	113	2	no	—
367	#121	—	113	2	no	—
368	#120	—	113	1	no	—
369	#120	—	113	1	no	—
370	#120	—	113	2	no	—
371	#120	—	113	1	no	—
372	#120	—	113	2	no	—
373	#120	C₂×D₁₁₃	1	1	yes	characteristic
374	C₄×Q₈	—	113	2	no	—
375	C₄×Q₈	—	113	2	no	—
376	C₄×D₄	—	113	2	no	—
377	C₄×D₄	—	113	2	no	—
378	C₄×D₄	—	113	2	no	—
379	C₄×D₄	—	113	2	no	—
380	C₄×D₄	—	113	2	no	—
381	C₄×D₄	—	113	2	no	—
382	C₄×D₄	—	113	2	no	—
383	C₄×D₄	—	113	2	no	—
384	C₄×D₄	—	113	2	no	—
385	C₄×D₄	—	113	2	no	—
386	C₄×D₄	—	113	2	no	—
387	C₄×D₄	—	113	2	no	—
388	C₄×D₄	—	113	2	no	—
389	C₄×D₄	—	113	2	no	—
390	C₄×D₄	—	113	2	no	—
391	C₄×D₄	—	113	2	no	—
392	C₄×D₄	—	113	2	no	—
393	C₄×D₄	—	113	2	no	—
394	C₄×D₄	—	113	2	no	—
395	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
396	#117	—	113	2	no	—
397	#117	—	113	1	no	—
398	#117	—	113	1	no	—
399	#117	—	113	2	no	—
400	#117	—	113	2	no	—
401	#117	C₂×D₁₁₃	1	2	yes	complemented
402	C₂×C₄⋊C₄	—	113	2	no	—
403	C₂×C₄⋊C₄	—	113	2	no	—
404	C₂×C₂²⋊C₄	—	113	2	no	—
405	C₂×C₂²⋊C₄	—	113	2	no	—
406	C₂×C₂²⋊C₄	—	113	2	no	—
407	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
408	C₂×C₄²	—	113	2	no	—
409	C₂×C₄²	—	113	2	no	—
410	C₂×C₄²	—	113	1	no	—
411	C₂⁴	—	113	1	no	—
412	C₂⁴	—	113	2	no	—
413	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
414	#41	—	452	2	no	—
415	#41	—	452	2	no	—
416	#41	—	226	8	no	—
417	C₂×Q₈	—	113	1	no	—
418	C₂×Q₈	—	113	2	no	—
419	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
420	C₂×D₄	—	113	2	no	—
421	C₂×D₄	—	113	1	no	—
422	C₂×D₄	—	113	1	no	—
423	C₂×D₄	—	113	2	no	—
424	C₂×D₄	—	113	2	no	—
425	C₂×D₄	—	113	2	no	—
426	C₂×D₄	—	113	2	no	—
427	C₂×D₄	—	113	2	no	—
428	C₂×D₄	—	113	1	no	—
429	C₂×D₄	—	113	2	no	—
430	C₂×D₄	—	113	2	no	—
431	C₂×D₄	—	113	2	no	—
432	C₂×D₄	—	226	8	no	—
433	C₂×D₄	—	226	8	no	—
434	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
435	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
436	C₂²×C₄	—	113	2	no	—
437	C₂²×C₄	—	113	1	no	—
438	C₂²×C₄	—	113	2	no	—
439	C₂²×C₄	—	113	2	no	—
440	C₂²×C₄	—	113	1	no	—
441	C₂²×C₄	—	113	1	no	—
442	C₂²×C₄	—	113	2	no	—
443	C₂²×C₄	—	113	2	no	—
444	C₂²×C₄	—	113	2	no	—
445	C₂²×C₄	—	113	2	no	—
446	C₂²×C₄	—	113	2	no	—
447	C₂²×C₄	—	113	2	no	—
448	C₂²×C₄	—	113	2	no	—
449	C₂²×C₄	—	113	1	no	—
450	C₂²×C₄	—	113	2	no	—
451	C₂²×C₄	—	452	2	no	—
452	C₂²×C₄	—	452	4	no	—
453	C₂²×C₄	—	452	2	no	—
454	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
455	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
457	C₄⋊C₄	—	113	2	no	—
458	C₄⋊C₄	—	113	2	no	—
459	C₄⋊C₄	—	113	2	no	—
460	C₄⋊C₄	—	113	2	no	—
461	C₄⋊C₄	—	113	2	no	—
462	C₄⋊C₄	—	113	2	no	—
463	C₄⋊C₄	—	113	2	no	—
464	C₄⋊C₄	—	113	2	no	—
465	C₄⋊C₄	—	113	2	no	—
466	C₄⋊C₄	—	113	2	no	—
467	C₄⋊C₄	—	113	2	no	—
468	C₄⋊C₄	—	113	2	no	—
469	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
470	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
473	C₂²⋊C₄	—	113	2	no	—
474	C₂²⋊C₄	—	113	2	no	—
475	C₂²⋊C₄	—	113	1	no	—
476	C₂²⋊C₄	—	113	1	no	—
477	C₂²⋊C₄	—	113	2	no	—
478	C₂²⋊C₄	—	113	2	no	—
479	C₂²⋊C₄	—	113	2	no	—
480	C₂²⋊C₄	—	113	2	no	—
481	C₂²⋊C₄	—	113	2	no	—
482	C₂²⋊C₄	—	113	2	no	—
483	C₂²⋊C₄	—	113	2	no	—
484	C₂²⋊C₄	—	113	2	no	—
485	C₂²⋊C₄	—	113	2	no	—
486	C₂²⋊C₄	—	113	2	no	—
487	C₂²⋊C₄	—	113	2	no	—
488	C₂²⋊C₄	—	113	2	no	—
489	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
495	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
496	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
497	C₄²	—	113	2	no	—
498	C₄²	—	113	2	no	—
499	C₄²	—	113	2	no	—
500	C₄²	—	113	2	no	—
501	C₄²	—	113	2	no	—
502	C₄²	—	113	2	no	—
503	C₄²	—	113	1	no	—
504	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
505	C₄²	C₂²×D₁₁₃	1	2	yes	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	113	2	no	—
509	C₂³	—	113	2	no	—
510	C₂³	—	113	1	no	—
511	C₂³	—	452	2	no	—
512	C₂³	—	452	1	no	—
513	C₂³	—	226	4	no	—
514	C₂³	—	226	4	no	—
515	C₂³	—	226	4	no	—
516	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
517	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
518	C₂³	C₂³×D₁₁₃	1	2	yes	—
519	Q₈	—	4	1	no	—
520	Q₈	—	452	1	no	—
521	Q₈	—	226	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	4	1	no	—
524	D₄	—	113	8	no	—
525	D₄	—	452	2	no	—
526	D₄	—	452	1	no	—
527	D₄	—	452	1	no	—
528	D₄	—	452	1	no	—
529	D₄	—	226	4	no	—
530	D₄	—	226	4	no	—
531	D₄	—	226	4	no	—
532	D₄	—	226	4	no	—
533	D₄	—	226	4	no	—
534	D₄	—	226	4	no	—
535	D₄	—	226	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	113	1	no	—
540	C₂×C₄	—	113	2	no	—
541	C₂×C₄	—	113	2	no	—
542	C₂×C₄	—	113	2	no	—
543	C₂×C₄	—	113	2	no	—
544	C₂×C₄	—	113	1	no	—
545	C₂×C₄	—	113	1	no	—
546	C₂×C₄	—	452	2	no	—
547	C₂×C₄	—	452	2	no	—
548	C₂×C₄	—	452	2	no	—
549	C₂×C₄	—	452	1	no	—
550	C₂×C₄	—	452	2	no	—
551	C₂×C₄	—	226	4	no	—
552	C₂×C₄	—	226	4	no	—
553	C₂×C₄	—	226	4	no	—
554	C₂×C₄	—	226	2	no	—
555	C₂×C₄	—	226	4	no	—
556	C₂×C₄	—	226	4	no	—
557	C₂×C₄	—	226	4	no	—
558	C₂×C₄	—	226	2	no	—
559	C₂×C₄	—	226	2	no	—
560	C₂×C₄	—	226	4	no	—
561	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
562	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
563	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
564	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
565	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	113	4	no	—
575	C₂²	—	452	8	no	—
576	C₂²	—	452	4	no	—
577	C₂²	—	226	2	no	—
578	C₂²	—	226	2	no	—
579	C₂²	—	226	2	no	—
580	C₂²	—	226	2	no	—
581	C₂²	—	226	1	no	—
582	C₂²	—	226	2	no	—
583	C₂²	—	226	2	no	—
584	C₂²	#41×D₁₁₃	1	4	yes	—
585	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	113	4	no	—
593	C₄	—	113	2	no	—
594	C₄	—	226	2	no	—
595	C₄	—	226	2	no	—
596	C₄	—	226	2	no	—
597	C₄	—	226	1	no	—
598	C₄	—	226	1	no	—
599	C₂	—	2	4	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	452	2	no	—
603	C₂	—	452	1	no	—
604	C₂	—	226	4	no	—
605	C₂	C₂×#41×D₁₁₃	1	2	yes	—
606	C₂	H(5,𝔽₂)×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#551×C₁₁₃	C₂
hypercenter	#551	D₁₁₃
hypocenter	C₁₁₃	#3481
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #20299332	C₂	semidirect
2. #20299302	C₂	semidirect
3. #20299299	C₂	semidirect
4. #20299297	C₂	semidirect
5. #20299278	C₂	semidirect
6. #20299272	C₂	semidirect
7. #20299240	C₂	semidirect
8. #20299238	C₂	semidirect
9. #20299230	C₂	semidirect
10. #20299147	C₂	semidirect
11. #20299131	C₂	semidirect
12. #20299125	C₂	semidirect
13. #20299111	C₂	semidirect
14. #20299106	C₂	semidirect
15. #20299104	C₂	semidirect
16. #20299066	C₂	semidirect
17. C₂×#16813582	C₂	semidirect
18. C₄×D₄×D₁₁₃	C₂	semidirect
19. #551×C₁₁₃	C₂	semidirect
20. C₂×#14268648	C₂²	semidirect
22. C₂×#14268646	C₂²	semidirect
25. C₂³×Dic₁₁₃	C₂²	semidirect
26. C₂²×C₄×D₁₁₃	C₂²	semidirect
27. C₂²×C₄×D₁₁₃	C₂²	semidirect
28. #16813620	C₂²	semidirect
30. #16813617	C₂²	semidirect
31. #16813616	C₂²	semidirect
32. #16813615	C₂²	semidirect
33. #16813612	C₂²	semidirect
34. #16813612	C₂²	semidirect
35. #16813610	C₂²	semidirect
36. #16813608	C₂²	semidirect
37. #16813608	C₂²	semidirect
38. #16813607	C₂²	semidirect
39. #16813607	C₂²	semidirect
40. #16813607	C₂²	semidirect
41. #16813606	C₂²	semidirect
42. #16813605	C₂²	semidirect
43. #16813605	C₂²	semidirect
44. #16813604	C₂²	semidirect
45. #16813603	C₂²	semidirect
46. #16813600	C₂²	semidirect
47. #16813600	C₂²	semidirect
48. #16813599	C₂²	semidirect
49. #16813599	C₂²	semidirect
50. #16813598	C₂²	semidirect
51. #16813597	C₂²	semidirect
52. #16813596	C₂²	semidirect
54. #16813595	C₂²	semidirect
55. #16813595	C₂²	semidirect
56. #16813595	C₂²	semidirect
58. #16813594	C₂²	semidirect
60. #16813592	C₂²	semidirect
61. #16813592	C₂²	semidirect
62. #16813591	C₂²	semidirect
64. #16813587	C₂²	semidirect
65. #16813587	C₂²	semidirect
66. C₄×D₄₅₂	C₂²	semidirect
67. D₄×Dic₁₁₃	C₂²	semidirect
68. #16813584	C₂²	semidirect
69. #16813584	C₂²	semidirect
70. #16813584	C₂²	semidirect
72. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
76. #16813582	C₂²	semidirect
77. #16813582	C₂²	semidirect
78. #16813582	C₂²	semidirect
79. #16813582	C₂²	semidirect
80. #16813582	C₂²	semidirect
81. #16813582	C₂²	semidirect
82. #16813582	C₂²	semidirect
83. #16813582	C₂²	semidirect
84. #16813582	C₂²	semidirect
85. #16813580	C₂²	semidirect
86. #16813579	C₂²	semidirect
87. #16813579	C₂²	semidirect
88. #16813578	C₂²	semidirect
89. #16813578	C₂²	semidirect
90. C₂×#14268626	C₂²	semidirect
91. C₄⋊C₄×D₁₁₃	C₂²	semidirect
92. C₂×#14268624	C₂²	semidirect
93. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
94. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
95. C₂×C₄×Dic₁₁₃	C₂²	semidirect
96. C₄²×D₁₁₃	C₂²	semidirect
97. C₄²×D₁₁₃	C₂²	semidirect
98. #126×C₁₁₃	C₂²	semidirect
99. #124×C₁₁₃	C₂²	semidirect
100. #123×C₁₁₃	C₂²	semidirect
101. #123×C₁₁₃	C₂²	semidirect
102. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
104. C₄×D₄×C₁₁₃	C₂²	semidirect
105. #117×C₁₁₃	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
234. C₂²⋊D₁₁₃	#41	semidirect
304. C₁₁₃	#3481	semidirect
311. #551	D₁₁₃	semidirect
337. #126	C₂×D₁₁₃	semidirect
343. #124	C₂×D₁₁₃	semidirect
352. #123	C₂×D₁₁₃	semidirect
353. #123	C₂×D₁₁₃	semidirect
359. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
395. C₄×D₄	C₂×D₁₁₃	semidirect
401. #117	C₂×D₁₁₃	semidirect
407. C₂×C₂²⋊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
#20299332	2
#20299302	2
#20299299	2
#20299297	2
#20299278	2
#20299272	2
#20299240	2
#20299238	2
#20299230	2
#20299147	2
#20299131	2
#20299125	2
#20299111	2
#20299106	2
#20299104	2
#20299066	2
C₂×#16813582	2
C₄×D₄×D₁₁₃	2
#551×C₁₁₃	2
#3481	113