Subgroups — #28404440

Order 14464.

1012 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299333	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299333	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299323	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299322	C₂	1	2	yes	maximal, complemented
5	#20299320	C₂	1	2	yes	maximal, complemented
6	#20299320	C₂	1	2	yes	maximal, complemented
7	#20299304	C₂	1	2	yes	maximal, complemented
8	#20299280	C₂	1	4	yes	maximal, complemented
9	#20299196	C₂	1	4	yes	maximal, complemented
10	#20299173	C₂	1	2	yes	maximal, complemented
11	#20299152	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299149	C₂	1	1	yes	maximal, characteristic
13	#20299135	C₂	1	2	yes	maximal, complemented
14	#20299133	C₂	1	2	yes	maximal, complemented
15	#20299080	C₂	1	2	yes	maximal, complemented
16	C₄×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#557×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	—
19	C₂×Q₈×D₁₁₃	C₂²	1	1	yes	characteristic
20	#16813621	C₂²	1	1	yes	characteristic
21	#16813620	C₂²	1	1	yes	characteristic
22	#16813620	C₂²	1	2	yes	—
23	#16813619	C₂²	1	1	yes	characteristic
24	#16813617	C₂²	1	4	yes	—
25	#16813617	C₂²	1	4	yes	—
26	#16813617	C₂²	1	4	yes	—
27	#16813616	C₂²	1	4	yes	—
28	#16813613	C₂²	1	2	yes	—
29	#16813612	C₂²	1	2	yes	—
30	#16813612	C₂²	1	4	yes	—
31	#16813611	C₂²	1	2	yes	—
32	#16813611	C₂²	1	2	yes	—
33	#16813611	C₂²	1	2	yes	—
34	#16813610	C₂²	1	2	yes	—
35	#16813610	C₂²	1	2	yes	—
36	#16813607	C₂²	1	4	yes	—
37	#16813607	C₂²	1	4	yes	—
38	#16813607	C₂²	1	4	yes	—
39	#16813607	C₂²	1	4	yes	—
40	#16813602	C₂²	1	4	yes	—
41	#16813602	C₂²	1	1	yes	characteristic
42	#16813600	C₂²	1	4	yes	—
43	#16813600	C₂²	1	4	yes	—
44	#16813600	C₂²	1	4	yes	—
45	#16813600	C₂²	1	2	yes	—
46	#16813598	C₂²	1	1	yes	characteristic
47	#16813597	C₂²	1	2	yes	—
48	#16813597	C₂²	1	2	yes	—
49	Q₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
50	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
51	C₄×Dic₂₂₆	C₂²	1	2	yes	—
52	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
53	C₄×Dic₂₂₆	C₂²	1	2	yes	—
54	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
55	#16813587	C₂²	1	2	yes	—
56	#16813587	C₂²	1	1	yes	characteristic
57	#16813587	C₂²	1	2	yes	—
58	C₄×D₄₅₂	C₂²	1	2	yes	—
59	C₄×D₄₅₂	C₂²	1	2	yes	—
60	C₄×D₄₅₂	C₂²	1	4	yes	—
61	#16813584	C₂²	1	2	yes	—
62	#16813584	C₂²	1	2	yes	—
63	#16813584	C₂²	1	2	yes	—
64	#16813584	C₂²	1	2	yes	—
65	#16813584	C₂²	1	4	yes	—
66	#16813580	C₂²	1	4	yes	—
67	#16813579	C₂²	1	4	yes	—
68	#16813579	C₂²	1	4	yes	—
69	#16813579	C₂²	1	2	yes	—
70	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
71	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
73	C₄²×D₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
76	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
77	#125×C₁₁₃	C₂²	1	4	yes	—
78	#125×C₁₁₃	C₂²	1	2	yes	—
79	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
80	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
81	C₄×Q₈×C₁₁₃	C₂²	1	2	yes	—
82	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
83	#14268648	—	2	8	no	—
84	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
85	C₂×Dic₂₂₆	C₂³	1	2	yes	—
86	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₂₆	C₂³	1	2	yes	—
88	Q₈×D₁₁₃	—	2	4	no	—
89	C₂×D₄₅₂	C₂³	1	2	yes	—
90	C₂×D₄₅₂	C₂³	1	4	yes	—
91	C₂×D₄₅₂	C₂³	1	2	yes	—
92	C₂×D₄₅₂	C₂³	1	2	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
99	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
104	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
105	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
106	#14268626	C₂³	1	2	yes	—
107	#14268626	C₂³	1	2	yes	—
108	#14268626	C₂³	1	2	yes	—
109	#14268626	C₂³	1	2	yes	—
110	#14268626	C₂³	1	2	yes	—
111	#14268626	C₂³	1	2	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	4	yes	—
114	#14268626	C₂³	1	2	yes	—
115	#14268626	C₂³	1	2	yes	—
116	#14268624	C₂³	1	4	yes	—
117	#14268624	C₂³	1	2	yes	—
118	#14268624	C₂³	1	4	yes	—
119	#14268624	C₂³	1	2	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	#14268624	C₂³	1	4	yes	—
123	#14268624	C₂³	1	4	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	4	yes	—
126	C₄×Dic₁₁₃	C₂³	1	2	yes	—
127	C₄×Dic₁₁₃	C₂³	1	2	yes	—
128	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
129	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
130	C₄×Dic₁₁₃	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₁₃	C₂³	1	4	yes	—
133	C₄×Dic₁₁₃	C₂³	1	2	yes	—
134	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
139	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
141	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
146	C₄²×C₁₁₃	C₂³	1	2	yes	—
147	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₁₃	C₂³	1	4	yes	—
149	C₄²×C₁₁₃	C₂³	1	2	yes	—
150	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
151	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
152	Q₈×C₁₁₃	—	2	2	no	—
153	Q₈×C₁₁₃	—	2	4	no	—
154	Q₈×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
165	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
166	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
167	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
169	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
170	D₄₅₂	—	2	8	no	—
171	D₄₅₂	—	2	4	no	—
172	D₄₅₂	—	2	4	no	—
173	D₄₅₂	—	4	2	no	—
174	C₄×D₁₁₃	—	2	4	no	—
175	C₄×D₁₁₃	—	2	2	no	—
176	C₄×D₁₁₃	—	2	8	no	—
177	C₄×D₁₁₃	—	4	1	no	—
178	C₄×D₁₁₃	—	4	4	no	—
179	C₄×D₁₁₃	—	4	4	no	—
180	C₄×D₁₁₃	—	4	2	no	—
181	C₄×D₁₁₃	#41	1	4	yes	—
182	Dic₂₂₆	—	2	2	no	—
183	Dic₂₂₆	—	2	2	no	—
184	Dic₂₂₆	—	2	4	no	—
185	Dic₂₂₆	—	4	2	no	—
186	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
187	C₂×D₁₁₃	—	2	1	no	—
188	C₂×D₁₁₃	—	2	1	no	—
189	C₂×D₁₁₃	—	2	4	no	—
190	C₂×D₁₁₃	—	2	4	no	—
191	C₂×D₁₁₃	—	2	4	no	—
192	C₂×D₁₁₃	C₂×#41	1	2	yes	—
193	C₄×C₁₁₃	—	2	2	no	—
194	C₄×C₁₁₃	—	2	4	no	—
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	2	no	—
197	C₄×C₁₁₃	—	2	2	no	—
198	C₄×C₁₁₃	—	2	1	no	—
199	C₄×C₁₁₃	C₂×#41	1	2	yes	—
200	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
201	Dic₁₁₃	—	2	2	no	—
202	Dic₁₁₃	—	2	2	no	—
203	Dic₁₁₃	—	2	1	no	—
204	Dic₁₁₃	—	2	1	no	—
205	Dic₁₁₃	—	2	2	no	—
206	Dic₁₁₃	—	2	2	no	—
207	Dic₁₁₃	C₂×#41	1	2	yes	—
208	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
209	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₁₁₃	#585	1	1	yes	characteristic
211	D₁₁₃	—	2	2	no	—
212	D₁₁₃	—	4	4	no	—
213	#3507	—	113	1	no	maximal, Sylow
214	C₁₁₃	#3507	1	1	yes	characteristic, complemented, Sylow
215	#559	—	113	1	no	—
216	#559	—	113	1	no	—
217	#557	—	113	1	no	—
218	#557	D₁₁₃	1	1	yes	characteristic, complemented
219	#556	—	113	2	no	—
220	#556	—	113	2	no	—
221	#556	—	113	2	no	—
222	#554	—	113	2	no	—
223	#552	—	113	4	no	—
224	#539	—	113	4	no	—
225	#536	—	113	2	no	—
226	#533	—	113	1	no	—
227	#532	—	113	1	no	—
228	#529	—	113	2	no	—
229	#529	—	113	2	no	—
230	#520	—	113	2	no	—
231	C₂×C₄×Q₈	—	113	1	no	—
232	C₂×#41	—	113	2	no	—
233	C₂²×Q₈	—	113	1	no	—
234	C₄⋊Q₈	—	113	1	no	—
235	C₄⋊Q₈	—	113	2	no	—
236	C₄⋊Q₈	—	113	1	no	—
237	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
238	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	—
239	#127	—	113	1	no	—
240	#126	—	113	4	no	—
241	#126	—	113	4	no	—
242	#126	—	113	4	no	—
243	#126	—	113	4	no	—
244	#125	—	113	2	no	—
245	#125	—	113	2	no	—
246	#125	—	113	4	no	—
247	#125	C₂×D₁₁₃	1	2	yes	—
248	#125	C₂×D₁₁₃	1	4	yes	—
249	#124	—	113	2	no	—
250	#124	—	113	2	no	—
251	#124	—	113	2	no	—
252	#124	—	113	2	no	—
253	#124	—	113	2	no	—
254	#123	—	113	4	no	—
255	#123	—	113	4	no	—
256	#123	—	113	4	no	—
257	#123	—	113	4	no	—
258	C₂²⋊Q₈	—	113	1	no	—
259	C₂²⋊Q₈	—	113	1	no	—
260	C₂²⋊Q₈	—	113	2	no	—
261	C₂²⋊Q₈	—	113	4	no	—
262	C₂²⋊Q₈	—	113	4	no	—
263	C₂²⋊Q₈	—	113	4	no	—
264	C₂²⋊Q₈	—	113	4	no	—
265	#121	—	113	2	no	—
266	#121	—	113	2	no	—
267	C₄×Q₈	—	113	1	no	—
268	C₄×Q₈	—	113	2	no	—
269	C₄×Q₈	—	113	2	no	—
270	C₄×Q₈	—	113	1	no	—
271	C₄×Q₈	—	113	2	no	—
272	C₄×Q₈	—	113	2	no	—
273	C₄×Q₈	—	113	1	no	—
274	C₄×Q₈	—	113	2	no	—
275	C₄×Q₈	—	113	1	no	—
276	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
277	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
278	C₄×Q₈	C₂×D₁₁₃	1	2	yes	—
279	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
280	C₄×D₄	—	113	4	no	—
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	2	no	—
284	C₄×D₄	—	113	2	no	—
285	C₄×D₄	—	113	4	no	—
286	C₄×D₄	—	113	2	no	—
287	C₄×D₄	—	113	2	no	—
288	#117	—	113	4	no	—
289	#117	—	113	2	no	—
290	#117	—	113	4	no	—
291	#117	—	113	4	no	—
292	C₂×C₄⋊C₄	—	113	1	no	—
293	C₂×C₄⋊C₄	—	113	2	no	—
294	C₂×C₄⋊C₄	—	113	4	no	—
295	C₂×C₄²	—	113	2	no	—
296	C₂×C₄²	—	113	1	no	—
297	#41	—	226	8	no	—
298	C₂×Q₈	—	113	2	no	—
299	C₂×Q₈	—	113	1	no	—
300	C₂×Q₈	—	113	2	no	—
301	C₂×Q₈	—	113	1	no	—
302	C₂×Q₈	—	226	4	no	—
303	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
304	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
305	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
306	C₂×D₄	—	113	2	no	—
307	C₂×D₄	—	113	2	no	—
308	C₂×D₄	—	113	4	no	—
309	C₂×D₄	—	113	2	no	—
310	C₂²×C₄	—	113	1	no	—
311	C₂²×C₄	—	113	2	no	—
312	C₂²×C₄	—	113	1	no	—
313	C₂²×C₄	—	113	4	no	—
314	C₂²×C₄	—	113	4	no	—
315	C₂²×C₄	—	113	1	no	—
316	C₂²×C₄	—	113	2	no	—
317	C₂²×C₄	—	113	4	no	—
318	C₄⋊C₄	—	113	2	no	—
319	C₄⋊C₄	—	113	2	no	—
320	C₄⋊C₄	—	113	1	no	—
321	C₄⋊C₄	—	113	4	no	—
322	C₄⋊C₄	—	113	2	no	—
323	C₄⋊C₄	—	113	2	no	—
324	C₄⋊C₄	—	113	2	no	—
325	C₄⋊C₄	—	113	2	no	—
326	C₄⋊C₄	—	113	2	no	—
327	C₄⋊C₄	—	113	2	no	—
328	C₄⋊C₄	—	113	4	no	—
329	C₄⋊C₄	—	113	1	no	—
330	C₄⋊C₄	—	113	2	no	—
331	C₄⋊C₄	—	113	4	no	—
332	C₄⋊C₄	—	113	2	no	—
333	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
334	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
335	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
336	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
337	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
339	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
340	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
341	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
342	C₂²⋊C₄	—	113	4	no	—
343	C₂²⋊C₄	—	113	2	no	—
344	C₂²⋊C₄	—	113	2	no	—
345	C₂²⋊C₄	—	113	4	no	—
346	C₂²⋊C₄	—	113	4	no	—
347	C₂²⋊C₄	—	113	4	no	—
348	C₂²⋊C₄	—	113	4	no	—
349	C₂²⋊C₄	—	113	4	no	—
350	C₂²⋊C₄	—	113	4	no	—
351	C₂²⋊C₄	—	113	4	no	—
352	C₄²	—	113	2	no	—
353	C₄²	—	113	2	no	—
354	C₄²	—	113	1	no	—
355	C₄²	—	113	1	no	—
356	C₄²	—	113	2	no	—
357	C₄²	—	113	1	no	—
358	C₄²	—	113	4	no	—
359	C₄²	—	113	2	no	—
360	C₄²	C₂²×D₁₁₃	1	2	yes	—
361	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
362	C₄²	C₂²×D₁₁₃	1	4	yes	—
363	C₄²	C₂²×D₁₁₃	1	2	yes	—
364	C₂³	—	113	1	no	—
365	C₂³	—	113	4	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	452	2	no	—
370	Q₈	—	226	4	no	—
371	Q₈	—	226	2	no	—
372	Q₈	—	226	2	no	—
373	D₄	—	452	2	no	—
374	D₄	—	226	8	no	—
375	D₄	—	226	4	no	—
376	D₄	—	226	4	no	—
377	C₂×C₄	—	113	1	no	—
378	C₂×C₄	—	113	4	no	—
379	C₂×C₄	—	113	1	no	—
380	C₂×C₄	—	113	2	no	—
381	C₂×C₄	—	113	2	no	—
382	C₂×C₄	—	113	2	no	—
383	C₂×C₄	—	113	1	no	—
384	C₂×C₄	—	113	2	no	—
385	C₂×C₄	—	452	2	no	—
386	C₂×C₄	—	452	4	no	—
387	C₂×C₄	—	452	4	no	—
388	C₂×C₄	—	452	1	no	—
389	C₂×C₄	—	226	8	no	—
390	C₂×C₄	—	226	4	no	—
391	C₂×C₄	—	226	2	no	—
392	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
393	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
394	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
395	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
397	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
398	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
400	C₂²	—	113	2	no	—
401	C₂²	—	226	4	no	—
402	C₂²	—	226	4	no	—
403	C₂²	—	226	4	no	—
404	C₂²	—	226	1	no	—
405	C₂²	—	226	1	no	—
406	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
407	C₄	—	2	4	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	1	no	—
413	C₄	—	113	2	no	—
414	C₄	—	226	2	no	—
415	C₄	—	226	1	no	—
416	C₄	—	226	2	no	—
417	C₄	—	226	2	no	—
418	C₄	—	226	2	no	—
419	C₄	—	226	1	no	—
420	C₄	#41×D₁₁₃	1	2	yes	—
421	C₄	#16813670	1	2	yes	—
422	C₂	—	452	4	no	—
423	C₂	—	226	2	no	—
424	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
425	C₂	C₂×#16813670	1	1	yes	characteristic
426	C₂	#20299435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#557×C₁₁₃	C₂
prime radical	#20299149	C₂
hypercenter	#557	D₁₁₃
hypocenter	C₁₁₃	#3507
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #557

Complements

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

N	H ≅ G/N	type
1. #20299333	C₂	semidirect
2. #20299333	C₂	semidirect
3. #20299323	C₂	semidirect
4. #20299322	C₂	semidirect
5. #20299320	C₂	semidirect
6. #20299320	C₂	semidirect
7. #20299304	C₂	semidirect
8. #20299280	C₂	semidirect
9. #20299196	C₂	semidirect
10. #20299173	C₂	semidirect
11. #20299152	C₂	semidirect
13. #20299135	C₂	semidirect
14. #20299133	C₂	semidirect
15. #20299080	C₂	semidirect
16. C₄×Q₈×D₁₁₃	C₂	semidirect
17. #557×C₁₁₃	C₂	semidirect
214. C₁₁₃	#3507	semidirect
218. #557	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299333	2
#20299323	2
#20299322	2
#20299320	2
#20299304	2
#20299280	2
#20299196	2
#20299173	2
#20299152	2
#20299149	2
#20299135	2
#20299133	2
#20299080	2
C₄×Q₈×D₁₁₃	2
#557×C₁₁₃	2
#3507	113