Subgroups — #28404589

Order 14464.

1010 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299321	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299319	C₂	1	2	yes	maximal, complemented
4	#20299318	C₂	1	2	yes	maximal, complemented
5	#20299315	C₂	1	4	yes	maximal, complemented
6	#20299313	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299312	C₂	1	2	yes	maximal, complemented
8	D₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299257	C₂	1	2	yes	maximal, complemented
10	#20299219	C₂	1	2	yes	maximal, complemented
11	#20299216	C₂	1	4	yes	maximal, complemented
12	#20299155	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299154	C₂	1	2	yes	maximal, complemented
14	#20299127	C₂	1	2	yes	maximal, complemented
15	#20299075	C₂	1	2	yes	maximal, complemented
16	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268647	C₂²	1	1	yes	characteristic
19	C₂²×Dic₂₂₆	C₂²	1	2	yes	—
20	#16813622	C₂²	1	1	yes	characteristic
21	#16813622	C₂²	1	1	yes	characteristic
22	#16813622	C₂²	1	2	yes	—
23	#16813621	C₂²	1	2	yes	—
24	#16813621	C₂²	1	2	yes	—
25	#16813621	C₂²	1	4	yes	—
26	#16813617	C₂²	1	4	yes	—
27	#16813617	C₂²	1	4	yes	—
28	#16813615	C₂²	1	4	yes	—
29	#16813615	C₂²	1	4	yes	—
30	#16813614	C₂²	1	2	yes	—
31	#16813610	C₂²	1	2	yes	—
32	#16813609	C₂²	1	4	yes	—
33	#16813608	C₂²	1	4	yes	—
34	#16813608	C₂²	1	4	yes	—
35	#16813608	C₂²	1	4	yes	—
36	#16813604	C₂²	1	4	yes	—
37	#16813601	C₂²	1	2	yes	—
38	#16813601	C₂²	1	2	yes	—
39	#16813601	C₂²	1	2	yes	—
40	#16813600	C₂²	1	4	yes	—
41	#16813600	C₂²	1	4	yes	—
42	#16813599	C₂²	1	4	yes	—
43	#16813598	C₂²	1	2	yes	—
44	#16813596	C₂²	1	2	yes	—
45	#16813594	C₂²	1	4	yes	—
46	#16813593	C₂²	1	2	yes	—
47	Q₈×Dic₁₁₃	C₂²	1	2	yes	—
48	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
49	C₄×Dic₂₂₆	C₂²	1	2	yes	—
50	C₄×Dic₂₂₆	C₂²	1	2	yes	—
51	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
52	C₄×Dic₂₂₆	C₂²	1	2	yes	—
53	C₄×Dic₂₂₆	C₂²	1	2	yes	—
54	#16813587	C₂²	1	4	yes	—
55	#16813587	C₂²	1	4	yes	—
56	#16813587	C₂²	1	4	yes	—
57	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
58	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
59	D₄×Dic₁₁₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	#16813582	C₂²	1	4	yes	—
63	#16813581	C₂²	1	2	yes	—
64	#16813581	C₂²	1	2	yes	—
65	#16813581	C₂²	1	1	yes	characteristic
66	#16813580	C₂²	1	2	yes	—
67	#16813580	C₂²	1	2	yes	—
68	#16813579	C₂²	1	2	yes	—
69	#16813578	C₂²	1	4	yes	—
70	#16813578	C₂²	1	4	yes	—
71	C₄²×D₁₁₃	C₂²	1	2	yes	—
72	#126×C₁₁₃	C₂²	1	2	yes	—
73	#125×C₁₁₃	C₂²	1	1	yes	characteristic
74	#124×C₁₁₃	C₂²	1	1	yes	characteristic
75	#123×C₁₁₃	C₂²	1	2	yes	—
76	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
77	#121×C₁₁₃	C₂²	1	1	yes	characteristic
78	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
79	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
80	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
81	#117×C₁₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
83	#14268647	—	2	4	no	—
84	C₂×Dic₂₂₆	—	2	8	no	—
85	C₂×Dic₂₂₆	C₂³	1	4	yes	—
86	C₂×Dic₂₂₆	C₂³	1	2	yes	—
87	C₂×Dic₂₂₆	C₂³	1	4	yes	—
88	C₂×Dic₂₂₆	C₂³	1	2	yes	—
89	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
90	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
93	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
97	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
100	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
101	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
104	#14268626	C₂³	1	2	yes	—
105	#14268626	C₂³	1	4	yes	—
106	#14268626	C₂³	1	4	yes	—
107	#14268626	C₂³	1	4	yes	—
108	#14268626	C₂³	1	2	yes	—
109	#14268626	C₂³	1	4	yes	—
110	#14268626	C₂³	1	4	yes	—
111	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
112	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
113	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
115	#14268624	C₂³	1	2	yes	—
116	#14268624	C₂³	1	2	yes	—
117	#14268624	C₂³	1	4	yes	—
118	#14268624	C₂³	1	4	yes	—
119	#14268624	C₂³	1	4	yes	—
120	C₄×Dic₁₁₃	C₂³	1	2	yes	—
121	C₄×Dic₁₁₃	C₂³	1	2	yes	—
122	C₄×Dic₁₁₃	C₂³	1	2	yes	—
123	C₄×Dic₁₁₃	C₂³	1	4	yes	—
124	C₄×Dic₁₁₃	C₂³	1	4	yes	—
125	C₄×Dic₁₁₃	C₂³	1	4	yes	—
126	C₄×Dic₁₁₃	C₂³	1	4	yes	—
127	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
132	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
137	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
138	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
139	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
140	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
141	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
143	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁₃	C₂³	1	2	yes	—
150	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
151	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
152	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
153	Q₈×C₁₁₃	—	2	2	no	—
154	D₄×C₁₁₃	—	2	2	no	—
155	D₄×C₁₁₃	—	4	2	no	—
156	C₂×C₄×C₁₁₃	—	2	4	no	—
157	C₂×C₄×C₁₁₃	—	2	2	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	4	1	no	—
160	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²⋊D₁₁₃	—	2	4	no	—
170	C₂²⋊D₁₁₃	—	4	4	no	—
171	C₂×Dic₁₁₃	—	2	8	no	—
172	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
176	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
177	D₄₅₂	—	2	2	no	—
178	C₄×D₁₁₃	—	2	4	no	—
179	C₄×D₁₁₃	—	2	4	no	—
180	C₄×D₁₁₃	—	4	2	no	—
181	Dic₂₂₆	—	2	4	no	—
182	Dic₂₂₆	—	2	8	no	—
183	Dic₂₂₆	—	4	4	no	—
184	Dic₂₂₆	—	4	2	no	—
185	Dic₂₂₆	#41	1	4	yes	—
186	C₂²×C₁₁₃	—	2	2	no	—
187	C₂²×C₁₁₃	—	2	1	no	—
188	C₂²×C₁₁₃	—	2	1	no	—
189	C₂²×C₁₁₃	—	2	2	no	—
190	C₂²×C₁₁₃	—	2	2	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
193	C₂×D₁₁₃	—	2	2	no	—
194	C₂×D₁₁₃	—	2	2	no	—
195	C₂×D₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	2	no	—
197	C₄×C₁₁₃	—	2	1	no	—
198	C₄×C₁₁₃	—	2	1	no	—
199	C₄×C₁₁₃	—	2	2	no	—
200	C₄×C₁₁₃	—	2	1	no	—
201	C₄×C₁₁₃	—	2	2	no	—
202	C₄×C₁₁₃	—	2	1	no	—
203	C₄×C₁₁₃	C₂×#41	1	2	yes	—
204	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
205	Dic₁₁₃	—	2	4	no	—
206	Dic₁₁₃	—	2	2	no	—
207	Dic₁₁₃	—	2	2	no	—
208	Dic₁₁₃	—	2	4	no	—
209	Dic₁₁₃	C₂×#41	1	4	yes	—
210	C₂×C₁₁₃	—	4	2	no	—
211	C₂×C₁₁₃	—	4	1	no	—
212	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
213	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
214	C₂×C₁₁₃	#585	1	1	yes	characteristic
215	D₁₁₃	—	4	2	no	—
216	#3518	—	113	1	no	maximal, Sylow
217	C₁₁₃	#3518	1	1	yes	characteristic, complemented, Sylow
218	Q₈²	—	113	1	no	—
219	#556	—	113	4	no	—
220	#556	—	113	2	no	—
221	#556	—	113	1	no	—
222	#556	—	113	2	no	—
223	#555	—	113	2	no	—
224	#555	—	113	1	no	—
225	D₄×Q₈	—	113	1	no	—
226	#548	—	113	2	no	—
227	#542	—	113	4	no	—
228	#542	—	113	2	no	—
229	#533	—	113	2	no	—
230	#533	—	113	1	no	—
231	#529	—	113	2	no	—
232	#529	D₁₁₃	1	1	yes	characteristic, complemented
233	#519	—	113	2	no	—
234	C₄×#41	—	113	1	no	—
235	C₂×#41	—	113	1	no	—
236	C₂²×Q₈	—	113	2	no	—
237	C₄⋊Q₈	—	113	2	no	—
238	C₄⋊Q₈	—	113	2	no	—
239	C₄⋊Q₈	—	113	4	no	—
240	C₄⋊Q₈	—	113	1	no	—
241	C₄⋊Q₈	—	113	1	no	—
242	C₄⋊Q₈	—	113	2	no	—
243	#126	—	113	4	no	—
244	#126	—	113	4	no	—
245	#126	—	113	4	no	—
246	#126	—	113	4	no	—
247	#126	C₂×D₁₁₃	1	2	yes	—
248	#125	—	113	2	no	—
249	#125	C₂×D₁₁₃	1	1	yes	characteristic
250	#124	—	113	4	no	—
251	#124	—	113	4	no	—
252	#124	—	113	4	no	—
253	#124	—	113	4	no	—
254	#124	—	113	2	no	—
255	#124	C₂×D₁₁₃	1	1	yes	characteristic
256	#123	—	113	4	no	—
257	#123	C₂×D₁₁₃	1	2	yes	—
258	C₂²⋊Q₈	—	113	2	no	—
259	C₂²⋊Q₈	—	113	2	no	—
260	C₂²⋊Q₈	—	113	2	no	—
261	C₂²⋊Q₈	—	113	2	no	—
262	C₂²⋊Q₈	—	113	4	no	—
263	C₂²⋊Q₈	—	113	4	no	—
264	C₂²⋊Q₈	—	113	4	no	—
265	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
266	#121	—	113	2	no	—
267	#121	—	113	4	no	—
268	#121	—	113	2	no	—
269	#121	C₂×D₁₁₃	1	1	yes	characteristic
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	4	no	—
272	C₄×Q₈	—	113	4	no	—
273	C₄×Q₈	—	113	4	no	—
274	C₄×Q₈	—	113	1	no	—
275	C₄×Q₈	—	113	1	no	—
276	C₄×Q₈	—	113	2	no	—
277	C₄×Q₈	—	113	2	no	—
278	C₄×Q₈	—	113	2	no	—
279	C₄×Q₈	—	113	2	no	—
280	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	—	113	2	no	—
283	C₄×D₄	—	113	2	no	—
284	C₄×D₄	—	113	4	no	—
285	C₄×D₄	—	113	1	no	—
286	C₄×D₄	—	113	1	no	—
287	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
288	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
289	#117	—	113	1	no	—
290	#117	—	113	2	no	—
291	#117	—	113	2	no	—
292	#117	—	113	2	no	—
293	#117	—	113	2	no	—
294	#117	—	113	4	no	—
295	#117	—	113	4	no	—
296	#117	—	113	2	no	—
297	#117	C₂×D₁₁₃	1	2	yes	—
298	C₂×C₄²	—	113	2	no	—
299	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
300	#41	—	226	4	no	—
301	C₂×Q₈	—	113	1	no	—
302	C₂×Q₈	—	113	2	no	—
303	C₂×Q₈	—	113	4	no	—
304	C₂×Q₈	—	113	4	no	—
305	C₂×Q₈	—	113	2	no	—
306	C₂×Q₈	—	226	8	no	—
307	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
308	C₂×D₄	—	113	4	no	—
309	C₂×D₄	—	113	2	no	—
310	C₂×D₄	—	113	1	no	—
311	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
312	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
313	C₂²×C₄	—	113	4	no	—
314	C₂²×C₄	—	113	2	no	—
315	C₂²×C₄	—	113	2	no	—
316	C₂²×C₄	—	113	2	no	—
317	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
320	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
321	C₄⋊C₄	—	113	2	no	—
322	C₄⋊C₄	—	113	1	no	—
323	C₄⋊C₄	—	113	2	no	—
324	C₄⋊C₄	—	113	2	no	—
325	C₄⋊C₄	—	113	2	no	—
326	C₄⋊C₄	—	113	1	no	—
327	C₄⋊C₄	—	113	4	no	—
328	C₄⋊C₄	—	113	2	no	—
329	C₄⋊C₄	—	113	4	no	—
330	C₄⋊C₄	—	113	4	no	—
331	C₄⋊C₄	—	113	4	no	—
332	C₄⋊C₄	—	113	4	no	—
333	C₄⋊C₄	—	113	2	no	—
334	C₄⋊C₄	—	113	4	no	—
335	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
336	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
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	C₂²⋊C₄	—	113	4	no	—
342	C₂²⋊C₄	—	113	2	no	—
343	C₂²⋊C₄	—	113	4	no	—
344	C₂²⋊C₄	—	113	4	no	—
345	C₂²⋊C₄	—	113	2	no	—
346	C₂²⋊C₄	—	113	2	no	—
347	C₂²⋊C₄	—	113	4	no	—
348	C₂²⋊C₄	—	113	4	no	—
349	C₂²⋊C₄	—	113	4	no	—
350	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
351	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
352	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
353	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
354	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
355	C₄²	—	113	2	no	—
356	C₄²	—	113	2	no	—
357	C₄²	—	113	2	no	—
358	C₄²	—	113	4	no	—
359	C₄²	—	113	4	no	—
360	C₄²	—	113	4	no	—
361	C₄²	—	113	4	no	—
362	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
363	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
364	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
365	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
366	C₄²	C₂²×D₁₁₃	1	2	yes	—
367	C₂³	—	113	2	no	—
368	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
369	C₂³	C₂³×D₁₁₃	1	2	yes	—
370	Q₈	—	2	2	no	—
371	Q₈	—	113	4	no	—
372	Q₈	—	452	2	no	—
373	Q₈	—	452	4	no	—
374	Q₈	—	226	8	no	—
375	Q₈	—	226	4	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	452	4	no	—
379	D₄	—	226	4	no	—
380	D₄	—	226	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	113	2	no	—
386	C₂×C₄	—	113	2	no	—
387	C₂×C₄	—	113	4	no	—
388	C₂×C₄	—	113	4	no	—
389	C₂×C₄	—	113	2	no	—
390	C₂×C₄	—	452	2	no	—
391	C₂×C₄	—	226	4	no	—
392	C₂×C₄	—	226	8	no	—
393	C₂×C₄	—	226	4	no	—
394	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
398	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
399	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
400	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
403	C₂²	—	2	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	226	2	no	—
410	C₂²	—	226	2	no	—
411	C₂²	—	226	2	no	—
412	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	113	4	no	—
421	C₄	—	226	4	no	—
422	C₄	—	226	2	no	—
423	C₄	—	226	2	no	—
424	C₄	—	226	4	no	—
425	C₄	#41×D₁₁₃	1	2	yes	—
426	C₄	#16813669	1	2	yes	—
427	C₂	—	4	2	no	—
428	C₂	—	4	1	no	—
429	C₂	—	452	2	no	—
430	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
431	C₂	C₂×#16813669	1	1	yes	characteristic
432	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#529×C₁₁₃	C₂
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3518
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. Q₈×Dic₂₂₆	C₂	semidirect
2. #20299321	C₂	semidirect
3. #20299319	C₂	semidirect
4. #20299318	C₂	semidirect
5. #20299315	C₂	semidirect
6. #20299313	C₂	semidirect
7. #20299312	C₂	semidirect
8. D₄×Dic₂₂₆	C₂	semidirect
9. #20299257	C₂	semidirect
10. #20299219	C₂	semidirect
11. #20299216	C₂	semidirect
12. #20299155	C₂	semidirect
13. #20299154	C₂	semidirect
14. #20299127	C₂	semidirect
15. #20299075	C₂	semidirect
16. C₄×#14268647	C₂	semidirect
17. #529×C₁₁₃	C₂	semidirect
217. C₁₁₃	#3518	semidirect
232. #529	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₂₂₆	2
#20299321	2
#20299319	2
#20299318	2
#20299315	2
#20299313	2
#20299312	2
D₄×Dic₂₂₆	2
#20299257	2
#20299219	2
#20299216	2
#20299155	2
#20299154	2
#20299127	2
#20299075	2
C₄×#14268647	2
#529×C₁₁₃	2
#3518	113