Subgroups — #28404668

Order 14464.

992 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299327	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299326	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299325	C₂	1	2	yes	maximal, complemented
4	#20299318	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299317	C₂	1	2	yes	maximal, complemented
6	#20299288	C₂	1	2	yes	maximal, complemented
7	#20299285	C₂	1	4	yes	maximal, complemented
8	D₄×Dic₂₂₆	C₂	1	2	yes	maximal, complemented
9	D₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299210	C₂	1	2	yes	maximal, complemented
11	#20299205	C₂	1	4	yes	maximal, complemented
12	#20299155	C₂	1	1	yes	maximal, characteristic, complemented
13	#20299150	C₂	1	2	yes	maximal, complemented
14	#20299129	C₂	1	2	yes	maximal
15	#20299075	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
17	#529×C₁₁₃	C₂	1	1	yes	maximal, characteristic
18	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
19	C₂²×Dic₂₂₆	C₂²	1	2	yes	—
20	#16813622	C₂²	1	1	yes	characteristic
21	#16813622	C₂²	1	2	yes	—
22	#16813622	C₂²	1	1	yes	characteristic
23	#16813621	C₂²	1	2	yes	—
24	#16813621	C₂²	1	4	yes	—
25	#16813620	C₂²	1	2	yes	—
26	#16813615	C₂²	1	4	yes	—
27	#16813615	C₂²	1	4	yes	—
28	#16813615	C₂²	1	4	yes	—
29	#16813615	C₂²	1	4	yes	—
30	#16813614	C₂²	1	2	yes	—
31	#16813614	C₂²	1	2	yes	—
32	#16813613	C₂²	1	4	yes	—
33	#16813613	C₂²	1	2	yes	—
34	#16813612	C₂²	1	4	yes	—
35	#16813612	C₂²	1	4	yes	—
36	#16813612	C₂²	1	4	yes	—
37	#16813612	C₂²	1	4	yes	—
38	#16813609	C₂²	1	2	yes	—
39	#16813603	C₂²	1	4	yes	—
40	#16813601	C₂²	1	2	yes	—
41	#16813601	C₂²	1	2	yes	—
42	#16813601	C₂²	1	2	yes	—
43	#16813601	C₂²	1	2	yes	—
44	#16813599	C₂²	1	4	yes	—
45	#16813599	C₂²	1	4	yes	—
46	#16813599	C₂²	1	4	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	2	yes	—
52	C₄×Dic₂₂₆	C₂²	1	2	yes	—
53	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
54	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
55	C₄×Dic₂₂₆	C₂²	1	2	yes	—
56	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
57	C₄×Dic₂₂₆	C₂²	1	2	yes	—
58	#16813587	C₂²	1	4	yes	—
59	#16813587	C₂²	1	2	yes	—
60	#16813587	C₂²	1	2	yes	—
61	#16813587	C₂²	1	4	yes	—
62	D₄×Dic₁₁₃	C₂²	1	4	yes	—
63	D₄×Dic₁₁₃	C₂²	1	2	yes	—
64	#16813581	C₂²	1	2	yes	—
65	#16813581	C₂²	1	2	yes	—
66	#16813578	C₂²	1	4	yes	—
67	#16813578	C₂²	1	4	yes	—
68	#16813578	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
70	C₂×#14268626	C₂²	1	2	yes	—
71	C₂×C₄×Dic₁₁₃	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	2	yes	—
80	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
81	#117×C₁₁₃	C₂²	1	2	yes	—
82	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
83	C₂×Dic₂₂₆	—	2	4	no	—
84	C₂×Dic₂₂₆	—	2	8	no	—
85	C₂×Dic₂₂₆	C₂³	1	2	yes	—
86	C₂×Dic₂₂₆	C₂³	1	4	yes	—
87	C₂×Dic₂₂₆	C₂³	1	2	yes	—
88	C₂×Dic₂₂₆	C₂³	1	2	yes	—
89	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
90	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
91	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
92	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
93	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
94	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
97	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
100	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
103	#14268626	C₂³	1	2	yes	—
104	#14268626	C₂³	1	2	yes	—
105	#14268626	C₂³	1	2	yes	—
106	#14268626	C₂³	1	2	yes	—
107	#14268626	C₂³	1	4	yes	—
108	#14268626	C₂³	1	4	yes	—
109	#14268626	C₂³	1	4	yes	—
110	#14268626	C₂³	1	4	yes	—
111	#14268626	C₂³	1	4	yes	—
112	#14268626	C₂³	1	4	yes	—
113	#14268626	C₂³	1	4	yes	—
114	#14268626	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
119	C₄×Dic₁₁₃	C₂³	1	2	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	2	yes	—
129	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
134	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
135	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
136	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
149	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
150	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
151	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
152	Q₈×C₁₁₃	—	2	2	no	—
153	D₄×C₁₁₃	—	2	4	no	—
154	D₄×C₁₁₃	—	2	2	no	—
155	C₂×C₄×C₁₁₃	—	2	2	no	—
156	C₂×C₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	2	4	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
164	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₁₁₃	—	2	4	no	—
169	C₂×Dic₁₁₃	—	2	4	no	—
170	C₂×Dic₁₁₃	—	2	8	no	—
171	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
176	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
177	Dic₂₂₆	—	2	2	no	—
178	Dic₂₂₆	—	2	4	no	—
179	Dic₂₂₆	—	2	4	no	—
180	Dic₂₂₆	—	2	8	no	—
181	Dic₂₂₆	—	2	4	no	—
182	Dic₂₂₆	#41	1	4	yes	—
183	C₂²×C₁₁₃	—	2	1	no	—
184	C₂²×C₁₁₃	—	2	1	no	—
185	C₂²×C₁₁₃	—	2	2	no	—
186	C₂²×C₁₁₃	—	2	2	no	—
187	C₂²×C₁₁₃	—	2	2	no	—
188	C₂²×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
189	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
190	C₄×C₁₁₃	—	2	1	no	—
191	C₄×C₁₁₃	—	2	2	no	—
192	C₄×C₁₁₃	—	2	1	no	—
193	C₄×C₁₁₃	—	2	1	no	—
194	C₄×C₁₁₃	—	2	1	no	—
195	C₄×C₁₁₃	—	2	2	no	—
196	C₄×C₁₁₃	—	2	2	no	—
197	C₄×C₁₁₃	C₂×#41	1	2	yes	—
198	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
199	Dic₁₁₃	—	2	4	no	—
200	Dic₁₁₃	—	2	2	no	—
201	Dic₁₁₃	—	2	4	no	—
202	Dic₁₁₃	—	2	2	no	—
203	Dic₁₁₃	—	2	2	no	—
204	Dic₁₁₃	C₂×#41	1	4	yes	—
205	C₂×C₁₁₃	—	2	2	no	—
206	C₂×C₁₁₃	—	4	2	no	—
207	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
208	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
209	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	#3523	—	113	1	no	maximal, Sylow
211	C₁₁₃	#3523	1	1	yes	characteristic, complemented, Sylow
212	#557	—	113	2	no	—
213	#557	—	113	1	no	—
214	#557	—	113	1	no	—
215	#556	—	113	2	no	—
216	#556	—	113	1	no	—
217	#552	—	113	4	no	—
218	#552	—	113	2	no	—
219	D₄×Q₈	—	113	2	no	—
220	D₄×Q₈	—	113	1	no	—
221	#541	—	113	4	no	—
222	#541	—	113	2	no	—
223	#533	—	113	2	no	—
224	#533	—	113	1	no	—
225	#529	—	113	2	no	—
226	#529	D₁₁₃	1	1	yes	characteristic
227	#519	—	113	2	no	—
228	C₂×C₄×Q₈	—	113	1	no	—
229	C₂²×Q₈	—	113	1	no	—
230	C₂²×Q₈	—	113	2	no	—
231	C₄⋊Q₈	—	113	2	no	—
232	C₄⋊Q₈	—	113	2	no	—
233	C₄⋊Q₈	—	113	4	no	—
234	C₄⋊Q₈	—	113	1	no	—
235	C₄⋊Q₈	—	113	1	no	—
236	C₄⋊Q₈	—	113	2	no	—
237	#126	—	113	4	no	—
238	#126	—	113	4	no	—
239	#126	—	113	4	no	—
240	#126	—	113	4	no	—
241	#126	C₂×D₁₁₃	1	2	yes	—
242	#125	—	113	2	no	—
243	#125	—	113	4	no	—
244	#125	—	113	4	no	—
245	#125	—	113	4	no	—
246	#125	—	113	4	no	—
247	#125	—	113	4	no	—
248	#125	—	113	2	no	—
249	#125	—	113	2	no	—
250	#125	C₂×D₁₁₃	1	1	yes	characteristic
251	#124	—	113	2	no	—
252	#124	C₂×D₁₁₃	1	1	yes	characteristic
253	#123	—	113	4	no	—
254	#123	C₂×D₁₁₃	1	2	yes	—
255	C₂²⋊Q₈	—	113	2	no	—
256	C₂²⋊Q₈	—	113	2	no	—
257	C₂²⋊Q₈	—	113	2	no	—
258	C₂²⋊Q₈	—	113	2	no	—
259	C₂²⋊Q₈	—	113	4	no	—
260	C₂²⋊Q₈	—	113	4	no	—
261	C₂²⋊Q₈	—	113	4	no	—
262	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
263	#121	C₂×D₁₁₃	1	1	yes	characteristic
264	C₄×Q₈	—	113	2	no	—
265	C₄×Q₈	—	113	4	no	—
266	C₄×Q₈	—	113	4	no	—
267	C₄×Q₈	—	113	2	no	—
268	C₄×Q₈	—	113	2	no	—
269	C₄×Q₈	—	113	1	no	—
270	C₄×Q₈	—	113	2	no	—
271	C₄×Q₈	—	113	1	no	—
272	C₄×Q₈	—	113	1	no	—
273	C₄×Q₈	—	113	2	no	—
274	C₄×Q₈	—	113	1	no	—
275	C₄×Q₈	—	113	2	no	—
276	C₄×Q₈	—	113	2	no	—
277	C₄×Q₈	—	113	2	no	—
278	C₄×Q₈	—	113	2	no	—
279	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
280	C₄×D₄	—	113	4	no	—
281	C₄×D₄	—	113	2	no	—
282	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
283	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
284	#117	—	113	2	no	—
285	#117	—	113	2	no	—
286	#117	—	113	4	no	—
287	#117	—	113	4	no	—
288	#117	—	113	4	no	—
289	#117	C₂×D₁₁₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	113	2	no	—
291	C₂×C₄⋊C₄	—	113	1	no	—
292	C₂×C₄²	—	113	2	no	—
293	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
294	C₂×Q₈	—	113	1	no	—
295	C₂×Q₈	—	113	2	no	—
296	C₂×Q₈	—	113	4	no	—
297	C₂×Q₈	—	113	2	no	—
298	C₂×Q₈	—	113	1	no	—
299	C₂×Q₈	—	113	2	no	—
300	C₂×Q₈	—	226	4	no	—
301	C₂×Q₈	—	226	8	no	—
302	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
303	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
304	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
305	C₂²×C₄	—	113	2	no	—
306	C₂²×C₄	—	113	2	no	—
307	C₂²×C₄	—	113	4	no	—
308	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
312	C₄⋊C₄	—	113	2	no	—
313	C₄⋊C₄	—	113	1	no	—
314	C₄⋊C₄	—	113	2	no	—
315	C₄⋊C₄	—	113	1	no	—
316	C₄⋊C₄	—	113	2	no	—
317	C₄⋊C₄	—	113	2	no	—
318	C₄⋊C₄	—	113	2	no	—
319	C₄⋊C₄	—	113	4	no	—
320	C₄⋊C₄	—	113	2	no	—
321	C₄⋊C₄	—	113	4	no	—
322	C₄⋊C₄	—	113	4	no	—
323	C₄⋊C₄	—	113	4	no	—
324	C₄⋊C₄	—	113	2	no	—
325	C₄⋊C₄	—	113	4	no	—
326	C₄⋊C₄	—	113	2	no	—
327	C₄⋊C₄	—	113	2	no	—
328	C₄⋊C₄	—	113	4	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	C₂²×D₁₁₃	1	2	yes	—
334	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
335	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
336	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
337	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
339	C₂²⋊C₄	—	113	4	no	—
340	C₂²⋊C₄	—	113	4	no	—
341	C₂²⋊C₄	—	113	4	no	—
342	C₂²⋊C₄	—	113	4	no	—
343	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
345	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
348	C₄²	—	113	2	no	—
349	C₄²	—	113	2	no	—
350	C₄²	—	113	2	no	—
351	C₄²	—	113	2	no	—
352	C₄²	—	113	4	no	—
353	C₄²	—	113	4	no	—
354	C₄²	—	113	4	no	—
355	C₄²	—	113	4	no	—
356	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
357	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
358	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
359	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
360	C₄²	C₂²×D₁₁₃	1	2	yes	—
361	C₂³	C₂³×D₁₁₃	1	2	yes	—
362	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	113	4	no	—
365	Q₈	—	226	8	no	—
366	Q₈	—	226	4	no	—
367	Q₈	—	226	2	no	—
368	Q₈	—	226	4	no	—
369	Q₈	—	226	4	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	113	2	no	—
377	C₂×C₄	—	113	2	no	—
378	C₂×C₄	—	113	4	no	—
379	C₂×C₄	—	113	2	no	—
380	C₂×C₄	—	113	2	no	—
381	C₂×C₄	—	113	4	no	—
382	C₂×C₄	—	226	4	no	—
383	C₂×C₄	—	226	8	no	—
384	C₂×C₄	—	226	4	no	—
385	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
386	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
388	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
389	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
390	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	#16813669	1	2	yes	—
400	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	113	4	no	—
409	C₄	—	226	2	no	—
410	C₄	—	226	4	no	—
411	C₄	—	226	2	no	—
412	C₄	—	226	2	no	—
413	C₄	—	226	4	no	—
414	C₄	#41×D₁₁₃	1	2	yes	—
415	C₄	#16813669	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
419	C₂	C₂×#16813669	1	1	yes	characteristic
420	C₂	C₂×#16813669	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#529×C₁₁₃	C₂
prime radical	#121×C₁₁₃	C₂²
hypercenter	#529	D₁₁₃
hypocenter	C₁₁₃	#3523
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. #20299327	C₂	semidirect
2. #20299326	C₂	semidirect
3. #20299325	C₂	semidirect
4. #20299318	C₂	semidirect
5. #20299317	C₂	semidirect
6. #20299288	C₂	semidirect
7. #20299285	C₂	semidirect
8. D₄×Dic₂₂₆	C₂	semidirect
9. D₄×Dic₂₂₆	C₂	semidirect
10. #20299210	C₂	semidirect
11. #20299205	C₂	semidirect
12. #20299155	C₂	semidirect
13. #20299150	C₂	semidirect
15. #20299075	C₂	semidirect
16. C₂×C₄×Dic₂₂₆	C₂	semidirect
211. C₁₁₃	#3523	semidirect

Maximal subgroups

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

subgroup	index
#20299327	2
#20299326	2
#20299325	2
#20299318	2
#20299317	2
#20299288	2
#20299285	2
D₄×Dic₂₂₆	2
#20299210	2
#20299205	2
#20299155	2
#20299150	2
#20299129	2
#20299075	2
C₂×C₄×Dic₂₂₆	2
#529×C₁₁₃	2
#3523	113