Subgroups — #28404001

Order 14464.

1012 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299226	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299219	C₂	1	2	yes	maximal, complemented
3	#20299213	C₂	1	2	yes	maximal, complemented
4	#20299210	C₂	1	2	yes	maximal, complemented
5	#20299206	C₂	1	2	yes	maximal, complemented
6	#20299190	C₂	1	4	yes	maximal, complemented
7	#20299176	C₂	1	1	yes	maximal, characteristic
8	#20299174	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299169	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299155	C₂	1	2	yes	maximal, complemented
11	#20299152	C₂	1	2	yes	maximal, complemented
12	#20299132	C₂	1	2	yes	maximal, complemented
13	#20299130	C₂	1	2	yes	maximal, complemented
14	#20299128	C₂	1	4	yes	maximal, complemented
15	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268647	C₂²	1	1	yes	characteristic
19	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
20	#16813622	C₂²	1	2	yes	—
21	#16813622	C₂²	1	2	yes	—
22	#16813621	C₂²	1	2	yes	—
23	#16813620	C₂²	1	2	yes	—
24	#16813617	C₂²	1	4	yes	—
25	#16813616	C₂²	1	4	yes	—
26	#16813615	C₂²	1	4	yes	—
27	#16813615	C₂²	1	4	yes	—
28	#16813614	C₂²	1	2	yes	—
29	#16813614	C₂²	1	4	yes	—
30	#16813613	C₂²	1	2	yes	—
31	#16813612	C₂²	1	4	yes	—
32	#16813612	C₂²	1	4	yes	—
33	#16813610	C₂²	1	2	yes	—
34	#16813609	C₂²	1	2	yes	—
35	#16813608	C₂²	1	4	yes	—
36	#16813606	C₂²	1	4	yes	—
37	#16813605	C₂²	1	4	yes	—
38	#16813604	C₂²	1	4	yes	—
39	#16813603	C₂²	1	4	yes	—
40	#16813602	C₂²	1	2	yes	—
41	#16813602	C₂²	1	2	yes	—
42	#16813601	C₂²	1	2	yes	—
43	#16813601	C₂²	1	2	yes	—
44	#16813601	C₂²	1	2	yes	—
45	#16813601	C₂²	1	4	yes	—
46	#16813600	C₂²	1	4	yes	—
47	#16813599	C₂²	1	4	yes	—
48	#16813598	C₂²	1	2	yes	—
49	#16813596	C₂²	1	2	yes	—
50	#16813594	C₂²	1	4	yes	—
51	#16813593	C₂²	1	2	yes	—
52	C₄×Dic₂₂₆	C₂²	1	2	yes	—
53	C₄×Dic₂₂₆	C₂²	1	2	yes	—
54	C₄×Dic₂₂₆	C₂²	1	2	yes	—
55	C₄×Dic₂₂₆	C₂²	1	2	yes	—
56	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
57	C₄×Dic₂₂₆	C₂²	1	1	yes	characteristic
58	C₄×Dic₂₂₆	C₂²	1	4	yes	—
59	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
60	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
63	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
64	#16813581	C₂²	1	1	yes	characteristic
65	#16813581	C₂²	1	4	yes	—
66	#16813579	C₂²	1	2	yes	—
67	#16813579	C₂²	1	4	yes	—
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
69	C₂×#14268626	C₂²	1	2	yes	—
70	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
71	C₄²×D₁₁₃	C₂²	1	2	yes	—
72	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
74	C₄×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
75	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
76	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
78	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
79	#117×C₁₁₃	C₂²	1	1	yes	characteristic
80	#117×C₁₁₃	C₂²	1	2	yes	—
81	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄²×C₁₁₃	C₂²	1	2	yes	—
83	#14268647	—	2	4	no	—
84	C₂×Dic₂₂₆	—	2	4	no	—
85	C₂×Dic₂₂₆	C₂³	1	2	yes	—
86	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₂₆	C₂³	1	2	yes	—
88	C₂×Dic₂₂₆	C₂³	1	4	yes	—
89	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
92	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
93	C₂²×Dic₁₁₃	C₂³	1	2	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	4	yes	—
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
103	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
104	#14268626	C₂³	1	4	yes	—
105	#14268626	C₂³	1	4	yes	—
106	#14268626	C₂³	1	2	yes	—
107	#14268626	C₂³	1	2	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	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
117	#14268624	C₂³	1	2	yes	—
118	#14268624	C₂³	1	2	yes	—
119	#14268624	C₂³	1	4	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	C₄×Dic₁₁₃	C₂³	1	2	yes	—
123	C₄×Dic₁₁₃	C₂³	1	2	yes	—
124	C₄×Dic₁₁₃	C₂³	1	2	yes	—
125	C₄×Dic₁₁₃	C₂³	1	4	yes	—
126	C₄×Dic₁₁₃	C₂³	1	4	yes	—
127	#41×C₁₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
138	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊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	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
145	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄²×C₁₁₃	C₂³	1	2	yes	—
147	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
149	C₄²×C₁₁₃	C₂³	1	2	yes	—
150	C₄²×C₁₁₃	C₂³	1	2	yes	—
151	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
152	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
154	Q₈×C₁₁₃	—	2	2	no	—
155	D₄×C₁₁₃	—	2	4	no	—
156	D₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	2	4	no	—
158	C₂×C₄×C₁₁₃	—	2	2	no	—
159	C₂×C₄×C₁₁₃	—	2	4	no	—
160	C₂×C₄×C₁₁₃	—	4	2	no	—
161	C₂×C₄×C₁₁₃	—	4	1	no	—
162	C₂×C₄×C₁₁₃	#41	1	4	yes	—
163	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₁₁₃	—	2	4	no	—
173	C₂²⋊D₁₁₃	—	4	4	no	—
174	C₂×Dic₁₁₃	—	2	4	no	—
175	C₂×Dic₁₁₃	—	4	2	no	—
176	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
177	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
178	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
179	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
180	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
181	D₄₅₂	—	2	2	no	—
182	C₄×D₁₁₃	—	2	4	no	—
183	C₄×D₁₁₃	—	2	4	no	—
184	C₄×D₁₁₃	—	4	2	no	—
185	Dic₂₂₆	—	2	4	no	—
186	Dic₂₂₆	—	2	4	no	—
187	Dic₂₂₆	—	2	2	no	—
188	Dic₂₂₆	—	4	4	no	—
189	C₂²×C₁₁₃	—	2	1	no	—
190	C₂²×C₁₁₃	—	2	1	no	—
191	C₂²×C₁₁₃	—	2	2	no	—
192	C₂²×C₁₁₃	—	2	2	no	—
193	C₂²×C₁₁₃	—	2	2	no	—
194	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
195	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
196	C₂×D₁₁₃	—	2	2	no	—
197	C₂×D₁₁₃	—	2	2	no	—
198	C₂×D₁₁₃	—	2	2	no	—
199	C₄×C₁₁₃	—	2	2	no	—
200	C₄×C₁₁₃	—	2	1	no	—
201	C₄×C₁₁₃	—	2	2	no	—
202	C₄×C₁₁₃	—	2	2	no	—
203	C₄×C₁₁₃	—	2	1	no	—
204	C₄×C₁₁₃	—	2	1	no	—
205	C₄×C₁₁₃	C₂×#41	1	2	yes	—
206	C₄×C₁₁₃	C₂×#41	1	2	yes	—
207	C₄×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
208	Dic₁₁₃	—	2	4	no	—
209	Dic₁₁₃	—	2	2	no	—
210	Dic₁₁₃	—	2	2	no	—
211	Dic₁₁₃	—	2	2	no	—
212	Dic₁₁₃	—	2	4	no	—
213	C₂×C₁₁₃	—	2	2	no	—
214	C₂×C₁₁₃	—	4	2	no	—
215	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
216	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
217	C₂×C₁₁₃	#585	1	1	yes	characteristic
218	D₁₁₃	—	4	2	no	—
219	#3461	—	113	1	no	maximal, Sylow
220	C₁₁₃	#3461	1	1	yes	characteristic, complemented, Sylow
221	#544	—	113	1	no	—
222	#542	—	113	2	no	—
223	#542	—	113	2	no	—
224	#541	—	113	2	no	—
225	#541	—	113	2	no	—
226	#539	—	113	4	no	—
227	#537	—	113	1	no	—
228	#536	—	113	1	no	—
229	#536	—	113	1	no	—
230	#533	—	113	2	no	—
231	#533	—	113	2	no	—
232	#529	—	113	4	no	—
233	#529	—	113	2	no	—
234	#529	—	113	2	no	—
235	C₄×#41	—	113	1	no	—
236	C₄×#41	D₁₁₃	1	1	yes	characteristic, complemented
237	C₂×C₄×Q₈	—	113	1	no	—
238	C₂×#41	—	113	1	no	—
239	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
240	C₂²×Q₈	—	113	1	no	—
241	C₄⋊Q₈	—	113	2	no	—
242	C₄⋊Q₈	—	113	2	no	—
243	C₄⋊Q₈	—	113	2	no	—
244	C₄⋊Q₈	—	113	2	no	—
245	#126	—	113	4	no	—
246	#126	—	113	4	no	—
247	#126	—	113	4	no	—
248	#126	—	113	4	no	—
249	#125	—	113	4	no	—
250	#125	—	113	2	no	—
251	#125	—	113	4	no	—
252	#125	—	113	2	no	—
253	#125	—	113	4	no	—
254	#124	—	113	2	no	—
255	#124	—	113	4	no	—
256	#124	—	113	2	no	—
257	#123	—	113	4	no	—
258	#123	—	113	4	no	—
259	#123	—	113	4	no	—
260	#123	—	113	4	no	—
261	C₂²⋊Q₈	—	113	2	no	—
262	C₂²⋊Q₈	—	113	2	no	—
263	C₂²⋊Q₈	—	113	2	no	—
264	C₂²⋊Q₈	—	113	2	no	—
265	C₂²⋊Q₈	—	113	4	no	—
266	C₂²⋊Q₈	—	113	2	no	—
267	C₂²⋊Q₈	—	113	2	no	—
268	C₂²⋊Q₈	—	113	4	no	—
269	C₂²⋊Q₈	—	113	4	no	—
270	#121	—	113	2	no	—
271	#121	—	113	4	no	—
272	#121	—	113	2	no	—
273	C₄×Q₈	—	113	2	no	—
274	C₄×Q₈	—	113	2	no	—
275	C₄×Q₈	—	113	2	no	—
276	C₄×Q₈	—	113	2	no	—
277	C₄×Q₈	—	113	1	no	—
278	C₄×Q₈	—	113	1	no	—
279	C₄×Q₈	—	113	4	no	—
280	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
281	C₄×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
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	1	yes	characteristic
288	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
289	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
290	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
291	#117	—	113	1	no	—
292	#117	—	113	4	no	—
293	#117	—	113	2	no	—
294	#117	—	113	4	no	—
295	#117	C₂×D₁₁₃	1	1	yes	characteristic
296	#117	C₂×D₁₁₃	1	2	yes	—
297	C₂×C₄⋊C₄	—	113	2	no	—
298	C₂×C₄⋊C₄	—	113	1	no	—
299	C₂×C₄²	—	113	2	no	—
300	C₂×C₄²	—	113	2	no	—
301	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
302	C₂×C₄²	C₂×D₁₁₃	1	2	yes	—
303	#41	—	2	4	no	—
304	#41	—	226	4	no	—
305	C₂×Q₈	—	113	4	no	—
306	C₂×Q₈	—	113	2	no	—
307	C₂×Q₈	—	113	2	no	—
308	C₂×Q₈	—	113	1	no	—
309	C₂×Q₈	—	226	4	no	—
310	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
311	C₂×D₄	—	113	4	no	—
312	C₂×D₄	—	113	2	no	—
313	C₂×D₄	—	113	1	no	—
314	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
315	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
316	C₂²×C₄	—	113	2	no	—
317	C₂²×C₄	—	113	2	no	—
318	C₂²×C₄	—	113	2	no	—
319	C₂²×C₄	—	113	2	no	—
320	C₂²×C₄	—	113	2	no	—
321	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
322	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
324	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
326	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
327	C₄⋊C₄	—	113	2	no	—
328	C₄⋊C₄	—	113	2	no	—
329	C₄⋊C₄	—	113	4	no	—
330	C₄⋊C₄	—	113	4	no	—
331	C₄⋊C₄	—	113	2	no	—
332	C₄⋊C₄	—	113	1	no	—
333	C₄⋊C₄	—	113	1	no	—
334	C₄⋊C₄	—	113	2	no	—
335	C₄⋊C₄	—	113	4	no	—
336	C₄⋊C₄	—	113	4	no	—
337	C₄⋊C₄	—	113	4	no	—
338	C₄⋊C₄	—	113	4	no	—
339	C₄⋊C₄	—	113	4	no	—
340	C₄⋊C₄	—	113	4	no	—
341	C₄⋊C₄	—	113	4	no	—
342	C₄⋊C₄	—	113	4	no	—
343	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
344	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
345	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
346	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
347	C₂²⋊C₄	—	113	2	no	—
348	C₂²⋊C₄	—	113	4	no	—
349	C₂²⋊C₄	—	113	4	no	—
350	C₂²⋊C₄	—	113	4	no	—
351	C₂²⋊C₄	—	113	2	no	—
352	C₂²⋊C₄	—	113	2	no	—
353	C₂²⋊C₄	—	113	4	no	—
354	C₂²⋊C₄	—	113	4	no	—
355	C₂²⋊C₄	—	113	4	no	—
356	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
357	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
358	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
359	C₄²	—	113	2	no	—
360	C₄²	—	113	2	no	—
361	C₄²	—	113	4	no	—
362	C₄²	—	113	4	no	—
363	C₄²	—	113	2	no	—
364	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
365	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
366	C₄²	C₂²×D₁₁₃	1	2	yes	—
367	C₄²	C₂²×D₁₁₃	1	2	yes	—
368	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
369	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
370	C₄²	C₂²×D₁₁₃	1	2	yes	—
371	C₂³	—	113	2	no	—
372	C₂³	C₂³×D₁₁₃	1	2	yes	—
373	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	452	4	no	—
376	Q₈	—	226	4	no	—
377	Q₈	—	226	4	no	—
378	Q₈	—	226	2	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	—	452	4	no	—
382	D₄	—	226	4	no	—
383	D₄	—	226	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	113	2	no	—
390	C₂×C₄	—	113	4	no	—
391	C₂×C₄	—	113	2	no	—
392	C₂×C₄	—	113	2	no	—
393	C₂×C₄	—	113	4	no	—
394	C₂×C₄	—	452	2	no	—
395	C₂×C₄	—	452	2	no	—
396	C₂×C₄	—	226	4	no	—
397	C₂×C₄	—	226	4	no	—
398	C₂×C₄	—	226	4	no	—
399	C₂×C₄	#14268647	1	4	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	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
404	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
405	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
406	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
408	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	226	2	no	—
415	C₂²	—	226	2	no	—
416	C₂²	—	226	2	no	—
417	C₂²	C₂×#14268647	1	2	yes	—
418	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	226	2	no	—
426	C₄	—	226	4	no	—
427	C₄	—	226	2	no	—
428	C₄	—	226	4	no	—
429	C₄	—	226	2	no	—
430	C₄	C₂×#14268647	1	2	yes	—
431	C₄	C₂×#14268647	1	2	yes	—
432	C₄	#16813669	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	4	2	no	—
435	C₂	—	452	2	no	—
436	C₂	C₂²×#14268647	1	1	yes	characteristic
437	C₂	C₂×#16813669	1	1	yes	characteristic
438	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₄×#41×C₁₁₃	C₂
prime radical	#20299176	C₂
hypercenter	C₄×#41	D₁₁₃
hypocenter	C₁₁₃	#3461
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20299226	C₂	semidirect
2. #20299219	C₂	semidirect
3. #20299213	C₂	semidirect
4. #20299210	C₂	semidirect
5. #20299206	C₂	semidirect
6. #20299190	C₂	semidirect
8. #20299174	C₂	semidirect
9. #20299169	C₂	semidirect
10. #20299155	C₂	semidirect
11. #20299152	C₂	semidirect
12. #20299132	C₂	semidirect
13. #20299130	C₂	semidirect
14. #20299128	C₂	semidirect
15. C₄×#14268647	C₂	semidirect
16. C₂×C₄×Dic₂₂₆	C₂	semidirect
17. C₄×#41×C₁₁₃	C₂	semidirect
220. C₁₁₃	#3461	semidirect
236. C₄×#41	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299226	2
#20299219	2
#20299213	2
#20299210	2
#20299206	2
#20299190	2
#20299176	2
#20299174	2
#20299169	2
#20299155	2
#20299152	2
#20299132	2
#20299130	2
#20299128	2
C₄×#14268647	2
C₂×C₄×Dic₂₂₆	2
C₄×#41×C₁₁₃	2
#3461	113