Subgroups — #28404329

Order 14464.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299322	C₂	1	2	yes	maximal, complemented
2	#20299309	C₂	1	2	yes	maximal, complemented
3	#20299290	C₂	1	4	yes	maximal, complemented
4	#20299286	C₂	1	2	yes	maximal, complemented
5	#20299286	C₂	1	2	yes	maximal, complemented
6	#20299275	C₂	1	4	yes	maximal, complemented
7	#20299222	C₂	1	2	yes	maximal, complemented
8	#20299211	C₂	1	2	yes	maximal, complemented
9	#20299174	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299153	C₂	1	2	yes	maximal, complemented
11	#20299133	C₂	1	2	yes	maximal, complemented
12	#20299110	C₂	1	1	yes	maximal, characteristic
13	C₂×#16813602	C₂	1	1	yes	maximal, characteristic, complemented
14	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299075	C₂	1	1	yes	maximal, characteristic, complemented
16	#117×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#544×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	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
21	#16813622	C₂²	1	2	yes	complemented
22	#16813617	C₂²	1	4	yes	—
23	#16813617	C₂²	1	4	yes	—
24	#16813617	C₂²	1	4	yes	complemented
25	#16813617	C₂²	1	4	yes	complemented
26	#16813613	C₂²	1	4	yes	complemented
27	#16813613	C₂²	1	4	yes	complemented
28	#16813613	C₂²	1	4	yes	complemented
29	#16813611	C₂²	1	4	yes	—
30	#16813610	C₂²	1	2	yes	complemented
31	#16813607	C₂²	1	4	yes	—
32	#16813607	C₂²	1	4	yes	—
33	#16813606	C₂²	1	4	yes	—
34	#16813606	C₂²	1	2	yes	—
35	#16813602	C₂²	1	2	yes	—
36	#16813602	C₂²	1	2	yes	—
37	#16813602	C₂²	1	2	yes	—
38	#16813602	C₂²	1	2	yes	—
39	#16813602	C₂²	1	1	yes	characteristic
40	#16813602	C₂²	1	1	yes	characteristic
41	#16813602	C₂²	1	2	yes	complemented
42	#16813602	C₂²	1	2	yes	complemented
43	#16813598	C₂²	1	4	yes	—
44	#16813598	C₂²	1	4	yes	complemented
45	#16813597	C₂²	1	1	yes	characteristic
46	#16813597	C₂²	1	1	yes	characteristic
47	#16813592	C₂²	1	2	yes	—
48	Q₈×Dic₁₁₃	C₂²	1	4	yes	complemented
49	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
50	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
51	#16813587	C₂²	1	2	yes	complemented
52	#16813587	C₂²	1	2	yes	complemented
53	#16813587	C₂²	1	2	yes	complemented
54	C₄×D₄₅₂	C₂²	1	2	yes	—
55	C₄×D₄₅₂	C₂²	1	2	yes	—
56	#16813584	C₂²	1	4	yes	—
57	#16813584	C₂²	1	2	yes	complemented
58	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
59	#16813581	C₂²	1	1	yes	characteristic
60	#16813580	C₂²	1	4	yes	—
61	#16813580	C₂²	1	1	yes	characteristic
62	#16813580	C₂²	1	1	yes	characteristic
63	#16813580	C₂²	1	4	yes	complemented
64	#16813580	C₂²	1	2	yes	complemented
65	#16813579	C₂²	1	2	yes	—
66	#16813578	C₂²	1	4	yes	—
67	#16813578	C₂²	1	2	yes	—
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
70	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
72	C₂×#14268624	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
74	C₄²×D₁₁₃	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
76	C₄⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
77	#125×C₁₁₃	C₂²	1	2	yes	complemented
78	#125×C₁₁₃	C₂²	1	2	yes	complemented
79	C₂²⋊Q₈×C₁₁₃	C₂²	1	4	yes	—
80	#117×C₁₁₃	C₂²	1	1	yes	characteristic
81	#117×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
83	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
84	#14268647	—	2	4	no	—
85	C₂×Dic₂₂₆	—	2	4	no	—
86	C₂×Dic₂₂₆	C₂³	1	2	yes	—
87	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
88	C₂×Dic₂₂₆	C₂³	1	2	yes	—
89	C₂×D₄₅₂	C₂³	1	2	yes	—
90	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
91	C₂×D₄₅₂	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
93	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
94	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₁₁₃	—	2	4	no	—
96	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
98	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
100	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
104	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
107	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
108	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
109	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
110	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
111	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
112	#14268626	C₂³	1	2	yes	—
113	#14268626	C₂³	1	2	yes	—
114	#14268626	C₂³	1	4	yes	—
115	#14268626	C₂³	1	4	yes	—
116	#14268626	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
118	#14268624	C₂³	1	2	yes	—
119	#14268624	C₂³	1	2	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	#14268624	C₂³	1	2	yes	—
123	#14268624	C₂³	1	2	yes	—
124	#14268624	C₂³	1	4	yes	—
125	#14268624	C₂³	1	4	yes	—
126	#14268624	C₂³	1	4	yes	—
127	#14268624	C₂³	1	2	yes	—
128	#14268624	C₂³	1	2	yes	—
129	C₄×Dic₁₁₃	C₂³	1	2	yes	—
130	C₄×Dic₁₁₃	C₂³	1	2	yes	—
131	C₄×Dic₁₁₃	C₂³	1	2	yes	—
132	C₄×Dic₁₁₃	C₂³	1	4	yes	—
133	C₄×Dic₁₁₃	C₂³	1	4	yes	—
134	C₄×Dic₁₁₃	C₂³	1	4	yes	—
135	C₂×Q₈×C₁₁₃	C₂³	1	4	yes	—
136	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
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	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
142	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
143	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
147	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
149	C₄²×C₁₁₃	C₂³	1	2	yes	—
150	C₄²×C₁₁₃	C₂³	1	2	yes	—
151	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
152	C₂²×D₁₁₃	—	2	2	no	—
153	C₂²×D₁₁₃	—	2	2	no	—
154	C₂²×D₁₁₃	—	4	1	no	—
155	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
156	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
157	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
158	Q₈×C₁₁₃	—	4	4	no	—
159	C₂×C₄×C₁₁₃	—	4	2	no	—
160	C₂×C₄×C₁₁₃	#41	1	4	yes	—
161	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
168	C₂²⋊D₁₁₃	—	2	4	no	—
169	C₂×Dic₁₁₃	—	2	2	no	—
170	C₂×Dic₁₁₃	—	2	4	no	—
171	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
176	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
177	D₄₅₂	—	2	4	no	—
178	D₄₅₂	—	2	2	no	—
179	D₄₅₂	—	4	2	no	—
180	C₄×D₁₁₃	—	2	4	no	—
181	C₄×D₁₁₃	—	2	2	no	—
182	C₄×D₁₁₃	—	2	2	no	—
183	C₄×D₁₁₃	—	2	2	no	—
184	C₄×D₁₁₃	—	2	2	no	—
185	C₄×D₁₁₃	—	2	4	no	—
186	C₄×D₁₁₃	—	4	4	no	—
187	C₄×D₁₁₃	—	4	2	no	—
188	Dic₂₂₆	—	2	4	no	—
189	Dic₂₂₆	—	2	4	no	—
190	Dic₂₂₆	—	2	2	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	—	2	1	no	—
193	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
194	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
195	C₂×D₁₁₃	—	2	1	no	—
196	C₂×D₁₁₃	—	2	1	no	—
197	C₂×D₁₁₃	—	2	1	no	—
198	C₂×D₁₁₃	—	2	2	no	—
199	C₂×D₁₁₃	—	2	2	no	—
200	C₂×D₁₁₃	—	2	1	no	—
201	C₂×D₁₁₃	—	2	2	no	—
202	C₂×D₁₁₃	—	2	1	no	—
203	C₂×D₁₁₃	—	4	4	no	—
204	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
205	C₄×C₁₁₃	—	2	2	no	—
206	C₄×C₁₁₃	—	2	2	no	—
207	C₄×C₁₁₃	—	2	4	no	—
208	C₄×C₁₁₃	—	2	2	no	—
209	C₄×C₁₁₃	—	2	2	no	—
210	C₄×C₁₁₃	C₂×#41	1	2	yes	—
211	C₄×C₁₁₃	C₂×#41	1	2	yes	—
212	Dic₁₁₃	—	2	4	no	—
213	Dic₁₁₃	—	2	2	no	—
214	Dic₁₁₃	—	2	1	no	—
215	Dic₁₁₃	—	2	1	no	—
216	Dic₁₁₃	—	2	2	no	—
217	Dic₁₁₃	—	2	2	no	—
218	C₂×C₁₁₃	—	2	2	no	—
219	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
220	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₁₁₃	#585	1	1	yes	characteristic
222	D₁₁₃	—	2	2	no	—
223	D₁₁₃	—	4	2	no	—
224	D₁₁₃	—	4	1	no	—
225	#3495	—	113	1	no	maximal, Sylow
226	C₁₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
227	#556	—	113	2	no	—
228	#554	—	113	2	no	—
229	#552	—	113	2	no	—
230	#552	—	113	2	no	—
231	#552	—	113	4	no	—
232	#551	—	113	4	no	—
233	#544	D₁₁₃	1	1	yes	characteristic, complemented
234	#542	—	113	2	no	—
235	#541	—	113	2	no	—
236	#536	—	113	1	no	—
237	#533	—	113	2	no	—
238	#529	—	113	2	no	—
239	#525	—	113	1	no	—
240	C₂×C₂²⋊Q₈	—	113	1	no	—
241	#520	—	113	1	no	—
242	#519	—	113	1	no	—
243	C₂×#117	—	113	1	no	—
244	C₂×#41	—	113	1	no	—
245	C₂²×Q₈	—	113	1	no	—
246	C₂³×C₄	—	113	1	no	—
247	C₄⋊Q₈	—	113	2	no	—
248	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
249	C₄⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
250	#126	—	113	4	no	—
251	#126	—	113	4	no	—
252	#126	—	113	4	no	—
253	#126	—	113	4	no	—
254	#125	—	113	4	no	—
255	#125	—	113	4	no	—
256	#125	—	113	4	no	—
257	#125	C₂×D₁₁₃	1	2	yes	complemented
258	#125	C₂×D₁₁₃	1	2	yes	complemented
259	#124	—	113	4	no	—
260	#124	—	113	2	no	—
261	#123	—	113	4	no	—
262	#123	—	113	4	no	—
263	#123	—	113	2	no	—
264	#123	—	113	4	no	—
265	C₂²⋊Q₈	—	113	4	no	—
266	C₂²⋊Q₈	—	113	4	no	—
267	C₂²⋊Q₈	—	113	2	no	—
268	C₂²⋊Q₈	—	113	2	no	—
269	C₂²⋊Q₈	—	113	2	no	—
270	C₂²⋊Q₈	—	113	2	no	—
271	C₂²⋊Q₈	—	113	1	no	—
272	C₂²⋊Q₈	—	113	1	no	—
273	C₂²⋊Q₈	—	113	2	no	—
274	C₂²⋊Q₈	—	113	2	no	—
275	C₂²⋊Q₈	C₂×D₁₁₃	1	4	yes	—
276	#121	—	113	1	no	—
277	#121	—	113	1	no	—
278	#120	—	113	2	no	—
279	C₄×Q₈	—	113	4	no	—
280	C₄×Q₈	—	113	2	no	—
281	C₄×Q₈	—	113	2	no	—
282	C₄×Q₈	—	113	2	no	—
283	C₄×Q₈	—	113	2	no	—
284	C₄×Q₈	—	113	2	no	—
285	C₄×D₄	—	113	4	no	—
286	C₄×D₄	—	113	2	no	—
287	C₄×D₄	—	113	4	no	—
288	C₄×D₄	—	113	2	no	—
289	C₄×D₄	—	113	2	no	—
290	#117	—	113	1	no	—
291	#117	—	113	1	no	—
292	#117	—	113	1	no	—
293	#117	—	113	2	no	—
294	#117	—	113	4	no	—
295	#117	—	113	4	no	—
296	#117	—	113	2	no	—
297	#117	—	113	4	no	—
298	#117	—	113	2	no	—
299	#117	C₂×D₁₁₃	1	1	yes	characteristic
300	#117	C₂×D₁₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	—	113	2	no	—
302	C₂×C₄⋊C₄	—	113	1	no	—
303	C₂×C₄⋊C₄	—	113	1	no	—
304	C₂×C₄⋊C₄	—	113	2	no	—
305	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	113	2	no	—
307	C₂×C₂²⋊C₄	—	113	2	no	—
308	C₂×C₄²	—	113	2	no	—
309	C₂⁴	—	113	1	no	—
310	#41	—	226	4	no	—
311	C₂×Q₈	—	113	2	no	—
312	C₂×Q₈	—	113	2	no	—
313	C₂×Q₈	—	113	1	no	—
314	C₂×Q₈	—	226	4	no	—
315	C₂×Q₈	C₂²×D₁₁₃	1	4	yes	—
316	C₂×D₄	—	113	2	no	—
317	C₂×D₄	—	113	2	no	—
318	C₂×D₄	—	113	2	no	—
319	C₂×D₄	—	113	1	no	—
320	C₂²×C₄	—	113	2	no	—
321	C₂²×C₄	—	113	1	no	—
322	C₂²×C₄	—	113	2	no	—
323	C₂²×C₄	—	113	4	no	—
324	C₂²×C₄	—	113	1	no	—
325	C₂²×C₄	—	113	2	no	—
326	C₂²×C₄	—	113	1	no	—
327	C₂²×C₄	—	113	2	no	—
328	C₂²×C₄	—	113	1	no	—
329	C₂²×C₄	—	113	1	no	—
330	C₂²×C₄	—	226	4	no	—
331	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
332	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
333	C₄⋊C₄	—	113	1	no	—
334	C₄⋊C₄	—	113	1	no	—
335	C₄⋊C₄	—	113	2	no	—
336	C₄⋊C₄	—	113	2	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	—	113	2	no	—
344	C₄⋊C₄	—	113	2	no	—
345	C₄⋊C₄	—	113	4	no	—
346	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
347	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
348	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
350	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
351	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
352	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
353	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
354	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
355	C₂²⋊C₄	—	113	2	no	—
356	C₂²⋊C₄	—	113	2	no	—
357	C₂²⋊C₄	—	113	2	no	—
358	C₂²⋊C₄	—	113	4	no	—
359	C₂²⋊C₄	—	113	4	no	—
360	C₂²⋊C₄	—	113	2	no	—
361	C₂²⋊C₄	—	113	2	no	—
362	C₂²⋊C₄	—	113	4	no	—
363	C₂²⋊C₄	—	113	4	no	—
364	C₂²⋊C₄	—	113	2	no	—
365	C₂²⋊C₄	—	113	2	no	—
366	C₂²⋊C₄	—	113	4	no	—
367	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
368	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
369	C₄²	—	113	2	no	—
370	C₄²	—	113	2	no	—
371	C₄²	—	113	2	no	—
372	C₄²	—	113	4	no	—
373	C₄²	—	113	4	no	—
374	C₄²	—	113	4	no	—
375	C₄²	C₂²×D₁₁₃	1	2	yes	—
376	C₄²	C₂²×D₁₁₃	1	2	yes	—
377	C₂³	—	113	1	no	—
378	C₂³	—	113	1	no	—
379	C₂³	—	113	2	no	—
380	C₂³	—	452	1	no	—
381	C₂³	—	226	2	no	—
382	C₂³	—	226	2	no	—
383	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
384	Q₈	—	4	4	no	—
385	Q₈	—	226	4	no	—
386	Q₈	—	226	4	no	—
387	Q₈	—	226	2	no	—
388	D₄	—	452	2	no	—
389	D₄	—	226	4	no	—
390	D₄	—	226	4	no	—
391	D₄	—	226	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	113	2	no	—
394	C₂×C₄	—	113	1	no	—
395	C₂×C₄	—	113	2	no	—
396	C₂×C₄	—	113	4	no	—
397	C₂×C₄	—	113	2	no	—
398	C₂×C₄	—	113	1	no	—
399	C₂×C₄	—	452	4	no	—
400	C₂×C₄	—	452	2	no	—
401	C₂×C₄	—	226	4	no	—
402	C₂×C₄	—	226	2	no	—
403	C₂×C₄	—	226	4	no	—
404	C₂×C₄	—	226	2	no	—
405	C₂×C₄	—	226	2	no	—
406	C₂×C₄	—	226	2	no	—
407	C₂×C₄	—	226	2	no	—
408	C₂×C₄	—	226	4	no	—
409	C₂×C₄	#14268648	1	4	yes	—
410	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
411	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
412	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
413	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
414	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
415	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	113	2	no	—
420	C₂²	—	452	4	no	—
421	C₂²	—	226	1	no	—
422	C₂²	—	226	2	no	—
423	C₂²	—	226	2	no	—
424	C₂²	—	226	1	no	—
425	C₂²	—	226	2	no	—
426	C₂²	—	226	1	no	—
427	C₂²	—	226	1	no	—
428	C₂²	—	226	1	no	—
429	C₂²	C₂×#14268648	1	2	yes	—
430	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	226	1	no	—
437	C₄	—	226	1	no	—
438	C₄	—	226	2	no	—
439	C₄	—	226	4	no	—
440	C₄	—	226	2	no	—
441	C₄	—	226	2	no	—
442	C₄	C₂×#14268648	1	2	yes	—
443	C₄	C₂×#14268648	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	452	1	no	—
446	C₂	—	452	2	no	—
447	C₂	—	226	2	no	—
448	C₂	C₂²×#14268648	1	1	yes	characteristic
449	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic
450	C₂	#20299433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#544×C₁₁₃	C₂
prime radical	#20299110	C₂
hypercenter	#544	D₁₁₃
hypocenter	C₁₁₃	#3495
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #544

Complements

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

N	H ≅ G/N	type
1. #20299322	C₂	semidirect
2. #20299309	C₂	semidirect
3. #20299290	C₂	semidirect
4. #20299286	C₂	semidirect
5. #20299286	C₂	semidirect
6. #20299275	C₂	semidirect
7. #20299222	C₂	semidirect
8. #20299211	C₂	semidirect
9. #20299174	C₂	semidirect
10. #20299153	C₂	semidirect
11. #20299133	C₂	semidirect
13. C₂×#16813602	C₂	semidirect
14. #20299079	C₂	semidirect
15. #20299075	C₂	semidirect
16. #117×D₁₁₃	C₂	semidirect
17. #544×C₁₁₃	C₂	semidirect
21. #16813622	C₂²	semidirect
24. #16813617	C₂²	semidirect
25. #16813617	C₂²	semidirect
26. #16813613	C₂²	semidirect
27. #16813613	C₂²	semidirect
28. #16813613	C₂²	semidirect
30. #16813610	C₂²	semidirect
41. #16813602	C₂²	semidirect
42. #16813602	C₂²	semidirect
44. #16813598	C₂²	semidirect
48. Q₈×Dic₁₁₃	C₂²	semidirect
49. C₄×Dic₂₂₆	C₂²	semidirect
50. C₄×Dic₂₂₆	C₂²	semidirect
51. #16813587	C₂²	semidirect
52. #16813587	C₂²	semidirect
53. #16813587	C₂²	semidirect
57. #16813584	C₂²	semidirect
63. #16813580	C₂²	semidirect
64. #16813580	C₂²	semidirect
71. C₄⋊C₄×D₁₁₃	C₂²	semidirect
75. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
76. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
77. #125×C₁₁₃	C₂²	semidirect
78. #125×C₁₁₃	C₂²	semidirect
226. C₁₁₃	#3495	semidirect
233. #544	D₁₁₃	semidirect
248. C₄⋊Q₈	C₂×D₁₁₃	semidirect
249. C₄⋊Q₈	C₂×D₁₁₃	semidirect
257. #125	C₂×D₁₁₃	semidirect
258. #125	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299322	2
#20299309	2
#20299290	2
#20299286	2
#20299275	2
#20299222	2
#20299211	2
#20299174	2
#20299153	2
#20299133	2
#20299110	2
C₂×#16813602	2
#20299079	2
#20299075	2
#117×D₁₁₃	2
#544×C₁₁₃	2
#3495	113