Subgroups — #28399315

Order 14464.

492 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813630	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16813628	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299145	C₂	1	1	yes	maximal, characteristic
4	#20298674	C₂	1	1	yes	maximal, characteristic, complemented
5	#20298673	C₂	1	1	yes	maximal, characteristic, complemented
6	#20298671	C₂	1	1	yes	maximal, characteristic, complemented
7	#20298670	C₂	1	1	yes	maximal, characteristic, complemented
8	#20298668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₂²⋊D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#20298661	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#20298563	C₂	1	1	yes	maximal, characteristic, complemented
13	#20298563	C₂	1	1	yes	maximal, characteristic, complemented
14	#20298550	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14268647	C₂²	1	1	yes	characteristic
17	C₂×#14268647	C₂²	1	1	yes	characteristic
18	#16813630	—	2	4	no	—
19	#16813628	—	2	4	no	—
20	C₂×#14268631	C₂²	1	1	yes	characteristic
21	C₂×#14268630	C₂²	1	1	yes	characteristic
22	C₂×#14268630	C₂²	1	1	yes	characteristic
23	C₂×#14268630	C₂²	1	1	yes	characteristic
24	C₂×#14268630	C₂²	1	1	yes	characteristic
25	C₂²×#11744751	C₂²	1	1	yes	characteristic
26	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
30	#16813621	C₄	1	1	yes	characteristic
31	#16813618	C₄	1	1	yes	characteristic
32	#16813608	C₄	1	1	yes	characteristic
33	#16813608	C₄	1	1	yes	characteristic
34	#16813597	C₄	1	1	yes	characteristic
35	#16813595	C₄	1	1	yes	characteristic
36	#16813595	C₄	1	1	yes	characteristic
37	#16813593	C₄	1	1	yes	characteristic
38	C₄×D₄₅₂	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
41	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
42	C₄⋊#11744751	C₂²	1	1	yes	characteristic
43	#16813551	C₂²	1	1	yes	characteristic
44	#16813551	C₂²	1	1	yes	characteristic
45	C₂²⋊#11744751	C₂²	1	1	yes	characteristic
46	C₂²⋊#11744751	C₂²	1	1	yes	characteristic
47	#16813534	C₂²	1	1	yes	characteristic
48	#16813534	C₂²	1	1	yes	characteristic
49	#16813534	C₂²	1	1	yes	characteristic
50	#16813534	C₂²	1	1	yes	characteristic
51	#16813533	C₂²	1	1	yes	characteristic
52	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
53	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
54	C₂×M₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
56	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
58	C₂²⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₁₁₃	C₂²	1	1	yes	characteristic
60	#97×C₁₁₃	C₂²	1	1	yes	characteristic
61	#14268647	—	2	2	no	—
62	#14268647	—	2	2	no	—
63	#14268647	—	2	2	no	—
64	#14268647	—	2	2	no	—
65	C₂×Dic₂₂₆	C₂×C₄	1	1	yes	characteristic
66	C₂×Dic₂₂₆	C₂×C₄	1	1	yes	characteristic
67	C₂×D₄₅₂	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄₅₂	C₂×C₄	1	1	yes	characteristic
69	C₂×D₄₅₂	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
81	#14268631	—	2	2	no	—
82	#14268630	—	2	2	no	—
83	#14268630	—	2	2	no	—
84	#14268630	—	2	2	no	—
85	#14268630	D₄	1	4	yes	complemented
86	C₂×#11744751	—	2	2	no	—
87	C₂×#11744751	C₂³	1	1	yes	characteristic
88	C₂×#11744751	C₂³	1	1	yes	characteristic
89	C₂×#11744751	C₂³	1	1	yes	characteristic
90	C₂×#11744751	C₂³	1	1	yes	characteristic
91	C₈×D₁₁₃	—	2	2	no	—
92	C₈×D₁₁₃	—	2	2	no	—
93	C₈×D₁₁₃	—	2	2	no	—
94	C₈×D₁₁₃	—	2	2	no	—
95	C₄⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
96	#14268626	C₂×C₄	1	1	yes	characteristic
97	#14268626	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
100	#14268624	C₂×C₄	1	1	yes	characteristic
101	#14268624	C₂×C₄	1	1	yes	characteristic
102	#14268624	C₂×C₄	1	1	yes	characteristic
103	#14268624	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
106	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
110	M₁₆×C₁₁₃	—	2	2	no	—
111	C₂×C₈×C₁₁₃	—	2	2	no	—
112	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
119	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
120	C₂³×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₁₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×D₁₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×D₁₁₃	C₂²×C₄	1	1	yes	characteristic
125	D₄×C₁₁₃	—	4	1	no	—
126	C₂×C₄×C₁₁₃	—	2	1	no	—
127	C₂×C₄×C₁₁₃	—	2	1	no	—
128	C₂×C₄×C₁₁₃	—	2	1	no	—
129	C₂×C₄×C₁₁₃	—	2	1	no	—
130	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊D₁₁₃	—	2	2	no	—
136	C₂²⋊D₁₁₃	—	2	2	no	—
137	C₂²⋊D₁₁₃	—	2	2	no	—
138	C₂²⋊D₁₁₃	—	2	2	no	—
139	C₂²⋊D₁₁₃	—	2	2	no	—
140	C₂²⋊D₁₁₃	—	2	2	no	—
141	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
146	D₄₅₂	—	2	2	no	—
147	D₄₅₂	—	2	2	no	—
148	D₄₅₂	—	4	1	no	—
149	C₄×D₁₁₃	—	2	1	no	—
150	C₄×D₁₁₃	—	2	1	no	—
151	C₄×D₁₁₃	—	2	1	no	—
152	C₄×D₁₁₃	—	2	1	no	—
153	C₄×D₁₁₃	—	2	2	no	—
154	C₄×D₁₁₃	—	4	1	no	—
155	C₄×D₁₁₃	C₂×D₄	1	2	yes	—
156	C₄×D₁₁₃	#41	1	2	yes	—
157	Dic₂₂₆	—	2	2	no	—
158	Dic₂₂₆	—	2	2	no	—
159	C₈×C₁₁₃	—	2	1	no	—
160	C₈×C₁₁₃	—	2	1	no	—
161	C₈×C₁₁₃	—	2	1	no	—
162	C₈×C₁₁₃	C₂×D₄	1	2	yes	—
163	#11744751	—	2	1	no	—
164	#11744751	—	2	1	no	—
165	#11744751	—	2	1	no	—
166	#11744751	C₂×D₄	1	2	yes	—
167	C₂²×C₁₁₃	—	2	1	no	—
168	C₂²×C₁₁₃	—	2	1	no	—
169	C₂²×C₁₁₃	—	2	1	no	—
170	C₂²×C₁₁₃	—	2	1	no	—
171	C₂²×C₁₁₃	—	2	1	no	—
172	C₂²×C₁₁₃	—	2	1	no	—
173	C₂²×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₁₁₃	—	2	1	no	—
175	C₂×D₁₁₃	—	2	1	no	—
176	C₂×D₁₁₃	—	2	1	no	—
177	C₂×D₁₁₃	—	2	1	no	—
178	C₂×D₁₁₃	—	2	1	no	—
179	C₂×D₁₁₃	—	2	1	no	—
180	C₂×D₁₁₃	—	2	1	no	—
181	C₂×D₁₁₃	—	2	1	no	—
182	C₂×D₁₁₃	C₄×D₄	1	2	yes	—
183	C₄×C₁₁₃	—	2	1	no	—
184	C₄×C₁₁₃	—	2	1	no	—
185	C₄×C₁₁₃	—	2	1	no	—
186	C₄×C₁₁₃	—	2	1	no	—
187	C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₄×C₁₁₃	C₂×#41	1	1	yes	characteristic
189	Dic₁₁₃	—	2	1	no	—
190	Dic₁₁₃	—	2	1	no	—
191	Dic₁₁₃	—	2	1	no	—
192	Dic₁₁₃	C₄×D₄	1	2	yes	—
193	Dic₁₁₃	#131	1	2	yes	complemented
194	C₂×C₁₁₃	—	4	1	no	—
195	C₂×C₁₁₃	—	4	1	no	—
196	C₂×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂×C₁₁₃	C₂×#131	1	1	yes	characteristic
198	C₂×C₁₁₃	#568	1	1	yes	characteristic
199	D₁₁₃	—	2	2	no	—
200	D₁₁₃	—	4	1	no	—
201	D₁₁₃	—	4	1	no	—
202	#2935	—	113	1	no	maximal, Sylow
203	C₁₁₃	#2935	1	1	yes	characteristic, complemented, Sylow
204	C₂×#131	—	113	1	no	—
205	C₂×#131	—	113	1	no	—
206	#532	—	113	1	no	—
207	#436	—	113	1	no	—
208	#436	—	113	1	no	—
209	#435	—	113	1	no	—
210	#435	—	113	1	no	—
211	#435	—	113	1	no	—
212	#435	D₁₁₃	1	1	yes	characteristic, complemented
213	C₈×D₄	—	113	1	no	—
214	C₈×D₄	—	113	1	no	—
215	C₂×C₄⋊C₈	—	113	1	no	—
216	#408	—	113	1	no	—
217	#408	—	113	1	no	—
218	C₄×M₁₆	—	113	1	no	—
219	C₂×#41	—	113	1	no	—
220	C₂×#41	—	113	1	no	—
221	#131	—	226	4	no	—
222	#131	—	226	4	no	—
223	C₂×M₁₆	—	113	1	no	—
224	C₂×M₁₆	—	113	1	no	—
225	C₂×M₁₆	—	113	1	no	—
226	C₂×M₁₆	—	113	1	no	—
227	C₂×M₁₆	—	113	1	no	—
228	C₂×M₁₆	C₂×D₁₁₃	1	1	yes	characteristic
229	C₂²×C₈	—	113	1	no	—
230	C₂²×C₈	—	113	1	no	—
231	C₂²×C₈	—	113	1	no	—
232	C₂²×C₈	—	113	1	no	—
233	C₂²×C₈	—	113	1	no	—
234	C₂²×C₈	C₂×D₁₁₃	1	1	yes	characteristic
235	C₄⋊Q₈	—	113	1	no	—
236	#127	—	113	1	no	—
237	#124	—	113	1	no	—
238	#124	—	113	1	no	—
239	#121	—	113	1	no	—
240	#121	—	113	1	no	—
241	#121	—	113	1	no	—
242	#121	—	113	1	no	—
243	C₄×D₄	—	113	1	no	—
244	C₄×D₄	—	113	1	no	—
245	C₄×D₄	—	113	1	no	—
246	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic
247	C₂×C₄²	—	113	1	no	—
248	C₄⋊C₈	—	113	1	no	—
249	C₄⋊C₈	—	113	1	no	—
250	C₄⋊C₈	—	113	1	no	—
251	C₄⋊C₈	C₂×D₁₁₃	1	1	yes	characteristic
252	C₂²⋊C₈	—	113	1	no	—
253	C₂²⋊C₈	—	113	1	no	—
254	C₂²⋊C₈	—	113	1	no	—
255	C₂²⋊C₈	—	113	1	no	—
256	C₂²⋊C₈	—	113	1	no	—
257	C₂²⋊C₈	—	113	1	no	—
258	C₂²⋊C₈	C₂×D₁₁₃	1	1	yes	characteristic
259	C₂²⋊C₈	C₂×D₁₁₃	1	1	yes	characteristic
260	#97	—	113	1	no	—
261	#97	C₂×D₁₁₃	1	1	yes	characteristic
262	C₄×C₈	—	113	1	no	—
263	C₄×C₈	—	113	1	no	—
264	#41	—	226	2	no	—
265	#41	—	226	2	no	—
266	#41	—	226	2	no	—
267	#41	—	226	2	no	—
268	C₂×Q₈	—	113	1	no	—
269	C₂×Q₈	—	113	1	no	—
270	C₂×D₄	—	113	1	no	—
271	C₂×D₄	—	113	1	no	—
272	C₂×D₄	—	113	1	no	—
273	C₂×D₄	—	113	1	no	—
274	C₂×D₄	—	113	1	no	—
275	C₂×D₄	—	113	1	no	—
276	C₂×D₄	—	113	1	no	—
277	C₂×D₄	—	113	1	no	—
278	C₂×D₄	—	113	1	no	—
279	C₂×D₄	C₄×D₁₁₃	1	1	yes	characteristic
280	C₂²×C₄	—	113	1	no	—
281	C₂²×C₄	—	113	1	no	—
282	C₂²×C₄	—	113	1	no	—
283	C₂²×C₄	—	113	1	no	—
284	C₂²×C₄	—	113	1	no	—
285	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
287	M₁₆	—	2	2	no	—
288	M₁₆	—	113	4	no	—
289	M₁₆	—	226	2	no	—
290	M₁₆	—	226	2	no	—
291	M₁₆	—	226	2	no	—
292	M₁₆	—	226	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	113	1	no	—
295	C₂×C₈	—	113	1	no	—
296	C₂×C₈	—	113	1	no	—
297	C₂×C₈	—	113	1	no	—
298	C₂×C₈	—	226	2	no	—
299	C₂×C₈	—	226	2	no	—
300	C₂×C₈	—	226	2	no	—
301	C₂×C₈	—	226	2	no	—
302	C₂×C₈	—	226	2	no	—
303	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
306	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
307	C₄⋊C₄	—	113	1	no	—
308	C₄⋊C₄	—	113	1	no	—
309	C₄⋊C₄	—	113	1	no	—
310	C₄⋊C₄	C₄×D₁₁₃	1	1	yes	characteristic
311	C₂²⋊C₄	—	113	1	no	—
312	C₂²⋊C₄	—	113	1	no	—
313	C₂²⋊C₄	—	113	1	no	—
314	C₂²⋊C₄	—	113	1	no	—
315	C₂²⋊C₄	—	113	1	no	—
316	C₂²⋊C₄	—	113	1	no	—
317	C₂²⋊C₄	C₄×D₁₁₃	1	1	yes	characteristic
318	C₂²⋊C₄	C₄×D₁₁₃	1	1	yes	characteristic
319	C₄²	—	113	1	no	—
320	C₄²	—	113	1	no	—
321	C₄²	—	113	1	no	—
322	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
323	C₂³	—	113	1	no	—
324	C₂³	—	113	1	no	—
325	C₂³	—	113	1	no	—
326	C₂³	C₂×C₄×D₁₁₃	1	1	yes	characteristic
327	C₂³	C₂×C₄×D₁₁₃	1	1	yes	characteristic
328	Q₈	—	226	2	no	—
329	Q₈	—	226	2	no	—
330	D₄	—	4	1	no	—
331	D₄	—	452	1	no	—
332	D₄	—	226	2	no	—
333	D₄	—	226	2	no	—
334	D₄	—	226	2	no	—
335	D₄	—	226	2	no	—
336	D₄	—	226	2	no	—
337	D₄	—	226	2	no	—
338	D₄	—	226	2	no	—
339	D₄	—	226	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	113	1	no	—
345	C₂×C₄	—	113	1	no	—
346	C₂×C₄	—	113	2	no	—
347	C₂×C₄	—	113	2	no	—
348	C₂×C₄	—	113	1	no	—
349	C₂×C₄	—	113	1	no	—
350	C₂×C₄	—	113	1	no	—
351	C₂×C₄	—	452	1	no	—
352	C₂×C₄	—	226	2	no	—
353	C₂×C₄	—	226	1	no	—
354	C₂×C₄	—	226	1	no	—
355	C₂×C₄	—	226	1	no	—
356	C₂×C₄	—	226	1	no	—
357	C₂×C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	113	2	no	—
366	C₈	—	226	1	no	—
367	C₈	—	226	1	no	—
368	C₈	—	226	1	no	—
369	C₈	D₄×D₁₁₃	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	113	2	no	—
377	C₂²	—	226	1	no	—
378	C₂²	—	226	1	no	—
379	C₂²	—	226	1	no	—
380	C₂²	—	226	1	no	—
381	C₂²	—	226	1	no	—
382	C₂²	—	226	1	no	—
383	C₂²	—	226	1	no	—
384	C₂²	—	226	1	no	—
385	C₂²	C₂²×C₄×D₁₁₃	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	113	2	no	—
391	C₄	—	113	2	no	—
392	C₄	—	226	1	no	—
393	C₄	—	226	1	no	—
394	C₄	—	226	1	no	—
395	C₄	C₂×D₄×D₁₁₃	1	1	yes	characteristic
396	C₄	#41×D₁₁₃	1	1	yes	characteristic
397	C₂	—	4	1	no	—
398	C₂	—	4	1	no	—
399	C₂	—	452	1	no	—
400	C₂	—	452	1	no	—
401	C₂	—	226	2	no	—
402	C₂	C₄×D₄×D₁₁₃	1	1	yes	characteristic
403	C₂	#131×D₁₁₃	1	1	yes	characteristic
404	C₂	#20299364	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁₃
commutator, socle	C₂²×C₁₁₃	C₂³×C₄
Fitting	#435×C₁₁₃	C₂
prime radical	#20299145	C₂
cosocle	C₂×C₄×C₁₁₃	C₂⁴
hypercenter	#435	D₁₁₃
hypocenter	C₁₁₃	#2935
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#16813630	C₂	semidirect
2. C₂×#16813628	C₂	semidirect
4. #20298674	C₂	semidirect
5. #20298673	C₂	semidirect
6. #20298671	C₂	semidirect
7. #20298670	C₂	semidirect
8. #20298668	C₂	semidirect
9. C₈×C₂²⋊D₁₁₃	C₂	semidirect
10. #20298661	C₂	semidirect
11. C₄⋊C₈×D₁₁₃	C₂	semidirect
12. #20298563	C₂	semidirect
13. #20298563	C₂	semidirect
14. #20298550	C₂	semidirect
15. #435×C₁₁₃	C₂	semidirect
85. #14268630	D₄	semidirect
193. Dic₁₁₃	#131	semidirect
203. C₁₁₃	#2935	semidirect
212. #435	D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813630	2
C₂×#16813628	2
#20299145	2
#20298674	2
#20298673	2
#20298671	2
#20298670	2
#20298668	2
C₈×C₂²⋊D₁₁₃	2
#20298661	2
C₄⋊C₈×D₁₁₃	2
#20298563	2
#20298550	2
#435×C₁₁₃	2
#2935	113