Subgroups — #28404361

Order 14464.

1540 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813669	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16813668	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299257	C₂	1	4	yes	maximal, complemented
4	#20299244	C₂	1	4	yes	maximal, complemented
5	#20299237	C₂	1	8	yes	maximal, complemented
6	#20299173	C₂	1	2	yes	maximal, complemented
7	#20299169	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299162	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299161	C₂	1	2	yes	maximal, complemented
10	#20299147	C₂	1	2	yes	maximal, complemented
11	C₂×#16813610	C₂	1	1	yes	maximal, characteristic, complemented
12	#124×D₁₁₃	C₂	1	2	yes	maximal, complemented
13	C₄×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
14	#532×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#16813669	—	2	8	no	—
16	#16813668	—	2	8	no	—
17	C₂×#14268648	C₂²	1	2	yes	—
18	C₂×#14268647	C₂²	1	2	yes	—
19	C₂×#14268647	C₂²	1	1	yes	characteristic
20	C₂×#14268647	C₂²	1	2	yes	complemented
21	C₂×#14268646	C₂²	1	2	yes	complemented
22	C₂×#14268646	C₂²	1	4	yes	complemented
23	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×Dic₂₂₆	C₂²	1	2	yes	complemented
25	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	complemented
26	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
27	C₂²×D₄₅₂	C₂²	1	2	yes	—
28	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
29	C₂×D₄×D₁₁₃	C₂²	1	4	yes	—
30	#16813620	C₂²	1	2	yes	complemented
31	#16813618	C₂²	1	2	yes	complemented
32	#16813611	C₂²	1	2	yes	complemented
33	#16813610	C₂²	1	2	yes	complemented
34	#16813610	C₂²	1	2	yes	complemented
35	#16813610	C₂²	1	4	yes	complemented
36	#16813609	C₂²	1	2	yes	complemented
37	#16813608	C₂²	1	8	yes	complemented
38	#16813607	C₂²	1	8	yes	complemented
39	#16813603	C₂²	1	4	yes	complemented
40	#16813601	C₂²	1	4	yes	complemented
41	#16813600	C₂²	1	8	yes	complemented
42	#16813596	C₂²	1	4	yes	complemented
43	#16813595	C₂²	1	8	yes	complemented
44	#16813594	C₂²	1	8	yes	complemented
45	#16813590	C₂²	1	8	yes	complemented
46	#16813590	C₂²	1	4	yes	complemented
47	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
48	C₄×D₄₅₂	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
50	#16813582	C₂²	1	8	yes	complemented
51	#16813581	C₂²	1	1	yes	characteristic, complemented
52	#16813579	C₂²	1	2	yes	complemented
53	C₂×#14268624	C₂²	1	4	yes	complemented
54	C₂²⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
55	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
56	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic
57	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
59	#127×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
60	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
61	#124×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
62	#121×C₁₁₃	C₂²	1	4	yes	complemented
63	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
64	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₂³×D₁₁₃	C₂³	1	4	yes	—
66	C₂³×D₁₁₃	C₂³	1	2	yes	—
67	#14268648	—	2	8	no	—
68	#14268647	—	2	8	no	—
69	#14268647	—	2	8	no	—
70	#14268647	D₄	1	8	yes	complemented
71	#14268646	—	2	16	no	—
72	#14268646	—	2	8	no	—
73	C₂×Dic₂₂₆	—	2	4	no	—
74	C₂×Dic₂₂₆	—	2	8	no	—
75	C₂×Dic₂₂₆	C₂³	1	4	yes	—
76	C₂×Dic₂₂₆	C₂³	1	2	yes	—
77	C₂×Dic₂₂₆	C₂³	1	2	yes	—
78	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
79	Q₈×D₁₁₃	—	2	8	no	—
80	C₂×D₄₅₂	—	2	4	no	—
81	C₂×D₄₅₂	—	2	8	no	—
82	C₂×D₄₅₂	C₂³	1	4	yes	—
83	C₂×D₄₅₂	C₂³	1	2	yes	—
84	C₂×D₄₅₂	C₂³	1	2	yes	—
85	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₁₃	C₂³	1	8	yes	—
89	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
90	D₄×D₁₁₃	—	2	16	no	—
91	D₄×D₁₁₃	—	2	8	no	—
92	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
93	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
94	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
95	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
96	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
97	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	#14268626	C₂³	1	4	yes	—
100	#14268626	C₂³	1	8	yes	—
101	C₂²⋊Dic₁₁₃	C₂³	1	8	yes	—
102	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
103	#14268624	C₂³	1	8	yes	—
104	#14268624	C₂³	1	8	yes	—
105	#14268624	C₂³	1	8	yes	—
106	#14268624	C₂³	1	4	yes	—
107	C₄×Dic₁₁₃	C₂³	1	2	yes	—
108	C₄×Dic₁₁₃	C₂³	1	4	yes	—
109	#41×C₁₁₃	—	2	4	no	—
110	#41×C₁₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
114	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
115	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
117	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
118	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
120	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
125	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
126	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
127	C₄²×C₁₁₃	C₂³	1	2	yes	—
128	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
129	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
130	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
131	C₂²×D₁₁₃	—	2	4	no	—
132	C₂²×D₁₁₃	—	2	8	no	—
133	C₂²×D₁₁₃	—	4	8	no	—
134	C₂²×D₁₁₃	—	4	4	no	—
135	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
136	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
137	Q₈×C₁₁₃	—	2	2	no	—
138	Q₈×C₁₁₃	—	2	2	no	—
139	D₄×C₁₁₃	—	2	4	no	—
140	D₄×C₁₁₃	—	2	4	no	—
141	D₄×C₁₁₃	—	2	2	no	—
142	D₄×C₁₁₃	—	2	2	no	—
143	D₄×C₁₁₃	—	4	4	no	—
144	C₂×C₄×C₁₁₃	—	2	4	no	—
145	C₂×C₄×C₁₁₃	—	2	4	no	—
146	C₂×C₄×C₁₁₃	—	4	2	no	—
147	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
148	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
149	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
153	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
154	C₂²⋊D₁₁₃	—	2	8	no	—
155	C₂²⋊D₁₁₃	—	2	8	no	—
156	C₂²⋊D₁₁₃	—	4	8	no	—
157	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	—
158	C₂×Dic₁₁₃	—	2	4	no	—
159	C₂×Dic₁₁₃	—	2	8	no	—
160	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
161	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
162	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
163	D₄₅₂	—	2	8	no	—
164	D₄₅₂	—	2	4	no	—
165	D₄₅₂	—	2	4	no	—
166	D₄₅₂	C₂×D₄	1	4	yes	—
167	C₄×D₁₁₃	—	2	8	no	—
168	C₄×D₁₁₃	—	2	8	no	—
169	C₄×D₁₁₃	—	4	4	no	—
170	C₄×D₁₁₃	C₂×D₄	1	8	yes	—
171	Dic₂₂₆	—	2	4	no	—
172	Dic₂₂₆	—	2	4	no	—
173	Dic₂₂₆	—	2	8	no	—
174	Dic₂₂₆	C₂×D₄	1	4	yes	—
175	C₂²×C₁₁₃	—	2	2	no	—
176	C₂²×C₁₁₃	—	2	2	no	—
177	C₂²×C₁₁₃	—	2	2	no	—
178	C₂²×C₁₁₃	—	2	4	no	—
179	C₂²×C₁₁₃	—	2	4	no	—
180	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
181	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
182	C₂×D₁₁₃	—	2	4	no	—
183	C₂×D₁₁₃	—	2	4	no	—
184	C₂×D₁₁₃	—	2	8	no	—
185	C₂×D₁₁₃	—	8	8	no	—
186	C₂×D₁₁₃	—	8	4	no	—
187	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	2	2	no	—
191	C₄×C₁₁₃	—	2	2	no	—
192	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
193	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
194	Dic₁₁₃	—	2	4	no	—
195	Dic₁₁₃	—	2	4	no	—
196	Dic₁₁₃	C₂²×D₄	1	4	yes	—
197	C₂×C₁₁₃	—	2	2	no	—
198	C₂×C₁₁₃	—	4	2	no	—
199	C₂×C₁₁₃	—	4	2	no	—
200	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
201	C₂×C₁₁₃	#585	1	2	yes	—
202	D₁₁₃	—	2	4	no	—
203	D₁₁₃	—	4	4	no	—
204	#3500	—	113	1	no	maximal, Sylow
205	C₁₁₃	#3500	1	1	yes	characteristic, complemented, Sylow
206	C₂×2₋¹⁺⁴	—	113	1	no	—
207	C₂×H(5,𝔽₂)	—	113	1	no	—
208	#548	—	113	4	no	—
209	#546	—	113	8	no	—
210	#546	—	113	4	no	—
211	#536	—	113	1	no	—
212	#536	—	113	2	no	—
213	#535	—	113	1	no	—
214	#535	—	113	2	no	—
215	#532	—	113	2	no	—
216	#532	D₁₁₃	1	1	yes	characteristic, complemented
217	C₂×#124	—	113	2	no	—
218	C₂×#124	—	113	1	no	—
219	C₄×#41	—	113	1	no	—
220	2₋¹⁺⁴	—	226	8	no	—
221	H(5,𝔽₂)	—	226	8	no	—
222	C₂×#41	—	113	2	no	—
223	C₂×#41	—	113	2	no	—
224	C₂×#41	—	113	4	no	—
225	C₂×#41	—	113	1	no	—
226	C₂×#41	—	113	2	no	—
227	C₂×#41	—	113	2	no	—
228	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic
229	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
230	C₂²×Q₈	—	113	2	no	—
231	C₂²×Q₈	—	113	1	no	—
232	C₂²×Q₈	—	113	2	no	—
233	C₂²×D₄	—	113	2	no	—
234	C₂²×D₄	—	113	4	no	—
235	C₂²×D₄	—	113	1	no	—
236	C₂²×D₄	—	113	2	no	—
237	C₄⋊Q₈	—	113	2	no	—
238	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
239	#127	—	113	2	no	—
240	#127	C₂×D₁₁₃	1	1	yes	characteristic, complemented
241	#124	—	113	2	no	—
242	#124	—	113	2	no	—
243	#124	—	113	8	no	—
244	#124	—	113	2	no	—
245	#124	—	113	2	no	—
246	#124	—	113	4	no	—
247	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
248	#124	C₂×D₁₁₃	1	1	yes	characteristic, complemented
249	#123	—	113	4	no	—
250	#123	—	113	8	no	—
251	C₂²⋊Q₈	—	113	4	no	—
252	C₂²⋊Q₈	—	113	8	no	—
253	#121	—	113	8	no	—
254	#121	—	113	4	no	—
255	#121	—	113	8	no	—
256	#121	C₂×D₁₁₃	1	4	yes	complemented
257	#120	—	113	8	no	—
258	#120	—	113	4	no	—
259	C₄×Q₈	—	113	2	no	—
260	C₄×D₄	—	113	4	no	—
261	C₄×D₄	—	113	8	no	—
262	C₄×D₄	—	113	2	no	—
263	C₄×D₄	C₂×D₁₁₃	1	4	yes	complemented
264	#117	—	113	1	no	—
265	#117	—	113	2	no	—
266	C₂×C₂²⋊C₄	—	113	4	no	—
267	C₂×C₂²⋊C₄	—	113	8	no	—
268	C₂×C₄²	—	113	2	no	—
269	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic, complemented
270	C₂⁴	—	113	4	no	—
271	C₂⁴	—	113	2	no	—
272	#41	—	2	4	no	—
273	#41	—	2	4	no	—
274	#41	—	113	8	no	—
275	#41	—	226	8	no	—
276	#41	—	226	8	no	—
277	#41	—	226	8	no	—
278	#41	—	226	8	no	—
279	#41	—	226	16	no	—
280	C₂×Q₈	—	113	1	no	—
281	C₂×Q₈	—	113	4	no	—
282	C₂×Q₈	—	113	2	no	—
283	C₂×Q₈	—	113	2	no	—
284	C₂×Q₈	—	226	8	no	—
285	C₂×Q₈	—	226	8	no	—
286	C₂×Q₈	—	226	4	no	—
287	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
288	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
289	C₂×D₄	—	113	2	no	—
290	C₂×D₄	—	113	8	no	—
291	C₂×D₄	—	113	4	no	—
292	C₂×D₄	—	113	4	no	—
293	C₂×D₄	—	113	1	no	—
294	C₂×D₄	—	113	4	no	—
295	C₂×D₄	—	113	2	no	—
296	C₂×D₄	—	113	2	no	—
297	C₂×D₄	—	226	8	no	—
298	C₂×D₄	—	226	8	no	—
299	C₂×D₄	—	226	16	no	—
300	C₂×D₄	—	226	4	no	—
301	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
302	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
303	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
304	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
306	C₂²×C₄	—	113	2	no	—
307	C₂²×C₄	—	113	2	no	—
308	C₂²×C₄	—	113	4	no	—
309	C₂²×C₄	—	113	4	no	—
310	C₂²×C₄	—	113	4	no	—
311	C₂²×C₄	—	113	4	no	—
312	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
313	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
314	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
315	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
316	C₄⋊C₄	—	113	4	no	—
317	C₄⋊C₄	—	113	2	no	—
318	C₄⋊C₄	—	113	8	no	—
319	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
320	C₂²⋊C₄	—	113	8	no	—
321	C₂²⋊C₄	—	113	2	no	—
322	C₂²⋊C₄	—	113	8	no	—
323	C₂²⋊C₄	—	113	8	no	—
324	C₂²⋊C₄	—	113	8	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
327	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
328	C₄²	—	113	2	no	—
329	C₄²	—	113	4	no	—
330	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
331	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
332	C₄²	C₂²×D₁₁₃	1	2	yes	—
333	C₂³	—	113	2	no	—
334	C₂³	—	113	4	no	—
335	C₂³	—	452	4	no	—
336	C₂³	—	452	8	no	—
337	C₂³	—	226	8	no	—
338	C₂³	—	226	4	no	—
339	C₂³	C₂³×D₁₁₃	1	2	yes	—
340	C₂³	C₂³×D₁₁₃	1	2	yes	—
341	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
342	Q₈	—	2	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	—	113	4	no	—
345	Q₈	—	226	8	no	—
346	Q₈	—	226	4	no	—
347	Q₈	—	226	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	4	4	no	—
353	D₄	—	113	8	no	—
354	D₄	—	113	4	no	—
355	D₄	—	452	8	no	—
356	D₄	—	226	8	no	—
357	D₄	—	226	8	no	—
358	D₄	—	226	8	no	—
359	D₄	—	226	4	no	—
360	D₄	—	226	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	113	2	no	—
365	C₂×C₄	—	113	8	no	—
366	C₂×C₄	—	113	4	no	—
367	C₂×C₄	—	113	4	no	—
368	C₂×C₄	—	452	4	no	—
369	C₂×C₄	—	226	8	no	—
370	C₂×C₄	—	226	8	no	—
371	C₂×C₄	—	226	8	no	—
372	C₂×C₄	—	226	4	no	—
373	C₂×C₄	D₄×D₁₁₃	1	4	yes	—
374	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
375	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
376	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
377	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
378	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	113	4	no	—
386	C₂²	—	904	4	no	—
387	C₂²	—	904	8	no	—
388	C₂²	—	226	4	no	—
389	C₂²	—	226	8	no	—
390	C₂²	—	226	4	no	—
391	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
392	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	113	4	no	—
398	C₄	—	226	4	no	—
399	C₄	—	226	4	no	—
400	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
401	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	—	4	2	no	—
405	C₂	—	452	4	no	—
406	C₂	—	226	4	no	—
407	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
408	C₂	#20299434	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#532×C₁₁₃	C₂
hypercenter	#532	D₁₁₃
hypocenter	C₁₁₃	#3500
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₂×#16813669	C₂	semidirect
2. C₂×#16813668	C₂	semidirect
3. #20299257	C₂	semidirect
4. #20299244	C₂	semidirect
5. #20299237	C₂	semidirect
6. #20299173	C₂	semidirect
7. #20299169	C₂	semidirect
8. #20299162	C₂	semidirect
9. #20299161	C₂	semidirect
10. #20299147	C₂	semidirect
11. C₂×#16813610	C₂	semidirect
12. #124×D₁₁₃	C₂	semidirect
13. C₄×#14268647	C₂	semidirect
14. #532×C₁₁₃	C₂	semidirect
20. C₂×#14268647	C₂²	semidirect
21. C₂×#14268646	C₂²	semidirect
22. C₂×#14268646	C₂²	semidirect
23. C₂²×Dic₂₂₆	C₂²	semidirect
24. C₂²×Dic₂₂₆	C₂²	semidirect
25. C₂×Q₈×D₁₁₃	C₂²	semidirect
30. #16813620	C₂²	semidirect
31. #16813618	C₂²	semidirect
32. #16813611	C₂²	semidirect
33. #16813610	C₂²	semidirect
34. #16813610	C₂²	semidirect
35. #16813610	C₂²	semidirect
36. #16813609	C₂²	semidirect
37. #16813608	C₂²	semidirect
38. #16813607	C₂²	semidirect
39. #16813603	C₂²	semidirect
40. #16813601	C₂²	semidirect
41. #16813600	C₂²	semidirect
42. #16813596	C₂²	semidirect
43. #16813595	C₂²	semidirect
44. #16813594	C₂²	semidirect
45. #16813590	C₂²	semidirect
46. #16813590	C₂²	semidirect
47. C₄×Dic₂₂₆	C₂²	semidirect
48. C₄×D₄₅₂	C₂²	semidirect
49. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
50. #16813582	C₂²	semidirect
51. #16813581	C₂²	semidirect
52. #16813579	C₂²	semidirect
53. C₂×#14268624	C₂²	semidirect
54. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
55. C₄²×D₁₁₃	C₂²	semidirect
57. C₂×#41×C₁₁₃	C₂²	semidirect
58. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
59. #127×C₁₁₃	C₂²	semidirect
60. #124×C₁₁₃	C₂²	semidirect
61. #124×C₁₁₃	C₂²	semidirect
62. #121×C₁₁₃	C₂²	semidirect
63. C₄×D₄×C₁₁₃	C₂²	semidirect
64. C₂×C₄²×C₁₁₃	C₂²	semidirect
70. #14268647	D₄	semidirect
205. C₁₁₃	#3500	semidirect
216. #532	D₁₁₃	semidirect
229. C₂×#41	C₂×D₁₁₃	semidirect
238. C₄⋊Q₈	C₂×D₁₁₃	semidirect
240. #127	C₂×D₁₁₃	semidirect
247. #124	C₂×D₁₁₃	semidirect
248. #124	C₂×D₁₁₃	semidirect
256. #121	C₂×D₁₁₃	semidirect
263. C₄×D₄	C₂×D₁₁₃	semidirect
269. C₂×C₄²	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813669	2
C₂×#16813668	2
#20299257	2
#20299244	2
#20299237	2
#20299173	2
#20299169	2
#20299162	2
#20299161	2
#20299147	2
C₂×#16813610	2
#124×D₁₁₃	2
C₄×#14268647	2
#532×C₁₁₃	2
#3500	113