Subgroups — #28403983

Order 14464.

1160 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299224	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299195	C₂	1	2	yes	maximal, complemented
3	#20299190	C₂	1	4	yes	maximal, complemented
4	#20299186	C₂	1	2	yes	maximal, complemented
5	#20299181	C₂	1	4	yes	maximal, complemented
6	#20299160	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299157	C₂	1	2	yes	maximal, complemented
8	#20299132	C₂	1	2	yes	maximal, complemented
9	#20299128	C₂	1	4	yes	maximal, complemented
10	#20299109	C₂	1	2	yes	maximal, complemented
11	#20299107	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×D₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14268647	C₂²	1	2	yes	complemented
15	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
16	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
17	#16813617	C₂²	1	4	yes	complemented
18	#16813616	C₂²	1	4	yes	complemented
19	#16813615	C₂²	1	4	yes	complemented
20	#16813614	C₂²	1	2	yes	complemented
21	#16813612	C₂²	1	4	yes	complemented
22	#16813610	C₂²	1	2	yes	complemented
23	#16813608	C₂²	1	4	yes	complemented
24	#16813607	C₂²	1	4	yes	complemented
25	#16813606	C₂²	1	4	yes	complemented
26	#16813605	C₂²	1	4	yes	complemented
27	#16813605	C₂²	1	4	yes	complemented
28	#16813604	C₂²	1	4	yes	complemented
29	#16813603	C₂²	1	4	yes	complemented
30	#16813601	C₂²	1	2	yes	complemented
31	#16813601	C₂²	1	2	yes	complemented
32	#16813601	C₂²	1	2	yes	complemented
33	#16813600	C₂²	1	4	yes	complemented
34	#16813599	C₂²	1	4	yes	complemented
35	#16813599	C₂²	1	4	yes	complemented
36	#16813596	C₂²	1	2	yes	—
37	#16813596	C₂²	1	2	yes	—
38	#16813596	C₂²	1	2	yes	complemented
39	#16813595	C₂²	1	4	yes	complemented
40	#16813594	C₂²	1	4	yes	—
41	#16813594	C₂²	1	4	yes	—
42	#16813592	C₂²	1	4	yes	complemented
43	#16813591	C₂²	1	4	yes	complemented
44	#16813590	C₂²	1	4	yes	complemented
45	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
46	C₄×D₄₅₂	C₂²	1	2	yes	complemented
47	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
48	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
49	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
51	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
52	#16813581	C₂²	1	2	yes	complemented
53	#16813579	C₂²	1	4	yes	complemented
54	C₂×#14268626	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
56	C₂×#14268624	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
58	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
61	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
62	C₄×D₄×C₁₁₃	C₂²	1	4	yes	complemented
63	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₁₁₃	C₂³	1	2	yes	—
68	#14268647	—	4	4	no	—
69	C₂×Dic₂₂₆	C₂³	1	2	yes	—
70	C₂×Dic₂₂₆	C₂³	1	2	yes	—
71	C₂×D₄₅₂	C₂³	1	2	yes	—
72	C₂×D₄₅₂	C₂³	1	2	yes	—
73	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
74	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
78	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
79	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
80	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
81	C₂×C₄×D₁₁₃	—	4	4	no	—
82	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
83	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
84	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
85	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
86	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
87	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
88	#14268626	C₂³	1	4	yes	—
89	#14268626	C₂³	1	4	yes	—
90	#14268626	C₂³	1	4	yes	—
91	#14268626	C₂³	1	4	yes	—
92	#14268626	C₂³	1	4	yes	—
93	#14268626	C₂³	1	4	yes	—
94	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
95	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
96	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
97	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
98	#14268624	C₂³	1	4	yes	—
99	#14268624	C₂³	1	4	yes	—
100	#14268624	C₂³	1	4	yes	—
101	#14268624	C₂³	1	4	yes	—
102	#14268624	C₂³	1	4	yes	—
103	#14268624	C₂³	1	4	yes	—
104	C₄×Dic₁₁₃	C₂³	1	4	yes	—
105	C₄×Dic₁₁₃	C₂³	1	4	yes	—
106	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
107	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₁₃	—	2	4	no	—
109	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
110	C₂²×C₄×C₁₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
113	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
114	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
117	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
121	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
122	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
124	C₄²×C₁₁₃	C₂³	1	2	yes	—
125	C₄²×C₁₁₃	C₂³	1	2	yes	—
126	C₂³×C₁₁₃	—	2	2	no	—
127	C₂³×C₁₁₃	—	4	1	no	—
128	C₂³×C₁₁₃	—	4	1	no	—
129	C₂³×C₁₁₃	—	4	1	no	—
130	C₂³×C₁₁₃	—	4	1	no	—
131	C₂³×C₁₁₃	#41	1	4	yes	complemented
132	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
133	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
134	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²×D₁₁₃	—	2	4	no	—
136	C₂²×D₁₁₃	—	4	2	no	—
137	C₂²×D₁₁₃	—	4	2	no	—
138	C₂²×D₁₁₃	C₂⁴	1	4	yes	—
139	D₄×C₁₁₃	—	2	8	no	—
140	C₂×C₄×C₁₁₃	—	2	2	no	—
141	C₂×C₄×C₁₁₃	—	2	2	no	—
142	C₂×C₄×C₁₁₃	—	2	4	no	—
143	C₂×C₄×C₁₁₃	—	2	4	no	—
144	C₂×C₄×C₁₁₃	—	4	1	no	—
145	C₂×C₄×C₁₁₃	—	4	2	no	—
146	C₂×C₄×C₁₁₃	—	4	1	no	—
147	C₂×C₄×C₁₁₃	—	4	2	no	—
148	C₂×C₄×C₁₁₃	—	4	1	no	—
149	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
153	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
154	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
155	C₂²⋊D₁₁₃	—	2	8	no	—
156	C₂²⋊D₁₁₃	—	2	8	no	—
157	C₂²⋊D₁₁₃	—	4	4	no	—
158	C₂²⋊D₁₁₃	—	4	4	no	—
159	C₂×Dic₁₁₃	—	2	4	no	—
160	C₂×Dic₁₁₃	—	4	2	no	—
161	C₂×Dic₁₁₃	—	4	2	no	—
162	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
163	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
164	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
165	D₄₅₂	—	4	2	no	—
166	D₄₅₂	—	4	2	no	—
167	C₄×D₁₁₃	—	2	8	no	—
168	C₄×D₁₁₃	—	4	4	no	—
169	Dic₂₂₆	—	4	2	no	—
170	Dic₂₂₆	—	4	2	no	—
171	C₂²×C₁₁₃	—	2	2	no	—
172	C₂²×C₁₁₃	—	2	1	no	—
173	C₂²×C₁₁₃	—	2	2	no	—
174	C₂²×C₁₁₃	—	2	1	no	—
175	C₂²×C₁₁₃	—	2	2	no	—
176	C₂²×C₁₁₃	—	2	2	no	—
177	C₂²×C₁₁₃	—	2	2	no	—
178	C₂²×C₁₁₃	—	4	4	no	—
179	C₂²×C₁₁₃	—	4	4	no	—
180	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
181	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
182	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
183	C₂×D₁₁₃	—	2	4	no	—
184	C₂×D₁₁₃	—	2	4	no	—
185	C₂×D₁₁₃	—	2	4	no	—
186	C₂×D₁₁₃	—	4	8	no	—
187	C₄×C₁₁₃	—	2	2	no	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	2	1	no	—
191	C₄×C₁₁₃	—	2	2	no	—
192	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
193	Dic₁₁₃	—	2	4	no	—
194	Dic₁₁₃	—	2	4	no	—
195	Dic₁₁₃	—	2	4	no	—
196	C₂×C₁₁₃	—	2	4	no	—
197	C₂×C₁₁₃	—	2	2	no	—
198	C₂×C₁₁₃	—	4	2	no	—
199	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
200	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₁₁₃	#585	1	1	yes	characteristic
202	D₁₁₃	—	4	4	no	—
203	#3459	—	113	1	no	maximal, Sylow
204	C₁₁₃	#3459	1	1	yes	characteristic, complemented, Sylow
205	#543	—	113	1	no	—
206	#539	—	113	4	no	—
207	#539	—	113	2	no	—
208	#538	—	113	4	no	—
209	#538	—	113	2	no	—
210	#534	—	113	2	no	—
211	#534	—	113	1	no	—
212	#529	—	113	4	no	—
213	#529	—	113	2	no	—
214	#525	—	113	2	no	—
215	#525	—	113	4	no	—
216	C₂×C₄×D₄	—	113	2	no	—
217	C₂×C₄×D₄	D₁₁₃	1	1	yes	characteristic, complemented
218	C₂×#41	—	113	2	no	—
219	C₂²×D₄	—	113	2	no	—
220	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
221	C₂³×C₄	—	113	2	no	—
222	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
224	#126	—	113	4	no	—
225	#126	—	113	4	no	—
226	#126	—	113	4	no	—
227	#125	—	113	4	no	—
228	#125	—	113	2	no	—
229	#124	—	113	4	no	—
230	#124	—	113	2	no	—
231	#123	—	113	4	no	—
232	#123	—	113	4	no	—
233	#123	—	113	4	no	—
234	#123	—	113	4	no	—
235	#123	—	113	4	no	—
236	#123	—	113	4	no	—
237	C₂²⋊Q₈	—	113	2	no	—
238	C₂²⋊Q₈	—	113	2	no	—
239	C₂²⋊Q₈	—	113	2	no	—
240	C₂²⋊Q₈	—	113	4	no	—
241	C₂²⋊Q₈	—	113	4	no	—
242	C₂²⋊Q₈	—	113	4	no	—
243	#121	—	113	4	no	—
244	#121	—	113	4	no	—
245	#121	—	113	2	no	—
246	#121	—	113	2	no	—
247	#121	—	113	2	no	—
248	#121	—	113	4	no	—
249	#120	—	113	4	no	—
250	#120	—	113	4	no	—
251	#120	—	113	4	no	—
252	C₄×Q₈	—	113	2	no	—
253	C₄×D₄	—	113	4	no	—
254	C₄×D₄	—	113	4	no	—
255	C₄×D₄	—	113	4	no	—
256	C₄×D₄	—	113	4	no	—
257	C₄×D₄	—	113	4	no	—
258	C₄×D₄	—	113	2	no	—
259	C₄×D₄	C₂×D₁₁₃	1	4	yes	complemented
260	C₄×D₄	C₂×D₁₁₃	1	4	yes	complemented
261	#117	—	113	2	no	—
262	#117	—	113	4	no	—
263	C₂×C₄⋊C₄	—	113	2	no	—
264	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
265	C₂×C₂²⋊C₄	—	113	2	no	—
266	C₂×C₂²⋊C₄	—	113	2	no	—
267	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
269	C₂×C₄²	—	113	2	no	—
270	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic, complemented
271	C₂⁴	—	113	2	no	—
272	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
273	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
274	#41	—	452	4	no	—
275	C₂×Q₈	—	113	2	no	—
276	C₂×Q₈	—	113	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	113	4	no	—
279	C₂×D₄	—	113	4	no	—
280	C₂×D₄	—	113	4	no	—
281	C₂×D₄	—	113	4	no	—
282	C₂×D₄	—	113	2	no	—
283	C₂×D₄	—	113	2	no	—
284	C₂×D₄	—	226	8	no	—
285	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	113	2	no	—
289	C₂²×C₄	—	113	2	no	—
290	C₂²×C₄	—	113	2	no	—
291	C₂²×C₄	—	113	4	no	—
292	C₂²×C₄	—	113	4	no	—
293	C₂²×C₄	—	452	4	no	—
294	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
295	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
296	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
298	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
299	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
300	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
303	C₄⋊C₄	—	113	4	no	—
304	C₄⋊C₄	—	113	4	no	—
305	C₄⋊C₄	—	113	4	no	—
306	C₄⋊C₄	—	113	2	no	—
307	C₄⋊C₄	—	113	4	no	—
308	C₄⋊C₄	—	113	2	no	—
309	C₄⋊C₄	—	113	4	no	—
310	C₄⋊C₄	—	113	2	no	—
311	C₄⋊C₄	—	113	4	no	—
312	C₄⋊C₄	—	113	2	no	—
313	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
314	C₂²⋊C₄	—	113	4	no	—
315	C₂²⋊C₄	—	113	4	no	—
316	C₂²⋊C₄	—	113	4	no	—
317	C₂²⋊C₄	—	113	4	no	—
318	C₂²⋊C₄	—	113	4	no	—
319	C₂²⋊C₄	—	113	4	no	—
320	C₂²⋊C₄	—	113	4	no	—
321	C₂²⋊C₄	—	113	4	no	—
322	C₂²⋊C₄	—	113	4	no	—
323	C₂²⋊C₄	—	113	4	no	—
324	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
325	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
326	C₄²	—	113	4	no	—
327	C₄²	—	113	4	no	—
328	C₄²	C₂²×D₁₁₃	1	2	yes	—
329	C₄²	C₂²×D₁₁₃	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	—	113	4	no	—
336	C₂³	—	452	2	no	—
337	C₂³	—	452	2	no	—
338	C₂³	—	226	4	no	—
339	C₂³	#14268647	1	4	yes	complemented
340	C₂³	C₂³×D₁₁₃	1	2	yes	—
341	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
342	C₂³	C₂³×D₁₁₃	1	2	yes	—
343	Q₈	—	452	2	no	—
344	Q₈	—	452	2	no	—
345	D₄	—	2	8	no	—
346	D₄	—	452	2	no	—
347	D₄	—	452	2	no	—
348	D₄	—	452	4	no	—
349	D₄	—	452	4	no	—
350	D₄	—	226	8	no	—
351	D₄	—	226	8	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	113	4	no	—
362	C₂×C₄	—	113	4	no	—
363	C₂×C₄	—	113	4	no	—
364	C₂×C₄	—	452	4	no	—
365	C₂×C₄	—	452	2	no	—
366	C₂×C₄	—	452	2	no	—
367	C₂×C₄	—	226	4	no	—
368	C₂×C₄	—	226	8	no	—
369	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
370	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
371	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
373	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
374	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	452	8	no	—
385	C₂²	—	226	4	no	—
386	C₂²	—	226	4	no	—
387	C₂²	—	226	4	no	—
388	C₂²	C₂×#14268647	1	2	yes	—
389	C₂²	C₂×#14268647	1	4	yes	—
390	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	226	4	no	—
397	C₄	—	226	4	no	—
398	C₄	—	226	4	no	—
399	C₄	#16813667	1	2	yes	—
400	C₂	—	2	2	no	—
401	C₂	—	2	4	no	—
402	C₂	—	4	2	no	—
403	C₂	—	452	4	no	—
404	C₂	C₂²×#14268647	1	1	yes	characteristic
405	C₂	C₂×#16813667	1	1	yes	characteristic
406	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	C₂×C₄×D₄×C₁₁₃	C₂
hypercenter	C₂×C₄×D₄	D₁₁₃
hypocenter	C₁₁₃	#3459
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #20299224	C₂	semidirect
2. #20299195	C₂	semidirect
3. #20299190	C₂	semidirect
4. #20299186	C₂	semidirect
5. #20299181	C₂	semidirect
6. #20299160	C₂	semidirect
7. #20299157	C₂	semidirect
8. #20299132	C₂	semidirect
9. #20299128	C₂	semidirect
10. #20299109	C₂	semidirect
11. #20299107	C₂	semidirect
12. C₂×C₄×C₂²⋊D₁₁₃	C₂	semidirect
13. C₂×C₄×D₄×C₁₁₃	C₂	semidirect
14. C₂×#14268647	C₂²	semidirect
16. C₂²×C₄×D₁₁₃	C₂²	semidirect
17. #16813617	C₂²	semidirect
18. #16813616	C₂²	semidirect
19. #16813615	C₂²	semidirect
20. #16813614	C₂²	semidirect
21. #16813612	C₂²	semidirect
22. #16813610	C₂²	semidirect
23. #16813608	C₂²	semidirect
24. #16813607	C₂²	semidirect
25. #16813606	C₂²	semidirect
26. #16813605	C₂²	semidirect
27. #16813605	C₂²	semidirect
28. #16813604	C₂²	semidirect
29. #16813603	C₂²	semidirect
30. #16813601	C₂²	semidirect
31. #16813601	C₂²	semidirect
32. #16813601	C₂²	semidirect
33. #16813600	C₂²	semidirect
34. #16813599	C₂²	semidirect
35. #16813599	C₂²	semidirect
38. #16813596	C₂²	semidirect
39. #16813595	C₂²	semidirect
42. #16813592	C₂²	semidirect
43. #16813591	C₂²	semidirect
44. #16813590	C₂²	semidirect
45. C₄×Dic₂₂₆	C₂²	semidirect
46. C₄×D₄₅₂	C₂²	semidirect
47. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
48. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
49. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
50. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
51. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
52. #16813581	C₂²	semidirect
53. #16813579	C₂²	semidirect
54. C₂×#14268626	C₂²	semidirect
56. C₂×#14268624	C₂²	semidirect
57. C₂×C₄×Dic₁₁₃	C₂²	semidirect
60. C₂³×C₄×C₁₁₃	C₂²	semidirect
61. C₄×D₄×C₁₁₃	C₂²	semidirect
62. C₄×D₄×C₁₁₃	C₂²	semidirect
63. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
66. C₂×C₄²×C₁₁₃	C₂²	semidirect
131. C₂³×C₁₁₃	#41	semidirect
204. C₁₁₃	#3459	semidirect
217. C₂×C₄×D₄	D₁₁₃	semidirect
223. C₂³×C₄	C₂×D₁₁₃	semidirect
259. C₄×D₄	C₂×D₁₁₃	semidirect
260. C₄×D₄	C₂×D₁₁₃	semidirect
264. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
268. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
270. C₂×C₄²	C₂×D₁₁₃	semidirect
339. C₂³	#14268647	semidirect

Maximal subgroups

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

subgroup	index
#20299224	2
#20299195	2
#20299190	2
#20299186	2
#20299181	2
#20299160	2
#20299157	2
#20299132	2
#20299128	2
#20299109	2
#20299107	2
C₂×C₄×C₂²⋊D₁₁₃	2
C₂×C₄×D₄×C₁₁₃	2
#3459	113