Subgroups — #547×D₁₁₃ #28404027

Order 14464.

1632 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₁₃	C₂	1	2	yes	maximal, complemented
2	#20299253	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299252	C₂	1	1	yes	maximal, characteristic, complemented
4	#20299251	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299250	C₂	1	2	yes	maximal, complemented
6	#20299249	C₂	1	2	yes	maximal, complemented
7	#20299248	C₂	1	2	yes	maximal, complemented
8	#20299247	C₂	1	2	yes	maximal, complemented
9	#20299246	C₂	1	4	yes	maximal, complemented
10	C₄⋊Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#123×D₁₁₃	C₂	1	4	yes	maximal, complemented
12	C₂²⋊Q₈×D₁₁₃	C₂	1	2	yes	maximal, complemented
13	#121×D₁₁₃	C₂	1	2	yes	maximal, complemented
14	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₁₁₃	C₂	1	2	yes	maximal, complemented
17	#547×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268648	C₂²	1	2	yes	complemented
19	C₂×#14268647	C₂²	1	4	yes	complemented
20	C₂×#14268647	C₂²	1	2	yes	complemented
21	C₂×#14268646	C₂²	1	4	yes	complemented
22	C₂×#14268646	C₂²	1	2	yes	complemented
23	#41×D₁₁₃	—	2	16	no	—
24	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
25	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₁₁₃	C₂²	1	4	yes	—
27	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
29	C₂²×C₄×D₁₁₃	C₂²	1	4	yes	—
30	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
31	#16813622	C₂²	1	1	yes	characteristic, complemented
32	#16813621	C₂²	1	2	yes	complemented
33	#16813621	C₂²	1	2	yes	complemented
34	#16813620	C₂²	1	2	yes	complemented
35	#16813607	C₂²	1	4	yes	complemented
36	#16813607	C₂²	1	4	yes	complemented
37	#16813606	C₂²	1	4	yes	complemented
38	#16813605	C₂²	1	4	yes	complemented
39	#16813604	C₂²	1	4	yes	complemented
40	#16813604	C₂²	1	4	yes	complemented
41	#16813603	C₂²	1	4	yes	complemented
42	#16813602	C₂²	1	2	yes	complemented
43	#16813601	C₂²	1	2	yes	complemented
44	#16813600	C₂²	1	4	yes	complemented
45	#16813599	C₂²	1	4	yes	complemented
46	#16813598	C₂²	1	2	yes	complemented
47	#16813597	C₂²	1	2	yes	complemented
48	#16813596	C₂²	1	2	yes	complemented
49	#16813595	C₂²	1	4	yes	complemented
50	#16813594	C₂²	1	4	yes	complemented
51	#16813593	C₂²	1	2	yes	complemented
52	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₄₅₂	C₂²	1	1	yes	characteristic, complemented
54	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
55	D₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
56	#16813584	C₂²	1	1	yes	characteristic, complemented
57	#16813584	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
60	#16813582	C₂²	1	2	yes	complemented
61	#16813582	C₂²	1	2	yes	complemented
62	C₂×C₄⋊Dic₁₁₃	C₂²	1	2	yes	complemented
63	C₂×#14268626	C₂²	1	4	yes	complemented
64	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
65	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
66	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	—
67	C₄⋊C₄×D₁₁₃	C₂²	1	1	yes	characteristic
68	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
70	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
72	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	—
74	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
75	C₄²×D₁₁₃	C₂²	1	1	yes	characteristic
76	C₂×#41×C₁₁₃	C₂²	1	2	yes	complemented
77	C₄⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
78	#123×C₁₁₃	C₂²	1	4	yes	complemented
79	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
80	#121×C₁₁₃	C₂²	1	2	yes	complemented
81	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
84	C₂³×D₁₁₃	C₂³	1	2	yes	—
85	C₂³×D₁₁₃	C₂³	1	2	yes	—
86	#14268648	—	2	8	no	—
87	#14268647	—	2	16	no	—
88	#14268647	—	2	8	no	—
89	#14268646	—	2	8	no	—
90	#14268646	—	2	16	no	—
91	C₂×Dic₂₂₆	C₂³	1	4	yes	—
92	C₂×Dic₂₂₆	C₂³	1	2	yes	—
93	Q₈×D₁₁₃	—	2	8	no	—
94	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
95	C₂×D₄₅₂	C₂³	1	4	yes	—
96	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
98	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
101	D₄×D₁₁₃	—	2	16	no	—
102	D₄×D₁₁₃	—	2	4	no	—
103	D₄×D₁₁₃	D₄	1	8	yes	complemented
104	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
105	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
106	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₁₃	—	2	16	no	—
108	C₂×C₄×D₁₁₃	—	2	8	no	—
109	C₂×C₄×D₁₁₃	—	2	8	no	—
110	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
113	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
114	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
115	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
116	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
117	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
118	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
119	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
120	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
123	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
124	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
125	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
126	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
127	#14268626	C₂³	1	2	yes	—
128	#14268626	C₂³	1	4	yes	—
129	#14268626	C₂³	1	4	yes	—
130	#14268626	C₂³	1	4	yes	—
131	#14268626	C₂³	1	2	yes	—
132	#14268626	C₂³	1	4	yes	—
133	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
134	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
135	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
136	#14268624	C₂³	1	2	yes	—
137	#14268624	C₂³	1	2	yes	—
138	#14268624	C₂³	1	2	yes	—
139	#14268624	C₂³	1	2	yes	—
140	#14268624	C₂³	1	4	yes	—
141	#14268624	C₂³	1	4	yes	—
142	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
143	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
144	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
145	#41×C₁₁₃	—	2	8	no	—
146	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
147	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
149	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
151	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
153	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
155	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
156	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
161	C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
162	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
163	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
164	C₂²×D₁₁₃	—	2	4	no	—
165	C₂²×D₁₁₃	—	2	4	no	—
166	C₂²×D₁₁₃	—	2	4	no	—
167	C₂²×D₁₁₃	—	2	4	no	—
168	C₂²×D₁₁₃	—	2	4	no	—
169	C₂²×D₁₁₃	C₂×D₄	1	8	yes	—
170	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
171	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
172	C₂²×D₁₁₃	C₂⁴	1	1	yes	characteristic
173	Q₈×C₁₁₃	—	2	4	no	—
174	D₄×C₁₁₃	—	2	8	no	—
175	D₄×C₁₁₃	—	2	2	no	—
176	D₄×C₁₁₃	C₂×D₄	1	4	yes	complemented
177	C₂×C₄×C₁₁₃	—	2	8	no	—
178	C₂×C₄×C₁₁₃	—	2	4	no	—
179	C₂×C₄×C₁₁₃	—	2	4	no	—
180	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
182	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
183	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
184	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²⋊D₁₁₃	—	2	8	no	—
187	C₂²⋊D₁₁₃	—	2	8	no	—
188	C₂²⋊D₁₁₃	—	2	4	no	—
189	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	complemented
190	C₂×Dic₁₁₃	—	2	8	no	—
191	C₂×Dic₁₁₃	—	2	4	no	—
192	C₂×Dic₁₁₃	—	2	4	no	—
193	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
194	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
195	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
196	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
197	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
198	C₂×Dic₁₁₃	C₂⁴	1	1	yes	characteristic
199	D₄₅₂	—	2	8	no	—
200	D₄₅₂	—	2	2	no	—
201	D₄₅₂	C₂×D₄	1	4	yes	complemented
202	C₄×D₁₁₃	—	2	4	no	—
203	C₄×D₁₁₃	—	2	8	no	—
204	C₄×D₁₁₃	—	2	8	no	—
205	C₄×D₁₁₃	—	2	8	no	—
206	C₄×D₁₁₃	—	2	4	no	—
207	C₄×D₁₁₃	—	2	2	no	—
208	C₄×D₁₁₃	—	2	4	no	—
209	C₄×D₁₁₃	—	2	4	no	—
210	C₄×D₁₁₃	—	2	4	no	—
211	C₄×D₁₁₃	—	2	4	no	—
212	C₄×D₁₁₃	C₂×D₄	1	4	yes	—
213	C₄×D₁₁₃	#41	1	4	yes	complemented
214	Dic₂₂₆	—	2	4	no	—
215	Dic₂₂₆	—	2	8	no	—
216	C₂²×C₁₁₃	—	2	2	no	—
217	C₂²×C₁₁₃	—	2	2	no	—
218	C₂²×C₁₁₃	—	2	2	no	—
219	C₂²×C₁₁₃	—	2	2	no	—
220	C₂²×C₁₁₃	—	2	2	no	—
221	C₂²×C₁₁₃	C₂²×D₄	1	4	yes	—
222	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
223	C₂×D₁₁₃	—	2	2	no	—
224	C₂×D₁₁₃	—	2	2	no	—
225	C₂×D₁₁₃	—	2	16	no	—
226	C₂×D₁₁₃	—	2	2	no	—
227	C₂×D₁₁₃	—	2	2	no	—
228	C₂×D₁₁₃	—	2	2	no	—
229	C₂×D₁₁₃	—	4	8	no	—
230	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
231	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
232	C₂×D₁₁₃	C₂×#41	1	2	yes	—
233	C₂×D₁₁₃	2₋¹⁺⁴	1	2	yes	—
234	C₄×C₁₁₃	—	2	4	no	—
235	C₄×C₁₁₃	—	2	2	no	—
236	C₄×C₁₁₃	—	2	2	no	—
237	C₄×C₁₁₃	—	2	1	no	—
238	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
239	C₄×C₁₁₃	C₂×#41	1	2	yes	complemented
240	Dic₁₁₃	—	2	4	no	—
241	Dic₁₁₃	—	2	2	no	—
242	Dic₁₁₃	—	2	2	no	—
243	Dic₁₁₃	—	2	1	no	—
244	Dic₁₁₃	C₂²×D₄	1	2	yes	—
245	Dic₁₁₃	C₂×#41	1	2	yes	complemented
246	C₂×C₁₁₃	—	2	4	no	—
247	C₂×C₁₁₃	—	4	2	no	—
248	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
249	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
250	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	D₁₁₃	—	2	4	no	—
252	D₁₁₃	—	4	2	no	—
253	D₁₁₃	#547	1	4	yes	direct product factor
254	C₂×#547	—	113	1	no	maximal, Sylow
255	C₁₁₃	C₂×#547	1	1	yes	characteristic, complemented, Sylow
256	C₂²×#41	—	113	2	no	—
257	#547	—	113	2	no	—
258	#547	—	113	1	no	—
259	#547	—	113	4	no	—
260	#547	—	113	2	no	—
261	#547	—	113	2	no	—
262	#547	—	113	1	no	—
263	#547	—	113	1	no	—
264	#547	—	113	2	no	—
265	#547	D₁₁₃	1	1	yes	characteristic, direct product factor
266	C₂×C₄⋊Q₈	—	113	1	no	—
267	C₂×#123	—	113	4	no	—
268	C₂×C₂²⋊Q₈	—	113	2	no	—
269	C₂×#121	—	113	2	no	—
270	C₂×C₄×D₄	—	113	1	no	—
271	C₂×C₄×D₄	—	113	1	no	—
272	C₂²×C₄⋊C₄	—	113	2	no	—
273	C₂×#41	—	113	2	no	—
274	C₂×#41	—	113	2	no	—
275	C₂×#41	—	113	4	no	—
276	C₂×#41	—	113	2	no	—
277	C₂×#41	—	113	4	no	—
278	C₂×#41	—	226	16	no	—
279	C₂×#41	C₂×D₁₁₃	1	2	yes	complemented
280	C₂²×Q₈	—	113	2	no	—
281	C₂²×D₄	—	113	1	no	—
282	C₂²×D₄	—	113	1	no	—
283	C₂²×D₄	—	113	4	no	—
284	C₂³×C₄	—	113	2	no	—
285	C₂³×C₄	—	113	4	no	—
286	C₂³×C₄	—	113	2	no	—
287	C₄⋊Q₈	—	113	2	no	—
288	C₄⋊Q₈	—	113	2	no	—
289	C₄⋊Q₈	—	113	2	no	—
290	C₄⋊Q₈	—	113	1	no	—
291	C₄⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
292	#123	—	113	4	no	—
293	#123	—	113	4	no	—
294	#123	—	113	4	no	—
295	#123	—	113	4	no	—
296	#123	—	113	4	no	—
297	#123	—	113	4	no	—
298	#123	—	113	4	no	—
299	#123	C₂×D₁₁₃	1	4	yes	complemented
300	C₂²⋊Q₈	—	113	2	no	—
301	C₂²⋊Q₈	—	113	2	no	—
302	C₂²⋊Q₈	—	113	4	no	—
303	C₂²⋊Q₈	—	113	2	no	—
304	C₂²⋊Q₈	—	113	4	no	—
305	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
306	#121	—	113	2	no	—
307	#121	—	113	4	no	—
308	#121	—	113	2	no	—
309	#121	—	113	2	no	—
310	#121	—	113	4	no	—
311	#121	C₂×D₁₁₃	1	2	yes	complemented
312	C₄×D₄	—	113	1	no	—
313	C₄×D₄	—	113	1	no	—
314	C₄×D₄	—	113	2	no	—
315	C₄×D₄	—	113	2	no	—
316	C₄×D₄	—	113	1	no	—
317	C₄×D₄	—	113	1	no	—
318	C₄×D₄	—	113	2	no	—
319	C₄×D₄	—	113	2	no	—
320	C₄×D₄	—	113	1	no	—
321	C₄×D₄	—	113	1	no	—
322	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
323	C₄×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
324	C₂×C₄⋊C₄	—	113	4	no	—
325	C₂×C₄⋊C₄	—	113	2	no	—
326	C₂×C₄⋊C₄	—	113	1	no	—
327	C₂×C₄⋊C₄	—	113	2	no	—
328	C₂×C₄⋊C₄	—	113	4	no	—
329	C₂×C₄⋊C₄	—	113	4	no	—
330	C₂×C₄⋊C₄	—	113	2	no	—
331	C₂×C₄⋊C₄	—	113	2	no	—
332	C₂×C₄⋊C₄	—	113	1	no	—
333	C₂×C₄⋊C₄	—	113	2	no	—
334	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
335	C₂×C₂²⋊C₄	—	113	2	no	—
336	C₂×C₂²⋊C₄	—	113	2	no	—
337	C₂×C₂²⋊C₄	—	113	4	no	—
338	C₂×C₄²	—	113	1	no	—
339	C₂⁴	—	113	2	no	—
340	C₂⁴	—	113	2	no	—
341	#41	—	2	8	no	—
342	#41	—	226	16	no	—
343	#41	—	226	8	no	—
344	#41	—	226	16	no	—
345	#41	—	226	8	no	—
346	#41	—	226	8	no	—
347	C₂×Q₈	—	113	4	no	—
348	C₂×Q₈	—	113	2	no	—
349	C₂×Q₈	—	226	8	no	—
350	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
351	C₂×D₄	—	113	2	no	—
352	C₂×D₄	—	113	8	no	—
353	C₂×D₄	—	113	2	no	—
354	C₂×D₄	—	113	4	no	—
355	C₂×D₄	—	113	4	no	—
356	C₂×D₄	—	113	1	no	—
357	C₂×D₄	—	113	1	no	—
358	C₂×D₄	—	113	4	no	—
359	C₂×D₄	—	226	4	no	—
360	C₂×D₄	—	226	16	no	—
361	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
362	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
363	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
364	C₂²×C₄	—	113	1	no	—
365	C₂²×C₄	—	113	1	no	—
366	C₂²×C₄	—	113	2	no	—
367	C₂²×C₄	—	113	4	no	—
368	C₂²×C₄	—	113	2	no	—
369	C₂²×C₄	—	113	1	no	—
370	C₂²×C₄	—	113	2	no	—
371	C₂²×C₄	—	113	2	no	—
372	C₂²×C₄	—	113	4	no	—
373	C₂²×C₄	—	113	2	no	—
374	C₂²×C₄	—	113	2	no	—
375	C₂²×C₄	—	113	4	no	—
376	C₂²×C₄	—	113	4	no	—
377	C₂²×C₄	—	113	2	no	—
378	C₂²×C₄	—	113	2	no	—
379	C₂²×C₄	—	226	8	no	—
380	C₂²×C₄	—	226	8	no	—
381	C₂²×C₄	—	226	16	no	—
382	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
383	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
384	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
385	C₄⋊C₄	—	113	2	no	—
386	C₄⋊C₄	—	113	1	no	—
387	C₄⋊C₄	—	113	4	no	—
388	C₄⋊C₄	—	113	2	no	—
389	C₄⋊C₄	—	113	4	no	—
390	C₄⋊C₄	—	113	4	no	—
391	C₄⋊C₄	—	113	4	no	—
392	C₄⋊C₄	—	113	2	no	—
393	C₄⋊C₄	—	113	1	no	—
394	C₄⋊C₄	—	113	4	no	—
395	C₄⋊C₄	—	113	2	no	—
396	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
398	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
399	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
400	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
401	C₂²⋊C₄	—	113	2	no	—
402	C₂²⋊C₄	—	113	2	no	—
403	C₂²⋊C₄	—	113	4	no	—
404	C₂²⋊C₄	—	113	2	no	—
405	C₂²⋊C₄	—	113	2	no	—
406	C₂²⋊C₄	—	113	2	no	—
407	C₂²⋊C₄	—	113	2	no	—
408	C₂²⋊C₄	—	113	4	no	—
409	C₂²⋊C₄	—	113	4	no	—
410	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
411	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
412	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
413	C₄²	—	113	1	no	—
414	C₄²	—	113	1	no	—
415	C₄²	—	113	1	no	—
416	C₄²	C₂²×D₁₁₃	1	1	yes	characteristic
417	C₂³	—	113	1	no	—
418	C₂³	—	113	8	no	—
419	C₂³	—	113	2	no	—
420	C₂³	—	113	2	no	—
421	C₂³	—	226	4	no	—
422	C₂³	—	226	4	no	—
423	C₂³	—	226	4	no	—
424	C₂³	—	226	4	no	—
425	C₂³	—	226	4	no	—
426	C₂³	C₂³×D₁₁₃	1	2	yes	—
427	C₂³	C₂³×D₁₁₃	1	2	yes	—
428	Q₈	—	2	4	no	—
429	Q₈	—	226	8	no	—
430	Q₈	—	226	4	no	—
431	D₄	—	2	8	no	—
432	D₄	—	2	2	no	—
433	D₄	—	113	8	no	—
434	D₄	—	113	4	no	—
435	D₄	—	226	8	no	—
436	D₄	—	226	4	no	—
437	D₄	—	226	8	no	—
438	D₄	—	226	8	no	—
439	D₄	—	226	2	no	—
440	D₄	D₄×D₁₁₃	1	4	yes	complemented
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	113	1	no	—
445	C₂×C₄	—	113	1	no	—
446	C₂×C₄	—	113	4	no	—
447	C₂×C₄	—	113	4	no	—
448	C₂×C₄	—	113	1	no	—
449	C₂×C₄	—	113	2	no	—
450	C₂×C₄	—	113	2	no	—
451	C₂×C₄	—	113	4	no	—
452	C₂×C₄	—	226	4	no	—
453	C₂×C₄	—	226	4	no	—
454	C₂×C₄	—	226	4	no	—
455	C₂×C₄	—	226	8	no	—
456	C₂×C₄	—	226	8	no	—
457	C₂×C₄	—	226	8	no	—
458	C₂×C₄	—	226	4	no	—
459	C₂×C₄	—	226	2	no	—
460	C₂×C₄	—	226	4	no	—
461	C₂×C₄	—	226	4	no	—
462	C₂×C₄	—	226	8	no	—
463	C₂×C₄	—	226	4	no	—
464	C₂×C₄	—	226	4	no	—
465	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
466	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
467	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
468	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
469	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	113	2	no	—
477	C₂²	—	113	2	no	—
478	C₂²	—	113	2	no	—
479	C₂²	—	113	4	no	—
480	C₂²	—	452	8	no	—
481	C₂²	—	226	16	no	—
482	C₂²	—	226	2	no	—
483	C₂²	—	226	2	no	—
484	C₂²	—	226	2	no	—
485	C₂²	—	226	2	no	—
486	C₂²	—	226	2	no	—
487	C₂²	C₂×D₄×D₁₁₃	1	4	yes	—
488	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
489	C₄	—	2	2	no	—
490	C₄	—	2	4	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	113	2	no	—
494	C₄	—	113	2	no	—
495	C₄	—	226	2	no	—
496	C₄	—	226	4	no	—
497	C₄	—	226	2	no	—
498	C₄	—	226	1	no	—
499	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
500	C₄	#41×D₁₁₃	1	2	yes	complemented
501	C₂	—	2	4	no	—
502	C₂	—	4	2	no	—
503	C₂	—	113	4	no	—
504	C₂	—	452	2	no	—
505	C₂	—	226	4	no	—
506	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
507	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
508	C₂	2₋¹⁺⁴×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#547×C₁₁₃	C₂
hypercenter	#547	D₁₁₃
hypocenter	C₁₁₃	C₂×#547
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₁₃	C₂	semidirect
2. #20299253	C₂	semidirect
3. #20299252	C₂	semidirect
4. #20299251	C₂	semidirect
5. #20299250	C₂	semidirect
6. #20299249	C₂	semidirect
7. #20299248	C₂	semidirect
8. #20299247	C₂	semidirect
9. #20299246	C₂	semidirect
10. C₄⋊Q₈×D₁₁₃	C₂	semidirect
11. #123×D₁₁₃	C₂	semidirect
12. C₂²⋊Q₈×D₁₁₃	C₂	semidirect
13. #121×D₁₁₃	C₂	semidirect
14. C₄×D₄×D₁₁₃	C₂	semidirect
15. C₄×D₄×D₁₁₃	C₂	semidirect
16. C₂×C₄⋊C₄×D₁₁₃	C₂	semidirect
17. #547×C₁₁₃	C₂	semidirect
18. C₂×#14268648	C₂²	semidirect
19. C₂×#14268647	C₂²	semidirect
20. C₂×#14268647	C₂²	semidirect
21. C₂×#14268646	C₂²	semidirect
22. C₂×#14268646	C₂²	semidirect
31. #16813622	C₂²	semidirect
32. #16813621	C₂²	semidirect
33. #16813621	C₂²	semidirect
34. #16813620	C₂²	semidirect
35. #16813607	C₂²	semidirect
36. #16813607	C₂²	semidirect
37. #16813606	C₂²	semidirect
38. #16813605	C₂²	semidirect
39. #16813604	C₂²	semidirect
40. #16813604	C₂²	semidirect
41. #16813603	C₂²	semidirect
42. #16813602	C₂²	semidirect
43. #16813601	C₂²	semidirect
44. #16813600	C₂²	semidirect
45. #16813599	C₂²	semidirect
46. #16813598	C₂²	semidirect
47. #16813597	C₂²	semidirect
48. #16813596	C₂²	semidirect
49. #16813595	C₂²	semidirect
50. #16813594	C₂²	semidirect
51. #16813593	C₂²	semidirect
52. C₄×D₄₅₂	C₂²	semidirect
53. C₄×D₄₅₂	C₂²	semidirect
54. D₄×Dic₁₁₃	C₂²	semidirect
55. D₄×Dic₁₁₃	C₂²	semidirect
56. #16813584	C₂²	semidirect
57. #16813584	C₂²	semidirect
58. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
59. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
60. #16813582	C₂²	semidirect
61. #16813582	C₂²	semidirect
62. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
63. C₂×#14268626	C₂²	semidirect
69. C₄⋊C₄×D₁₁₃	C₂²	semidirect
70. C₄⋊C₄×D₁₁₃	C₂²	semidirect
71. C₄⋊C₄×D₁₁₃	C₂²	semidirect
76. C₂×#41×C₁₁₃	C₂²	semidirect
77. C₄⋊Q₈×C₁₁₃	C₂²	semidirect
78. #123×C₁₁₃	C₂²	semidirect
79. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
80. #121×C₁₁₃	C₂²	semidirect
81. C₄×D₄×C₁₁₃	C₂²	semidirect
82. C₄×D₄×C₁₁₃	C₂²	semidirect
83. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
103. D₄×D₁₁₃	D₄	semidirect
176. D₄×C₁₁₃	C₂×D₄	semidirect
189. C₂²⋊D₁₁₃	C₂×D₄	semidirect
201. D₄₅₂	C₂×D₄	semidirect
213. C₄×D₁₁₃	#41	semidirect
239. C₄×C₁₁₃	C₂×#41	semidirect
245. Dic₁₁₃	C₂×#41	semidirect
253. D₁₁₃	#547	direct (N × H)
255. C₁₁₃	C₂×#547	semidirect
265. #547	D₁₁₃	direct (N × H)
279. C₂×#41	C₂×D₁₁₃	semidirect
291. C₄⋊Q₈	C₂×D₁₁₃	semidirect
299. #123	C₂×D₁₁₃	semidirect
305. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
311. #121	C₂×D₁₁₃	semidirect
322. C₄×D₄	C₂×D₁₁₃	semidirect
323. C₄×D₄	C₂×D₁₁₃	semidirect
334. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
440. D₄	D₄×D₁₁₃	semidirect
500. 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
C₂×#41×D₁₁₃	2
#20299253	2
#20299252	2
#20299251	2
#20299250	2
#20299249	2
#20299248	2
#20299247	2
#20299246	2
C₄⋊Q₈×D₁₁₃	2
#123×D₁₁₃	2
C₂²⋊Q₈×D₁₁₃	2
#121×D₁₁₃	2
C₄×D₄×D₁₁₃	2
C₂×C₄⋊C₄×D₁₁₃	2
#547×C₁₁₃	2
C₂×#547	113

Subgroups — #547×D113 #28404027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #547×D₁₁₃ #28404027