Subgroups — #26216408

Order 12032.

1336 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
2	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243487	C₂	1	2	yes	maximal, complemented
4	#20243408	C₂	1	4	yes	maximal, complemented
5	#20243332	C₂	1	2	yes	maximal
6	#20243198	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
8	#15689180	—	2	1	no	—
9	#15689180	—	2	1	no	—
10	#15689176	—	2	1	no	—
11	#15689176	—	2	1	no	—
12	#15689147	C₂²	1	2	yes	complemented
13	C₂×#13093951	C₂²	1	8	yes	—
14	#15689087	C₂²	1	2	yes	—
15	C₄×#10625329	C₂²	1	2	yes	complemented
16	#15688991	—	2	1	no	—
17	#15688989	—	2	1	no	—
18	#15688986	—	2	1	no	—
19	#15688983	—	2	1	no	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
21	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
22	#15688969	C₂²	1	2	yes	complemented
23	#15688882	C₂²	1	8	yes	complemented
24	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
25	C₄×#41×C₄₇	—	2	1	no	—
26	C₄×#41×C₄₇	—	2	1	no	—
27	C₄×#41×C₄₇	—	2	1	no	—
28	C₄×#41×C₄₇	—	2	1	no	—
29	C₄×#41×C₄₇	C₄	1	2	yes	complemented
30	C₄×#41×C₄₇	C₄	1	2	yes	complemented
31	C₄×#41×C₄₇	C₂²	1	2	yes	—
32	C₄×#41×C₄₇	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₄₇	—	2	1	no	—
36	C₂×C₄×D₄×C₄₇	—	2	1	no	—
37	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
39	C₂×#117×C₄₇	—	2	1	no	—
40	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₄₇	—	2	1	no	—
42	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#10625329	C₂³	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	—	2	2	no	—
45	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
46	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
47	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
48	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
49	#13093951	—	2	16	no	—
50	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
51	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
52	#13093935	—	2	2	no	—
53	C₄×C₄₇⋊C₈	—	2	2	no	—
54	C₄₇⋊#95	—	2	2	no	—
55	C₄₇⋊#95	—	2	2	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	—	2	2	no	—
58	C₂×#41×C₄₇	—	2	8	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	—	2	1	no	—
61	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×#41×C₄₇	C₂³	1	2	yes	—
63	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₄₇	—	2	1	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	—	2	1	no	—
67	C₂³×C₄×C₄₇	—	2	1	no	—
68	C₂³×C₄×C₄₇	—	2	1	no	—
69	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₄×Q₈×C₄₇	—	2	1	no	—
73	C₄×Q₈×C₄₇	—	2	1	no	—
74	C₄×Q₈×C₄₇	—	2	1	no	—
75	C₄×Q₈×C₄₇	—	2	1	no	—
76	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₄₇	—	2	2	no	—
81	C₄×D₄×C₄₇	—	2	2	no	—
82	C₄×D₄×C₄₇	—	2	2	no	—
83	C₄×D₄×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	—	2	2	no	—
85	C₄×D₄×C₄₇	—	2	2	no	—
86	C₄×D₄×C₄₇	—	2	2	no	—
87	C₄×D₄×C₄₇	—	2	2	no	—
88	C₄×D₄×C₄₇	—	2	1	no	—
89	C₄×D₄×C₄₇	—	2	1	no	—
90	C₄×D₄×C₄₇	—	2	1	no	—
91	C₄×D₄×C₄₇	—	2	1	no	—
92	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
94	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
95	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
96	#117×C₄₇	—	2	1	no	—
97	#117×C₄₇	—	2	1	no	—
98	#117×C₄₇	—	2	2	no	—
99	#117×C₄₇	—	2	2	no	—
100	#117×C₄₇	—	2	2	no	—
101	#117×C₄₇	—	2	2	no	—
102	#117×C₄₇	C₂×C₄	1	2	yes	—
103	#117×C₄₇	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
111	C₂×C₄²×C₄₇	—	2	1	no	—
112	C₂×C₄²×C₄₇	—	2	1	no	—
113	C₂×C₄²×C₄₇	—	2	1	no	—
114	C₂×C₄²×C₄₇	—	2	2	no	—
115	C₂×C₄²×C₄₇	—	2	2	no	—
116	C₂×C₄²×C₄₇	—	2	2	no	—
117	C₂×C₄²×C₄₇	—	2	2	no	—
118	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
130	C₂⁴×C₄₇	—	2	1	no	—
131	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
132	#41×C₄₇	—	2	8	no	—
133	#41×C₄₇	—	2	8	no	—
134	#41×C₄₇	—	2	4	no	—
135	#41×C₄₇	—	2	4	no	—
136	#41×C₄₇	—	2	4	no	—
137	#41×C₄₇	#41	1	8	yes	—
138	C₂×Q₈×C₄₇	—	2	4	no	—
139	C₂×Q₈×C₄₇	—	2	1	no	—
140	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂×D₄×C₄₇	—	2	8	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	—	2	4	no	—
145	C₂×D₄×C₄₇	—	2	1	no	—
146	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₄₇	—	2	8	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	—	2	2	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	4	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	2	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	—	4	2	no	—
159	C₂²×C₄×C₄₇	—	4	2	no	—
160	C₂²×C₄×C₄₇	—	4	4	no	—
161	C₂²×C₄×C₄₇	—	4	4	no	—
162	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
180	C₂²×Dic₄₇	—	2	4	no	—
181	C₄⋊C₄×C₄₇	—	2	2	no	—
182	C₄⋊C₄×C₄₇	—	2	2	no	—
183	C₄⋊C₄×C₄₇	—	2	2	no	—
184	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	—	2	1	no	—
186	C₄⋊C₄×C₄₇	—	2	1	no	—
187	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
188	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₂²⋊C₄×C₄₇	—	2	2	no	—
191	C₂²⋊C₄×C₄₇	—	2	2	no	—
192	C₂²⋊C₄×C₄₇	—	2	2	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₄²×C₄₇	—	2	2	no	—
196	C₄²×C₄₇	—	2	2	no	—
197	C₄²×C₄₇	—	2	2	no	—
198	C₄²×C₄₇	—	2	2	no	—
199	C₄²×C₄₇	—	2	2	no	—
200	C₄²×C₄₇	—	2	2	no	—
201	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
211	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
212	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
216	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
217	C₂²⋊Dic₄₇	—	4	4	no	—
218	C₄⋊Dic₄₇	—	4	4	no	—
219	C₄×Dic₄₇	—	2	8	no	—
220	#10625329	—	2	8	no	—
221	C₂×C₄₇⋊C₈	—	2	4	no	—
222	C₂³×C₄₇	—	2	4	no	—
223	C₂³×C₄₇	—	2	2	no	—
224	C₂³×C₄₇	—	2	2	no	—
225	C₂³×C₄₇	—	2	2	no	—
226	C₂³×C₄₇	—	4	1	no	—
227	C₂³×C₄₇	—	4	2	no	—
228	C₂³×C₄₇	—	4	2	no	—
229	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₄₇	—	2	4	no	—
233	Q₈×C₄₇	—	2	2	no	—
234	Q₈×C₄₇	#117	1	4	yes	—
235	D₄×C₄₇	—	2	8	no	—
236	D₄×C₄₇	—	2	4	no	—
237	D₄×C₄₇	—	2	8	no	—
238	D₄×C₄₇	—	2	2	no	—
239	D₄×C₄₇	#117	1	4	yes	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	8	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	2	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	8	no	—
250	C₂×C₄×C₄₇	—	2	2	no	—
251	C₂×C₄×C₄₇	—	2	2	no	—
252	C₂×C₄×C₄₇	—	2	2	no	—
253	C₂×C₄×C₄₇	—	2	2	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	2	2	no	—
256	C₂×C₄×C₄₇	—	4	1	no	—
257	C₂×C₄×C₄₇	—	4	1	no	—
258	C₂×C₄×C₄₇	—	4	1	no	—
259	C₂×C₄×C₄₇	—	4	1	no	—
260	C₂×C₄×C₄₇	—	4	1	no	—
261	C₂×C₄×C₄₇	—	4	1	no	—
262	C₂×C₄×C₄₇	—	4	1	no	—
263	C₂×C₄×C₄₇	—	4	4	no	—
264	C₂×C₄×C₄₇	—	4	4	no	—
265	C₂×C₄×C₄₇	—	4	4	no	—
266	C₂×C₄×C₄₇	—	4	2	no	—
267	C₂×C₄×C₄₇	—	4	2	no	—
268	C₂×C₄×C₄₇	—	4	4	no	—
269	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
282	C₂×Dic₄₇	—	4	4	no	—
283	C₂×Dic₄₇	—	4	4	no	—
284	C₂×Dic₄₇	—	4	4	no	—
285	C₄₇⋊C₈	—	4	4	no	—
286	#20748	—	47	1	no	maximal, Sylow
287	C₂²×C₄₇	—	2	1	no	—
288	C₂²×C₄₇	—	2	1	no	—
289	C₂²×C₄₇	—	2	1	no	—
290	C₂²×C₄₇	—	2	1	no	—
291	C₂²×C₄₇	—	2	1	no	—
292	C₂²×C₄₇	—	2	1	no	—
293	C₂²×C₄₇	—	2	1	no	—
294	C₂²×C₄₇	—	2	4	no	—
295	C₂²×C₄₇	—	4	4	no	—
296	C₂²×C₄₇	—	4	8	no	—
297	C₂²×C₄₇	—	4	2	no	—
298	C₂²×C₄₇	—	4	2	no	—
299	C₂²×C₄₇	#421	1	2	yes	—
300	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
301	C₂²×C₄₇	#525	1	2	yes	—
302	C₄×C₄₇	—	2	1	no	—
303	C₄×C₄₇	—	2	1	no	—
304	C₄×C₄₇	—	2	1	no	—
305	C₄×C₄₇	—	2	1	no	—
306	C₄×C₄₇	—	2	1	no	—
307	C₄×C₄₇	—	2	1	no	—
308	C₄×C₄₇	—	2	1	no	—
309	C₄×C₄₇	—	2	1	no	—
310	C₄×C₄₇	—	2	4	no	—
311	C₄×C₄₇	—	2	1	no	—
312	C₄×C₄₇	—	4	2	no	—
313	C₄×C₄₇	—	4	2	no	—
314	C₄×C₄₇	#421	1	2	yes	—
315	C₄×C₄₇	C₂×#117	1	2	yes	—
316	C₄×C₄₇	#525	1	2	yes	—
317	Dic₄₇	—	8	4	no	—
318	C₂×C₄×#41	D₄₇	1	1	yes	characteristic
319	#2920	—	47	1	no	—
320	#2283	—	47	1	no	—
321	#1826	—	47	2	no	—
322	#1806	—	47	4	no	—
323	#1789	—	47	2	no	—
324	#1759	—	47	4	no	—
325	C₂×C₄₇	—	2	2	no	—
326	C₂×C₄₇	—	2	2	no	—
327	C₂×C₄₇	—	4	1	no	—
328	C₂×C₄₇	—	4	4	no	—
329	C₂×C₄₇	#2280	1	1	yes	characteristic
330	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
331	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
332	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
333	C₄×#41	—	2	1	no	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	—	2	1	no	—
336	C₄×#41	—	2	1	no	—
337	C₄×#41	Dic₄₇	1	2	yes	complemented
338	C₄×#41	Dic₄₇	1	2	yes	complemented
339	C₄×#41	C₂×D₄₇	1	2	yes	—
340	C₄×#41	C₂×D₄₇	1	2	yes	—
341	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
342	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
343	C₂×C₄×D₄	—	2	1	no	—
344	C₂×C₄×D₄	—	2	1	no	—
345	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
346	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
347	C₂×#117	—	2	1	no	—
348	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
349	C₂²×C₄²	—	2	1	no	—
350	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
351	#432	—	94	1	no	—
352	#432	—	94	1	no	—
353	#431	—	94	1	no	—
354	#431	—	94	1	no	—
355	#423	—	47	2	no	—
356	C₂×#104	—	47	8	no	—
357	#407	—	47	2	no	—
358	C₄×M₁₆	—	47	2	no	—
359	#383	—	94	1	no	—
360	#382	—	94	1	no	—
361	#381	—	94	1	no	—
362	#380	—	94	1	no	—
363	C₄×C₄⋊C₄	—	47	2	no	—
364	C₄×C₂²⋊C₄	—	47	2	no	—
365	#376	—	47	2	no	—
366	#339	—	47	8	no	—
367	C₄₇	#20748	1	1	yes	characteristic, complemented, Sylow
368	C₂×#41	—	2	8	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	C₂×Dic₄₇	1	2	yes	—
372	C₂×#41	C₂²×D₄₇	1	2	yes	—
373	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
374	C₂²×D₄	—	2	1	no	—
375	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	—	2	1	no	—
379	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
382	C₂×M₁₆	—	47	4	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
388	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
389	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
390	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
404	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
405	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
406	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	2	no	—
410	#117	—	2	2	no	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	C₂×Dic₄₇	1	2	yes	—
414	#117	C₂²×D₄₇	1	2	yes	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	94	2	no	—
418	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	94	2	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	2	no	—
428	C₂×C₄²	—	2	2	no	—
429	C₂×C₄²	—	2	2	no	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	—	47	4	no	—
432	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
433	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
434	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
435	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
436	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
437	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
438	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
439	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
440	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
441	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
442	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
443	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
444	C₄⋊C₈	—	94	2	no	—
445	C₄⋊C₈	—	94	2	no	—
446	#104	—	94	16	no	—
447	C₂²⋊C₈	—	94	2	no	—
448	C₂²⋊C₈	—	94	2	no	—
449	#97	—	94	2	no	—
450	C₄×C₈	—	94	2	no	—
451	#95	—	94	2	no	—
452	#95	—	94	2	no	—
453	#95	—	94	2	no	—
454	#95	—	94	2	no	—
455	C₂⁴	—	2	1	no	—
456	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
457	#41	—	2	8	no	—
458	#41	—	2	8	no	—
459	#41	—	2	4	no	—
460	#41	—	2	4	no	—
461	#41	—	2	4	no	—
462	#41	#10625350	1	8	yes	—
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	—	94	4	no	—
488	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
490	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
491	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
492	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
493	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
494	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
495	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
496	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
497	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
505	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
506	M₁₆	—	94	8	no	—
507	C₂×C₈	—	94	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	188	4	no	—
515	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
516	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	188	4	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	94	8	no	—
531	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
532	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
533	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
534	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
535	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
536	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
537	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
538	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
539	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
540	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
541	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
542	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
543	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
544	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
545	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
546	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
547	C₂³	—	2	4	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
555	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
556	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
557	Q₈	—	2	4	no	—
558	Q₈	—	2	2	no	—
559	Q₈	#13093983	1	4	yes	—
560	D₄	—	2	8	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	8	no	—
563	D₄	—	2	2	no	—
564	D₄	#13093983	1	4	yes	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	188	4	no	—
595	C₂×C₄	—	188	4	no	—
596	C₂×C₄	—	188	4	no	—
597	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
598	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
599	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
600	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
601	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
602	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
603	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
604	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
605	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
608	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
609	C₂×C₄	C₂×#10625350	1	4	yes	—
610	C₈	—	188	4	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	8	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	#15689140	1	2	yes	—
624	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
625	C₂²	#15689634	1	2	yes	—
626	C₄	—	2	1	no	—
627	C₄	—	2	4	no	—
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	2	no	—
638	C₄	—	376	4	no	—
639	C₄	#15689140	1	2	yes	—
640	C₄	C₂×#13093983	1	2	yes	—
641	C₄	#15689634	1	2	yes	—
642	C₂	—	2	2	no	—
643	C₂	—	2	2	no	—
644	C₂	—	4	1	no	—
645	C₂	—	4	4	no	—
646	C₂	#20245771	1	1	yes	characteristic
647	C₂	C₂×#15689140	1	1	yes	characteristic
648	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	#20748
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	semidirect
2. #20245786	C₂	semidirect
3. #20243487	C₂	semidirect
4. #20243408	C₂	semidirect
6. #20243198	C₂	semidirect
12. #15689147	C₂²	semidirect
15. C₄×#10625329	C₂²	semidirect
20. C₄×C₄⋊Dic₄₇	C₂²	semidirect
22. #15688969	C₂²	semidirect
23. #15688882	C₂²	semidirect
29. C₄×#41×C₄₇	C₄	semidirect
30. C₄×#41×C₄₇	C₄	semidirect
33. C₂×C₄×Q₈×C₄₇	C₄	semidirect
34. C₂×C₄×Q₈×C₄₇	C₄	semidirect
37. C₂×C₄×D₄×C₄₇	C₄	semidirect
38. C₂×C₄×D₄×C₄₇	C₄	semidirect
337. C₄×#41	Dic₄₇	semidirect
338. C₄×#41	Dic₄₇	semidirect
341. C₂×C₄×Q₈	Dic₄₇	semidirect
342. C₂×C₄×Q₈	Dic₄₇	semidirect
345. C₂×C₄×D₄	Dic₄₇	semidirect
346. C₂×C₄×D₄	Dic₄₇	semidirect
367. C₄₇	#20748	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
#20245786	2
#20243487	2
#20243408	2
#20243332	2
#20243198	2
C₂×C₄×#41×C₄₇	2
#20748	47