Subgroups — #26183583

Order 12032.

1058 conjugacy classes of subgroups.

The subgroup lattice has 634 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	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241931	C₂	1	4	yes	maximal, complemented
4	#20241926	C₂	1	4	yes	maximal, complemented
5	#20241887	C₂	1	2	yes	maximal, complemented
6	#20241883	C₂	1	2	yes	maximal, complemented
7	C₄₇×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂×#13093983	—	2	1	no	—
9	#15689180	—	2	1	no	—
10	#15689180	C₂²	1	2	yes	—
11	#15689176	—	2	1	no	—
12	#15689176	C₂²	1	2	yes	—
13	#15689147	—	2	1	no	—
14	#15689087	C₂²	1	2	yes	—
15	C₄×#10625329	—	2	1	no	—
16	#15688993	—	2	1	no	—
17	#15688989	C₂²	1	2	yes	—
18	#15688983	—	2	1	no	—
19	#15688983	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	—	2	1	no	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
22	#15688860	C₂²	1	8	yes	—
23	#15688857	C₂²	1	8	yes	—
24	C₄₇×#533	C₄	1	1	yes	characteristic, complemented
25	C₄₇×#533	C₄	1	1	yes	characteristic, complemented
26	C₄₇×#533	C₂²	1	1	yes	characteristic
27	C₄₇×#532	C₄	1	1	yes	characteristic, complemented
28	C₄₇×#532	C₄	1	1	yes	characteristic, complemented
29	C₄₇×#532	C₂²	1	1	yes	characteristic
30	C₄₇×#529	—	2	1	no	—
31	C₄₇×#529	—	2	1	no	—
32	C₄₇×#529	—	2	1	no	—
33	C₄₇×#529	—	2	1	no	—
34	C₄₇×#529	C₄	1	2	yes	complemented
35	C₄₇×#529	C₂²	1	2	yes	—
36	C₄₇×#525	—	2	1	no	—
37	C₄₇×#525	—	2	1	no	—
38	C₄₇×#525	C₂²	1	2	yes	—
39	C₄×#41×C₄₇	—	2	1	no	—
40	C₄×#41×C₄₇	—	2	1	no	—
41	C₄×#41×C₄₇	C₄	1	2	yes	complemented
42	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#10625329	—	2	2	no	—
44	#13093983	—	4	4	no	—
45	C₂×C₄⋊Dic₄₇	—	2	2	no	—
46	C₂×C₄⋊Dic₄₇	—	2	2	no	—
47	C₂×C₄⋊Dic₄₇	—	2	2	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄×Dic₄₇	—	2	2	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
54	#13093935	—	2	2	no	—
55	C₄×C₄₇⋊C₈	—	2	2	no	—
56	C₄₇⋊#95	—	2	2	no	—
57	C₄₇⋊#95	C₂³	1	4	yes	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
67	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
68	#126×C₄₇	—	2	2	no	—
69	#126×C₄₇	—	2	2	no	—
70	#125×C₄₇	—	2	1	no	—
71	#125×C₄₇	—	2	1	no	—
72	#125×C₄₇	C₂×C₄	1	2	yes	—
73	#124×C₄₇	—	2	1	no	—
74	#124×C₄₇	—	2	1	no	—
75	#124×C₄₇	C₂×C₄	1	2	yes	—
76	#123×C₄₇	—	2	2	no	—
77	#123×C₄₇	—	2	2	no	—
78	#123×C₄₇	—	2	2	no	—
79	C₂²⋊Q₈×C₄₇	—	2	1	no	—
80	C₂²⋊Q₈×C₄₇	—	2	1	no	—
81	C₂²⋊Q₈×C₄₇	—	2	1	no	—
82	C₂²⋊Q₈×C₄₇	—	2	1	no	—
83	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	1	no	—
87	#121×C₄₇	—	2	1	no	—
88	#121×C₄₇	—	2	1	no	—
89	#121×C₄₇	C₂×C₄	1	2	yes	—
90	#121×C₄₇	C₂³	1	2	yes	—
91	#120×C₄₇	—	2	2	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	—	2	1	no	—
94	C₄×Q₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	—	2	1	no	—
96	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₄×D₄×C₄₇	—	2	2	no	—
100	C₄×D₄×C₄₇	—	2	2	no	—
101	C₄×D₄×C₄₇	—	2	2	no	—
102	C₄×D₄×C₄₇	—	2	2	no	—
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	—	2	1	no	—
107	C₄×D₄×C₄₇	—	2	1	no	—
108	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
110	#117×C₄₇	—	2	1	no	—
111	#117×C₄₇	—	2	1	no	—
112	#117×C₄₇	—	2	2	no	—
113	#117×C₄₇	—	2	2	no	—
114	#117×C₄₇	—	2	2	no	—
115	#117×C₄₇	C₂×C₄	1	2	yes	—
116	C₂×C₄²×C₄₇	—	2	2	no	—
117	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
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	D₄	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	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
130	#41×C₄₇	—	4	4	no	—
131	#41×C₄₇	—	4	4	no	—
132	#41×C₄₇	—	4	2	no	—
133	#41×C₄₇	—	4	2	no	—
134	C₂×Q₈×C₄₇	—	2	1	no	—
135	C₂×Q₈×C₄₇	—	2	1	no	—
136	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	1	no	—
141	C₂×D₄×C₄₇	—	2	1	no	—
142	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	—	2	2	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	4	2	no	—
149	C₂²×C₄×C₄₇	—	4	2	no	—
150	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂²×Dic₄₇	—	2	4	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	1	no	—
173	C₄⋊C₄×C₄₇	—	2	2	no	—
174	C₄⋊C₄×C₄₇	—	2	2	no	—
175	C₄⋊C₄×C₄₇	—	2	2	no	—
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	—	2	2	no	—
179	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
180	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
181	C₂²⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	—	2	2	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₂²⋊C₄×C₄₇	—	2	2	no	—
190	C₄²×C₄₇	—	2	2	no	—
191	C₄²×C₄₇	—	2	2	no	—
192	C₄²×C₄₇	—	2	2	no	—
193	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
195	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
196	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₂²⋊Dic₄₇	—	4	4	no	—
210	C₄⋊Dic₄₇	—	4	4	no	—
211	C₄⋊Dic₄₇	—	4	4	no	—
212	C₄⋊Dic₄₇	—	4	4	no	—
213	C₄×Dic₄₇	—	4	4	no	—
214	#10625329	—	4	4	no	—
215	C₂×C₄₇⋊C₈	—	2	4	no	—
216	C₂³×C₄₇	—	2	1	no	—
217	C₂³×C₄₇	—	2	1	no	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	4	1	no	—
220	C₂³×C₄₇	—	4	1	no	—
221	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₄₇	—	4	2	no	—
225	Q₈×C₄₇	—	4	2	no	—
226	Q₈×C₄₇	—	4	2	no	—
227	D₄×C₄₇	—	4	2	no	—
228	D₄×C₄₇	—	4	4	no	—
229	D₄×C₄₇	—	4	4	no	—
230	D₄×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	2	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	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	—	4	1	no	—
250	C₂×C₄×C₄₇	—	4	1	no	—
251	C₂×C₄×C₄₇	—	4	1	no	—
252	C₂×C₄×C₄₇	—	4	1	no	—
253	C₂×C₄×C₄₇	—	4	1	no	—
254	C₂×C₄×C₄₇	—	4	1	no	—
255	C₂×C₄×C₄₇	—	4	4	no	—
256	C₂×C₄×C₄₇	—	4	4	no	—
257	C₂×C₄×C₄₇	—	4	4	no	—
258	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄×C₄₇	#137	1	2	yes	—
270	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
272	C₂×Dic₄₇	—	4	4	no	—
273	C₂×Dic₄₇	—	4	4	no	—
274	C₂×Dic₄₇	—	4	4	no	—
275	C₄₇⋊C₈	—	4	4	no	—
276	#17563	—	47	1	no	maximal, Sylow
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	1	no	—
281	C₂²×C₄₇	—	2	1	no	—
282	C₂²×C₄₇	—	2	1	no	—
283	C₂²×C₄₇	—	2	1	no	—
284	C₂²×C₄₇	—	2	1	no	—
285	C₂²×C₄₇	—	4	2	no	—
286	C₂²×C₄₇	—	4	2	no	—
287	C₂²×C₄₇	—	4	2	no	—
288	C₂²×C₄₇	—	4	2	no	—
289	C₂²×C₄₇	—	4	2	no	—
290	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	1	no	—
295	C₄×C₄₇	—	2	1	no	—
296	C₄×C₄₇	—	2	1	no	—
297	C₄×C₄₇	—	2	1	no	—
298	C₄×C₄₇	—	2	1	no	—
299	C₄×C₄₇	—	2	1	no	—
300	C₄×C₄₇	—	2	1	no	—
301	C₄×C₄₇	—	4	2	no	—
302	C₄×C₄₇	—	4	2	no	—
303	C₄×C₄₇	—	4	2	no	—
304	C₄×C₄₇	#410	1	2	yes	—
305	C₄×C₄₇	#417	1	2	yes	—
306	C₄×C₄₇	#417	1	2	yes	—
307	C₄×C₄₇	#421	1	2	yes	—
308	Dic₄₇	—	8	4	no	—
309	#3444	D₄₇	1	1	yes	characteristic
310	#2920	—	47	1	no	—
311	#2285	—	47	1	no	—
312	#1513	—	47	4	no	—
313	#1512	—	47	4	no	—
314	#1503	—	47	2	no	—
315	#1502	—	47	2	no	—
316	C₂×C₄₇	—	2	1	no	—
317	C₂×C₄₇	—	2	1	no	—
318	C₂×C₄₇	—	4	1	no	—
319	C₂×C₄₇	—	4	1	no	—
320	C₂×C₄₇	—	8	2	no	—
321	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
322	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
323	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
324	#533	Dic₄₇	1	1	yes	characteristic, complemented
325	#533	Dic₄₇	1	1	yes	characteristic, complemented
326	#533	C₂×D₄₇	1	1	yes	characteristic
327	#532	Dic₄₇	1	1	yes	characteristic, complemented
328	#532	Dic₄₇	1	1	yes	characteristic, complemented
329	#532	C₂×D₄₇	1	1	yes	characteristic
330	#529	—	2	1	no	—
331	#529	—	2	1	no	—
332	#529	—	2	1	no	—
333	#529	—	2	1	no	—
334	#529	Dic₄₇	1	2	yes	complemented
335	#529	C₂×D₄₇	1	2	yes	—
336	#525	—	2	1	no	—
337	#525	—	2	1	no	—
338	#525	C₂×D₄₇	1	2	yes	—
339	C₄×#41	—	2	1	no	—
340	C₄×#41	—	2	1	no	—
341	C₄×#41	Dic₄₇	1	2	yes	complemented
342	C₂×#117	—	94	1	no	—
343	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
344	#432	—	47	2	no	—
345	#432	—	94	1	no	—
346	#431	—	47	2	no	—
347	#431	—	94	1	no	—
348	#423	—	94	1	no	—
349	#407	—	47	2	no	—
350	C₄×M₁₆	—	94	1	no	—
351	#384	—	94	1	no	—
352	#382	—	47	2	no	—
353	#380	—	47	2	no	—
354	#380	—	94	1	no	—
355	C₄×C₄⋊C₄	—	47	2	no	—
356	C₄×C₄⋊C₄	—	94	1	no	—
357	#328	—	47	8	no	—
358	#327	—	47	8	no	—
359	C₄₇	#17563	1	1	yes	characteristic, complemented, Sylow
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	C₂×Dic₄₇	1	2	yes	—
363	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
364	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
366	C₂×M₁₆	—	94	2	no	—
367	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
368	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
370	#127	C₂×Dic₄₇	1	1	yes	characteristic
371	#126	—	2	2	no	—
372	#126	—	2	2	no	—
373	#125	—	2	1	no	—
374	#125	—	2	1	no	—
375	#125	C₂×Dic₄₇	1	2	yes	—
376	#124	—	2	1	no	—
377	#124	—	2	1	no	—
378	#124	C₂×Dic₄₇	1	2	yes	—
379	#123	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
387	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	C₂×Dic₄₇	1	2	yes	—
393	#121	C₂²×D₄₇	1	2	yes	—
394	#120	—	2	2	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	—	2	1	no	—
398	C₄×Q₈	—	2	1	no	—
399	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
400	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
401	C₄×D₄	—	2	2	no	—
402	C₄×D₄	—	2	2	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
412	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	—	2	2	no	—
418	#117	—	188	4	no	—
419	#117	C₂×Dic₄₇	1	2	yes	—
420	C₂×C₄⋊C₄	—	94	2	no	—
421	C₂×C₄⋊C₄	—	94	2	no	—
422	C₂×C₄⋊C₄	—	94	2	no	—
423	C₂×C₂²⋊C₄	—	94	2	no	—
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	—	94	2	no	—
426	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
427	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
428	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
429	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
430	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
431	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
432	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
433	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
434	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
435	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
438	C₄⋊C₈	—	94	2	no	—
439	C₄⋊C₈	—	94	2	no	—
440	C₂²⋊C₈	—	47	4	no	—
441	C₂²⋊C₈	—	94	2	no	—
442	#97	—	94	2	no	—
443	C₄×C₈	—	94	2	no	—
444	#95	—	47	4	no	—
445	#95	—	94	2	no	—
446	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
447	#41	—	4	4	no	—
448	#41	—	4	4	no	—
449	#41	—	4	2	no	—
450	#41	—	4	2	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	4	2	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	—	94	4	no	—
468	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
473	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
474	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
475	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
485	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
486	M₁₆	—	188	4	no	—
487	C₂×C₈	—	94	4	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	188	4	no	—
499	C₄⋊C₄	—	188	4	no	—
500	C₄⋊C₄	—	188	4	no	—
501	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
502	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	188	4	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	2	no	—
516	C₄²	—	188	4	no	—
517	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
518	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
519	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
520	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
521	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
522	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
523	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
524	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
525	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
526	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
527	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
528	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
529	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
530	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
531	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
532	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	4	1	no	—
538	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
539	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
540	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
541	Q₈	—	4	2	no	—
542	Q₈	—	4	2	no	—
543	Q₈	—	4	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	4	no	—
575	C₂×C₄	—	188	4	no	—
576	C₂×C₄	—	188	4	no	—
577	C₂×C₄	—	188	4	no	—
578	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
579	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
580	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
584	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
585	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
586	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
587	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
588	C₂×C₄	#13094049	1	2	yes	—
589	C₂×C₄	#13094054	1	2	yes	—
590	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
592	C₈	—	188	4	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	1	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
607	C₂²	C₂×#13094049	1	1	yes	characteristic
608	C₂²	C₂×#13094054	1	1	yes	characteristic
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	376	4	no	—
621	C₄	#15689097	1	2	yes	—
622	C₄	#15689124	1	2	yes	—
623	C₄	#15689124	1	2	yes	—
624	C₄	#15689140	1	2	yes	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	4	1	no	—
628	C₂	—	4	1	no	—
629	C₂	—	8	2	no	—
630	C₂	C₂×#15689097	1	1	yes	characteristic
631	C₂	C₂×#15689124	1	1	yes	characteristic
632	C₂	C₂×#15689140	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3444	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3444	D₄₇
hypocenter	C₄₇	#17563
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	semidirect
2. #20245795	C₂	semidirect
3. #20241931	C₂	semidirect
4. #20241926	C₂	semidirect
5. #20241887	C₂	semidirect
6. #20241883	C₂	semidirect
24. C₄₇×#533	C₄	semidirect
25. C₄₇×#533	C₄	semidirect
27. C₄₇×#532	C₄	semidirect
28. C₄₇×#532	C₄	semidirect
34. C₄₇×#529	C₄	semidirect
41. C₄×#41×C₄₇	C₄	semidirect
324. #533	Dic₄₇	semidirect
325. #533	Dic₄₇	semidirect
327. #532	Dic₄₇	semidirect
328. #532	Dic₄₇	semidirect
334. #529	Dic₄₇	semidirect
341. C₄×#41	Dic₄₇	semidirect
359. C₄₇	#17563	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
#20245795	2
#20241931	2
#20241926	2
#20241887	2
#20241883	2
C₄₇×#3444	2
#17563	47