Subgroups — #26184451

Order 12032.

940 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252408	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252039	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242019	C₂	1	2	yes	maximal, complemented
4	#20242012	C₂	1	2	yes	maximal, complemented
5	#20241999	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241995	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241995	C₂	1	2	yes	maximal, complemented
8	#20241986	C₂	1	2	yes	maximal, complemented
9	#20241980	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241976	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3514	C₂	1	1	yes	maximal, characteristic
12	Q₈×C₄₇⋊C₈	—	2	1	no	—
13	#15689201	—	2	1	no	—
14	#15689201	—	2	2	no	—
15	#15689184	—	2	2	no	—
16	#15689180	C₂²	1	2	yes	complemented
17	#15689180	C₂²	1	1	yes	characteristic, complemented
18	#15689180	C₂²	1	2	yes	complemented
19	#15689180	C₂²	1	2	yes	complemented
20	#15689150	—	2	1	no	—
21	#15689090	—	2	1	no	—
22	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
23	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
24	C₄×#10625329	C₂²	1	2	yes	complemented
25	C₂×#13093935	C₂²	1	1	yes	characteristic, complemented
26	#15688865	C₂²	1	1	yes	characteristic, complemented
27	#15688865	C₂²	1	1	yes	characteristic, complemented
28	#15688865	C₂²	1	2	yes	complemented
29	#15688863	C₂²	1	1	yes	characteristic
30	#15688863	C₂²	1	1	yes	characteristic
31	#15688863	C₂²	1	2	yes	—
32	#15688863	C₂²	1	2	yes	complemented
33	#15688863	C₂²	1	2	yes	complemented
34	#15688863	C₂²	1	2	yes	complemented
35	#15688863	C₂²	1	2	yes	complemented
36	C₄₇×#559	C₄	1	1	yes	characteristic
37	C₄₇×#556	C₄	1	1	yes	characteristic
38	C₄₇×#555	—	2	1	no	—
39	C₄₇×#551	—	2	2	no	—
40	D₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
41	C₄₇×#548	C₄	1	2	yes	—
42	C₄₇×#546	—	2	1	no	—
43	C₄₇×#546	C₄	1	2	yes	—
44	D₄²×C₄₇	C₄	1	1	yes	characteristic
45	C₄₇×#542	—	2	1	no	—
46	C₄₇×#538	—	2	2	no	—
47	C₄₇×#532	C₂²	1	1	yes	characteristic
48	C₄₇×#529	C₂²	1	1	yes	characteristic
49	C₄₇×#529	C₂²	1	2	yes	—
50	C₂×#124×C₄₇	C₂²	1	2	yes	—
51	C₄₇×#518	—	2	1	no	—
52	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂×#10625329	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
65	#13093935	—	2	1	no	—
66	#13093935	C₂³	1	1	yes	characteristic
67	#13093935	C₂³	1	1	yes	characteristic
68	#13093935	C₂³	1	1	yes	characteristic
69	#13093935	C₂³	1	1	yes	characteristic
70	#13093935	C₂³	1	2	yes	—
71	#13093935	C₂³	1	2	yes	—
72	C₄×C₄₇⋊C₈	—	2	1	no	—
73	C₄×C₄₇⋊C₈	—	2	2	no	—
74	C₄×C₄₇⋊C₈	—	2	1	no	—
75	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
77	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
78	C₂²×D₄×C₄₇	—	2	1	no	—
79	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
80	C₄⋊Q₈×C₄₇	—	2	1	no	—
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#126×C₄₇	—	2	2	no	—
84	#126×C₄₇	—	2	2	no	—
85	#126×C₄₇	—	2	1	no	—
86	#125×C₄₇	C₂³	1	1	yes	characteristic
87	#124×C₄₇	—	2	1	no	—
88	#124×C₄₇	—	2	2	no	—
89	#124×C₄₇	—	2	2	no	—
90	#124×C₄₇	—	2	2	no	—
91	#124×C₄₇	C₂×C₄	1	2	yes	—
92	#124×C₄₇	C₂×C₄	1	2	yes	—
93	#124×C₄₇	C₂³	1	1	yes	characteristic
94	#124×C₄₇	C₂³	1	2	yes	—
95	#123×C₄₇	—	2	1	no	—
96	#123×C₄₇	—	2	2	no	—
97	#123×C₄₇	—	2	2	no	—
98	#123×C₄₇	—	2	2	no	—
99	C₂²⋊Q₈×C₄₇	—	2	1	no	—
100	C₂²⋊Q₈×C₄₇	—	2	2	no	—
101	C₂²⋊Q₈×C₄₇	—	2	2	no	—
102	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
103	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
104	#121×C₄₇	—	2	2	no	—
105	#121×C₄₇	—	2	1	no	—
106	#121×C₄₇	—	2	1	no	—
107	#121×C₄₇	—	2	1	no	—
108	#121×C₄₇	—	2	2	no	—
109	#121×C₄₇	C₂×C₄	1	2	yes	—
110	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
111	#120×C₄₇	—	2	2	no	—
112	#120×C₄₇	—	2	2	no	—
113	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
114	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
117	C₄×D₄×C₄₇	—	2	1	no	—
118	C₄×D₄×C₄₇	—	2	2	no	—
119	C₄×D₄×C₄₇	—	2	1	no	—
120	C₄×D₄×C₄₇	—	2	1	no	—
121	C₄×D₄×C₄₇	—	2	2	no	—
122	C₄×D₄×C₄₇	—	2	1	no	—
123	C₄×D₄×C₄₇	—	2	1	no	—
124	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
126	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
127	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
128	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
129	C₄×D₄×C₄₇	D₄	1	2	yes	—
130	#117×C₄₇	—	2	1	no	—
131	#117×C₄₇	—	2	1	no	—
132	#117×C₄₇	—	2	2	no	—
133	#117×C₄₇	D₄	1	2	yes	—
134	#117×C₄₇	D₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
136	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
139	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
140	C₂⁴×C₄₇	—	2	2	no	—
141	#41×C₄₇	—	4	2	no	—
142	#41×C₄₇	—	8	2	no	—
143	C₂×Q₈×C₄₇	—	2	2	no	—
144	C₂×Q₈×C₄₇	—	8	2	no	—
145	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	2	1	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	1	no	—
152	C₂×D₄×C₄₇	—	2	1	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	4	4	no	—
155	C₂×D₄×C₄₇	—	8	2	no	—
156	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
157	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
158	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₇	—	2	2	no	—
161	C₂²×C₄×C₄₇	—	2	1	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	2	1	no	—
174	C₄⋊C₄×C₄₇	—	2	2	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	1	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
178	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
179	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
181	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
182	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	1	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	1	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
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	1	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	—	2	1	no	—
195	C₂²⋊C₄×C₄₇	—	2	1	no	—
196	C₂²⋊C₄×C₄₇	—	2	2	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
199	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
200	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
201	C₄²×C₄₇	—	2	2	no	—
202	C₄²×C₄₇	—	2	1	no	—
203	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
204	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂×D₄	1	2	yes	—
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂×D₄	1	2	yes	—
209	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
210	#10625329	—	4	4	no	—
211	#10625329	—	4	2	no	—
212	#10625329	—	4	2	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	2	2	no	—
216	C₂×C₄₇⋊C₈	—	2	2	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	—	2	1	no	—
219	C₂×C₄₇⋊C₈	—	4	2	no	—
220	C₂³×C₄₇	—	2	1	no	—
221	C₂³×C₄₇	—	2	2	no	—
222	C₂³×C₄₇	—	4	4	no	—
223	C₂³×C₄₇	—	8	2	no	—
224	C₂³×C₄₇	—	8	2	no	—
225	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	Q₈×C₄₇	—	2	2	no	—
228	Q₈×C₄₇	—	4	1	no	—
229	Q₈×C₄₇	—	4	2	no	—
230	Q₈×C₄₇	—	8	2	no	—
231	D₄×C₄₇	—	2	2	no	—
232	D₄×C₄₇	—	4	2	no	—
233	D₄×C₄₇	—	4	1	no	—
234	D₄×C₄₇	—	4	2	no	—
235	D₄×C₄₇	—	4	4	no	—
236	D₄×C₄₇	—	4	2	no	—
237	D₄×C₄₇	—	8	1	no	—
238	D₄×C₄₇	—	8	2	no	—
239	D₄×C₄₇	—	8	1	no	—
240	D₄×C₄₇	—	8	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	1	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	—	4	1	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	8	2	no	—
253	C₂×C₄×C₄₇	—	8	2	no	—
254	C₂×C₄×C₄₇	—	8	2	no	—
255	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
264	C₄₇⋊C₈	—	2	2	no	—
265	C₄₇⋊C₈	—	4	1	no	—
266	C₄₇⋊C₈	—	4	1	no	—
267	C₄₇⋊C₈	—	4	2	no	—
268	C₄₇⋊C₈	—	4	1	no	—
269	C₄₇⋊C₈	—	4	2	no	—
270	#17681	—	47	1	no	maximal, Sylow
271	C₂²×C₄₇	—	2	2	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	2	no	—
275	C₂²×C₄₇	—	2	1	no	—
276	C₂²×C₄₇	—	2	2	no	—
277	C₂²×C₄₇	—	4	2	no	—
278	C₂²×C₄₇	—	4	1	no	—
279	C₂²×C₄₇	—	4	1	no	—
280	C₂²×C₄₇	—	4	2	no	—
281	C₂²×C₄₇	—	4	2	no	—
282	C₂²×C₄₇	—	4	1	no	—
283	C₂²×C₄₇	—	16	4	no	—
284	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	2	2	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	2	2	no	—
292	C₄×C₄₇	—	2	1	no	—
293	C₄×C₄₇	—	4	2	no	—
294	C₄×C₄₇	—	4	1	no	—
295	C₄×C₄₇	—	4	1	no	—
296	C₄×C₄₇	—	4	1	no	—
297	C₄×C₄₇	#421	1	2	yes	—
298	#3514	D₄₇	1	1	yes	characteristic
299	#2971	—	47	1	no	—
300	#2923	—	47	1	no	—
301	#1535	—	47	2	no	—
302	#1533	—	47	2	no	—
303	#1530	—	47	1	no	—
304	#1529	—	47	1	no	—
305	#1529	—	47	2	no	—
306	#1527	—	47	2	no	—
307	#1525	—	47	1	no	—
308	#1524	—	47	1	no	—
309	C₂×C₄₇	—	4	1	no	—
310	C₂×C₄₇	—	4	2	no	—
311	C₂×C₄₇	—	8	2	no	—
312	C₂×C₄₇	—	8	1	no	—
313	C₂×C₄₇	#2888	1	1	yes	characteristic
314	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
315	C₂×C₄₇	#2901	1	1	yes	characteristic
316	#559	Dic₄₇	1	1	yes	characteristic
317	#556	Dic₄₇	1	1	yes	characteristic
318	#555	—	2	1	no	—
319	#551	—	2	2	no	—
320	D₄×Q₈	Dic₄₇	1	1	yes	characteristic
321	#548	Dic₄₇	1	2	yes	—
322	#546	—	2	1	no	—
323	#546	Dic₄₇	1	2	yes	—
324	D₄²	Dic₄₇	1	1	yes	characteristic
325	#542	—	2	1	no	—
326	#538	—	2	2	no	—
327	#532	C₂×D₄₇	1	1	yes	characteristic
328	#529	C₂×D₄₇	1	1	yes	characteristic
329	#529	C₂×D₄₇	1	2	yes	—
330	C₂×#124	C₂×D₄₇	1	2	yes	—
331	#518	—	2	1	no	—
332	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
333	C₈×Q₈	—	94	1	no	—
334	#436	—	94	1	no	—
335	#436	—	94	2	no	—
336	#433	—	94	2	no	—
337	#432	—	47	2	no	—
338	#432	—	47	2	no	—
339	#432	—	47	1	no	—
340	#432	—	47	2	no	—
341	#424	—	94	1	no	—
342	#408	—	94	1	no	—
343	C₄×M₁₆	—	47	1	no	—
344	C₄×M₁₆	—	47	1	no	—
345	C₄×M₁₆	—	47	2	no	—
346	C₂×#97	—	47	1	no	—
347	#330	—	47	1	no	—
348	#330	—	47	1	no	—
349	#330	—	47	2	no	—
350	#329	—	47	1	no	—
351	#329	—	47	1	no	—
352	#329	—	47	2	no	—
353	#329	—	47	2	no	—
354	#329	—	47	2	no	—
355	#329	—	47	2	no	—
356	#329	—	47	2	no	—
357	C₄₇	#17681	1	1	yes	characteristic, complemented, Sylow
358	C₂×#41	C₂×Dic₄₇	1	2	yes	—
359	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
363	C₂×M₁₆	—	94	1	no	—
364	C₂×M₁₆	—	94	2	no	—
365	C₂×M₁₆	—	94	1	no	—
366	C₂²×C₈	—	94	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
369	#127	C₂×Dic₄₇	1	1	yes	characteristic
370	#126	—	2	2	no	—
371	#126	—	2	2	no	—
372	#126	—	2	1	no	—
373	#125	C₂²×D₄₇	1	1	yes	characteristic
374	#124	—	2	1	no	—
375	#124	—	2	2	no	—
376	#124	—	2	2	no	—
377	#124	—	2	2	no	—
378	#124	C₂×Dic₄₇	1	2	yes	—
379	#124	C₂×Dic₄₇	1	2	yes	—
380	#124	C₂²×D₄₇	1	1	yes	characteristic
381	#124	C₂²×D₄₇	1	2	yes	—
382	#123	—	2	1	no	—
383	#123	—	2	2	no	—
384	#123	—	2	2	no	—
385	#123	—	2	2	no	—
386	C₂²⋊Q₈	—	2	1	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
390	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
391	#121	—	2	2	no	—
392	#121	—	2	1	no	—
393	#121	—	2	1	no	—
394	#121	—	2	1	no	—
395	#121	—	2	2	no	—
396	#121	C₂×Dic₄₇	1	2	yes	—
397	#121	C₂×Dic₄₇	1	1	yes	characteristic
398	#120	—	2	2	no	—
399	#120	—	2	2	no	—
400	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
401	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
402	C₄×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
403	C₄×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
412	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
413	C₄×D₄	C₂×Dic₄₇	1	1	yes	characteristic
414	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
415	C₄×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
416	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
417	#117	—	2	1	no	—
418	#117	—	2	1	no	—
419	#117	—	2	2	no	—
420	#117	C₂²⋊D₄₇	1	2	yes	—
421	#117	C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
426	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
427	C₄⋊C₈	—	94	2	no	—
428	C₄⋊C₈	—	94	2	no	—
429	C₄⋊C₈	—	94	1	no	—
430	C₄⋊C₈	—	94	2	no	—
431	C₂²⋊C₈	—	94	2	no	—
432	C₂²⋊C₈	—	94	2	no	—
433	C₂²⋊C₈	—	94	2	no	—
434	C₂²⋊C₈	—	94	1	no	—
435	#97	—	47	1	no	—
436	#97	—	47	1	no	—
437	#97	—	47	1	no	—
438	#97	—	47	1	no	—
439	#97	—	47	2	no	—
440	#97	—	47	2	no	—
441	#97	—	94	1	no	—
442	C₄×C₈	—	94	1	no	—
443	C₄×C₈	—	94	1	no	—
444	C₄×C₈	—	94	2	no	—
445	C₂⁴	—	2	2	no	—
446	#41	—	4	2	no	—
447	#41	—	8	2	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	8	2	no	—
450	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
451	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
452	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	—	8	2	no	—
461	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
462	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
463	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
464	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
470	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
473	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
474	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
475	M₁₆	—	188	4	no	—
476	M₁₆	—	188	2	no	—
477	M₁₆	—	188	2	no	—
478	C₂×C₈	—	94	1	no	—
479	C₂×C₈	—	94	2	no	—
480	C₂×C₈	—	94	1	no	—
481	C₂×C₈	—	94	2	no	—
482	C₂×C₈	—	94	1	no	—
483	C₂×C₈	—	94	1	no	—
484	C₂×C₈	—	188	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
494	C₄⋊C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
495	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
496	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
497	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	1	no	—
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	1	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	—	2	1	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
514	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
515	C₂²⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	C₂²×Dic₄₇	1	2	yes	—
519	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
520	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
521	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
522	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
523	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
524	C₄²	C₂³×D₄₇	1	1	yes	characteristic
525	C₂³	—	2	1	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	8	2	no	—
529	C₂³	—	8	2	no	—
530	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
531	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
532	Q₈	—	2	2	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	2	no	—
535	Q₈	—	8	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	4	no	—
541	D₄	—	4	2	no	—
542	D₄	—	8	1	no	—
543	D₄	—	8	2	no	—
544	D₄	—	8	1	no	—
545	D₄	—	8	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	8	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
561	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
562	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
563	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
564	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
565	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
566	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
569	C₈	—	94	2	no	—
570	C₈	—	188	1	no	—
571	C₈	—	188	1	no	—
572	C₈	—	188	2	no	—
573	C₈	—	188	1	no	—
574	C₈	—	188	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	16	4	no	—
588	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	1	no	—
601	C₄	#15689140	1	2	yes	—
602	C₂	—	4	2	no	—
603	C₂	—	4	1	no	—
604	C₂	—	8	1	no	—
605	C₂	—	8	2	no	—
606	C₂	#20251867	1	1	yes	characteristic
607	C₂	C₂×#15689140	1	1	yes	characteristic
608	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3514	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3514	D₄₇
hypocenter	C₄₇	#17681
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3514

Complements

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

N	H ≅ G/N	type
1. #20252408	C₂	semidirect
2. #20252039	C₂	semidirect
3. #20242019	C₂	semidirect
4. #20242012	C₂	semidirect
5. #20241999	C₂	semidirect
6. #20241995	C₂	semidirect
7. #20241995	C₂	semidirect
8. #20241986	C₂	semidirect
9. #20241980	C₂	semidirect
10. #20241976	C₂	semidirect
16. #15689180	C₂²	semidirect
17. #15689180	C₂²	semidirect
18. #15689180	C₂²	semidirect
19. #15689180	C₂²	semidirect
22. C₄×#10625329	C₂²	semidirect
23. C₄×#10625329	C₂²	semidirect
24. C₄×#10625329	C₂²	semidirect
25. C₂×#13093935	C₂²	semidirect
26. #15688865	C₂²	semidirect
27. #15688865	C₂²	semidirect
28. #15688865	C₂²	semidirect
32. #15688863	C₂²	semidirect
33. #15688863	C₂²	semidirect
34. #15688863	C₂²	semidirect
35. #15688863	C₂²	semidirect
357. C₄₇	#17681	semidirect

Maximal subgroups

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

subgroup	index
#20252408	2
#20252039	2
#20242019	2
#20242012	2
#20241999	2
#20241995	2
#20241986	2
#20241980	2
#20241976	2
C₄₇×#3514	2
#17681	47