Subgroups — #26183548

Order 12032.

1014 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	#20256684	C₂	1	1	yes	maximal, characteristic
2	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241938	C₂	1	2	yes	maximal, complemented
4	#20241934	C₂	1	2	yes	maximal, complemented
5	#20241929	C₂	1	4	yes	maximal, complemented
6	#20241872	C₂	1	4	yes	maximal, complemented
7	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689680	C₄	1	1	yes	characteristic, complemented
9	#15689680	C₄	1	1	yes	characteristic, complemented
10	#15689680	C₂²	1	1	yes	characteristic
11	#15689673	C₄	1	1	yes	characteristic, complemented
12	#15689673	C₄	1	1	yes	characteristic, complemented
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689657	—	2	1	no	—
15	#15689657	—	2	1	no	—
16	#15689657	—	2	1	no	—
17	#15689657	—	2	1	no	—
18	#15689657	C₄	1	2	yes	complemented
19	#15689657	C₂²	1	2	yes	—
20	#15689634	—	2	1	no	—
21	#15689634	—	2	1	no	—
22	#15689634	C₂²	1	2	yes	—
23	C₄×#10625350	—	2	1	no	—
24	C₄×#10625350	—	2	1	no	—
25	C₄×#10625350	C₄	1	2	yes	complemented
26	#15689180	—	2	1	no	—
27	#15689180	C₂²	1	2	yes	—
28	#15689176	—	2	1	no	—
29	#15689176	C₂²	1	2	yes	—
30	#15689147	—	2	1	no	—
31	#15689087	C₂²	1	2	yes	—
32	C₄×#10625329	—	2	1	no	—
33	#15688859	C₂²	1	8	yes	—
34	#15688856	C₂²	1	8	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#383	C₂²	1	2	yes	—
37	C₄₇×#382	—	2	1	no	—
38	C₄₇×#381	—	2	1	no	—
39	C₄₇×#380	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
42	C₄₇×#376	C₂²	1	2	yes	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	—	2	1	no	—
45	C₂×#10625350	C₂×C₄	1	2	yes	—
46	C₂×#10625329	—	2	2	no	—
47	#13094024	C₂×C₄	1	1	yes	characteristic
48	#13094024	C₂×C₄	1	1	yes	characteristic
49	#13094024	C₂×C₄	1	1	yes	characteristic
50	#13094021	C₂×C₄	1	1	yes	characteristic
51	#13094018	—	2	2	no	—
52	#13094018	—	2	2	no	—
53	#13094016	—	2	1	no	—
54	#13094016	—	2	1	no	—
55	#13094016	C₂×C₄	1	2	yes	—
56	#13094012	—	2	1	no	—
57	#13094012	—	2	1	no	—
58	#13094012	C₂×C₄	1	2	yes	—
59	#13094007	—	2	2	no	—
60	#13094007	—	2	2	no	—
61	#13094007	—	2	2	no	—
62	#13094003	—	2	1	no	—
63	#13094003	—	2	1	no	—
64	#13094003	—	2	1	no	—
65	#13094003	—	2	1	no	—
66	#13094003	C₂×C₄	1	2	yes	—
67	#13094003	C₂³	1	2	yes	—
68	#13093998	—	2	1	no	—
69	#13093998	—	2	1	no	—
70	#13093998	—	2	1	no	—
71	#13093998	—	2	1	no	—
72	#13093998	C₂×C₄	1	2	yes	—
73	#13093998	C₂³	1	2	yes	—
74	#13093993	—	2	2	no	—
75	C₄×Dic₉₄	—	2	1	no	—
76	C₄×Dic₉₄	—	2	1	no	—
77	C₄×Dic₉₄	—	2	1	no	—
78	C₄×Dic₉₄	—	2	1	no	—
79	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
80	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
81	C₄×D₁₈₈	—	2	1	no	—
82	C₄×D₁₈₈	—	2	1	no	—
83	C₄×D₁₈₈	—	2	1	no	—
84	C₄×D₁₈₈	—	2	1	no	—
85	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
86	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
87	C₄×C₂²⋊D₄₇	—	2	2	no	—
88	C₄×C₂²⋊D₄₇	—	2	2	no	—
89	C₄×C₂²⋊D₄₇	—	2	2	no	—
90	C₄×C₂²⋊D₄₇	—	2	2	no	—
91	C₄×C₂²⋊D₄₇	—	2	2	no	—
92	C₄×C₂²⋊D₄₇	—	2	2	no	—
93	#13093983	—	2	1	no	—
94	#13093983	—	2	1	no	—
95	#13093983	C₂×C₄	1	2	yes	—
96	#13093981	—	2	2	no	—
97	#13093981	—	2	2	no	—
98	#13093981	—	2	2	no	—
99	C₄²×D₄₇	—	2	2	no	—
100	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
101	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
102	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
103	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
104	#13093935	—	2	2	no	—
105	C₄×C₄₇⋊C₈	—	2	2	no	—
106	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
111	C₂×C₄²×C₄₇	—	2	2	no	—
112	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
124	#95×C₄₇	—	2	2	no	—
125	#95×C₄₇	—	2	2	no	—
126	#95×C₄₇	—	2	2	no	—
127	#95×C₄₇	C₂³	1	4	yes	—
128	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	4	2	no	—
131	C₂²×C₄×C₄₇	—	4	2	no	—
132	C₂²×C₄×C₄₇	—	4	2	no	—
133	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
151	C₂×C₂²⋊D₄₇	—	2	2	no	—
152	C₂×C₂²⋊D₄₇	—	2	2	no	—
153	C₂×C₂²⋊D₄₇	—	2	2	no	—
154	#10625350	—	4	4	no	—
155	#10625350	—	4	4	no	—
156	#10625350	—	4	4	no	—
157	C₂×D₁₈₈	—	2	1	no	—
158	C₂×D₁₈₈	—	2	1	no	—
159	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
160	C₂×C₄×D₄₇	—	2	2	no	—
161	C₂×C₄×D₄₇	—	2	2	no	—
162	C₂×C₄×D₄₇	—	2	2	no	—
163	C₂×Dic₉₄	—	2	1	no	—
164	C₂×Dic₉₄	—	2	1	no	—
165	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₄₇	—	4	4	no	—
167	C₂²⋊C₄×C₄₇	—	4	4	no	—
168	C₄²×C₄₇	—	4	4	no	—
169	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
185	C₂²⋊Dic₄₇	—	2	2	no	—
186	C₂²⋊Dic₄₇	—	2	2	no	—
187	C₂²⋊Dic₄₇	—	2	2	no	—
188	(C₂×D₄₇)⋊C₄	—	2	2	no	—
189	(C₂×D₄₇)⋊C₄	—	2	2	no	—
190	(C₂×D₄₇)⋊C₄	—	2	2	no	—
191	(C₂×D₄₇)⋊C₄	—	2	2	no	—
192	(C₂×D₄₇)⋊C₄	—	2	2	no	—
193	(C₂×D₄₇)⋊C₄	—	2	2	no	—
194	C₄⋊Dic₄₇	—	2	1	no	—
195	C₄⋊Dic₄₇	—	2	1	no	—
196	C₄⋊Dic₄₇	—	2	1	no	—
197	C₄⋊Dic₄₇	—	2	1	no	—
198	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
199	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
200	Dic₄₇⋊C₄	—	2	2	no	—
201	Dic₄₇⋊C₄	—	2	2	no	—
202	Dic₄₇⋊C₄	—	2	2	no	—
203	Dic₄₇⋊C₄	—	2	2	no	—
204	Dic₄₇⋊C₄	—	2	2	no	—
205	Dic₄₇⋊C₄	—	2	2	no	—
206	C₄×Dic₄₇	—	2	2	no	—
207	C₄×Dic₄₇	—	2	2	no	—
208	C₄×Dic₄₇	—	2	2	no	—
209	#10625329	—	4	4	no	—
210	C₂×C₄₇⋊C₈	—	2	4	no	—
211	C₂³×C₄₇	—	2	2	no	—
212	C₂³×C₄₇	—	4	1	no	—
213	C₂³×C₄₇	—	4	1	no	—
214	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
217	C₂²×D₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	4	1	no	—
227	C₂×C₄×C₄₇	—	4	1	no	—
228	C₂×C₄×C₄₇	—	4	1	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	1	no	—
233	C₂×C₄×C₄₇	—	4	1	no	—
234	C₂×C₄×C₄₇	—	4	1	no	—
235	C₂×C₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	4	4	no	—
237	C₂×C₄×C₄₇	—	4	4	no	—
238	C₂×C₄×C₄₇	—	4	4	no	—
239	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
251	C₂²⋊D₄₇	—	4	4	no	—
252	C₂²⋊D₄₇	—	4	4	no	—
253	C₂²⋊D₄₇	—	4	4	no	—
254	C₂×Dic₄₇	—	2	2	no	—
255	C₂×Dic₄₇	—	2	2	no	—
256	C₂×Dic₄₇	—	2	2	no	—
257	D₁₈₈	—	4	2	no	—
258	D₁₈₈	—	4	2	no	—
259	D₁₈₈	—	4	2	no	—
260	C₄×D₄₇	—	4	4	no	—
261	C₄×D₄₇	—	4	4	no	—
262	C₄×D₄₇	—	4	4	no	—
263	Dic₉₄	—	4	2	no	—
264	Dic₉₄	—	4	2	no	—
265	Dic₉₄	—	4	2	no	—
266	C₄₇⋊C₈	—	4	4	no	—
267	#17558	—	47	1	no	maximal, Sylow
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	2	1	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×C₄₇	#575	1	2	yes	—
279	C₂×D₄₇	—	4	2	no	—
280	C₂×D₄₇	—	4	2	no	—
281	C₂×D₄₇	—	4	2	no	—
282	C₄×C₄₇	—	2	1	no	—
283	C₄×C₄₇	—	2	1	no	—
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	1	no	—
289	C₄×C₄₇	—	2	1	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	8	4	no	—
293	C₄×C₄₇	#410	1	2	yes	—
294	C₄×C₄₇	#421	1	2	yes	—
295	Dic₄₇	—	4	2	no	—
296	Dic₄₇	—	4	2	no	—
297	Dic₄₇	—	4	2	no	—
298	#3444	—	47	1	no	—
299	#2920	—	47	1	no	—
300	#2283	D₄₇	1	1	yes	characteristic, complemented
301	#1515	—	47	2	no	—
302	#1514	—	47	2	no	—
303	#1513	—	47	4	no	—
304	#1500	—	47	4	no	—
305	C₂×C₄₇	—	2	2	no	—
306	C₂×C₄₇	—	4	1	no	—
307	C₂×C₄₇	—	4	1	no	—
308	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
309	C₂×C₄₇	#2896	1	1	yes	characteristic
310	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
311	D₄₇	—	8	2	no	—
312	#533	—	47	1	no	—
313	#533	—	47	1	no	—
314	#533	—	47	1	no	—
315	#532	—	47	1	no	—
316	#532	—	47	1	no	—
317	#532	—	47	1	no	—
318	#529	—	47	2	no	—
319	#529	—	47	2	no	—
320	#529	—	94	1	no	—
321	#529	—	94	1	no	—
322	#529	—	94	1	no	—
323	#529	—	94	1	no	—
324	#525	—	47	2	no	—
325	#525	—	94	1	no	—
326	#525	—	94	1	no	—
327	C₄×#41	—	47	2	no	—
328	C₄×#41	—	94	1	no	—
329	C₄×#41	—	94	1	no	—
330	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
331	#432	—	47	2	no	—
332	#432	—	94	1	no	—
333	#431	—	47	2	no	—
334	#431	—	94	1	no	—
335	#423	—	94	1	no	—
336	#407	—	47	2	no	—
337	C₄×M₁₆	—	94	1	no	—
338	#383	C₂×D₄₇	1	2	yes	—
339	#382	—	2	1	no	—
340	#381	—	2	1	no	—
341	#380	C₂×D₄₇	1	2	yes	—
342	C₄×C₄⋊C₄	—	2	1	no	—
343	C₄×C₂²⋊C₄	—	2	1	no	—
344	#376	C₂×D₄₇	1	2	yes	—
345	#328	—	47	8	no	—
346	#327	—	47	8	no	—
347	C₄₇	#17558	1	1	yes	characteristic, complemented, Sylow
348	C₂×#41	—	47	2	no	—
349	C₂×#41	—	94	1	no	—
350	C₂×#41	—	94	1	no	—
351	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
354	C₂×M₁₆	—	94	2	no	—
355	C₄⋊Q₈	—	47	1	no	—
356	C₄⋊Q₈	—	47	1	no	—
357	C₄⋊Q₈	—	47	1	no	—
358	#127	—	47	1	no	—
359	#126	—	94	2	no	—
360	#126	—	94	2	no	—
361	#125	—	47	2	no	—
362	#125	—	94	1	no	—
363	#125	—	94	1	no	—
364	#124	—	47	2	no	—
365	#124	—	94	1	no	—
366	#124	—	94	1	no	—
367	#123	—	94	2	no	—
368	#123	—	94	2	no	—
369	#123	—	94	2	no	—
370	C₂²⋊Q₈	—	47	2	no	—
371	C₂²⋊Q₈	—	47	2	no	—
372	C₂²⋊Q₈	—	94	1	no	—
373	C₂²⋊Q₈	—	94	1	no	—
374	C₂²⋊Q₈	—	94	1	no	—
375	C₂²⋊Q₈	—	94	1	no	—
376	#121	—	47	2	no	—
377	#121	—	47	2	no	—
378	#121	—	94	1	no	—
379	#121	—	94	1	no	—
380	#121	—	94	1	no	—
381	#121	—	94	1	no	—
382	#120	—	94	2	no	—
383	C₄×Q₈	—	47	2	no	—
384	C₄×Q₈	—	47	2	no	—
385	C₄×Q₈	—	94	1	no	—
386	C₄×Q₈	—	94	1	no	—
387	C₄×Q₈	—	94	1	no	—
388	C₄×Q₈	—	94	1	no	—
389	C₄×D₄	—	47	2	no	—
390	C₄×D₄	—	47	2	no	—
391	C₄×D₄	—	94	2	no	—
392	C₄×D₄	—	94	2	no	—
393	C₄×D₄	—	94	2	no	—
394	C₄×D₄	—	94	2	no	—
395	C₄×D₄	—	94	2	no	—
396	C₄×D₄	—	94	2	no	—
397	C₄×D₄	—	94	1	no	—
398	C₄×D₄	—	94	1	no	—
399	C₄×D₄	—	94	1	no	—
400	C₄×D₄	—	94	1	no	—
401	#117	—	47	2	no	—
402	#117	—	94	1	no	—
403	#117	—	94	1	no	—
404	#117	—	94	2	no	—
405	#117	—	94	2	no	—
406	#117	—	94	2	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₂²⋊C₄	—	2	2	no	—
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	—	94	2	no	—
411	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
416	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
417	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
418	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
419	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
420	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
421	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
422	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
423	C₄⋊C₈	—	94	2	no	—
424	C₄⋊C₈	—	94	2	no	—
425	C₂²⋊C₈	—	47	4	no	—
426	C₂²⋊C₈	—	94	2	no	—
427	#97	—	94	2	no	—
428	C₄×C₈	—	94	2	no	—
429	#95	—	2	2	no	—
430	#95	—	2	2	no	—
431	#95	—	2	2	no	—
432	#95	C₂²×D₄₇	1	4	yes	—
433	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
434	#41	—	188	4	no	—
435	#41	—	188	4	no	—
436	#41	—	188	4	no	—
437	C₂×Q₈	—	47	2	no	—
438	C₂×Q₈	—	94	1	no	—
439	C₂×Q₈	—	94	1	no	—
440	C₂×D₄	—	47	2	no	—
441	C₂×D₄	—	94	2	no	—
442	C₂×D₄	—	94	2	no	—
443	C₂×D₄	—	94	2	no	—
444	C₂×D₄	—	94	1	no	—
445	C₂×D₄	—	94	1	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	2	no	—
449	C₂²×C₄	—	4	2	no	—
450	C₂²×C₄	—	94	2	no	—
451	C₂²×C₄	—	94	2	no	—
452	C₂²×C₄	—	94	2	no	—
453	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
454	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
455	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
456	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
457	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
458	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
459	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
460	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
471	M₁₆	—	188	4	no	—
472	C₂×C₈	—	94	4	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	47	2	no	—
475	C₄⋊C₄	—	47	2	no	—
476	C₄⋊C₄	—	94	2	no	—
477	C₄⋊C₄	—	94	2	no	—
478	C₄⋊C₄	—	94	2	no	—
479	C₄⋊C₄	—	94	2	no	—
480	C₄⋊C₄	—	94	2	no	—
481	C₄⋊C₄	—	94	1	no	—
482	C₄⋊C₄	—	94	1	no	—
483	C₄⋊C₄	—	94	1	no	—
484	C₄⋊C₄	—	94	1	no	—
485	C₄⋊C₄	—	94	2	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	94	2	no	—
488	C₂²⋊C₄	—	94	2	no	—
489	C₂²⋊C₄	—	94	2	no	—
490	C₂²⋊C₄	—	94	2	no	—
491	C₂²⋊C₄	—	94	2	no	—
492	C₂²⋊C₄	—	94	2	no	—
493	C₂²⋊C₄	—	94	2	no	—
494	C₂²⋊C₄	—	94	2	no	—
495	C₂²⋊C₄	—	94	2	no	—
496	C₄²	—	4	4	no	—
497	C₄²	—	94	2	no	—
498	C₄²	—	94	2	no	—
499	C₄²	—	94	2	no	—
500	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
501	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
502	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
503	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
504	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
505	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
506	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
507	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
508	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
509	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
510	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
511	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
512	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
513	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
514	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
515	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
516	C₂³	—	2	2	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	—	94	2	no	—
520	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
521	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
522	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
523	Q₈	—	188	2	no	—
524	Q₈	—	188	2	no	—
525	Q₈	—	188	2	no	—
526	D₄	—	188	2	no	—
527	D₄	—	188	2	no	—
528	D₄	—	188	2	no	—
529	D₄	—	188	4	no	—
530	D₄	—	188	4	no	—
531	D₄	—	188	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	94	2	no	—
554	C₂×C₄	—	94	2	no	—
555	C₂×C₄	—	94	2	no	—
556	C₂×C₄	—	188	4	no	—
557	C₂×C₄	—	188	4	no	—
558	C₂×C₄	—	188	4	no	—
559	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
560	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
568	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
570	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
571	C₈	—	188	4	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	188	2	no	—
582	C₂²	—	188	2	no	—
583	C₂²	—	188	2	no	—
584	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
585	C₂²	#15689921	1	2	yes	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	8	4	no	—
597	C₄	—	188	2	no	—
598	C₄	—	188	2	no	—
599	C₄	—	188	2	no	—
600	C₄	#15689096	1	2	yes	—
601	C₄	#15689141	1	2	yes	—
602	C₂	—	2	2	no	—
603	C₂	—	4	1	no	—
604	C₂	—	4	1	no	—
605	C₂	—	376	2	no	—
606	C₂	C₂×#15689096	1	1	yes	characteristic
607	C₂	#20251905	1	1	yes	characteristic
608	C₂	C₂×#15689141	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2283	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	#20256684	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2283	D₄₇
hypocenter	C₄₇	#17558
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2283

Complements

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

N	H ≅ G/N	type
2. #20252021	C₂	semidirect
3. #20241938	C₂	semidirect
4. #20241934	C₂	semidirect
5. #20241929	C₂	semidirect
6. #20241872	C₂	semidirect
7. C₄₇×#2283	C₂	semidirect
8. #15689680	C₄	semidirect
9. #15689680	C₄	semidirect
11. #15689673	C₄	semidirect
12. #15689673	C₄	semidirect
18. #15689657	C₄	semidirect
25. C₄×#10625350	C₄	semidirect
300. #2283	D₄₇	semidirect
347. C₄₇	#17558	semidirect

Maximal subgroups

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

subgroup	index
#20256684	2
#20252021	2
#20241938	2
#20241934	2
#20241929	2
#20241872	2
C₄₇×#2283	2
#17558	47