Subgroups — #26185411

Order 12032.

602 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	#20252507	C₂	1	1	yes	maximal, characteristic
2	#20252496	C₂	1	1	yes	maximal, characteristic
3	#20252027	C₂	1	1	yes	maximal, characteristic
4	#20242176	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242175	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242174	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242170	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242167	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242163	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242161	C₂	1	1	yes	maximal, characteristic, complemented
11	#20242137	C₂	1	1	yes	maximal, characteristic, complemented
12	#20242137	C₂	1	1	yes	maximal, characteristic, complemented
13	#20242135	C₂	1	1	yes	maximal, characteristic, complemented
14	#335×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#10625350	C₂²	1	1	yes	characteristic
17	#15689251	—	2	1	no	—
18	C₈×Dic₉₄	—	2	1	no	—
19	#15689198	—	2	1	no	—
20	#15689197	—	2	1	no	—
21	#15689196	—	2	1	no	—
22	C₈×D₁₈₈	—	2	1	no	—
23	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
24	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
25	#15689183	C₄	1	2	yes	—
26	#15689181	C₄	1	2	yes	—
27	#15689179	C₂²	1	1	yes	characteristic
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689175	C₂²	1	1	yes	characteristic
30	#15689175	C₂²	1	1	yes	characteristic
31	#15689175	C₂²	1	1	yes	characteristic
32	#15689174	C₂²	1	1	yes	characteristic
33	#15689174	C₂²	1	1	yes	characteristic
34	#15689148	C₄	1	2	yes	—
35	#15689147	C₂²	1	1	yes	characteristic
36	#15689145	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
41	#15689088	C₄	1	2	yes	—
42	C₄×#10625324	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
44	#15688876	C₂²	1	1	yes	characteristic
45	#15688876	C₂²	1	1	yes	characteristic
46	#15688876	C₂²	1	1	yes	characteristic
47	#15688876	C₂²	1	1	yes	characteristic
48	#15688875	C₂²	1	1	yes	characteristic
49	#15688875	C₂²	1	1	yes	characteristic
50	#15688875	C₂²	1	1	yes	characteristic
51	#15688875	C₂²	1	1	yes	characteristic
52	#15688873	C₂²	1	1	yes	characteristic
53	#15688873	C₂²	1	1	yes	characteristic
54	#15688873	C₂²	1	1	yes	characteristic
55	#15688873	C₂²	1	1	yes	characteristic
56	C₄₇×#432	C₂²	1	1	yes	characteristic
57	C₄₇×#431	C₂²	1	1	yes	characteristic
58	C₄₇×#431	C₂²	1	1	yes	characteristic
59	C₄₇×#335	C₂²	1	1	yes	characteristic
60	C₄₇×#335	C₂²	1	1	yes	characteristic
61	C₄₇×#334	C₂²	1	1	yes	characteristic
62	C₄₇×#334	C₂²	1	1	yes	characteristic
63	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
64	C₂×#10625329	—	2	1	no	—
65	C₂×#10625324	—	2	1	no	—
66	C₂×#10625324	C₂×C₄	1	2	yes	—
67	C₂²×C₄₇⋊C₈	—	2	1	no	—
68	C₂×C₈×D₄₇	—	2	1	no	—
69	C₂×C₈×D₄₇	—	2	1	no	—
70	C₂×C₈×D₄₇	—	2	1	no	—
71	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
72	C₄×Dic₉₄	D₄	1	1	yes	characteristic
73	C₄×Dic₉₄	Q₈	1	1	yes	characteristic
74	C₄×D₁₈₈	D₄	1	1	yes	characteristic
75	C₄×D₁₈₈	Q₈	1	1	yes	characteristic
76	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₄₇	Q₈	1	1	yes	characteristic
79	C₄×C₂²⋊D₄₇	Q₈	1	1	yes	characteristic
80	#13093983	C₂×C₄	1	1	yes	characteristic
81	#13093981	C₂×C₄	1	1	yes	characteristic
82	#13093981	C₂×C₄	1	1	yes	characteristic
83	C₄²×D₄₇	C₂³	1	1	yes	characteristic
84	C₄²×D₄₇	C₂³	1	1	yes	characteristic
85	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
86	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
87	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
88	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
89	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
90	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
91	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
92	Dic₄₇⋊C₈	—	2	1	no	—
93	Dic₄₇⋊C₈	—	2	1	no	—
94	Dic₄₇⋊C₈	—	2	1	no	—
95	Dic₄₇⋊C₈	—	2	1	no	—
96	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
97	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
98	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
99	(C₂×D₄₇)⋊C₈	—	2	1	no	—
100	(C₂×D₄₇)⋊C₈	—	2	1	no	—
101	(C₂×D₄₇)⋊C₈	—	2	1	no	—
102	(C₂×D₄₇)⋊C₈	—	2	1	no	—
103	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
104	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
105	#13093934	—	2	1	no	—
106	#13093934	C₂×C₄	1	2	yes	—
107	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
109	C₈×Dic₄₇	—	2	1	no	—
110	C₈×Dic₄₇	—	2	1	no	—
111	C₈×Dic₄₇	—	2	1	no	—
112	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
115	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²⋊C₈×C₄₇	—	2	1	no	—
120	C₂²⋊C₈×C₄₇	—	2	1	no	—
121	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
122	#97×C₄₇	—	2	1	no	—
123	C₄×C₈×C₄₇	—	2	1	no	—
124	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
131	#10625350	—	2	4	no	—
132	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
138	C₂×C₄×D₄₇	C₂×Q₈	1	1	yes	characteristic
139	C₂×Dic₉₄	C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
149	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
151	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
152	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
153	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
154	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
155	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
156	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
157	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
158	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
159	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
160	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
161	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
162	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
165	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
167	C₄×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
168	#10625329	—	8	1	no	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	—	8	1	no	—
174	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
176	#10625324	—	2	4	no	—
177	#10625324	—	8	1	no	—
178	C₈×D₄₇	—	2	4	no	—
179	C₈×D₄₇	—	8	1	no	—
180	C₈×D₄₇	—	8	1	no	—
181	C₈×D₄₇	—	8	1	no	—
182	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	4	1	no	—
189	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
195	C₂²⋊D₄₇	—	2	2	no	—
196	C₂²⋊D₄₇	—	2	2	no	—
197	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
203	D₁₈₈	—	2	2	no	—
204	C₄×D₄₇	—	2	2	no	—
205	C₄×D₄₇	—	2	1	no	—
206	C₄×D₄₇	—	2	1	no	—
207	C₄×D₄₇	—	2	1	no	—
208	C₄×D₄₇	—	2	1	no	—
209	C₄×D₄₇	—	4	1	no	—
210	C₄×D₄₇	—	4	1	no	—
211	C₄×D₄₇	#131	1	4	yes	—
212	Dic₉₄	—	2	2	no	—
213	C₈×C₄₇	—	2	2	no	—
214	C₈×C₄₇	—	2	2	no	—
215	C₈×C₄₇	—	4	1	no	—
216	C₈×C₄₇	—	4	1	no	—
217	C₈×C₄₇	—	4	1	no	—
218	C₈×C₄₇	—	4	1	no	—
219	C₄₇⋊C₈	—	2	2	no	—
220	C₄₇⋊C₈	—	2	2	no	—
221	C₄₇⋊C₈	—	4	1	no	—
222	C₄₇⋊C₈	—	4	1	no	—
223	C₄₇⋊C₈	—	4	1	no	—
224	C₄₇⋊C₈	—	4	1	no	—
225	#17812	—	47	1	no	maximal, Sylow
226	C₂²×C₄₇	—	2	1	no	—
227	C₂²×C₄₇	—	2	1	no	—
228	C₂²×C₄₇	—	2	1	no	—
229	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
230	C₂×D₄₇	—	2	1	no	—
231	C₂×D₄₇	—	2	1	no	—
232	C₂×D₄₇	—	2	1	no	—
233	C₂×D₄₇	—	2	1	no	—
234	C₂×D₄₇	—	2	1	no	—
235	C₂×D₄₇	#424	1	2	yes	—
236	C₄×C₄₇	—	2	1	no	—
237	C₄×C₄₇	—	2	1	no	—
238	C₄×C₄₇	—	2	1	no	—
239	C₄×C₄₇	—	2	1	no	—
240	C₄×C₄₇	C₂×#131	1	2	yes	—
241	C₄×C₄₇	#576	1	1	yes	characteristic
242	C₄×C₄₇	#578	1	1	yes	characteristic
243	Dic₄₇	—	2	1	no	—
244	Dic₄₇	—	2	1	no	—
245	Dic₄₇	—	2	1	no	—
246	Dic₄₇	—	2	1	no	—
247	Dic₄₇	—	2	1	no	—
248	Dic₄₇	#424	1	2	yes	—
249	#2989	—	47	1	no	—
250	#2988	—	47	1	no	—
251	#2922	—	47	1	no	—
252	#1574	—	47	1	no	—
253	#1574	—	47	1	no	—
254	#1573	—	47	1	no	—
255	#1573	—	47	1	no	—
256	#1572	—	47	1	no	—
257	#1572	D₄₇	1	1	yes	characteristic, complemented
258	#1571	—	47	1	no	—
259	#1571	—	47	1	no	—
260	#1565	—	47	1	no	—
261	#1565	—	47	1	no	—
262	#1564	—	47	1	no	—
263	C₂×#335	—	47	1	no	—
264	C₂×C₄₇	—	4	1	no	—
265	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
266	C₂×C₄₇	#2913	1	1	yes	characteristic
267	C₂×C₄₇	#2916	1	1	yes	characteristic
268	D₄₇	—	2	2	no	—
269	D₄₇	—	4	1	no	—
270	C₄×#41	—	47	1	no	—
271	#446	—	94	1	no	—
272	C₈×Q₈	—	94	1	no	—
273	#436	—	94	1	no	—
274	#435	—	94	1	no	—
275	#435	—	94	1	no	—
276	C₈×D₄	—	94	1	no	—
277	C₈×D₄	—	94	1	no	—
278	C₈×D₄	—	94	1	no	—
279	#433	—	47	2	no	—
280	#433	—	47	2	no	—
281	#432	—	47	1	no	—
282	#432	C₂×D₄₇	1	1	yes	characteristic
283	#431	—	47	1	no	—
284	#431	—	47	1	no	—
285	#431	—	47	1	no	—
286	#431	—	47	1	no	—
287	#431	—	47	1	no	—
288	#431	—	47	1	no	—
289	#431	C₂×D₄₇	1	1	yes	characteristic
290	#431	C₂×D₄₇	1	1	yes	characteristic
291	#424	—	47	2	no	—
292	#423	—	47	1	no	—
293	#423	—	47	1	no	—
294	C₂×C₄⋊C₈	—	47	1	no	—
295	C₂×C₄⋊C₈	—	47	1	no	—
296	C₂×C₄⋊C₈	—	47	1	no	—
297	C₂×C₄⋊C₈	—	47	1	no	—
298	#408	—	47	2	no	—
299	C₄×M₁₆	—	47	1	no	—
300	C₂×C₄×C₈	—	47	1	no	—
301	#335	—	47	1	no	—
302	#335	—	47	1	no	—
303	#335	—	47	1	no	—
304	#335	—	47	1	no	—
305	#335	—	47	1	no	—
306	#335	—	47	1	no	—
307	#335	—	47	1	no	—
308	#335	—	47	1	no	—
309	#335	C₂×D₄₇	1	1	yes	characteristic
310	#335	C₂×D₄₇	1	1	yes	characteristic
311	#334	—	47	1	no	—
312	#334	—	47	1	no	—
313	#334	—	47	1	no	—
314	#334	—	47	1	no	—
315	#334	C₂×D₄₇	1	1	yes	characteristic
316	#334	C₂×D₄₇	1	1	yes	characteristic
317	C₄₇	#17812	1	1	yes	characteristic, complemented, Sylow
318	C₂×#41	—	47	1	no	—
319	C₂×M₁₆	—	47	2	no	—
320	C₂×M₁₆	—	94	1	no	—
321	C₂×M₁₆	—	94	1	no	—
322	C₂²×C₈	—	47	2	no	—
323	C₂²×C₈	—	94	1	no	—
324	C₂²×C₈	—	94	1	no	—
325	C₂²×C₈	—	94	1	no	—
326	C₂²×C₈	—	94	1	no	—
327	C₄×Q₈	—	47	1	no	—
328	C₄×Q₈	—	47	1	no	—
329	C₄×D₄	—	47	1	no	—
330	C₄×D₄	—	47	1	no	—
331	C₄×D₄	—	47	1	no	—
332	C₄×D₄	—	47	1	no	—
333	C₄×D₄	—	47	1	no	—
334	C₄×D₄	—	47	1	no	—
335	#117	—	47	1	no	—
336	#117	—	47	1	no	—
337	#117	—	47	1	no	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
341	C₄⋊C₈	—	47	2	no	—
342	C₄⋊C₈	—	47	2	no	—
343	C₄⋊C₈	—	47	2	no	—
344	C₄⋊C₈	—	47	1	no	—
345	C₄⋊C₈	—	47	1	no	—
346	C₄⋊C₈	—	47	1	no	—
347	C₄⋊C₈	—	47	1	no	—
348	C₄⋊C₈	—	94	1	no	—
349	C₄⋊C₈	—	94	1	no	—
350	C₄⋊C₈	—	94	1	no	—
351	C₄⋊C₈	—	94	1	no	—
352	C₄⋊C₈	—	94	1	no	—
353	C₄⋊C₈	—	94	1	no	—
354	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
355	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
356	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
357	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	47	2	no	—
362	C₂²⋊C₈	—	47	2	no	—
363	C₂²⋊C₈	—	47	2	no	—
364	C₂²⋊C₈	—	94	1	no	—
365	C₂²⋊C₈	—	94	1	no	—
366	C₂²⋊C₈	—	94	1	no	—
367	C₂²⋊C₈	—	94	1	no	—
368	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
369	#97	—	2	1	no	—
370	#97	—	47	2	no	—
371	#97	—	94	1	no	—
372	C₄×C₈	—	2	1	no	—
373	C₄×C₈	—	47	2	no	—
374	C₄×C₈	—	47	1	no	—
375	C₄×C₈	—	47	1	no	—
376	C₄×C₈	—	94	1	no	—
377	C₄×C₈	—	94	1	no	—
378	C₄×C₈	—	94	1	no	—
379	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
380	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
381	#41	—	94	4	no	—
382	C₂×Q₈	—	47	1	no	—
383	C₂×D₄	—	47	1	no	—
384	C₂×D₄	—	47	1	no	—
385	C₂×D₄	—	47	1	no	—
386	C₂²×C₄	—	47	1	no	—
387	C₂²×C₄	—	47	1	no	—
388	C₂²×C₄	—	47	1	no	—
389	C₂²×C₄	—	47	1	no	—
390	C₂²×C₄	—	47	1	no	—
391	C₂²×C₄	—	47	1	no	—
392	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
393	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
394	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
395	M₁₆	—	94	4	no	—
396	M₁₆	—	376	1	no	—
397	M₁₆	—	376	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	47	2	no	—
403	C₂×C₈	—	47	2	no	—
404	C₂×C₈	—	94	4	no	—
405	C₂×C₈	—	94	1	no	—
406	C₂×C₈	—	94	1	no	—
407	C₂×C₈	—	94	1	no	—
408	C₂×C₈	—	94	1	no	—
409	C₂×C₈	—	376	1	no	—
410	C₂×C₈	—	376	1	no	—
411	C₂×C₈	—	376	1	no	—
412	C₂×C₈	—	376	1	no	—
413	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
414	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
415	C₄⋊C₄	—	47	1	no	—
416	C₄⋊C₄	—	47	1	no	—
417	C₄⋊C₄	—	47	1	no	—
418	C₄⋊C₄	—	47	1	no	—
419	C₄⋊C₄	—	47	1	no	—
420	C₄⋊C₄	—	47	1	no	—
421	C₂²⋊C₄	—	47	1	no	—
422	C₂²⋊C₄	—	47	1	no	—
423	C₂²⋊C₄	—	47	1	no	—
424	C₂²⋊C₄	—	47	1	no	—
425	C₂²⋊C₄	—	47	1	no	—
426	C₂²⋊C₄	—	47	1	no	—
427	C₄²	—	47	1	no	—
428	C₄²	—	47	1	no	—
429	C₄²	—	47	1	no	—
430	C₄²	—	47	1	no	—
431	C₄²	—	47	1	no	—
432	C₄²	—	47	1	no	—
433	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
434	C₄²	D₄×D₄₇	1	1	yes	characteristic
435	C₄²	Q₈×D₄₇	1	1	yes	characteristic
436	C₄²	C₂³×D₄₇	1	1	yes	characteristic
437	C₂³	—	47	1	no	—
438	C₂³	—	47	1	no	—
439	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
440	Q₈	—	94	2	no	—
441	D₄	—	94	2	no	—
442	D₄	—	94	2	no	—
443	D₄	—	94	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	47	1	no	—
449	C₂×C₄	—	47	4	no	—
450	C₂×C₄	—	47	1	no	—
451	C₂×C₄	—	47	1	no	—
452	C₂×C₄	—	47	1	no	—
453	C₂×C₄	—	47	1	no	—
454	C₂×C₄	—	47	1	no	—
455	C₂×C₄	—	94	2	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	94	1	no	—
459	C₂×C₄	—	94	1	no	—
460	C₂×C₄	—	188	1	no	—
461	C₂×C₄	—	188	1	no	—
462	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
463	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
464	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	1	no	—
474	C₈	—	94	2	no	—
475	C₈	—	94	2	no	—
476	C₈	—	188	1	no	—
477	C₈	—	188	1	no	—
478	C₈	—	188	1	no	—
479	C₈	—	188	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	47	2	no	—
484	C₂²	—	94	1	no	—
485	C₂²	—	94	1	no	—
486	C₂²	—	94	1	no	—
487	C₂²	—	94	1	no	—
488	C₂²	—	94	1	no	—
489	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	47	2	no	—
495	C₄	—	94	1	no	—
496	C₄	—	94	1	no	—
497	C₄	—	94	1	no	—
498	C₄	—	94	1	no	—
499	C₄	—	94	1	no	—
500	C₄	#131×D₄₇	1	2	yes	—
501	C₄	#15689925	1	1	yes	characteristic
502	C₄	#15689937	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	94	2	no	—
505	C₂	—	188	1	no	—
506	C₂	#424×D₄₇	1	1	yes	characteristic
507	C₂	#20251985	1	1	yes	characteristic
508	C₂	#20251998	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1572	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1572	D₄₇
hypocenter	C₄₇	#17812
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. #20242176	C₂	semidirect
5. #20242175	C₂	semidirect
6. #20242174	C₂	semidirect
7. #20242170	C₂	semidirect
8. #20242167	C₂	semidirect
9. #20242163	C₂	semidirect
10. #20242161	C₂	semidirect
11. #20242137	C₂	semidirect
12. #20242137	C₂	semidirect
13. #20242135	C₂	semidirect
14. #335×D₄₇	C₂	semidirect
15. C₄₇×#1572	C₂	semidirect
257. #1572	D₄₇	semidirect
317. C₄₇	#17812	semidirect

Maximal subgroups

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

subgroup	index
#20252507	2
#20252496	2
#20252027	2
#20242176	2
#20242175	2
#20242174	2
#20242170	2
#20242167	2
#20242163	2
#20242161	2
#20242137	2
#20242135	2
#335×D₄₇	2
C₄₇×#1572	2
#17812	47