Subgroups — #26223172

Order 12032.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689395	C₂	1	1	yes	maximal, characteristic
2	#20252203	C₂	1	2	yes	maximal
3	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20251810	C₂	1	1	yes	maximal, characteristic
5	#20244173	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244046	C₂	1	2	yes	maximal, complemented
7	#20243900	C₂	1	2	yes	maximal
8	#20243449	C₂	1	1	yes	maximal, characteristic
9	#108×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#101×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094055	C₂²	1	2	yes	—
13	C₂×#13094032	C₂²	1	1	yes	characteristic
14	C₂×#13094030	C₂²	1	1	yes	characteristic
15	#15689591	C₂²	1	1	yes	characteristic
16	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
17	#15689395	C₄	1	8	yes	complemented
18	#15689227	—	2	2	no	—
19	#15689226	—	2	2	no	—
20	Q₁₆×Dic₄₇	—	2	1	no	—
21	Q₁₆×Dic₄₇	—	2	1	no	—
22	Q₁₆×Dic₄₇	—	2	1	no	—
23	Q₁₆×Dic₄₇	—	2	1	no	—
24	#15689215	—	2	2	no	—
25	#15689208	—	2	2	no	—
26	C₂×#13093960	C₂²	1	1	yes	characteristic
27	#15689166	C₂²	1	2	yes	—
28	C₂×#13093958	C₂²	1	1	yes	characteristic
29	#15689125	C₂²	1	2	yes	—
30	C₂×#13093948	C₂²	1	2	yes	—
31	C₂×#13093943	C₂²	1	2	yes	—
32	#15689080	—	2	1	no	—
33	#15689079	C₂²	1	1	yes	characteristic
34	#15689077	—	2	1	no	—
35	#15689075	—	2	1	no	—
36	M₁₆×Dic₄₇	C₂²	1	2	yes	—
37	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₄₇	—	2	1	no	—
40	#15688891	C₂²	1	2	yes	—
41	#15688891	C₂²	1	2	yes	—
42	#15688887	C₂²	1	2	yes	—
43	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#419	C₂²	1	2	yes	—
46	C₂×#101×C₄₇	C₂²	1	2	yes	—
47	C₄₇×#405	C₂²	1	1	yes	characteristic
48	C₂×#10625350	C₂³	1	1	yes	characteristic
49	#13094055	—	2	4	no	—
50	#13094055	C₂×C₄	1	8	yes	—
51	C₂×#10625337	—	2	2	no	—
52	C₂×#10625336	—	2	2	no	—
53	#13094032	—	2	2	no	—
54	#13094032	—	2	2	no	—
55	#13094030	—	2	2	no	—
56	#13094030	C₂×C₄	1	4	yes	—
57	C₂×#10625329	C₂³	1	1	yes	characteristic
58	C₂×#10625329	C₂³	1	2	yes	—
59	C₂×#10625324	—	2	1	no	—
60	C₂×#10625324	—	2	1	no	—
61	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₄₇	—	2	1	no	—
63	C₂×C₈×D₄₇	—	2	1	no	—
64	Q₈×Dic₄₇	—	2	2	no	—
65	Q₈×Dic₄₇	—	2	2	no	—
66	Q₈×Dic₄₇	—	2	2	no	—
67	Q₈×Dic₄₇	—	2	2	no	—
68	#13093989	D₄	1	1	yes	characteristic
69	#13093989	D₄	1	1	yes	characteristic
70	#13093986	D₄	1	1	yes	characteristic
71	#13093986	D₄	1	1	yes	characteristic
72	(C₂²⋊D₄₇)⋊C₄	—	2	1	no	—
73	(C₂²⋊D₄₇)⋊C₄	—	2	1	no	—
74	#13093981	—	2	1	no	—
75	C₂×C₄⋊Dic₄₇	—	2	2	no	—
76	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
77	C₂×C₄×Dic₄₇	—	2	2	no	—
78	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
79	C₄²×D₄₇	—	2	1	no	—
80	#13093960	C₂×C₄	1	4	yes	complemented
81	#13093958	—	2	1	no	—
82	#13093958	—	2	1	no	—
83	#13093957	—	2	2	no	—
84	#13093955	—	2	2	no	—
85	#13093949	—	2	2	no	—
86	#13093948	—	2	2	no	—
87	#13093948	—	2	2	no	—
88	#13093946	—	2	2	no	—
89	#13093943	C₂×C₄	1	8	yes	complemented
90	#13093935	—	2	1	no	—
91	#13093934	—	2	2	no	—
92	#13093934	—	2	1	no	—
93	C₄×C₄₇⋊C₈	—	2	1	no	—
94	C₈×Dic₄₇	—	2	1	no	—
95	C₈×Dic₄₇	—	2	2	no	—
96	C₈×Dic₄₇	D₄	1	1	yes	characteristic
97	C₈×Dic₄₇	D₄	1	1	yes	characteristic
98	C₈×Dic₄₇	D₄	1	1	yes	characteristic
99	C₈×Dic₄₇	D₄	1	1	yes	characteristic
100	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₄₇	—	2	1	no	—
102	C₂×Q₁₆×C₄₇	—	2	1	no	—
103	C₂×Q₁₆×C₄₇	—	2	2	no	—
104	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
105	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
106	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	#117×C₄₇	C₂³	1	1	yes	characteristic
109	#108×C₄₇	—	2	2	no	—
110	#103×C₄₇	—	2	2	no	—
111	#103×C₄₇	—	2	2	no	—
112	#101×C₄₇	—	2	4	no	—
113	#97×C₄₇	—	2	1	no	—
114	C₄×C₈×C₄₇	—	2	1	no	—
115	C₂×Q₈×C₄₇	—	2	2	no	—
116	C₂×Q₈×C₄₇	—	2	2	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	2	no	—
120	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
123	C₂×C₂²⋊D₄₇	—	2	1	no	—
124	C₂²×Dic₄₇	—	2	2	no	—
125	C₂²×Dic₄₇	#41	1	1	yes	characteristic
126	C₂²×Dic₄₇	#41	1	1	yes	characteristic
127	#10625350	—	2	1	no	—
128	#10625350	—	2	1	no	—
129	#10625350	C₂²×C₄	1	2	yes	—
130	#10625350	#41	1	2	yes	—
131	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×D₄₇	—	2	1	no	—
133	C₂×C₄×D₄₇	—	2	1	no	—
134	C₂×C₄×D₄₇	—	2	1	no	—
135	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
136	Q₁₆×C₄₇	—	2	4	no	—
137	Q₁₆×C₄₇	—	2	4	no	—
138	M₁₆×C₄₇	—	2	1	no	—
139	M₁₆×C₄₇	—	2	2	no	—
140	M₁₆×C₄₇	—	2	2	no	—
141	M₁₆×C₄₇	#41	1	2	yes	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₄₇	#41	1	2	yes	—
148	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²⋊C₄×C₄₇	—	2	1	no	—
151	C₄²×C₄₇	—	2	1	no	—
152	#10625337	—	2	8	no	—
153	#10625336	—	2	8	no	—
154	(C₂×D₄₇)⋊C₄	—	2	1	no	—
155	(C₂×D₄₇)⋊C₄	—	2	1	no	—
156	C₄⋊Dic₄₇	—	2	2	no	—
157	C₄⋊Dic₄₇	—	2	2	no	—
158	C₄⋊Dic₄₇	—	4	2	no	—
159	C₄⋊Dic₄₇	—	4	2	no	—
160	Dic₄₇⋊C₄	—	2	1	no	—
161	Dic₄₇⋊C₄	—	2	1	no	—
162	C₄×Dic₄₇	—	2	1	no	—
163	C₄×Dic₄₇	—	2	1	no	—
164	C₄×Dic₄₇	—	4	2	no	—
165	C₄×Dic₄₇	—	4	2	no	—
166	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
167	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
168	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
169	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
170	#10625329	—	2	1	no	—
171	#10625329	—	2	2	no	—
172	#10625329	C₂²×C₄	1	2	yes	—
173	#10625329	C₂²×C₄	1	4	yes	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	—	2	2	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
179	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
180	#10625324	—	2	4	no	—
181	#10625324	—	2	4	no	—
182	C₈×D₄₇	—	2	4	no	—
183	C₈×D₄₇	—	2	4	no	—
184	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂²×D₄₇	—	2	1	no	—
186	Q₈×C₄₇	—	2	4	no	—
187	Q₈×C₄₇	—	2	4	no	—
188	Q₈×C₄₇	—	4	2	no	—
189	Q₈×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂²⋊D₄₇	—	2	2	no	—
202	C₂²⋊D₄₇	—	2	2	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	2	no	—
205	C₂×Dic₄₇	—	4	1	no	—
206	C₂×Dic₄₇	—	4	2	no	—
207	C₂×Dic₄₇	—	8	2	no	—
208	C₂×Dic₄₇	#121	1	1	yes	characteristic
209	C₂×Dic₄₇	#121	1	1	yes	characteristic
210	C₂×Dic₄₇	#121	1	1	yes	characteristic
211	C₂×Dic₄₇	#121	1	1	yes	characteristic
212	D₁₈₈	—	2	1	no	—
213	D₁₈₈	C₄×D₄	1	2	yes	—
214	C₄×D₄₇	—	2	2	no	—
215	C₄×D₄₇	—	2	2	no	—
216	C₄×D₄₇	—	4	2	no	—
217	C₄×D₄₇	—	4	2	no	—
218	Dic₉₄	—	2	1	no	—
219	Dic₉₄	C₄×D₄	1	2	yes	—
220	C₈×C₄₇	—	2	2	no	—
221	C₈×C₄₇	—	4	2	no	—
222	C₈×C₄₇	C₄×D₄	1	2	yes	—
223	C₈×C₄₇	C₄×D₄	1	2	yes	—
224	C₄₇⋊C₈	—	2	2	no	—
225	C₄₇⋊C₈	—	2	4	no	—
226	C₄₇⋊C₈	—	2	1	no	—
227	C₄₇⋊C₈	—	2	1	no	—
228	C₄×#473	—	47	1	no	maximal, Sylow
229	C₂²×C₄₇	—	2	1	no	—
230	C₂²×C₄₇	—	2	1	no	—
231	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
233	C₂²×C₄₇	#529	1	1	yes	characteristic
234	C₂×D₄₇	—	2	2	no	—
235	C₂×D₄₇	—	4	1	no	—
236	C₂×D₄₇	—	4	1	no	—
237	C₄×C₄₇	—	4	1	no	—
238	C₄×C₄₇	—	4	1	no	—
239	C₄×C₄₇	—	4	4	no	—
240	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
242	C₄×C₄₇	#525	1	1	yes	characteristic
243	C₄×C₄₇	#532	1	1	yes	characteristic
244	Dic₄₇	—	2	1	no	—
245	Dic₄₇	—	2	1	no	—
246	Dic₄₇	—	2	1	no	—
247	Dic₄₇	—	2	2	no	—
248	Dic₄₇	—	8	2	no	—
249	Dic₄₇	#473	1	2	yes	complemented
250	C₂×#473	—	47	1	no	—
251	C₄×#137	—	47	2	no	—
252	C₂×C₄×Q₁₆	—	47	1	no	—
253	C₄×#131	—	47	1	no	—
254	#1979	D₄₇	1	1	yes	characteristic, complemented
255	#1952	—	47	1	no	—
256	#1930	—	47	2	no	—
257	#1908	—	47	2	no	—
258	#1816	—	47	1	no	—
259	C₄×#108	—	47	1	no	—
260	C₄×#101	—	47	2	no	—
261	C₂×C₄₇	—	2	1	no	—
262	C₂×C₄₇	—	2	1	no	—
263	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
264	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
265	C₂×C₄₇	#3067	1	1	yes	characteristic
266	D₄₇	—	4	2	no	—
267	C₂×#137	—	47	2	no	—
268	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
269	C₂×#131	—	47	1	no	—
270	C₂×#131	—	47	1	no	—
271	C₄×#41	—	47	1	no	—
272	C₂×C₄×Q₈	—	47	2	no	—
273	#473	—	47	8	no	—
274	#441	—	94	2	no	—
275	#440	—	94	2	no	—
276	C₄×Q₁₆	—	94	1	no	—
277	C₄×Q₁₆	—	94	1	no	—
278	C₄×Q₁₆	—	94	1	no	—
279	C₄×Q₁₆	—	94	1	no	—
280	C₄×Q₁₆	—	94	2	no	—
281	C₄×SD₁₆	—	94	2	no	—
282	C₂×#108	—	47	1	no	—
283	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
284	#428	—	47	2	no	—
285	C₂×#107	—	47	1	no	—
286	#419	C₂×D₄₇	1	2	yes	—
287	#417	—	47	2	no	—
288	C₂×#103	—	47	2	no	—
289	C₂×#101	—	47	2	no	—
290	C₂×#101	C₂×D₄₇	1	2	yes	—
291	#405	—	47	1	no	—
292	#405	—	94	1	no	—
293	#405	—	94	1	no	—
294	#405	C₂×D₄₇	1	1	yes	characteristic
295	C₄×M₁₆	—	47	1	no	—
296	C₄×M₁₆	—	47	2	no	—
297	C₄×M₁₆	—	94	1	no	—
298	C₂×C₄×C₈	—	47	1	no	—
299	C₂×C₄×C₈	—	94	1	no	—
300	#343	—	47	2	no	—
301	#343	—	47	2	no	—
302	#341	—	47	2	no	—
303	C₄₇	C₄×#473	1	1	yes	characteristic, complemented, Sylow
304	C₂×#41	—	47	1	no	—
305	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
306	#137	—	47	8	no	—
307	#137	—	94	4	no	—
308	C₂×Q₁₆	—	2	1	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	94	2	no	—
312	C₂×Q₁₆	C₄×D₄₇	1	4	yes	complemented
313	C₂×SD₁₆	—	94	2	no	—
314	#131	—	47	4	no	—
315	#131	—	94	2	no	—
316	#131	—	94	2	no	—
317	#131	—	94	2	no	—
318	C₂×M₁₆	—	47	1	no	—
319	C₂×M₁₆	—	47	2	no	—
320	C₂×M₁₆	—	94	1	no	—
321	C₂×M₁₆	—	94	1	no	—
322	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
323	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
324	C₂²×C₈	—	47	1	no	—
325	C₂²×C₈	—	94	1	no	—
326	C₂²×C₈	—	94	1	no	—
327	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
328	C₄×Q₈	—	47	1	no	—
329	C₄×Q₈	—	47	1	no	—
330	C₄×Q₈	—	94	2	no	—
331	C₄×Q₈	—	94	2	no	—
332	C₄×Q₈	—	94	2	no	—
333	C₄×Q₈	—	94	2	no	—
334	C₄×D₄	—	47	1	no	—
335	C₄×D₄	—	47	1	no	—
336	C₄×D₄	—	94	1	no	—
337	C₄×D₄	—	94	1	no	—
338	#117	—	94	1	no	—
339	#117	C₂²×D₄₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	—	47	2	no	—
341	C₂×C₄⋊C₄	—	94	2	no	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	—	94	1	no	—
344	C₂×C₄²	—	94	2	no	—
345	#108	—	2	2	no	—
346	#108	—	47	4	no	—
347	#107	—	94	1	no	—
348	#107	—	94	1	no	—
349	#107	—	94	2	no	—
350	#106	—	94	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	94	2	no	—
354	#103	—	94	2	no	—
355	#103	—	94	2	no	—
356	#102	—	94	2	no	—
357	#101	—	2	4	no	—
358	#101	—	47	8	no	—
359	#97	—	2	1	no	—
360	#97	—	94	1	no	—
361	#97	—	94	1	no	—
362	#97	—	94	2	no	—
363	C₄×C₈	—	2	1	no	—
364	C₄×C₈	—	47	1	no	—
365	C₄×C₈	—	47	1	no	—
366	C₄×C₈	—	47	1	no	—
367	C₄×C₈	—	47	1	no	—
368	C₄×C₈	—	94	1	no	—
369	C₄×C₈	—	94	1	no	—
370	C₄×C₈	—	94	2	no	—
371	#41	—	47	2	no	—
372	#41	—	47	2	no	—
373	#41	—	94	1	no	—
374	#41	—	94	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	47	1	no	—
381	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
382	C₂×D₄	—	47	1	no	—
383	C₂×D₄	—	94	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	47	1	no	—
386	C₂²×C₄	—	47	1	no	—
387	C₂²×C₄	—	94	1	no	—
388	C₂²×C₄	—	94	1	no	—
389	C₂²×C₄	—	94	1	no	—
390	C₂²×C₄	—	94	2	no	—
391	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	Q₁₆	—	2	4	no	—
394	Q₁₆	—	94	8	no	—
395	SD₁₆	—	94	8	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	47	2	no	—
400	M₁₆	—	47	4	no	—
401	M₁₆	—	94	4	no	—
402	M₁₆	—	94	2	no	—
403	M₁₆	—	94	1	no	—
404	M₁₆	—	94	4	no	—
405	M₁₆	#10625352	1	2	yes	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	47	1	no	—
409	C₂×C₈	—	47	1	no	—
410	C₂×C₈	—	94	4	no	—
411	C₂×C₈	—	94	1	no	—
412	C₂×C₈	—	94	2	no	—
413	C₂×C₈	—	94	1	no	—
414	C₂×C₈	—	94	1	no	—
415	C₂×C₈	—	94	4	no	—
416	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
417	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
418	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
419	C₂×C₈	#10625352	1	2	yes	—
420	C₄⋊C₄	—	94	1	no	—
421	C₄⋊C₄	—	94	1	no	—
422	C₄⋊C₄	—	94	2	no	—
423	C₄⋊C₄	—	94	2	no	—
424	C₄⋊C₄	—	188	2	no	—
425	C₄⋊C₄	—	188	2	no	—
426	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
427	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	94	1	no	—
430	C₂²⋊C₄	—	94	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	47	1	no	—
433	C₄²	—	47	1	no	—
434	C₄²	—	47	1	no	—
435	C₄²	—	47	1	no	—
436	C₄²	—	94	1	no	—
437	C₄²	—	94	1	no	—
438	C₄²	—	188	2	no	—
439	C₄²	—	188	2	no	—
440	C₂³	—	94	1	no	—
441	C₂³	#41×D₄₇	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	47	2	no	—
447	Q₈	—	94	1	no	—
448	D₄	—	47	2	no	—
449	D₄	—	94	2	no	—
450	D₄	—	94	2	no	—
451	D₄	—	94	1	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	47	1	no	—
458	C₂×C₄	—	47	1	no	—
459	C₂×C₄	—	47	1	no	—
460	C₂×C₄	—	47	1	no	—
461	C₂×C₄	—	94	2	no	—
462	C₂×C₄	—	94	1	no	—
463	C₂×C₄	—	94	2	no	—
464	C₂×C₄	—	94	2	no	—
465	C₂×C₄	—	376	2	no	—
466	C₂×C₄	—	188	2	no	—
467	C₂×C₄	—	188	2	no	—
468	C₂×C₄	—	188	1	no	—
469	C₂×C₄	—	188	2	no	—
470	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
471	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
472	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
474	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
475	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
476	C₈	—	2	2	no	—
477	C₈	—	4	2	no	—
478	C₈	—	94	4	no	—
479	C₈	—	94	2	no	—
480	C₈	—	94	1	no	—
481	C₈	—	94	1	no	—
482	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
483	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	94	2	no	—
487	C₂²	—	188	1	no	—
488	C₂²	—	188	1	no	—
489	C₂²	C₄×#10625352	1	1	yes	characteristic
490	C₂²	#121×D₄₇	1	1	yes	characteristic
491	C₂²	#15689652	1	1	yes	characteristic
492	C₄	—	4	4	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	47	2	no	—
496	C₄	—	94	2	no	—
497	C₄	—	94	1	no	—
498	C₄	—	94	1	no	—
499	C₄	—	94	1	no	—
500	C₄	—	376	2	no	—
501	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
502	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
503	C₄	#15689633	1	1	yes	characteristic
504	C₄	#15689671	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	188	2	no	—
508	C₂	#20245904	1	1	yes	characteristic
509	C₂	#473×D₄₇	1	1	yes	characteristic
510	C₂	#20253110	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1979	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625350	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1979	D₄₇
hypocenter	C₄₇	C₄×#473
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1979

Complements

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

N	H ≅ G/N	type
3. C₂×Q₁₆×Dic₄₇	C₂	semidirect
5. #20244173	C₂	semidirect
6. #20244046	C₂	semidirect
9. #108×Dic₄₇	C₂	semidirect
10. #101×Dic₄₇	C₂	semidirect
11. C₄₇×#1979	C₂	semidirect
17. #15689395	C₄	semidirect
80. #13093960	C₂×C₄	semidirect
89. #13093943	C₂×C₄	semidirect
104. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
249. Dic₄₇	#473	semidirect
254. #1979	D₄₇	semidirect
303. C₄₇	C₄×#473	semidirect
312. C₂×Q₁₆	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689395	2
#20252203	2
C₂×Q₁₆×Dic₄₇	2
#20251810	2
#20244173	2
#20244046	2
#20243900	2
#20243449	2
#108×Dic₄₇	2
#101×Dic₄₇	2
C₄₇×#1979	2
C₄×#473	47