Subgroups — #26222971

Order 12032.

954 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689081	C₂	1	1	yes	maximal, characteristic
3	#20246072	C₂	1	2	yes	maximal
4	#20244260	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244132	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244066	C₂	1	2	yes	maximal, complemented
7	#20243812	C₂	1	2	yes	maximal
8	#20243421	C₂	1	1	yes	maximal, characteristic
9	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243220	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#470	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂×#13093983	C₂²	1	1	yes	characteristic
15	Q₁₆×Dic₄₇	—	2	4	no	—
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	#15689081	—	2	4	no	—
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15689030	C₂²	1	2	yes	—
26	#15689022	—	2	2	no	—
27	#15689022	C₂²	1	2	yes	—
28	#15689016	—	2	2	no	—
29	#15689016	—	2	2	no	—
30	#15689009	—	2	2	no	—
31	#15688983	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#470	C₄	1	8	yes	complemented
40	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₄₇	C₂²	1	2	yes	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	Q₈×Dic₄₇	—	2	4	no	—
48	Q₈×Dic₄₇	—	2	4	no	—
49	#13093983	—	2	2	no	—
50	#13093983	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
58	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
59	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	2	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	#13093958	—	2	2	no	—
65	#13093956	—	2	2	no	—
66	#13093948	—	2	4	no	—
67	#13093948	—	2	4	no	—
68	#13093934	—	2	2	no	—
69	#13093934	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	D₄	1	4	yes	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×Q₁₆×C₄₇	—	2	2	no	—
80	C₂×Q₁₆×C₄₇	—	2	2	no	—
81	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
82	C₂×M₁₆×C₄₇	—	2	2	no	—
83	C₂×M₁₆×C₄₇	—	2	2	no	—
84	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²⋊Q₈×C₄₇	—	2	4	no	—
88	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
89	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	#106×C₄₇	C₂×C₄	1	4	yes	—
93	#103×C₄₇	C₂×C₄	1	8	yes	—
94	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	2	no	—
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
117	Q₁₆×C₄₇	—	2	8	no	—
118	M₁₆×C₄₇	—	2	8	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₇	#41	1	2	yes	—
125	C₄⋊C₄×C₄₇	—	2	8	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
128	C₂²⋊C₄×C₄₇	—	2	8	no	—
129	C₂²⋊Dic₄₇	—	2	2	no	—
130	C₂²⋊Dic₄₇	—	2	2	no	—
131	C₂²⋊Dic₄₇	—	8	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	4	4	no	—
139	C₄⋊Dic₄₇	—	8	2	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	—	4	4	no	—
143	C₄×Dic₄₇	—	8	2	no	—
144	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
145	C₄×Dic₄₇	#41	1	2	yes	—
146	C₂×C₄₇⋊C₈	—	2	8	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	#41	1	2	yes	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	C₄×D₄	1	2	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₇	—	2	4	no	—
160	Q₈×C₄₇	—	2	4	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	4	2	no	—
189	C₂×Dic₄₇	—	4	2	no	—
190	C₂×Dic₄₇	—	4	2	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	#121	1	2	yes	—
195	C₂×Dic₄₇	#121	1	2	yes	—
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	C₄×D₄	1	4	yes	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	#21537	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	1	no	—
205	C₂²×C₄₇	—	4	1	no	—
206	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
208	C₂²×C₄₇	#532	1	1	yes	characteristic
209	C₂²×C₄₇	#577	1	2	yes	—
210	C₂²×C₄₇	#578	1	2	yes	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
216	C₄×C₄₇	#525	1	1	yes	characteristic
217	C₄×C₄₇	#529	1	1	yes	characteristic
218	Dic₄₇	—	2	2	no	—
219	Dic₄₇	—	2	2	no	—
220	Dic₄₇	—	4	1	no	—
221	Dic₄₇	—	4	1	no	—
222	Dic₄₇	—	8	2	no	—
223	Dic₄₇	—	8	2	no	—
224	C₂×#470	D₄₇	1	1	yes	characteristic
225	C₂×C₄×Q₁₆	—	47	1	no	—
226	C₂×#405	—	47	1	no	—
227	#2323	—	47	2	no	—
228	#1971	—	47	1	no	—
229	#1944	—	47	1	no	—
230	#1933	—	47	2	no	—
231	#1892	—	47	2	no	—
232	#1809	—	47	1	no	—
233	C₄×#106	—	47	1	no	—
234	#1763	—	47	2	no	—
235	C₂×C₄₇	—	4	2	no	—
236	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
237	C₂×C₄₇	#2947	1	2	yes	—
238	C₂×C₄₇	#3059	1	1	yes	characteristic
239	C₂×C₄₇	#3060	1	1	yes	characteristic
240	C₂×C₄₇	#3178	1	2	yes	—
241	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
242	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
243	C₂³×C₈	—	47	1	no	—
244	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
245	C₂×C₄×Q₈	—	47	2	no	—
246	C₂×#117	—	47	1	no	—
247	#470	Dic₄₇	1	8	yes	complemented
248	C₄×Q₁₆	—	94	4	no	—
249	C₂×#107	—	47	1	no	—
250	C₂×#106	—	47	1	no	—
251	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
252	C₂×#103	—	47	2	no	—
253	C₂×#103	—	47	2	no	—
254	C₂×#103	C₂×D₄₇	1	2	yes	—
255	#405	—	94	4	no	—
256	C₂×#97	—	47	1	no	—
257	C₂×#97	—	47	1	no	—
258	C₂×C₄×C₈	—	47	1	no	—
259	C₂×C₄×C₈	—	47	1	no	—
260	#391	—	47	2	no	—
261	#389	—	47	2	no	—
262	#389	—	94	2	no	—
263	#388	—	94	2	no	—
264	#388	—	94	2	no	—
265	#387	—	94	2	no	—
266	#380	—	47	2	no	—
267	C₄×C₄⋊C₄	—	47	2	no	—
268	#340	—	47	2	no	—
269	#340	—	47	2	no	—
270	#340	—	47	2	no	—
271	C₄₇	#21537	1	1	yes	characteristic, complemented, Sylow
272	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
273	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
280	C₂²×C₈	—	47	1	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	94	2	no	—
283	C₂²×C₈	—	94	2	no	—
284	C₂²×C₈	—	94	2	no	—
285	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
289	C₄×Q₈	—	94	4	no	—
290	C₄×Q₈	—	94	4	no	—
291	#117	—	94	2	no	—
292	#117	—	94	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	47	1	no	—
296	C₂×C₄⋊C₄	—	47	2	no	—
297	C₂×C₄⋊C₄	—	47	2	no	—
298	C₂×C₄⋊C₄	—	94	2	no	—
299	C₂×C₄⋊C₄	—	94	2	no	—
300	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	47	1	no	—
303	C₂×C₂²⋊C₄	—	47	1	no	—
304	C₂×C₂²⋊C₄	—	94	2	no	—
305	C₂×C₄²	—	47	1	no	—
306	C₂×C₄²	—	47	1	no	—
307	C₂×C₄²	—	94	2	no	—
308	C₂×C₄²	—	94	2	no	—
309	#107	—	94	2	no	—
310	#106	—	94	2	no	—
311	#106	C₂×Dic₄₇	1	4	yes	—
312	#103	—	94	4	no	—
313	#103	—	94	4	no	—
314	#103	C₂×Dic₄₇	1	8	yes	—
315	#97	—	94	2	no	—
316	#97	—	94	2	no	—
317	C₄×C₈	—	47	4	no	—
318	C₄×C₈	—	94	2	no	—
319	#95	—	94	2	no	—
320	#95	—	94	2	no	—
321	#95	—	94	2	no	—
322	#95	—	94	2	no	—
323	#95	—	94	2	no	—
324	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	47	1	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	1	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	—	94	2	no	—
343	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
344	C₂²×C₄	#10625352	1	2	yes	—
345	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
346	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
347	Q₁₆	—	2	8	no	—
348	M₁₆	—	2	8	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	47	2	no	—
352	C₂×C₈	—	47	2	no	—
353	C₂×C₈	—	94	8	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	94	1	no	—
358	C₂×C₈	D₄×D₄₇	1	2	yes	—
359	C₂×C₈	#10625352	1	2	yes	—
360	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
361	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	94	2	no	—
365	C₄⋊C₄	—	94	2	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	376	2	no	—
371	C₄⋊C₄	—	188	4	no	—
372	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	94	2	no	—
375	C₂²⋊C₄	—	94	2	no	—
376	C₂²⋊C₄	—	376	2	no	—
377	C₄²	—	47	2	no	—
378	C₄²	—	47	2	no	—
379	C₄²	—	94	1	no	—
380	C₄²	—	94	1	no	—
381	C₄²	—	376	2	no	—
382	C₄²	—	188	4	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	D₄×Dic₄₇	1	2	yes	—
388	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	47	2	no	—
406	C₂×C₄	—	47	2	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	2	no	—
417	C₂×C₄	—	188	2	no	—
418	C₂×C₄	—	188	2	no	—
419	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
420	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
422	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
423	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
425	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	94	2	no	—
428	C₈	—	94	2	no	—
429	C₈	D₄×Dic₄₇	1	4	yes	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
436	C₂²	#121×D₄₇	1	1	yes	characteristic
437	C₂²	#15689668	1	1	yes	characteristic
438	C₂²	#15689932	1	2	yes	—
439	C₂²	#15689939	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	4	no	—
443	C₄	—	94	2	no	—
444	C₄	—	94	2	no	—
445	C₄	—	376	2	no	—
446	C₄	—	376	2	no	—
447	C₄	—	188	1	no	—
448	C₄	—	188	1	no	—
449	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
450	C₄	#41×Dic₄₇	1	1	yes	characteristic
451	C₄	#15689633	1	1	yes	characteristic
452	C₄	#15689654	1	1	yes	characteristic
453	C₂	—	4	2	no	—
454	C₂	#121×Dic₄₇	1	1	yes	characteristic
455	C₂	#20252232	1	2	yes	—
456	C₂	#20253041	1	1	yes	characteristic
457	C₂	#20253052	1	1	yes	characteristic
458	C₂	#20254057	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#470	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#470	D₄₇
hypocenter	C₄₇	#21537
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#470

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×Dic₄₇	C₂	semidirect
4. #20244260	C₂	semidirect
5. #20244132	C₂	semidirect
6. #20244066	C₂	semidirect
9. #106×Dic₄₇	C₂	semidirect
10. #20243220	C₂	semidirect
39. C₄₇×#470	C₄	semidirect
247. #470	Dic₄₇	semidirect
271. C₄₇	#21537	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×Dic₄₇	2
C₂×#15689081	2
#20246072	2
#20244260	2
#20244132	2
#20244066	2
#20243812	2
#20243421	2
#106×Dic₄₇	2
#20243220	2
C₂×C₄₇×#470	2
#21537	47