Subgroups — #26222816

Order 12032.

954 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689361	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
3	#20246064	C₂	1	2	yes	maximal
4	#20244250	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244119	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244075	C₂	1	2	yes	maximal, complemented
7	#20243818	C₂	1	2	yes	maximal
8	#20243414	C₂	1	1	yes	maximal, characteristic
9	C₄×#13093958	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243218	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13094000	C₂²	1	2	yes	—
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	#15689361	C₄	1	8	yes	complemented
17	C₂×#13093958	C₂²	1	1	yes	characteristic
18	C₂×#13093958	C₂²	1	1	yes	characteristic
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093948	C₂²	1	2	yes	—
21	#15689077	—	2	4	no	—
22	C₂×#13093935	C₂²	1	1	yes	characteristic
23	C₂×#13093934	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15689030	C₂²	1	2	yes	—
26	#15689019	C₂²	1	2	yes	—
27	#15689018	—	2	2	no	—
28	#15689014	—	2	2	no	—
29	#15689013	—	2	2	no	—
30	#15689007	—	2	2	no	—
31	#15688980	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	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄×Q₁₆×C₄₇	—	2	4	no	—
39	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
43	C₂×#10625324	—	2	2	no	—
44	C₂×#10625324	—	2	2	no	—
45	C₂×#10625324	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₈×D₄₇	—	2	2	no	—
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
51	#13094000	—	2	4	no	—
52	#13094000	C₂×C₄	1	8	yes	—
53	#13093981	—	2	2	no	—
54	#13093981	—	2	2	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×Dic₄₇⋊C₄	—	2	2	no	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	D₄	1	1	yes	characteristic
61	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
64	C₂×(C₂×D₄₇)⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	#13093958	—	2	2	no	—
68	#13093958	C₂×C₄	1	4	yes	—
69	#13093948	—	2	4	no	—
70	#13093948	C₂×C₄	1	8	yes	—
71	#13093935	—	2	2	no	—
72	#13093934	—	2	2	no	—
73	C₈×Dic₄₇	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₄₇⋊#95	—	2	2	no	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₄₇	—	2	2	no	—
81	C₂×Q₁₆×C₄₇	—	2	2	no	—
82	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₄₇	—	2	4	no	—
86	C₄×Q₈×C₄₇	—	2	4	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	—	2	2	no	—
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	#107×C₄₇	—	2	2	no	—
92	#103×C₄₇	—	2	4	no	—
93	C₄×C₈×C₄₇	D₄	1	4	yes	—
94	C₂³×D₄₇	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	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₄×D₄₇	#41	1	2	yes	—
117	Q₁₆×C₄₇	—	2	8	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	#41	1	2	yes	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	4	4	no	—
127	C₄²×C₄₇	—	4	4	no	—
128	C₄²×C₄₇	C₂×D₄	1	2	yes	—
129	C₄²×C₄₇	#41	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	—	2	8	no	—
131	(C₂×D₄₇)⋊C₄	—	2	2	no	—
132	(C₂×D₄₇)⋊C₄	—	2	2	no	—
133	(C₂×D₄₇)⋊C₄	—	8	2	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
138	Dic₄₇⋊C₄	—	2	2	no	—
139	Dic₄₇⋊C₄	—	2	2	no	—
140	Dic₄₇⋊C₄	—	2	8	no	—
141	Dic₄₇⋊C₄	—	8	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	8	2	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	#41	1	2	yes	—
151	#10625324	—	2	8	no	—
152	C₈×D₄₇	—	2	8	no	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂²×D₄₇	—	2	1	no	—
155	C₂²×D₄₇	—	2	1	no	—
156	C₂²×D₄₇	—	2	1	no	—
157	C₂²×D₄₇	—	2	1	no	—
158	C₂²×D₄₇	—	2	1	no	—
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	C₄×D₄	1	2	yes	—
161	Q₈×C₄₇	—	2	4	no	—
162	Q₈×C₄₇	—	2	4	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	4	2	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	#121	1	2	yes	—
176	C₂×C₄×C₄₇	#121	1	2	yes	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	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×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	4	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	2	no	—
195	C₂×Dic₄₇	—	4	2	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
198	C₄×D₄₇	—	2	2	no	—
199	C₄×D₄₇	—	2	2	no	—
200	C₄×D₄₇	—	2	2	no	—
201	C₄×D₄₇	—	2	2	no	—
202	C₈×C₄₇	—	2	2	no	—
203	C₈×C₄₇	C₄×D₄	1	4	yes	—
204	C₄₇⋊C₈	—	2	2	no	—
205	C₄₇⋊C₈	—	2	2	no	—
206	#21525	—	47	1	no	maximal, Sylow
207	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
209	C₂²×C₄₇	#532	1	1	yes	characteristic
210	C₂²×C₄₇	#576	1	1	yes	characteristic
211	C₂²×C₄₇	#578	1	1	yes	characteristic
212	C₂²×C₄₇	#578	1	1	yes	characteristic
213	C₂²×C₄₇	#578	1	1	yes	characteristic
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	—	2	2	no	—
216	C₂×D₄₇	—	2	2	no	—
217	C₂×D₄₇	—	4	1	no	—
218	C₂×D₄₇	—	4	1	no	—
219	C₂×D₄₇	—	4	1	no	—
220	C₂×D₄₇	—	4	1	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	2	2	no	—
223	C₄×C₄₇	—	4	4	no	—
224	C₄×C₄₇	—	8	2	no	—
225	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
227	C₄×C₄₇	#525	1	1	yes	characteristic
228	C₄×C₄₇	#529	1	1	yes	characteristic
229	Dic₄₇	—	2	2	no	—
230	Dic₄₇	—	4	4	no	—
231	Dic₄₇	—	4	1	no	—
232	Dic₄₇	—	4	1	no	—
233	Dic₄₇	—	8	2	no	—
234	C₂×#467	—	47	1	no	—
235	C₂×C₄×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
236	C₂×#405	—	47	1	no	—
237	#2323	—	47	2	no	—
238	#1969	—	47	1	no	—
239	#1942	—	47	1	no	—
240	#1935	—	47	2	no	—
241	#1894	—	47	2	no	—
242	#1808	—	47	1	no	—
243	C₄×#107	—	47	1	no	—
244	#1763	—	47	2	no	—
245	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
246	C₂×C₄₇	#2950	1	1	yes	characteristic
247	C₂×C₄₇	#2951	1	1	yes	characteristic
248	C₂×C₄₇	#3059	1	1	yes	characteristic
249	C₂×C₄₇	#3061	1	1	yes	characteristic
250	C₂×C₄₇	#3175	1	1	yes	characteristic
251	C₂×C₄₇	#3177	1	1	yes	characteristic
252	D₄₇	—	4	2	no	—
253	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
254	C₂²×M₁₆	—	47	1	no	—
255	C₂³×C₈	—	47	1	no	—
256	C₂×C₂²⋊Q₈	—	47	2	no	—
257	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
258	C₂×#117	—	47	1	no	—
259	#467	—	47	8	no	—
260	C₄×Q₁₆	—	2	4	no	—
261	C₂×#107	—	47	1	no	—
262	C₂×#107	—	47	1	no	—
263	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
264	C₂×#103	—	47	2	no	—
265	C₂×#103	—	47	2	no	—
266	C₂×#103	C₂×D₄₇	1	2	yes	—
267	#405	—	94	4	no	—
268	C₂×#97	—	47	1	no	—
269	C₂×#97	—	47	1	no	—
270	C₂×C₄×C₈	—	47	1	no	—
271	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
272	#391	—	47	2	no	—
273	#389	—	47	2	no	—
274	#389	—	94	2	no	—
275	#388	—	94	2	no	—
276	#388	—	94	2	no	—
277	#387	—	94	2	no	—
278	#380	—	47	2	no	—
279	C₄×C₄⋊C₄	—	47	2	no	—
280	#340	—	47	2	no	—
281	#340	—	47	2	no	—
282	#340	—	47	2	no	—
283	C₄₇	#21525	1	1	yes	characteristic, complemented, Sylow
284	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
285	C₂³×C₄	—	47	1	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	C₄×D₄₇	1	4	yes	—
289	C₂×M₁₆	—	94	2	no	—
290	C₂×M₁₆	—	94	2	no	—
291	C₂×M₁₆	—	94	2	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	47	4	no	—
295	C₂²×C₈	—	94	2	no	—
296	C₂²×C₈	—	94	2	no	—
297	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₂²⋊Q₈	—	47	8	no	—
300	C₂²⋊Q₈	—	94	4	no	—
301	C₄×Q₈	—	2	4	no	—
302	C₄×Q₈	—	2	4	no	—
303	#117	—	94	2	no	—
304	#117	—	94	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	47	2	no	—
307	C₂×C₄⋊C₄	—	47	1	no	—
308	C₂×C₄⋊C₄	—	47	1	no	—
309	C₂×C₄⋊C₄	—	47	2	no	—
310	C₂×C₄⋊C₄	—	94	2	no	—
311	C₂×C₄⋊C₄	—	94	2	no	—
312	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
313	C₂×C₂²⋊C₄	—	47	1	no	—
314	C₂×C₂²⋊C₄	—	47	1	no	—
315	C₂×C₂²⋊C₄	—	94	2	no	—
316	C₂×C₂²⋊C₄	—	94	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	94	2	no	—
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	#107	—	47	4	no	—
323	#107	—	94	2	no	—
324	#103	—	2	4	no	—
325	#103	—	47	8	no	—
326	#103	—	94	4	no	—
327	#97	—	94	2	no	—
328	#97	—	94	2	no	—
329	C₄×C₈	—	94	2	no	—
330	C₄×C₈	C₂²⋊D₄₇	1	4	yes	—
331	#95	—	94	2	no	—
332	#95	—	94	2	no	—
333	#95	—	94	2	no	—
334	#95	—	94	2	no	—
335	#95	—	94	2	no	—
336	C₂⁴	—	47	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	47	1	no	—
346	C₂²×C₄	—	47	2	no	—
347	C₂²×C₄	—	47	2	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	1	no	—
350	C₂²×C₄	—	94	1	no	—
351	C₂²×C₄	—	94	1	no	—
352	C₂²×C₄	—	94	1	no	—
353	C₂²×C₄	—	94	1	no	—
354	C₂²×C₄	—	94	2	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
357	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
358	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
359	Q₁₆	—	2	8	no	—
360	M₁₆	—	94	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	47	2	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	8	no	—
370	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
371	C₂×C₈	#10625350	1	2	yes	—
372	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
373	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	47	4	no	—
378	C₄⋊C₄	—	94	8	no	—
379	C₄⋊C₄	—	94	2	no	—
380	C₄⋊C₄	—	94	2	no	—
381	C₄⋊C₄	—	94	2	no	—
382	C₄⋊C₄	—	94	2	no	—
383	C₄⋊C₄	—	94	2	no	—
384	C₄⋊C₄	—	376	2	no	—
385	C₂²⋊C₄	—	94	8	no	—
386	C₂²⋊C₄	—	94	2	no	—
387	C₂²⋊C₄	—	94	2	no	—
388	C₂²⋊C₄	—	376	2	no	—
389	C₄²	—	4	4	no	—
390	C₄²	—	94	1	no	—
391	C₄²	—	94	1	no	—
392	C₄²	—	376	2	no	—
393	C₄²	#10625352	1	2	yes	—
394	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
395	C₂³	—	47	2	no	—
396	C₂³	—	94	1	no	—
397	C₂³	—	94	1	no	—
398	C₂³	—	94	1	no	—
399	C₂³	—	94	1	no	—
400	C₂³	—	94	1	no	—
401	C₂³	—	94	1	no	—
402	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	47	2	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	4	no	—
425	C₂×C₄	—	94	1	no	—
426	C₂×C₄	—	94	1	no	—
427	C₂×C₄	—	94	1	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	94	1	no	—
430	C₂×C₄	—	94	1	no	—
431	C₂×C₄	—	188	2	no	—
432	C₂×C₄	—	188	2	no	—
433	C₂×C₄	—	188	2	no	—
434	C₂×C₄	—	188	2	no	—
435	C₂×C₄	—	188	2	no	—
436	C₂×C₄	#13093995	1	2	yes	—
437	C₂×C₄	#13093995	1	2	yes	—
438	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
440	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
441	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
443	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	94	2	no	—
446	C₈	—	94	2	no	—
447	C₈	C₄×C₂²⋊D₄₇	1	4	yes	—
448	C₂²	—	94	2	no	—
449	C₂²	—	94	2	no	—
450	C₂²	—	94	2	no	—
451	C₂²	—	188	1	no	—
452	C₂²	—	188	1	no	—
453	C₂²	—	188	1	no	—
454	C₂²	—	188	1	no	—
455	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
456	C₂²	C₂×#13093995	1	1	yes	characteristic
457	C₂²	#15689670	1	1	yes	characteristic
458	C₂²	#15689925	1	1	yes	characteristic
459	C₂²	#15689936	1	1	yes	characteristic
460	C₂²	#15689936	1	1	yes	characteristic
461	C₂²	#15689937	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	4	no	—
465	C₄	—	8	2	no	—
466	C₄	—	94	2	no	—
467	C₄	—	376	2	no	—
468	C₄	—	188	4	no	—
469	C₄	—	188	1	no	—
470	C₄	—	188	1	no	—
471	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₄	C₄×#10625352	1	1	yes	characteristic
473	C₄	#15689630	1	1	yes	characteristic
474	C₄	#15689655	1	1	yes	characteristic
475	C₂	—	188	2	no	—
476	C₂	C₄×#13093995	1	1	yes	characteristic
477	C₂	#20252251	1	1	yes	characteristic
478	C₂	#20252263	1	1	yes	characteristic
479	C₂	#20253039	1	1	yes	characteristic
480	C₂	#20253054	1	1	yes	characteristic
481	C₂	#20254029	1	1	yes	characteristic
482	C₂	#20254043	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×Q₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#21525
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #20244250	C₂	semidirect
5. #20244119	C₂	semidirect
6. #20244075	C₂	semidirect
9. C₄×#13093958	C₂	semidirect
10. #20243218	C₂	semidirect
11. C₂×C₄×Q₁₆×C₄₇	C₂	semidirect
16. #15689361	C₄	semidirect
235. C₂×C₄×Q₁₆	D₄₇	semidirect
283. C₄₇	#21525	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689361	2
C₂×#15689077	2
#20246064	2
#20244250	2
#20244119	2
#20244075	2
#20243818	2
#20243414	2
C₄×#13093958	2
#20243218	2
C₂×C₄×Q₁₆×C₄₇	2
#21525	47