Subgroups — #26233872

Order 12032.

704 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252045	C₂	1	2	yes	maximal
2	#427×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243990	C₂	1	2	yes	maximal, complemented
5	#20243984	C₂	1	2	yes	maximal, complemented
6	#20243486	C₂	1	2	yes	maximal
7	#20243423	C₂	1	1	yes	maximal, characteristic
8	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	#117×D₄₇	C₂²	1	2	yes	—
14	#15689183	—	2	2	no	—
15	#15689183	—	2	2	no	—
16	#15689179	—	2	2	no	—
17	#15689175	—	2	2	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	#15689161	C₂²	1	1	yes	characteristic
20	#15689160	C₄	1	1	yes	characteristic, complemented
21	#15689160	C₄	1	1	yes	characteristic, complemented
22	#15689159	C₂²	1	2	yes	—
23	#15689158	C₄	1	2	yes	complemented
24	#107×D₄₇	C₄	1	1	yes	characteristic, complemented
25	#107×D₄₇	C₄	1	1	yes	characteristic, complemented
26	#106×D₄₇	C₄	1	2	yes	complemented
27	#15689150	C₂²	1	2	yes	—
28	#15689086	C₂²	1	2	yes	—
29	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
30	#15689081	C₂²	1	2	yes	—
31	#15689078	C₂²	1	2	yes	—
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
34	#15688887	C₂²	1	2	yes	—
35	#15688884	C₂²	1	2	yes	—
36	#15688883	C₂²	1	2	yes	—
37	#15688882	C₂²	1	2	yes	—
38	#15688878	C₂²	1	1	yes	characteristic
39	#15688877	C₂²	1	1	yes	characteristic
40	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#427	C₂²	1	1	yes	characteristic
42	C₄₇×#424	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#339	C₂²	1	2	yes	—
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂×#10625329	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
55	#13093983	C₂³	1	2	yes	—
56	#13093982	C₂×C₄	1	2	yes	—
57	#13093982	C₂×C₄	1	2	yes	—
58	#13093981	—	2	2	no	—
59	#13093980	—	2	2	no	—
60	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
61	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
63	C₂²⋊C₄×D₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₄²×D₄₇	—	2	2	no	—
66	#13093960	—	2	2	no	—
67	#13093958	C₂×C₄	1	1	yes	characteristic
68	#13093958	C₂×C₄	1	1	yes	characteristic
69	#13093957	C₂×C₄	1	2	yes	—
70	#13093957	C₂×C₄	1	2	yes	—
71	#13093956	C₂×C₄	1	2	yes	—
72	#13093955	C₂×C₄	1	2	yes	—
73	#13093955	C₂×C₄	1	2	yes	—
74	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	—	2	2	no	—
77	(C₂×D₄₇)⋊C₈	—	2	2	no	—
78	(C₂×D₄₇)⋊C₈	D₄	1	1	yes	characteristic
79	(C₂×D₄₇)⋊C₈	D₄	1	1	yes	characteristic
80	(C₂×D₄₇)⋊C₈	D₄	1	1	yes	characteristic
81	(C₂×D₄₇)⋊C₈	D₄	1	1	yes	characteristic
82	#13093934	—	2	2	no	—
83	#13093934	—	2	2	no	—
84	C₈×Dic₄₇	—	2	2	no	—
85	C₈×Dic₄₇	—	2	2	no	—
86	C₈×Dic₄₇	—	2	2	no	—
87	C₄₇⋊#95	—	2	1	no	—
88	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	#117×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#108×C₄₇	—	2	2	no	—
94	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
95	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
96	#106×C₄₇	C₂×C₄	1	2	yes	—
97	C₄⋊C₈×C₄₇	—	2	2	no	—
98	C₄⋊C₈×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	—	2	2	no	—
100	C₂³×D₄₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	2	1	no	—
104	C₂²×Dic₄₇	#41	1	1	yes	characteristic
105	C₂×C₄×D₄₇	—	2	1	no	—
106	C₂×C₄×D₄₇	—	2	1	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
115	M₁₆×C₄₇	—	2	2	no	—
116	M₁₆×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	#41	1	2	yes	—
125	C₂×C₈×C₄₇	#41	1	2	yes	—
126	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₂²⋊Dic₄₇	—	2	2	no	—
133	(C₂×D₄₇)⋊C₄	—	2	4	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	(C₂×D₄₇)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
138	Dic₄₇⋊C₄	—	2	2	no	—
139	Dic₄₇⋊C₄	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	#10625329	—	2	2	no	—
146	#10625329	—	2	2	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	—	2	2	no	—
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₈×D₄₇	—	2	2	no	—
157	C₈×D₄₇	—	2	2	no	—
158	C₈×D₄₇	—	2	2	no	—
159	C₈×D₄₇	—	2	2	no	—
160	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	—	2	1	no	—
163	C₂²×D₄₇	—	2	2	no	—
164	C₂²×D₄₇	—	4	1	no	—
165	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
166	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	4	1	no	—
184	C₂×Dic₄₇	—	4	1	no	—
185	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
187	C₄×D₄₇	—	2	1	no	—
188	C₄×D₄₇	—	2	1	no	—
189	C₄×D₄₇	—	2	1	no	—
190	C₄×D₄₇	—	2	1	no	—
191	C₄×D₄₇	—	2	1	no	—
192	C₄×D₄₇	—	2	1	no	—
193	C₄×D₄₇	—	2	1	no	—
194	C₄×D₄₇	—	2	1	no	—
195	C₄×D₄₇	—	4	4	no	—
196	C₄×D₄₇	—	8	2	no	—
197	C₈×C₄₇	—	2	1	no	—
198	C₈×C₄₇	—	2	1	no	—
199	C₈×C₄₇	—	4	2	no	—
200	C₈×C₄₇	#117	1	2	yes	—
201	C₈×C₄₇	#117	1	2	yes	—
202	C₄₇⋊C₈	—	2	1	no	—
203	C₄₇⋊C₈	—	2	1	no	—
204	C₄₇⋊C₈	—	2	1	no	—
205	C₄₇⋊C₈	—	2	1	no	—
206	C₄₇⋊C₈	—	4	2	no	—
207	#22606	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	1	no	—
210	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₄₇	#552	1	1	yes	characteristic
212	C₂²×C₄₇	#552	1	1	yes	characteristic
213	C₂×D₄₇	—	2	1	no	—
214	C₂×D₄₇	—	2	1	no	—
215	C₂×D₄₇	—	2	1	no	—
216	C₂×D₄₇	—	2	1	no	—
217	C₂×D₄₇	—	2	1	no	—
218	C₂×D₄₇	—	4	2	no	—
219	C₂×D₄₇	—	4	2	no	—
220	C₂×D₄₇	#443	1	2	yes	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
225	C₄×C₄₇	#519	1	1	yes	characteristic
226	C₄×C₄₇	#547	1	1	yes	characteristic
227	C₄×C₄₇	#547	1	1	yes	characteristic
228	Dic₄₇	—	2	1	no	—
229	Dic₄₇	—	2	1	no	—
230	Dic₄₇	—	4	2	no	—
231	Dic₄₇	—	4	2	no	—
232	Dic₄₇	—	4	2	no	—
233	#2924	—	47	2	no	—
234	C₂×#427	—	47	1	no	—
235	#1945	—	47	1	no	—
236	#1945	D₄₇	1	1	yes	characteristic, complemented
237	#1922	—	47	2	no	—
238	#1922	—	47	2	no	—
239	#1826	—	47	2	no	—
240	#1810	—	47	1	no	—
241	#1772	—	47	1	no	—
242	#1772	—	47	1	no	—
243	C₈×C₂²⋊C₄	—	47	1	no	—
244	C₂×C₄₇	—	2	1	no	—
245	C₂×C₄₇	—	2	1	no	—
246	C₂×C₄₇	#2344	1	1	yes	characteristic
247	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
248	C₂×C₄₇	#2957	1	1	yes	characteristic
249	D₄₇	—	2	2	no	—
250	D₄₇	—	4	1	no	—
251	C₂³×C₈	—	47	1	no	—
252	C₂×#117	—	47	2	no	—
253	#433	—	94	2	no	—
254	#433	—	94	2	no	—
255	#432	—	94	2	no	—
256	#431	—	94	2	no	—
257	C₂×#108	—	47	1	no	—
258	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
259	#427	—	47	1	no	—
260	#427	—	47	2	no	—
261	#427	—	47	1	no	—
262	#427	—	47	1	no	—
263	#427	—	47	2	no	—
264	#427	C₂×D₄₇	1	1	yes	characteristic
265	C₂×#107	—	47	1	no	—
266	C₂×#107	—	47	1	no	—
267	C₂×#106	—	47	2	no	—
268	#424	—	47	2	no	—
269	#424	C₂×D₄₇	1	2	yes	—
270	#407	—	47	2	no	—
271	C₂×C₂²⋊C₈	—	47	1	no	—
272	#405	—	47	2	no	—
273	#405	—	47	2	no	—
274	C₂×C₄×C₈	—	47	1	no	—
275	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
276	C₄×C₂²⋊C₄	—	47	1	no	—
277	#341	—	47	2	no	—
278	#339	—	47	2	no	—
279	#339	—	47	2	no	—
280	#339	—	47	2	no	—
281	#339	C₂×D₄₇	1	2	yes	—
282	#336	—	47	1	no	—
283	#336	—	47	1	no	—
284	C₄₇	#22606	1	1	yes	characteristic, complemented, Sylow
285	C₂³×C₄	—	47	1	no	—
286	C₂×M₁₆	—	47	2	no	—
287	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
288	C₂²×C₈	—	47	1	no	—
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	1	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	94	2	no	—
295	C₂²×C₈	—	94	2	no	—
296	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	#117	—	47	2	no	—
299	#117	—	47	2	no	—
300	#117	—	47	2	no	—
301	#117	—	94	2	no	—
302	#117	—	94	2	no	—
303	#117	C₂²×D₄₇	1	2	yes	—
304	C₂×C₄⋊C₄	—	47	2	no	—
305	C₂×C₄⋊C₄	—	47	2	no	—
306	C₂×C₂²⋊C₄	—	94	2	no	—
307	C₂×C₂²⋊C₄	—	94	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	—	94	2	no	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	#108	—	2	2	no	—
312	#108	—	94	2	no	—
313	#107	—	47	1	no	—
314	#107	—	47	1	no	—
315	#107	—	47	2	no	—
316	#107	—	47	2	no	—
317	#107	C₄×D₄₇	1	1	yes	characteristic
318	#107	C₄×D₄₇	1	1	yes	characteristic
319	#106	—	47	2	no	—
320	#106	—	47	2	no	—
321	#106	—	47	2	no	—
322	#106	C₄×D₄₇	1	2	yes	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	94	2	no	—
326	C₄⋊C₈	—	94	2	no	—
327	C₂²⋊C₈	—	47	1	no	—
328	C₂²⋊C₈	—	47	1	no	—
329	C₂²⋊C₈	—	47	1	no	—
330	C₂²⋊C₈	—	47	1	no	—
331	C₂²⋊C₈	—	94	2	no	—
332	C₂²⋊C₈	—	94	2	no	—
333	#97	—	94	2	no	—
334	#97	—	94	2	no	—
335	C₄×C₈	—	2	2	no	—
336	C₄×C₈	—	94	2	no	—
337	C₄×C₈	—	94	2	no	—
338	C₄×C₈	—	94	2	no	—
339	#95	—	94	1	no	—
340	C₂⁴	—	47	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	47	1	no	—
344	C₂²×C₄	—	47	1	no	—
345	C₂²×C₄	—	47	1	no	—
346	C₂²×C₄	—	47	1	no	—
347	C₂²×C₄	—	94	2	no	—
348	C₂²×C₄	—	94	2	no	—
349	C₂²×C₄	—	94	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	C₂³×D₄₇	1	1	yes	characteristic
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	94	2	no	—
358	M₁₆	—	94	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	47	1	no	—
363	C₂×C₈	—	47	1	no	—
364	C₂×C₈	—	47	1	no	—
365	C₂×C₈	—	47	1	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	2	no	—
375	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
377	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
378	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
379	C₂×C₈	#10625352	1	2	yes	—
380	C₂×C₈	#10625354	1	2	yes	—
381	C₄⋊C₄	—	47	2	no	—
382	C₄⋊C₄	—	47	2	no	—
383	C₄⋊C₄	—	94	2	no	—
384	C₄⋊C₄	—	94	2	no	—
385	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
386	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	94	2	no	—
389	C₂²⋊C₄	—	94	2	no	—
390	C₂²⋊C₄	—	94	4	no	—
391	C₂²⋊C₄	—	94	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	94	2	no	—
396	C₄²	—	94	2	no	—
397	C₄²	—	94	2	no	—
398	C₄²	—	94	1	no	—
399	C₄²	—	94	1	no	—
400	C₂³	—	47	1	no	—
401	C₂³	—	47	1	no	—
402	C₂³	—	94	2	no	—
403	C₂³	—	94	1	no	—
404	C₂³	—	94	1	no	—
405	C₂³	—	188	1	no	—
406	C₂³	#41×D₄₇	1	1	yes	characteristic
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	47	1	no	—
413	C₂×C₄	—	47	1	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	1	no	—
418	C₂×C₄	—	94	1	no	—
419	C₂×C₄	—	94	1	no	—
420	C₂×C₄	—	94	1	no	—
421	C₂×C₄	—	94	1	no	—
422	C₂×C₄	—	94	1	no	—
423	C₂×C₄	—	94	1	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	376	2	no	—
428	C₂×C₄	—	188	4	no	—
429	C₂×C₄	—	188	1	no	—
430	C₂×C₄	—	188	1	no	—
431	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
434	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
435	C₂×C₄	#13094071	1	1	yes	characteristic
436	C₂×C₄	#13094072	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	94	1	no	—
441	C₈	—	94	1	no	—
442	C₈	—	94	1	no	—
443	C₈	—	94	1	no	—
444	C₈	—	188	2	no	—
445	C₈	#13093982	1	2	yes	—
446	C₈	#13093982	1	2	yes	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	47	2	no	—
450	C₂²	—	94	1	no	—
451	C₂²	—	94	1	no	—
452	C₂²	—	94	1	no	—
453	C₂²	—	94	1	no	—
454	C₂²	—	94	1	no	—
455	C₂²	—	188	2	no	—
456	C₂²	—	188	2	no	—
457	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
458	C₂²	#15689807	1	1	yes	characteristic
459	C₂²	#15689811	1	1	yes	characteristic
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	94	1	no	—
464	C₄	—	94	1	no	—
465	C₄	—	188	2	no	—
466	C₄	—	188	2	no	—
467	C₄	—	188	2	no	—
468	C₄	C₂×#13093982	1	1	yes	characteristic
469	C₄	#15689599	1	1	yes	characteristic
470	C₄	#15689773	1	1	yes	characteristic
471	C₄	#15689776	1	1	yes	characteristic
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	94	2	no	—
475	C₂	—	188	1	no	—
476	C₂	#20246256	1	1	yes	characteristic
477	C₂	#443×D₄₇	1	1	yes	characteristic
478	C₂	#20252300	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1945	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1945	D₄₇
hypocenter	C₄₇	#22606
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1945

Complements

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

N	H ≅ G/N	type
3. #20244137	C₂	semidirect
4. #20243990	C₂	semidirect
5. #20243984	C₂	semidirect
8. #20243270	C₂	semidirect
9. #20243267	C₂	semidirect
11. C₄₇×#1945	C₂	semidirect
20. #15689160	C₄	semidirect
21. #15689160	C₄	semidirect
23. #15689158	C₄	semidirect
24. #107×D₄₇	C₄	semidirect
25. #107×D₄₇	C₄	semidirect
26. #106×D₄₇	C₄	semidirect
236. #1945	D₄₇	semidirect
284. C₄₇	#22606	semidirect

Maximal subgroups

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

subgroup	index
#20252045	2
#427×D₄₇	2
#20244137	2
#20243990	2
#20243984	2
#20243486	2
#20243423	2
#20243270	2
#20243267	2
C₈×(C₂×D₄₇)⋊C₄	2
C₄₇×#1945	2
#22606	47