Subgroups — #26223049

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252965	C₂	1	1	yes	maximal, characteristic
2	#20252080	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244277	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244134	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244089	C₂	1	2	yes	maximal, complemented
7	#20243828	C₂	1	2	yes	maximal, complemented
8	#20243423	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243223	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	#15689630	C₂²	1	2	yes	—
15	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
16	#15689361	C₄	1	2	yes	complemented
17	#15689356	C₄	1	2	yes	complemented
18	#15689349	C₄	1	4	yes	complemented
19	#15689192	—	2	4	no	—
20	C₈×C₂²⋊D₄₇	—	2	4	no	—
21	C₂×#13093960	C₂²	1	1	yes	characteristic
22	#15689161	C₂²	1	1	yes	characteristic
23	#15689151	C₂²	1	2	yes	—
24	C₂×#13093951	C₂²	1	2	yes	—
25	#15689119	C₂²	1	2	yes	—
26	#15689090	C₂²	1	2	yes	—
27	#15689086	C₂²	1	2	yes	—
28	#15689078	C₂²	1	2	yes	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₄₇	—	2	4	no	—
33	#15688887	C₂²	1	2	yes	—
34	#15688884	C₂²	1	2	yes	—
35	#15688883	C₂²	1	2	yes	—
36	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#131×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#443	—	2	4	no	—
39	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#104×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	—	2	1	no	—
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625329	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	—	2	2	no	—
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₄₇	D₄	1	2	yes	—
54	C₂×C₈×D₄₇	D₄	1	2	yes	—
55	#13094005	—	2	2	no	—
56	#13094000	C₂×C₄	1	4	yes	—
57	#13093995	C₂×C₄	1	4	yes	—
58	#13093992	—	2	2	no	—
59	C₄×C₂²⋊D₄₇	—	2	4	no	—
60	#13093983	C₂³	1	2	yes	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₄²×D₄₇	—	2	2	no	—
64	C₄²×D₄₇	—	2	2	no	—
65	#13093960	—	2	2	no	—
66	#13093958	C₂×C₄	1	2	yes	complemented
67	#13093956	C₂×C₄	1	2	yes	complemented
68	Dic₄₇⋊C₈	—	2	4	no	—
69	#13093951	—	2	4	no	—
70	#13093948	C₂×C₄	1	4	yes	complemented
71	#13093945	C₂×C₄	1	4	yes	complemented
72	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
73	(C₂×D₄₇)⋊C₈	—	2	4	no	—
74	#13093934	—	2	2	no	—
75	C₄×C₄₇⋊C₈	—	2	2	no	—
76	C₈×Dic₄₇	—	2	2	no	—
77	C₈×Dic₄₇	—	2	2	no	—
78	C₈×Dic₄₇	—	2	2	no	—
79	C₂×#41×C₄₇	C₂³	1	2	yes	—
80	#135×C₄₇	—	2	2	no	—
81	#135×C₄₇	—	2	2	no	—
82	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
83	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
84	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
85	#131×C₄₇	—	2	4	no	—
86	#131×C₄₇	—	2	4	no	—
87	C₂×M₁₆×C₄₇	—	2	2	no	—
88	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	—	2	2	no	—
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#108×C₄₇	—	2	2	no	—
94	#104×C₄₇	—	2	4	no	—
95	C₄×C₈×C₄₇	D₄	1	4	yes	complemented
96	C₂³×D₄₇	#41	1	1	yes	characteristic
97	#41×C₄₇	—	2	2	no	—
98	#41×C₄₇	—	2	2	no	—
99	#41×C₄₇	—	2	2	no	—
100	#41×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	—	2	1	no	—
109	C₂²×Dic₄₇	#41	1	1	yes	characteristic
110	C₂×C₄×D₄₇	—	2	4	no	—
111	C₂×C₄×D₄₇	—	2	8	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	—	2	1	no	—
116	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
118	Q₁₆×C₄₇	—	2	2	no	—
119	SD₁₆×C₄₇	—	2	4	no	—
120	D₈×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	—	4	4	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	4	4	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₄₇	#41	1	2	yes	—
133	C₂×C₈×C₄₇	#41	1	2	yes	—
134	C₄²×C₄₇	—	2	1	no	—
135	C₄²×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²⋊Dic₄₇	—	2	2	no	—
137	C₂²⋊Dic₄₇	—	2	4	no	—
138	(C₂×D₄₇)⋊C₄	—	2	4	no	—
139	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
140	Dic₄₇⋊C₄	—	2	4	no	—
141	C₄×Dic₄₇	—	2	4	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	#41	1	2	yes	—
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	2	yes	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	C₈×D₄₇	—	2	4	no	—
155	C₈×D₄₇	—	2	4	no	—
156	C₈×D₄₇	—	2	4	no	—
157	C₈×D₄₇	—	2	4	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	—	2	4	no	—
163	C₂²×D₄₇	C₄×D₄	1	2	yes	—
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	2	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	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	C₂²⋊D₄₇	—	4	8	no	—
182	C₂×Dic₄₇	—	2	4	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	4	no	—
187	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
188	C₄×D₄₇	—	2	16	no	—
189	C₄×D₄₇	—	2	2	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	2	no	—
192	C₄×D₄₇	—	2	2	no	—
193	C₈×C₄₇	—	4	2	no	—
194	C₈×C₄₇	C₄×D₄	1	2	yes	—
195	C₈×C₄₇	C₄×D₄	1	2	yes	—
196	C₈×C₄₇	#121	1	2	yes	—
197	C₈×C₄₇	#121	1	2	yes	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	#21544	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₄₇	#525	1	1	yes	characteristic
207	C₂²×C₄₇	#529	1	1	yes	characteristic
208	C₂×D₄₇	—	2	4	no	—
209	C₂×D₄₇	—	2	4	no	—
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	#443	1	4	yes	complemented
213	C₄×C₄₇	—	2	4	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
217	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
218	C₄×C₄₇	#532	1	1	yes	characteristic
219	Dic₄₇	—	2	4	no	—
220	Dic₄₇	—	2	2	no	—
221	Dic₄₇	—	4	4	no	—
222	#3050	—	47	1	no	—
223	C₂×#443	D₄₇	1	1	yes	characteristic, complemented
224	#2929	—	47	2	no	—
225	C₂²×C₄×C₈	—	47	1	no	—
226	#1974	—	47	1	no	—
227	#1945	—	47	1	no	—
228	#1937	—	47	2	no	—
229	#1896	—	47	2	no	—
230	#1810	—	47	1	no	—
231	#1772	—	47	1	no	—
232	#1764	—	47	2	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	—	8	2	no	—
236	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
237	C₂×C₄₇	C₂×#443	1	2	yes	—
238	D₄₇	—	2	4	no	—
239	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#131	C₂×D₄₇	1	2	yes	—
241	C₂³×C₈	—	47	1	no	—
242	C₂³×C₈	—	47	1	no	—
243	#525	—	47	2	no	—
244	C₂²×C₄²	—	47	1	no	—
245	#467	—	47	2	no	—
246	#466	—	47	2	no	—
247	#465	—	47	4	no	—
248	#443	—	2	4	no	—
249	#435	—	94	4	no	—
250	C₈×D₄	—	94	4	no	—
251	C₂×#108	—	47	1	no	—
252	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
253	#427	—	47	1	no	—
254	#424	—	47	2	no	—
255	C₂×#104	—	47	2	no	—
256	C₂×#104	C₂×D₄₇	1	2	yes	—
257	#416	—	47	2	no	—
258	#408	—	47	2	no	—
259	#407	—	47	2	no	—
260	#405	—	47	2	no	—
261	C₂×C₄×C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	C₂×C₄×C₈	—	94	4	no	—
265	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
266	#341	—	47	2	no	—
267	#339	—	47	2	no	—
268	#339	—	47	2	no	—
269	C₄₇	#21544	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	C₂²×D₄₇	1	2	yes	—
271	C₂³×C₄	—	47	1	no	—
272	C₂³×C₄	—	94	1	no	—
273	#135	—	2	2	no	—
274	#135	—	2	2	no	—
275	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
276	C₂×SD₁₆	C₄×D₄₇	1	2	yes	complemented
277	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic, complemented
278	#131	—	2	4	no	—
279	#131	—	2	4	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	47	2	no	—
282	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	—	47	1	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	47	2	no	—
288	C₂²×C₈	—	47	2	no	—
289	C₂²×C₈	—	47	2	no	—
290	C₂²×C₈	—	94	2	no	—
291	C₂²×C₈	—	94	2	no	—
292	C₂²×C₈	—	94	2	no	—
293	C₂²×C₈	—	94	2	no	—
294	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
296	#123	—	94	2	no	—
297	C₂²⋊Q₈	—	47	4	no	—
298	#121	—	47	4	no	—
299	#120	—	94	2	no	—
300	C₄×D₄	—	94	4	no	—
301	#117	—	47	2	no	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	94	2	no	—
304	C₂×C₄²	—	94	1	no	—
305	C₂×C₄²	—	94	2	no	—
306	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
307	#108	—	2	2	no	—
308	#108	—	94	2	no	—
309	#107	—	47	2	no	—
310	#106	—	47	2	no	—
311	C₄⋊C₈	—	94	4	no	—
312	#104	—	2	4	no	—
313	#104	—	94	4	no	—
314	#103	—	47	4	no	—
315	#102	—	47	4	no	—
316	C₂²⋊C₈	—	94	4	no	—
317	C₂²⋊C₈	—	94	4	no	—
318	#97	—	94	2	no	—
319	C₄×C₈	—	94	2	no	—
320	C₄×C₈	—	94	2	no	—
321	C₄×C₈	—	94	2	no	—
322	C₄×C₈	—	94	2	no	—
323	C₄×C₈	C₂²⋊D₄₇	1	4	yes	complemented
324	C₂⁴	—	47	1	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	94	4	no	—
332	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	47	1	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	47	2	no	—
338	C₂²×C₄	—	94	4	no	—
339	C₂²×C₄	—	94	8	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
346	Q₁₆	—	2	2	no	—
347	SD₁₆	—	2	4	no	—
348	D₈	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	4	no	—
352	M₁₆	—	94	2	no	—
353	M₁₆	—	94	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	4	no	—
356	C₂×C₈	—	47	2	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	94	1	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	4	no	—
363	C₂×C₈	—	94	4	no	—
364	C₂×C₈	—	94	4	no	—
365	C₂×C₈	—	94	4	no	—
366	C₂×C₈	—	94	2	no	—
367	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₈	#10625350	1	2	yes	—
370	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
371	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₈	#10625352	1	2	yes	—
373	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
375	C₄⋊C₄	—	47	4	no	—
376	C₄⋊C₄	—	94	4	no	—
377	C₂²⋊C₄	—	94	4	no	—
378	C₂²⋊C₄	—	94	4	no	—
379	C₂²⋊C₄	—	94	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	47	2	no	—
382	C₄²	—	94	4	no	—
383	C₄²	—	94	2	no	—
384	C₄²	—	94	1	no	—
385	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
386	C₂³	—	2	2	no	—
387	C₂³	—	47	2	no	—
388	C₂³	—	94	4	no	—
389	C₂³	—	94	1	no	—
390	C₂³	—	94	1	no	—
391	C₂³	#41×D₄₇	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	188	8	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	47	2	no	—
405	C₂×C₄	—	94	16	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	1	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	2	no	—
414	C₂×C₄	—	94	4	no	—
415	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
418	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
420	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
421	C₈	—	4	2	no	—
422	C₈	—	94	2	no	—
423	C₈	—	94	2	no	—
424	C₈	—	188	2	no	—
425	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
426	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
427	C₈	#13093995	1	2	yes	—
428	C₈	#13093995	1	2	yes	—
429	C₂²	—	2	2	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	47	4	no	—
433	C₂²	—	94	4	no	—
434	C₂²	—	94	4	no	—
435	C₂²	—	94	2	no	—
436	C₂²	—	94	2	no	—
437	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
438	C₂²	#15689630	1	1	yes	characteristic
439	C₂²	#15689655	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	4	2	no	—
442	C₄	—	94	4	no	—
443	C₄	—	94	2	no	—
444	C₄	—	188	4	no	—
445	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
446	C₄	C₄×#10625352	1	1	yes	characteristic
447	C₄	C₂×#13093995	1	1	yes	characteristic
448	C₄	#15689670	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	8	2	no	—
452	C₂	—	94	4	no	—
453	C₂	C₄×#13093995	1	1	yes	characteristic
454	C₂	#443×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#443	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252965	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#443	D₄₇
hypocenter	C₄₇	#21544
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. #20252080	C₂	semidirect
3. C₂×C₄×C₈×D₄₇	C₂	semidirect
4. #20244277	C₂	semidirect
5. #20244134	C₂	semidirect
6. #20244089	C₂	semidirect
7. #20243828	C₂	semidirect
8. #20243423	C₂	semidirect
9. #20243267	C₂	semidirect
10. #20243223	C₂	semidirect
11. C₂×C₄₇×#443	C₂	semidirect
16. #15689361	C₄	semidirect
17. #15689356	C₄	semidirect
18. #15689349	C₄	semidirect
66. #13093958	C₂×C₄	semidirect
67. #13093956	C₂×C₄	semidirect
70. #13093948	C₂×C₄	semidirect
71. #13093945	C₂×C₄	semidirect
82. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
83. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
84. C₂×D₈×C₄₇	C₂×C₄	semidirect
95. C₄×C₈×C₄₇	D₄	semidirect
212. C₂×D₄₇	#443	semidirect
223. C₂×#443	D₄₇	semidirect
269. C₄₇	#21544	semidirect
275. C₂×Q₁₆	C₄×D₄₇	semidirect
276. C₂×SD₁₆	C₄×D₄₇	semidirect
277. C₂×D₈	C₄×D₄₇	semidirect
323. C₄×C₈	C₂²⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252965	2
#20252080	2
C₂×C₄×C₈×D₄₇	2
#20244277	2
#20244134	2
#20244089	2
#20243828	2
#20243423	2
#20243267	2
#20243223	2
C₂×C₄₇×#443	2
#21544	47