Subgroups — #26200177

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253198	C₂	1	2	yes	maximal
3	C₈×#10625354	C₂	1	1	yes	maximal, characteristic
4	#20242758	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242756	C₂	1	2	yes	maximal, complemented
6	#20242754	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242752	C₂	1	2	yes	maximal, complemented
8	#20242750	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242145	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242071	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₄₇	—	2	1	no	—
13	C₂×Q₁₆×D₄₇	—	2	1	no	—
14	C₄⋊Q₈×D₄₇	C₂²	1	2	yes	—
15	C₄×#10625354	C₂²	1	1	yes	characteristic
16	#15689503	C₂²	1	1	yes	characteristic
17	#15689502	C₂²	1	2	yes	—
18	#15689501	—	2	1	no	—
19	#15689501	—	2	1	no	—
20	#15689416	—	2	2	no	—
21	#15689412	—	2	2	no	—
22	#15689408	C₂²	1	2	yes	—
23	#15689404	C₂²	1	2	yes	—
24	#15689400	C₂²	1	2	yes	—
25	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₈×D₁₈₈	—	2	1	no	—
27	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
28	#15689188	—	2	1	no	—
29	#15689188	C₂²	1	1	yes	characteristic
30	#15689175	—	2	1	no	—
31	#15689175	C₂²	1	1	yes	characteristic
32	#15689162	—	2	2	no	—
33	#15689145	C₂²	1	2	yes	—
34	#15689123	—	2	2	no	—
35	C₄×C₈×D₄₇	—	2	1	no	—
36	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
37	#15688876	C₂²	1	1	yes	characteristic
38	#15688875	C₂²	1	2	yes	—
39	#15688870	C₂²	1	2	yes	—
40	#15688869	C₂²	1	2	yes	—
41	#15688868	C₂²	1	2	yes	—
42	C₄₇×#494	C₂²	1	1	yes	characteristic
43	C₄₇×#475	C₂²	1	2	yes	—
44	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	1	yes	characteristic
46	C₄₇×#332	C₂²	1	2	yes	—
47	C₂×#10625354	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₄₇	—	2	2	no	—
49	C₂×Dic₁₈₈	—	2	1	no	—
50	C₂×Dic₁₈₈	—	2	1	no	—
51	C₂×#10625337	—	2	2	no	—
52	C₂×#10625337	—	2	2	no	—
53	Q₁₆×D₄₇	—	4	4	no	—
54	Q₁₆×D₄₇	—	4	4	no	—
55	C₂×#10625324	—	2	2	no	—
56	C₂×C₈×D₄₇	—	2	1	no	—
57	C₂×C₈×D₄₇	—	2	1	no	—
58	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
59	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
60	#13094024	C₂³	1	2	yes	—
61	#13094023	—	2	2	no	—
62	#13094023	—	2	2	no	—
63	#13094022	—	2	2	no	—
64	Q₈×Dic₄₇	D₄	1	1	yes	characteristic
65	C₄×D₁₈₈	—	2	1	no	—
66	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
67	#13093986	—	2	1	no	—
68	#13093986	D₄	1	1	yes	characteristic
69	#13093982	—	2	1	no	—
70	#13093982	D₄	1	1	yes	characteristic
71	C₄⋊C₄×D₄₇	—	2	2	no	—
72	C₄⋊C₄×D₄₇	—	2	2	no	—
73	C₄²×D₄₇	—	2	1	no	—
74	C₄²×D₄₇	C₂³	1	1	yes	characteristic
75	#13093958	—	2	2	no	—
76	#13093957	—	2	2	no	—
77	#13093955	—	2	2	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
81	Dic₄₇⋊C₈	—	2	2	no	—
82	#13093948	—	2	2	no	—
83	#13093946	—	2	2	no	—
84	#13093944	—	2	2	no	—
85	(C₂×D₄₇)⋊C₈	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	C₄×C₄₇⋊C₈	—	2	1	no	—
89	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×Dic₄₇	—	2	1	no	—
91	C₈×Dic₄₇	D₄	1	1	yes	characteristic
92	C₈×Dic₄₇	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₄₇	—	2	1	no	—
94	C₂×Q₁₆×C₄₇	—	2	1	no	—
95	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
96	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
97	#106×C₄₇	—	2	2	no	—
98	C₄⋊C₈×C₄₇	—	2	1	no	—
99	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
101	#103×C₄₇	—	2	2	no	—
102	C₄×C₈×C₄₇	—	2	1	no	—
103	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
106	#10625354	—	2	2	no	—
107	#10625354	Q₁₆	1	4	yes	complemented
108	Q₈×D₄₇	—	4	4	no	—
109	Q₈×D₄₇	—	4	4	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
116	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
119	C₂×Dic₉₄	—	2	2	no	—
120	C₂×Dic₉₄	—	4	2	no	—
121	Q₁₆×C₄₇	—	4	2	no	—
122	Q₁₆×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
133	#10625337	—	4	4	no	—
134	#10625337	—	4	4	no	—
135	(C₂×D₄₇)⋊C₄	—	2	1	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	C₄⋊Dic₄₇	—	2	1	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
142	Dic₄₇⋊C₄	—	4	2	no	—
143	Dic₄₇⋊C₄	—	4	2	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
147	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₄₇	#41	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
153	Dic₁₈₈	—	4	2	no	—
154	Dic₁₈₈	—	4	2	no	—
155	#10625324	—	4	4	no	—
156	C₈×D₄₇	—	2	2	no	—
157	C₈×D₄₇	—	2	2	no	—
158	C₈×D₄₇	—	4	2	no	—
159	C₈×D₄₇	—	4	2	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	#121	1	1	yes	characteristic
162	Q₈×C₄₇	—	2	1	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	Q₈×C₄₇	C₂×Q₁₆	1	2	yes	complemented
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	#121	1	1	yes	characteristic
175	C₂×Dic₄₇	#121	1	1	yes	characteristic
176	C₂×Dic₄₇	#121	1	1	yes	characteristic
177	D₁₈₈	—	2	4	no	—
178	D₁₈₈	—	2	1	no	—
179	D₁₈₈	C₂×Q₁₆	1	2	yes	complemented
180	C₄×D₄₇	—	2	1	no	—
181	C₄×D₄₇	—	2	1	no	—
182	C₄×D₄₇	—	2	4	no	—
183	C₄×D₄₇	—	2	2	no	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	1	no	—
186	C₄×D₄₇	—	4	2	no	—
187	C₄×D₄₇	—	8	4	no	—
188	C₄×D₄₇	C₂×Q₁₆	1	2	yes	—
189	C₄×D₄₇	#135	1	2	yes	—
190	Dic₉₄	—	4	2	no	—
191	Dic₉₄	—	4	2	no	—
192	Dic₉₄	—	8	4	no	—
193	C₈×C₄₇	—	2	1	no	—
194	C₈×C₄₇	—	4	2	no	—
195	C₈×C₄₇	—	4	1	no	—
196	C₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
197	C₄₇⋊C₈	—	2	1	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	C₄₇⋊C₈	—	4	1	no	—
200	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
201	#19268	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
203	C₂×D₄₇	—	2	1	no	—
204	C₂×D₄₇	—	2	1	no	—
205	C₂×D₄₇	—	2	2	no	—
206	C₂×D₄₇	—	4	1	no	—
207	C₂×D₄₇	—	4	1	no	—
208	C₂×D₄₇	#467	1	2	yes	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	4	1	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
215	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	Dic₄₇	—	2	1	no	—
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	8	2	no	—
220	Dic₄₇	#467	1	2	yes	—
221	Dic₄₇	#473	1	2	yes	—
222	C₂×#494	—	47	1	no	—
223	#3079	—	47	2	no	—
224	C₈×#41	—	47	1	no	—
225	#1670	—	47	2	no	—
226	#1670	—	47	1	no	—
227	#1670	D₄₇	1	1	yes	characteristic, complemented
228	#1669	—	47	1	no	—
229	#1669	—	47	1	no	—
230	#1669	—	47	2	no	—
231	#1567	—	47	1	no	—
232	#1549	—	47	2	no	—
233	C₂×C₄₇	#3038	1	1	yes	characteristic
234	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
236	D₄₇	—	2	2	no	—
237	D₄₇	—	4	2	no	—
238	C₂²×Q₁₆	—	94	1	no	—
239	C₂²×Q₁₆	—	94	1	no	—
240	C₂×C₄⋊Q₈	—	47	2	no	—
241	C₄×#41	—	47	1	no	—
242	#494	—	47	2	no	—
243	#494	—	47	1	no	—
244	#494	—	94	1	no	—
245	#494	—	94	1	no	—
246	#494	C₂×D₄₇	1	1	yes	characteristic
247	#477	—	94	2	no	—
248	#476	—	94	2	no	—
249	#475	—	47	2	no	—
250	#475	C₂×D₄₇	1	2	yes	—
251	#474	—	47	2	no	—
252	#474	—	47	2	no	—
253	C₈×Q₈	—	47	1	no	—
254	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic
255	C₈×D₄	—	47	1	no	—
256	C₈×D₄	—	47	1	no	—
257	C₈×D₄	—	94	1	no	—
258	C₈×D₄	—	94	1	no	—
259	#431	—	47	1	no	—
260	#431	—	94	1	no	—
261	#428	—	94	2	no	—
262	#423	—	47	2	no	—
263	#417	—	94	2	no	—
264	C₂×C₄×C₈	—	47	1	no	—
265	C₂×C₄×C₈	—	94	1	no	—
266	#335	—	47	2	no	—
267	#335	—	47	1	no	—
268	#335	C₂×D₄₇	1	1	yes	characteristic
269	#332	—	47	2	no	—
270	#332	—	47	2	no	—
271	#332	—	47	2	no	—
272	#332	C₂×D₄₇	1	2	yes	—
273	C₄₇	#19268	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	47	1	no	—
275	C₂²×Q₈	—	94	2	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	—	2	1	no	—
278	C₂×Q₁₆	—	94	2	no	—
279	C₂×Q₁₆	—	94	2	no	—
280	C₂×Q₁₆	—	94	1	no	—
281	C₂×Q₁₆	—	94	1	no	—
282	C₂×Q₁₆	—	188	4	no	—
283	C₂×Q₁₆	—	188	4	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	94	1	no	—
288	C₂²×C₈	—	94	1	no	—
289	C₄⋊Q₈	—	47	2	no	—
290	C₄⋊Q₈	—	94	2	no	—
291	C₄⋊Q₈	—	94	2	no	—
292	C₄⋊Q₈	—	94	2	no	—
293	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
294	C₄×Q₈	—	47	1	no	—
295	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
296	C₄×D₄	—	47	1	no	—
297	C₄×D₄	—	47	1	no	—
298	C₄×D₄	—	94	1	no	—
299	C₄×D₄	—	94	1	no	—
300	#117	—	47	1	no	—
301	#117	—	94	1	no	—
302	C₂×C₄⋊C₄	—	94	2	no	—
303	C₂×C₄⋊C₄	—	94	2	no	—
304	C₂×C₄²	—	47	1	no	—
305	C₂×C₄²	—	94	1	no	—
306	#107	—	94	2	no	—
307	#107	—	94	2	no	—
308	#106	—	2	2	no	—
309	#106	—	94	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	47	1	no	—
312	C₄⋊C₈	—	47	2	no	—
313	C₄⋊C₈	—	94	1	no	—
314	C₄⋊C₈	—	94	2	no	—
315	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
317	#103	—	2	2	no	—
318	#103	—	94	2	no	—
319	#102	—	94	2	no	—
320	#102	—	94	2	no	—
321	C₂²⋊C₈	—	94	1	no	—
322	C₂²⋊C₈	—	94	1	no	—
323	C₂²⋊C₈	—	94	1	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	47	1	no	—
326	C₄×C₈	—	47	1	no	—
327	C₄×C₈	—	47	1	no	—
328	C₄×C₈	—	94	1	no	—
329	C₄×C₈	—	94	1	no	—
330	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
331	#41	—	47	4	no	—
332	#41	—	94	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	94	2	no	—
335	C₂×Q₈	—	188	2	no	—
336	C₂×Q₈	—	188	4	no	—
337	C₂×Q₈	—	188	4	no	—
338	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
339	C₂×D₄	—	47	1	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	47	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	—	94	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	188	2	no	—
348	Q₁₆	—	4	2	no	—
349	Q₁₆	—	4	2	no	—
350	Q₁₆	—	188	2	no	—
351	Q₁₆	—	188	4	no	—
352	Q₁₆	—	188	4	no	—
353	Q₁₆	—	188	2	no	—
354	M₁₆	—	188	4	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	47	1	no	—
358	C₂×C₈	—	47	1	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	94	1	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	188	2	no	—
364	C₂×C₈	—	188	2	no	—
365	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
366	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	47	1	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	—	188	2	no	—
375	C₄⋊C₄	—	188	2	no	—
376	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
377	C₂²⋊C₄	—	94	1	no	—
378	C₂²⋊C₄	—	94	1	no	—
379	C₂²⋊C₄	—	94	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	47	1	no	—
382	C₄²	—	47	1	no	—
383	C₄²	—	47	1	no	—
384	C₄²	—	94	1	no	—
385	C₄²	—	94	1	no	—
386	C₄²	C₂³×D₄₇	1	1	yes	characteristic
387	C₂³	—	47	1	no	—
388	C₂³	—	94	1	no	—
389	Q₈	—	2	1	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	376	4	no	—
393	Q₈	—	188	2	no	—
394	Q₈	—	188	2	no	—
395	Q₈	Q₁₆×D₄₇	1	2	yes	complemented
396	D₄	—	47	2	no	—
397	D₄	—	94	4	no	—
398	D₄	—	94	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	47	1	no	—
403	C₂×C₄	—	47	1	no	—
404	C₂×C₄	—	47	2	no	—
405	C₂×C₄	—	47	2	no	—
406	C₂×C₄	—	47	1	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	4	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	376	4	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	—	188	1	no	—
416	C₂×C₄	—	188	1	no	—
417	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	47	2	no	—
424	C₈	—	94	1	no	—
425	C₈	—	188	2	no	—
426	C₈	—	188	1	no	—
427	C₈	#13094051	1	2	yes	—
428	C₂²	—	47	2	no	—
429	C₂²	—	94	1	no	—
430	C₂²	—	94	1	no	—
431	C₂²	—	94	2	no	—
432	C₂²	—	188	1	no	—
433	C₂²	—	188	1	no	—
434	C₂²	#121×D₄₇	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	47	2	no	—
440	C₄	—	47	2	no	—
441	C₄	—	94	1	no	—
442	C₄	—	376	2	no	—
443	C₄	—	188	1	no	—
444	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
445	C₄	#135×D₄₇	1	1	yes	characteristic
446	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
447	C₄	C₂×#13094051	1	1	yes	characteristic
448	C₂	—	94	2	no	—
449	C₂	—	188	2	no	—
450	C₂	#20252865	1	1	yes	characteristic
451	C₂	#467×D₄₇	1	1	yes	characteristic
452	C₂	#473×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1670	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625354	D₄
hypercenter	#1670	D₄₇
hypocenter	C₄₇	#19268
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
1. #494×D₄₇	C₂	semidirect
4. #20242758	C₂	semidirect
5. #20242756	C₂	semidirect
6. #20242754	C₂	semidirect
7. #20242752	C₂	semidirect
8. #20242750	C₂	semidirect
9. #20242145	C₂	semidirect
10. #20242071	C₂	semidirect
11. C₄₇×#1670	C₂	semidirect
107. #10625354	Q₁₆	semidirect
165. Q₈×C₄₇	C₂×Q₁₆	semidirect
179. D₁₈₈	C₂×Q₁₆	semidirect
227. #1670	D₄₇	semidirect
273. C₄₇	#19268	semidirect
395. Q₈	Q₁₆×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#494×D₄₇	2
#20253198	2
C₈×#10625354	2
#20242758	2
#20242756	2
#20242754	2
#20242752	2
#20242750	2
#20242145	2
#20242071	2
C₄₇×#1670	2
#19268	47