Subgroups — #26204146

Order 12032.

848 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	#20254331	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253943	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253930	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253841	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689471	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243015	C₂	1	2	yes	maximal, complemented
7	#20243012	C₂	1	2	yes	maximal, complemented
8	#20242991	C₂	1	2	yes	maximal, complemented
9	#20242978	C₂	1	2	yes	maximal, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094049	—	2	2	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	C₂×#13094021	C₂²	1	1	yes	characteristic
15	#15689529	—	2	2	no	—
16	#15689526	C₂²	1	2	yes	complemented
17	#15689519	C₂²	1	2	yes	complemented
18	#15689519	C₂²	1	1	yes	characteristic, complemented
19	#15689513	—	2	2	no	—
20	#15689499	C₂²	1	2	yes	—
21	#15689497	C₂²	1	2	yes	—
22	#15689496	C₂²	1	2	yes	—
23	#15689495	C₂²	1	1	yes	characteristic, complemented
24	#15689475	C₂²	1	1	yes	characteristic, complemented
25	#15689471	—	2	2	no	—
26	#15689471	C₂²	1	2	yes	—
27	#15689471	C₂²	1	2	yes	—
28	#15689470	C₂²	1	2	yes	—
29	#15689469	C₂²	1	1	yes	characteristic, complemented
30	#15689350	—	2	2	no	—
31	#15689324	—	2	2	no	—
32	#15689276	—	2	2	no	—
33	C₄×#10625335	—	2	2	no	—
34	#15689163	—	2	2	no	—
35	C₂×#13093944	—	2	2	no	—
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688845	C₂²	1	2	yes	complemented
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#492	C₂²	1	2	yes	complemented
43	C₄₇×#487	C₂²	1	2	yes	complemented
44	C₄₇×#461	—	2	2	no	—
45	C₄₇×#448	—	2	2	no	—
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₂²×D₁₈₈	—	2	1	no	—
48	C₂²×D₁₈₈	—	2	1	no	—
49	C₂²×D₁₈₈	—	2	1	no	—
50	#13094049	—	4	8	no	—
51	C₂×#10625325	—	2	4	no	—
52	C₂×#10625335	—	2	2	no	—
53	C₂×#10625336	—	2	4	no	—
54	C₂×#10625334	—	2	4	no	—
55	C₂×#10625329	D₄	1	2	yes	—
56	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
57	#13094024	C₂³	1	1	yes	characteristic
58	#13094024	C₂³	1	1	yes	characteristic
59	#13094021	—	2	1	no	—
60	#13094021	—	2	1	no	—
61	#13094021	—	2	1	no	—
62	#13094021	C₂³	1	2	yes	—
63	#13094016	—	2	1	no	—
64	#13094003	—	2	1	no	—
65	#13094003	—	2	1	no	—
66	C₄×Dic₉₄	—	2	1	no	—
67	C₄×Dic₉₄	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093957	—	2	4	no	—
70	#13093955	—	2	4	no	—
71	#13093955	—	2	2	no	—
72	#13093947	—	2	2	no	—
73	#13093946	—	2	4	no	—
74	#13093945	—	2	2	no	—
75	#13093944	—	2	4	no	—
76	#13093944	—	2	4	no	—
77	#13093935	D₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
82	C₂×#41×C₄₇	—	2	1	no	—
83	C₂²×Q₈×C₄₇	—	2	1	no	—
84	C₂×SD₁₆×C₄₇	—	2	4	no	—
85	C₄⋊Q₈×C₄₇	—	2	1	no	—
86	C₄⋊Q₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	—	2	1	no	—
88	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
90	#127×C₄₇	C₂³	1	1	yes	characteristic
91	#124×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	#121×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
100	#103×C₄₇	—	2	4	no	—
101	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
102	C₄×C₈×C₄₇	C₂³	1	2	yes	—
103	C₂³×D₄₇	—	4	1	no	—
104	#41×C₄₇	—	4	4	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	—	4	1	no	—
108	C₂×Q₈×C₄₇	—	8	2	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	4	1	no	—
113	C₂²×C₄×C₄₇	—	4	1	no	—
114	C₂²×C₄×C₄₇	—	4	1	no	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×D₁₈₈	—	2	2	no	—
119	C₂×D₁₈₈	—	2	2	no	—
120	C₂×D₁₈₈	—	2	2	no	—
121	C₂×D₁₈₈	—	4	4	no	—
122	C₂×D₁₈₈	—	4	4	no	—
123	C₂×D₁₈₈	—	4	1	no	—
124	C₂×D₁₈₈	—	4	1	no	—
125	C₂×D₁₈₈	—	4	1	no	—
126	C₂×D₁₈₈	—	8	2	no	—
127	C₂×Dic₉₄	—	2	1	no	—
128	C₂×Dic₉₄	—	2	1	no	—
129	SD₁₆×C₄₇	—	8	4	no	—
130	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	4	1	no	—
136	C₄⋊C₄×C₄₇	—	4	1	no	—
137	C₂²⋊C₄×C₄₇	—	4	1	no	—
138	C₂²⋊C₄×C₄₇	—	4	1	no	—
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₇	—	4	1	no	—
144	#10625336	—	4	8	no	—
145	#10625335	—	4	4	no	—
146	#10625334	—	4	8	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	Dic₄₇⋊C₄	—	4	1	no	—
152	Dic₄₇⋊C₄	—	4	1	no	—
153	C₄×Dic₄₇	—	4	1	no	—
154	#10625329	SD₁₆	1	8	yes	complemented
155	C₂×C₄₇⋊C₈	—	4	2	no	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
159	#10625325	—	8	4	no	—
160	C₂³×C₄₇	—	4	1	no	—
161	C₂³×C₄₇	#127	1	1	yes	characteristic
162	C₂²×D₄₇	—	4	2	no	—
163	C₂²×D₄₇	—	8	2	no	—
164	C₂²×D₄₇	—	8	2	no	—
165	C₂²×D₄₇	—	8	2	no	—
166	Q₈×C₄₇	—	4	2	no	—
167	Q₈×C₄₇	—	4	4	no	—
168	Q₈×C₄₇	—	8	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	4	2	no	—
171	D₄×C₄₇	—	4	2	no	—
172	D₄×C₄₇	—	8	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	8	2	no	—
178	C₂×C₄×C₄₇	—	8	2	no	—
179	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
181	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×Dic₄₇	—	4	1	no	—
187	C₂×Dic₄₇	—	4	1	no	—
188	D₁₈₈	—	4	4	no	—
189	D₁₈₈	—	4	4	no	—
190	D₁₈₈	—	4	4	no	—
191	D₁₈₈	—	8	2	no	—
192	D₁₈₈	—	8	2	no	—
193	D₁₈₈	—	8	2	no	—
194	Dic₉₄	—	4	2	no	—
195	Dic₉₄	—	4	2	no	—
196	C₈×C₄₇	—	2	4	no	—
197	C₄₇⋊C₈	—	2	2	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	C₂×SD₁₆	1	8	yes	—
200	#19623	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	8	1	no	—
204	C₂²×C₄₇	—	8	1	no	—
205	C₂²×C₄₇	—	8	1	no	—
206	C₂²×C₄₇	#492	1	2	yes	—
207	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
208	C₂×D₄₇	—	8	2	no	—
209	C₂×D₄₇	—	8	2	no	—
210	C₂×D₄₇	—	8	2	no	—
211	C₂×D₄₇	—	16	4	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	8	1	no	—
215	C₄×C₄₇	—	8	2	no	—
216	C₄×C₄₇	#492	1	2	yes	—
217	C₄×C₄₇	C₂²×SD₁₆	1	2	yes	—
218	C₄×C₄₇	#575	1	2	yes	—
219	C₄×C₄₇	#576	1	2	yes	—
220	Dic₄₇	—	8	1	no	—
221	Dic₄₇	—	8	1	no	—
222	#3208	—	47	1	no	—
223	#3206	D₄₇	1	1	yes	characteristic, complemented
224	#3167	—	47	1	no	—
225	#3165	—	47	1	no	—
226	#3151	—	47	1	no	—
227	C₂×#486	—	47	1	no	—
228	#1715	—	47	2	no	—
229	#1714	—	47	2	no	—
230	#1708	—	47	2	no	—
231	#1706	—	47	2	no	—
232	C₈×M₁₆	—	47	1	no	—
233	C₂×C₄₇	—	2	2	no	—
234	C₂×C₄₇	—	16	1	no	—
235	C₂×C₄₇	C₂×#492	1	1	yes	characteristic
236	C₂×C₄₇	#3153	1	1	yes	characteristic
237	C₂×C₄₇	#3155	1	1	yes	characteristic
238	D₄₇	—	16	2	no	—
239	C₂×AGL(1,ℤ/8)	—	94	2	no	—
240	#533	—	47	1	no	—
241	#532	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
243	C₂×#127	—	47	1	no	—
244	#501	—	94	2	no	—
245	#500	—	47	2	no	—
246	#498	—	47	2	no	—
247	#498	—	47	1	no	—
248	#496	—	94	2	no	—
249	#493	—	47	2	no	—
250	#492	—	47	2	no	—
251	#492	—	47	1	no	—
252	#492	—	47	2	no	—
253	#492	C₂×D₄₇	1	2	yes	complemented
254	#487	—	47	1	no	—
255	#487	C₂×D₄₇	1	2	yes	complemented
256	#486	—	47	2	no	—
257	#486	—	47	2	no	—
258	#486	—	47	1	no	—
259	#486	—	47	2	no	—
260	#486	—	94	2	no	—
261	#465	—	94	2	no	—
262	#461	—	2	2	no	—
263	#460	—	94	2	no	—
264	#450	—	94	2	no	—
265	#448	—	2	2	no	—
266	C₄×SD₁₆	—	94	2	no	—
267	#431	C₂×D₄₇	1	1	yes	characteristic
268	#428	—	94	2	no	—
269	C₂×#102	—	94	2	no	—
270	C₄×M₁₆	—	47	1	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	#322	—	47	2	no	—
273	C₈²	—	47	2	no	—
274	C₄₇	#19623	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	2	1	no	—
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×D₄	—	94	1	no	—
278	C₂²×D₄	—	94	1	no	—
279	C₂²×D₄	—	94	1	no	—
280	AGL(1,ℤ/8)	—	188	8	no	—
281	C₂×SD₁₆	—	2	4	no	—
282	C₂×SD₁₆	—	94	2	no	—
283	C₂×SD₁₆	—	94	4	no	—
284	C₂×SD₁₆	—	94	4	no	—
285	C₂×D₈	—	94	4	no	—
286	C₂×M₁₆	—	47	2	no	—
287	C₂²×C₈	—	47	2	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	—	47	1	no	—
292	C₄⋊Q₈	—	47	1	no	—
293	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
294	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
295	#127	—	47	2	no	—
296	#127	—	94	1	no	—
297	#127	—	94	1	no	—
298	#127	—	94	1	no	—
299	#127	C₂²×D₄₇	1	1	yes	characteristic
300	#125	—	94	1	no	—
301	#124	—	2	1	no	—
302	C₂²⋊Q₈	—	94	1	no	—
303	C₂²⋊Q₈	—	94	1	no	—
304	#121	—	2	1	no	—
305	#121	—	2	1	no	—
306	C₄×Q₈	—	94	1	no	—
307	C₄×Q₈	—	94	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	#117	—	94	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
314	#107	—	94	4	no	—
315	#106	—	94	4	no	—
316	#106	—	94	2	no	—
317	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
318	#103	—	2	4	no	—
319	#103	—	94	2	no	—
320	#102	—	94	4	no	—
321	#102	—	94	4	no	—
322	#102	—	94	2	no	—
323	#102	—	94	4	no	—
324	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
325	#97	—	47	2	no	—
326	C₄×C₈	—	47	2	no	—
327	C₄×C₈	—	47	1	no	—
328	C₄×C₈	—	47	2	no	—
329	C₄×C₈	—	47	1	no	—
330	C₄×C₈	C₂²×D₄₇	1	2	yes	—
331	C₂⁴	—	188	1	no	—
332	#41	—	4	4	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	1	no	—
336	C₂×Q₈	—	8	2	no	—
337	C₂×Q₈	—	94	1	no	—
338	C₂×Q₈	—	94	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	94	2	no	—
344	C₂×D₄	—	94	2	no	—
345	C₂×D₄	—	94	2	no	—
346	C₂×D₄	—	376	2	no	—
347	C₂×D₄	—	188	4	no	—
348	C₂×D₄	—	188	1	no	—
349	C₂×D₄	—	188	1	no	—
350	C₂×D₄	—	188	1	no	—
351	C₂×D₄	—	188	4	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	SD₁₆	—	8	4	no	—
358	SD₁₆	—	376	4	no	—
359	SD₁₆	—	188	8	no	—
360	SD₁₆	—	188	4	no	—
361	D₈	—	188	8	no	—
362	M₁₆	—	47	8	no	—
363	C₂×C₈	—	47	4	no	—
364	C₂×C₈	—	47	2	no	—
365	C₂×C₈	—	47	2	no	—
366	C₂×C₈	—	188	2	no	—
367	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	94	1	no	—
375	C₄⋊C₄	—	94	1	no	—
376	C₄⋊C₄	—	94	1	no	—
377	C₄⋊C₄	—	94	1	no	—
378	C₄⋊C₄	—	188	1	no	—
379	C₄⋊C₄	—	188	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	188	1	no	—
383	C₄²	—	188	1	no	—
384	C₄²	D₄×D₄₇	1	1	yes	characteristic
385	C₄²	D₄×D₄₇	1	1	yes	characteristic
386	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₄²	C₂³×D₄₇	1	1	yes	characteristic
388	C₂³	—	4	1	no	—
389	C₂³	—	376	2	no	—
390	C₂³	—	376	2	no	—
391	C₂³	—	376	2	no	—
392	C₂³	—	188	2	no	—
393	C₂³	#13094020	1	1	yes	characteristic
394	Q₈	—	4	2	no	—
395	Q₈	—	4	4	no	—
396	Q₈	—	8	2	no	—
397	Q₈	—	188	2	no	—
398	Q₈	—	188	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	376	2	no	—
404	D₄	—	376	2	no	—
405	D₄	—	376	2	no	—
406	D₄	—	188	4	no	—
407	D₄	—	188	4	no	—
408	D₄	—	188	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	188	1	no	—
416	C₂×C₄	—	188	1	no	—
417	C₂×C₄	#13094020	1	1	yes	characteristic
418	C₂×C₄	#13094020	1	1	yes	characteristic
419	C₂×C₄	#13094020	1	1	yes	characteristic
420	C₂×C₄	SD₁₆×D₄₇	1	4	yes	—
421	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
424	C₈	—	2	4	no	—
425	C₈	—	47	8	no	—
426	C₈	—	94	2	no	—
427	C₈	—	94	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	376	2	no	—
434	C₂²	—	376	2	no	—
435	C₂²	—	376	2	no	—
436	C₂²	—	752	4	no	—
437	C₂²	#15689494	1	2	yes	—
438	C₂²	C₂×#13094020	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	—	376	1	no	—
444	C₄	—	376	1	no	—
445	C₄	#15689494	1	2	yes	—
446	C₄	C₂×SD₁₆×D₄₇	1	2	yes	—
447	C₄	#15689922	1	2	yes	—
448	C₄	#15689926	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	16	1	no	—
451	C₂	—	752	2	no	—
452	C₂	C₂×#15689494	1	1	yes	characteristic
453	C₂	#20253855	1	1	yes	characteristic
454	C₂	#20253871	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3206	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#20253841	C₂
hypercenter	#3206	D₄₇
hypocenter	C₄₇	#19623
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3206

Complements

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

N	H ≅ G/N	type
1. #20254331	C₂	semidirect
2. #20253943	C₂	semidirect
3. #20253930	C₂	semidirect
5. C₂×#15689471	C₂	semidirect
6. #20243015	C₂	semidirect
7. #20243012	C₂	semidirect
8. #20242991	C₂	semidirect
9. #20242978	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#3206	C₂	semidirect
16. #15689526	C₂²	semidirect
17. #15689519	C₂²	semidirect
18. #15689519	C₂²	semidirect
23. #15689495	C₂²	semidirect
24. #15689475	C₂²	semidirect
29. #15689469	C₂²	semidirect
38. #15688845	C₂²	semidirect
39. C₈×C₄₇⋊C₈	C₂²	semidirect
42. C₄₇×#492	C₂²	semidirect
43. C₄₇×#487	C₂²	semidirect
154. #10625329	SD₁₆	semidirect
223. #3206	D₄₇	semidirect
253. #492	C₂×D₄₇	semidirect
255. #487	C₂×D₄₇	semidirect
274. C₄₇	#19623	semidirect

Maximal subgroups

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

subgroup	index
#20254331	2
#20253943	2
#20253930	2
#20253841	2
C₂×#15689471	2
#20243015	2
#20243012	2
#20242991	2
#20242978	2
#20241669	2
C₄₇×#3206	2
#19623	47