Subgroups — #26223059

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252969	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689239	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252087	C₂	1	2	yes	maximal, complemented
4	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244274	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244134	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244097	C₂	1	2	yes	maximal, complemented
8	#20243834	C₂	1	2	yes	maximal, complemented
9	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243231	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	C₂²×#10625329	C₂²	1	1	yes	characteristic
15	#15689634	C₂²	1	2	yes	—
16	C₂×#13093983	C₂²	1	1	yes	characteristic
17	#15689364	C₄	1	2	yes	complemented
18	#15689359	C₄	1	2	yes	complemented
19	#15689352	C₄	1	4	yes	complemented
20	#15689239	—	2	4	no	—
21	#15689198	—	2	4	no	—
22	#15689197	—	2	4	no	—
23	#15689161	C₂²	1	1	yes	characteristic
24	#15689151	C₂²	1	2	yes	—
25	C₂×#13093950	C₂²	1	2	yes	—
26	C₂×#13093950	C₂²	1	2	yes	—
27	#15689120	C₂²	1	2	yes	—
28	#15689091	C₂²	1	2	yes	—
29	#15689081	C₂²	1	2	yes	—
30	#15689078	—	2	4	no	—
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688884	C₂²	1	2	yes	—
36	#15688884	C₂²	1	2	yes	—
37	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#407	C₂²	1	2	yes	—
41	C₄₇×#341	C₂²	1	2	yes	—
42	C₂×#10625350	C₂³	1	2	yes	—
43	#13094046	—	2	2	no	—
44	#13094046	—	2	2	no	—
45	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
46	C₂×#10625325	C₂×C₄	1	2	yes	—
47	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
48	#13094032	—	2	4	no	—
49	#13094032	—	2	4	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625329	—	2	2	no	—
52	C₂×#10625329	D₄	1	2	yes	—
53	C₂×#10625329	D₄	1	2	yes	—
54	C₂×#10625324	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₄₇	—	2	2	no	—
58	#13094007	—	2	2	no	—
59	#13094003	C₂×C₄	1	4	yes	—
60	#13093998	C₂×C₄	1	4	yes	—
61	#13093993	—	2	2	no	—
62	C₄×C₂²⋊D₄₇	—	2	4	no	—
63	#13093983	—	2	2	no	—
64	#13093983	—	2	2	no	—
65	#13093983	C₂³	1	2	yes	—
66	C₂×C₄⋊Dic₄₇	—	2	1	no	—
67	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	#13093958	C₂×C₄	1	2	yes	—
71	#13093956	C₂×C₄	1	2	yes	—
72	Dic₄₇⋊C₈	—	2	4	no	—
73	#13093950	—	2	4	no	—
74	#13093950	—	2	4	no	—
75	#13093949	C₂×C₄	1	4	yes	—
76	#13093946	C₂×C₄	1	4	yes	—
77	(C₂×D₄₇)⋊C₈	—	2	4	no	—
78	#13093934	—	2	2	no	—
79	#13093934	—	2	2	no	—
80	#13093934	—	2	2	no	—
81	C₈×Dic₄₇	—	2	2	no	—
82	C₈×Dic₄₇	—	2	2	no	—
83	C₈×Dic₄₇	D₄	1	4	yes	complemented
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
86	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₇	—	2	2	no	—
88	C₂²×C₈×C₄₇	—	2	2	no	—
89	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
90	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	#108×C₄₇	—	2	2	no	—
94	#108×C₄₇	—	2	2	no	—
95	C₂²⋊C₈×C₄₇	—	2	4	no	—
96	C₂⁴×C₄₇	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	2	no	—
106	C₂×C₂²⋊D₄₇	—	2	4	no	—
107	C₂²×Dic₄₇	—	2	1	no	—
108	C₂²×Dic₄₇	—	2	1	no	—
109	#10625350	—	2	2	no	—
110	#10625350	—	2	2	no	—
111	#10625350	—	2	2	no	—
112	#10625350	—	2	2	no	—
113	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
116	M₁₆×C₄₇	—	2	2	no	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	4	no	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	#41	1	2	yes	—
131	C₂²⋊Dic₄₇	—	2	4	no	—
132	C₂²⋊Dic₄₇	—	2	4	no	—
133	C₂²⋊Dic₄₇	—	2	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	4	no	—
135	C₄⋊Dic₄₇	—	2	4	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
137	Dic₄₇⋊C₄	—	2	4	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
142	C₄×Dic₄₇	#41	1	2	yes	—
143	#10625329	—	2	4	no	—
144	#10625329	—	2	4	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄₇⋊C₈	#41	1	2	yes	—
152	Dic₁₈₈	—	2	2	no	—
153	D₃₇₆	—	2	2	no	—
154	#10625325	—	2	4	no	—
155	#10625324	—	4	4	no	—
156	C₈×D₄₇	—	4	4	no	—
157	C₂³×C₄₇	—	2	1	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	C₄×D₄	1	2	yes	—
161	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂²×D₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	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	C₂²⋊D₄₇	—	4	2	no	—
177	C₂²⋊D₄₇	—	4	2	no	—
178	C₂²⋊D₄₇	—	8	4	no	—
179	C₂×Dic₄₇	—	2	4	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	D₁₈₈	—	2	2	no	—
186	D₁₈₈	—	2	2	no	—
187	C₄×D₄₇	—	4	2	no	—
188	C₄×D₄₇	—	4	2	no	—
189	Dic₉₄	—	2	2	no	—
190	Dic₉₄	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	4	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	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	#121	1	2	yes	—
198	C₄₇⋊C₈	#121	1	2	yes	—
199	#21545	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	2	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₄₇	#525	1	1	yes	characteristic
208	C₂²×C₄₇	#529	1	1	yes	characteristic
209	C₂×D₄₇	—	4	4	no	—
210	C₂×D₄₇	—	4	2	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
215	C₄×C₄₇	#532	1	1	yes	characteristic
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	4	4	no	—
219	Dic₄₇	—	4	2	no	—
220	#3050	—	47	1	no	—
221	C₂×#443	—	47	1	no	—
222	#2930	—	47	2	no	—
223	C₂×#405	—	47	1	no	—
224	#1974	—	47	1	no	—
225	#1945	—	47	1	no	—
226	#1938	—	47	2	no	—
227	#1897	—	47	2	no	—
228	#1810	D₄₇	1	1	yes	characteristic, complemented
229	#1772	—	47	1	no	—
230	#1765	—	47	2	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	4	2	no	—
234	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
235	C₂×C₄₇	#2957	1	2	yes	—
236	D₄₇	—	8	2	no	—
237	C₂×#135	—	47	1	no	—
238	C₂×#131	—	47	2	no	—
239	C₂²×M₁₆	—	47	1	no	—
240	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
241	#525	—	47	2	no	—
242	C₂×#117	—	47	1	no	—
243	#467	—	47	2	no	—
244	#466	—	47	2	no	—
245	#465	—	47	4	no	—
246	#443	—	94	4	no	—
247	#436	—	94	4	no	—
248	#435	—	94	4	no	—
249	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
250	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
251	#427	—	47	1	no	—
252	#424	—	47	2	no	—
253	C₂×#104	—	47	2	no	—
254	C₂×#104	—	47	2	no	—
255	#416	—	47	2	no	—
256	#408	—	47	2	no	—
257	#407	C₂×D₄₇	1	2	yes	—
258	#405	—	47	2	no	—
259	#405	—	94	4	no	—
260	C₂×#97	—	47	1	no	—
261	C₂×#97	—	47	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	#341	C₂×D₄₇	1	2	yes	—
265	#339	—	47	2	no	—
266	#339	—	47	2	no	—
267	C₄₇	#21545	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	47	2	no	—
269	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
270	#135	—	94	2	no	—
271	#135	—	94	2	no	—
272	C₂×Q₁₆	—	47	1	no	—
273	C₂×SD₁₆	—	47	2	no	—
274	C₂×D₈	—	47	1	no	—
275	#131	—	94	4	no	—
276	#131	—	94	4	no	—
277	C₂×M₁₆	—	47	2	no	—
278	C₂×M₁₆	—	47	2	no	—
279	C₂×M₁₆	—	94	2	no	—
280	C₂×M₁₆	—	94	2	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
283	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₂²×C₈	C₄×D₄₇	1	2	yes	—
290	C₂²×C₈	C₄×D₄₇	1	2	yes	—
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
293	#123	—	94	2	no	—
294	C₂²⋊Q₈	—	47	4	no	—
295	#121	—	47	4	no	—
296	#120	—	94	2	no	—
297	C₄×D₄	—	94	4	no	—
298	#117	—	47	2	no	—
299	#117	—	94	2	no	—
300	#117	—	94	2	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₂²⋊C₄	—	94	1	no	—
303	C₂×C₄²	—	47	1	no	—
304	C₂×C₄²	—	47	1	no	—
305	#108	—	2	2	no	—
306	#108	—	2	2	no	—
307	#107	—	47	2	no	—
308	#106	—	47	2	no	—
309	C₄⋊C₈	—	94	4	no	—
310	#104	—	94	4	no	—
311	#104	—	94	4	no	—
312	#103	—	47	4	no	—
313	#102	—	47	4	no	—
314	C₂²⋊C₈	—	2	4	no	—
315	C₂²⋊C₈	—	94	4	no	—
316	#97	—	94	2	no	—
317	#97	—	94	2	no	—
318	#97	—	94	2	no	—
319	C₄×C₈	—	47	4	no	—
320	C₄×C₈	—	94	2	no	—
321	C₄×C₈	—	94	2	no	—
322	C₂⁴	#10625354	1	1	yes	characteristic
323	#41	—	94	2	no	—
324	#41	—	94	2	no	—
325	#41	—	94	2	no	—
326	#41	—	94	2	no	—
327	C₂×Q₈	—	47	2	no	—
328	C₂×D₄	—	47	2	no	—
329	C₂×D₄	—	94	4	no	—
330	C₂×D₄	—	94	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	94	2	no	—
338	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
339	C₂²×C₄	D₄×D₄₇	1	2	yes	—
340	C₂²×C₄	#10625354	1	1	yes	characteristic
341	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
342	Q₁₆	—	94	2	no	—
343	SD₁₆	—	94	4	no	—
344	D₈	—	94	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	94	4	no	—
350	M₁₆	—	94	4	no	—
351	M₁₆	—	188	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	47	1	no	—
360	C₂×C₈	—	47	1	no	—
361	C₂×C₈	—	47	2	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	94	1	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	188	4	no	—
366	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
367	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₈	D₄×D₄₇	1	2	yes	—
370	C₂×C₈	#10625352	1	2	yes	—
371	C₄⋊C₄	—	47	4	no	—
372	C₄⋊C₄	—	94	4	no	—
373	C₄⋊C₄	—	94	4	no	—
374	C₂²⋊C₄	—	94	4	no	—
375	C₂²⋊C₄	—	94	4	no	—
376	C₂²⋊C₄	—	94	2	no	—
377	C₂²⋊C₄	—	94	4	no	—
378	C₄²	—	47	2	no	—
379	C₄²	—	47	2	no	—
380	C₄²	—	94	1	no	—
381	C₄²	—	94	2	no	—
382	C₄²	—	94	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	94	2	no	—
387	C₂³	#13093986	1	2	yes	—
388	C₂³	C₂×#10625354	1	1	yes	characteristic
389	Q₈	—	94	2	no	—
390	Q₈	—	94	2	no	—
391	D₄	—	94	2	no	—
392	D₄	—	94	2	no	—
393	D₄	—	376	4	no	—
394	D₄	—	188	2	no	—
395	D₄	—	188	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	94	4	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	#13093986	1	2	yes	—
411	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
415	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	47	2	no	—
421	C₈	—	47	2	no	—
422	C₈	—	94	2	no	—
423	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
424	C₈	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	188	2	no	—
432	C₂²	—	188	4	no	—
433	C₂²	C₂×#13093986	1	1	yes	characteristic
434	C₂²	#15689636	1	1	yes	characteristic
435	C₂²	#15689659	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	188	2	no	—
438	C₄	—	188	2	no	—
439	C₄	—	188	2	no	—
440	C₄	—	188	4	no	—
441	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
442	C₄	#15689591	1	1	yes	characteristic
443	C₄	#121×D₄₇	1	1	yes	characteristic
444	C₄	#15689668	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	4	2	no	—
448	C₂	—	376	2	no	—
449	C₂	#20245894	1	1	yes	characteristic
450	C₂	#20252304	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1810	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252969	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1810	D₄₇
hypocenter	C₄₇	#21545
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1810

Complements

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

N	H ≅ G/N	type
2. C₂×#15689239	C₂	semidirect
3. #20252087	C₂	semidirect
4. C₂×#15689078	C₂	semidirect
5. #20244274	C₂	semidirect
6. #20244134	C₂	semidirect
7. #20244097	C₂	semidirect
8. #20243834	C₂	semidirect
9. #20243270	C₂	semidirect
10. #20243231	C₂	semidirect
11. C₄₇×#1810	C₂	semidirect
17. #15689364	C₄	semidirect
18. #15689359	C₄	semidirect
19. #15689352	C₄	semidirect
83. C₈×Dic₄₇	D₄	semidirect
228. #1810	D₄₇	semidirect
267. C₄₇	#21545	semidirect

Maximal subgroups

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

subgroup	index
#20252969	2
C₂×#15689239	2
#20252087	2
C₂×#15689078	2
#20244274	2
#20244134	2
#20244097	2
#20243834	2
#20243270	2
#20243231	2
C₄₇×#1810	2
#21545	47