Subgroups — #26198754

Order 12032.

664 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	#20253967	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253449	C₂	1	2	yes	maximal, complemented
3	C₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242805	C₂	1	2	yes	maximal, complemented
5	#20242798	C₂	1	2	yes	maximal, complemented
6	#20242793	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242788	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242749	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242744	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242048	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	2	yes	—
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689528	C₂²	1	1	yes	characteristic
15	#15689500	C₂²	1	1	yes	characteristic
16	#15689470	C₂²	1	2	yes	—
17	#15689448	—	2	2	no	—
18	#15689419	C₂²	1	2	yes	—
19	#15689414	C₂²	1	2	yes	—
20	#15689359	—	2	1	no	—
21	#15689359	—	2	1	no	—
22	#15689324	C₂²	1	2	yes	—
23	#15689319	C₂²	1	2	yes	—
24	#15689270	—	2	2	no	—
25	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
27	C₄×#10625325	—	2	2	no	—
28	C₄×D₃₇₆	—	2	1	no	—
29	C₄×D₃₇₆	—	2	1	no	—
30	C₄×D₃₇₆	—	2	2	no	—
31	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
32	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₄₇	—	2	1	no	—
34	C₈×C₂²⋊D₄₇	—	2	1	no	—
35	#15689176	C₂²	1	1	yes	characteristic
36	#15689174	—	2	1	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688871	C₂²	1	2	yes	—
39	#15688871	C₂²	1	2	yes	—
40	#15688866	C₂²	1	2	yes	—
41	#15688866	C₂²	1	2	yes	—
42	C₄₇×#431	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#335	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	1	yes	characteristic
46	C₄₇×#334	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	2	no	—
48	C₂×#10625350	D₄	1	1	yes	characteristic
49	C₂×#10625325	—	2	2	no	—
50	C₂×D₃₇₆	—	2	2	no	—
51	C₂×D₃₇₆	—	2	1	no	—
52	C₂×D₃₇₆	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	1	no	—
55	#13094024	C₂³	1	2	yes	—
56	#13094021	C₂³	1	2	yes	—
57	#13094012	—	2	2	no	—
58	#13093998	—	2	2	no	—
59	#13093998	—	2	2	no	—
60	C₄×Dic₉₄	D₄	1	1	yes	characteristic
61	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
62	C₄×D₁₈₈	—	2	2	no	—
63	C₄×D₁₈₈	—	2	2	no	—
64	C₄×D₁₈₈	D₄	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₇	—	2	1	no	—
67	C₄×C₂²⋊D₄₇	—	2	1	no	—
68	#13093983	D₄	1	1	yes	characteristic
69	#13093981	—	2	1	no	—
70	C₄²×D₄₇	—	2	1	no	—
71	#13093958	—	2	1	no	—
72	#13093958	—	2	1	no	—
73	#13093958	—	2	2	no	—
74	#13093956	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₇⋊C₈	—	2	1	no	—
78	Dic₄₇⋊C₈	—	2	1	no	—
79	#13093949	—	2	2	no	—
80	#13093946	—	2	2	no	—
81	#13093946	—	2	2	no	—
82	#13093946	—	2	2	no	—
83	#13093946	—	2	2	no	—
84	#13093946	—	2	2	no	—
85	C₂²⋊(C₄₇⋊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	C₈×Dic₄₇	—	2	1	no	—
90	C₈×Dic₄₇	—	2	1	no	—
91	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
95	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
96	C₂²⋊C₈×C₄₇	—	2	2	no	—
97	C₄×C₈×C₄₇	—	2	2	no	—
98	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	1	no	—
106	C₂×C₂²⋊D₄₇	—	4	2	no	—
107	#10625350	—	2	2	no	—
108	#10625350	—	2	2	no	—
109	#10625350	—	8	4	no	—
110	C₂×D₁₈₈	—	2	2	no	—
111	C₂×D₁₈₈	—	2	2	no	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	4	2	no	—
118	C₂×Dic₉₄	—	2	2	no	—
119	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	4	1	no	—
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	#41	1	1	yes	characteristic
131	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₄₇	—	2	1	no	—
133	(C₂×D₄₇)⋊C₄	—	2	1	no	—
134	(C₂×D₄₇)⋊C₄	—	2	1	no	—
135	(C₂×D₄₇)⋊C₄	—	4	2	no	—
136	(C₂×D₄₇)⋊C₄	—	4	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
141	Dic₄₇⋊C₄	—	2	1	no	—
142	Dic₄₇⋊C₄	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	D₃₇₆	—	4	2	no	—
149	D₃₇₆	—	4	4	no	—
150	D₃₇₆	—	4	2	no	—
151	#10625325	—	4	4	no	—
152	C₈×D₄₇	—	4	2	no	—
153	C₈×D₄₇	—	4	2	no	—
154	C₂³×C₄₇	#121	1	1	yes	characteristic
155	C₂²×D₄₇	—	2	1	no	—
156	C₂²×D₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₄₇	—	2	4	no	—
169	C₂²⋊D₄₇	—	8	4	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	D₁₈₈	—	2	1	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	4	2	no	—
177	D₁₈₈	—	4	2	no	—
178	D₁₈₈	—	4	2	no	—
179	D₁₈₈	—	8	2	no	—
180	D₁₈₈	#135	1	2	yes	—
181	C₄×D₄₇	—	2	4	no	—
182	C₄×D₄₇	—	4	1	no	—
183	C₄×D₄₇	—	4	1	no	—
184	C₄×D₄₇	—	4	2	no	—
185	C₄×D₄₇	—	8	4	no	—
186	Dic₉₄	—	2	1	no	—
187	Dic₉₄	—	8	2	no	—
188	Dic₉₄	#135	1	2	yes	—
189	C₈×C₄₇	—	2	1	no	—
190	C₈×C₄₇	—	2	1	no	—
191	C₈×C₄₇	—	2	1	no	—
192	C₈×C₄₇	—	4	2	no	—
193	C₈×C₄₇	—	4	2	no	—
194	C₈×C₄₇	#135	1	2	yes	—
195	C₄₇⋊C₈	—	4	1	no	—
196	C₄₇⋊C₈	—	4	1	no	—
197	#19128	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
202	C₂×D₄₇	—	2	2	no	—
203	C₂×D₄₇	—	4	1	no	—
204	C₂×D₄₇	—	4	1	no	—
205	C₂×D₄₇	—	8	2	no	—
206	C₂×D₄₇	—	8	2	no	—
207	C₂×D₄₇	—	8	2	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	#472	1	2	yes	—
212	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
213	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
215	C₄×C₄₇	#575	1	1	yes	characteristic
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	4	1	no	—
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	8	2	no	—
220	#3169	—	47	1	no	—
221	#3106	—	47	2	no	—
222	C₈×#41	—	47	1	no	—
223	#1678	—	47	2	no	—
224	#1677	—	47	2	no	—
225	#1676	—	47	1	no	—
226	#1675	—	47	1	no	—
227	#1668	—	47	1	no	—
228	#1667	—	47	1	no	—
229	#1564	D₄₇	1	1	yes	characteristic, complemented
230	#1543	—	47	2	no	—
231	C₂×C₄₇	—	4	1	no	—
232	C₂×C₄₇	#3035	1	1	yes	characteristic
233	C₂×C₄₇	#3050	1	1	yes	characteristic
234	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
235	D₄₇	—	4	2	no	—
236	D₄₇	—	16	2	no	—
237	#532	—	47	2	no	—
238	C₄×#41	—	47	1	no	—
239	#500	—	47	1	no	—
240	#493	—	47	1	no	—
241	#486	—	47	2	no	—
242	#482	—	94	2	no	—
243	#477	—	47	2	no	—
244	#476	—	47	2	no	—
245	#466	—	94	1	no	—
246	#466	—	94	1	no	—
247	#460	—	47	2	no	—
248	#459	—	47	2	no	—
249	#449	—	94	2	no	—
250	C₈×Q₈	—	47	1	no	—
251	C₈×Q₈	—	47	1	no	—
252	C₄×SD₁₆	—	94	2	no	—
253	C₄×D₈	—	94	2	no	—
254	C₄×D₈	—	94	1	no	—
255	C₄×D₈	—	94	1	no	—
256	C₈×D₄	—	47	1	no	—
257	C₈×D₄	—	47	1	no	—
258	C₈×D₄	—	94	1	no	—
259	C₈×D₄	—	94	1	no	—
260	#431	—	47	1	no	—
261	#431	—	94	1	no	—
262	#431	C₂×D₄₇	1	2	yes	—
263	C₂×C₄×C₈	—	94	1	no	—
264	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
265	#335	C₂×D₄₇	1	1	yes	characteristic
266	#335	C₂×D₄₇	1	1	yes	characteristic
267	#334	C₂×D₄₇	1	2	yes	—
268	#333	—	47	2	no	—
269	#333	—	47	2	no	—
270	#331	—	47	2	no	—
271	#331	—	47	2	no	—
272	C₄₇	#19128	1	1	yes	characteristic, complemented, Sylow
273	C₂×#41	—	47	1	no	—
274	C₂×#41	—	94	2	no	—
275	C₂×SD₁₆	—	94	2	no	—
276	C₂×D₈	—	94	2	no	—
277	C₂×D₈	—	94	1	no	—
278	C₂×D₈	—	94	1	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₂²×C₈	—	94	1	no	—
281	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
282	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
283	C₄⋊Q₈	—	47	2	no	—
284	#127	—	47	2	no	—
285	#124	—	94	2	no	—
286	#121	—	94	2	no	—
287	#121	—	94	2	no	—
288	C₄×Q₈	—	47	1	no	—
289	C₄×Q₈	—	47	1	no	—
290	C₄×D₄	—	47	1	no	—
291	C₄×D₄	—	47	1	no	—
292	C₄×D₄	—	94	1	no	—
293	C₄×D₄	—	94	1	no	—
294	C₄×D₄	—	94	2	no	—
295	C₄×D₄	—	94	2	no	—
296	#117	—	47	1	no	—
297	#117	—	94	1	no	—
298	C₂×C₄²	—	94	1	no	—
299	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
300	#107	—	94	2	no	—
301	#107	—	94	1	no	—
302	#107	—	94	1	no	—
303	#106	—	94	2	no	—
304	C₄⋊C₈	—	47	1	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	—	94	1	no	—
307	C₄⋊C₈	—	94	1	no	—
308	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
309	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
310	#103	—	94	2	no	—
311	#102	—	94	2	no	—
312	#102	—	94	2	no	—
313	#102	—	94	2	no	—
314	#102	—	94	2	no	—
315	#102	—	94	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	94	1	no	—
318	C₂²⋊C₈	—	94	1	no	—
319	C₂²⋊C₈	—	94	1	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	94	1	no	—
322	C₄×C₈	—	94	1	no	—
323	C₄×C₈	—	94	1	no	—
324	C₄×C₈	D₁₈₈	1	1	yes	characteristic
325	C₄×C₈	D₁₈₈	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
328	#41	—	94	2	no	—
329	#41	—	94	2	no	—
330	#41	—	376	4	no	—
331	C₂×Q₈	—	47	1	no	—
332	C₂×Q₈	—	94	2	no	—
333	C₂×D₄	—	47	1	no	—
334	C₂×D₄	—	94	1	no	—
335	C₂×D₄	—	94	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂×D₄	—	94	2	no	—
338	C₂×D₄	—	188	2	no	—
339	C₂²×C₄	—	94	1	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	—	188	2	no	—
343	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
344	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
345	C₂²×C₄	#10625354	1	1	yes	characteristic
346	SD₁₆	—	188	4	no	—
347	D₈	—	188	2	no	—
348	D₈	—	188	4	no	—
349	D₈	—	188	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	188	2	no	—
357	C₂×C₈	—	188	2	no	—
358	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
359	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
360	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
361	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
362	C₄⋊C₄	—	47	1	no	—
363	C₄⋊C₄	—	47	1	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₂²⋊C₄	—	94	1	no	—
369	C₂²⋊C₄	—	94	1	no	—
370	C₂²⋊C₄	—	94	1	no	—
371	C₂²⋊C₄	—	188	2	no	—
372	C₂²⋊C₄	—	188	2	no	—
373	C₄²	—	94	1	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	1	no	—
376	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
377	C₄²	D₄×D₄₇	1	1	yes	characteristic
378	C₄²	#10625354	1	1	yes	characteristic
379	C₄²	C₂³×D₄₇	1	1	yes	characteristic
380	C₂³	—	94	1	no	—
381	C₂³	—	188	2	no	—
382	C₂³	#13093999	1	1	yes	characteristic
383	Q₈	—	47	2	no	—
384	Q₈	—	94	1	no	—
385	Q₈	—	376	2	no	—
386	D₄	—	47	2	no	—
387	D₄	—	94	4	no	—
388	D₄	—	94	1	no	—
389	D₄	—	376	2	no	—
390	D₄	—	376	4	no	—
391	D₄	—	188	2	no	—
392	D₄	—	188	2	no	—
393	D₄	—	188	2	no	—
394	D₄	—	188	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	94	4	no	—
401	C₂×C₄	—	94	1	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	376	4	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	#13093999	1	1	yes	characteristic
410	C₂×C₄	#13093999	1	1	yes	characteristic
411	C₂×C₄	#13093999	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	188	1	no	—
421	C₈	—	188	1	no	—
422	C₈	#13094046	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	94	2	no	—
427	C₂²	—	376	2	no	—
428	C₂²	—	376	2	no	—
429	C₂²	—	376	2	no	—
430	C₂²	—	188	1	no	—
431	C₂²	—	188	1	no	—
432	C₂²	C₂×#13093999	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	94	2	no	—
437	C₄	—	376	2	no	—
438	C₄	—	188	1	no	—
439	C₄	—	188	1	no	—
440	C₄	#15689394	1	2	yes	—
441	C₄	#135×D₄₇	1	1	yes	characteristic
442	C₄	#135×D₄₇	1	1	yes	characteristic
443	C₄	C₂×#13094046	1	1	yes	characteristic
444	C₄	#15689923	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	188	2	no	—
447	C₂	—	752	2	no	—
448	C₂	#20252845	1	1	yes	characteristic
449	C₂	#20252970	1	1	yes	characteristic
450	C₂	C₂×#15689394	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093999
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1564	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#1564	D₄₇
hypocenter	C₄₇	#19128
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #20253967	C₂	semidirect
2. #20253449	C₂	semidirect
3. C₈×#10625350	C₂	semidirect
4. #20242805	C₂	semidirect
5. #20242798	C₂	semidirect
6. #20242793	C₂	semidirect
7. #20242788	C₂	semidirect
8. #20242749	C₂	semidirect
9. #20242744	C₂	semidirect
10. #20242048	C₂	semidirect
11. C₄₇×#1564	C₂	semidirect
229. #1564	D₄₇	semidirect
272. C₄₇	#19128	semidirect

Maximal subgroups

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

subgroup	index
#20253967	2
#20253449	2
C₈×#10625350	2
#20242805	2
#20242798	2
#20242793	2
#20242788	2
#20242749	2
#20242744	2
#20242048	2
C₄₇×#1564	2
#19128	47