Subgroups — #26204215

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254511	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253963	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689526	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253848	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253845	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243061	C₂	1	2	yes	maximal, complemented
7	#20243058	C₂	1	2	yes	maximal, complemented
8	#20243005	C₂	1	2	yes	maximal, complemented
9	#20242979	C₂	1	2	yes	maximal, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094055	—	2	2	no	—
13	C₂×#13094054	—	2	2	no	—
14	#15689673	C₂²	1	1	yes	characteristic
15	C₂×#13094024	C₂²	1	1	yes	characteristic
16	#15689528	C₂²	1	2	yes	—
17	#15689526	—	2	2	no	—
18	#15689526	C₂²	1	1	yes	characteristic
19	#15689526	C₂²	1	2	yes	—
20	#15689526	C₂²	1	2	yes	—
21	#15689518	—	2	2	no	—
22	#15689515	—	2	2	no	—
23	#15689502	C₂²	1	2	yes	—
24	#15689502	C₂²	1	2	yes	—
25	#15689499	C₂²	1	1	yes	characteristic
26	#15689497	C₂²	1	2	yes	—
27	#15689495	C₂²	1	2	yes	—
28	#15689471	C₂²	1	1	yes	characteristic
29	#15689470	C₂²	1	2	yes	—
30	#15689469	C₂²	1	1	yes	characteristic
31	#15689437	—	2	2	no	—
32	#15689404	—	2	2	no	—
33	#15689357	—	2	2	no	—
34	C₄×#10625334	—	2	2	no	—
35	C₂×#13093957	—	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	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#500	C₂²	1	2	yes	—
43	C₄₇×#486	C₂²	1	2	yes	—
44	C₄₇×#480	—	2	2	no	—
45	C₄₇×#474	—	2	2	no	—
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	—	2	1	no	—
49	#13094055	—	4	8	no	—
50	#13094054	—	4	8	no	—
51	C₂×#10625337	—	2	4	no	—
52	C₂×#10625337	—	2	4	no	—
53	C₂×#10625335	—	2	4	no	—
54	C₂×#10625336	—	2	4	no	—
55	C₂×#10625334	—	2	2	no	—
56	C₂×#10625329	D₄	1	2	yes	—
57	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
58	#13094024	—	2	1	no	—
59	#13094024	—	2	1	no	—
60	#13094024	—	2	1	no	—
61	#13094024	C₂³	1	2	yes	—
62	#13094024	C₂³	1	1	yes	characteristic
63	#13094021	C₂³	1	1	yes	characteristic
64	#13094012	—	2	1	no	—
65	#13093998	—	2	1	no	—
66	#13093998	—	2	1	no	—
67	C₄×D₁₈₈	—	2	1	no	—
68	C₄×D₁₈₈	—	2	1	no	—
69	C₂×C₄⋊Dic₄₇	—	2	1	no	—
70	C₂×C₄⋊Dic₄₇	—	2	1	no	—
71	#13093958	—	2	4	no	—
72	#13093957	—	2	4	no	—
73	#13093957	—	2	4	no	—
74	#13093957	—	2	2	no	—
75	#13093946	—	2	4	no	—
76	#13093945	—	2	2	no	—
77	#13093944	—	2	2	no	—
78	#13093935	D₄	1	2	yes	—
79	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
80	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
81	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×#41×C₄₇	—	2	1	no	—
84	C₂²×Q₈×C₄₇	—	2	1	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	2	yes	—
89	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
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	#107×C₄₇	—	2	4	no	—
100	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
101	#102×C₄₇	—	2	4	no	—
102	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
103	C₄×C₈×C₄₇	C₂³	1	2	yes	—
104	#41×C₄₇	—	4	4	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	4	1	no	—
108	C₂×Q₈×C₄₇	—	4	4	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×C₂²⋊D₄₇	—	4	1	no	—
119	C₂²×Dic₄₇	—	4	1	no	—
120	#10625350	—	4	4	no	—
121	C₂×D₁₈₈	—	2	1	no	—
122	C₂×D₁₈₈	—	2	1	no	—
123	C₂×D₁₈₈	—	2	1	no	—
124	C₂×C₄×D₄₇	—	4	1	no	—
125	C₂×Dic₉₄	—	2	1	no	—
126	C₂×Dic₉₄	—	2	2	no	—
127	C₂×Dic₉₄	—	4	4	no	—
128	C₂×Dic₉₄	—	4	1	no	—
129	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	4	1	no	—
135	C₄⋊C₄×C₄₇	—	4	1	no	—
136	C₂²⋊C₄×C₄₇	—	4	1	no	—
137	C₂²⋊C₄×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
142	#10625337	—	4	8	no	—
143	#10625337	—	4	8	no	—
144	#10625336	—	4	8	no	—
145	#10625335	—	4	8	no	—
146	#10625334	—	4	4	no	—
147	(C₂×D₄₇)⋊C₄	—	4	1	no	—
148	(C₂×D₄₇)⋊C₄	—	4	1	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	2	no	—
151	C₄⋊Dic₄₇	—	2	2	no	—
152	C₄⋊Dic₄₇	—	2	1	no	—
153	C₄⋊Dic₄₇	—	4	1	no	—
154	C₄⋊Dic₄₇	—	4	1	no	—
155	#10625329	D₈	1	8	yes	complemented
156	C₂×C₄₇⋊C₈	—	2	4	no	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
159	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
160	C₂³×C₄₇	—	4	1	no	—
161	C₂³×C₄₇	#127	1	1	yes	characteristic
162	C₂²×D₄₇	—	4	1	no	—
163	Q₈×C₄₇	—	4	4	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	Q₈×C₄₇	—	8	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	8	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	—	8	2	no	—
176	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
177	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
178	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂²⋊D₄₇	—	8	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₂×Dic₄₇	—	4	1	no	—
186	C₂×Dic₄₇	—	8	2	no	—
187	D₁₈₈	—	4	2	no	—
188	D₁₈₈	—	4	2	no	—
189	D₁₈₈	—	4	2	no	—
190	C₄×D₄₇	—	8	2	no	—
191	Dic₉₄	—	4	4	no	—
192	Dic₉₄	—	4	2	no	—
193	Dic₉₄	—	8	2	no	—
194	C₈×C₄₇	—	2	4	no	—
195	C₄₇⋊C₈	—	2	2	no	—
196	C₄₇⋊C₈	C₂×D₈	1	8	yes	—
197	C₄₇⋊C₈	#137	1	4	yes	complemented
198	#19630	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	8	1	no	—
202	C₂²×C₄₇	—	8	1	no	—
203	C₂²×C₄₇	—	8	1	no	—
204	C₂²×C₄₇	#493	1	2	yes	—
205	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
206	C₂×D₄₇	—	8	1	no	—
207	C₂×D₄₇	—	8	1	no	—
208	C₂×D₄₇	—	8	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	8	1	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	#493	1	2	yes	—
214	C₄×C₄₇	C₂²×D₈	1	2	yes	—
215	C₄×C₄₇	C₂×#137	1	2	yes	—
216	C₄×C₄₇	#578	1	2	yes	—
217	Dic₄₇	—	8	2	no	—
218	Dic₄₇	—	8	1	no	—
219	#3226	—	47	1	no	—
220	#3226	D₄₇	1	1	yes	characteristic, complemented
221	#3169	—	47	1	no	—
222	C₂×#500	—	47	1	no	—
223	#3152	—	47	1	no	—
224	#3152	—	47	1	no	—
225	#1722	—	47	2	no	—
226	#1722	—	47	2	no	—
227	#1713	—	47	2	no	—
228	#1706	—	47	2	no	—
229	C₈×M₁₆	—	47	1	no	—
230	C₂×C₄₇	—	2	2	no	—
231	C₂×C₄₇	—	16	1	no	—
232	C₂×C₄₇	C₂×#493	1	1	yes	characteristic
233	C₂×C₄₇	#3152	1	1	yes	characteristic
234	C₂×C₄₇	#3156	1	1	yes	characteristic
235	D₄₇	—	16	1	no	—
236	C₂×#137	—	94	2	no	—
237	C₂×#137	—	94	2	no	—
238	#532	—	47	1	no	—
239	#532	C₂×D₄₇	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	—	47	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
242	#500	—	47	2	no	—
243	#500	—	47	2	no	—
244	#500	—	47	1	no	—
245	#500	—	47	2	no	—
246	#500	—	94	2	no	—
247	#500	C₂×D₄₇	1	2	yes	—
248	#497	—	94	2	no	—
249	#497	—	94	2	no	—
250	#494	—	47	2	no	—
251	#494	—	47	2	no	—
252	#493	—	47	1	no	—
253	#492	—	47	2	no	—
254	#492	—	47	2	no	—
255	#486	—	47	1	no	—
256	#486	—	47	1	no	—
257	#486	—	47	2	no	—
258	#486	C₂×D₄₇	1	2	yes	—
259	#480	—	2	2	no	—
260	#480	—	94	2	no	—
261	#474	—	2	2	no	—
262	#474	—	94	2	no	—
263	#466	—	94	2	no	—
264	C₄×D₈	—	94	2	no	—
265	#431	C₂×D₄₇	1	1	yes	characteristic
266	C₂×#107	—	94	2	no	—
267	C₄×M₁₆	—	47	1	no	—
268	C₂×C₄×C₈	—	47	1	no	—
269	#322	—	47	2	no	—
270	C₈²	—	47	2	no	—
271	C₄₇	#19630	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	2	1	no	—
273	C₂×#41	—	94	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	—	94	1	no	—
276	#137	—	188	8	no	—
277	#137	—	188	8	no	—
278	C₂×Q₁₆	—	94	4	no	—
279	C₂×Q₁₆	—	94	4	no	—
280	C₂×SD₁₆	—	94	4	no	—
281	C₂×SD₁₆	—	94	4	no	—
282	C₂×D₈	—	94	2	no	—
283	C₂×M₁₆	—	47	2	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	47	2	no	—
289	C₄⋊Q₈	—	47	1	no	—
290	C₄⋊Q₈	—	94	1	no	—
291	C₄⋊Q₈	—	94	1	no	—
292	C₄⋊Q₈	—	94	1	no	—
293	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
294	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
295	#127	—	47	1	no	—
296	#127	C₂²×D₄₇	1	1	yes	characteristic
297	#124	—	2	1	no	—
298	#124	—	94	1	no	—
299	#121	—	2	1	no	—
300	#121	—	2	1	no	—
301	#121	—	94	1	no	—
302	#121	—	94	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	94	1	no	—
306	C₄×D₄	—	94	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	94	1	no	—
310	C₂×C₄⋊C₄	—	94	1	no	—
311	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
312	#107	—	2	4	no	—
313	#107	—	94	4	no	—
314	#107	—	94	4	no	—
315	#107	—	94	2	no	—
316	#107	—	94	4	no	—
317	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
318	#102	—	2	4	no	—
319	#102	—	94	2	no	—
320	#102	—	94	2	no	—
321	#102	—	94	4	no	—
322	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
323	#97	—	47	2	no	—
324	C₄×C₈	—	47	2	no	—
325	C₄×C₈	—	47	1	no	—
326	C₄×C₈	—	47	2	no	—
327	C₄×C₈	—	47	1	no	—
328	C₄×C₈	C₂²×D₄₇	1	2	yes	—
329	#41	—	4	4	no	—
330	#41	—	188	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	4	1	no	—
334	C₂×Q₈	—	4	4	no	—
335	C₂×Q₈	—	94	1	no	—
336	C₂×Q₈	—	94	2	no	—
337	C₂×Q₈	—	188	4	no	—
338	C₂×Q₈	—	188	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	1	no	—
344	C₂×D₄	—	94	1	no	—
345	C₂×D₄	—	94	1	no	—
346	C₂×D₄	—	188	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	188	1	no	—
350	C₂²×C₄	—	188	1	no	—
351	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
354	Q₁₆	—	188	8	no	—
355	Q₁₆	—	188	8	no	—
356	SD₁₆	—	188	8	no	—
357	SD₁₆	—	188	8	no	—
358	D₈	—	188	4	no	—
359	M₁₆	—	47	8	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	47	4	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	94	4	no	—
364	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	—	94	1	no	—
375	C₄⋊C₄	—	188	1	no	—
376	C₄⋊C₄	—	188	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	188	1	no	—
380	C₂²⋊C₄	—	188	1	no	—
381	C₄²	D₄×D₄₇	1	1	yes	characteristic
382	C₄²	D₄×D₄₇	1	1	yes	characteristic
383	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₄²	C₂³×D₄₇	1	1	yes	characteristic
385	C₂³	—	4	1	no	—
386	C₂³	—	188	1	no	—
387	C₂³	#13094020	1	1	yes	characteristic
388	Q₈	—	4	4	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	8	2	no	—
391	Q₈	—	376	2	no	—
392	Q₈	—	188	4	no	—
393	Q₈	—	188	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	376	2	no	—
399	D₄	—	188	2	no	—
400	D₄	—	188	2	no	—
401	D₄	—	188	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	376	2	no	—
409	C₂×C₄	—	376	2	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	2	no	—
412	C₂×C₄	#13094020	1	1	yes	characteristic
413	C₂×C₄	#13094020	1	1	yes	characteristic
414	C₂×C₄	#13094020	1	1	yes	characteristic
415	C₂×C₄	D₈×D₄₇	1	4	yes	—
416	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₈	—	47	8	no	—
421	C₈	—	47	4	no	—
422	C₈	—	94	2	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	376	1	no	—
429	C₂²	—	376	1	no	—
430	C₂²	—	376	1	no	—
431	C₂²	#15689498	1	2	yes	—
432	C₂²	C₂×#13094020	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	8	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	376	1	no	—
438	C₄	—	376	2	no	—
439	C₄	#15689498	1	2	yes	—
440	C₄	C₂×D₈×D₄₇	1	2	yes	—
441	C₄	#137×D₄₇	1	2	yes	—
442	C₄	#15689938	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	16	1	no	—
445	C₂	—	752	1	no	—
446	C₂	C₂×#15689498	1	1	yes	characteristic
447	C₂	#20253843	1	1	yes	characteristic
448	C₂	#20253879	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3226	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#20253963	C₂
hypercenter	#3226	D₄₇
hypocenter	C₄₇	#19630
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3226

Complements

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

N	H ≅ G/N	type
1. #20254511	C₂	semidirect
3. C₂×#15689526	C₂	semidirect
4. #20253848	C₂	semidirect
5. #20253845	C₂	semidirect
6. #20243061	C₂	semidirect
7. #20243058	C₂	semidirect
8. #20243005	C₂	semidirect
9. #20242979	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#3226	C₂	semidirect
155. #10625329	D₈	semidirect
197. C₄₇⋊C₈	#137	semidirect
220. #3226	D₄₇	semidirect
271. C₄₇	#19630	semidirect

Maximal subgroups

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

subgroup	index
#20254511	2
#20253963	2
C₂×#15689526	2
#20253848	2
#20253845	2
#20243061	2
#20243058	2
#20243005	2
#20242979	2
#20241669	2
C₄₇×#3226	2
#19630	47