Subgroups — #26105724

Order 12032.

684 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252016	C₂	1	1	yes	maximal, characteristic
2	#431×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
4	#20241221	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241220	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241220	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13093981	—	2	1	no	—
9	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
10	#15689179	C₄	1	2	yes	complemented
11	#15689177	—	2	1	no	—
12	#15689176	C₂²	1	1	yes	characteristic
13	#15689176	C₂²	1	1	yes	characteristic
14	#15689175	C₄	1	2	yes	complemented
15	#15689174	—	2	1	no	—
16	#15689174	—	2	1	no	—
17	#15689173	—	2	1	no	—
18	#15689145	C₄	1	2	yes	complemented
19	C₄⋊C₈×D₄₇	C₄	1	2	yes	complemented
20	#15689085	—	2	1	no	—
21	C₂²⋊C₈×D₄₇	—	2	1	no	—
22	C₄×#10625324	—	2	1	no	—
23	C₄×C₈×D₄₇	—	2	1	no	—
24	C₄×Dic₄₇⋊C₄	—	2	1	no	—
25	C₄×Dic₄₇⋊C₄	C₄	1	2	yes	—
26	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
27	C₄×(C₂×D₄₇)⋊C₄	C₄	1	2	yes	—
28	#15688969	—	2	1	no	—
29	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#431	C₂²	1	1	yes	characteristic
31	C₄₇×#431	C₂²	1	1	yes	characteristic
32	C₄³×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
36	C₂×#10625324	—	2	2	no	—
37	C₂×C₈×D₄₇	—	2	2	no	—
38	#13093981	—	2	8	no	—
39	C₂×Dic₄₇⋊C₄	—	2	2	no	—
40	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	1	no	—
42	C₂×C₄×Dic₄₇	—	2	1	no	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
47	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₄₇	D₄	1	1	yes	characteristic
52	C₄²×D₄₇	D₄	1	1	yes	characteristic
53	C₄²×D₄₇	Q₈	1	1	yes	characteristic
54	C₄²×D₄₇	Q₈	1	1	yes	characteristic
55	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
57	Dic₄₇⋊C₈	—	2	2	no	—
58	Dic₄₇⋊C₈	—	2	2	no	—
59	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
61	(C₂×D₄₇)⋊C₈	—	2	2	no	—
62	(C₂×D₄₇)⋊C₈	—	2	2	no	—
63	#13093934	—	2	2	no	—
64	C₄×C₄₇⋊C₈	—	2	1	no	—
65	C₄×C₄₇⋊C₈	—	2	1	no	—
66	C₈×Dic₄₇	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	1	no	—
70	C₂×C₄²×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
74	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
75	C₂²⋊C₈×C₄₇	—	2	1	no	—
76	C₂²⋊C₈×C₄₇	—	2	1	no	—
77	C₄×C₈×C₄₇	—	2	1	no	—
78	C₄×C₈×C₄₇	—	2	1	no	—
79	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₄₇	—	2	2	no	—
85	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₄₇	—	2	2	no	—
89	C₂×C₄×D₄₇	—	2	2	no	—
90	C₂×C₄×D₄₇	—	2	4	no	—
91	C₂×C₄×D₄₇	—	4	2	no	—
92	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	4	2	no	—
110	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
114	(C₂×D₄₇)⋊C₄	—	2	8	no	—
115	Dic₄₇⋊C₄	—	2	8	no	—
116	C₄×Dic₄₇	—	2	4	no	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	—	4	2	no	—
120	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
121	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
122	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	#10625324	—	4	4	no	—
135	C₈×D₄₇	—	4	4	no	—
136	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	—	2	2	no	—
139	C₂²×D₄₇	—	4	1	no	—
140	C₂²×D₄₇	#95	1	1	yes	characteristic
141	C₂²×D₄₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#131	1	2	yes	—
154	C₂×C₄×C₄₇	#131	1	2	yes	—
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	4	1	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	#95	1	1	yes	characteristic
162	C₂×Dic₄₇	#95	1	1	yes	characteristic
163	C₂×Dic₄₇	#95	1	1	yes	characteristic
164	C₂×Dic₄₇	#95	1	1	yes	characteristic
165	C₂×Dic₄₇	#95	1	1	yes	characteristic
166	C₂×Dic₄₇	#95	1	1	yes	characteristic
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	2	1	no	—
169	C₄×D₄₇	—	2	1	no	—
170	C₄×D₄₇	—	2	1	no	—
171	C₄×D₄₇	—	2	1	no	—
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	2	2	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	4	1	no	—
180	C₄×D₄₇	#104	1	4	yes	—
181	C₈×C₄₇	—	4	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	—	4	2	no	—
185	#7869	—	47	1	no	maximal, Sylow
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
189	C₂²×C₄₇	#408	1	2	yes	—
190	C₂×D₄₇	—	2	1	no	—
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	2	1	no	—
193	C₂×D₄₇	—	2	1	no	—
194	C₂×D₄₇	—	2	1	no	—
195	C₂×D₄₇	—	4	4	no	—
196	C₂×D₄₇	#339	1	2	yes	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	4	4	no	—
200	C₄×C₄₇	#405	1	1	yes	characteristic
201	C₄×C₄₇	#405	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#104	1	2	yes	—
203	C₄×C₄₇	#421	1	2	yes	—
204	C₄×C₄₇	#424	1	2	yes	—
205	Dic₄₇	—	2	1	no	—
206	Dic₄₇	—	2	1	no	—
207	Dic₄₇	—	2	1	no	—
208	Dic₄₇	—	2	1	no	—
209	Dic₄₇	—	2	1	no	—
210	Dic₄₇	—	4	4	no	—
211	Dic₄₇	#339	1	2	yes	—
212	#2920	—	47	1	no	—
213	C₂×#431	—	47	1	no	—
214	C₄×#117	—	47	1	no	—
215	#1276	—	47	1	no	—
216	#1276	—	47	1	no	—
217	#1276	—	47	1	no	—
218	#1276	D₄₇	1	1	yes	characteristic, complemented
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	#1729	1	1	yes	characteristic
221	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
222	C₂×C₄₇	#1733	1	1	yes	characteristic
223	D₄₇	—	2	2	no	—
224	D₄₇	—	4	1	no	—
225	C₂×#117	—	94	1	no	—
226	C₂²×C₄²	—	47	1	no	—
227	#432	—	47	2	no	—
228	#432	—	94	1	no	—
229	#431	—	47	1	no	—
230	#431	—	47	1	no	—
231	#431	—	47	2	no	—
232	#431	—	94	1	no	—
233	#431	—	94	1	no	—
234	#431	—	94	1	no	—
235	#431	C₂×D₄₇	1	1	yes	characteristic
236	#431	C₂×D₄₇	1	1	yes	characteristic
237	#423	—	47	2	no	—
238	C₂×C₄⋊C₈	—	47	2	no	—
239	#407	—	94	1	no	—
240	C₂×C₂²⋊C₈	—	94	1	no	—
241	C₄×M₁₆	—	94	1	no	—
242	C₂×C₄×C₈	—	94	1	no	—
243	C₄×C₄⋊C₄	—	47	2	no	—
244	C₄×C₄⋊C₄	—	94	1	no	—
245	C₄×C₂²⋊C₄	—	47	2	no	—
246	C₄×C₂²⋊C₄	—	94	1	no	—
247	#376	—	94	1	no	—
248	C₄³	—	47	1	no	—
249	C₄³	C₂×D₄₇	1	1	yes	characteristic
250	C₄₇	#7869	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₄	—	47	1	no	—
252	C₂³×C₄	—	47	1	no	—
253	C₂³×C₄	—	47	1	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂²×C₈	—	94	2	no	—
256	#117	—	94	8	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₂²⋊C₄	—	94	2	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	47	1	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	2	no	—
273	C₂×C₄²	—	94	1	no	—
274	C₂×C₄²	—	94	1	no	—
275	C₂×C₄²	C₄×D₄₇	1	2	yes	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	C₄⋊C₈	—	47	2	no	—
278	C₄⋊C₈	—	47	2	no	—
279	C₄⋊C₈	—	94	2	no	—
280	C₄⋊C₈	—	94	2	no	—
281	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
282	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₂²⋊C₈	—	94	2	no	—
287	C₂²⋊C₈	—	94	1	no	—
288	C₂²⋊C₈	—	94	1	no	—
289	#97	—	94	2	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	94	2	no	—
293	C₄×C₈	—	94	1	no	—
294	C₄×C₈	—	94	1	no	—
295	#95	—	94	2	no	—
296	#95	—	94	2	no	—
297	C₂⁴	—	47	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	94	4	no	—
315	C₂²×C₄	—	94	2	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	—	188	2	no	—
319	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
322	M₁₆	—	188	4	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	188	4	no	—
328	C₄⋊C₄	—	94	8	no	—
329	C₂²⋊C₄	—	94	8	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	4	2	no	—
334	C₄²	—	47	1	no	—
335	C₄²	—	47	1	no	—
336	C₄²	—	47	1	no	—
337	C₄²	—	47	1	no	—
338	C₄²	—	47	1	no	—
339	C₄²	—	47	1	no	—
340	C₄²	—	47	1	no	—
341	C₄²	—	47	1	no	—
342	C₄²	—	47	1	no	—
343	C₄²	—	47	1	no	—
344	C₄²	—	47	1	no	—
345	C₄²	—	47	1	no	—
346	C₄²	—	94	4	no	—
347	C₄²	—	94	2	no	—
348	C₄²	—	94	2	no	—
349	C₄²	—	188	2	no	—
350	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
351	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
352	C₄²	D₄×D₄₇	1	1	yes	characteristic
353	C₄²	Q₈×D₄₇	1	1	yes	characteristic
354	C₂³	—	47	1	no	—
355	C₂³	—	47	1	no	—
356	C₂³	—	94	2	no	—
357	C₂³	—	94	2	no	—
358	C₂³	—	188	1	no	—
359	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	47	1	no	—
366	C₂×C₄	—	47	4	no	—
367	C₂×C₄	—	47	1	no	—
368	C₂×C₄	—	47	1	no	—
369	C₂×C₄	—	47	1	no	—
370	C₂×C₄	—	47	1	no	—
371	C₂×C₄	—	47	1	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	1	no	—
378	C₂×C₄	—	94	1	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	4	no	—
386	C₂×C₄	—	188	1	no	—
387	C₂×C₄	—	188	1	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	2	no	—
391	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
395	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	#13094030	1	2	yes	—
398	C₂×C₄	#13094032	1	2	yes	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	188	2	no	—
402	C₈	—	188	2	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	47	2	no	—
406	C₂²	—	94	1	no	—
407	C₂²	—	94	1	no	—
408	C₂²	—	94	1	no	—
409	C₂²	—	94	1	no	—
410	C₂²	—	94	1	no	—
411	C₂²	—	188	4	no	—
412	C₂²	#95×D₄₇	1	1	yes	characteristic
413	C₂²	#15689088	1	2	yes	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	4	no	—
417	C₄	—	47	2	no	—
418	C₄	—	94	1	no	—
419	C₄	—	94	1	no	—
420	C₄	—	94	1	no	—
421	C₄	—	94	1	no	—
422	C₄	—	94	1	no	—
423	C₄	—	188	4	no	—
424	C₄	#15689077	1	1	yes	characteristic
425	C₄	#15689080	1	1	yes	characteristic
426	C₄	#104×D₄₇	1	2	yes	—
427	C₄	#15689138	1	2	yes	—
428	C₄	#15689148	1	2	yes	—
429	C₂	—	2	2	no	—
430	C₂	—	94	2	no	—
431	C₂	—	188	1	no	—
432	C₂	#20243083	1	1	yes	characteristic
433	C₂	#339×D₄₇	1	1	yes	characteristic
434	C₂	#20243096	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1276	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1276	D₄₇
hypocenter	C₄₇	#7869
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1276

Complements

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

N	H ≅ G/N	type
4. #20241221	C₂	semidirect
5. #20241220	C₂	semidirect
6. #20241220	C₂	semidirect
7. C₄₇×#1276	C₂	semidirect
10. #15689179	C₄	semidirect
14. #15689175	C₄	semidirect
18. #15689145	C₄	semidirect
19. C₄⋊C₈×D₄₇	C₄	semidirect
218. #1276	D₄₇	semidirect
250. C₄₇	#7869	semidirect

Maximal subgroups

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

subgroup	index
#20252016	2
#431×D₄₇	2
C₄×#13093981	2
#20241221	2
#20241220	2
C₄₇×#1276	2
#7869	47