Subgroups — #26106584

Order 12032.

584 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252020	C₂	1	1	yes	maximal, characteristic
2	#431×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20241291	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241290	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
9	#15689179	—	2	1	no	—
10	#15689179	C₄	1	2	yes	complemented
11	#15689176	C₂²	1	1	yes	characteristic
12	#15689175	—	2	1	no	—
13	#15689175	C₄	1	2	yes	complemented
14	#15689175	C₄	1	2	yes	complemented
15	#15689174	—	2	1	no	—
16	#15689173	—	2	1	no	—
17	#15689147	C₂²	1	1	yes	characteristic
18	C₄⋊C₈×D₄₇	C₄	1	2	yes	complemented
19	#15689086	—	2	1	no	—
20	C₂²⋊C₈×D₄₇	—	2	1	no	—
21	M₁₆×Dic₄₇	—	2	1	no	—
22	C₄×C₈×D₄₇	—	2	1	no	—
23	#15688990	C₄	1	2	yes	—
24	#15688988	—	2	1	no	—
25	#15688985	C₄	1	2	yes	—
26	#15688980	—	2	1	no	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
29	#15688969	—	2	1	no	—
30	C₄₇×#431	C₂²	1	1	yes	characteristic
31	C₄₇×#423	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×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×#10625329	—	2	1	no	—
37	C₂×C₈×D₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	1	no	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
44	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₄₇	D₄	1	1	yes	characteristic
49	C₄²×D₄₇	D₄	1	1	yes	characteristic
50	C₄²×D₄₇	Q₈	1	1	yes	characteristic
51	C₄²×D₄₇	Q₈	1	1	yes	characteristic
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
54	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
55	Dic₄₇⋊C₈	—	2	2	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
57	(C₂×D₄₇)⋊C₈	—	2	2	no	—
58	(C₂×D₄₇)⋊C₈	—	2	2	no	—
59	(C₂×D₄₇)⋊C₈	—	2	2	no	—
60	#13093934	—	2	2	no	—
61	C₄×C₄₇⋊C₈	—	2	1	no	—
62	C₈×Dic₄₇	—	2	2	no	—
63	C₈×Dic₄₇	—	2	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₂×M₁₆×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄²×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₄₇	—	2	1	no	—
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	C₄×C₈×C₄₇	—	2	1	no	—
77	#95×C₄₇	C₂×C₄	1	2	yes	—
78	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₄₇	—	2	2	no	—
84	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₄₇	—	2	1	no	—
88	C₂×C₄×D₄₇	—	2	1	no	—
89	C₂×C₄×D₄₇	—	2	1	no	—
90	C₂×C₄×D₄₇	—	2	1	no	—
91	C₂×C₄×D₄₇	—	4	2	no	—
92	C₂×C₄×D₄₇	—	4	2	no	—
93	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₄²	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	C₂²⋊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×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
105	M₁₆×C₄₇	—	4	1	no	—
106	M₁₆×C₄₇	—	4	1	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	4	2	no	—
110	C₄²×C₄₇	—	4	1	no	—
111	C₄²×C₄₇	—	4	1	no	—
112	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
116	(C₂×D₄₇)⋊C₄	—	4	4	no	—
117	C₄⋊Dic₄₇	—	4	2	no	—
118	C₄×Dic₄₇	—	4	1	no	—
119	C₄×Dic₄₇	—	4	1	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	#10625329	—	4	1	no	—
133	#10625329	—	4	1	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₈×D₄₇	—	4	4	no	—
137	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×D₄₇	—	2	1	no	—
139	C₂²×D₄₇	—	2	1	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	4	1	no	—
142	C₂²×D₄₇	#95	1	1	yes	characteristic
143	C₂²×D₄₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	4	1	no	—
162	C₂×Dic₄₇	—	4	1	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	#95	1	1	yes	characteristic
167	C₂×Dic₄₇	#95	1	1	yes	characteristic
168	C₂×Dic₄₇	#95	1	1	yes	characteristic
169	C₂×Dic₄₇	#95	1	1	yes	characteristic
170	C₂×Dic₄₇	#95	1	1	yes	characteristic
171	C₂×Dic₄₇	#95	1	1	yes	characteristic
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	2	1	no	—
175	C₄×D₄₇	—	2	1	no	—
176	C₄×D₄₇	—	2	1	no	—
177	C₄×D₄₇	—	2	1	no	—
178	C₄×D₄₇	—	2	2	no	—
179	C₄×D₄₇	—	2	2	no	—
180	C₄×D₄₇	—	2	1	no	—
181	C₄×D₄₇	—	2	1	no	—
182	C₄×D₄₇	—	2	1	no	—
183	C₄×D₄₇	—	2	1	no	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	1	no	—
186	C₄×D₄₇	—	4	1	no	—
187	C₄×D₄₇	—	4	1	no	—
188	C₈×C₄₇	—	4	2	no	—
189	C₈×C₄₇	—	4	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	#8096	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
196	C₂²×C₄₇	#416	1	1	yes	characteristic
197	C₂²×C₄₇	#416	1	1	yes	characteristic
198	C₂×D₄₇	—	2	1	no	—
199	C₂×D₄₇	—	2	1	no	—
200	C₂×D₄₇	—	2	1	no	—
201	C₂×D₄₇	—	2	1	no	—
202	C₂×D₄₇	—	2	1	no	—
203	C₂×D₄₇	—	4	2	no	—
204	C₂×D₄₇	—	4	2	no	—
205	C₂×D₄₇	#344	1	2	yes	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	#416	1	1	yes	characteristic
211	C₄×C₄₇	#416	1	1	yes	characteristic
212	C₄×C₄₇	#421	1	2	yes	—
213	C₄×C₄₇	#427	1	1	yes	characteristic
214	C₄×C₄₇	#427	1	1	yes	characteristic
215	Dic₄₇	—	2	1	no	—
216	Dic₄₇	—	2	1	no	—
217	Dic₄₇	—	2	1	no	—
218	Dic₄₇	—	2	1	no	—
219	Dic₄₇	—	2	1	no	—
220	Dic₄₇	—	2	1	no	—
221	Dic₄₇	—	8	2	no	—
222	#2920	—	47	1	no	—
223	C₂×#431	—	47	1	no	—
224	#2283	—	47	1	no	—
225	#1303	—	47	1	no	—
226	#1303	—	47	1	no	—
227	#1303	—	47	1	no	—
228	#1303	D₄₇	1	1	yes	characteristic, complemented
229	C₂×C₄₇	—	2	1	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	#1733	1	1	yes	characteristic
232	C₂×C₄₇	#1735	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
234	D₄₇	—	2	2	no	—
235	D₄₇	—	4	1	no	—
236	C₂²×C₄²	—	47	1	no	—
237	#432	—	47	2	no	—
238	#432	—	94	1	no	—
239	#431	—	47	1	no	—
240	#431	—	47	2	no	—
241	#431	—	47	2	no	—
242	#431	—	94	1	no	—
243	#431	—	94	1	no	—
244	#431	—	94	1	no	—
245	#431	C₂×D₄₇	1	1	yes	characteristic
246	#423	—	47	1	no	—
247	#423	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄⋊C₈	—	47	2	no	—
249	#407	—	94	1	no	—
250	C₂×C₂²⋊C₈	—	94	1	no	—
251	C₄×M₁₆	—	94	1	no	—
252	C₂×C₄×C₈	—	94	1	no	—
253	#383	—	47	2	no	—
254	#382	—	94	1	no	—
255	#381	—	47	2	no	—
256	#380	—	94	1	no	—
257	C₄×C₄⋊C₄	—	47	1	no	—
258	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
259	C₄×C₂²⋊C₄	—	94	1	no	—
260	#376	—	94	1	no	—
261	C₄₇	#8096	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₄	—	47	1	no	—
263	C₂³×C₄	—	47	1	no	—
264	C₂³×C₄	—	47	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	94	1	no	—
267	C₂²×C₈	—	94	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	94	1	no	—
270	C₂×C₂²⋊C₄	—	94	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	47	1	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	1	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	1	no	—
283	C₂×C₄²	—	94	1	no	—
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	47	2	no	—
287	C₄⋊C₈	—	47	2	no	—
288	C₄⋊C₈	—	94	2	no	—
289	C₄⋊C₈	—	94	1	no	—
290	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
291	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	94	2	no	—
294	C₂²⋊C₈	—	94	2	no	—
295	C₂²⋊C₈	—	94	2	no	—
296	C₂²⋊C₈	—	94	1	no	—
297	#97	—	94	2	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	94	2	no	—
300	C₄×C₈	—	94	2	no	—
301	C₄×C₈	—	94	1	no	—
302	#95	—	47	2	no	—
303	#95	—	94	2	no	—
304	#95	—	94	2	no	—
305	#95	—	94	2	no	—
306	#95	C₄×D₄₇	1	2	yes	—
307	C₂⁴	—	47	1	no	—
308	C₂²×C₄	—	2	2	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	—	47	1	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	47	1	no	—
317	C₂²×C₄	—	47	1	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	47	1	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	94	1	no	—
325	C₂²×C₄	—	94	1	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	188	2	no	—
330	C₂²×C₄	—	188	2	no	—
331	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
334	M₁₆	—	4	1	no	—
335	M₁₆	—	4	1	no	—
336	M₁₆	—	188	1	no	—
337	M₁₆	—	188	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	188	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	188	2	no	—
345	C₂²⋊C₄	—	188	4	no	—
346	C₄²	—	4	1	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	47	1	no	—
349	C₄²	—	47	1	no	—
350	C₄²	—	47	1	no	—
351	C₄²	—	47	1	no	—
352	C₄²	—	47	1	no	—
353	C₄²	—	47	1	no	—
354	C₄²	—	47	1	no	—
355	C₄²	—	47	1	no	—
356	C₄²	—	47	1	no	—
357	C₄²	—	47	1	no	—
358	C₄²	—	47	1	no	—
359	C₄²	—	47	1	no	—
360	C₄²	—	188	1	no	—
361	C₄²	—	188	1	no	—
362	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
364	C₄²	D₄×D₄₇	1	1	yes	characteristic
365	C₄²	Q₈×D₄₇	1	1	yes	characteristic
366	C₂³	—	47	1	no	—
367	C₂³	—	47	1	no	—
368	C₂³	—	94	2	no	—
369	C₂³	—	94	1	no	—
370	C₂³	—	94	1	no	—
371	C₂³	—	188	1	no	—
372	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	47	1	no	—
379	C₂×C₄	—	47	1	no	—
380	C₂×C₄	—	47	1	no	—
381	C₂×C₄	—	47	1	no	—
382	C₂×C₄	—	47	1	no	—
383	C₂×C₄	—	47	1	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	94	1	no	—
388	C₂×C₄	—	94	1	no	—
389	C₂×C₄	—	94	1	no	—
390	C₂×C₄	—	94	1	no	—
391	C₂×C₄	—	94	1	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	1	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	188	1	no	—
399	C₂×C₄	—	188	1	no	—
400	C₂×C₄	—	188	1	no	—
401	C₂×C₄	—	188	1	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	—	188	1	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	#13094043	1	1	yes	characteristic
414	C₂×C₄	#13094045	1	1	yes	characteristic
415	C₂×C₄	#13094045	1	1	yes	characteristic
416	C₂×C₄	#13094047	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₈	—	188	2	no	—
420	C₈	—	188	2	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	47	2	no	—
424	C₂²	—	94	1	no	—
425	C₂²	—	94	1	no	—
426	C₂²	—	94	1	no	—
427	C₂²	—	94	1	no	—
428	C₂²	—	94	1	no	—
429	C₂²	—	188	2	no	—
430	C₂²	—	188	2	no	—
431	C₂²	#95×D₄₇	1	1	yes	characteristic
432	C₂²	#15689116	1	1	yes	characteristic
433	C₂²	#15689118	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	94	1	no	—
439	C₄	—	94	1	no	—
440	C₄	—	94	1	no	—
441	C₄	—	94	1	no	—
442	C₄	—	94	1	no	—
443	C₄	—	94	1	no	—
444	C₄	—	376	2	no	—
445	C₄	#15689116	1	1	yes	characteristic
446	C₄	#15689118	1	1	yes	characteristic
447	C₄	#15689138	1	2	yes	—
448	C₄	#15689158	1	1	yes	characteristic
449	C₄	#15689160	1	1	yes	characteristic
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	94	2	no	—
453	C₂	—	188	1	no	—
454	C₂	#20243096	1	1	yes	characteristic
455	C₂	#20243103	1	1	yes	characteristic
456	C₂	#344×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1303	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1303	D₄₇
hypocenter	C₄₇	#8096
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

Complements

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

N	H ≅ G/N	type
4. #20241291	C₂	semidirect
5. #20241290	C₂	semidirect
6. #20241289	C₂	semidirect
7. C₄₇×#1303	C₂	semidirect
10. #15689179	C₄	semidirect
13. #15689175	C₄	semidirect
14. #15689175	C₄	semidirect
18. C₄⋊C₈×D₄₇	C₄	semidirect
228. #1303	D₄₇	semidirect
261. C₄₇	#8096	semidirect

Maximal subgroups

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

subgroup	index
#20252020	2
#431×D₄₇	2
#20245784	2
#20241291	2
#20241290	2
#20241289	2
C₄₇×#1303	2
#8096	47