Subgroups — D₄₇×#2170 #26369502

Order 12032.

662 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504×D₄₇	C₂	1	2	yes	maximal, complemented
2	#443×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245226	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245225	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245224	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245223	C₂	1	2	yes	maximal, complemented
7	#20245222	C₂	1	2	yes	maximal, complemented
8	#364×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#350×D₄₇	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₄₇	C₄	1	1	yes	characteristic
13	#131×D₄₇	C₂²	1	2	yes	—
14	#15689541	—	2	2	no	—
15	#15689541	C₂²	1	2	yes	complemented
16	#15689540	C₂²	1	2	yes	complemented
17	#15689539	—	2	2	no	—
18	#15689539	C₂²	1	2	yes	complemented
19	M₃₂×D₄₇	—	2	2	no	—
20	M₃₂×D₄₇	C₂²	1	2	yes	—
21	C₂×C₁₆×D₄₇	—	2	2	no	—
22	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
24	#15689241	C₂²	1	1	yes	characteristic
25	#15689240	C₄	1	1	yes	characteristic
26	#15689239	C₄	1	1	yes	characteristic
27	#15689238	C₂²	1	2	yes	—
28	#15689237	C₄	1	2	yes	—
29	#108×D₄₇	C₄	1	1	yes	characteristic
30	#104×D₄₇	C₄	1	2	yes	—
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688944	C₂²	1	1	yes	characteristic, complemented
33	#15688943	C₂²	1	2	yes	complemented
34	#15688908	C₂²	1	2	yes	complemented
35	#15688907	C₂²	1	2	yes	complemented
36	#15688906	C₂²	1	2	yes	complemented
37	C₄×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#504	C₂²	1	2	yes	complemented
41	C₄₇×#443	C₂²	1	1	yes	characteristic
42	C₄₇×#364	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#350	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
45	#41×D₄₇	C₂×C₄	1	2	yes	—
46	#13094047	C₈	1	1	yes	characteristic
47	#13094046	C₂×C₄	1	1	yes	characteristic
48	#13094045	C₈	1	2	yes	—
49	#13094044	C₂×C₄	1	2	yes	—
50	#13094043	C₈	1	1	yes	characteristic
51	Q₁₆×D₄₇	C₈	1	1	yes	characteristic
52	SD₁₆×D₄₇	C₈	1	2	yes	—
53	D₈×D₄₇	C₈	1	1	yes	characteristic
54	#13094032	—	2	2	no	—
55	#13094032	C₂×C₄	1	2	yes	—
56	#13094031	C₂×C₄	1	2	yes	—
57	#13094030	—	2	2	no	—
58	#13094030	C₂³	1	2	yes	—
59	M₁₆×D₄₇	—	2	2	no	—
60	M₁₆×D₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₄₇	—	2	2	no	—
62	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
64	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
65	#13093964	—	2	2	no	—
66	#13093964	C₂³	1	2	yes	—
67	#13093963	—	2	2	no	—
68	#13093963	—	2	2	no	—
69	#13093963	—	2	2	no	—
70	C₂×C₄₇⋊C₁₆	—	2	2	no	—
71	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
73	C₁₆×D₄₇	—	2	2	no	—
74	C₁₆×D₄₇	—	2	1	no	—
75	C₁₆×D₄₇	—	2	1	no	—
76	C₁₆×D₄₇	—	2	2	no	—
77	C₁₆×D₄₇	—	2	2	no	—
78	C₁₆×D₄₇	D₄	1	1	yes	characteristic
79	C₁₆×D₄₇	D₄	1	1	yes	characteristic
80	C₁₆×D₄₇	D₄	1	1	yes	characteristic
81	C₁₆×D₄₇	D₄	1	1	yes	characteristic
82	#13093960	C₂×C₄	1	1	yes	characteristic
83	#13093959	C₂×C₄	1	2	yes	—
84	#13093952	C₂×C₄	1	2	yes	—
85	#13093951	C₂×C₄	1	2	yes	—
86	#13093950	C₂×C₄	1	2	yes	—
87	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
90	#135×C₄₇	C₂×C₄	1	1	yes	characteristic
91	#131×C₄₇	C₂³	1	2	yes	—
92	M₃₂×C₄₇	—	2	2	no	—
93	M₃₂×C₄₇	C₂³	1	2	yes	—
94	C₂×C₁₆×C₄₇	—	2	2	no	—
95	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
97	#108×C₄₇	C₂×C₄	1	1	yes	characteristic
98	#104×C₄₇	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	#41×C₄₇	C₂²×C₄	1	2	yes	—
101	#10625354	C₂×C₈	1	2	yes	—
102	Q₈×D₄₇	C₂×C₈	1	2	yes	—
103	#10625352	—	2	2	no	—
104	#10625352	C₂×C₈	1	2	yes	—
105	D₄×D₄₇	—	2	2	no	—
106	D₄×D₄₇	C₂×C₈	1	2	yes	—
107	#10625350	—	2	2	no	—
108	#10625350	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
112	Q₁₆×C₄₇	C₂×C₈	1	1	yes	characteristic
113	SD₁₆×C₄₇	C₂×C₈	1	2	yes	—
114	D₈×C₄₇	C₂×C₈	1	1	yes	characteristic
115	M₁₆×C₄₇	—	2	2	no	—
116	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	#10625337	C₂×C₈	1	2	yes	—
122	#10625336	C₂×C₈	1	2	yes	—
123	#10625335	C₂×C₈	1	2	yes	—
124	#10625334	C₂×C₈	1	2	yes	—
125	C₄×Dic₄₇	—	2	1	no	—
126	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
127	#10625329	—	2	2	no	—
128	#10625329	C₂²×C₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	Dic₁₈₈	C₂×C₈	1	1	yes	characteristic
133	D₃₇₆	C₂×C₈	1	1	yes	characteristic
134	#10625325	C₂×C₈	1	2	yes	—
135	#10625324	—	2	2	no	—
136	#10625324	—	2	2	no	—
137	#10625324	—	2	2	no	—
138	C₈×D₄₇	—	2	2	no	—
139	C₈×D₄₇	—	2	2	no	—
140	C₈×D₄₇	—	2	2	no	—
141	C₈×D₄₇	C₂×C₈	1	1	yes	characteristic
142	C₈×D₄₇	C₂×C₈	1	1	yes	characteristic
143	C₈×D₄₇	C₂×C₈	1	1	yes	characteristic
144	C₈×D₄₇	C₂×C₈	1	1	yes	characteristic
145	C₈×D₄₇	C₂×D₄	1	1	yes	characteristic
146	C₈×D₄₇	C₂×D₄	1	1	yes	characteristic
147	C₈×D₄₇	#41	1	1	yes	characteristic
148	C₈×D₄₇	#41	1	1	yes	characteristic
149	C₁₆×C₄₇	—	2	2	no	—
150	C₁₆×C₄₇	—	2	1	no	—
151	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₁₆×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₄₇⋊C₁₆	—	2	2	no	—
154	C₄₇⋊C₁₆	—	2	1	no	—
155	C₄₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
156	C₄₇⋊C₁₆	C₂×D₄	1	1	yes	characteristic
157	C₂²×D₄₇	—	2	2	no	—
158	C₂²×D₄₇	#131	1	1	yes	characteristic
159	Q₈×C₄₇	C₂²×C₈	1	2	yes	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₄₇	—	2	2	no	—
166	C₂²⋊D₄₇	—	2	2	no	—
167	C₂²⋊D₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	#131	1	1	yes	characteristic
171	D₁₈₈	—	2	2	no	—
172	D₁₈₈	C₂²×C₈	1	2	yes	—
173	C₄×D₄₇	—	2	4	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
178	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
179	C₄×D₄₇	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₄₇	C₂²×C₈	1	1	yes	characteristic
181	Dic₉₄	—	2	2	no	—
182	Dic₉₄	C₂²×C₈	1	2	yes	—
183	C₈×C₄₇	—	2	2	no	—
184	C₈×C₄₇	C₂²×C₈	1	1	yes	characteristic
185	C₈×C₄₇	C₂²×C₈	1	1	yes	characteristic
186	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	C₄×D₄	1	1	yes	characteristic
190	C₄₇⋊C₈	C₄×D₄	1	1	yes	characteristic
191	C₄₇⋊C₈	C₂²×C₈	1	1	yes	characteristic
192	C₄₇⋊C₈	C₂²×C₈	1	1	yes	characteristic
193	C₂×#2170	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
196	C₂×D₄₇	—	2	2	no	—
197	C₂×D₄₇	—	2	2	no	—
198	C₂×D₄₇	—	4	4	no	—
199	C₂×D₄₇	C₈×D₄	1	1	yes	characteristic
200	C₂×D₄₇	C₈×D₄	1	1	yes	characteristic
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
205	Dic₄₇	—	2	2	no	—
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	C₈×D₄	1	1	yes	characteristic
208	Dic₄₇	C₈×D₄	1	1	yes	characteristic
209	C₂×#504	—	47	2	no	—
210	C₂×#443	—	47	1	no	—
211	#2170	—	47	2	no	—
212	#2170	—	47	1	no	—
213	#2170	—	47	1	no	—
214	#2170	—	47	2	no	—
215	#2170	—	47	1	no	—
216	#2170	D₄₇	1	1	yes	characteristic, direct product factor
217	C₂×#364	—	47	1	no	—
218	C₂×#350	—	47	2	no	—
219	C₂×C₄×C₁₆	—	47	1	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	4	2	no	—
222	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
223	D₄₇	—	2	1	no	—
224	D₄₇	—	4	2	no	—
225	D₄₇	#2170	1	2	yes	direct product factor
226	C₂×#135	—	47	1	no	—
227	C₂×#131	—	47	2	no	—
228	#504	—	47	2	no	—
229	#504	—	47	2	no	—
230	#504	—	47	2	no	—
231	#504	—	94	2	no	—
232	#504	—	94	2	no	—
233	#504	C₂×D₄₇	1	2	yes	complemented
234	C₂×M₃₂	—	47	2	no	—
235	C₂×M₃₂	—	94	2	no	—
236	C₂²×C₁₆	—	47	1	no	—
237	C₂²×C₁₆	—	47	1	no	—
238	C₂²×C₁₆	—	94	2	no	—
239	#443	—	47	1	no	—
240	#443	—	47	2	no	—
241	#443	—	47	1	no	—
242	#443	—	47	2	no	—
243	#443	—	47	1	no	—
244	#443	C₂×D₄₇	1	1	yes	characteristic
245	C₂×#108	—	47	1	no	—
246	C₂×#104	—	47	2	no	—
247	C₂×C₄×C₈	—	47	1	no	—
248	#364	—	47	2	no	—
249	#364	—	47	1	no	—
250	#364	C₂×D₄₇	1	1	yes	characteristic, complemented
251	#350	—	47	2	no	—
252	#350	—	47	2	no	—
253	#350	—	47	2	no	—
254	#350	C₂×D₄₇	1	2	yes	complemented
255	C₄×C₁₆	—	47	1	no	—
256	C₄×C₁₆	—	47	1	no	—
257	C₄×C₁₆	—	47	1	no	—
258	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
259	C₄₇	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	47	2	no	—
261	#135	—	47	2	no	—
262	#135	—	47	1	no	—
263	#135	—	47	2	no	—
264	#135	—	47	1	no	—
265	#135	—	47	1	no	—
266	#135	C₄×D₄₇	1	1	yes	characteristic
267	C₂×Q₁₆	—	47	1	no	—
268	C₂×SD₁₆	—	47	2	no	—
269	C₂×D₈	—	47	1	no	—
270	#131	—	47	2	no	—
271	#131	—	47	2	no	—
272	#131	—	47	2	no	—
273	#131	—	94	2	no	—
274	#131	—	94	2	no	—
275	#131	C₂²×D₄₇	1	2	yes	—
276	C₂×M₁₆	—	47	2	no	—
277	C₂×M₁₆	—	94	2	no	—
278	C₂²×C₈	—	47	1	no	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	94	2	no	—
281	C₂×C₄²	—	47	1	no	—
282	M₃₂	—	2	2	no	—
283	M₃₂	—	47	2	no	—
284	M₃₂	—	94	2	no	—
285	M₃₂	—	94	2	no	—
286	M₃₂	—	94	2	no	—
287	M₃₂	—	94	2	no	—
288	M₃₂	C₂²×D₄₇	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	47	1	no	—
291	C₂×C₁₆	—	47	1	no	—
292	C₂×C₁₆	—	47	1	no	—
293	C₂×C₁₆	—	47	1	no	—
294	C₂×C₁₆	—	47	1	no	—
295	C₂×C₁₆	—	47	1	no	—
296	C₂×C₁₆	—	94	2	no	—
297	C₂×C₁₆	—	94	1	no	—
298	C₂×C₁₆	—	94	1	no	—
299	C₂×C₁₆	—	94	2	no	—
300	C₂×C₁₆	—	94	2	no	—
301	C₂×C₁₆	—	94	2	no	—
302	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
304	#108	—	47	2	no	—
305	#108	—	47	1	no	—
306	#108	C₄×D₄₇	1	1	yes	characteristic
307	#104	—	47	2	no	—
308	#104	—	47	2	no	—
309	#104	—	47	2	no	—
310	#104	C₄×D₄₇	1	2	yes	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	1	no	—
313	C₄×C₈	—	47	1	no	—
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	#41	—	47	2	no	—
316	#41	—	47	2	no	—
317	#41	—	47	2	no	—
318	#41	—	94	2	no	—
319	#41	—	94	2	no	—
320	#41	C₂×C₄×D₄₇	1	2	yes	—
321	C₂×Q₈	—	47	2	no	—
322	C₂×D₄	—	47	2	no	—
323	C₂×D₄	—	94	2	no	—
324	C₂²×C₄	—	47	1	no	—
325	C₂²×C₄	—	94	2	no	—
326	C₂²×C₄	—	94	1	no	—
327	Q₁₆	—	47	2	no	—
328	Q₁₆	—	47	1	no	—
329	Q₁₆	C₈×D₄₇	1	1	yes	characteristic
330	SD₁₆	—	47	2	no	—
331	SD₁₆	—	47	2	no	—
332	SD₁₆	—	47	2	no	—
333	SD₁₆	C₈×D₄₇	1	2	yes	—
334	D₈	—	47	2	no	—
335	D₈	—	47	1	no	—
336	D₈	C₈×D₄₇	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	47	2	no	—
339	M₁₆	—	94	2	no	—
340	M₁₆	—	94	2	no	—
341	M₁₆	—	94	2	no	—
342	M₁₆	—	94	2	no	—
343	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	47	1	no	—
346	C₂×C₈	—	47	1	no	—
347	C₂×C₈	—	47	1	no	—
348	C₂×C₈	—	47	1	no	—
349	C₂×C₈	—	47	1	no	—
350	C₂×C₈	—	47	1	no	—
351	C₂×C₈	—	47	1	no	—
352	C₂×C₈	—	47	1	no	—
353	C₂×C₈	—	47	1	no	—
354	C₂×C₈	—	47	1	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
361	C₄²	—	47	1	no	—
362	C₄²	—	94	1	no	—
363	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	1	no	—
366	C₁₆	—	47	1	no	—
367	C₁₆	—	47	1	no	—
368	C₁₆	—	94	2	no	—
369	C₁₆	—	94	1	no	—
370	C₁₆	D₄×D₄₇	1	1	yes	characteristic
371	C₁₆	D₄×D₄₇	1	1	yes	characteristic
372	C₂³	—	47	1	no	—
373	C₂³	—	94	2	no	—
374	Q₈	—	47	2	no	—
375	Q₈	—	94	2	no	—
376	Q₈	C₂×C₈×D₄₇	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	47	2	no	—
379	D₄	—	94	2	no	—
380	D₄	—	94	2	no	—
381	D₄	—	94	2	no	—
382	D₄	—	94	2	no	—
383	D₄	C₂×C₈×D₄₇	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	47	1	no	—
387	C₂×C₄	—	47	1	no	—
388	C₂×C₄	—	47	1	no	—
389	C₂×C₄	—	47	1	no	—
390	C₂×C₄	—	47	1	no	—
391	C₂×C₄	—	94	2	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	4	no	—
394	C₂×C₄	—	94	2	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	2	no	—
397	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	47	1	no	—
400	C₈	—	47	1	no	—
401	C₈	—	47	1	no	—
402	C₈	—	47	1	no	—
403	C₈	—	94	2	no	—
404	C₈	C₂×C₈×D₄₇	1	1	yes	characteristic
405	C₈	C₂×C₈×D₄₇	1	1	yes	characteristic
406	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
407	C₈	#41×D₄₇	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	47	1	no	—
410	C₂²	—	47	1	no	—
411	C₂²	—	94	2	no	—
412	C₂²	—	94	2	no	—
413	C₂²	—	188	4	no	—
414	C₂²	#131×D₄₇	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	47	1	no	—
418	C₄	—	47	1	no	—
419	C₄	—	94	2	no	—
420	C₄	—	94	2	no	—
421	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	47	2	no	—
426	C₂	—	94	1	no	—
427	C₂	—	188	2	no	—
428	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2170	C₂
socle	C₂×C₄₇	C₂×C₈×D₄
prime radical	#135×D₄₇	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2170	D₄₇
hypocenter	C₄₇	C₂×#2170
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #504×D₄₇	C₂	semidirect
3. #20245226	C₂	semidirect
4. #20245225	C₂	semidirect
5. #20245224	C₂	semidirect
6. #20245223	C₂	semidirect
7. #20245222	C₂	semidirect
8. #364×D₄₇	C₂	semidirect
9. #350×D₄₇	C₂	semidirect
10. C₄×C₁₆×D₄₇	C₂	semidirect
11. C₄₇×#2170	C₂	semidirect
15. #15689541	C₂²	semidirect
16. #15689540	C₂²	semidirect
18. #15689539	C₂²	semidirect
32. #15688944	C₂²	semidirect
33. #15688943	C₂²	semidirect
34. #15688908	C₂²	semidirect
35. #15688907	C₂²	semidirect
36. #15688906	C₂²	semidirect
37. C₄×C₄₇⋊C₁₆	C₂²	semidirect
38. C₁₆×Dic₄₇	C₂²	semidirect
39. C₁₆×Dic₄₇	C₂²	semidirect
40. C₄₇×#504	C₂²	semidirect
42. C₄₇×#364	C₂²	semidirect
43. C₄₇×#350	C₂²	semidirect
44. C₄×C₁₆×C₄₇	C₂²	semidirect
216. #2170	D₄₇	direct (N × H)
225. D₄₇	#2170	direct (N × H)
233. #504	C₂×D₄₇	semidirect
250. #364	C₂×D₄₇	semidirect
254. #350	C₂×D₄₇	semidirect
258. C₄×C₁₆	C₂×D₄₇	semidirect
259. C₄₇	C₂×#2170	semidirect

Maximal subgroups

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

subgroup	index
#504×D₄₇	2
#443×D₄₇	2
#20245226	2
#20245225	2
#20245224	2
#20245223	2
#20245222	2
#364×D₄₇	2
#350×D₄₇	2
C₄×C₁₆×D₄₇	2
C₄₇×#2170	2
C₂×#2170	47

Subgroups — D47×#2170 #26369502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2170 #26369502