Subgroups — D₄₇×#2230 #26371004

Order 12032.

558 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#498×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#443×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245560	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245559	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245558	C₂	1	2	yes	maximal, complemented
6	#20245557	C₂	1	2	yes	maximal, complemented
7	#20245556	C₂	1	1	yes	maximal, characteristic, complemented
8	#365×D₄₇	C₂	1	2	yes	maximal, complemented
9	#364×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#360×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#2230	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₄₇	C₂²	1	1	yes	characteristic
13	#131×D₄₇	—	2	1	no	—
14	C₄⋊Q₈×D₄₇	—	2	1	no	—
15	M₃₂×D₄₇	C₂²	1	2	yes	—
16	#15689521	C₂²	1	1	yes	characteristic, complemented
17	#15689520	—	2	1	no	—
18	#15689520	C₂²	1	2	yes	complemented
19	#15689519	—	2	1	no	—
20	#15689241	C₂²	1	1	yes	characteristic
21	#15689240	C₂²	1	1	yes	characteristic
22	#15689239	C₂²	1	1	yes	characteristic
23	#15689238	—	2	1	no	—
24	#15689237	—	2	1	no	—
25	#108×D₄₇	C₂²	1	1	yes	characteristic
26	#106×D₄₇	—	2	1	no	—
27	#106×D₄₇	C₂²	1	2	yes	—
28	#104×D₄₇	—	2	1	no	—
29	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
30	#15688947	C₂²	1	2	yes	complemented
31	#15688946	C₂²	1	2	yes	complemented
32	#15688945	C₂²	1	2	yes	complemented
33	#15688944	C₂²	1	1	yes	characteristic, complemented
34	#15688943	C₂²	1	2	yes	complemented
35	#15688934	C₂²	1	2	yes	—
36	#15688933	C₂²	1	2	yes	—
37	#15688932	C₂²	1	2	yes	—
38	C₄₇×#498	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#443	C₂²	1	1	yes	characteristic
40	C₄₇×#365	C₂²	1	2	yes	complemented
41	C₄₇×#364	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×#360	C₂²	1	2	yes	—
43	#41×D₄₇	—	2	1	no	—
44	C₂×Q₈×D₄₇	—	4	1	no	—
45	#13094047	Q₈	1	1	yes	characteristic, complemented
46	#13094046	C₂³	1	1	yes	characteristic
47	#13094045	—	2	1	no	—
48	#13094044	—	2	1	no	—
49	#13094043	Q₈	1	1	yes	characteristic, complemented
50	Q₁₆×D₄₇	Q₈	1	1	yes	characteristic, complemented
51	SD₁₆×D₄₇	—	2	1	no	—
52	D₈×D₄₇	Q₈	1	1	yes	characteristic, complemented
53	#13094032	—	2	1	no	—
54	#13094032	—	4	1	no	—
55	#13094031	—	2	1	no	—
56	#13094030	—	2	1	no	—
57	#13094030	—	4	1	no	—
58	M₁₆×D₄₇	—	2	1	no	—
59	M₁₆×D₄₇	—	4	1	no	—
60	C₂×C₈×D₄₇	—	4	1	no	—
61	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
62	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
63	#13094024	—	2	1	no	—
64	#13094023	—	2	2	no	—
65	#13094023	—	4	1	no	—
66	#13094022	—	4	1	no	—
67	C₄⋊C₄×D₄₇	—	2	2	no	—
68	C₄⋊C₄×D₄₇	—	4	1	no	—
69	C₄²×D₄₇	D₄	1	1	yes	characteristic
70	#13093964	C₂³	1	2	yes	—
71	#13093963	—	2	2	no	—
72	C₁₆×D₄₇	—	2	2	no	—
73	#13093960	C₂³	1	1	yes	characteristic
74	#13093959	—	2	1	no	—
75	#13093956	—	2	1	no	—
76	#13093956	C₂³	1	2	yes	—
77	#13093955	—	2	2	no	—
78	#13093955	—	2	2	no	—
79	#13093952	—	2	1	no	—
80	#13093951	—	2	1	no	—
81	#13093950	—	2	1	no	—
82	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
83	C₈×Dic₄₇	D₄	1	1	yes	characteristic
84	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
85	#135×C₄₇	C₂³	1	1	yes	characteristic
86	#131×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	—	2	1	no	—
88	M₃₂×C₄₇	C₂³	1	2	yes	—
89	#108×C₄₇	C₂³	1	1	yes	characteristic
90	#106×C₄₇	—	2	1	no	—
91	#106×C₄₇	C₂³	1	2	yes	—
92	#104×C₄₇	—	2	1	no	—
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	#41×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	4	1	no	—
96	#10625354	—	2	1	no	—
97	Q₈×D₄₇	—	2	1	no	—
98	Q₈×D₄₇	—	8	4	no	—
99	#10625352	—	2	1	no	—
100	#10625352	—	4	1	no	—
101	D₄×D₄₇	—	2	1	no	—
102	D₄×D₄₇	—	4	1	no	—
103	#10625350	—	2	1	no	—
104	#10625350	—	4	1	no	—
105	C₂×C₄×D₄₇	—	2	1	no	—
106	C₂×C₄×D₄₇	—	4	1	no	—
107	C₂×C₄×D₄₇	—	4	2	no	—
108	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×Dic₉₄	—	4	2	no	—
110	C₂×Dic₉₄	—	4	1	no	—
111	Q₁₆×C₄₇	C₂×Q₈	1	1	yes	characteristic, complemented
112	SD₁₆×C₄₇	—	2	1	no	—
113	D₈×C₄₇	C₂×Q₈	1	1	yes	characteristic, complemented
114	M₁₆×C₄₇	—	2	1	no	—
115	M₁₆×C₄₇	—	4	1	no	—
116	C₂×C₈×C₄₇	—	4	1	no	—
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	4	1	no	—
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	#10625337	—	2	1	no	—
123	#10625336	—	2	1	no	—
124	#10625335	—	2	1	no	—
125	#10625334	—	2	1	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	—	4	1	no	—
128	Dic₄₇⋊C₄	—	4	2	no	—
129	Dic₄₇⋊C₄	—	4	2	no	—
130	C₄×Dic₄₇	—	2	1	no	—
131	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
132	#10625329	—	2	1	no	—
133	#10625329	—	4	1	no	—
134	C₂×C₄₇⋊C₈	—	4	1	no	—
135	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
137	Dic₁₈₈	C₂×Q₈	1	1	yes	characteristic, complemented
138	D₃₇₆	C₂×Q₈	1	1	yes	characteristic, complemented
139	#10625325	—	2	1	no	—
140	#10625324	—	4	1	no	—
141	#10625324	—	4	1	no	—
142	#10625324	—	4	1	no	—
143	C₈×D₄₇	—	4	1	no	—
144	C₈×D₄₇	—	4	1	no	—
145	C₈×D₄₇	—	4	1	no	—
146	C₈×D₄₇	SD₁₆	1	1	yes	characteristic
147	C₈×D₄₇	SD₁₆	1	1	yes	characteristic
148	C₈×D₄₇	SD₁₆	1	1	yes	characteristic
149	C₈×D₄₇	SD₁₆	1	1	yes	characteristic
150	C₈×D₄₇	C₂×Q₈	1	1	yes	characteristic
151	C₈×D₄₇	C₂×Q₈	1	1	yes	characteristic
152	C₈×D₄₇	#41	1	1	yes	characteristic
153	C₈×D₄₇	#41	1	1	yes	characteristic
154	C₁₆×C₄₇	—	2	2	no	—
155	C₄₇⋊C₁₆	—	2	2	no	—
156	C₂²×D₄₇	—	4	1	no	—
157	C₂²×D₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
158	Q₈×C₄₇	—	2	1	no	—
159	Q₈×C₄₇	—	8	2	no	—
160	D₄×C₄₇	—	2	1	no	—
161	D₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₄₇	—	4	1	no	—
167	C₂²⋊D₄₇	—	4	1	no	—
168	C₂²⋊D₄₇	—	4	1	no	—
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
173	D₁₈₈	—	2	1	no	—
174	D₁₈₈	—	4	1	no	—
175	C₄×D₄₇	—	2	4	no	—
176	C₄×D₄₇	—	4	1	no	—
177	C₄×D₄₇	—	4	1	no	—
178	C₄×D₄₇	—	4	1	no	—
179	C₄×D₄₇	—	8	4	no	—
180	C₄×D₄₇	C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×D₄₇	C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×D₄₇	C₂×SD₁₆	1	1	yes	characteristic
183	C₄×D₄₇	C₂×SD₁₆	1	1	yes	characteristic
184	Dic₉₄	—	2	1	no	—
185	Dic₉₄	—	4	1	no	—
186	Dic₉₄	—	8	4	no	—
187	Dic₉₄	—	8	2	no	—
188	C₈×C₄₇	—	4	1	no	—
189	C₈×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
190	C₈×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
191	C₈×C₄₇	C₂²×Q₈	1	1	yes	characteristic
192	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₄₇⋊C₈	—	4	1	no	—
194	C₄₇⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
195	C₄₇⋊C₈	C₂²⋊Q₈	1	1	yes	characteristic
196	C₄₇⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
197	C₄₇⋊C₈	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×#2230	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	4	1	no	—
200	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂×D₄₇	—	2	2	no	—
202	C₂×D₄₇	—	4	1	no	—
203	C₂×D₄₇	—	8	2	no	—
204	C₂×D₄₇	#476	1	1	yes	characteristic
205	C₂×D₄₇	#476	1	1	yes	characteristic
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	4	1	no	—
208	C₄×C₄₇	—	8	2	no	—
209	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
211	Dic₄₇	—	2	2	no	—
212	Dic₄₇	—	4	1	no	—
213	Dic₄₇	—	8	2	no	—
214	Dic₄₇	#476	1	1	yes	characteristic
215	Dic₄₇	#476	1	1	yes	characteristic
216	C₂×#498	—	47	1	no	—
217	C₂×#443	—	47	1	no	—
218	#2230	—	47	1	no	—
219	#2230	—	47	1	no	—
220	#2230	—	47	2	no	—
221	#2230	—	47	1	no	—
222	#2230	—	47	2	no	—
223	#2230	D₄₇	1	1	yes	characteristic, direct product factor
224	C₂×#365	—	47	2	no	—
225	C₂×#364	—	47	1	no	—
226	C₂×#360	—	47	2	no	—
227	C₂×C₄₇	—	2	1	no	—
228	C₂×C₄₇	—	8	1	no	—
229	C₂×C₄₇	C₂×#476	1	1	yes	characteristic
230	D₄₇	—	2	1	no	—
231	D₄₇	—	8	1	no	—
232	D₄₇	#2230	1	2	yes	direct product factor
233	C₂×#135	—	47	1	no	—
234	C₂×#131	—	94	1	no	—
235	C₂×C₄⋊Q₈	—	94	1	no	—
236	C₂×M₃₂	—	47	2	no	—
237	#498	—	47	2	no	—
238	#498	—	47	1	no	—
239	#498	—	94	1	no	—
240	#498	—	94	1	no	—
241	#498	C₂×D₄₇	1	1	yes	characteristic, complemented
242	#443	—	47	1	no	—
243	#443	—	47	1	no	—
244	#443	—	47	1	no	—
245	#443	—	94	1	no	—
246	#443	—	94	1	no	—
247	#443	C₂×D₄₇	1	1	yes	characteristic
248	C₂×#108	—	47	1	no	—
249	C₂×#106	—	47	2	no	—
250	C₂×#106	—	94	1	no	—
251	C₂×#104	—	94	1	no	—
252	C₂×C₄×C₈	—	47	1	no	—
253	#365	—	47	2	no	—
254	#365	—	47	2	no	—
255	#365	—	47	2	no	—
256	#365	C₂×D₄₇	1	2	yes	complemented
257	#364	—	47	2	no	—
258	#364	—	47	1	no	—
259	#364	C₂×D₄₇	1	1	yes	characteristic, complemented
260	#360	—	47	2	no	—
261	#360	—	47	2	no	—
262	#360	—	47	2	no	—
263	#360	C₂×D₄₇	1	2	yes	—
264	C₄₇	C₂×#2230	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	—	94	1	no	—
266	C₂²×Q₈	—	188	1	no	—
267	#135	—	47	1	no	—
268	#135	—	47	1	no	—
269	#135	—	47	1	no	—
270	#135	—	94	1	no	—
271	#135	—	94	1	no	—
272	#135	C₂²×D₄₇	1	1	yes	characteristic
273	C₂×Q₁₆	—	47	1	no	—
274	C₂×SD₁₆	—	94	1	no	—
275	C₂×D₈	—	47	1	no	—
276	#131	—	2	1	no	—
277	#131	—	94	1	no	—
278	#131	—	94	1	no	—
279	#131	—	94	1	no	—
280	#131	—	188	1	no	—
281	#131	—	188	1	no	—
282	C₂×M₁₆	—	94	1	no	—
283	C₂×M₁₆	—	188	1	no	—
284	C₂²×C₈	—	47	1	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	188	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	94	2	no	—
289	C₄⋊Q₈	—	94	1	no	—
290	C₄⋊Q₈	—	188	1	no	—
291	C₄⋊Q₈	—	188	1	no	—
292	C₂×C₄⋊C₄	—	94	2	no	—
293	C₂×C₄⋊C₄	—	188	1	no	—
294	C₂×C₄²	—	47	1	no	—
295	M₃₂	—	47	2	no	—
296	M₃₂	—	94	2	no	—
297	M₃₂	C₂²×D₄₇	1	2	yes	—
298	C₂×C₁₆	—	94	2	no	—
299	#108	—	47	1	no	—
300	#108	—	94	1	no	—
301	#108	C₂²×D₄₇	1	1	yes	characteristic
302	#106	—	2	1	no	—
303	#106	—	47	2	no	—
304	#106	—	94	2	no	—
305	#106	—	94	2	no	—
306	#106	—	94	1	no	—
307	#106	C₂²×D₄₇	1	2	yes	—
308	#104	—	2	1	no	—
309	#104	—	94	1	no	—
310	#104	—	94	1	no	—
311	#104	—	94	1	no	—
312	C₄×C₈	—	47	1	no	—
313	C₄×C₈	—	47	1	no	—
314	C₄×C₈	—	47	1	no	—
315	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
316	#41	—	2	1	no	—
317	#41	—	94	1	no	—
318	#41	—	94	1	no	—
319	#41	—	94	1	no	—
320	#41	—	188	1	no	—
321	#41	—	188	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	94	1	no	—
324	C₂×Q₈	—	376	4	no	—
325	C₂×Q₈	—	188	1	no	—
326	C₂×Q₈	—	188	2	no	—
327	C₂×D₄	—	94	1	no	—
328	C₂×D₄	—	188	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	188	1	no	—
332	C₂²×C₄	—	188	2	no	—
333	Q₁₆	—	47	1	no	—
334	Q₁₆	—	94	1	no	—
335	Q₁₆	Q₈×D₄₇	1	1	yes	characteristic, complemented
336	SD₁₆	—	2	1	no	—
337	SD₁₆	—	94	1	no	—
338	SD₁₆	—	94	1	no	—
339	SD₁₆	—	94	1	no	—
340	D₈	—	47	1	no	—
341	D₈	—	94	1	no	—
342	D₈	Q₈×D₄₇	1	1	yes	characteristic, complemented
343	M₁₆	—	2	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	94	1	no	—
346	M₁₆	—	188	1	no	—
347	M₁₆	—	188	1	no	—
348	M₁₆	—	188	1	no	—
349	M₁₆	—	188	1	no	—
350	C₂×C₈	—	4	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	—	47	1	no	—
356	C₂×C₈	—	47	1	no	—
357	C₂×C₈	—	47	1	no	—
358	C₂×C₈	—	47	1	no	—
359	C₂×C₈	—	47	1	no	—
360	C₂×C₈	—	47	1	no	—
361	C₂×C₈	—	188	1	no	—
362	C₂×C₈	—	188	1	no	—
363	C₂×C₈	—	188	1	no	—
364	C₂×C₈	—	188	1	no	—
365	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	94	2	no	—
370	C₄⋊C₄	—	188	1	no	—
371	C₄⋊C₄	—	188	2	no	—
372	C₄⋊C₄	—	188	2	no	—
373	C₄²	—	47	1	no	—
374	C₄²	—	94	1	no	—
375	C₄²	D₄×D₄₇	1	1	yes	characteristic
376	C₁₆	—	2	2	no	—
377	C₁₆	—	94	2	no	—
378	C₂³	—	47	1	no	—
379	C₂³	—	188	1	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	8	2	no	—
382	Q₈	—	94	1	no	—
383	Q₈	—	376	2	no	—
384	Q₈	—	376	4	no	—
385	Q₈	—	188	1	no	—
386	D₄	—	2	1	no	—
387	D₄	—	4	1	no	—
388	D₄	—	94	1	no	—
389	D₄	—	188	1	no	—
390	D₄	—	188	1	no	—
391	D₄	—	188	1	no	—
392	D₄	—	188	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	47	1	no	—
397	C₂×C₄	—	47	1	no	—
398	C₂×C₄	—	47	1	no	—
399	C₂×C₄	—	47	1	no	—
400	C₂×C₄	—	47	1	no	—
401	C₂×C₄	—	94	4	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	376	4	no	—
404	C₂×C₄	—	188	1	no	—
405	C₂×C₄	—	188	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	47	1	no	—
412	C₈	—	47	1	no	—
413	C₈	—	47	1	no	—
414	C₈	—	47	1	no	—
415	C₈	—	188	1	no	—
416	C₈	SD₁₆×D₄₇	1	1	yes	characteristic
417	C₈	SD₁₆×D₄₇	1	1	yes	characteristic
418	C₈	C₂×Q₈×D₄₇	1	1	yes	characteristic
419	C₈	#41×D₄₇	1	1	yes	characteristic
420	C₂²	—	4	1	no	—
421	C₂²	—	47	1	no	—
422	C₂²	—	47	1	no	—
423	C₂²	—	94	2	no	—
424	C₂²	—	376	2	no	—
425	C₂²	—	188	1	no	—
426	C₂²	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	2	no	—
430	C₄	—	47	1	no	—
431	C₄	—	47	1	no	—
432	C₄	—	94	2	no	—
433	C₄	—	376	2	no	—
434	C₄	—	188	1	no	—
435	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
436	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
437	C₂	—	2	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	47	2	no	—
440	C₂	—	94	1	no	—
441	C₂	—	376	1	no	—
442	C₂	#476×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#476×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₄₇×#2230	C₂
socle	C₂×C₄₇	C₂×#476
prime radical	#135×D₄₇	C₂²
hypercenter	#2230	D₄₇
hypocenter	C₄₇	C₂×#2230
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2230

Complements

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

N	H ≅ G/N	type
1. #498×D₄₇	C₂	semidirect
3. #20245560	C₂	semidirect
4. #20245559	C₂	semidirect
5. #20245558	C₂	semidirect
6. #20245557	C₂	semidirect
7. #20245556	C₂	semidirect
8. #365×D₄₇	C₂	semidirect
9. #364×D₄₇	C₂	semidirect
11. C₄₇×#2230	C₂	semidirect
16. #15689521	C₂²	semidirect
18. #15689520	C₂²	semidirect
30. #15688947	C₂²	semidirect
31. #15688946	C₂²	semidirect
32. #15688945	C₂²	semidirect
33. #15688944	C₂²	semidirect
34. #15688943	C₂²	semidirect
38. C₄₇×#498	C₂²	semidirect
40. C₄₇×#365	C₂²	semidirect
41. C₄₇×#364	C₂²	semidirect
45. #13094047	Q₈	semidirect
49. #13094043	Q₈	semidirect
50. Q₁₆×D₄₇	Q₈	semidirect
52. D₈×D₄₇	Q₈	semidirect
111. Q₁₆×C₄₇	C₂×Q₈	semidirect
113. D₈×C₄₇	C₂×Q₈	semidirect
137. Dic₁₈₈	C₂×Q₈	semidirect
138. D₃₇₆	C₂×Q₈	semidirect
223. #2230	D₄₇	direct (N × H)
232. D₄₇	#2230	direct (N × H)
241. #498	C₂×D₄₇	semidirect
256. #365	C₂×D₄₇	semidirect
259. #364	C₂×D₄₇	semidirect
264. C₄₇	C₂×#2230	semidirect
335. Q₁₆	Q₈×D₄₇	semidirect
342. D₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#498×D₄₇	2
#443×D₄₇	2
#20245560	2
#20245559	2
#20245558	2
#20245557	2
#20245556	2
#365×D₄₇	2
#364×D₄₇	2
#360×D₄₇	2
C₄₇×#2230	2
C₂×#2230	47

Subgroups — D47×#2230 #26371004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2230 #26371004