Subgroups — C₄₇×#19942 #26059640

Order 12032.

590 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3396	C₂	1	1	yes	maximal, characteristic
2	Q₈×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3375	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1706	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1698	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1668	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#1630	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1623	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#559	C₂²	1	2	yes	—
13	Q₈²×C₄₇	C₂²	1	2	yes	—
14	C₄₇×#500	—	2	1	no	—
15	C₄₇×#500	C₂²	1	1	yes	characteristic
16	C₄₇×#495	—	2	1	no	—
17	C₄₇×#493	C₂²	1	1	yes	characteristic
18	C₄₇×#492	C₂²	1	2	yes	—
19	C₄₇×#489	—	2	2	no	—
20	C₄₇×#486	C₂²	1	2	yes	—
21	C₄₇×#477	—	2	2	no	—
22	C₄₇×#477	C₂²	1	2	yes	—
23	C₄₇×#477	C₂²	1	2	yes	—
24	C₄₇×#474	—	2	2	no	—
25	C₄₇×#464	—	2	2	no	—
26	C₄₇×#463	—	2	2	no	—
27	C₄₇×#460	C₂²	1	2	yes	—
28	C₄₇×#460	C₂²	1	2	yes	—
29	C₄₇×#446	C₂²	1	2	yes	—
30	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#440	—	2	2	no	—
33	C₄×Q₁₆×C₄₇	—	2	1	no	—
34	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₄₇	—	2	1	no	—
37	C₄₇×#335	C₂²	1	1	yes	characteristic
38	C₄₇×#335	C₂²	1	1	yes	characteristic
39	C₄₇×#333	C₂²	1	2	yes	—
40	C₄₇×#331	C₂²	1	2	yes	—
41	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₄₇	—	2	2	no	—
48	C₂×SD₁₆×C₄₇	—	2	2	no	—
49	C₂×SD₁₆×C₄₇	—	4	2	no	—
50	C₂×D₈×C₄₇	—	2	1	no	—
51	C₂×D₈×C₄₇	—	2	1	no	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	—	4	2	no	—
55	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
56	#127×C₄₇	C₂³	1	2	yes	—
57	#124×C₄₇	—	2	2	no	—
58	#124×C₄₇	—	2	2	no	—
59	#123×C₄₇	—	4	2	no	—
60	C₄×Q₈×C₄₇	—	2	2	no	—
61	C₄×Q₈×C₄₇	—	2	2	no	—
62	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
64	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₄₇	—	2	2	no	—
66	C₄×D₄×C₄₇	—	2	2	no	—
67	#107×C₄₇	—	2	1	no	—
68	#107×C₄₇	—	2	1	no	—
69	#107×C₄₇	—	2	2	no	—
70	#107×C₄₇	—	2	2	no	—
71	#107×C₄₇	D₄	1	1	yes	characteristic
72	#107×C₄₇	D₄	1	1	yes	characteristic
73	C₄⋊C₈×C₄₇	—	2	1	no	—
74	C₄⋊C₈×C₄₇	—	2	2	no	—
75	C₄⋊C₈×C₄₇	—	2	1	no	—
76	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
78	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
79	#103×C₄₇	—	2	2	no	—
80	#103×C₄₇	—	2	2	no	—
81	#103×C₄₇	D₄	1	2	yes	—
82	#103×C₄₇	D₄	1	1	yes	characteristic
83	#103×C₄₇	D₄	1	1	yes	characteristic
84	#102×C₄₇	—	2	2	no	—
85	#102×C₄₇	—	2	2	no	—
86	#102×C₄₇	—	2	2	no	—
87	#102×C₄₇	—	2	2	no	—
88	#97×C₄₇	—	2	2	no	—
89	C₄×C₈×C₄₇	—	2	1	no	—
90	C₄×C₈×C₄₇	—	2	1	no	—
91	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	4	2	no	—
96	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
98	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	Q₁₆×C₄₇	—	2	2	no	—
104	Q₁₆×C₄₇	—	2	2	no	—
105	SD₁₆×C₄₇	—	4	4	no	—
106	SD₁₆×C₄₇	—	8	4	no	—
107	SD₁₆×C₄₇	—	8	2	no	—
108	D₈×C₄₇	—	4	2	no	—
109	D₈×C₄₇	—	8	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₄₇	—	4	2	no	—
129	C₂²⋊C₄×C₄₇	—	4	2	no	—
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	4	2	no	—
135	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₄₇	—	4	2	no	—
137	Q₈×C₄₇	—	2	1	no	—
138	Q₈×C₄₇	—	2	1	no	—
139	Q₈×C₄₇	—	2	2	no	—
140	Q₈×C₄₇	—	2	2	no	—
141	Q₈×C₄₇	—	2	1	no	—
142	Q₈×C₄₇	—	8	2	no	—
143	Q₈×C₄₇	—	16	2	no	—
144	Q₈×C₄₇	#135	1	2	yes	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	8	2	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	16	2	no	—
158	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₄₇	—	2	2	no	—
162	C₈×C₄₇	—	2	1	no	—
163	C₈×C₄₇	—	2	1	no	—
164	C₈×C₄₇	—	2	1	no	—
165	C₈×C₄₇	—	4	2	no	—
166	C₈×C₄₇	—	4	1	no	—
167	C₈×C₄₇	—	4	1	no	—
168	C₈×C₄₇	#137	1	2	yes	—
169	#19942	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₇	—	8	2	no	—
171	C₂²×C₄₇	—	8	2	no	—
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	D₄²	1	1	yes	characteristic
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	—	4	1	no	—
178	C₄×C₄₇	—	4	1	no	—
179	C₄×C₄₇	—	4	2	no	—
180	C₄×C₄₇	—	4	1	no	—
181	C₄×C₄₇	—	8	2	no	—
182	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
183	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
184	C₄×C₄₇	#577	1	1	yes	characteristic
185	C₄×C₄₇	#578	1	1	yes	characteristic
186	#3396	C₂×C₄₇	1	1	yes	characteristic
187	Q₈×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
188	#3375	C₂×C₄₇	1	2	yes	complemented
189	#1706	C₂×C₄₇	1	1	yes	characteristic
190	#1698	C₂×C₄₇	1	2	yes	complemented
191	#1676	C₂×C₄₇	1	1	yes	characteristic, complemented
192	#1668	C₂×C₄₇	1	1	yes	characteristic
193	#1630	C₂×C₄₇	1	2	yes	complemented
194	#1623	C₂×C₄₇	1	2	yes	complemented
195	#1591	C₂×C₄₇	1	1	yes	characteristic, complemented
196	C₈×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
197	C₂×C₄₇	—	16	2	no	—
198	C₂×C₄₇	#3278	1	1	yes	characteristic
199	C₂×C₄₇	#3285	1	1	yes	characteristic
200	C₂×C₄₇	#3292	1	1	yes	characteristic
201	#559	C₂²×C₄₇	1	2	yes	—
202	Q₈²	C₂²×C₄₇	1	2	yes	—
203	#500	—	2	1	no	—
204	#500	C₂²×C₄₇	1	1	yes	characteristic
205	#495	—	2	1	no	—
206	#493	C₂²×C₄₇	1	1	yes	characteristic
207	#492	C₂²×C₄₇	1	2	yes	—
208	#489	—	2	2	no	—
209	#486	C₂²×C₄₇	1	2	yes	—
210	#477	—	2	2	no	—
211	#477	C₂²×C₄₇	1	2	yes	—
212	#477	C₂²×C₄₇	1	2	yes	—
213	#474	—	2	2	no	—
214	#464	—	2	2	no	—
215	#463	—	2	2	no	—
216	#460	C₂²×C₄₇	1	2	yes	—
217	#460	C₂²×C₄₇	1	2	yes	—
218	#446	C₂²×C₄₇	1	2	yes	—
219	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
220	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
221	#440	—	2	2	no	—
222	C₄×Q₁₆	—	2	1	no	—
223	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
224	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
225	C₄×D₈	—	2	1	no	—
226	#335	C₂²×C₄₇	1	1	yes	characteristic
227	#335	C₂²×C₄₇	1	1	yes	characteristic
228	#333	C₂²×C₄₇	1	2	yes	—
229	#331	C₂²×C₄₇	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
231	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
232	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
233	C₈²	C₂²×C₄₇	1	1	yes	characteristic
234	C₄₇	#19942	1	1	yes	characteristic, direct product factor, Sylow
235	C₂×Q₁₆	D₄×C₄₇	1	1	yes	characteristic
236	C₂×Q₁₆	D₄×C₄₇	1	1	yes	characteristic
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×SD₁₆	—	4	2	no	—
240	C₂×D₈	—	2	1	no	—
241	C₂×D₈	—	2	1	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	4	2	no	—
245	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
246	#127	C₂³×C₄₇	1	2	yes	—
247	#124	—	2	2	no	—
248	#124	—	2	2	no	—
249	#123	—	4	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
253	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
254	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	#107	—	2	1	no	—
258	#107	—	2	1	no	—
259	#107	—	2	2	no	—
260	#107	—	2	2	no	—
261	#107	D₄×C₄₇	1	1	yes	characteristic
262	#107	D₄×C₄₇	1	1	yes	characteristic
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
267	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
268	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
269	#103	—	2	2	no	—
270	#103	—	2	2	no	—
271	#103	D₄×C₄₇	1	1	yes	characteristic
272	#103	D₄×C₄₇	1	2	yes	—
273	#103	D₄×C₄₇	1	1	yes	characteristic
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#97	—	2	2	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
287	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
288	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	8	4	no	—
297	SD₁₆	—	8	2	no	—
298	D₈	—	4	2	no	—
299	D₈	—	8	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
316	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
317	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
326	C₂³	—	4	2	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	2	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	8	2	no	—
333	Q₈	—	16	2	no	—
334	Q₈	#135×C₄₇	1	2	yes	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	16	2	no	—
348	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
350	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
351	C₈	—	2	2	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	1	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	1	no	—
358	C₈	#137×C₄₇	1	2	yes	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	D₄²×C₄₇	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	2	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	8	2	no	—
371	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
372	C₄	C₂×#137×C₄₇	1	1	yes	characteristic
373	C₄	C₄₇×#577	1	1	yes	characteristic
374	C₄	C₄₇×#578	1	1	yes	characteristic
375	C₂	—	16	2	no	—
376	C₂	C₄₇×#3278	1	1	yes	characteristic
377	C₂	C₄₇×#3285	1	1	yes	characteristic
378	C₂	C₄₇×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#493	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×Q₁₆×C₄₇	C₂	semidirect
3. C₄₇×#3375	C₂	semidirect
5. C₄₇×#1698	C₂	semidirect
6. C₄₇×#1676	C₂	semidirect
8. C₄₇×#1630	C₂	semidirect
9. C₄₇×#1623	C₂	semidirect
10. C₄₇×#1591	C₂	semidirect
11. C₈×Q₁₆×C₄₇	C₂	semidirect
169. #19942	C₄₇	direct (N × H)
187. Q₈×Q₁₆	C₂×C₄₇	semidirect
188. #3375	C₂×C₄₇	semidirect
190. #1698	C₂×C₄₇	semidirect
191. #1676	C₂×C₄₇	semidirect
193. #1630	C₂×C₄₇	semidirect
194. #1623	C₂×C₄₇	semidirect
195. #1591	C₂×C₄₇	semidirect
196. C₈×Q₁₆	C₂×C₄₇	semidirect
234. C₄₇	#19942	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3396	2
Q₈×Q₁₆×C₄₇	2
C₄₇×#3375	2
C₄₇×#1706	2
C₄₇×#1698	2
C₄₇×#1676	2
C₄₇×#1668	2
C₄₇×#1630	2
C₄₇×#1623	2
C₄₇×#1591	2
C₈×Q₁₆×C₄₇	2
#19942	47

Subgroups — C47×#19942 #26059640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#19942 #26059640