Subgroups — C₄₇×#17967 #26057665

Order 12032.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3172	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2966	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1591	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1590	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1579	C₂	1	2	yes	maximal, complemented
7	C₄₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1569	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1495	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#533	C₂²	1	1	yes	characteristic
13	C₄₇×#529	C₂²	1	1	yes	characteristic
14	C₄₇×#501	C₄	1	1	yes	characteristic
15	C₄₇×#497	C₄	1	1	yes	characteristic
16	C₄₇×#491	C₄	1	1	yes	characteristic
17	C₄₇×#489	C₄	1	1	yes	characteristic
18	C₄₇×#470	C₄	1	2	yes	—
19	C₄₇×#468	C₄	1	2	yes	—
20	C₄₇×#446	—	2	1	no	—
21	C₄₇×#446	C₂²	1	2	yes	—
22	C₄₇×#446	C₂²	1	1	yes	characteristic
23	C₈×Q₈×C₄₇	—	2	1	no	—
24	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
25	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	—
27	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
28	C₄₇×#436	C₂²	1	1	yes	characteristic
29	C₄₇×#435	—	2	1	no	—
30	C₈×D₄×C₄₇	—	2	1	no	—
31	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#433	—	2	1	no	—
33	C₄₇×#432	C₂²	1	1	yes	characteristic
34	C₄₇×#431	C₂²	1	1	yes	characteristic
35	C₄₇×#424	—	2	1	no	—
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₄₇×#405	—	2	1	no	—
38	C₄₇×#405	—	2	1	no	—
39	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#335	C₂²	1	2	yes	—
42	C₄₇×#334	C₂²	1	2	yes	—
43	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₄₇×#322	C₂²	1	2	yes	—
48	C₈²×C₄₇	C₂²	1	2	yes	—
49	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
50	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₄₇	—	2	1	no	—
52	C₂×M₁₆×C₄₇	—	2	1	no	—
53	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₄₇	—	2	1	no	—
55	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
59	#126×C₄₇	—	2	1	no	—
60	#125×C₄₇	—	2	1	no	—
61	#125×C₄₇	C₂×C₄	1	1	yes	characteristic
62	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
63	#123×C₄₇	—	2	1	no	—
64	C₂²⋊Q₈×C₄₇	—	2	1	no	—
65	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
66	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
67	#121×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₄₇	—	2	1	no	—
69	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
71	C₄×D₄×C₄₇	—	2	1	no	—
72	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
73	#117×C₄₇	—	2	1	no	—
74	#117×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	#107×C₄₇	C₂×C₄	1	2	yes	—
77	#106×C₄₇	C₂×C₄	1	2	yes	—
78	C₄⋊C₈×C₄₇	—	2	2	no	—
79	C₄⋊C₈×C₄₇	—	2	2	no	—
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	—	2	1	no	—
82	C₄⋊C₈×C₄₇	—	2	1	no	—
83	C₄⋊C₈×C₄₇	—	2	1	no	—
84	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
85	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
87	#103×C₄₇	C₂×C₄	1	2	yes	—
88	#103×C₄₇	C₂×C₄	1	2	yes	—
89	#103×C₄₇	C₂×C₄	1	2	yes	—
90	#102×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	C₂²⋊C₈×C₄₇	—	2	1	no	—
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	#97×C₄₇	—	2	1	no	—
96	#97×C₄₇	—	2	2	no	—
97	#97×C₄₇	—	2	1	no	—
98	#97×C₄₇	C₂×C₄	1	1	yes	characteristic
99	#97×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	—	2	1	no	—
101	C₄×C₈×C₄₇	—	2	2	no	—
102	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₄₇	C₂³	1	2	yes	—
105	C₄×C₈×C₄₇	C₂³	1	2	yes	—
106	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	—	2	1	no	—
109	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	Q₁₆×C₄₇	—	2	4	no	—
118	SD₁₆×C₄₇	—	2	4	no	—
119	M₁₆×C₄₇	—	2	4	no	—
120	M₁₆×C₄₇	—	4	2	no	—
121	M₁₆×C₄₇	—	4	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	4	1	no	—
128	C₂×C₈×C₄₇	—	4	2	no	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	2	1	no	—
144	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂²⋊C₄×C₄₇	—	2	2	no	—
148	C₂²⋊C₄×C₄₇	—	2	1	no	—
149	C₂²⋊C₄×C₄₇	—	2	1	no	—
150	C₂²⋊C₄×C₄₇	—	2	1	no	—
151	C₂²⋊C₄×C₄₇	—	2	1	no	—
152	C₂²⋊C₄×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₄²×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₄₇	#41	1	1	yes	characteristic
158	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
161	Q₈×C₄₇	—	2	2	no	—
162	Q₈×C₄₇	—	2	2	no	—
163	Q₈×C₄₇	—	2	2	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₈×C₄₇	—	2	2	no	—
185	C₈×C₄₇	—	2	1	no	—
186	C₈×C₄₇	—	2	1	no	—
187	C₈×C₄₇	—	2	1	no	—
188	C₈×C₄₇	—	4	2	no	—
189	C₈×C₄₇	—	4	1	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₈×C₄₇	—	4	2	no	—
192	C₈×C₄₇	#131	1	4	yes	—
193	C₈×C₄₇	#137	1	2	yes	—
194	#17967	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	4	1	no	—
199	C₂²×C₄₇	—	4	1	no	—
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	4	1	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	—	4	1	no	—
209	C₄×C₄₇	—	4	1	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	C₂×#131	1	2	yes	—
212	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
213	C₄×C₄₇	#575	1	1	yes	characteristic
214	#3172	C₂×C₄₇	1	1	yes	characteristic
215	#2966	C₂×C₄₇	1	1	yes	characteristic
216	#2960	C₂×C₄₇	1	1	yes	characteristic, complemented
217	#1591	C₂×C₄₇	1	2	yes	complemented
218	#1590	C₂×C₄₇	1	2	yes	complemented
219	#1579	C₂×C₄₇	1	2	yes	complemented
220	SD₁₆⋊C₈	C₂×C₄₇	1	2	yes	complemented
221	#1569	C₂×C₄₇	1	1	yes	characteristic, complemented
222	#1497	C₂×C₄₇	1	1	yes	characteristic, complemented
223	#1495	C₂×C₄₇	1	1	yes	characteristic
224	C₈×M₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
225	C₂×C₄₇	—	4	1	no	—
226	C₂×C₄₇	—	8	1	no	—
227	C₂×C₄₇	#2931	1	1	yes	characteristic
228	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
229	C₂×C₄₇	#2955	1	1	yes	characteristic
230	#533	C₂²×C₄₇	1	1	yes	characteristic
231	#529	C₂²×C₄₇	1	1	yes	characteristic
232	#501	C₄×C₄₇	1	1	yes	characteristic
233	#497	C₄×C₄₇	1	1	yes	characteristic
234	#491	C₄×C₄₇	1	1	yes	characteristic
235	#489	C₄×C₄₇	1	1	yes	characteristic
236	#470	C₄×C₄₇	1	2	yes	—
237	#468	C₄×C₄₇	1	2	yes	—
238	#446	—	2	1	no	—
239	#446	C₂²×C₄₇	1	2	yes	—
240	#446	C₂²×C₄₇	1	1	yes	characteristic
241	C₈×Q₈	—	2	1	no	—
242	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
243	C₈×Q₈	C₂²×C₄₇	1	1	yes	characteristic
244	C₄×Q₁₆	C₂²×C₄₇	1	2	yes	—
245	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
246	#436	C₂²×C₄₇	1	1	yes	characteristic
247	#435	—	2	1	no	—
248	C₈×D₄	—	2	1	no	—
249	C₈×D₄	C₂²×C₄₇	1	1	yes	characteristic
250	#433	—	2	1	no	—
251	#432	C₂²×C₄₇	1	1	yes	characteristic
252	#431	C₂²×C₄₇	1	1	yes	characteristic
253	#424	—	2	1	no	—
254	#423	C₂²×C₄₇	1	1	yes	characteristic
255	#405	—	2	1	no	—
256	#405	—	2	1	no	—
257	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
259	#335	C₂²×C₄₇	1	2	yes	—
260	#334	C₂²×C₄₇	1	2	yes	—
261	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
262	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
263	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
264	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
265	#322	C₂²×C₄₇	1	2	yes	—
266	C₈²	C₂²×C₄₇	1	2	yes	—
267	C₄₇	#17967	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×Q₁₆	C₂×C₄×C₄₇	1	2	yes	—
269	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	C₂×C₄×C₄₇	1	2	yes	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
275	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
276	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
277	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
278	#126	—	2	1	no	—
279	#125	—	2	1	no	—
280	#125	C₂×C₄×C₄₇	1	1	yes	characteristic
281	#124	C₂×C₄×C₄₇	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
285	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
286	#121	C₂×C₄×C₄₇	1	1	yes	characteristic
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	#117	—	2	1	no	—
294	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
295	#107	C₂×C₄×C₄₇	1	2	yes	—
296	#106	C₂×C₄×C₄₇	1	2	yes	—
297	C₄⋊C₈	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
304	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
306	#103	C₂×C₄×C₄₇	1	2	yes	—
307	#103	C₂×C₄×C₄₇	1	2	yes	—
308	#103	C₂×C₄×C₄₇	1	2	yes	—
309	#102	C₂×C₄×C₄₇	1	2	yes	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	2	no	—
316	#97	—	2	1	no	—
317	#97	C₂×C₄×C₄₇	1	1	yes	characteristic
318	#97	C₂×C₄×C₄₇	1	1	yes	characteristic
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
322	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
323	C₄×C₈	C₂³×C₄₇	1	2	yes	—
324	C₄×C₈	C₂³×C₄₇	1	2	yes	—
325	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
329	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
335	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
336	Q₁₆	—	2	4	no	—
337	SD₁₆	—	2	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	4	2	no	—
340	M₁₆	—	4	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
349	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
350	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
353	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
364	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
365	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	2	no	—
374	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
376	C₄²	#41×C₄₇	1	1	yes	characteristic
377	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
378	C₂³	—	2	1	no	—
379	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
398	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
399	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	2	no	—
411	C₈	#131×C₄₇	1	4	yes	—
412	C₈	#137×C₄₇	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	2	no	—
429	C₄	C₂×#131×C₄₇	1	2	yes	—
430	C₄	C₂×#137×C₄₇	1	1	yes	characteristic
431	C₄	C₄₇×#575	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	8	1	no	—
434	C₂	C₄₇×#2931	1	1	yes	characteristic
435	C₂	C₄×#137×C₄₇	1	1	yes	characteristic
436	C₂	C₄₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#121×C₄₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂×C₄×C₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₇×#2960	C₂	semidirect
4. C₄₇×#1591	C₂	semidirect
5. C₄₇×#1590	C₂	semidirect
6. C₄₇×#1579	C₂	semidirect
7. C₄₇×SD₁₆⋊C₈	C₂	semidirect
8. C₄₇×#1569	C₂	semidirect
9. C₄₇×#1497	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
194. #17967	C₄₇	direct (N × H)
216. #2960	C₂×C₄₇	semidirect
217. #1591	C₂×C₄₇	semidirect
218. #1590	C₂×C₄₇	semidirect
219. #1579	C₂×C₄₇	semidirect
220. SD₁₆⋊C₈	C₂×C₄₇	semidirect
221. #1569	C₂×C₄₇	semidirect
222. #1497	C₂×C₄₇	semidirect
224. C₈×M₁₆	C₂×C₄₇	semidirect
267. C₄₇	#17967	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×#3172	2
C₄₇×#2966	2
C₄₇×#2960	2
C₄₇×#1591	2
C₄₇×#1590	2
C₄₇×#1579	2
C₄₇×SD₁₆⋊C₈	2
C₄₇×#1569	2
C₄₇×#1497	2
C₄₇×#1495	2
C₈×M₁₆×C₄₇	2
#17967	47

Subgroups — C47×#17967 #26057665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17967 #26057665