Subgroups — C₄₇×#17874 #26057572

Order 12032.

648 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	C₄₇×#2989	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2982	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#137×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1588	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1587	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1584	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1583	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₇	C₄	1	1	yes	characteristic
13	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₄₇	—	2	1	no	—
17	C₈×Q₈×C₄₇	—	2	1	no	—
18	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
19	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#441	C₄	1	2	yes	—
21	C₄₇×#440	C₄	1	2	yes	—
22	C₄×Q₁₆×C₄₇	C₂²	1	2	yes	—
23	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#436	C₂²	1	2	yes	—
25	C₄₇×#435	—	2	2	no	—
26	C₄₇×#432	—	2	1	no	—
27	C₄₇×#431	—	2	2	no	—
28	C₄₇×#431	C₂²	1	1	yes	characteristic
29	C₄₇×#431	C₂²	1	1	yes	characteristic
30	C₄₇×#428	C₄	1	1	yes	characteristic
31	C₄₇×#423	—	2	1	no	—
32	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#419	C₄	1	1	yes	characteristic
34	C₄₇×#417	C₄	1	1	yes	characteristic
35	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#335	C₂²	1	2	yes	—
38	C₄₇×#334	C₂²	1	2	yes	—
39	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₄₇×#322	C₂²	1	2	yes	—
46	C₄₇×#322	C₂²	1	2	yes	—
47	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
49	#137×C₄₇	—	2	4	no	—
50	C₂×Q₁₆×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₄₇	—	2	1	no	—
56	C₂²×C₈×C₄₇	—	2	1	no	—
57	C₄×Q₈×C₄₇	—	2	1	no	—
58	C₄×Q₈×C₄₇	—	2	1	no	—
59	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
62	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₄₇	—	2	1	no	—
64	C₄×D₄×C₄₇	—	2	1	no	—
65	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
67	#117×C₄₇	—	2	1	no	—
68	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	#107×C₄₇	C₂×C₄	1	2	yes	—
75	#106×C₄₇	C₂×C₄	1	2	yes	—
76	C₄⋊C₈×C₄₇	—	2	2	no	—
77	C₄⋊C₈×C₄₇	—	2	2	no	—
78	C₄⋊C₈×C₄₇	—	2	2	no	—
79	C₄⋊C₈×C₄₇	—	2	1	no	—
80	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
82	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
85	#103×C₄₇	C₂×C₄	1	2	yes	—
86	#103×C₄₇	C₂×C₄	1	2	yes	—
87	#103×C₄₇	C₂×C₄	1	2	yes	—
88	#102×C₄₇	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₄₇	—	2	1	no	—
90	C₂²⋊C₈×C₄₇	—	2	2	no	—
91	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
92	#97×C₄₇	—	2	2	no	—
93	#97×C₄₇	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	2	no	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	—	2	1	no	—
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	#41×C₄₇	—	2	2	no	—
103	#41×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	M₁₆	1	4	yes	complemented
107	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	Q₁₆×C₄₇	—	2	4	no	—
120	SD₁₆×C₄₇	—	2	4	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	—	8	2	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	4	2	no	—
130	C₂×C₈×C₄₇	—	8	1	no	—
131	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²⋊C₄×C₄₇	—	2	1	no	—
144	C₂²⋊C₄×C₄₇	—	2	1	no	—
145	C₂²⋊C₄×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₇	#41	1	1	yes	characteristic
154	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
157	Q₈×C₄₇	—	2	2	no	—
158	Q₈×C₄₇	—	2	4	no	—
159	Q₈×C₄₇	—	2	1	no	—
160	Q₈×C₄₇	—	2	1	no	—
161	Q₈×C₄₇	C₂×M₁₆	1	4	yes	—
162	D₄×C₄₇	—	2	1	no	—
163	D₄×C₄₇	—	2	1	no	—
164	D₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	1	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	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	8	1	no	—
178	C₂×C₄×C₄₇	—	8	1	no	—
179	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₄₇	#131	1	2	yes	—
184	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₈×C₄₇	—	4	1	no	—
194	C₈×C₄₇	—	4	2	no	—
195	C₈×C₄₇	—	4	1	no	—
196	#17874	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	4	1	no	—
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	—	4	1	no	—
202	C₂²×C₄₇	#435	1	2	yes	—
203	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₇	—	2	4	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	4	1	no	—
209	C₄×C₄₇	—	4	1	no	—
210	C₄×C₄₇	—	4	1	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	#435	1	2	yes	—
213	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
215	C₄×C₄₇	#577	1	1	yes	characteristic
216	C₄×C₄₇	#578	1	1	yes	characteristic
217	#2989	C₂×C₄₇	1	1	yes	characteristic
218	#2982	C₂×C₄₇	1	1	yes	characteristic, complemented
219	C₄×#137	C₂×C₄₇	1	1	yes	characteristic
220	#1588	C₂×C₄₇	1	2	yes	complemented
221	#1587	C₂×C₄₇	1	2	yes	complemented
222	#1584	C₂×C₄₇	1	2	yes	complemented
223	#1583	C₂×C₄₇	1	2	yes	complemented
224	#1565	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#1476	C₂×C₄₇	1	1	yes	characteristic
226	C₂×Q₈⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
227	#1451	C₂×C₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	—	8	1	no	—
230	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
231	C₂×C₄₇	#2947	1	1	yes	characteristic
232	C₂×C₄₇	#2956	1	1	yes	characteristic
233	C₂×#137	C₄×C₄₇	1	1	yes	characteristic
234	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
235	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
236	#446	C₂²×C₄₇	1	2	yes	—
237	C₈×Q₈	—	2	1	no	—
238	C₈×Q₈	—	2	1	no	—
239	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
240	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
241	#441	C₄×C₄₇	1	2	yes	—
242	#440	C₄×C₄₇	1	2	yes	—
243	C₄×Q₁₆	C₂²×C₄₇	1	2	yes	—
244	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
245	#436	C₂²×C₄₇	1	2	yes	—
246	#435	—	2	2	no	—
247	#432	—	2	1	no	—
248	#431	—	2	2	no	—
249	#431	C₂²×C₄₇	1	1	yes	characteristic
250	#431	C₂²×C₄₇	1	1	yes	characteristic
251	#428	C₄×C₄₇	1	1	yes	characteristic
252	#423	—	2	1	no	—
253	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
254	#419	C₄×C₄₇	1	1	yes	characteristic
255	#417	C₄×C₄₇	1	1	yes	characteristic
256	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
258	#335	C₂²×C₄₇	1	2	yes	—
259	#334	C₂²×C₄₇	1	2	yes	—
260	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
261	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
262	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
263	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
264	D₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
265	D₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
266	#322	C₂²×C₄₇	1	2	yes	—
267	#322	C₂²×C₄₇	1	2	yes	—
268	C₄₇	#17874	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#41	C₂×C₄×C₄₇	1	1	yes	characteristic
270	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
271	#137	—	2	4	no	—
272	C₂×Q₁₆	C₂×C₄×C₄₇	1	2	yes	—
273	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
282	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
283	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
284	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
288	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	C₂×C₄×C₄₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
296	#107	C₂×C₄×C₄₇	1	2	yes	—
297	#106	C₂×C₄×C₄₇	1	2	yes	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
303	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
307	#103	C₂×C₄×C₄₇	1	2	yes	—
308	#103	C₂×C₄×C₄₇	1	2	yes	—
309	#103	C₂×C₄×C₄₇	1	2	yes	—
310	#102	C₂×C₄×C₄₇	1	2	yes	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
314	#97	—	2	2	no	—
315	#97	C₂×C₄×C₄₇	1	2	yes	—
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	2	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
321	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₄₇	1	2	yes	—
323	C₄×C₈	C₂³×C₄₇	1	2	yes	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	M₁₆×C₄₇	1	4	yes	complemented
329	C₂×Q₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
330	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
340	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
341	Q₁₆	—	2	4	no	—
342	SD₁₆	—	2	4	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	8	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	8	1	no	—
353	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
354	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
355	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
363	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
375	C₄²	#41×C₄₇	1	1	yes	characteristic
376	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	4	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	C₂×M₁₆×C₄₇	1	4	yes	—
384	D₄	—	2	1	no	—
385	D₄	—	2	1	no	—
386	D₄	—	4	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
402	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
403	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×M₁₆×C₄₇	1	2	yes	—
405	C₂×C₄	#131×C₄₇	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	C₄₇×#435	1	2	yes	—
424	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
425	C₄	—	2	4	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	C₄₇×#435	1	2	yes	—
434	C₄	C₂²×M₁₆×C₄₇	1	1	yes	characteristic
435	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
436	C₄	C₄₇×#577	1	1	yes	characteristic
437	C₄	C₄₇×#578	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	C₂×C₄₇×#435	1	1	yes	characteristic
441	C₂	C₄₇×#2947	1	1	yes	characteristic
442	C₂	C₄₇×#2956	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	C₂×#41×C₄₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₄₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2982	C₂	semidirect
4. C₄₇×#1588	C₂	semidirect
5. C₄₇×#1587	C₂	semidirect
6. C₄₇×#1584	C₂	semidirect
7. C₄₇×#1583	C₂	semidirect
8. C₄₇×#1565	C₂	semidirect
10. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
11. C₄₇×#1451	C₂	semidirect
106. C₂×Q₈×C₄₇	M₁₆	semidirect
196. #17874	C₄₇	direct (N × H)
218. #2982	C₂×C₄₇	semidirect
220. #1588	C₂×C₄₇	semidirect
221. #1587	C₂×C₄₇	semidirect
222. #1584	C₂×C₄₇	semidirect
223. #1583	C₂×C₄₇	semidirect
224. #1565	C₂×C₄₇	semidirect
226. C₂×Q₈⋊C₈	C₂×C₄₇	semidirect
227. #1451	C₂×C₄₇	semidirect
268. C₄₇	#17874	direct (N × H)
328. C₂×Q₈	M₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#2989	2
C₄₇×#2982	2
C₄×#137×C₄₇	2
C₄₇×#1588	2
C₄₇×#1587	2
C₄₇×#1584	2
C₄₇×#1583	2
C₄₇×#1565	2
C₄₇×#1476	2
C₂×C₄₇×Q₈⋊C₈	2
C₄₇×#1451	2
#17874	47

Subgroups — C47×#17874 #26057572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17874 #26057572