Subgroups — C₄₇×#22687 #26062385

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2943	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2906	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1866	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1866	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1849	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1806	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#131×C₄₇	C₂²	1	2	yes	—
14	C₂×#131×C₄₇	C₂²	1	2	yes	—
15	C₄×#41×C₄₇	C₂²	1	2	yes	—
16	C₄₇×#444	—	2	4	no	—
17	C₄₇×#443	—	2	4	no	—
18	C₄₇×#442	C₄	1	2	yes	complemented
19	C₄₇×#441	C₄	1	2	yes	complemented
20	C₄₇×#440	C₄	1	2	yes	complemented
21	C₄₇×#440	C₄	1	2	yes	complemented
22	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#108×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#427	C₂²	1	1	yes	characteristic
26	C₄₇×#424	—	2	2	no	—
27	C₄₇×#424	—	2	2	no	—
28	C₄₇×#424	C₂²	1	2	yes	—
29	C₄₇×#424	C₂²	1	2	yes	—
30	C₄₇×#423	—	2	2	no	—
31	C₄₇×#423	C₂²	1	2	yes	—
32	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#104×C₄₇	C₂²	1	2	yes	—
35	C₂×#104×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#416	C₂²	1	2	yes	—
37	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#339	C₂²	1	2	yes	—
42	C₄₇×#339	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₄₇×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₇	C₂³	1	2	yes	—
46	#135×C₄₇	D₄	1	4	yes	—
47	#135×C₄₇	Q₈	1	4	yes	—
48	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
50	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
51	#131×C₄₇	—	2	4	no	—
52	#131×C₄₇	—	2	4	no	—
53	#131×C₄₇	—	4	2	no	—
54	#131×C₄₇	—	4	2	no	—
55	C₂×M₁₆×C₄₇	—	2	2	no	—
56	C₂×M₁₆×C₄₇	—	2	2	no	—
57	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
58	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	2	no	—
61	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
66	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₄×D₄×C₄₇	—	2	2	no	—
68	C₄×D₄×C₄₇	—	2	2	no	—
69	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
71	#117×C₄₇	—	2	2	no	—
72	#117×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#108×C₄₇	—	2	2	no	—
79	#108×C₄₇	—	2	2	no	—
80	#108×C₄₇	—	4	2	no	—
81	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#106×C₄₇	C₂×C₄	1	2	yes	—
84	C₄⋊C₈×C₄₇	—	2	2	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	C₄⋊C₈×C₄₇	—	2	2	no	—
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	C₄⋊C₈×C₄₇	—	2	2	no	—
90	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
91	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
92	#104×C₄₇	—	2	4	no	—
93	#104×C₄₇	—	2	4	no	—
94	#103×C₄₇	C₂×C₄	1	2	yes	—
95	#103×C₄₇	C₂×C₄	1	2	yes	—
96	#102×C₄₇	C₂×C₄	1	2	yes	—
97	#102×C₄₇	C₂×C₄	1	2	yes	—
98	#97×C₄₇	—	2	2	no	—
99	#97×C₄₇	C₂×C₄	1	2	yes	—
100	#97×C₄₇	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₄₇	—	2	2	no	—
102	#95×C₄₇	—	2	1	no	—
103	#41×C₄₇	—	2	2	no	—
104	#41×C₄₇	—	2	2	no	—
105	#41×C₄₇	C₂×D₄	1	4	yes	—
106	#41×C₄₇	C₂×Q₈	1	4	yes	—
107	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₄₇	C₄⋊C₄	1	4	yes	complemented
119	SD₁₆×C₄₇	C₄⋊C₄	1	8	yes	complemented
120	D₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	—	2	2	no	—
124	M₁₆×C₄₇	—	2	2	no	—
125	M₁₆×C₄₇	—	4	4	no	—
126	M₁₆×C₄₇	—	4	4	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	4	4	no	—
136	C₂×C₈×C₄₇	—	4	4	no	—
137	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	—	4	2	no	—
148	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
150	C₂²⋊C₄×C₄₇	—	2	2	no	—
151	C₂²⋊C₄×C₄₇	—	2	2	no	—
152	C₂²⋊C₄×C₄₇	—	2	2	no	—
153	C₄²×C₄₇	—	2	2	no	—
154	C₄²×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	—	2	2	no	—
156	C₄²×C₄₇	—	2	1	no	—
157	C₄²×C₄₇	—	2	1	no	—
158	C₄²×C₄₇	—	2	1	no	—
159	C₄²×C₄₇	—	2	1	no	—
160	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
161	C₄²×C₄₇	C₂×D₄	1	2	yes	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	8	2	no	—
185	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	2	1	no	—
195	C₈×C₄₇	—	2	2	no	—
196	C₈×C₄₇	—	2	1	no	—
197	C₈×C₄₇	—	4	2	no	—
198	C₈×C₄₇	—	4	2	no	—
199	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
200	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
201	#22687	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₇	#547	1	1	yes	characteristic
209	C₂²×C₄₇	#554	1	1	yes	characteristic
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	4	2	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	—	8	1	no	—
217	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₄×C₄₇	#520	1	1	yes	characteristic
219	C₄×C₄₇	D₄²	1	1	yes	characteristic
220	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
221	C₂×#444	C₂×C₄₇	1	1	yes	characteristic
222	C₂×#443	C₂×C₄₇	1	1	yes	characteristic
223	#2943	C₂×C₄₇	1	1	yes	characteristic
224	#2906	C₂×C₄₇	1	2	yes	complemented
225	#1946	C₂×C₄₇	1	1	yes	characteristic, complemented
226	#1945	C₂×C₄₇	1	1	yes	characteristic, complemented
227	#1866	C₂×C₄₇	1	2	yes	complemented
228	#1866	C₂×C₄₇	1	2	yes	complemented
229	#1849	C₂×C₄₇	1	1	yes	characteristic, complemented
230	#1806	C₂×C₄₇	1	2	yes	complemented
231	#1771	C₂×C₄₇	1	1	yes	characteristic, complemented
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	4	4	no	—
235	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄₇	#2955	1	1	yes	characteristic
237	C₂×C₄₇	#2956	1	1	yes	characteristic
238	C₂×#135	C₂²×C₄₇	1	1	yes	characteristic
239	C₂×#131	C₂²×C₄₇	1	2	yes	—
240	C₂×#131	C₂²×C₄₇	1	2	yes	—
241	C₄×#41	C₂²×C₄₇	1	2	yes	—
242	#444	—	2	4	no	—
243	#443	—	2	4	no	—
244	#442	C₄×C₄₇	1	2	yes	complemented
245	#441	C₄×C₄₇	1	2	yes	complemented
246	#440	C₄×C₄₇	1	2	yes	complemented
247	#440	C₄×C₄₇	1	2	yes	complemented
248	C₂×#108	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×#108	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×#108	C₂²×C₄₇	1	2	yes	—
251	#427	C₂²×C₄₇	1	1	yes	characteristic
252	#424	—	2	2	no	—
253	#424	—	2	2	no	—
254	#424	C₂²×C₄₇	1	2	yes	—
255	#424	C₂²×C₄₇	1	2	yes	—
256	#423	—	2	2	no	—
257	#423	C₂²×C₄₇	1	2	yes	—
258	C₂×C₄⋊C₈	—	2	2	no	—
259	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
260	C₂×#104	C₂²×C₄₇	1	2	yes	—
261	C₂×#104	C₂²×C₄₇	1	2	yes	—
262	#416	C₂²×C₄₇	1	2	yes	—
263	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
267	#339	C₂²×C₄₇	1	2	yes	—
268	#339	C₂²×C₄₇	1	2	yes	—
269	#336	C₂²×C₄₇	1	1	yes	characteristic
270	#336	C₂²×C₄₇	1	1	yes	characteristic
271	C₄₇	#22687	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×#41	C₂³×C₄₇	1	2	yes	—
273	#135	D₄×C₄₇	1	4	yes	—
274	#135	Q₈×C₄₇	1	4	yes	—
275	C₂×Q₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
277	C₂×D₈	C₂×C₄×C₄₇	1	1	yes	characteristic
278	#131	—	2	4	no	—
279	#131	—	2	4	no	—
280	#131	—	4	2	no	—
281	#131	—	4	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
285	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
292	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
293	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
297	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
298	#117	—	2	2	no	—
299	#117	C₂³×C₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
305	#108	—	2	2	no	—
306	#108	—	2	2	no	—
307	#108	—	4	2	no	—
308	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
309	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
310	#106	C₂×C₄×C₄₇	1	2	yes	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	—	2	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	2	2	no	—
317	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
318	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
319	#104	—	2	4	no	—
320	#104	—	2	4	no	—
321	#103	C₂×C₄×C₄₇	1	2	yes	—
322	#103	C₂×C₄×C₄₇	1	2	yes	—
323	#102	C₂×C₄×C₄₇	1	2	yes	—
324	#102	C₂×C₄×C₄₇	1	2	yes	—
325	#97	—	2	2	no	—
326	#97	C₂×C₄×C₄₇	1	2	yes	—
327	#97	C₂×C₄×C₄₇	1	2	yes	—
328	C₄×C₈	—	2	2	no	—
329	#95	—	2	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	C₂×D₄×C₄₇	1	4	yes	—
333	#41	C₂×Q₈×C₄₇	1	4	yes	—
334	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
343	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
345	Q₁₆	C₄⋊C₄×C₄₇	1	4	yes	complemented
346	SD₁₆	C₄⋊C₄×C₄₇	1	8	yes	complemented
347	D₈	C₄⋊C₄×C₄₇	1	4	yes	complemented
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	4	no	—
353	M₁₆	—	4	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	4	4	no	—
363	C₂×C₈	—	4	4	no	—
364	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
365	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
371	C₂×C₈	C₂×Q₈×C₄₇	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
376	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
388	C₄²	C₂×D₄×C₄₇	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	8	2	no	—
412	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
413	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
414	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
418	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
419	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	2	no	—
423	C₈	—	2	1	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
427	C₈	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
434	C₂²	C₄₇×#547	1	1	yes	characteristic
435	C₂²	C₄₇×#554	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
444	C₄	C₄₇×#520	1	1	yes	characteristic
445	C₄	D₄²×C₄₇	1	1	yes	characteristic
446	C₄	D₄×Q₈×C₄₇	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	D₄×C₄⋊C₄×C₄₇	1	1	yes	characteristic
451	C₂	C₄₇×#2955	1	1	yes	characteristic
452	C₂	C₄₇×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#135×C₄₇	C₂²
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
4. C₄₇×#2906	C₂	semidirect
5. C₄₇×#1946	C₂	semidirect
6. C₄₇×#1945	C₂	semidirect
7. C₄₇×#1866	C₂	semidirect
8. C₄₇×#1866	C₂	semidirect
9. C₄₇×#1849	C₂	semidirect
10. C₄₇×#1806	C₂	semidirect
11. C₄₇×#1771	C₂	semidirect
18. C₄₇×#442	C₄	semidirect
19. C₄₇×#441	C₄	semidirect
20. C₄₇×#440	C₄	semidirect
21. C₄₇×#440	C₄	semidirect
118. Q₁₆×C₄₇	C₄⋊C₄	semidirect
119. SD₁₆×C₄₇	C₄⋊C₄	semidirect
120. D₈×C₄₇	C₄⋊C₄	semidirect
201. #22687	C₄₇	direct (N × H)
224. #2906	C₂×C₄₇	semidirect
225. #1946	C₂×C₄₇	semidirect
226. #1945	C₂×C₄₇	semidirect
227. #1866	C₂×C₄₇	semidirect
228. #1866	C₂×C₄₇	semidirect
229. #1849	C₂×C₄₇	semidirect
230. #1806	C₂×C₄₇	semidirect
231. #1771	C₂×C₄₇	semidirect
244. #442	C₄×C₄₇	semidirect
245. #441	C₄×C₄₇	semidirect
246. #440	C₄×C₄₇	semidirect
247. #440	C₄×C₄₇	semidirect
271. C₄₇	#22687	direct (N × H)
345. Q₁₆	C₄⋊C₄×C₄₇	semidirect
346. SD₁₆	C₄⋊C₄×C₄₇	semidirect
347. D₈	C₄⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#444	2
C₂×C₄₇×#443	2
C₄₇×#2943	2
C₄₇×#2906	2
C₄₇×#1946	2
C₄₇×#1945	2
C₄₇×#1866	2
C₄₇×#1849	2
C₄₇×#1806	2
C₄₇×#1771	2
#22687	47

Subgroups — C47×#22687 #26062385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#22687 #26062385