Subgroups — C₄₇×#20738 #26060436

Order 12032.

1782 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1824	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1802	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1786	C₂	1	2	yes	maximal
7	C₄₇×#1762	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	—	2	1	no	—
10	C₂×C₄×D₄×C₄₇	—	2	1	no	—
11	C₂×C₄×D₄×C₄₇	—	2	1	no	—
12	C₂×C₄×D₄×C₄₇	—	2	4	no	—
13	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
14	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
16	C₂×#117×C₄₇	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#432	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
22	C₂×#102×C₄₇	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×#97×C₄₇	C₂²	1	2	yes	complemented
25	C₄₇×#384	C₂²	1	2	yes	complemented
26	C₄₇×#382	—	2	1	no	—
27	C₄₇×#380	—	2	1	no	—
28	C₄₇×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
31	C₄₇×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	—	2	8	no	—
34	C₂²×D₄×C₄₇	—	2	1	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	—	2	8	no	—
40	C₂³×C₄×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	—	2	2	no	—
42	C₂³×C₄×C₄₇	—	4	8	no	—
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
47	C₄×D₄×C₄₇	—	2	8	no	—
48	C₄×D₄×C₄₇	—	2	8	no	—
49	C₄×D₄×C₄₇	—	2	4	no	—
50	C₄×D₄×C₄₇	—	2	4	no	—
51	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
53	#117×C₄₇	—	4	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	D₄	1	4	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₄₇	—	2	4	no	—
73	#102×C₄₇	—	2	16	no	—
74	C₂²⋊C₈×C₄₇	—	2	4	no	—
75	#97×C₄₇	—	2	4	no	—
76	#95×C₄₇	—	2	2	no	—
77	#95×C₄₇	—	2	2	no	—
78	C₂⁴×C₄₇	—	2	8	no	—
79	C₂⁴×C₄₇	—	2	4	no	—
80	C₂⁴×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	—	4	4	no	—
82	C₂⁴×C₄₇	—	4	2	no	—
83	C₂⁴×C₄₇	—	4	2	no	—
84	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂×D₄×C₄₇	—	2	8	no	—
86	C₂×D₄×C₄₇	—	2	16	no	—
87	C₂×D₄×C₄₇	—	2	16	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂×D₄×C₄₇	#41	1	8	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	8	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	4	8	no	—
103	C₂²×C₄×C₄₇	—	4	32	no	—
104	C₂²×C₄×C₄₇	—	4	4	no	—
105	C₂²×C₄×C₄₇	—	4	8	no	—
106	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₄₇	—	2	4	no	—
117	C₂×C₈×C₄₇	—	2	8	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	8	no	—
121	C₄⋊C₄×C₄₇	—	4	4	no	—
122	C₄⋊C₄×C₄₇	—	4	4	no	—
123	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂²⋊C₄×C₄₇	—	2	8	no	—
125	C₂²⋊C₄×C₄₇	—	2	8	no	—
126	C₂²⋊C₄×C₄₇	—	4	4	no	—
127	C₄²×C₄₇	—	4	4	no	—
128	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
129	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
130	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₇	C₂×D₄	1	2	yes	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	16	no	—
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	4	8	no	—
140	C₂³×C₄₇	—	4	16	no	—
141	C₂³×C₄₇	—	4	16	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	8	no	—
146	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
148	C₂³×C₄₇	#137	1	2	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	D₄×C₄₇	—	2	16	no	—
151	D₄×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	#117	1	8	yes	complemented
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	8	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	8	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	16	no	—
166	C₂×C₄×C₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	—	4	16	no	—
169	C₂×C₄×C₄₇	—	4	4	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
181	C₈×C₄₇	—	4	4	no	—
182	#20738	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	8	no	—
188	C₂²×C₄₇	—	4	32	no	—
189	C₂²×C₄₇	—	4	8	no	—
190	C₂²×C₄₇	—	4	8	no	—
191	C₂²×C₄₇	—	4	4	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	#417	1	4	yes	—
194	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	#525	1	2	yes	—
196	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
198	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
199	C₄×C₄₇	—	2	2	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	4	4	no	—
204	C₄×C₄₇	—	8	4	no	—
205	C₄×C₄₇	#418	1	4	yes	—
206	C₄×C₄₇	C₂×#117	1	2	yes	—
207	C₄×C₄₇	#525	1	2	yes	—
208	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
209	C₂×#432	C₂×C₄₇	1	1	yes	characteristic, complemented
210	#2285	C₂×C₄₇	1	1	yes	characteristic, complemented
211	#1824	C₂×C₄₇	1	2	yes	complemented
212	#1802	C₂×C₄₇	1	4	yes	complemented
213	#1786	C₂×C₄₇	1	2	yes	—
214	#1762	C₂×C₄₇	1	4	yes	complemented
215	C₂×C₄₇	—	2	4	no	—
216	C₂×C₄₇	—	4	8	no	—
217	C₂×C₄₇	#2280	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
220	C₂×C₄₇	#3109	1	2	yes	—
221	C₂×C₄₇	#3110	1	2	yes	—
222	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
223	C₂⁴×C₄	—	2	1	no	—
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	—	2	1	no	—
226	C₂×C₄×D₄	—	2	4	no	—
227	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
228	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
229	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
230	C₂×#117	—	2	1	no	—
231	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	—	2	1	no	—
233	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
234	#432	—	2	4	no	—
235	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
236	C₂×#102	C₂²×C₄₇	1	8	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
238	C₂×#97	C₂²×C₄₇	1	2	yes	complemented
239	#384	C₂²×C₄₇	1	2	yes	complemented
240	#382	—	2	1	no	—
241	#380	—	2	1	no	—
242	#380	C₂²×C₄₇	1	2	yes	—
243	C₄×C₄⋊C₄	—	2	1	no	—
244	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
245	#340	C₂²×C₄₇	1	8	yes	complemented
246	C₄₇	#20738	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁵	—	2	1	no	—
248	C₂²×D₄	—	2	8	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
252	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
253	C₂³×C₄	—	2	1	no	—
254	C₂³×C₄	—	2	8	no	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	4	8	no	—
258	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
259	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
262	C₄×D₄	—	2	8	no	—
263	C₄×D₄	—	2	8	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
267	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
268	#117	—	4	4	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
275	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	8	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
282	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₄₇	1	4	yes	—
285	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
287	C₄⋊C₈	—	2	4	no	—
288	#102	—	2	16	no	—
289	C₂²⋊C₈	—	2	4	no	—
290	#97	—	2	4	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₂⁴	—	2	8	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	4	4	no	—
297	C₂⁴	—	4	2	no	—
298	C₂⁴	—	4	2	no	—
299	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	16	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
307	C₂×D₄	#41×C₄₇	1	8	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	8	no	—
318	C₂²×C₄	—	4	32	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
322	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
323	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	8	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₄²	—	4	4	no	—
343	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
344	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
345	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
346	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
347	C₄²	C₂×D₄×C₄₇	1	2	yes	—
348	C₄²	C₂×D₄×C₄₇	1	2	yes	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	16	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	4	16	no	—
356	C₂³	—	4	16	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	8	no	—
361	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
362	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
363	C₂³	#137×C₄₇	1	2	yes	—
364	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
365	D₄	—	2	16	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	8	no	—
368	D₄	#117×C₄₇	1	8	yes	complemented
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	16	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
392	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
393	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
396	C₈	—	4	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	8	no	—
402	C₂²	—	4	32	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	C₄₇×#417	1	4	yes	—
408	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
409	C₂²	C₄₇×#525	1	2	yes	—
410	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
411	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
412	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	8	4	no	—
419	C₄	C₄₇×#418	1	4	yes	—
420	C₄	C₂×#117×C₄₇	1	2	yes	—
421	C₄	C₄₇×#525	1	2	yes	—
422	C₂	—	2	4	no	—
423	C₂	—	4	8	no	—
424	C₂	C₄₇×#2280	1	1	yes	characteristic
425	C₂	C₂×C₄₇×#418	1	1	yes	characteristic
426	C₂	C₂×C₄₇×#417	1	1	yes	characteristic
427	C₂	C₄₇×#3109	1	2	yes	—
428	C₂	C₄₇×#3110	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#432	C₂	semidirect
3. C₄₇×#2285	C₂	semidirect
4. C₄₇×#1824	C₂	semidirect
5. C₄₇×#1802	C₂	semidirect
7. C₄₇×#1762	C₂	semidirect
13. C₂×C₄×D₄×C₄₇	C₄	semidirect
21. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
24. C₂×#97×C₄₇	C₂²	semidirect
25. C₄₇×#384	C₂²	semidirect
30. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
31. C₄₇×#340	C₂²	semidirect
153. D₄×C₄₇	#117	semidirect
182. #20738	C₄₇	direct (N × H)
209. C₂×#432	C₂×C₄₇	semidirect
210. #2285	C₂×C₄₇	semidirect
211. #1824	C₂×C₄₇	semidirect
212. #1802	C₂×C₄₇	semidirect
214. #1762	C₂×C₄₇	semidirect
227. C₂×C₄×D₄	C₄×C₄₇	semidirect
235. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
238. C₂×#97	C₂²×C₄₇	semidirect
239. #384	C₂²×C₄₇	semidirect
244. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
245. #340	C₂²×C₄₇	semidirect
246. C₄₇	#20738	direct (N × H)
368. D₄	#117×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₇	2
C₂×C₄₇×#432	2
C₄₇×#2285	2
C₄₇×#1824	2
C₄₇×#1802	2
C₄₇×#1786	2
C₄₇×#1762	2
#20738	47

Subgroups — C47×#20738 #26060436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20738 #26060436