Subgroups — C₄₇×#35088 #26074786

Order 12032.

5386 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#534	C₂	1	2	yes	maximal, complemented
3	C₂²×#123×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2849	C₂	1	4	yes	maximal, complemented
5	C₄₇×#2614	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2613	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2430	C₂	1	8	yes	maximal, complemented
8	C₄₇×#2406	C₂	1	4	yes	maximal, complemented
9	C₄₇×#2404	C₂	1	4	yes	maximal, complemented
10	C₄₇×#2308	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#381	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₇	—	2	16	no	—
13	C₂²×#41×C₄₇	—	2	8	no	—
14	C₂²×#41×C₄₇	C₂²	1	4	yes	—
15	C₂²×#41×C₄₇	C₂²	1	4	yes	complemented
16	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
19	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	complemented
22	C₄₇×#534	—	2	16	no	—
23	C₂×#123×C₄₇	—	2	8	no	—
24	C₂×#123×C₄₇	C₂²	1	2	yes	—
25	C₂×#123×C₄₇	C₂²	1	4	yes	—
26	C₂×#123×C₄₇	C₂²	1	2	yes	—
27	C₂×#123×C₄₇	C₂²	1	4	yes	complemented
28	C₂×#123×C₄₇	C₂²	1	4	yes	complemented
29	C₂×#121×C₄₇	C₂²	1	8	yes	complemented
30	C₂×#120×C₄₇	C₂²	1	4	yes	—
31	C₂×#120×C₄₇	C₂²	1	4	yes	complemented
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
36	C₄₇×#395	C₂²	1	8	yes	complemented
37	C₄₇×#394	C₂²	1	8	yes	complemented
38	C₄₇×#393	C₂²	1	8	yes	complemented
39	C₄₇×#392	C₂²	1	8	yes	complemented
40	C₄₇×#386	C₂²	1	8	yes	complemented
41	C₄₇×#386	C₂²	1	8	yes	complemented
42	C₄₇×#386	C₂²	1	16	yes	complemented
43	C₄₇×#385	C₂²	1	16	yes	complemented
44	C₄₇×#381	C₂²	1	2	yes	complemented
45	C₄₇×#381	C₂²	1	2	yes	complemented
46	C₄₇×#381	C₂²	1	4	yes	complemented
47	C₄₇×#381	C₂²	1	4	yes	complemented
48	C₄₇×#379	C₂²	1	4	yes	complemented
49	C₂×#95×C₄₇	C₂²	1	4	yes	complemented
50	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
51	C₂⁵×C₄₇	C₂³	1	2	yes	—
52	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×#41×C₄₇	—	2	128	no	—
54	C₂×#41×C₄₇	—	2	32	no	—
55	C₂×#41×C₄₇	—	2	32	no	—
56	C₂×#41×C₄₇	—	2	16	no	—
57	C₂×#41×C₄₇	—	2	16	no	—
58	C₂²×Q₈×C₄₇	—	2	8	no	—
59	C₂²×Q₈×C₄₇	—	2	4	no	—
60	C₂²×Q₈×C₄₇	C₂³	1	4	yes	—
61	C₂²×D₄×C₄₇	—	2	8	no	—
62	C₂²×D₄×C₄₇	—	2	8	no	—
63	C₂²×D₄×C₄₇	—	2	8	no	—
64	C₂²×D₄×C₄₇	—	2	4	no	—
65	C₂²×D₄×C₄₇	—	2	8	no	—
66	C₂²×D₄×C₄₇	—	2	4	no	—
67	C₂²×D₄×C₄₇	D₄	1	16	yes	complemented
68	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
69	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
70	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
71	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
72	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
73	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
74	C₂³×C₄×C₄₇	—	2	8	no	—
75	C₂³×C₄×C₄₇	—	2	8	no	—
76	C₂³×C₄×C₄₇	—	2	8	no	—
77	C₂³×C₄×C₄₇	—	2	8	no	—
78	C₂³×C₄×C₄₇	D₄	1	8	yes	complemented
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
81	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
86	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
88	#123×C₄₇	—	2	16	no	—
89	#123×C₄₇	—	2	8	no	—
90	#123×C₄₇	—	2	8	no	—
91	#123×C₄₇	—	2	16	no	—
92	#123×C₄₇	—	2	16	no	—
93	#121×C₄₇	—	2	32	no	—
94	#120×C₄₇	—	2	16	no	—
95	#120×C₄₇	—	2	16	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
97	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
102	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
103	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
112	#95×C₄₇	C₂³	1	8	yes	—
113	#95×C₄₇	C₂³	1	8	yes	—
114	#95×C₄₇	C₂³	1	16	yes	—
115	C₂⁴×C₄₇	—	2	4	no	—
116	C₂⁴×C₄₇	—	2	4	no	—
117	C₂⁴×C₄₇	—	2	2	no	—
118	C₂⁴×C₄₇	—	2	4	no	—
119	C₂⁴×C₄₇	—	4	4	no	—
120	C₂⁴×C₄₇	—	4	8	no	—
121	C₂⁴×C₄₇	—	4	4	no	—
122	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
123	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
124	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
125	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
126	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
127	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
130	#41×C₄₇	—	2	128	no	—
131	#41×C₄₇	—	2	128	no	—
132	C₂×Q₈×C₄₇	—	2	32	no	—
133	C₂×Q₈×C₄₇	—	2	16	no	—
134	C₂×Q₈×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	32	no	—
136	C₂×D₄×C₄₇	—	2	64	no	—
137	C₂×D₄×C₄₇	—	2	16	no	—
138	C₂×D₄×C₄₇	—	2	8	no	—
139	C₂×D₄×C₄₇	—	2	8	no	—
140	C₂×D₄×C₄₇	—	2	8	no	—
141	C₂×D₄×C₄₇	—	2	8	no	—
142	C₂×D₄×C₄₇	—	2	8	no	—
143	C₂×D₄×C₄₇	—	2	8	no	—
144	C₂×D₄×C₄₇	—	2	4	no	—
145	C₂×D₄×C₄₇	—	2	4	no	—
146	C₂×D₄×C₄₇	—	2	16	no	—
147	C₂×D₄×C₄₇	—	2	8	no	—
148	C₂×D₄×C₄₇	—	4	16	no	—
149	C₂×D₄×C₄₇	—	4	16	no	—
150	C₂×D₄×C₄₇	C₂×D₄	1	16	yes	—
151	C₂×D₄×C₄₇	C₂×D₄	1	16	yes	—
152	C₂²×C₄×C₄₇	—	2	64	no	—
153	C₂²×C₄×C₄₇	—	2	32	no	—
154	C₂²×C₄×C₄₇	—	2	4	no	—
155	C₂²×C₄×C₄₇	—	2	4	no	—
156	C₂²×C₄×C₄₇	—	2	4	no	—
157	C₂²×C₄×C₄₇	—	2	4	no	—
158	C₂²×C₄×C₄₇	—	2	16	no	—
159	C₂²×C₄×C₄₇	—	2	8	no	—
160	C₂²×C₄×C₄₇	—	2	8	no	—
161	C₂²×C₄×C₄₇	—	2	16	no	—
162	C₂²×C₄×C₄₇	—	2	16	no	—
163	C₂²×C₄×C₄₇	—	2	4	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	4	no	—
166	C₂²×C₄×C₄₇	—	2	8	no	—
167	C₂²×C₄×C₄₇	—	4	4	no	—
168	C₂²×C₄×C₄₇	—	4	8	no	—
169	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
170	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
172	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
174	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
176	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
180	C₄⋊C₄×C₄₇	—	2	8	no	—
181	C₄⋊C₄×C₄₇	—	2	8	no	—
182	C₄⋊C₄×C₄₇	—	2	16	no	—
183	C₂²⋊C₄×C₄₇	—	2	8	no	—
184	C₂²⋊C₄×C₄₇	—	2	8	no	—
185	C₂²⋊C₄×C₄₇	—	2	4	no	—
186	C₂²⋊C₄×C₄₇	—	2	4	no	—
187	C₂²⋊C₄×C₄₇	—	2	16	no	—
188	C₂²⋊C₄×C₄₇	—	2	8	no	—
189	C₂²⋊C₄×C₄₇	—	2	8	no	—
190	C₂²⋊C₄×C₄₇	—	2	16	no	—
191	C₂²⋊C₄×C₄₇	—	4	16	no	—
192	C₂³×C₄₇	—	2	4	no	—
193	C₂³×C₄₇	—	2	4	no	—
194	C₂³×C₄₇	—	2	4	no	—
195	C₂³×C₄₇	—	2	16	no	—
196	C₂³×C₄₇	—	2	4	no	—
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	16	no	—
199	C₂³×C₄₇	—	2	2	no	—
200	C₂³×C₄₇	—	2	4	no	—
201	C₂³×C₄₇	—	2	8	no	—
202	C₂³×C₄₇	—	4	8	no	—
203	C₂³×C₄₇	—	4	16	no	—
204	C₂³×C₄₇	—	4	16	no	—
205	C₂³×C₄₇	—	4	16	no	—
206	C₂³×C₄₇	—	4	16	no	—
207	C₂³×C₄₇	—	4	8	no	—
208	C₂³×C₄₇	—	4	4	no	—
209	C₂³×C₄₇	—	8	8	no	—
210	C₂³×C₄₇	#120	1	16	yes	—
211	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
212	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
213	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
214	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
215	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
216	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
217	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
218	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
219	Q₈×C₄₇	—	2	32	no	—
220	D₄×C₄₇	—	2	32	no	—
221	D₄×C₄₇	—	2	32	no	—
222	D₄×C₄₇	—	2	32	no	—
223	D₄×C₄₇	—	4	8	no	—
224	D₄×C₄₇	—	4	8	no	—
225	D₄×C₄₇	—	8	16	no	—
226	C₂×C₄×C₄₇	—	2	64	no	—
227	C₂×C₄×C₄₇	—	2	8	no	—
228	C₂×C₄×C₄₇	—	2	16	no	—
229	C₂×C₄×C₄₇	—	2	8	no	—
230	C₂×C₄×C₄₇	—	2	16	no	—
231	C₂×C₄×C₄₇	—	2	16	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	4	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	4	no	—
237	C₂×C₄×C₄₇	—	2	8	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	2	no	—
240	C₂×C₄×C₄₇	—	2	8	no	—
241	C₂×C₄×C₄₇	—	2	16	no	—
242	C₂×C₄×C₄₇	—	4	8	no	—
243	C₂×C₄×C₄₇	—	4	4	no	—
244	C₂×C₄×C₄₇	—	8	8	no	—
245	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
247	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
248	#35088	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂²×C₄₇	—	2	4	no	—
250	C₂²×C₄₇	—	2	4	no	—
251	C₂²×C₄₇	—	2	4	no	—
252	C₂²×C₄₇	—	2	8	no	—
253	C₂²×C₄₇	—	2	8	no	—
254	C₂²×C₄₇	—	2	8	no	—
255	C₂²×C₄₇	—	2	8	no	—
256	C₂²×C₄₇	—	2	16	no	—
257	C₂²×C₄₇	—	4	16	no	—
258	C₂²×C₄₇	—	4	32	no	—
259	C₂²×C₄₇	—	4	8	no	—
260	C₂²×C₄₇	—	4	8	no	—
261	C₂²×C₄₇	—	4	2	no	—
262	C₂²×C₄₇	—	4	4	no	—
263	C₂²×C₄₇	—	4	8	no	—
264	C₂²×C₄₇	—	8	8	no	—
265	C₂²×C₄₇	C₂×#120	1	4	yes	—
266	C₂²×C₄₇	C₂×#120	1	4	yes	—
267	C₂²×C₄₇	C₂×#120	1	4	yes	—
268	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
269	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
270	C₂²×C₄₇	#585	1	4	yes	—
271	C₄×C₄₇	—	2	4	no	—
272	C₄×C₄₇	—	2	8	no	—
273	C₄×C₄₇	—	2	4	no	—
274	C₄×C₄₇	—	4	2	no	—
275	C₄×C₄₇	—	4	4	no	—
276	C₄×C₄₇	—	4	8	no	—
277	C₂³×#41	C₂×C₄₇	1	1	yes	characteristic, complemented
278	C₂×#534	C₂×C₄₇	1	2	yes	complemented
279	C₂²×#123	C₂×C₄₇	1	1	yes	characteristic, complemented
280	#2849	C₂×C₄₇	1	4	yes	complemented
281	#2614	C₂×C₄₇	1	2	yes	complemented
282	#2613	C₂×C₄₇	1	2	yes	complemented
283	#2430	C₂×C₄₇	1	8	yes	complemented
284	#2406	C₂×C₄₇	1	4	yes	complemented
285	#2404	C₂×C₄₇	1	4	yes	complemented
286	#2308	C₂×C₄₇	1	2	yes	complemented
287	C₂×#381	C₂×C₄₇	1	1	yes	characteristic, complemented
288	C₂×C₄₇	—	2	4	no	—
289	C₂×C₄₇	—	2	4	no	—
290	C₂×C₄₇	—	2	4	no	—
291	C₂×C₄₇	—	4	8	no	—
292	C₂×C₄₇	—	8	2	no	—
293	C₂×C₄₇	C₂²×#120	1	1	yes	characteristic
294	C₂×C₄₇	#3449	1	2	yes	—
295	C₂×C₄₇	#3485	1	4	yes	—
296	C₂²×#41	—	2	16	no	—
297	C₂²×#41	—	2	8	no	—
298	C₂²×#41	C₂²×C₄₇	1	4	yes	—
299	C₂²×#41	C₂²×C₄₇	1	4	yes	complemented
300	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
301	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
302	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
303	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
304	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
305	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	complemented
306	#534	—	2	16	no	—
307	C₂×#123	—	2	8	no	—
308	C₂×#123	C₂²×C₄₇	1	2	yes	—
309	C₂×#123	C₂²×C₄₇	1	4	yes	—
310	C₂×#123	C₂²×C₄₇	1	2	yes	—
311	C₂×#123	C₂²×C₄₇	1	4	yes	complemented
312	C₂×#123	C₂²×C₄₇	1	4	yes	complemented
313	C₂×#121	C₂²×C₄₇	1	8	yes	complemented
314	C₂×#120	C₂²×C₄₇	1	4	yes	—
315	C₂×#120	C₂²×C₄₇	1	4	yes	complemented
316	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
317	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
320	#395	C₂²×C₄₇	1	8	yes	complemented
321	#394	C₂²×C₄₇	1	8	yes	complemented
322	#393	C₂²×C₄₇	1	8	yes	complemented
323	#392	C₂²×C₄₇	1	8	yes	complemented
324	#386	C₂²×C₄₇	1	8	yes	complemented
325	#386	C₂²×C₄₇	1	8	yes	complemented
326	#386	C₂²×C₄₇	1	16	yes	complemented
327	#385	C₂²×C₄₇	1	16	yes	complemented
328	#381	C₂²×C₄₇	1	4	yes	complemented
329	#381	C₂²×C₄₇	1	2	yes	complemented
330	#381	C₂²×C₄₇	1	2	yes	complemented
331	#381	C₂²×C₄₇	1	4	yes	complemented
332	#379	C₂²×C₄₇	1	4	yes	complemented
333	C₂×#95	C₂²×C₄₇	1	4	yes	complemented
334	C₄₇	#35088	1	1	yes	characteristic, direct product factor, Sylow
335	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
336	C₂⁵	C₂³×C₄₇	1	2	yes	—
337	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
338	C₂×#41	—	2	128	no	—
339	C₂×#41	—	2	32	no	—
340	C₂×#41	—	2	32	no	—
341	C₂×#41	—	2	16	no	—
342	C₂×#41	—	2	16	no	—
343	C₂²×Q₈	—	2	8	no	—
344	C₂²×Q₈	—	2	4	no	—
345	C₂²×Q₈	C₂³×C₄₇	1	4	yes	—
346	C₂²×D₄	—	2	8	no	—
347	C₂²×D₄	—	2	8	no	—
348	C₂²×D₄	—	2	8	no	—
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	8	no	—
351	C₂²×D₄	—	2	4	no	—
352	C₂²×D₄	D₄×C₄₇	1	16	yes	complemented
353	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
354	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
355	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
356	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
357	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
358	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
359	C₂³×C₄	—	2	8	no	—
360	C₂³×C₄	—	2	8	no	—
361	C₂³×C₄	—	2	8	no	—
362	C₂³×C₄	—	2	8	no	—
363	C₂³×C₄	D₄×C₄₇	1	8	yes	complemented
364	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
366	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
367	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
370	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
371	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
372	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
373	#123	—	2	16	no	—
374	#123	—	2	8	no	—
375	#123	—	2	8	no	—
376	#123	—	2	16	no	—
377	#123	—	2	16	no	—
378	#121	—	2	32	no	—
379	#120	—	2	16	no	—
380	#120	—	2	16	no	—
381	C₂×C₄⋊C₄	—	2	8	no	—
382	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
383	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
385	C₂×C₂²⋊C₄	—	2	4	no	—
386	C₂×C₂²⋊C₄	—	2	8	no	—
387	C₂×C₂²⋊C₄	—	2	8	no	—
388	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
397	#95	C₂³×C₄₇	1	8	yes	—
398	#95	C₂³×C₄₇	1	8	yes	—
399	#95	C₂³×C₄₇	1	16	yes	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	4	4	no	—
405	C₂⁴	—	4	8	no	—
406	C₂⁴	—	4	4	no	—
407	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
408	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
409	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
410	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
411	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
412	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
413	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
414	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
415	#41	—	2	128	no	—
416	#41	—	2	128	no	—
417	C₂×Q₈	—	2	32	no	—
418	C₂×Q₈	—	2	16	no	—
419	C₂×Q₈	—	2	8	no	—
420	C₂×D₄	—	2	32	no	—
421	C₂×D₄	—	2	64	no	—
422	C₂×D₄	—	2	16	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	8	no	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	8	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	16	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	4	16	no	—
434	C₂×D₄	—	4	16	no	—
435	C₂×D₄	C₂×D₄×C₄₇	1	16	yes	—
436	C₂×D₄	C₂×D₄×C₄₇	1	16	yes	—
437	C₂²×C₄	—	2	64	no	—
438	C₂²×C₄	—	2	32	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	16	no	—
444	C₂²×C₄	—	2	8	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	2	16	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	8	no	—
454	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
455	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
456	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
457	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
458	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
459	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
460	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	16	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	16	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	16	no	—
476	C₂²⋊C₄	—	4	16	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	16	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	16	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	4	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	16	no	—
489	C₂³	—	4	16	no	—
490	C₂³	—	4	16	no	—
491	C₂³	—	4	16	no	—
492	C₂³	—	4	8	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	8	8	no	—
495	C₂³	#120×C₄₇	1	16	yes	—
496	C₂³	C₂²×D₄×C₄₇	1	8	yes	—
497	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
498	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
499	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
500	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
501	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
502	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
503	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
504	Q₈	—	2	32	no	—
505	D₄	—	2	32	no	—
506	D₄	—	2	32	no	—
507	D₄	—	2	32	no	—
508	D₄	—	4	8	no	—
509	D₄	—	4	8	no	—
510	D₄	—	8	16	no	—
511	C₂×C₄	—	2	64	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	16	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	16	no	—
516	C₂×C₄	—	2	16	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	16	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	8	8	no	—
530	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
531	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
532	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	2	8	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	2	16	no	—
541	C₂²	—	4	16	no	—
542	C₂²	—	4	32	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	8	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	8	no	—
548	C₂²	—	8	8	no	—
549	C₂²	C₂×#120×C₄₇	1	4	yes	—
550	C₂²	C₂×#120×C₄₇	1	4	yes	—
551	C₂²	C₂×#120×C₄₇	1	4	yes	—
552	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
553	C₂²	C₂³×D₄×C₄₇	1	2	yes	—
554	C₂²	C₄₇×#585	1	4	yes	—
555	C₄	—	2	4	no	—
556	C₄	—	2	8	no	—
557	C₄	—	2	4	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	8	no	—
561	C₂	—	2	4	no	—
562	C₂	—	2	4	no	—
563	C₂	—	2	4	no	—
564	C₂	—	4	8	no	—
565	C₂	—	8	2	no	—
566	C₂	C₂²×#120×C₄₇	1	1	yes	characteristic
567	C₂	C₄₇×#3449	1	2	yes	—
568	C₂	C₄₇×#3485	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₄₇	C₂	semidirect
2. C₂×C₄₇×#534	C₂	semidirect
3. C₂²×#123×C₄₇	C₂	semidirect
4. C₄₇×#2849	C₂	semidirect
5. C₄₇×#2614	C₂	semidirect
6. C₄₇×#2613	C₂	semidirect
7. C₄₇×#2430	C₂	semidirect
8. C₄₇×#2406	C₂	semidirect
9. C₄₇×#2404	C₂	semidirect
10. C₄₇×#2308	C₂	semidirect
11. C₂×C₄₇×#381	C₂	semidirect
15. C₂²×#41×C₄₇	C₂²	semidirect
16. C₂³×Q₈×C₄₇	C₂²	semidirect
19. C₂³×D₄×C₄₇	C₂²	semidirect
21. C₂⁴×C₄×C₄₇	C₂²	semidirect
27. C₂×#123×C₄₇	C₂²	semidirect
28. C₂×#123×C₄₇	C₂²	semidirect
29. C₂×#121×C₄₇	C₂²	semidirect
31. C₂×#120×C₄₇	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
35. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
36. C₄₇×#395	C₂²	semidirect
37. C₄₇×#394	C₂²	semidirect
38. C₄₇×#393	C₂²	semidirect
39. C₄₇×#392	C₂²	semidirect
40. C₄₇×#386	C₂²	semidirect
41. C₄₇×#386	C₂²	semidirect
42. C₄₇×#386	C₂²	semidirect
43. C₄₇×#385	C₂²	semidirect
44. C₄₇×#381	C₂²	semidirect
45. C₄₇×#381	C₂²	semidirect
46. C₄₇×#381	C₂²	semidirect
47. C₄₇×#381	C₂²	semidirect
48. C₄₇×#379	C₂²	semidirect
49. C₂×#95×C₄₇	C₂²	semidirect
67. C₂²×D₄×C₄₇	D₄	semidirect
78. C₂³×C₄×C₄₇	D₄	semidirect
248. #35088	C₄₇	direct (N × H)
277. C₂³×#41	C₂×C₄₇	semidirect
278. C₂×#534	C₂×C₄₇	semidirect
279. C₂²×#123	C₂×C₄₇	semidirect
280. #2849	C₂×C₄₇	semidirect
281. #2614	C₂×C₄₇	semidirect
282. #2613	C₂×C₄₇	semidirect
283. #2430	C₂×C₄₇	semidirect
284. #2406	C₂×C₄₇	semidirect
285. #2404	C₂×C₄₇	semidirect
286. #2308	C₂×C₄₇	semidirect
287. C₂×#381	C₂×C₄₇	semidirect
299. C₂²×#41	C₂²×C₄₇	semidirect
300. C₂³×Q₈	C₂²×C₄₇	semidirect
303. C₂³×D₄	C₂²×C₄₇	semidirect
305. C₂⁴×C₄	C₂²×C₄₇	semidirect
311. C₂×#123	C₂²×C₄₇	semidirect
312. C₂×#123	C₂²×C₄₇	semidirect
313. C₂×#121	C₂²×C₄₇	semidirect
315. C₂×#120	C₂²×C₄₇	semidirect
316. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
319. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
320. #395	C₂²×C₄₇	semidirect
321. #394	C₂²×C₄₇	semidirect
322. #393	C₂²×C₄₇	semidirect
323. #392	C₂²×C₄₇	semidirect
324. #386	C₂²×C₄₇	semidirect
325. #386	C₂²×C₄₇	semidirect
326. #386	C₂²×C₄₇	semidirect
327. #385	C₂²×C₄₇	semidirect
328. #381	C₂²×C₄₇	semidirect
329. #381	C₂²×C₄₇	semidirect
330. #381	C₂²×C₄₇	semidirect
331. #381	C₂²×C₄₇	semidirect
332. #379	C₂²×C₄₇	semidirect
333. C₂×#95	C₂²×C₄₇	semidirect
334. C₄₇	#35088	direct (N × H)
352. C₂²×D₄	D₄×C₄₇	semidirect
363. C₂³×C₄	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₄₇	2
C₂×C₄₇×#534	2
C₂²×#123×C₄₇	2
C₄₇×#2849	2
C₄₇×#2614	2
C₄₇×#2613	2
C₄₇×#2430	2
C₄₇×#2406	2
C₄₇×#2404	2
C₄₇×#2308	2
C₂×C₄₇×#381	2
#35088	47

Subgroups — C47×#35088 #26074786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#35088 #26074786