Subgroups — C₄₇×#35084 #26074782

Order 12032.

2898 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2855	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2848	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2638	C₂	1	4	yes	maximal, complemented
6	C₄₇×#2583	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2561	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2486	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2483	C₂	1	2	yes	maximal, complemented
10	C₄₇×#2415	C₂	1	4	yes	maximal, complemented
11	C₄₇×#2409	C₂	1	2	yes	maximal, complemented
12	C₄₇×#2405	C₂	1	2	yes	maximal
13	C₄₇×#2322	C₂	1	4	yes	maximal, complemented
14	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#123×C₄₇	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₄₇	—	2	8	no	—
21	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
26	C₂×C₄×D₄×C₄₇	—	2	8	no	—
27	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
31	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
34	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#398	C₂²	1	4	yes	complemented
40	C₄₇×#397	C₂²	1	4	yes	complemented
41	C₄₇×#397	C₂²	1	8	yes	complemented
42	C₄₇×#395	C₂²	1	4	yes	complemented
43	C₄₇×#394	C₂²	1	8	yes	—
44	C₄₇×#393	C₂²	1	4	yes	complemented
45	C₄₇×#391	C₂²	1	4	yes	complemented
46	C₄₇×#389	C₂²	1	8	yes	complemented
47	C₄₇×#389	C₂²	1	4	yes	complemented
48	C₄₇×#388	C₂²	1	8	yes	complemented
49	C₄₇×#387	C₂²	1	8	yes	complemented
50	C₄₇×#386	C₂²	1	4	yes	—
51	C₄₇×#385	C₂²	1	4	yes	—
52	C₄₇×#385	C₂²	1	4	yes	—
53	C₄₇×#385	C₂²	1	8	yes	complemented
54	C₄₇×#385	C₂²	1	4	yes	complemented
55	C₄₇×#381	C₂²	1	4	yes	—
56	C₄₇×#381	C₂²	1	2	yes	complemented
57	C₄₇×#381	C₂²	1	4	yes	complemented
58	C₄₇×#380	C₂²	1	2	yes	—
59	C₄₇×#380	C₂²	1	2	yes	complemented
60	C₄₇×#380	C₂²	1	4	yes	complemented
61	C₄₇×#379	C₂²	1	2	yes	—
62	C₄₇×#379	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
65	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
66	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₄₇	—	2	4	no	—
68	C₂²×Q₈×C₄₇	—	4	4	no	—
69	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
70	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
71	C₂²×D₄×C₄₇	—	2	4	no	—
72	C₂²×D₄×C₄₇	—	2	8	no	—
73	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
74	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₇	—	2	4	no	—
76	C₂³×C₄×C₄₇	—	4	4	no	—
77	C₂³×C₄×C₄₇	—	4	4	no	—
78	C₂³×C₄×C₄₇	D₄	1	8	yes	—
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
92	#123×C₄₇	—	2	16	no	—
93	C₂²⋊Q₈×C₄₇	—	2	8	no	—
94	C₂²⋊Q₈×C₄₇	—	2	8	no	—
95	C₂²⋊Q₈×C₄₇	—	2	8	no	—
96	C₂²⋊Q₈×C₄₇	—	2	8	no	—
97	C₂²⋊Q₈×C₄₇	—	4	8	no	—
98	C₄×D₄×C₄₇	—	2	8	no	—
99	C₄×D₄×C₄₇	—	2	8	no	—
100	C₄×D₄×C₄₇	—	2	8	no	—
101	C₄×D₄×C₄₇	—	2	8	no	—
102	#117×C₄₇	—	4	4	no	—
103	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
114	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
117	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
129	C₂×C₄²×C₄₇	—	2	4	no	—
130	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
131	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
132	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
133	#95×C₄₇	C₂³	1	4	yes	—
134	#95×C₄₇	C₂³	1	4	yes	—
135	#95×C₄₇	C₂³	1	8	yes	—
136	#95×C₄₇	C₂³	1	8	yes	—
137	#95×C₄₇	C₂³	1	8	yes	—
138	#95×C₄₇	C₂³	1	8	yes	—
139	C₂⁴×C₄₇	—	2	2	no	—
140	C₂⁴×C₄₇	—	2	4	no	—
141	C₂⁴×C₄₇	—	2	4	no	—
142	C₂⁴×C₄₇	—	2	4	no	—
143	C₂⁴×C₄₇	—	2	4	no	—
144	C₂⁴×C₄₇	—	4	2	no	—
145	C₂⁴×C₄₇	—	4	2	no	—
146	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
147	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
149	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
151	C₂×Q₈×C₄₇	—	2	4	no	—
152	C₂×Q₈×C₄₇	—	2	4	no	—
153	C₂×Q₈×C₄₇	—	2	8	no	—
154	C₂×Q₈×C₄₇	—	4	4	no	—
155	C₂×Q₈×C₄₇	—	4	16	no	—
156	C₂×D₄×C₄₇	—	2	32	no	—
157	C₂×D₄×C₄₇	—	2	4	no	—
158	C₂×D₄×C₄₇	—	2	4	no	—
159	C₂×D₄×C₄₇	—	2	4	no	—
160	C₂×D₄×C₄₇	—	2	4	no	—
161	C₂×D₄×C₄₇	—	2	4	no	—
162	C₂×D₄×C₄₇	#41	1	8	yes	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	4	no	—
165	C₂²×C₄×C₄₇	—	2	4	no	—
166	C₂²×C₄×C₄₇	—	2	4	no	—
167	C₂²×C₄×C₄₇	—	2	4	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	4	no	—
170	C₂²×C₄×C₄₇	—	2	2	no	—
171	C₂²×C₄×C₄₇	—	2	4	no	—
172	C₂²×C₄×C₄₇	—	2	8	no	—
173	C₂²×C₄×C₄₇	—	2	4	no	—
174	C₂²×C₄×C₄₇	—	2	4	no	—
175	C₂²×C₄×C₄₇	—	2	4	no	—
176	C₂²×C₄×C₄₇	—	2	8	no	—
177	C₂²×C₄×C₄₇	—	4	16	no	—
178	C₂²×C₄×C₄₇	—	4	2	no	—
179	C₂²×C₄×C₄₇	—	4	2	no	—
180	C₂²×C₄×C₄₇	—	4	2	no	—
181	C₂²×C₄×C₄₇	—	4	4	no	—
182	C₂²×C₄×C₄₇	—	4	2	no	—
183	C₂²×C₄×C₄₇	—	4	4	no	—
184	C₂²×C₄×C₄₇	—	4	16	no	—
185	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
188	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
193	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
201	C₄⋊C₄×C₄₇	—	2	4	no	—
202	C₄⋊C₄×C₄₇	—	2	4	no	—
203	C₄⋊C₄×C₄₇	—	2	4	no	—
204	C₄⋊C₄×C₄₇	—	2	4	no	—
205	C₄⋊C₄×C₄₇	—	2	8	no	—
206	C₄⋊C₄×C₄₇	—	2	8	no	—
207	C₄⋊C₄×C₄₇	—	2	16	no	—
208	C₄⋊C₄×C₄₇	—	2	8	no	—
209	C₄⋊C₄×C₄₇	—	4	8	no	—
210	C₂²⋊C₄×C₄₇	—	2	4	no	—
211	C₂²⋊C₄×C₄₇	—	2	4	no	—
212	C₂²⋊C₄×C₄₇	—	2	8	no	—
213	C₂²⋊C₄×C₄₇	—	2	8	no	—
214	C₂²⋊C₄×C₄₇	—	2	8	no	—
215	C₂²⋊C₄×C₄₇	—	2	16	no	—
216	C₂²⋊C₄×C₄₇	—	2	8	no	—
217	C₂²⋊C₄×C₄₇	—	2	4	no	—
218	C₂²⋊C₄×C₄₇	—	2	4	no	—
219	C₂²⋊C₄×C₄₇	—	4	4	no	—
220	C₂²⋊C₄×C₄₇	—	4	8	no	—
221	C₄²×C₄₇	—	2	4	no	—
222	C₄²×C₄₇	—	2	4	no	—
223	C₄²×C₄₇	—	4	4	no	—
224	C₂³×C₄₇	—	2	2	no	—
225	C₂³×C₄₇	—	2	2	no	—
226	C₂³×C₄₇	—	2	2	no	—
227	C₂³×C₄₇	—	2	2	no	—
228	C₂³×C₄₇	—	2	8	no	—
229	C₂³×C₄₇	—	2	8	no	—
230	C₂³×C₄₇	—	2	8	no	—
231	C₂³×C₄₇	—	2	2	no	—
232	C₂³×C₄₇	—	2	2	no	—
233	C₂³×C₄₇	—	2	2	no	—
234	C₂³×C₄₇	—	2	2	no	—
235	C₂³×C₄₇	—	2	4	no	—
236	C₂³×C₄₇	—	2	2	no	—
237	C₂³×C₄₇	—	2	4	no	—
238	C₂³×C₄₇	—	4	4	no	—
239	C₂³×C₄₇	—	4	16	no	—
240	C₂³×C₄₇	—	4	16	no	—
241	C₂³×C₄₇	—	4	4	no	—
242	C₂³×C₄₇	—	4	4	no	—
243	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
244	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
245	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
246	C₂³×C₄₇	C₂×#41	1	4	yes	—
247	C₂³×C₄₇	C₂×#41	1	4	yes	—
248	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
249	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
250	Q₈×C₄₇	—	4	8	no	—
251	Q₈×C₄₇	—	4	8	no	—
252	D₄×C₄₇	—	2	16	no	—
253	D₄×C₄₇	—	2	16	no	—
254	C₂×C₄×C₄₇	—	2	8	no	—
255	C₂×C₄×C₄₇	—	2	2	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	2	no	—
260	C₂×C₄×C₄₇	—	2	8	no	—
261	C₂×C₄×C₄₇	—	2	8	no	—
262	C₂×C₄×C₄₇	—	2	8	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	4	no	—
265	C₂×C₄×C₄₇	—	2	2	no	—
266	C₂×C₄×C₄₇	—	2	4	no	—
267	C₂×C₄×C₄₇	—	2	8	no	—
268	C₂×C₄×C₄₇	—	2	8	no	—
269	C₂×C₄×C₄₇	—	2	8	no	—
270	C₂×C₄×C₄₇	—	2	8	no	—
271	C₂×C₄×C₄₇	—	2	4	no	—
272	C₂×C₄×C₄₇	—	2	8	no	—
273	C₂×C₄×C₄₇	—	2	4	no	—
274	C₂×C₄×C₄₇	—	4	4	no	—
275	C₂×C₄×C₄₇	—	4	4	no	—
276	C₂×C₄×C₄₇	—	4	4	no	—
277	C₂×C₄×C₄₇	—	4	8	no	—
278	C₂×C₄×C₄₇	—	4	4	no	—
279	C₂×C₄×C₄₇	—	4	8	no	—
280	C₂×C₄×C₄₇	—	4	8	no	—
281	C₂×C₄×C₄₇	—	4	4	no	—
282	C₂×C₄×C₄₇	—	4	8	no	—
283	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
288	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
289	#35084	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	2	2	no	—
292	C₂²×C₄₇	—	2	2	no	—
293	C₂²×C₄₇	—	2	2	no	—
294	C₂²×C₄₇	—	2	8	no	—
295	C₂²×C₄₇	—	2	8	no	—
296	C₂²×C₄₇	—	2	2	no	—
297	C₂²×C₄₇	—	2	4	no	—
298	C₂²×C₄₇	—	2	2	no	—
299	C₂²×C₄₇	—	2	2	no	—
300	C₂²×C₄₇	—	2	8	no	—
301	C₂²×C₄₇	—	4	16	no	—
302	C₂²×C₄₇	—	4	16	no	—
303	C₂²×C₄₇	—	4	2	no	—
304	C₂²×C₄₇	—	4	2	no	—
305	C₂²×C₄₇	—	4	4	no	—
306	C₂²×C₄₇	—	4	4	no	—
307	C₂²×C₄₇	#525	1	4	yes	—
308	C₂²×C₄₇	#536	1	4	yes	—
309	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
310	C₂²×C₄₇	C₂²×#41	1	2	yes	—
311	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
312	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
313	C₄×C₄₇	—	2	4	no	—
314	C₄×C₄₇	—	2	2	no	—
315	C₄×C₄₇	—	2	2	no	—
316	C₄×C₄₇	—	2	2	no	—
317	C₄×C₄₇	—	4	4	no	—
318	C₄×C₄₇	—	4	2	no	—
319	C₄×C₄₇	—	4	4	no	—
320	C₄×C₄₇	—	4	2	no	—
321	C₄×C₄₇	—	4	8	no	—
322	C₄×C₄₇	#534	1	4	yes	—
323	C₂²×C₂²⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
324	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
325	#2855	C₂×C₄₇	1	2	yes	complemented
326	#2848	C₂×C₄₇	1	2	yes	complemented
327	#2638	C₂×C₄₇	1	4	yes	complemented
328	#2583	C₂×C₄₇	1	2	yes	complemented
329	#2561	C₂×C₄₇	1	2	yes	complemented
330	#2486	C₂×C₄₇	1	2	yes	complemented
331	#2483	C₂×C₄₇	1	2	yes	complemented
332	#2415	C₂×C₄₇	1	4	yes	complemented
333	#2409	C₂×C₄₇	1	2	yes	complemented
334	#2405	C₂×C₄₇	1	2	yes	—
335	#2322	C₂×C₄₇	1	4	yes	complemented
336	#2280	C₂×C₄₇	1	1	yes	characteristic, complemented
337	C₂×C₄₇	—	2	4	no	—
338	C₂×C₄₇	—	2	4	no	—
339	C₂×C₄₇	—	4	2	no	—
340	C₂×C₄₇	—	4	4	no	—
341	C₂×C₄₇	C₂×#525	1	1	yes	characteristic
342	C₂×C₄₇	C₂×#534	1	1	yes	characteristic
343	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
344	C₂×C₄₇	#3520	1	4	yes	—
345	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
346	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
347	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
348	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
349	C₂×#123	C₂²×C₄₇	1	4	yes	—
350	C₂×C₂²⋊Q₈	—	2	8	no	—
351	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
352	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
353	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	complemented
354	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	complemented
355	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	4	yes	complemented
356	C₂×C₄×D₄	—	2	8	no	—
357	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
358	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
359	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
360	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
361	C₂×#117	C₂²×C₄₇	1	2	yes	complemented
362	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
364	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic, complemented
365	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
368	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
369	#398	C₂²×C₄₇	1	4	yes	complemented
370	#397	C₂²×C₄₇	1	4	yes	complemented
371	#397	C₂²×C₄₇	1	8	yes	complemented
372	#395	C₂²×C₄₇	1	4	yes	complemented
373	#394	C₂²×C₄₇	1	8	yes	—
374	#393	C₂²×C₄₇	1	4	yes	complemented
375	#391	C₂²×C₄₇	1	4	yes	complemented
376	#389	C₂²×C₄₇	1	8	yes	complemented
377	#389	C₂²×C₄₇	1	4	yes	complemented
378	#388	C₂²×C₄₇	1	8	yes	complemented
379	#387	C₂²×C₄₇	1	8	yes	complemented
380	#386	C₂²×C₄₇	1	4	yes	—
381	#385	C₂²×C₄₇	1	4	yes	—
382	#385	C₂²×C₄₇	1	4	yes	—
383	#385	C₂²×C₄₇	1	8	yes	complemented
384	#385	C₂²×C₄₇	1	4	yes	complemented
385	#381	C₂²×C₄₇	1	4	yes	—
386	#381	C₂²×C₄₇	1	4	yes	complemented
387	#381	C₂²×C₄₇	1	2	yes	complemented
388	#380	C₂²×C₄₇	1	2	yes	—
389	#380	C₂²×C₄₇	1	4	yes	complemented
390	#380	C₂²×C₄₇	1	2	yes	complemented
391	#379	C₂²×C₄₇	1	4	yes	—
392	#379	C₂²×C₄₇	1	2	yes	—
393	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	complemented
395	C₄₇	#35084	1	1	yes	characteristic, direct product factor, Sylow
396	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
397	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
398	C₂²×Q₈	—	2	4	no	—
399	C₂²×Q₈	—	4	4	no	—
400	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
401	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
402	C₂²×D₄	—	2	4	no	—
403	C₂²×D₄	—	2	8	no	—
404	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
405	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
406	C₂³×C₄	—	2	4	no	—
407	C₂³×C₄	—	4	4	no	—
408	C₂³×C₄	—	4	4	no	—
409	C₂³×C₄	D₄×C₄₇	1	8	yes	—
410	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
411	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
412	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
414	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
415	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
416	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
419	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
420	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
423	#123	—	2	16	no	—
424	C₂²⋊Q₈	—	2	8	no	—
425	C₂²⋊Q₈	—	2	8	no	—
426	C₂²⋊Q₈	—	2	8	no	—
427	C₂²⋊Q₈	—	2	8	no	—
428	C₂²⋊Q₈	—	4	8	no	—
429	C₄×D₄	—	2	8	no	—
430	C₄×D₄	—	2	8	no	—
431	C₄×D₄	—	2	8	no	—
432	C₄×D₄	—	2	8	no	—
433	#117	—	4	4	no	—
434	C₂×C₄⋊C₄	—	2	4	no	—
435	C₂×C₄⋊C₄	—	2	4	no	—
436	C₂×C₄⋊C₄	—	2	8	no	—
437	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
445	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
446	C₂×C₂²⋊C₄	—	2	4	no	—
447	C₂×C₂²⋊C₄	—	2	8	no	—
448	C₂×C₂²⋊C₄	—	2	4	no	—
449	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
460	C₂×C₄²	—	2	4	no	—
461	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
462	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
463	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
464	#95	C₂³×C₄₇	1	4	yes	—
465	#95	C₂³×C₄₇	1	4	yes	—
466	#95	C₂³×C₄₇	1	8	yes	—
467	#95	C₂³×C₄₇	1	8	yes	—
468	#95	C₂³×C₄₇	1	8	yes	—
469	#95	C₂³×C₄₇	1	8	yes	—
470	C₂⁴	—	2	2	no	—
471	C₂⁴	—	2	4	no	—
472	C₂⁴	—	2	4	no	—
473	C₂⁴	—	2	4	no	—
474	C₂⁴	—	2	4	no	—
475	C₂⁴	—	4	2	no	—
476	C₂⁴	—	4	2	no	—
477	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
478	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
479	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
480	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
481	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	4	no	—
484	C₂×Q₈	—	2	8	no	—
485	C₂×Q₈	—	4	4	no	—
486	C₂×Q₈	—	4	16	no	—
487	C₂×D₄	—	2	32	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	#41×C₄₇	1	8	yes	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	8	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	8	no	—
508	C₂²×C₄	—	4	16	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	4	2	no	—
512	C₂²×C₄	—	4	4	no	—
513	C₂²×C₄	—	4	2	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	16	no	—
516	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
517	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
518	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
519	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
520	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
521	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
524	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	16	no	—
539	C₄⋊C₄	—	2	8	no	—
540	C₄⋊C₄	—	4	8	no	—
541	C₂²⋊C₄	—	2	4	no	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	8	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	16	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	4	4	no	—
551	C₂²⋊C₄	—	4	8	no	—
552	C₄²	—	2	4	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	4	4	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	8	no	—
560	C₂³	—	2	8	no	—
561	C₂³	—	2	8	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	4	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	4	4	no	—
570	C₂³	—	4	16	no	—
571	C₂³	—	4	16	no	—
572	C₂³	—	4	4	no	—
573	C₂³	—	4	4	no	—
574	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
575	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
576	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
577	C₂³	C₂×#41×C₄₇	1	4	yes	—
578	C₂³	C₂×#41×C₄₇	1	4	yes	—
579	C₂³	2₋¹⁺⁴×C₄₇	1	4	yes	—
580	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
581	Q₈	—	4	8	no	—
582	Q₈	—	4	8	no	—
583	D₄	—	2	16	no	—
584	D₄	—	2	16	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	2	8	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	8	no	—
600	C₂×C₄	—	2	8	no	—
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	8	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
616	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
617	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
618	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
619	C₂×C₄	H(5,𝔽₂)×C₄₇	1	4	yes	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	8	no	—
625	C₂²	—	2	8	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	4	16	no	—
632	C₂²	—	4	16	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	C₄₇×#525	1	4	yes	—
638	C₂²	C₄₇×#536	1	4	yes	—
639	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
640	C₂²	C₂²×#41×C₄₇	1	2	yes	—
641	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	2	yes	—
642	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	2	yes	—
643	C₄	—	2	4	no	—
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	4	4	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	4	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	8	no	—
652	C₄	C₄₇×#534	1	4	yes	—
653	C₂	—	2	4	no	—
654	C₂	—	2	4	no	—
655	C₂	—	4	2	no	—
656	C₂	—	4	4	no	—
657	C₂	C₂×C₄₇×#525	1	1	yes	characteristic
658	C₂	C₂×C₄₇×#534	1	1	yes	characteristic
659	C₂	C₂×C₄₇×#536	1	1	yes	characteristic
660	C₂	C₄₇×#3520	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
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. C₂²×C₂²⋊Q₈×C₄₇	C₂	semidirect
3. C₄₇×#2855	C₂	semidirect
4. C₄₇×#2848	C₂	semidirect
5. C₄₇×#2638	C₂	semidirect
6. C₄₇×#2583	C₂	semidirect
7. C₄₇×#2561	C₂	semidirect
8. C₄₇×#2486	C₂	semidirect
9. C₄₇×#2483	C₂	semidirect
10. C₄₇×#2415	C₂	semidirect
11. C₄₇×#2409	C₂	semidirect
13. C₄₇×#2322	C₂	semidirect
14. C₄₇×#2280	C₂	semidirect
15. C₂³×Q₈×C₄₇	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
24. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₄₇	C₂²	semidirect
31. C₂×#117×C₄₇	C₂²	semidirect
33. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
34. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
39. C₄₇×#398	C₂²	semidirect
40. C₄₇×#397	C₂²	semidirect
41. C₄₇×#397	C₂²	semidirect
42. C₄₇×#395	C₂²	semidirect
44. C₄₇×#393	C₂²	semidirect
45. C₄₇×#391	C₂²	semidirect
46. C₄₇×#389	C₂²	semidirect
47. C₄₇×#389	C₂²	semidirect
48. C₄₇×#388	C₂²	semidirect
49. C₄₇×#387	C₂²	semidirect
53. C₄₇×#385	C₂²	semidirect
54. C₄₇×#385	C₂²	semidirect
56. C₄₇×#381	C₂²	semidirect
57. C₄₇×#381	C₂²	semidirect
59. C₄₇×#380	C₂²	semidirect
60. C₄₇×#380	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₄₇	C₂²	semidirect
289. #35084	C₄₇	direct (N × H)
323. C₂²×C₂²⋊Q₈	C₂×C₄₇	semidirect
325. #2855	C₂×C₄₇	semidirect
326. #2848	C₂×C₄₇	semidirect
327. #2638	C₂×C₄₇	semidirect
328. #2583	C₂×C₄₇	semidirect
329. #2561	C₂×C₄₇	semidirect
330. #2486	C₂×C₄₇	semidirect
331. #2483	C₂×C₄₇	semidirect
332. #2415	C₂×C₄₇	semidirect
333. #2409	C₂×C₄₇	semidirect
335. #2322	C₂×C₄₇	semidirect
336. #2280	C₂×C₄₇	semidirect
345. C₂³×Q₈	C₂²×C₄₇	semidirect
353. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
354. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
355. C₂×C₂²⋊Q₈	C₂²×C₄₇	semidirect
361. C₂×#117	C₂²×C₄₇	semidirect
363. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
364. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
369. #398	C₂²×C₄₇	semidirect
370. #397	C₂²×C₄₇	semidirect
371. #397	C₂²×C₄₇	semidirect
372. #395	C₂²×C₄₇	semidirect
374. #393	C₂²×C₄₇	semidirect
375. #391	C₂²×C₄₇	semidirect
376. #389	C₂²×C₄₇	semidirect
377. #389	C₂²×C₄₇	semidirect
378. #388	C₂²×C₄₇	semidirect
379. #387	C₂²×C₄₇	semidirect
383. #385	C₂²×C₄₇	semidirect
384. #385	C₂²×C₄₇	semidirect
386. #381	C₂²×C₄₇	semidirect
387. #381	C₂²×C₄₇	semidirect
389. #380	C₂²×C₄₇	semidirect
390. #380	C₂²×C₄₇	semidirect
394. C₄×C₂²⋊C₄	C₂²×C₄₇	semidirect
395. C₄₇	#35084	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₄₇×#2855	2
C₄₇×#2848	2
C₄₇×#2638	2
C₄₇×#2583	2
C₄₇×#2561	2
C₄₇×#2486	2
C₄₇×#2483	2
C₄₇×#2415	2
C₄₇×#2409	2
C₄₇×#2405	2
C₄₇×#2322	2
C₄₇×#2280	2
#35084	47

Subgroups — C47×#35084 #26074782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#35084 #26074782