Subgroups — Q₈×#41×D₄₇ #27123346

Order 12032.

7522 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10625354	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256970	C₂	1	3	yes	maximal, complemented
3	Q₈×#10625350	C₂	1	3	yes	maximal, complemented
4	#41×Dic₉₄	C₂	1	3	yes	maximal, complemented
5	#20256967	C₂	1	9	yes	maximal, complemented
6	#20256966	C₂	1	9	yes	maximal, complemented
7	Q₈×#10625352	C₂	1	3	yes	maximal, complemented
8	Q₈²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#557×D₄₇	C₂	1	3	yes	maximal, complemented
10	#554×D₄₇	C₂	1	9	yes	maximal, complemented
11	D₄×Q₈×D₄₇	C₂	1	3	yes	maximal, complemented
12	#533×D₄₇	C₂	1	9	yes	maximal, complemented
13	C₄×#41×D₄₇	C₂	1	3	yes	maximal
14	C₂×C₄×Q₈×D₄₇	C₂	1	3	yes	maximal, complemented
15	Q₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₄₇	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×D₄₇	C₂²	1	3	yes	—
18	Q₈×Dic₉₄	C₂²	1	3	yes	complemented
19	Q₈×Dic₉₄	C₂²	1	3	yes	complemented
20	#15689853	C₂²	1	9	yes	complemented
21	#15689852	C₂²	1	3	yes	complemented
22	#15689851	C₂²	1	9	yes	complemented
23	#15689850	C₂²	1	18	yes	complemented
24	#15689849	C₂²	1	6	yes	complemented
25	#15689848	C₂²	1	9	yes	complemented
26	#15689834	C₂²	1	9	yes	complemented
27	#15689833	C₂²	1	9	yes	complemented
28	#15689832	C₂²	1	18	yes	complemented
29	#15689831	C₂²	1	18	yes	complemented
30	#15689830	C₂²	1	9	yes	complemented
31	#15689829	C₂²	1	18	yes	complemented
32	#15689828	C₂²	1	18	yes	complemented
33	#15689827	C₂²	1	36	yes	complemented
34	Q₈×D₁₈₈	C₂²	1	3	yes	complemented
35	D₄×Dic₉₄	C₂²	1	9	yes	complemented
36	#15689788	C₂²	1	9	yes	complemented
37	Q₈×C₂²⋊D₄₇	C₂²	1	6	yes	complemented
38	#15689786	C₂²	1	18	yes	complemented
39	#15689680	C₂²	1	9	yes	complemented
40	#15689679	C₂²	1	18	yes	complemented
41	#15689678	C₂²	1	9	yes	complemented
42	#15689678	C₂²	1	9	yes	complemented
43	#15689677	C₂²	1	18	yes	complemented
44	#15689677	C₂²	1	18	yes	complemented
45	#15689676	C₂²	1	18	yes	complemented
46	#15689675	C₂²	1	18	yes	complemented
47	#15689675	C₂²	1	18	yes	complemented
48	C₄⋊Q₈×D₄₇	C₂²	1	9	yes	—
49	C₄⋊Q₈×D₄₇	C₂²	1	9	yes	—
50	#125×D₄₇	C₂²	1	18	yes	—
51	C₂²⋊Q₈×D₄₇	C₂²	1	18	yes	—
52	C₂²⋊Q₈×D₄₇	C₂²	1	18	yes	—
53	#41×Dic₄₇	C₂²	1	3	yes	—
54	C₄×#10625354	C₂²	1	3	yes	—
55	C₄×#10625354	C₂²	1	3	yes	—
56	C₄×#10625350	C₂²	1	9	yes	—
57	#15689591	C₂²	1	9	yes	—
58	C₄×#10625352	C₂²	1	9	yes	—
59	C₄×#10625352	C₂²	1	9	yes	—
60	C₂×Q₈×Dic₄₇	C₂²	1	3	yes	complemented
61	C₂×C₄×Dic₉₄	C₂²	1	9	yes	complemented
62	C₂×#13093989	C₂²	1	9	yes	complemented
63	C₄×Q₈×D₄₇	C₂²	1	1	yes	characteristic
64	C₄×Q₈×D₄₇	C₂²	1	3	yes	—
65	C₄×Q₈×D₄₇	C₂²	1	9	yes	—
66	C₄×Q₈×D₄₇	C₂²	1	9	yes	—
67	C₄×Q₈×D₄₇	C₂²	1	3	yes	—
68	C₄×Q₈×D₄₇	C₂²	1	3	yes	—
69	C₄×Q₈×D₄₇	C₂²	1	6	yes	—
70	C₄×Q₈×D₄₇	C₂²	1	3	yes	complemented
71	C₄×Q₈×D₄₇	C₂²	1	9	yes	complemented
72	C₄×Q₈×D₄₇	C₂²	1	9	yes	complemented
73	C₄×Q₈×D₄₇	C₂²	1	3	yes	complemented
74	C₄×D₄×D₄₇	C₂²	1	9	yes	—
75	C₄×D₄×D₄₇	C₂²	1	9	yes	—
76	#117×D₄₇	C₂²	1	9	yes	—
77	C₂×C₄⋊C₄×D₄₇	C₂²	1	9	yes	—
78	C₂×C₄²×D₄₇	C₂²	1	9	yes	—
79	Q₈²×C₄₇	C₂²	1	1	yes	characteristic, complemented
80	C₄₇×#557	C₂²	1	3	yes	complemented
81	C₄₇×#554	C₂²	1	9	yes	complemented
82	D₄×Q₈×C₄₇	C₂²	1	3	yes	complemented
83	C₄₇×#533	C₂²	1	9	yes	complemented
84	C₄×#41×C₄₇	C₂²	1	3	yes	—
85	C₂×C₄×Q₈×C₄₇	C₂²	1	3	yes	complemented
86	C₂×#10625354	C₂³	1	1	yes	characteristic
87	C₂×#10625350	C₂³	1	3	yes	—
88	C₂×#10625352	C₂³	1	3	yes	—
89	#41×D₄₇	Q₈	1	16	yes	direct product factor
90	C₂²×Dic₉₄	C₂³	1	9	yes	—
91	C₂×Q₈×D₄₇	—	2	24	no	—
92	C₂×Q₈×D₄₇	C₂³	1	9	yes	—
93	C₂×Q₈×D₄₇	C₂³	1	3	yes	—
94	C₂×Q₈×D₄₇	C₂³	1	9	yes	—
95	C₂×Q₈×D₄₇	C₂³	1	6	yes	—
96	C₂×Q₈×D₄₇	C₂³	1	1	yes	characteristic
97	C₂×Q₈×D₄₇	C₂³	1	1	yes	characteristic
98	C₂×D₄×D₄₇	C₂³	1	3	yes	—
99	C₂²×C₄×D₄₇	C₂³	1	9	yes	—
100	C₂²×C₄×D₄₇	C₂³	1	9	yes	—
101	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
102	#13094024	C₂³	1	9	yes	—
103	#13094024	C₂³	1	9	yes	—
104	#13094023	C₂³	1	18	yes	—
105	#13094023	C₂³	1	18	yes	—
106	#13094023	C₂³	1	18	yes	—
107	#13094023	C₂³	1	18	yes	—
108	#13094022	C₂³	1	18	yes	—
109	#13094022	C₂³	1	18	yes	—
110	#13094016	C₂³	1	18	yes	—
111	#13094015	C₂³	1	18	yes	—
112	#13094015	C₂³	1	18	yes	—
113	#13094014	C₂³	1	36	yes	—
114	#13094014	C₂³	1	36	yes	—
115	#13094004	C₂³	1	18	yes	—
116	#13094004	C₂³	1	18	yes	—
117	#13094003	C₂³	1	18	yes	—
118	#13094003	C₂³	1	18	yes	—
119	#13094002	C₂³	1	36	yes	—
120	#13094002	C₂³	1	36	yes	—
121	#13094001	C₂³	1	36	yes	—
122	#13094001	C₂³	1	36	yes	—
123	#13094000	C₂³	1	18	yes	—
124	#13094000	C₂³	1	18	yes	—
125	Q₈×Dic₄₇	C₂³	1	3	yes	—
126	Q₈×Dic₄₇	C₂³	1	9	yes	—
127	Q₈×Dic₄₇	C₂³	1	1	yes	characteristic
128	Q₈×Dic₄₇	C₂³	1	9	yes	—
129	Q₈×Dic₄₇	C₂³	1	3	yes	—
130	Q₈×Dic₄₇	C₂³	1	3	yes	—
131	Q₈×Dic₄₇	C₂³	1	6	yes	—
132	C₄×Dic₉₄	C₂³	1	9	yes	—
133	C₄×Dic₉₄	C₂³	1	18	yes	—
134	C₄×Dic₉₄	C₂³	1	9	yes	—
135	C₄×Dic₉₄	C₂³	1	3	yes	—
136	C₄×Dic₉₄	C₂³	1	18	yes	—
137	C₄×Dic₉₄	C₂³	1	9	yes	—
138	C₄×Dic₉₄	C₂³	1	9	yes	—
139	C₄×Dic₉₄	C₂³	1	9	yes	—
140	C₄×Dic₉₄	C₂³	1	18	yes	—
141	#13093989	C₂³	1	9	yes	—
142	#13093989	C₂³	1	18	yes	—
143	#13093989	C₂³	1	9	yes	—
144	#13093989	C₂³	1	3	yes	—
145	#13093989	C₂³	1	9	yes	—
146	#13093989	C₂³	1	18	yes	—
147	#13093989	C₂³	1	9	yes	—
148	#13093989	C₂³	1	9	yes	—
149	#13093989	C₂³	1	18	yes	—
150	C₄×D₁₈₈	C₂³	1	9	yes	—
151	C₄×D₁₈₈	C₂³	1	9	yes	—
152	D₄×Dic₄₇	C₂³	1	9	yes	—
153	D₄×Dic₄₇	C₂³	1	9	yes	—
154	#13093986	C₂³	1	9	yes	—
155	#13093986	C₂³	1	9	yes	—
156	C₄×C₂²⋊D₄₇	C₂³	1	18	yes	—
157	C₄×C₂²⋊D₄₇	C₂³	1	18	yes	—
158	(C₂²⋊D₄₇)⋊C₄	C₂³	1	18	yes	—
159	(C₂²⋊D₄₇)⋊C₄	C₂³	1	18	yes	—
160	#13093983	C₂³	1	9	yes	—
161	#13093982	C₂³	1	9	yes	—
162	#13093982	C₂³	1	9	yes	—
163	#13093981	C₂³	1	18	yes	—
164	#13093980	C₂³	1	18	yes	—
165	C₂×C₄⋊Dic₄₇	C₂³	1	9	yes	—
166	C₂×Dic₄₇⋊C₄	C₂³	1	18	yes	—
167	C₄⋊C₄×D₄₇	C₂³	1	18	yes	—
168	C₄⋊C₄×D₄₇	C₂³	1	3	yes	—
169	C₄⋊C₄×D₄₇	C₂³	1	9	yes	—
170	C₄⋊C₄×D₄₇	C₂³	1	9	yes	—
171	C₄⋊C₄×D₄₇	C₂³	1	18	yes	—
172	C₄⋊C₄×D₄₇	C₂³	1	9	yes	—
173	C₄⋊C₄×D₄₇	C₂³	1	9	yes	—
174	C₄⋊C₄×D₄₇	C₂³	1	9	yes	—
175	C₄⋊C₄×D₄₇	C₂³	1	18	yes	—
176	C₂²⋊C₄×D₄₇	C₂³	1	18	yes	—
177	C₂×C₄×Dic₄₇	C₂³	1	9	yes	—
178	C₂×C₄×Dic₄₇	C₂³	1	9	yes	—
179	C₂×C₄×Dic₄₇	C₂³	1	9	yes	—
180	C₄²×D₄₇	C₂³	1	3	yes	—
181	C₄²×D₄₇	C₂³	1	9	yes	—
182	C₄²×D₄₇	C₂³	1	9	yes	—
183	C₄²×D₄₇	C₂³	1	9	yes	—
184	C₄²×D₄₇	C₂³	1	9	yes	—
185	C₄²×D₄₇	C₂³	1	9	yes	—
186	C₄²×D₄₇	C₂³	1	9	yes	—
187	C₄²×D₄₇	C₂³	1	9	yes	—
188	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₄₇	C₂³	1	3	yes	—
190	C₄⋊Q₈×C₄₇	C₂³	1	9	yes	—
191	C₄⋊Q₈×C₄₇	C₂³	1	9	yes	—
192	#125×C₄₇	C₂³	1	18	yes	—
193	C₂²⋊Q₈×C₄₇	C₂³	1	18	yes	—
194	C₂²⋊Q₈×C₄₇	C₂³	1	18	yes	—
195	C₄×Q₈×C₄₇	C₂³	1	3	yes	—
196	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
197	C₄×Q₈×C₄₇	C₂³	1	9	yes	—
198	C₄×Q₈×C₄₇	C₂³	1	9	yes	—
199	C₄×Q₈×C₄₇	C₂³	1	3	yes	—
200	C₄×Q₈×C₄₇	C₂³	1	3	yes	—
201	C₄×Q₈×C₄₇	C₂³	1	6	yes	—
202	C₄×D₄×C₄₇	C₂³	1	9	yes	—
203	C₄×D₄×C₄₇	C₂³	1	9	yes	—
204	#117×C₄₇	C₂³	1	9	yes	—
205	C₂×C₄⋊C₄×C₄₇	C₂³	1	9	yes	—
206	C₂×C₄²×C₄₇	C₂³	1	9	yes	—
207	C₂³×D₄₇	C₂⁴	1	3	yes	—
208	#41×C₄₇	C₂×Q₈	1	8	yes	complemented
209	C₂×Q₈×C₄₇	—	2	12	no	—
210	C₂×Q₈×C₄₇	C₂⁴	1	9	yes	—
211	C₂×Q₈×C₄₇	C₂⁴	1	6	yes	—
212	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
214	C₂×D₄×C₄₇	C₂⁴	1	3	yes	—
215	C₂²×C₄×C₄₇	C₂⁴	1	9	yes	—
216	C₂²×C₄×C₄₇	C₂⁴	1	9	yes	—
217	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
218	C₂×C₂²⋊D₄₇	C₂⁴	1	6	yes	—
219	C₂²×Dic₄₇	C₂⁴	1	9	yes	—
220	C₂²×Dic₄₇	C₂⁴	1	9	yes	—
221	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
222	#10625354	C₂×Q₈	1	8	yes	complemented
223	Q₈×D₄₇	—	2	12	no	—
224	Q₈×D₄₇	—	2	36	no	—
225	Q₈×D₄₇	—	2	36	no	—
226	Q₈×D₄₇	—	4	12	no	—
227	Q₈×D₄₇	C₂×Q₈	1	8	yes	complemented
228	Q₈×D₄₇	#41	1	8	yes	direct product factor
229	#10625352	C₂×Q₈	1	24	yes	complemented
230	D₄×D₄₇	C₂×Q₈	1	24	yes	complemented
231	#10625350	C₂×Q₈	1	24	yes	complemented
232	C₂×D₁₈₈	C₂⁴	1	3	yes	—
233	C₂×C₄×D₄₇	—	2	36	no	—
234	C₂×C₄×D₄₇	—	4	18	no	—
235	C₂×C₄×D₄₇	C₂×Q₈	1	24	yes	complemented
236	C₂×C₄×D₄₇	C₂⁴	1	3	yes	—
237	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
238	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
239	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
240	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
241	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
242	C₂×C₄×D₄₇	C₂⁴	1	9	yes	—
243	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×D₄₇	C₂⁴	1	3	yes	—
245	C₂×C₄×D₄₇	C₂⁴	1	3	yes	—
246	C₂×C₄×D₄₇	C₂⁴	1	3	yes	—
247	C₂×C₄×D₄₇	C₂⁴	1	3	yes	—
248	C₂×Dic₉₄	—	2	36	no	—
249	C₂×Dic₉₄	C₂⁴	1	18	yes	—
250	C₂×Dic₉₄	C₂⁴	1	9	yes	—
251	C₂×Dic₉₄	C₂⁴	1	18	yes	—
252	C₂×Dic₉₄	C₂⁴	1	3	yes	—
253	C₂×Dic₉₄	C₂⁴	1	3	yes	—
254	C₄⋊C₄×C₄₇	C₂⁴	1	3	yes	—
255	C₄⋊C₄×C₄₇	C₂⁴	1	18	yes	—
256	C₄⋊C₄×C₄₇	C₂⁴	1	9	yes	—
257	C₄⋊C₄×C₄₇	C₂⁴	1	9	yes	—
258	C₄⋊C₄×C₄₇	C₂⁴	1	9	yes	—
259	C₄⋊C₄×C₄₇	C₂⁴	1	18	yes	—
260	C₂²⋊C₄×C₄₇	C₂⁴	1	18	yes	—
261	C₄²×C₄₇	C₂⁴	1	3	yes	—
262	C₄²×C₄₇	C₂⁴	1	9	yes	—
263	C₄²×C₄₇	C₂⁴	1	9	yes	—
264	C₄²×C₄₇	C₂⁴	1	9	yes	—
265	C₂²⋊Dic₄₇	C₂⁴	1	18	yes	—
266	(C₂×D₄₇)⋊C₄	C₂⁴	1	18	yes	—
267	(C₂×D₄₇)⋊C₄	C₂⁴	1	18	yes	—
268	C₄⋊Dic₄₇	C₂⁴	1	3	yes	—
269	C₄⋊Dic₄₇	C₂⁴	1	9	yes	—
270	C₄⋊Dic₄₇	C₂⁴	1	18	yes	—
271	C₄⋊Dic₄₇	C₂⁴	1	9	yes	—
272	C₄⋊Dic₄₇	C₂⁴	1	9	yes	—
273	C₄⋊Dic₄₇	C₂⁴	1	18	yes	—
274	Dic₄₇⋊C₄	C₂⁴	1	6	yes	—
275	Dic₄₇⋊C₄	C₂⁴	1	18	yes	—
276	Dic₄₇⋊C₄	C₂⁴	1	18	yes	—
277	Dic₄₇⋊C₄	C₂⁴	1	18	yes	—
278	Dic₄₇⋊C₄	C₂⁴	1	18	yes	—
279	Dic₄₇⋊C₄	C₂⁴	1	18	yes	—
280	Dic₄₇⋊C₄	C₂⁴	1	36	yes	—
281	C₄×Dic₄₇	C₂⁴	1	3	yes	—
282	C₄×Dic₄₇	C₂⁴	1	3	yes	—
283	C₄×Dic₄₇	C₂⁴	1	3	yes	—
284	C₄×Dic₄₇	C₂⁴	1	9	yes	—
285	C₄×Dic₄₇	C₂⁴	1	9	yes	—
286	C₄×Dic₄₇	C₂⁴	1	9	yes	—
287	C₄×Dic₄₇	C₂⁴	1	9	yes	—
288	C₄×Dic₄₇	C₂⁴	1	9	yes	—
289	C₄×Dic₄₇	C₂⁴	1	9	yes	—
290	C₄×Dic₄₇	C₂⁴	1	9	yes	—
291	C₄×Dic₄₇	C₂⁴	1	9	yes	—
292	C₄×Dic₄₇	C₂⁴	1	9	yes	—
293	C₂³×C₄₇	C₂⁵	1	3	yes	—
294	C₂²×D₄₇	—	2	6	no	—
295	C₂²×D₄₇	—	2	6	no	—
296	C₂²×D₄₇	C₂²×Q₈	1	12	yes	—
297	C₂²×D₄₇	C₂⁵	1	3	yes	—
298	C₂²×D₄₇	C₂⁵	1	1	yes	characteristic
299	Q₈×C₄₇	—	2	18	no	—
300	Q₈×C₄₇	—	4	6	no	—
301	Q₈×C₄₇	C₂²×Q₈	1	4	yes	complemented
302	Q₈×C₄₇	C₂×#41	1	4	yes	complemented
303	D₄×C₄₇	C₂²×Q₈	1	12	yes	complemented
304	C₂×C₄×C₄₇	—	2	18	no	—
305	C₂×C₄×C₄₇	—	4	9	no	—
306	C₂×C₄×C₄₇	C₂²×Q₈	1	12	yes	complemented
307	C₂×C₄×C₄₇	C₂⁵	1	3	yes	—
308	C₂×C₄×C₄₇	C₂⁵	1	9	yes	—
309	C₂×C₄×C₄₇	C₂⁵	1	9	yes	—
310	C₂×C₄×C₄₇	C₂⁵	1	3	yes	—
311	C₂×C₄×C₄₇	C₂⁵	1	3	yes	—
312	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
313	C₂²⋊D₄₇	C₂²×Q₈	1	24	yes	complemented
314	C₂×Dic₄₇	—	2	18	no	—
315	C₂×Dic₄₇	—	4	9	no	—
316	C₂×Dic₄₇	C₂²×Q₈	1	12	yes	complemented
317	C₂×Dic₄₇	C₂⁵	1	3	yes	—
318	C₂×Dic₄₇	C₂⁵	1	9	yes	—
319	C₂×Dic₄₇	C₂⁵	1	9	yes	—
320	C₂×Dic₄₇	C₂⁵	1	1	yes	characteristic
321	C₂×Dic₄₇	C₂⁵	1	3	yes	—
322	C₂×Dic₄₇	C₂⁵	1	3	yes	—
323	D₁₈₈	C₂²×Q₈	1	12	yes	complemented
324	C₄×D₄₇	—	2	18	no	—
325	C₄×D₄₇	—	2	6	no	—
326	C₄×D₄₇	—	2	18	no	—
327	C₄×D₄₇	—	2	18	no	—
328	C₄×D₄₇	—	2	18	no	—
329	C₄×D₄₇	—	4	9	no	—
330	C₄×D₄₇	—	4	9	no	—
331	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
332	C₄×D₄₇	C₂²×Q₈	1	12	yes	—
333	C₄×D₄₇	C₂²×Q₈	1	12	yes	complemented
334	C₄×D₄₇	C₂²×Q₈	1	12	yes	complemented
335	C₄×D₄₇	C₂×#41	1	12	yes	—
336	Dic₉₄	—	2	18	no	—
337	Dic₉₄	—	2	36	no	—
338	Dic₉₄	—	4	18	no	—
339	Dic₉₄	C₂²×Q₈	1	12	yes	complemented
340	Dic₉₄	C₂×#41	1	12	yes	complemented
341	C₂×Q₈×#41	—	47	1	no	maximal, Sylow
342	C₂²×C₄₇	—	2	3	no	—
343	C₂²×C₄₇	—	2	3	no	—
344	C₂²×C₄₇	C₂³×Q₈	1	6	yes	—
345	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
346	C₂×D₄₇	—	2	3	no	—
347	C₂×D₄₇	—	2	3	no	—
348	C₂×D₄₇	—	2	24	no	—
349	C₂×D₄₇	C₂³×Q₈	1	6	yes	—
350	C₂×D₄₇	C₂³×Q₈	1	2	yes	—
351	C₂×D₄₇	C₂²×#41	1	2	yes	—
352	C₂×D₄₇	#585	1	2	yes	—
353	C₄×C₄₇	—	2	9	no	—
354	C₄×C₄₇	—	2	9	no	—
355	C₄×C₄₇	—	2	3	no	—
356	C₄×C₄₇	C₂³×Q₈	1	6	yes	—
357	C₄×C₄₇	C₂³×Q₈	1	2	yes	—
358	C₄×C₄₇	C₂²×#41	1	6	yes	—
359	Dic₄₇	—	2	9	no	—
360	Dic₄₇	—	2	9	no	—
361	Dic₄₇	—	2	3	no	—
362	Dic₄₇	C₂³×Q₈	1	6	yes	—
363	Dic₄₇	C₂³×Q₈	1	2	yes	—
364	Dic₄₇	C₂²×#41	1	6	yes	—
365	Q₈×#41	—	47	1	no	—
366	Q₈×#41	—	47	3	no	—
367	Q₈×#41	—	47	9	no	—
368	Q₈×#41	—	47	3	no	—
369	Q₈×#41	—	47	9	no	—
370	Q₈×#41	—	47	3	no	—
371	Q₈×#41	—	47	3	no	—
372	Q₈×#41	D₄₇	1	1	yes	characteristic, direct product factor
373	C₂×Q₈²	—	47	1	no	—
374	C₂×#557	—	47	3	no	—
375	C₂×#554	—	47	9	no	—
376	C₂×D₄×Q₈	—	47	3	no	—
377	C₂×#533	—	47	9	no	—
378	C₂×C₄×#41	—	47	3	no	—
379	C₂²×C₄×Q₈	—	47	3	no	—
380	C₂×C₄₇	—	2	6	no	—
381	C₂×C₄₇	C₂⁴×Q₈	1	1	yes	characteristic
382	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
383	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
384	D₄₇	—	2	6	no	—
385	D₄₇	Q₈×#41	1	4	yes	direct product factor
386	C₂²×#41	—	47	1	no	—
387	C₂³×Q₈	—	47	3	no	—
388	Q₈²	—	47	9	no	—
389	Q₈²	—	47	3	no	—
390	Q₈²	—	47	3	no	—
391	Q₈²	C₂×D₄₇	1	1	yes	characteristic, complemented
392	#557	—	47	9	no	—
393	#557	—	47	18	no	—
394	#557	—	47	6	no	—
395	#557	—	47	9	no	—
396	#557	—	47	3	no	—
397	#557	C₂×D₄₇	1	3	yes	complemented
398	#554	—	47	9	no	—
399	#554	—	47	18	no	—
400	#554	—	47	36	no	—
401	#554	—	47	18	no	—
402	#554	—	47	9	no	—
403	#554	—	47	9	no	—
404	#554	—	47	18	no	—
405	#554	—	47	18	no	—
406	#554	C₂×D₄₇	1	9	yes	complemented
407	D₄×Q₈	—	47	6	no	—
408	D₄×Q₈	—	47	9	no	—
409	D₄×Q₈	—	47	18	no	—
410	D₄×Q₈	—	47	3	no	—
411	D₄×Q₈	—	47	9	no	—
412	D₄×Q₈	C₂×D₄₇	1	3	yes	complemented
413	#533	—	47	9	no	—
414	#533	—	47	9	no	—
415	#533	—	47	18	no	—
416	#533	—	47	18	no	—
417	#533	—	47	18	no	—
418	#533	—	47	18	no	—
419	#533	—	47	18	no	—
420	#533	—	47	18	no	—
421	#533	—	47	9	no	—
422	#533	C₂×D₄₇	1	9	yes	complemented
423	C₂×C₄⋊Q₈	—	47	9	no	—
424	C₂×C₄⋊Q₈	—	47	9	no	—
425	C₂×#125	—	47	18	no	—
426	C₂×C₂²⋊Q₈	—	47	18	no	—
427	C₂×C₂²⋊Q₈	—	47	18	no	—
428	C₄×#41	—	47	3	no	—
429	C₄×#41	—	47	3	no	—
430	C₄×#41	—	47	3	no	—
431	C₄×#41	—	47	9	no	—
432	C₄×#41	—	47	9	no	—
433	C₄×#41	—	47	9	no	—
434	C₄×#41	—	47	9	no	—
435	C₄×#41	C₂×D₄₇	1	3	yes	—
436	C₂×C₄×Q₈	—	47	3	no	—
437	C₂×C₄×Q₈	—	47	1	no	—
438	C₂×C₄×Q₈	—	47	9	no	—
439	C₂×C₄×Q₈	—	47	3	no	—
440	C₂×C₄×Q₈	—	47	9	no	—
441	C₂×C₄×Q₈	—	47	3	no	—
442	C₂×C₄×Q₈	—	47	9	no	—
443	C₂×C₄×Q₈	—	47	3	no	—
444	C₂×C₄×Q₈	—	47	9	no	—
445	C₂×C₄×Q₈	—	47	3	no	—
446	C₂×C₄×Q₈	—	47	3	no	—
447	C₂×C₄×Q₈	—	47	6	no	—
448	C₂×C₄×Q₈	—	47	9	no	—
449	C₂×C₄×Q₈	—	47	9	no	—
450	C₂×C₄×Q₈	C₂×D₄₇	1	3	yes	complemented
451	C₂×C₄×D₄	—	47	9	no	—
452	C₂×C₄×D₄	—	47	9	no	—
453	C₂×#117	—	47	9	no	—
454	C₂²×C₄⋊C₄	—	47	9	no	—
455	C₂²×C₄²	—	47	9	no	—
456	C₄₇	C₂×Q₈×#41	1	1	yes	characteristic, complemented, Sylow
457	C₂×#41	—	47	16	no	—
458	C₂×#41	—	47	1	no	—
459	C₂×#41	—	47	3	no	—
460	C₂×#41	—	47	3	no	—
461	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
462	C₂²×Q₈	—	47	1	no	—
463	C₂²×Q₈	—	47	1	no	—
464	C₂²×Q₈	—	47	9	no	—
465	C₂²×Q₈	—	47	9	no	—
466	C₂²×Q₈	—	47	3	no	—
467	C₂²×Q₈	—	47	6	no	—
468	C₂²×Q₈	—	47	9	no	—
469	C₂²×Q₈	—	94	24	no	—
470	C₂²×Q₈	C₂²×D₄₇	1	3	yes	—
471	C₂²×D₄	—	47	3	no	—
472	C₂³×C₄	—	47	3	no	—
473	C₂³×C₄	—	47	9	no	—
474	C₂³×C₄	—	47	9	no	—
475	C₄⋊Q₈	—	47	18	no	—
476	C₄⋊Q₈	—	47	18	no	—
477	C₄⋊Q₈	—	47	18	no	—
478	C₄⋊Q₈	—	47	18	no	—
479	C₄⋊Q₈	—	47	18	no	—
480	C₄⋊Q₈	—	47	18	no	—
481	C₄⋊Q₈	—	47	9	no	—
482	C₄⋊Q₈	—	47	9	no	—
483	C₄⋊Q₈	C₂²×D₄₇	1	9	yes	—
484	C₄⋊Q₈	C₂²×D₄₇	1	9	yes	—
485	#125	—	47	36	no	—
486	#125	—	47	36	no	—
487	#125	—	47	18	no	—
488	#125	—	47	18	no	—
489	#125	—	47	18	no	—
490	#125	C₂²×D₄₇	1	18	yes	—
491	C₂²⋊Q₈	—	47	18	no	—
492	C₂²⋊Q₈	—	47	18	no	—
493	C₂²⋊Q₈	—	47	18	no	—
494	C₂²⋊Q₈	—	47	18	no	—
495	C₂²⋊Q₈	—	47	36	no	—
496	C₂²⋊Q₈	—	47	18	no	—
497	C₂²⋊Q₈	—	47	36	no	—
498	C₂²⋊Q₈	—	47	18	no	—
499	C₂²⋊Q₈	—	47	36	no	—
500	C₂²⋊Q₈	—	47	36	no	—
501	C₂²⋊Q₈	C₂²×D₄₇	1	18	yes	—
502	C₂²⋊Q₈	C₂²×D₄₇	1	18	yes	—
503	C₄×Q₈	—	47	1	no	—
504	C₄×Q₈	—	47	9	no	—
505	C₄×Q₈	—	47	3	no	—
506	C₄×Q₈	—	47	9	no	—
507	C₄×Q₈	—	47	3	no	—
508	C₄×Q₈	—	47	3	no	—
509	C₄×Q₈	—	47	6	no	—
510	C₄×Q₈	—	47	3	no	—
511	C₄×Q₈	—	47	9	no	—
512	C₄×Q₈	—	47	18	no	—
513	C₄×Q₈	—	47	9	no	—
514	C₄×Q₈	—	47	18	no	—
515	C₄×Q₈	—	47	9	no	—
516	C₄×Q₈	—	47	9	no	—
517	C₄×Q₈	—	47	9	no	—
518	C₄×Q₈	—	47	18	no	—
519	C₄×Q₈	—	47	3	no	—
520	C₄×Q₈	—	47	18	no	—
521	C₄×Q₈	—	47	9	no	—
522	C₄×Q₈	—	47	9	no	—
523	C₄×Q₈	—	47	9	no	—
524	C₄×Q₈	—	47	18	no	—
525	C₄×Q₈	—	47	9	no	—
526	C₄×Q₈	—	47	9	no	—
527	C₄×Q₈	—	47	18	no	—
528	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
529	C₄×Q₈	C₂²×D₄₇	1	9	yes	—
530	C₄×Q₈	C₂²×D₄₇	1	3	yes	—
531	C₄×Q₈	C₂²×D₄₇	1	9	yes	—
532	C₄×Q₈	C₂²×D₄₇	1	3	yes	—
533	C₄×Q₈	C₂²×D₄₇	1	3	yes	—
534	C₄×Q₈	C₂²×D₄₇	1	6	yes	—
535	C₄×D₄	—	47	9	no	—
536	C₄×D₄	—	47	9	no	—
537	C₄×D₄	—	47	18	no	—
538	C₄×D₄	—	47	18	no	—
539	C₄×D₄	—	47	9	no	—
540	C₄×D₄	—	47	9	no	—
541	C₄×D₄	—	47	18	no	—
542	C₄×D₄	—	47	18	no	—
543	C₄×D₄	—	47	9	no	—
544	C₄×D₄	—	47	9	no	—
545	C₄×D₄	C₂²×D₄₇	1	9	yes	—
546	C₄×D₄	C₂²×D₄₇	1	9	yes	—
547	#117	—	47	9	no	—
548	#117	—	47	9	no	—
549	#117	—	47	9	no	—
550	#117	—	47	18	no	—
551	#117	—	47	18	no	—
552	#117	C₂²×D₄₇	1	9	yes	—
553	C₂×C₄⋊C₄	—	47	18	no	—
554	C₂×C₄⋊C₄	—	47	9	no	—
555	C₂×C₄⋊C₄	—	47	3	no	—
556	C₂×C₄⋊C₄	—	47	18	no	—
557	C₂×C₄⋊C₄	—	47	9	no	—
558	C₂×C₄⋊C₄	—	47	18	no	—
559	C₂×C₄⋊C₄	—	47	9	no	—
560	C₂×C₄⋊C₄	—	47	9	no	—
561	C₂×C₄⋊C₄	—	47	9	no	—
562	C₂×C₄⋊C₄	—	47	9	no	—
563	C₂×C₄⋊C₄	—	47	18	no	—
564	C₂×C₄⋊C₄	C₂²×D₄₇	1	9	yes	—
565	C₂×C₂²⋊C₄	—	47	18	no	—
566	C₂×C₄²	—	47	9	no	—
567	C₂×C₄²	—	47	9	no	—
568	C₂×C₄²	—	47	9	no	—
569	C₂×C₄²	—	47	9	no	—
570	C₂×C₄²	—	47	9	no	—
571	C₂×C₄²	—	47	9	no	—
572	C₂×C₄²	—	47	3	no	—
573	C₂×C₄²	—	47	9	no	—
574	C₂×C₄²	—	47	9	no	—
575	C₂×C₄²	—	47	9	no	—
576	C₂×C₄²	—	47	9	no	—
577	C₂×C₄²	C₂²×D₄₇	1	9	yes	—
578	C₂⁴	—	47	3	no	—
579	#41	—	47	8	no	—
580	#41	—	47	24	no	—
581	#41	—	47	24	no	—
582	#41	Q₈×D₄₇	1	8	yes	direct product factor
583	C₂×Q₈	—	2	12	no	—
584	C₂×Q₈	—	47	8	no	—
585	C₂×Q₈	—	47	8	no	—
586	C₂×Q₈	—	47	3	no	—
587	C₂×Q₈	—	47	3	no	—
588	C₂×Q₈	—	47	18	no	—
589	C₂×Q₈	—	47	9	no	—
590	C₂×Q₈	—	47	18	no	—
591	C₂×Q₈	—	94	36	no	—
592	C₂×Q₈	—	94	36	no	—
593	C₂×Q₈	—	94	36	no	—
594	C₂×Q₈	—	94	12	no	—
595	C₂×Q₈	—	188	12	no	—
596	C₂×Q₈	C₂³×D₄₇	1	9	yes	—
597	C₂×Q₈	C₂³×D₄₇	1	6	yes	—
598	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
599	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
600	C₂×D₄	—	47	6	no	—
601	C₂×D₄	—	47	24	no	—
602	C₂×D₄	—	47	3	no	—
603	C₂×D₄	C₂³×D₄₇	1	3	yes	—
604	C₂²×C₄	—	47	3	no	—
605	C₂²×C₄	—	47	24	no	—
606	C₂²×C₄	—	47	3	no	—
607	C₂²×C₄	—	47	3	no	—
608	C₂²×C₄	—	47	3	no	—
609	C₂²×C₄	—	47	1	no	—
610	C₂²×C₄	—	47	3	no	—
611	C₂²×C₄	—	47	9	no	—
612	C₂²×C₄	—	47	9	no	—
613	C₂²×C₄	—	47	3	no	—
614	C₂²×C₄	—	47	9	no	—
615	C₂²×C₄	—	47	9	no	—
616	C₂²×C₄	—	47	9	no	—
617	C₂²×C₄	—	47	9	no	—
618	C₂²×C₄	—	47	9	no	—
619	C₂²×C₄	—	47	9	no	—
620	C₂²×C₄	—	94	36	no	—
621	C₂²×C₄	—	188	18	no	—
622	C₂²×C₄	C₂³×D₄₇	1	9	yes	—
623	C₂²×C₄	C₂³×D₄₇	1	9	yes	—
624	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
625	C₄⋊C₄	—	47	6	no	—
626	C₄⋊C₄	—	47	18	no	—
627	C₄⋊C₄	—	47	18	no	—
628	C₄⋊C₄	—	47	18	no	—
629	C₄⋊C₄	—	47	18	no	—
630	C₄⋊C₄	—	47	18	no	—
631	C₄⋊C₄	—	47	36	no	—
632	C₄⋊C₄	—	47	3	no	—
633	C₄⋊C₄	—	47	18	no	—
634	C₄⋊C₄	—	47	9	no	—
635	C₄⋊C₄	—	47	9	no	—
636	C₄⋊C₄	—	47	9	no	—
637	C₄⋊C₄	—	47	18	no	—
638	C₄⋊C₄	C₂³×D₄₇	1	3	yes	—
639	C₄⋊C₄	C₂³×D₄₇	1	18	yes	—
640	C₄⋊C₄	C₂³×D₄₇	1	9	yes	—
641	C₄⋊C₄	C₂³×D₄₇	1	9	yes	—
642	C₄⋊C₄	C₂³×D₄₇	1	9	yes	—
643	C₄⋊C₄	C₂³×D₄₇	1	18	yes	—
644	C₂²⋊C₄	—	47	18	no	—
645	C₂²⋊C₄	—	47	18	no	—
646	C₂²⋊C₄	—	47	18	no	—
647	C₂²⋊C₄	C₂³×D₄₇	1	18	yes	—
648	C₄²	—	47	3	no	—
649	C₄²	—	47	3	no	—
650	C₄²	—	47	9	no	—
651	C₄²	—	47	9	no	—
652	C₄²	—	47	9	no	—
653	C₄²	—	47	9	no	—
654	C₄²	—	47	9	no	—
655	C₄²	—	47	9	no	—
656	C₄²	—	47	9	no	—
657	C₄²	—	47	9	no	—
658	C₄²	—	47	3	no	—
659	C₄²	—	47	9	no	—
660	C₄²	C₂³×D₄₇	1	9	yes	—
661	C₄²	C₂³×D₄₇	1	9	yes	—
662	C₄²	C₂³×D₄₇	1	3	yes	—
663	C₄²	C₂³×D₄₇	1	9	yes	—
664	C₂³	—	47	1	no	—
665	C₂³	—	47	12	no	—
666	C₂³	—	47	3	no	—
667	C₂³	—	94	6	no	—
668	C₂³	—	94	6	no	—
669	C₂³	C₂⁴×D₄₇	1	3	yes	—
670	Q₈	—	2	18	no	—
671	Q₈	—	4	6	no	—
672	Q₈	—	47	12	no	—
673	Q₈	—	47	12	no	—
674	Q₈	—	94	36	no	—
675	Q₈	—	94	18	no	—
676	Q₈	—	188	18	no	—
677	Q₈	C₂×Q₈×D₄₇	1	4	yes	complemented
678	Q₈	#41×D₄₇	1	4	yes	direct product factor
679	D₄	—	47	24	no	—
680	D₄	—	47	12	no	—
681	D₄	C₂×Q₈×D₄₇	1	12	yes	complemented
682	C₂×C₄	—	2	18	no	—
683	C₂×C₄	—	4	9	no	—
684	C₂×C₄	—	47	12	no	—
685	C₂×C₄	—	47	1	no	—
686	C₂×C₄	—	47	3	no	—
687	C₂×C₄	—	47	3	no	—
688	C₂×C₄	—	47	4	no	—
689	C₂×C₄	—	47	12	no	—
690	C₂×C₄	—	47	12	no	—
691	C₂×C₄	—	47	12	no	—
692	C₂×C₄	—	47	12	no	—
693	C₂×C₄	—	47	3	no	—
694	C₂×C₄	—	47	9	no	—
695	C₂×C₄	—	47	9	no	—
696	C₂×C₄	—	94	18	no	—
697	C₂×C₄	—	94	18	no	—
698	C₂×C₄	—	94	6	no	—
699	C₂×C₄	—	94	18	no	—
700	C₂×C₄	—	94	18	no	—
701	C₂×C₄	—	94	18	no	—
702	C₂×C₄	—	188	9	no	—
703	C₂×C₄	—	188	9	no	—
704	C₂×C₄	—	188	9	no	—
705	C₂×C₄	C₂×Q₈×D₄₇	1	12	yes	complemented
706	C₂×C₄	C₂⁴×D₄₇	1	3	yes	—
707	C₂×C₄	C₂⁴×D₄₇	1	9	yes	—
708	C₂×C₄	C₂⁴×D₄₇	1	9	yes	—
709	C₂×C₄	C₂⁴×D₄₇	1	3	yes	—
710	C₂×C₄	C₂⁴×D₄₇	1	3	yes	—
711	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
712	C₂²	—	2	3	no	—
713	C₂²	—	2	3	no	—
714	C₂²	—	47	2	no	—
715	C₂²	—	47	2	no	—
716	C₂²	—	47	2	no	—
717	C₂²	—	47	6	no	—
718	C₂²	—	94	24	no	—
719	C₂²	—	94	3	no	—
720	C₂²	—	94	3	no	—
721	C₂²	C₂²×Q₈×D₄₇	1	6	yes	—
722	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
723	C₄	—	2	9	no	—
724	C₄	—	2	3	no	—
725	C₄	—	2	9	no	—
726	C₄	—	47	2	no	—
727	C₄	—	47	6	no	—
728	C₄	—	47	6	no	—
729	C₄	—	94	9	no	—
730	C₄	—	94	3	no	—
731	C₄	—	94	9	no	—
732	C₄	C₂²×Q₈×D₄₇	1	2	yes	—
733	C₄	C₂²×Q₈×D₄₇	1	6	yes	—
734	C₄	C₂×#41×D₄₇	1	6	yes	—
735	C₂	—	2	6	no	—
736	C₂	—	47	4	no	—
737	C₂	—	94	6	no	—
738	C₂	C₂³×Q₈×D₄₇	1	1	yes	characteristic
739	C₂	C₂²×#41×D₄₇	1	1	yes	characteristic
740	C₂	#585×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	Q₈×#41×C₄₇	C₂
prime radical	C₂×#41×D₄₇	C₂²
hypercenter	Q₈×#41	D₄₇
hypocenter	C₄₇	C₂×Q₈×#41
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
1. Q₈×#10625354	C₂	semidirect
2. #20256970	C₂	semidirect
3. Q₈×#10625350	C₂	semidirect
4. #41×Dic₉₄	C₂	semidirect
5. #20256967	C₂	semidirect
6. #20256966	C₂	semidirect
7. Q₈×#10625352	C₂	semidirect
8. Q₈²×D₄₇	C₂	semidirect
9. #557×D₄₇	C₂	semidirect
10. #554×D₄₇	C₂	semidirect
11. D₄×Q₈×D₄₇	C₂	semidirect
12. #533×D₄₇	C₂	semidirect
14. C₂×C₄×Q₈×D₄₇	C₂	semidirect
15. Q₈×#41×C₄₇	C₂	semidirect
18. Q₈×Dic₉₄	C₂²	semidirect
19. Q₈×Dic₉₄	C₂²	semidirect
20. #15689853	C₂²	semidirect
21. #15689852	C₂²	semidirect
22. #15689851	C₂²	semidirect
23. #15689850	C₂²	semidirect
24. #15689849	C₂²	semidirect
25. #15689848	C₂²	semidirect
26. #15689834	C₂²	semidirect
27. #15689833	C₂²	semidirect
28. #15689832	C₂²	semidirect
29. #15689831	C₂²	semidirect
30. #15689830	C₂²	semidirect
31. #15689829	C₂²	semidirect
32. #15689828	C₂²	semidirect
33. #15689827	C₂²	semidirect
34. Q₈×D₁₈₈	C₂²	semidirect
35. D₄×Dic₉₄	C₂²	semidirect
36. #15689788	C₂²	semidirect
37. Q₈×C₂²⋊D₄₇	C₂²	semidirect
38. #15689786	C₂²	semidirect
39. #15689680	C₂²	semidirect
40. #15689679	C₂²	semidirect
41. #15689678	C₂²	semidirect
42. #15689678	C₂²	semidirect
43. #15689677	C₂²	semidirect
44. #15689677	C₂²	semidirect
45. #15689676	C₂²	semidirect
46. #15689675	C₂²	semidirect
47. #15689675	C₂²	semidirect
60. C₂×Q₈×Dic₄₇	C₂²	semidirect
61. C₂×C₄×Dic₉₄	C₂²	semidirect
62. C₂×#13093989	C₂²	semidirect
70. C₄×Q₈×D₄₇	C₂²	semidirect
71. C₄×Q₈×D₄₇	C₂²	semidirect
72. C₄×Q₈×D₄₇	C₂²	semidirect
73. C₄×Q₈×D₄₇	C₂²	semidirect
79. Q₈²×C₄₇	C₂²	semidirect
80. C₄₇×#557	C₂²	semidirect
81. C₄₇×#554	C₂²	semidirect
82. D₄×Q₈×C₄₇	C₂²	semidirect
83. C₄₇×#533	C₂²	semidirect
85. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
89. #41×D₄₇	Q₈	direct (N × H)
208. #41×C₄₇	C₂×Q₈	semidirect
222. #10625354	C₂×Q₈	semidirect
227. Q₈×D₄₇	C₂×Q₈	semidirect
228. Q₈×D₄₇	#41	direct (N × H)
229. #10625352	C₂×Q₈	semidirect
230. D₄×D₄₇	C₂×Q₈	semidirect
231. #10625350	C₂×Q₈	semidirect
235. C₂×C₄×D₄₇	C₂×Q₈	semidirect
301. Q₈×C₄₇	C₂²×Q₈	semidirect
302. Q₈×C₄₇	C₂×#41	semidirect
303. D₄×C₄₇	C₂²×Q₈	semidirect
306. C₂×C₄×C₄₇	C₂²×Q₈	semidirect
313. C₂²⋊D₄₇	C₂²×Q₈	semidirect
316. C₂×Dic₄₇	C₂²×Q₈	semidirect
323. D₁₈₈	C₂²×Q₈	semidirect
333. C₄×D₄₇	C₂²×Q₈	semidirect
334. C₄×D₄₇	C₂²×Q₈	semidirect
339. Dic₉₄	C₂²×Q₈	semidirect
340. Dic₉₄	C₂×#41	semidirect
372. Q₈×#41	D₄₇	direct (N × H)
385. D₄₇	Q₈×#41	direct (N × H)
391. Q₈²	C₂×D₄₇	semidirect
397. #557	C₂×D₄₇	semidirect
406. #554	C₂×D₄₇	semidirect
412. D₄×Q₈	C₂×D₄₇	semidirect
422. #533	C₂×D₄₇	semidirect
450. C₂×C₄×Q₈	C₂×D₄₇	semidirect
456. C₄₇	C₂×Q₈×#41	semidirect
582. #41	Q₈×D₄₇	direct (N × H)
677. Q₈	C₂×Q₈×D₄₇	semidirect
678. Q₈	#41×D₄₇	direct (N × H)
681. D₄	C₂×Q₈×D₄₇	semidirect
705. C₂×C₄	C₂×Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10625354	2
#20256970	2
Q₈×#10625350	2
#41×Dic₉₄	2
#20256967	2
#20256966	2
Q₈×#10625352	2
Q₈²×D₄₇	2
#557×D₄₇	2
#554×D₄₇	2
D₄×Q₈×D₄₇	2
#533×D₄₇	2
C₄×#41×D₄₇	2
C₂×C₄×Q₈×D₄₇	2
Q₈×#41×C₄₇	2
C₂×Q₈×#41	47

Subgroups — Q8×#41×D47 #27123346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#41×D₄₇ #27123346