Subgroups — Q₈×(C₂×D₄₇)⋊C₈ #26232791

Order 12032.

1356 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244324	C₂	1	3	yes	maximal, complemented
4	#20244323	C₂	1	3	yes	maximal, complemented
5	#20243365	C₂	1	3	yes	maximal
6	C₄×(C₂×D₄₇)⋊C₈	C₂	1	3	yes	maximal
7	C₂×C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×D₄₇	C₄	1	1	yes	characteristic
9	C₂×Q₈×Dic₄₇	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₉₄	C₂²	1	3	yes	—
11	C₂×#13093989	C₄	1	3	yes	—
12	C₄×Q₈×D₄₇	—	2	4	no	—
13	C₄×Q₈×D₄₇	—	2	4	no	—
14	C₂×C₄⋊C₄×D₄₇	C₄	1	3	yes	—
15	C₂×C₄²×D₄₇	C₂²	1	3	yes	—
16	Q₈×C₄₇⋊C₈	—	2	4	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	3	yes	—
18	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	3	yes	—
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
21	#15688877	C₂²	1	3	yes	—
22	#15688877	C₂²	1	6	yes	—
23	#15688877	C₂²	1	3	yes	—
24	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₄₇	—	2	4	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	3	yes	—
27	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	—
28	C₂²×Dic₉₄	C₂×C₄	1	3	yes	—
29	C₂×Q₈×D₄₇	—	2	4	no	—
30	C₂×Q₈×D₄₇	—	2	4	no	—
31	C₂×Q₈×D₄₇	C₈	1	8	yes	complemented
32	C₂²×C₄×D₄₇	C₂×C₄	1	3	yes	—
33	C₂²×C₄×D₄₇	C₂×C₄	1	3	yes	—
34	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
35	C₂²×C₄₇⋊C₈	C₂³	1	3	yes	—
36	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
37	Q₈×Dic₄₇	—	2	4	no	—
38	C₄×Dic₉₄	—	2	6	no	—
39	C₄×Dic₉₄	—	2	6	no	—
40	#13093989	—	2	12	no	—
41	C₂×C₄⋊Dic₄₇	C₂×C₄	1	3	yes	—
42	C₂×Dic₄₇⋊C₄	C₂×C₄	1	6	yes	—
43	C₄⋊C₄×D₄₇	—	2	12	no	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	3	yes	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	3	yes	—
46	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
47	C₄²×D₄₇	—	2	6	no	—
48	C₄²×D₄₇	—	2	6	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	6	no	—
50	(C₂×D₄₇)⋊C₈	—	2	6	no	—
51	(C₂×D₄₇)⋊C₈	Q₈	1	4	yes	direct product factor
52	C₄×C₄₇⋊C₈	—	2	6	no	—
53	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₄×Q₈×C₄₇	D₄	1	4	yes	—
57	C₄×Q₈×C₄₇	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	3	yes	—
59	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
60	C₄⋊C₈×C₄₇	—	2	6	no	—
61	C₄×C₈×C₄₇	—	2	6	no	—
62	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
64	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	—
65	C₂×Q₈×C₄₇	M₁₆	1	4	yes	—
66	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
67	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
68	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
69	C₂²×Dic₄₇	C₂²×C₄	1	3	yes	—
70	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂²×Dic₄₇	C₂²×C₄	1	3	yes	—
72	Q₈×D₄₇	—	2	32	no	—
73	C₂×C₄×D₄₇	—	2	6	no	—
74	C₂×C₄×D₄₇	—	2	6	no	—
75	C₂×C₄×D₄₇	—	2	1	no	—
76	C₂×C₄×D₄₇	—	2	1	no	—
77	C₂×C₄×D₄₇	—	2	1	no	—
78	C₂×C₄×D₄₇	—	2	1	no	—
79	C₂×C₄×D₄₇	—	2	6	no	—
80	C₂×C₄×D₄₇	—	2	6	no	—
81	C₂×C₄×D₄₇	—	4	3	no	—
82	C₂×C₄×D₄₇	C₂×C₈	1	12	yes	—
83	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
84	C₂×C₄×D₄₇	#41	1	2	yes	—
85	C₂×Dic₉₄	—	2	6	no	—
86	C₂×Dic₉₄	—	2	6	no	—
87	C₂×Dic₉₄	C₂×C₈	1	12	yes	—
88	C₂×C₈×C₄₇	—	2	1	no	—
89	C₂×C₈×C₄₇	—	2	1	no	—
90	C₂×C₈×C₄₇	—	2	3	no	—
91	C₂×C₈×C₄₇	—	2	3	no	—
92	C₂×C₈×C₄₇	—	2	3	no	—
93	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	complemented
94	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	12	yes	—
95	C₄²×C₄₇	C₂×D₄	1	6	yes	—
96	C₄²×C₄₇	C₂×D₄	1	6	yes	—
97	C₄⋊Dic₄₇	—	2	6	no	—
98	Dic₄₇⋊C₄	—	2	12	no	—
99	C₄×Dic₄₇	—	2	6	no	—
100	C₄×Dic₄₇	—	2	6	no	—
101	C₄×Dic₄₇	—	2	3	no	—
102	C₄×Dic₄₇	—	2	3	no	—
103	C₂×C₄₇⋊C₈	—	2	1	no	—
104	C₂×C₄₇⋊C₈	—	2	1	no	—
105	C₂×C₄₇⋊C₈	—	2	3	no	—
106	C₂×C₄₇⋊C₈	—	2	3	no	—
107	C₂×C₄₇⋊C₈	—	2	3	no	—
108	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	complemented
109	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
110	C₂²×D₄₇	—	2	1	no	—
111	C₂²×D₄₇	—	2	1	no	—
112	C₂²×D₄₇	—	2	1	no	—
113	C₂²×D₄₇	—	2	1	no	—
114	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
115	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
116	C₂²×D₄₇	#131	1	2	yes	—
117	Q₈×C₄₇	C₂²⋊C₈	1	16	yes	complemented
118	C₂×C₄×C₄₇	—	2	3	no	—
119	C₂×C₄×C₄₇	—	2	3	no	—
120	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	6	yes	—
121	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	6	yes	—
122	C₂×C₄×C₄₇	C₂²×C₈	1	6	yes	—
123	C₂×C₄×C₄₇	C₂×M₁₆	1	6	yes	—
124	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
125	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
127	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
128	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
129	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
130	C₂×Dic₄₇	—	2	1	no	—
131	C₂×Dic₄₇	—	2	3	no	—
132	C₂×Dic₄₇	—	2	1	no	—
133	C₂×Dic₄₇	—	2	3	no	—
134	C₂×Dic₄₇	—	2	3	no	—
135	C₂×Dic₄₇	—	2	3	no	—
136	C₂×Dic₄₇	—	2	3	no	—
137	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
138	C₂×Dic₄₇	C₂²×C₈	1	6	yes	—
139	C₄×D₄₇	—	2	2	no	—
140	C₄×D₄₇	—	2	2	no	—
141	C₄×D₄₇	—	2	2	no	—
142	C₄×D₄₇	—	2	2	no	—
143	C₄×D₄₇	—	2	24	no	—
144	C₄×D₄₇	—	4	12	no	—
145	Dic₉₄	—	2	24	no	—
146	C₈×C₄₇	—	2	2	no	—
147	C₈×C₄₇	—	4	3	no	—
148	C₄₇⋊C₈	—	2	2	no	—
149	C₄₇⋊C₈	—	4	3	no	—
150	Q₈×C₂²⋊C₈	—	47	1	no	maximal, Sylow
151	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
153	C₂²×C₄₇	#519	1	1	yes	characteristic
154	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
155	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
156	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
157	C₂²×C₄₇	#568	1	1	yes	characteristic
158	C₂×D₄₇	—	2	2	no	—
159	C₂×D₄₇	—	2	2	no	—
160	C₂×D₄₇	—	2	2	no	—
161	C₂×D₄₇	—	2	2	no	—
162	C₂×D₄₇	—	2	2	no	—
163	C₂×D₄₇	—	2	2	no	—
164	C₂×D₄₇	C₈×Q₈	1	4	yes	complemented
165	C₄×C₄₇	—	2	6	no	—
166	C₄×C₄₇	C₂×C₂²⋊C₈	1	12	yes	—
167	C₄×C₄₇	#548	1	1	yes	characteristic
168	C₄×C₄₇	#548	1	1	yes	characteristic
169	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
170	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
171	Dic₄₇	—	2	2	no	—
172	Dic₄₇	—	2	6	no	—
173	Dic₄₇	—	4	3	no	—
174	C₂²×C₄×Q₈	—	47	1	no	—
175	C₂×C₈×Q₈	—	47	1	no	—
176	C₂×C₈×Q₈	D₄₇	1	1	yes	characteristic, complemented
177	#1984	—	47	3	no	—
178	#1984	—	47	3	no	—
179	#1797	—	47	3	no	—
180	C₄×C₂²⋊C₈	—	47	3	no	—
181	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
183	C₂×C₄₇	#2880	1	1	yes	characteristic
184	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
185	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
186	C₂×C₄₇	#2982	1	1	yes	characteristic
187	C₂×C₄₇	#2984	1	1	yes	characteristic
188	D₄₇	—	2	4	no	—
189	C₂³×Q₈	—	47	1	no	—
190	C₂×C₄×Q₈	—	47	1	no	—
191	C₂×C₄×Q₈	—	47	3	no	—
192	C₂×C₄×Q₈	—	47	3	no	—
193	C₂×C₄×Q₈	—	94	4	no	—
194	C₂×C₄×Q₈	—	94	4	no	—
195	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	—	47	3	no	—
197	C₂²×C₄²	—	47	3	no	—
198	C₈×Q₈	—	2	4	no	—
199	C₈×Q₈	—	94	4	no	—
200	C₂×C₄⋊C₈	—	47	3	no	—
201	C₂×C₄⋊C₈	C₂×D₄₇	1	3	yes	—
202	C₂×C₂²⋊C₈	—	47	1	no	—
203	C₂×C₂²⋊C₈	—	47	3	no	—
204	C₂×C₄×C₈	—	47	3	no	—
205	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	—
206	#336	—	47	6	no	—
207	#336	—	47	3	no	—
208	#336	—	47	3	no	—
209	C₄₇	Q₈×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
210	C₂²×Q₈	—	47	8	no	—
211	C₂²×Q₈	—	47	3	no	—
212	C₂²×Q₈	—	94	4	no	—
213	C₂²×Q₈	—	94	4	no	—
214	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
215	C₂³×C₄	—	47	3	no	—
216	C₂³×C₄	—	47	1	no	—
217	C₂³×C₄	—	47	3	no	—
218	C₂²×C₈	—	47	1	no	—
219	C₂²×C₈	—	47	3	no	—
220	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
221	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
222	C₄×Q₈	—	94	4	no	—
223	C₄×Q₈	—	94	12	no	—
224	C₄×Q₈	—	94	6	no	—
225	C₄×Q₈	—	94	6	no	—
226	C₄×Q₈	D₁₈₈	1	4	yes	—
227	C₄×Q₈	C₂²⋊D₄₇	1	4	yes	—
228	C₂×C₄⋊C₄	—	47	6	no	—
229	C₂×C₄⋊C₄	—	47	3	no	—
230	C₂×C₄⋊C₄	—	94	12	no	—
231	C₂×C₄⋊C₄	C₄×D₄₇	1	3	yes	—
232	C₂×C₄²	—	47	3	no	—
233	C₂×C₄²	—	47	3	no	—
234	C₂×C₄²	—	47	3	no	—
235	C₂×C₄²	—	94	6	no	—
236	C₂×C₄²	—	94	6	no	—
237	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
238	C₄⋊C₈	—	2	6	no	—
239	C₄⋊C₈	—	94	6	no	—
240	C₂²⋊C₈	—	47	4	no	—
241	C₂²⋊C₈	—	94	6	no	—
242	C₄×C₈	—	2	6	no	—
243	C₄×C₈	—	94	6	no	—
244	C₂⁴	—	47	1	no	—
245	C₂×Q₈	—	47	12	no	—
246	C₂×Q₈	—	94	32	no	—
247	C₂×Q₈	—	94	6	no	—
248	C₂×Q₈	—	94	6	no	—
249	C₂×Q₈	C₈×D₄₇	1	4	yes	—
250	C₂×Q₈	#10625324	1	4	yes	—
251	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	4	yes	—
252	C₂²×C₄	—	47	1	no	—
253	C₂²×C₄	—	47	3	no	—
254	C₂²×C₄	—	47	12	no	—
255	C₂²×C₄	—	47	2	no	—
256	C₂²×C₄	—	47	2	no	—
257	C₂²×C₄	—	47	3	no	—
258	C₂²×C₄	—	94	6	no	—
259	C₂²×C₄	—	94	6	no	—
260	C₂²×C₄	—	94	6	no	—
261	C₂²×C₄	—	94	1	no	—
262	C₂²×C₄	—	94	1	no	—
263	C₂²×C₄	—	94	1	no	—
264	C₂²×C₄	—	94	1	no	—
265	C₂²×C₄	—	94	6	no	—
266	C₂²×C₄	—	188	3	no	—
267	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
268	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
269	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	3	no	—
273	C₂×C₈	—	2	3	no	—
274	C₂×C₈	—	2	3	no	—
275	C₂×C₈	—	47	2	no	—
276	C₂×C₈	—	94	1	no	—
277	C₂×C₈	—	94	1	no	—
278	C₂×C₈	—	94	3	no	—
279	C₂×C₈	—	94	3	no	—
280	C₂×C₈	—	94	3	no	—
281	C₂×C₈	Q₈×D₄₇	1	2	yes	complemented
282	C₄⋊C₄	—	94	12	no	—
283	C₄⋊C₄	—	94	6	no	—
284	C₄⋊C₄	(C₂×D₄₇)⋊C₄	1	12	yes	—
285	C₄²	—	94	6	no	—
286	C₄²	—	94	6	no	—
287	C₄²	—	94	3	no	—
288	C₄²	—	94	3	no	—
289	C₄²	C₂×D₁₈₈	1	6	yes	—
290	C₄²	C₂×C₂²⋊D₄₇	1	6	yes	—
291	C₂³	—	47	2	no	—
292	C₂³	—	47	2	no	—
293	C₂³	—	47	2	no	—
294	C₂³	—	94	1	no	—
295	C₂³	—	94	1	no	—
296	C₂³	—	94	1	no	—
297	C₂³	—	94	1	no	—
298	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
299	Q₈	—	94	24	no	—
300	Q₈	(C₂×D₄₇)⋊C₈	1	16	yes	direct product factor
301	C₂×C₄	—	2	3	no	—
302	C₂×C₄	—	2	3	no	—
303	C₂×C₄	—	47	2	no	—
304	C₂×C₄	—	47	6	no	—
305	C₂×C₄	—	94	1	no	—
306	C₂×C₄	—	94	3	no	—
307	C₂×C₄	—	94	1	no	—
308	C₂×C₄	—	94	3	no	—
309	C₂×C₄	—	94	2	no	—
310	C₂×C₄	—	94	2	no	—
311	C₂×C₄	—	94	2	no	—
312	C₂×C₄	—	94	2	no	—
313	C₂×C₄	—	94	24	no	—
314	C₂×C₄	—	94	3	no	—
315	C₂×C₄	—	94	3	no	—
316	C₂×C₄	—	94	3	no	—
317	C₂×C₄	—	188	12	no	—
318	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	6	yes	—
319	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	6	yes	—
320	C₂×C₄	C₂×C₈×D₄₇	1	6	yes	—
321	C₂×C₄	C₂×#10625324	1	6	yes	—
322	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
324	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
325	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
326	C₂×C₄	#13094071	1	1	yes	characteristic
327	C₂×C₄	#13094072	1	1	yes	characteristic
328	C₈	—	2	2	no	—
329	C₈	—	4	3	no	—
330	C₈	—	94	2	no	—
331	C₈	—	188	3	no	—
332	C₂²	—	47	4	no	—
333	C₂²	—	94	2	no	—
334	C₂²	—	94	2	no	—
335	C₂²	—	94	2	no	—
336	C₂²	—	94	2	no	—
337	C₂²	—	94	2	no	—
338	C₂²	—	94	2	no	—
339	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
340	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
341	C₂²	#15689599	1	1	yes	characteristic
342	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
343	C₂²	C₂²×#10625324	1	1	yes	characteristic
344	C₂²	#131×D₄₇	1	1	yes	characteristic
345	C₂²	#15689888	1	1	yes	characteristic
346	C₄	—	2	6	no	—
347	C₄	—	94	6	no	—
348	C₄	—	94	2	no	—
349	C₄	—	188	3	no	—
350	C₄	C₂×(C₂×D₄₇)⋊C₈	1	12	yes	—
351	C₄	#15689780	1	1	yes	characteristic
352	C₄	#15689785	1	1	yes	characteristic
353	C₄	Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
355	C₂	—	94	4	no	—
356	C₂	Q₈×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
357	C₂	C₂²×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
358	C₂	#20251835	1	1	yes	characteristic
359	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
360	C₂	Q₈×#10625324	1	1	yes	characteristic
361	C₂	#20252467	1	1	yes	characteristic
362	C₂	#20252476	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₂×C₈×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×Q₈	D₄₇
hypocenter	C₄₇	Q₈×C₂²⋊C₈
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
3. #20244324	C₂	semidirect
4. #20244323	C₂	semidirect
7. C₂×C₈×Q₈×C₄₇	C₂	semidirect
31. C₂×Q₈×D₄₇	C₈	semidirect
51. (C₂×D₄₇)⋊C₈	Q₈	direct (N × H)
93. C₂×C₈×C₄₇	C₂×Q₈	semidirect
108. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
117. Q₈×C₄₇	C₂²⋊C₈	semidirect
164. C₂×D₄₇	C₈×Q₈	semidirect
176. C₂×C₈×Q₈	D₄₇	semidirect
209. C₄₇	Q₈×C₂²⋊C₈	semidirect
281. C₂×C₈	Q₈×D₄₇	semidirect
300. Q₈	(C₂×D₄₇)⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₈×D₄₇	2
C₂×Q₈×C₄₇⋊C₈	2
#20244324	2
#20244323	2
#20243365	2
C₄×(C₂×D₄₇)⋊C₈	2
C₂×C₈×Q₈×C₄₇	2
Q₈×C₂²⋊C₈	47

Subgroups — Q8×(C2×D47)⋊C8 #26232791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×(C₂×D₄₇)⋊C₈ #26232791