Subgroups — C₂×Q₈×#10625334 #27096690

Order 12032.

2286 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#10625334	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689526	C₂	1	3	yes	maximal, complemented
4	C₂×#15689403	C₂	1	3	yes	maximal, complemented
5	C₂×#15689400	C₂	1	3	yes	maximal, complemented
6	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×#10625334	C₂	1	3	yes	maximal
8	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×D₄₇	—	2	1	no	—
10	C₂²×#10625334	C₂²	1	1	yes	characteristic
11	Q₈×D₁₈₈	—	2	4	no	—
12	Q₈×D₁₈₈	C₂²	1	8	yes	complemented
13	C₂×#13094024	C₂²	1	3	yes	—
14	C₂×#13094004	—	2	3	no	—
15	C₂×C₄×D₁₈₈	C₂²	1	3	yes	—
16	#15689526	C₂²	1	24	yes	complemented
17	#15689403	C₂²	1	24	yes	complemented
18	#15689400	C₂²	1	24	yes	complemented
19	Q₈×C₄₇⋊C₈	C₂²	1	8	yes	complemented
20	C₄×#10625334	C₂²	1	24	yes	—
21	C₂×#13093957	C₂²	1	3	yes	—
22	C₂×#13093957	C₂²	1	6	yes	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	3	yes	—
24	C₂×#13093945	C₂²	1	3	yes	—
25	C₂×#13093944	C₂²	1	3	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
27	C₂³×Q₈×C₄₇	—	2	1	no	—
28	D₄×Q₈×C₄₇	—	2	4	no	—
29	D₄×Q₈×C₄₇	C₂²	1	8	yes	complemented
30	C₂×C₄⋊Q₈×C₄₇	C₂²	1	3	yes	—
31	C₂×C₂²⋊Q₈×C₄₇	—	2	3	no	—
32	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₇	C₂²	1	3	yes	—
34	C₂²×Dic₉₄	—	2	3	no	—
35	C₂×Q₈×D₄₇	—	2	8	no	—
36	C₂×Q₈×D₄₇	—	4	8	no	—
37	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
38	C₂²×C₄×D₄₇	—	2	3	no	—
39	C₂×#10625334	Q₈	1	8	yes	direct product factor
40	C₂×#10625334	C₂³	1	4	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	3	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	#13094024	—	2	6	no	—
44	#13094024	C₂³	1	12	yes	—
45	#13094004	—	2	24	no	—
46	C₄×D₁₈₈	—	2	6	no	—
47	C₄×D₁₈₈	C₂³	1	12	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	3	no	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
50	C₂×(C₂×D₄₇)⋊C₄	—	2	3	no	—
51	#13093957	C₂³	1	12	yes	—
52	#13093957	C₂³	1	24	yes	—
53	C₄⋊(C₄₇⋊C₈)	C₂³	1	12	yes	—
54	#13093945	C₂³	1	12	yes	—
55	#13093944	C₂³	1	12	yes	—
56	C₄×C₄₇⋊C₈	C₂³	1	12	yes	—
57	C₂²×Q₈×C₄₇	—	2	8	no	—
58	C₂²×Q₈×C₄₇	—	2	3	no	—
59	C₂²×Q₈×C₄₇	—	4	8	no	—
60	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	—	2	3	no	—
63	C₄⋊Q₈×C₄₇	—	2	6	no	—
64	C₄⋊Q₈×C₄₇	C₂³	1	12	yes	—
65	C₂²⋊Q₈×C₄₇	—	2	24	no	—
66	C₄×Q₈×C₄₇	D₄	1	4	yes	—
67	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
68	C₄×D₄×C₄₇	—	2	6	no	—
69	C₄×D₄×C₄₇	C₂³	1	12	yes	—
70	C₂×C₄⋊C₄×C₄₇	—	2	3	no	—
71	C₂×C₄⋊C₄×C₄₇	D₄	1	3	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	3	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	3	no	—
74	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
75	C₂⁴×C₄₇	—	2	1	no	—
76	C₂³×D₄₇	—	2	1	no	—
77	C₂×Q₈×C₄₇	—	2	12	no	—
78	C₂×Q₈×C₄₇	—	4	32	no	—
79	C₂×Q₈×C₄₇	—	4	12	no	—
80	C₂×Q₈×C₄₇	D₈	1	8	yes	complemented
81	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
82	C₂×D₄×C₄₇	—	2	1	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	C₂×Q₈	1	4	yes	complemented
85	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
86	C₂²×C₄×C₄₇	—	2	3	no	—
87	C₂²×C₄×C₄₇	—	2	12	no	—
88	C₂²×C₄×C₄₇	—	4	12	no	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
91	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₇	—	2	3	no	—
93	Q₈×D₄₇	—	4	32	no	—
94	C₂×D₁₈₈	—	2	1	no	—
95	C₂×D₁₈₈	—	2	2	no	—
96	C₂×D₁₈₈	C₂×Q₈	1	4	yes	complemented
97	C₂×D₁₈₈	C₂⁴	1	2	yes	—
98	C₂×C₄×D₄₇	—	2	12	no	—
99	C₂×C₄×D₄₇	—	4	12	no	—
100	C₂×Dic₉₄	—	2	12	no	—
101	C₂×Dic₉₄	—	4	12	no	—
102	C₄⋊C₄×C₄₇	—	2	12	no	—
103	C₄⋊C₄×C₄₇	—	2	3	no	—
104	C₄⋊C₄×C₄₇	C₂×D₄	1	12	yes	—
105	C₄⋊C₄×C₄₇	C₂⁴	1	6	yes	—
106	C₂²⋊C₄×C₄₇	—	2	12	no	—
107	C₄²×C₄₇	C₂×D₄	1	6	yes	—
108	C₄²×C₄₇	C₂⁴	1	6	yes	—
109	#10625334	C₂×Q₈	1	16	yes	direct product factor
110	(C₂×D₄₇)⋊C₄	—	2	12	no	—
111	C₄⋊Dic₄₇	—	2	12	no	—
112	C₄⋊Dic₄₇	—	2	3	no	—
113	C₄⋊Dic₄₇	C₂⁴	1	6	yes	—
114	C₂×C₄₇⋊C₈	—	2	6	no	—
115	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
116	C₂×C₄₇⋊C₈	C₂⁴	1	6	yes	—
117	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	2	no	—
122	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
123	C₂²×D₄₇	—	2	4	no	—
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	4	2	no	—
126	C₂²×D₄₇	—	4	2	no	—
127	Q₈×C₄₇	—	4	24	no	—
128	Q₈×C₄₇	C₂×D₈	1	16	yes	complemented
129	D₄×C₄₇	—	2	4	no	—
130	D₄×C₄₇	—	2	2	no	—
131	D₄×C₄₇	C₂²×Q₈	1	4	yes	complemented
132	C₂×C₄×C₄₇	—	2	6	no	—
133	C₂×C₄×C₄₇	—	2	6	no	—
134	C₂×C₄×C₄₇	—	4	6	no	—
135	C₂×C₄×C₄₇	—	4	24	no	—
136	C₂×C₄×C₄₇	C₂×D₈	1	12	yes	—
137	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
138	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
140	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
141	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
142	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
143	C₂×Dic₄₇	—	2	6	no	—
144	C₂×Dic₄₇	—	4	6	no	—
145	D₁₈₈	—	2	4	no	—
146	D₁₈₈	—	2	2	no	—
147	D₁₈₈	C₂²×Q₈	1	4	yes	complemented
148	C₄×D₄₇	—	4	24	no	—
149	Dic₉₄	—	4	24	no	—
150	C₄₇⋊C₈	—	2	6	no	—
151	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	complemented
152	C₂×Q₈×D₈	—	47	1	no	maximal, Sylow
153	C₂²×C₄₇	—	2	4	no	—
154	C₂²×C₄₇	—	4	8	no	—
155	C₂²×C₄₇	—	4	2	no	—
156	C₂²×C₄₇	—	4	2	no	—
157	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
158	C₂²×C₄₇	C₂²×D₈	1	2	yes	—
159	C₂²×C₄₇	#578	1	2	yes	—
160	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
161	C₂×D₄₇	—	2	4	no	—
162	C₂×D₄₇	—	4	8	no	—
163	C₂×D₄₇	—	4	2	no	—
164	C₂×D₄₇	—	4	2	no	—
165	C₄×C₄₇	—	2	6	no	—
166	C₄×C₄₇	—	4	6	no	—
167	C₄×C₄₇	D₄×Q₈	1	2	yes	—
168	C₄×C₄₇	C₂²×D₈	1	12	yes	—
169	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
170	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
171	Dic₄₇	—	4	6	no	—
172	C₂×D₄×Q₈	—	47	1	no	—
173	C₂×D₄×Q₈	D₄₇	1	1	yes	characteristic, complemented
174	Q₈×D₈	—	47	16	no	—
175	C₂×#500	—	47	3	no	—
176	C₂×#474	—	47	3	no	—
177	C₂×#474	—	47	3	no	—
178	C₂×C₈×Q₈	—	47	1	no	—
179	C₂×C₄×D₈	—	47	3	no	—
180	C₂×C₄₇	—	4	4	no	—
181	C₂×C₄₇	Q₈×D₈	1	4	yes	complemented
182	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
183	C₂×C₄₇	C₂³×D₈	1	1	yes	characteristic
184	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
185	D₄₇	—	4	4	no	—
186	C₂³×Q₈	—	2	1	no	—
187	C₂³×Q₈	—	94	1	no	—
188	C₂²×D₈	—	47	1	no	—
189	D₄×Q₈	—	2	4	no	—
190	D₄×Q₈	—	47	8	no	—
191	D₄×Q₈	—	94	4	no	—
192	D₄×Q₈	C₂×D₄₇	1	8	yes	complemented
193	C₂×C₄⋊Q₈	—	47	3	no	—
194	C₂×C₄⋊Q₈	C₂×D₄₇	1	3	yes	—
195	C₂×C₂²⋊Q₈	—	2	3	no	—
196	C₂×C₂²⋊Q₈	—	94	3	no	—
197	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
198	C₂×C₄×D₄	—	47	3	no	—
199	C₂×C₄×D₄	C₂×D₄₇	1	3	yes	—
200	#500	—	47	24	no	—
201	#474	—	47	24	no	—
202	#474	—	47	24	no	—
203	C₈×Q₈	—	47	8	no	—
204	C₄×D₈	—	47	24	no	—
205	C₂×#107	—	47	3	no	—
206	C₂×#107	—	47	6	no	—
207	C₂×C₄⋊C₈	—	47	3	no	—
208	C₂×#102	—	47	3	no	—
209	C₂×#102	—	47	3	no	—
210	C₂×C₄×C₈	—	47	3	no	—
211	C₄₇	C₂×Q₈×D₈	1	1	yes	characteristic, complemented, Sylow
212	C₂²×Q₈	—	2	8	no	—
213	C₂²×Q₈	—	2	3	no	—
214	C₂²×Q₈	—	4	8	no	—
215	C₂²×Q₈	—	94	8	no	—
216	C₂²×Q₈	—	94	3	no	—
217	C₂²×Q₈	—	188	8	no	—
218	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
219	C₂²×D₄	—	47	1	no	—
220	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
221	C₂³×C₄	—	2	3	no	—
222	C₂³×C₄	—	94	3	no	—
223	C₂×D₈	—	47	8	no	—
224	C₂×D₈	—	47	4	no	—
225	C₂²×C₈	—	47	1	no	—
226	C₂²×C₈	—	47	3	no	—
227	C₄⋊Q₈	—	2	6	no	—
228	C₄⋊Q₈	—	47	12	no	—
229	C₄⋊Q₈	—	94	6	no	—
230	C₄⋊Q₈	C₂²×D₄₇	1	12	yes	—
231	C₂²⋊Q₈	—	2	24	no	—
232	C₂²⋊Q₈	—	94	24	no	—
233	C₄×Q₈	C₂²⋊D₄₇	1	4	yes	—
234	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
235	C₄×D₄	—	2	6	no	—
236	C₄×D₄	—	47	12	no	—
237	C₄×D₄	—	94	6	no	—
238	C₄×D₄	C₂²×D₄₇	1	12	yes	—
239	C₂×C₄⋊C₄	—	2	3	no	—
240	C₂×C₄⋊C₄	—	47	3	no	—
241	C₂×C₄⋊C₄	—	94	3	no	—
242	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	3	yes	—
243	C₂×C₄⋊C₄	C₂²×D₄₇	1	3	yes	—
244	C₂×C₂²⋊C₄	—	2	3	no	—
245	C₂×C₂²⋊C₄	—	94	3	no	—
246	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
247	#107	—	47	12	no	—
248	#107	—	47	24	no	—
249	C₄⋊C₈	—	47	12	no	—
250	#102	—	47	12	no	—
251	#102	—	47	12	no	—
252	C₄×C₈	—	47	12	no	—
253	C₂⁴	—	2	1	no	—
254	C₂⁴	—	94	1	no	—
255	C₂×Q₈	—	2	12	no	—
256	C₂×Q₈	—	4	32	no	—
257	C₂×Q₈	—	4	12	no	—
258	C₂×Q₈	—	94	12	no	—
259	C₂×Q₈	—	188	32	no	—
260	C₂×Q₈	—	188	12	no	—
261	C₂×Q₈	#10625334	1	8	yes	direct product factor
262	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
263	C₂×D₄	—	2	1	no	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	47	4	no	—
266	C₂×D₄	—	47	2	no	—
267	C₂×D₄	—	94	1	no	—
268	C₂×D₄	—	94	2	no	—
269	C₂×D₄	Q₈×D₄₇	1	4	yes	complemented
270	C₂×D₄	C₂³×D₄₇	1	2	yes	—
271	C₂²×C₄	—	2	3	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	4	12	no	—
274	C₂²×C₄	—	94	3	no	—
275	C₂²×C₄	—	94	12	no	—
276	C₂²×C₄	—	188	12	no	—
277	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
278	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
279	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
280	D₈	—	47	16	no	—
281	C₂×C₈	—	47	4	no	—
282	C₂×C₈	—	47	2	no	—
283	C₂×C₈	—	47	6	no	—
284	C₂×C₈	—	94	6	no	—
285	C₄⋊C₄	—	2	12	no	—
286	C₄⋊C₄	—	2	3	no	—
287	C₄⋊C₄	—	47	6	no	—
288	C₄⋊C₄	—	94	3	no	—
289	C₄⋊C₄	—	94	12	no	—
290	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
291	C₄⋊C₄	C₂³×D₄₇	1	6	yes	—
292	C₂²⋊C₄	—	2	12	no	—
293	C₂²⋊C₄	—	94	12	no	—
294	C₄²	C₂×C₂²⋊D₄₇	1	6	yes	—
295	C₄²	C₂³×D₄₇	1	6	yes	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	4	2	no	—
299	C₂³	—	4	2	no	—
300	C₂³	—	94	4	no	—
301	C₂³	—	94	2	no	—
302	C₂³	—	188	2	no	—
303	C₂³	—	188	2	no	—
304	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
305	Q₈	—	4	24	no	—
306	Q₈	—	188	24	no	—
307	Q₈	C₂×#10625334	1	16	yes	direct product factor
308	D₄	—	2	4	no	—
309	D₄	—	2	2	no	—
310	D₄	—	47	4	no	—
311	D₄	—	94	4	no	—
312	D₄	—	94	2	no	—
313	D₄	C₂×Q₈×D₄₇	1	4	yes	complemented
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	6	no	—
316	C₂×C₄	—	4	6	no	—
317	C₂×C₄	—	4	24	no	—
318	C₂×C₄	—	94	6	no	—
319	C₂×C₄	—	188	6	no	—
320	C₂×C₄	—	188	24	no	—
321	C₂×C₄	C₂×#10625334	1	12	yes	—
322	C₂×C₄	C₂²×C₂²⋊D₄₇	1	6	yes	—
323	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₂²⋊D₄₇	1	6	yes	—
325	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
326	C₂×C₄	#13094072	1	2	yes	—
327	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
328	C₈	—	47	4	no	—
329	C₈	—	94	6	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	8	no	—
334	C₂²	—	94	4	no	—
335	C₂²	—	188	2	no	—
336	C₂²	—	188	2	no	—
337	C₂²	—	188	8	no	—
338	C₂²	Q₈×C₂²⋊D₄₇	1	2	yes	—
339	C₂²	C₂²×#10625334	1	2	yes	—
340	C₂²	#15689938	1	2	yes	—
341	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₄	—	2	6	no	—
343	C₄	—	4	6	no	—
344	C₄	—	188	6	no	—
345	C₄	Q₈×C₂²⋊D₄₇	1	2	yes	—
346	C₄	C₂²×#10625334	1	12	yes	—
347	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
348	C₄	C₂×#13094072	1	1	yes	characteristic
349	C₂	—	4	4	no	—
350	C₂	—	188	4	no	—
351	C₂	Q₈×#10625334	1	4	yes	direct product factor
352	C₂	C₂×Q₈×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂	C₂³×#10625334	1	1	yes	characteristic
354	C₂	C₂×#15689938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×D₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×#10625334	C₂²
hypercenter	C₂×D₄×Q₈	D₄₇
hypocenter	C₄₇	C₂×Q₈×D₈
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×D₁₈₈	C₂	semidirect
2. Q₈×#10625334	C₂	direct (N × H)
3. C₂×#15689526	C₂	semidirect
4. C₂×#15689403	C₂	semidirect
5. C₂×#15689400	C₂	semidirect
6. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
8. C₂×D₄×Q₈×C₄₇	C₂	semidirect
12. Q₈×D₁₈₈	C₂²	semidirect
16. #15689526	C₂²	semidirect
17. #15689403	C₂²	semidirect
18. #15689400	C₂²	semidirect
19. Q₈×C₄₇⋊C₈	C₂²	semidirect
29. D₄×Q₈×C₄₇	C₂²	semidirect
39. C₂×#10625334	Q₈	direct (N × H)
80. C₂×Q₈×C₄₇	D₈	semidirect
84. C₂×D₄×C₄₇	C₂×Q₈	semidirect
96. C₂×D₁₈₈	C₂×Q₈	semidirect
109. #10625334	C₂×Q₈	direct (N × H)
115. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
128. Q₈×C₄₇	C₂×D₈	semidirect
131. D₄×C₄₇	C₂²×Q₈	semidirect
147. D₁₈₈	C₂²×Q₈	semidirect
151. C₄₇⋊C₈	C₂²×Q₈	semidirect
173. C₂×D₄×Q₈	D₄₇	semidirect
181. C₂×C₄₇	Q₈×D₈	semidirect
192. D₄×Q₈	C₂×D₄₇	semidirect
211. C₄₇	C₂×Q₈×D₈	semidirect
261. C₂×Q₈	#10625334	direct (N × H)
269. C₂×D₄	Q₈×D₄₇	semidirect
307. Q₈	C₂×#10625334	direct (N × H)
313. D₄	C₂×Q₈×D₄₇	semidirect
351. C₂	Q₈×#10625334	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×Q₈×D₁₈₈	2
Q₈×#10625334	2
C₂×#15689526	2
C₂×#15689403	2
C₂×#15689400	2
C₂×Q₈×C₄₇⋊C₈	2
C₂×C₄×#10625334	2
C₂×D₄×Q₈×C₄₇	2
C₂×Q₈×D₈	47

Subgroups — C2×Q8×#10625334 #27096690

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×#10625334 #27096690