Subgroups — M₃₂×D₁₈₈ #26369493

Order 12032.

734 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×M₃₂×D₄₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20245221	C₂	1	2	yes	maximal, complemented
4	#20245215	C₂	1	4	yes	maximal, complemented
5	C₁₆×D₁₈₈	C₂	1	2	yes	maximal, complemented
6	#20245144	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244998	C₂	1	2	yes	maximal, complemented
8	C₄×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
10	C₂×C₄×D₁₈₈	C₄	1	1	yes	characteristic
11	C₂×#13093964	C₂²	1	2	yes	—
12	C₂×#13093963	C₂²	1	4	yes	complemented
13	M₃₂×D₄₇	—	2	8	no	—
14	C₂×C₁₆×D₄₇	C₂²	1	4	yes	complemented
15	C₈×D₁₈₈	C₄	1	2	yes	—
16	C₈×D₁₈₈	C₄	1	1	yes	characteristic
17	C₈×D₁₈₈	C₄	1	1	yes	characteristic
18	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
19	C₈×D₁₈₈	C₂²	1	2	yes	—
20	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
22	C₂×(C₂×D₄₇)⋊C₈	C₄	1	2	yes	—
23	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
24	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
25	(C₂×D₄₇)⋊C₁₆	C₂²	1	4	yes	complemented
26	(C₂×D₄₇)⋊C₁₆	C₂²	1	4	yes	complemented
27	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#346	C₂²	1	2	yes	complemented
31	C₄×C₁₆×C₄₇	C₂²	1	2	yes	complemented
32	C₂²×D₁₈₈	C₈	1	1	yes	characteristic
33	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
34	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
35	C₂×C₈×D₄₇	—	2	4	no	—
36	C₂×C₈×D₄₇	—	2	4	no	—
37	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₄₇	C₂³	1	2	yes	—
40	C₂×C₈×D₄₇	C₂³	1	2	yes	—
41	C₄×D₁₈₈	C₈	1	2	yes	—
42	C₄×D₁₈₈	C₈	1	1	yes	characteristic
43	C₄×D₁₈₈	C₈	1	1	yes	characteristic
44	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
45	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
46	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₄₇	C₈	1	1	yes	characteristic
48	C₂×(C₂×D₄₇)⋊C₄	C₈	1	2	yes	—
49	#13093964	—	2	4	no	—
50	#13093963	—	2	8	no	—
51	C₂×C₄₇⋊C₁₆	C₂³	1	4	yes	—
52	C₁₆×D₄₇	—	2	8	no	—
53	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
54	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
56	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
57	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
58	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
59	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
63	M₃₂×C₄₇	—	2	2	no	—
64	M₃₂×C₄₇	D₄	1	4	yes	complemented
65	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
66	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
67	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂³×D₄₇	C₂×C₈	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
76	C₂×D₁₈₈	—	2	4	no	—
77	C₂×D₁₈₈	C₂×C₈	1	2	yes	—
78	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
79	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
80	C₂×C₄×D₄₇	—	2	4	no	—
81	C₂×C₄×D₄₇	—	2	4	no	—
82	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
83	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
84	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
85	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
86	C₂×C₈×C₄₇	—	2	2	no	—
87	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
91	C₂×C₈×C₄₇	#41	1	2	yes	—
92	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₄²×C₄₇	C₂×C₈	1	1	yes	characteristic
94	C₄²×C₄₇	C₂×C₈	1	1	yes	characteristic
95	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
98	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
99	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
100	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
101	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	—
102	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
103	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄₇⋊C₈	—	2	4	no	—
105	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
106	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
107	C₈×D₄₇	—	2	4	no	—
108	C₈×D₄₇	—	2	4	no	—
109	C₈×D₄₇	—	2	2	no	—
110	C₈×D₄₇	—	2	2	no	—
111	C₈×D₄₇	—	2	2	no	—
112	C₈×D₄₇	—	2	2	no	—
113	C₁₆×C₄₇	—	2	2	no	—
114	C₁₆×C₄₇	C₂×D₄	1	4	yes	complemented
115	C₄₇⋊C₁₆	—	2	4	no	—
116	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
117	C₂²×D₄₇	—	2	4	no	—
118	C₂²×D₄₇	—	2	4	no	—
119	C₂²×D₄₇	—	4	2	no	—
120	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
121	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	4	1	no	—
124	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
126	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#131	1	2	yes	—
131	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
132	C₂×Dic₄₇	—	2	4	no	—
133	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
134	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
135	D₁₈₈	—	2	4	no	—
136	D₁₈₈	—	2	2	no	—
137	D₁₈₈	M₃₂	1	4	yes	direct product factor
138	C₄×D₄₇	—	2	2	no	—
139	C₄×D₄₇	—	2	2	no	—
140	C₄×D₄₇	—	2	2	no	—
141	C₄×D₄₇	—	2	2	no	—
142	C₄×D₄₇	—	2	4	no	—
143	C₄×D₄₇	—	2	4	no	—
144	C₈×C₄₇	—	2	1	no	—
145	C₈×C₄₇	—	2	1	no	—
146	C₈×C₄₇	C₄×D₄	1	2	yes	—
147	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₄₇⋊C₈	—	2	2	no	—
150	C₄₇⋊C₈	—	2	2	no	—
151	D₄×M₃₂	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	—	2	1	no	—
153	C₂²×C₄₇	—	2	1	no	—
154	C₂²×C₄₇	C₈×D₄	1	2	yes	—
155	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
156	C₂×D₄₇	—	2	2	no	—
157	C₂×D₄₇	—	2	2	no	—
158	C₂×D₄₇	—	2	2	no	—
159	C₂×D₄₇	—	2	2	no	—
160	C₂×D₄₇	—	2	2	no	—
161	C₂×D₄₇	—	4	8	no	—
162	C₂×D₄₇	C₂×M₃₂	1	4	yes	complemented
163	C₄×C₄₇	—	2	1	no	—
164	C₄×C₄₇	—	2	1	no	—
165	C₄×C₄₇	—	2	1	no	—
166	C₄×C₄₇	C₈×D₄	1	2	yes	—
167	C₄×C₄₇	C₂×M₃₂	1	2	yes	complemented
168	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
170	Dic₄₇	—	2	2	no	—
171	Dic₄₇	—	2	2	no	—
172	C₂²×M₃₂	—	47	2	no	—
173	C₂×C₈×D₄	—	47	1	no	—
174	#2169	—	47	2	no	—
175	#2168	—	47	4	no	—
176	D₄×C₁₆	—	47	2	no	—
177	#2150	—	47	1	no	—
178	#2112	—	47	2	no	—
179	C₄×M₃₂	D₄₇	1	1	yes	characteristic, complemented
180	C₂×C₄₇	—	2	2	no	—
181	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
182	C₂×C₄₇	C₂²×M₃₂	1	1	yes	characteristic
183	C₂×C₄₇	#3407	1	1	yes	characteristic
184	D₄₇	—	2	4	no	—
185	D₄₇	—	4	2	no	—
186	C₂³×C₈	—	47	2	no	—
187	C₂×C₄×D₄	—	47	1	no	—
188	C₂×M₃₂	—	47	2	no	—
189	C₂×M₃₂	—	47	4	no	—
190	C₂×M₃₂	—	94	8	no	—
191	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
192	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
193	C₂²×C₁₆	—	47	4	no	—
194	C₈×D₄	—	47	2	no	—
195	C₈×D₄	—	47	1	no	—
196	C₈×D₄	—	47	1	no	—
197	C₈×D₄	—	47	1	no	—
198	C₈×D₄	—	47	2	no	—
199	C₈×D₄	—	47	1	no	—
200	C₂×C₄⋊C₈	—	47	1	no	—
201	C₂×C₂²⋊C₈	—	47	2	no	—
202	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
203	C₄⋊C₁₆	—	47	2	no	—
204	C₄⋊C₁₆	—	47	2	no	—
205	C₂²⋊C₁₆	—	47	4	no	—
206	C₂²⋊C₁₆	—	47	4	no	—
207	#346	C₂×D₄₇	1	2	yes	complemented
208	C₄×C₁₆	C₂×D₄₇	1	2	yes	complemented
209	C₄₇	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
210	C₂²×D₄	—	47	1	no	—
211	C₂³×C₄	—	47	2	no	—
212	C₂²×C₈	—	47	2	no	—
213	C₂²×C₈	—	47	2	no	—
214	C₂²×C₈	—	47	2	no	—
215	C₂²×C₈	—	47	2	no	—
216	C₂²×C₈	—	47	2	no	—
217	C₂²×C₈	—	94	4	no	—
218	C₂²×C₈	—	94	4	no	—
219	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
220	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
221	C₄×D₄	—	47	1	no	—
222	C₄×D₄	—	47	2	no	—
223	C₄×D₄	—	47	1	no	—
224	C₄×D₄	—	47	1	no	—
225	C₄×D₄	—	47	2	no	—
226	C₄×D₄	—	47	1	no	—
227	C₂×C₄⋊C₄	—	47	1	no	—
228	C₂×C₂²⋊C₄	—	47	2	no	—
229	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
230	M₃₂	—	2	2	no	—
231	M₃₂	—	94	4	no	—
232	M₃₂	—	94	8	no	—
233	M₃₂	D₁₈₈	1	4	yes	direct product factor
234	C₂×C₁₆	—	47	4	no	—
235	C₂×C₁₆	—	94	8	no	—
236	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
237	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
238	C₄⋊C₈	—	47	1	no	—
239	C₄⋊C₈	—	47	2	no	—
240	C₄⋊C₈	—	47	1	no	—
241	C₂²⋊C₈	—	47	2	no	—
242	C₂²⋊C₈	—	47	2	no	—
243	C₂²⋊C₈	—	47	2	no	—
244	C₂²⋊C₈	—	47	2	no	—
245	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
246	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
247	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
249	C₂⁴	—	47	2	no	—
250	C₂×D₄	—	47	1	no	—
251	C₂×D₄	—	47	2	no	—
252	C₂×D₄	—	47	1	no	—
253	C₂×D₄	—	94	4	no	—
254	C₂²×C₄	—	47	2	no	—
255	C₂²×C₄	—	47	2	no	—
256	C₂²×C₄	—	47	2	no	—
257	C₂²×C₄	—	47	2	no	—
258	C₂²×C₄	—	47	2	no	—
259	C₂²×C₄	—	94	4	no	—
260	C₂²×C₄	—	94	4	no	—
261	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
262	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	47	2	no	—
266	C₂×C₈	—	47	2	no	—
267	C₂×C₈	—	94	4	no	—
268	C₂×C₈	—	94	4	no	—
269	C₂×C₈	—	94	4	no	—
270	C₂×C₈	—	94	2	no	—
271	C₂×C₈	—	94	2	no	—
272	C₂×C₈	—	94	2	no	—
273	C₂×C₈	—	94	2	no	—
274	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
275	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
276	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
277	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
278	C₂×C₈	#10625350	1	2	yes	—
279	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
280	C₄⋊C₄	—	47	2	no	—
281	C₄⋊C₄	—	47	1	no	—
282	C₄⋊C₄	—	47	1	no	—
283	C₂²⋊C₄	—	47	2	no	—
284	C₂²⋊C₄	—	47	2	no	—
285	C₂²⋊C₄	—	47	2	no	—
286	C₂²⋊C₄	—	47	2	no	—
287	C₄²	C₈×D₄₇	1	1	yes	characteristic
288	C₄²	C₈×D₄₇	1	1	yes	characteristic
289	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
291	C₁₆	—	2	2	no	—
292	C₁₆	—	94	4	no	—
293	C₁₆	C₂×D₁₈₈	1	4	yes	complemented
294	C₂³	—	47	2	no	—
295	C₂³	—	47	2	no	—
296	C₂³	—	94	4	no	—
297	C₂³	—	94	4	no	—
298	C₂³	—	188	2	no	—
299	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
300	D₄	—	47	4	no	—
301	D₄	—	94	4	no	—
302	D₄	—	94	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	4	1	no	—
305	C₂×C₄	—	47	2	no	—
306	C₂×C₄	—	47	2	no	—
307	C₂×C₄	—	94	4	no	—
308	C₂×C₄	—	94	2	no	—
309	C₂×C₄	—	94	2	no	—
310	C₂×C₄	—	94	2	no	—
311	C₂×C₄	—	94	2	no	—
312	C₂×C₄	—	94	4	no	—
313	C₂×C₄	—	94	4	no	—
314	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
315	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
316	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
317	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
318	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
319	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
320	C₂×C₄	#13094030	1	2	yes	—
321	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
322	C₈	—	2	1	no	—
323	C₈	—	2	1	no	—
324	C₈	—	94	2	no	—
325	C₈	—	94	2	no	—
326	C₈	C₄×D₁₈₈	1	2	yes	—
327	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
328	C₈	C₂×#10625350	1	1	yes	characteristic
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	47	4	no	—
332	C₂²	—	94	2	no	—
333	C₂²	—	94	2	no	—
334	C₂²	—	94	2	no	—
335	C₂²	—	94	2	no	—
336	C₂²	—	94	2	no	—
337	C₂²	—	188	8	no	—
338	C₂²	C₈×D₁₈₈	1	2	yes	—
339	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	94	2	no	—
344	C₄	—	94	2	no	—
345	C₄	C₈×D₁₈₈	1	2	yes	—
346	C₄	M₃₂×D₄₇	1	2	yes	complemented
347	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
348	C₄	C₂×#13094030	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	94	4	no	—
351	C₂	—	188	2	no	—
352	C₂	C₂×C₈×D₁₈₈	1	1	yes	characteristic
353	C₂	C₂×M₃₂×D₄₇	1	1	yes	characteristic
354	C₂	#20256490	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₄×M₃₂×C₄₇	C₂
prime radical	C₂²×D₁₈₈	C₈
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₄×M₃₂	D₄₇
hypocenter	C₄₇	D₄×M₃₂
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₄₇	C₂	semidirect
3. #20245221	C₂	semidirect
4. #20245215	C₂	semidirect
5. C₁₆×D₁₈₈	C₂	semidirect
6. #20245144	C₂	semidirect
7. #20244998	C₂	semidirect
8. C₄×M₃₂×C₄₇	C₂	semidirect
12. C₂×#13093963	C₂²	semidirect
14. C₂×C₁₆×D₄₇	C₂²	semidirect
23. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
24. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
25. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
26. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
30. C₄₇×#346	C₂²	semidirect
31. C₄×C₁₆×C₄₇	C₂²	semidirect
64. M₃₂×C₄₇	D₄	semidirect
114. C₁₆×C₄₇	C₂×D₄	semidirect
137. D₁₈₈	M₃₂	direct (N × H)
162. C₂×D₄₇	C₂×M₃₂	semidirect
167. C₄×C₄₇	C₂×M₃₂	semidirect
179. C₄×M₃₂	D₄₇	semidirect
207. #346	C₂×D₄₇	semidirect
208. C₄×C₁₆	C₂×D₄₇	semidirect
209. C₄₇	D₄×M₃₂	semidirect
233. M₃₂	D₁₈₈	direct (N × H)
293. C₁₆	C₂×D₁₈₈	semidirect
346. C₄	M₃₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₇	2
C₂×C₈×D₁₈₈	2
#20245221	2
#20245215	2
C₁₆×D₁₈₈	2
#20245144	2
#20244998	2
C₄×M₃₂×C₄₇	2
D₄×M₃₂	47

Subgroups — M32×D188 #26369493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×D₁₈₈ #26369493