Subgroups — M₁₆×D₃₇₆ #26187702

Order 12032.

794 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₁₈₈	C₂	1	2	yes	maximal, complemented
3	#20242274	C₂	1	2	yes	maximal, complemented
4	#20242219	C₂	1	4	yes	maximal, complemented
5	C₈×D₃₇₆	C₂	1	2	yes	maximal, complemented
6	#20242147	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241814	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₃₇₆	C₄	1	1	yes	characteristic
10	C₂×M₁₆×D₄₇	—	2	2	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
12	C₄×D₃₇₆	C₄	1	1	yes	characteristic
13	C₄×D₃₇₆	C₄	1	2	yes	—
14	C₄×D₃₇₆	C₄	1	1	yes	characteristic
15	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
16	C₄×D₃₇₆	C₂²	1	2	yes	—
17	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
18	#15689202	C₂²	1	4	yes	complemented
19	#15689196	—	2	4	no	—
20	C₈×D₁₈₈	C₂²	1	4	yes	complemented
21	C₂×#13093958	C₄	1	1	yes	characteristic
22	#15689147	C₂²	1	2	yes	—
23	C₂×#13093946	C₄	1	2	yes	—
24	#15689086	—	2	2	no	—
25	#15688876	C₂²	1	2	yes	complemented
26	#15688876	C₂²	1	2	yes	complemented
27	#15688852	C₂²	1	4	yes	complemented
28	#15688852	C₂²	1	4	yes	complemented
29	C₄₇×#431	C₂²	1	1	yes	characteristic
30	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#322	C₂²	1	2	yes	complemented
33	C₈²×C₄₇	C₂²	1	2	yes	complemented
34	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
35	C₂²×C₄×D₄₇	—	2	2	no	—
36	C₂×D₃₇₆	—	2	4	no	—
37	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
38	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
39	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
40	C₂×#10625329	—	2	2	no	—
41	C₂×#10625324	—	2	4	no	—
42	M₁₆×D₄₇	—	4	8	no	—
43	C₂×C₈×D₄₇	—	2	4	no	—
44	C₄×D₁₈₈	—	2	2	no	—
45	C₄×D₁₈₈	—	2	2	no	—
46	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
47	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
48	C₄×D₁₈₈	C₂³	1	2	yes	—
49	C₄×D₁₈₈	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
51	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
52	#13093958	C₂×C₄	1	2	yes	—
53	#13093958	C₂×C₄	1	1	yes	characteristic
54	#13093958	C₂×C₄	1	1	yes	characteristic
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
57	#13093946	C₂×C₄	1	2	yes	—
58	#13093946	C₂×C₄	1	2	yes	—
59	#13093946	C₂×C₄	1	2	yes	—
60	#13093946	C₂×C₄	1	2	yes	—
61	(C₂×D₄₇)⋊C₈	—	2	4	no	—
62	(C₂×D₄₇)⋊C₈	—	2	4	no	—
63	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
64	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	1	no	—
69	C₂²⋊C₈×C₄₇	—	2	1	no	—
70	#97×C₄₇	D₄	1	2	yes	—
71	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₄₇	C₂³	1	2	yes	—
74	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂³×D₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
81	C₂²×Dic₄₇	—	2	2	no	—
82	C₂×D₁₈₈	—	2	4	no	—
83	C₂×D₁₈₈	—	2	2	no	—
84	C₂×D₁₈₈	—	4	2	no	—
85	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
86	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
87	C₂×C₄×D₄₇	—	2	2	no	—
88	C₂×C₄×D₄₇	—	2	2	no	—
89	C₂×C₄×D₄₇	—	2	2	no	—
90	C₂×C₄×D₄₇	—	2	2	no	—
91	C₂×C₄×D₄₇	—	4	4	no	—
92	C₂×C₄×D₄₇	—	4	4	no	—
93	M₁₆×C₄₇	—	2	2	no	—
94	M₁₆×C₄₇	D₈	1	4	yes	complemented
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
104	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₄₇	#41	1	1	yes	characteristic
107	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
108	(C₂×D₄₇)⋊C₄	—	2	2	no	—
109	(C₂×D₄₇)⋊C₄	—	2	2	no	—
110	(C₂×D₄₇)⋊C₄	—	2	2	no	—
111	(C₂×D₄₇)⋊C₄	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
114	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
115	#10625329	—	4	4	no	—
116	C₂×C₄₇⋊C₈	—	2	4	no	—
117	D₃₇₆	—	2	4	no	—
118	D₃₇₆	—	2	2	no	—
119	D₃₇₆	M₁₆	1	4	yes	direct product factor
120	#10625324	—	4	8	no	—
121	C₈×D₄₇	—	4	8	no	—
122	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
123	C₂²×D₄₇	—	2	2	no	—
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	4	4	no	—
126	C₂²×D₄₇	—	4	4	no	—
127	C₂²×D₄₇	—	8	2	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	4	1	no	—
131	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₄₇	#135	1	2	yes	—
136	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
139	C₂×Dic₄₇	—	2	2	no	—
140	C₂×Dic₄₇	—	2	2	no	—
141	C₂×Dic₄₇	—	4	4	no	—
142	D₁₈₈	—	2	2	no	—
143	D₁₈₈	—	2	2	no	—
144	D₁₈₈	—	2	2	no	—
145	D₁₈₈	—	4	4	no	—
146	D₁₈₈	C₂×M₁₆	1	4	yes	complemented
147	C₄×D₄₇	—	4	2	no	—
148	C₄×D₄₇	—	4	2	no	—
149	C₄×D₄₇	—	4	2	no	—
150	C₄×D₄₇	—	4	2	no	—
151	C₄×D₄₇	—	4	4	no	—
152	C₄×D₄₇	—	4	4	no	—
153	C₈×C₄₇	—	2	1	no	—
154	C₈×C₄₇	—	2	1	no	—
155	C₈×C₄₇	—	2	1	no	—
156	C₈×C₄₇	—	2	2	no	—
157	C₈×C₄₇	—	4	2	no	—
158	C₈×C₄₇	C₂×M₁₆	1	2	yes	complemented
159	C₈×C₄₇	C₂×D₈	1	4	yes	complemented
160	C₄₇⋊C₈	—	4	4	no	—
161	M₁₆×D₈	—	47	1	no	maximal, Sylow
162	C₂²×C₄₇	—	2	1	no	—
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	C₄×D₈	1	2	yes	—
165	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂×D₄₇	—	2	4	no	—
167	C₂×D₄₇	—	4	2	no	—
168	C₂×D₄₇	—	4	2	no	—
169	C₂×D₄₇	—	4	2	no	—
170	C₂×D₄₇	—	4	2	no	—
171	C₂×D₄₇	—	4	2	no	—
172	C₂×D₄₇	—	8	8	no	—
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	—	2	1	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	C₄×D₈	1	2	yes	—
177	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
178	C₄×C₄₇	#568	1	1	yes	characteristic
179	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
180	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
181	Dic₄₇	—	4	2	no	—
182	Dic₄₇	—	4	2	no	—
183	C₂×C₄×D₈	—	47	1	no	—
184	D₄×M₁₆	—	47	2	no	—
185	#1589	—	47	2	no	—
186	#1581	—	47	4	no	—
187	C₈×D₈	—	47	2	no	—
188	#1567	—	47	1	no	—
189	#1486	—	47	2	no	—
190	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
191	C₂×C₄₇	—	2	2	no	—
192	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
193	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
194	C₂×C₄₇	#2957	1	1	yes	characteristic
195	D₄₇	—	4	4	no	—
196	D₄₇	—	8	2	no	—
197	C₂²×D₈	—	47	1	no	—
198	C₂²×M₁₆	—	94	2	no	—
199	C₂×C₄×D₄	—	47	2	no	—
200	C₄×D₈	—	47	1	no	—
201	C₄×D₈	—	47	2	no	—
202	C₄×D₈	—	47	1	no	—
203	C₄×D₈	—	47	1	no	—
204	C₄×D₈	—	47	2	no	—
205	C₄×D₈	—	47	1	no	—
206	#436	—	47	4	no	—
207	#435	—	94	4	no	—
208	C₈×D₄	—	47	4	no	—
209	#431	C₂×D₄₇	1	1	yes	characteristic
210	C₂×#107	—	47	1	no	—
211	#423	—	47	2	no	—
212	C₂×#102	—	47	2	no	—
213	#407	—	94	2	no	—
214	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
216	#335	—	47	2	no	—
217	#335	—	47	2	no	—
218	D₄⋊C₈	—	47	4	no	—
219	D₄⋊C₈	—	47	4	no	—
220	#322	C₂×D₄₇	1	2	yes	complemented
221	C₈²	C₂×D₄₇	1	2	yes	complemented
222	C₄₇	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
223	C₂²×D₄	—	47	2	no	—
224	C₂³×C₄	—	94	2	no	—
225	C₂×D₈	—	47	1	no	—
226	C₂×D₈	—	47	2	no	—
227	C₂×D₈	—	47	1	no	—
228	C₂×D₈	—	94	4	no	—
229	C₂×M₁₆	—	94	2	no	—
230	C₂×M₁₆	—	94	4	no	—
231	C₂×M₁₆	—	188	8	no	—
232	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
233	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
234	C₂²×C₈	—	94	4	no	—
235	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
237	C₄×D₄	—	47	2	no	—
238	C₄×D₄	—	47	2	no	—
239	C₄×D₄	—	47	2	no	—
240	C₄×D₄	—	47	2	no	—
241	C₄×D₄	—	94	2	no	—
242	C₄×D₄	—	94	2	no	—
243	C₂×C₄⋊C₄	—	47	2	no	—
244	C₂×C₂²⋊C₄	—	94	2	no	—
245	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
246	#107	—	47	2	no	—
247	#107	—	47	1	no	—
248	#107	—	47	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	47	4	no	—
251	C₄⋊C₈	—	94	2	no	—
252	#102	—	47	2	no	—
253	#102	—	47	2	no	—
254	#102	—	47	2	no	—
255	#102	—	47	2	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	—	94	4	no	—
258	C₂²⋊C₈	—	94	4	no	—
259	#97	D₁₈₈	1	2	yes	—
260	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
261	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
262	C₄×C₈	C₂²×D₄₇	1	2	yes	—
263	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
264	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
265	C₄×C₈	C₂²×D₄₇	1	2	yes	—
266	C₂⁴	—	94	2	no	—
267	C₂×D₄	—	47	2	no	—
268	C₂×D₄	—	47	2	no	—
269	C₂×D₄	—	94	4	no	—
270	C₂×D₄	—	94	2	no	—
271	C₂×D₄	—	188	2	no	—
272	C₂²×C₄	—	94	2	no	—
273	C₂²×C₄	—	94	2	no	—
274	C₂²×C₄	—	94	2	no	—
275	C₂²×C₄	—	94	2	no	—
276	C₂²×C₄	—	94	2	no	—
277	C₂²×C₄	—	188	4	no	—
278	C₂²×C₄	—	188	4	no	—
279	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
281	C₂²×C₄	#10625350	1	1	yes	characteristic
282	D₈	—	47	4	no	—
283	D₈	—	94	4	no	—
284	D₈	—	94	2	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	188	4	no	—
287	M₁₆	—	188	8	no	—
288	M₁₆	D₃₇₆	1	4	yes	direct product factor
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	94	4	no	—
293	C₂×C₈	—	188	8	no	—
294	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
296	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
299	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
300	C₄⋊C₄	—	47	2	no	—
301	C₄⋊C₄	—	47	2	no	—
302	C₄⋊C₄	—	94	2	no	—
303	C₂²⋊C₄	—	94	2	no	—
304	C₂²⋊C₄	—	94	2	no	—
305	C₂²⋊C₄	—	94	2	no	—
306	C₂²⋊C₄	—	94	2	no	—
307	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
308	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
309	C₄²	#10625350	1	1	yes	characteristic
310	C₄²	C₂³×D₄₇	1	1	yes	characteristic
311	C₂³	—	94	2	no	—
312	C₂³	—	94	2	no	—
313	C₂³	—	376	2	no	—
314	C₂³	—	188	4	no	—
315	C₂³	—	188	4	no	—
316	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
317	D₄	—	47	4	no	—
318	D₄	—	94	2	no	—
319	D₄	—	94	2	no	—
320	D₄	—	94	2	no	—
321	D₄	—	188	4	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	94	2	no	—
326	C₂×C₄	—	94	2	no	—
327	C₂×C₄	—	188	4	no	—
328	C₂×C₄	—	188	2	no	—
329	C₂×C₄	—	188	2	no	—
330	C₂×C₄	—	188	2	no	—
331	C₂×C₄	—	188	2	no	—
332	C₂×C₄	—	188	4	no	—
333	C₂×C₄	—	188	4	no	—
334	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
335	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
336	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
337	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
338	C₂×C₄	#13094046	1	2	yes	—
339	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
341	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	—	4	2	no	—
347	C₈	—	188	4	no	—
348	C₈	M₁₆×D₄₇	1	2	yes	complemented
349	C₈	C₂×D₃₇₆	1	4	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	94	4	no	—
353	C₂²	—	376	8	no	—
354	C₂²	—	188	2	no	—
355	C₂²	—	188	2	no	—
356	C₂²	—	188	2	no	—
357	C₂²	—	188	2	no	—
358	C₂²	—	188	2	no	—
359	C₂²	C₄×D₃₇₆	1	2	yes	—
360	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	188	2	no	—
365	C₄	—	188	2	no	—
366	C₄	C₄×D₃₇₆	1	2	yes	—
367	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
368	C₄	#15689889	1	1	yes	characteristic
369	C₄	C₂²×D₃₇₆	1	1	yes	characteristic
370	C₄	C₂×#13094046	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	376	2	no	—
373	C₂	—	188	4	no	—
374	C₂	M₁₆×D₁₈₈	1	1	yes	characteristic
375	C₂	C₂×C₄×D₃₇₆	1	1	yes	characteristic
376	C₂	#20252306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×D₃₇₆	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×D₁₈₈	C₂	semidirect
3. #20242274	C₂	semidirect
4. #20242219	C₂	semidirect
5. C₈×D₃₇₆	C₂	semidirect
6. #20242147	C₂	semidirect
7. #20241814	C₂	semidirect
8. C₈×M₁₆×C₄₇	C₂	semidirect
18. #15689202	C₂²	semidirect
20. C₈×D₁₈₈	C₂²	semidirect
25. #15688876	C₂²	semidirect
26. #15688876	C₂²	semidirect
27. #15688852	C₂²	semidirect
28. #15688852	C₂²	semidirect
32. C₄₇×#322	C₂²	semidirect
33. C₈²×C₄₇	C₂²	semidirect
94. M₁₆×C₄₇	D₈	semidirect
119. D₃₇₆	M₁₆	direct (N × H)
146. D₁₈₈	C₂×M₁₆	semidirect
158. C₈×C₄₇	C₂×M₁₆	semidirect
159. C₈×C₄₇	C₂×D₈	semidirect
190. C₈×M₁₆	D₄₇	semidirect
220. #322	C₂×D₄₇	semidirect
221. C₈²	C₂×D₄₇	semidirect
222. C₄₇	M₁₆×D₈	semidirect
288. M₁₆	D₃₇₆	direct (N × H)
348. C₈	M₁₆×D₄₇	semidirect
349. C₈	C₂×D₃₇₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃₇₆	2
M₁₆×D₁₈₈	2
#20242274	2
#20242219	2
C₈×D₃₇₆	2
#20242147	2
#20241814	2
C₈×M₁₆×C₄₇	2
M₁₆×D₈	47

Subgroups — M16×D376 #26187702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₃₇₆ #26187702