Subgroups — M₁₆×D₅₃₆ #30827255

Order 17152.

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×D₅₃₆	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₂₆₈	C₂	1	2	yes	maximal, complemented
3	#22559095	C₂	1	2	yes	maximal, complemented
4	#22559040	C₂	1	4	yes	maximal, complemented
5	C₈×D₅₃₆	C₂	1	2	yes	maximal, complemented
6	#22558968	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558635	C₂	1	2	yes	maximal, complemented
8	C₈×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₅₃₆	C₄	1	1	yes	characteristic
10	C₂×M₁₆×D₆₇	—	2	2	no	—
11	C₂×C₄×D₂₆₈	C₂²	1	2	yes	—
12	C₄×D₅₃₆	C₄	1	1	yes	characteristic
13	C₄×D₅₃₆	C₄	1	2	yes	—
14	C₄×D₅₃₆	C₄	1	1	yes	characteristic
15	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
16	C₄×D₅₃₆	C₂²	1	2	yes	—
17	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
18	#16863475	C₂²	1	4	yes	complemented
19	#16863469	—	2	4	no	—
20	C₈×D₂₆₈	C₂²	1	4	yes	complemented
21	C₂×#14523977	C₄	1	1	yes	characteristic
22	#16863420	C₂²	1	2	yes	—
23	C₂×#14523965	C₄	1	2	yes	—
24	#16863359	—	2	2	no	—
25	#16863149	C₂²	1	2	yes	complemented
26	#16863149	C₂²	1	2	yes	complemented
27	#16863125	C₂²	1	4	yes	complemented
28	#16863125	C₂²	1	4	yes	complemented
29	#431×C₆₇	C₂²	1	1	yes	characteristic
30	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	#322×C₆₇	C₂²	1	2	yes	complemented
33	C₈²×C₆₇	C₂²	1	2	yes	complemented
34	C₂²×D₂₆₈	C₂×C₄	1	2	yes	—
35	C₂²×C₄×D₆₇	—	2	2	no	—
36	C₂×D₅₃₆	—	2	4	no	—
37	C₂×D₅₃₆	C₂×C₄	1	2	yes	—
38	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
39	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
40	C₂×#11761612	—	2	2	no	—
41	C₂×#11761611	—	2	4	no	—
42	M₁₆×D₆₇	—	4	8	no	—
43	C₂×C₈×D₆₇	—	2	4	no	—
44	C₄×D₂₆₈	—	2	2	no	—
45	C₄×D₂₆₈	—	2	2	no	—
46	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
47	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
48	C₄×D₂₆₈	C₂³	1	2	yes	—
49	C₄×D₂₆₈	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₆₇	C₂×C₄	1	2	yes	—
51	C₂×(C₂×D₆₇)⋊C₄	—	2	2	no	—
52	#14523977	C₂×C₄	1	2	yes	—
53	#14523977	C₂×C₄	1	1	yes	characteristic
54	#14523977	C₂×C₄	1	1	yes	characteristic
55	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
57	#14523965	C₂×C₄	1	2	yes	—
58	#14523965	C₂×C₄	1	2	yes	—
59	#14523965	C₂×C₄	1	2	yes	—
60	#14523965	C₂×C₄	1	2	yes	—
61	(C₂×D₆₇)⋊C₈	—	2	4	no	—
62	(C₂×D₆₇)⋊C₈	—	2	4	no	—
63	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
64	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₆₇	—	2	1	no	—
69	C₂²⋊C₈×C₆₇	—	2	1	no	—
70	#97×C₆₇	D₄	1	2	yes	—
71	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₆₇	C₂³	1	2	yes	—
74	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₆₇	C₂³	1	2	yes	—
77	C₂³×D₆₇	—	2	2	no	—
78	C₂×D₂₆₈	—	2	4	no	—
79	C₂×D₂₆₈	—	2	2	no	—
80	C₂×D₂₆₈	—	4	2	no	—
81	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
82	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
83	C₂²×Dic₆₇	—	2	2	no	—
84	C₂×C₄×D₆₇	—	2	2	no	—
85	C₂×C₄×D₆₇	—	2	2	no	—
86	C₂×C₄×D₆₇	—	2	2	no	—
87	C₂×C₄×D₆₇	—	2	2	no	—
88	C₂×C₄×D₆₇	—	4	4	no	—
89	C₂×C₄×D₆₇	—	4	4	no	—
90	D₅₃₆	—	2	4	no	—
91	D₅₃₆	—	2	2	no	—
92	D₅₃₆	M₁₆	1	4	yes	direct product factor
93	#11761612	—	4	4	no	—
94	#11761611	—	4	8	no	—
95	C₂×C₆₇⋊C₈	—	2	4	no	—
96	C₈×D₆₇	—	4	8	no	—
97	C₄⋊Dic₆₇	—	2	2	no	—
98	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
99	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
100	(C₂×D₆₇)⋊C₄	—	2	2	no	—
101	(C₂×D₆₇)⋊C₄	—	2	2	no	—
102	(C₂×D₆₇)⋊C₄	—	2	2	no	—
103	(C₂×D₆₇)⋊C₄	—	2	2	no	—
104	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
107	M₁₆×C₆₇	—	2	2	no	—
108	M₁₆×C₆₇	D₈	1	4	yes	complemented
109	C₂×C₈×C₆₇	—	2	2	no	—
110	C₂×C₈×C₆₇	—	2	2	no	—
111	C₂×C₈×C₆₇	—	4	1	no	—
112	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
118	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₆₇	#41	1	1	yes	characteristic
121	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
122	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
123	C₂²×D₆₇	—	2	2	no	—
124	C₂²×D₆₇	—	2	2	no	—
125	C₂²×D₆₇	—	4	4	no	—
126	C₂²×D₆₇	—	4	4	no	—
127	C₂²×D₆₇	—	8	2	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	4	1	no	—
131	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₆₇	#135	1	2	yes	—
136	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
139	C₂×Dic₆₇	—	2	2	no	—
140	C₂×Dic₆₇	—	2	2	no	—
141	C₂×Dic₆₇	—	4	4	no	—
142	D₂₆₈	—	2	2	no	—
143	D₂₆₈	—	2	2	no	—
144	D₂₆₈	—	2	2	no	—
145	D₂₆₈	—	4	4	no	—
146	D₂₆₈	C₂×M₁₆	1	4	yes	complemented
147	C₄×D₆₇	—	4	2	no	—
148	C₄×D₆₇	—	4	2	no	—
149	C₄×D₆₇	—	4	2	no	—
150	C₄×D₆₇	—	4	2	no	—
151	C₄×D₆₇	—	4	4	no	—
152	C₄×D₆₇	—	4	4	no	—
153	C₈×C₆₇	—	2	1	no	—
154	C₈×C₆₇	—	2	1	no	—
155	C₈×C₆₇	—	2	1	no	—
156	C₈×C₆₇	—	2	2	no	—
157	C₈×C₆₇	—	4	2	no	—
158	C₈×C₆₇	C₂×M₁₆	1	2	yes	complemented
159	C₈×C₆₇	C₂×D₈	1	4	yes	complemented
160	C₆₇⋊C₈	—	4	4	no	—
161	C₂²×C₆₇	—	2	1	no	—
162	C₂²×C₆₇	—	2	1	no	—
163	C₂²×C₆₇	C₄×D₈	1	2	yes	—
164	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
165	C₂×D₆₇	—	2	4	no	—
166	C₂×D₆₇	—	4	2	no	—
167	C₂×D₆₇	—	4	2	no	—
168	C₂×D₆₇	—	4	2	no	—
169	C₂×D₆₇	—	4	2	no	—
170	C₂×D₆₇	—	4	2	no	—
171	C₂×D₆₇	—	8	8	no	—
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	C₄×D₈	1	2	yes	—
176	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
177	C₄×C₆₇	#568	1	1	yes	characteristic
178	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
179	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
180	Dic₆₇	—	4	2	no	—
181	Dic₆₇	—	4	2	no	—
182	M₁₆×D₈	—	67	1	no	maximal, Sylow
183	C₂×C₆₇	—	2	2	no	—
184	C₂×C₆₇	D₄×M₁₆	1	1	yes	characteristic
185	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
186	C₂×C₆₇	#2957	1	1	yes	characteristic
187	D₆₇	—	4	4	no	—
188	D₆₇	—	8	2	no	—
189	C₂×C₄×D₈	—	67	1	no	—
190	D₄×M₁₆	—	67	2	no	—
191	#1589	—	67	2	no	—
192	#1581	—	67	4	no	—
193	C₈×D₈	—	67	2	no	—
194	#1567	—	67	1	no	—
195	#1486	—	67	2	no	—
196	C₈×M₁₆	D₆₇	1	1	yes	characteristic, complemented
197	C₆₇	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
198	C₂²×D₈	—	67	1	no	—
199	C₂²×M₁₆	—	134	2	no	—
200	C₂×C₄×D₄	—	67	2	no	—
201	C₄×D₈	—	67	1	no	—
202	C₄×D₈	—	67	2	no	—
203	C₄×D₈	—	67	1	no	—
204	C₄×D₈	—	67	1	no	—
205	C₄×D₈	—	67	2	no	—
206	C₄×D₈	—	67	1	no	—
207	#436	—	67	4	no	—
208	#435	—	134	4	no	—
209	C₈×D₄	—	67	4	no	—
210	#431	C₂×D₆₇	1	1	yes	characteristic
211	C₂×#107	—	67	1	no	—
212	#423	—	67	2	no	—
213	C₂×#102	—	67	2	no	—
214	#407	—	134	2	no	—
215	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
217	#335	—	67	2	no	—
218	#335	—	67	2	no	—
219	D₄⋊C₈	—	67	4	no	—
220	D₄⋊C₈	—	67	4	no	—
221	#322	C₂×D₆₇	1	2	yes	complemented
222	C₈²	C₂×D₆₇	1	2	yes	complemented
223	C₂²×D₄	—	67	2	no	—
224	C₂³×C₄	—	134	2	no	—
225	C₂×D₈	—	67	1	no	—
226	C₂×D₈	—	67	2	no	—
227	C₂×D₈	—	67	1	no	—
228	C₂×D₈	—	134	4	no	—
229	C₂×M₁₆	—	268	8	no	—
230	C₂×M₁₆	—	134	2	no	—
231	C₂×M₁₆	—	134	4	no	—
232	C₂×M₁₆	D₂₆₈	1	1	yes	characteristic
233	C₂×M₁₆	D₂₆₈	1	1	yes	characteristic
234	C₂²×C₈	—	134	4	no	—
235	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
237	C₄×D₄	—	67	2	no	—
238	C₄×D₄	—	67	2	no	—
239	C₄×D₄	—	67	2	no	—
240	C₄×D₄	—	67	2	no	—
241	C₄×D₄	—	134	2	no	—
242	C₄×D₄	—	134	2	no	—
243	C₂×C₄⋊C₄	—	67	2	no	—
244	C₂×C₂²⋊C₄	—	134	2	no	—
245	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
246	#107	—	67	2	no	—
247	#107	—	67	1	no	—
248	#107	—	67	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	67	4	no	—
251	C₄⋊C₈	—	134	2	no	—
252	#102	—	67	2	no	—
253	#102	—	67	2	no	—
254	#102	—	67	2	no	—
255	#102	—	67	2	no	—
256	C₂²⋊C₈	—	2	1	no	—
257	C₂²⋊C₈	—	134	4	no	—
258	C₂²⋊C₈	—	134	4	no	—
259	#97	D₂₆₈	1	2	yes	—
260	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
261	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
262	C₄×C₈	C₂²×D₆₇	1	2	yes	—
263	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
264	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
265	C₄×C₈	C₂²×D₆₇	1	2	yes	—
266	C₂⁴	—	134	2	no	—
267	C₂×D₄	—	268	2	no	—
268	C₂×D₄	—	67	2	no	—
269	C₂×D₄	—	67	2	no	—
270	C₂×D₄	—	134	4	no	—
271	C₂×D₄	—	134	2	no	—
272	C₂²×C₄	—	268	4	no	—
273	C₂²×C₄	—	268	4	no	—
274	C₂²×C₄	—	134	2	no	—
275	C₂²×C₄	—	134	2	no	—
276	C₂²×C₄	—	134	2	no	—
277	C₂²×C₄	—	134	2	no	—
278	C₂²×C₄	—	134	2	no	—
279	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
281	C₂²×C₄	#11761628	1	1	yes	characteristic
282	D₈	—	67	4	no	—
283	D₈	—	134	4	no	—
284	D₈	—	134	2	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	268	4	no	—
287	M₁₆	—	268	8	no	—
288	M₁₆	D₅₃₆	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	—	268	8	no	—
293	C₂×C₈	—	134	4	no	—
294	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
295	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
296	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
297	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
298	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
299	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
300	C₄⋊C₄	—	67	2	no	—
301	C₄⋊C₄	—	67	2	no	—
302	C₄⋊C₄	—	134	2	no	—
303	C₂²⋊C₄	—	134	2	no	—
304	C₂²⋊C₄	—	134	2	no	—
305	C₂²⋊C₄	—	134	2	no	—
306	C₂²⋊C₄	—	134	2	no	—
307	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
308	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
309	C₄²	#11761628	1	1	yes	characteristic
310	C₄²	C₂³×D₆₇	1	1	yes	characteristic
311	C₂³	—	268	4	no	—
312	C₂³	—	268	4	no	—
313	C₂³	—	536	2	no	—
314	C₂³	—	134	2	no	—
315	C₂³	—	134	2	no	—
316	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
317	D₄	—	268	4	no	—
318	D₄	—	67	4	no	—
319	D₄	—	134	2	no	—
320	D₄	—	134	2	no	—
321	D₄	—	134	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	268	4	no	—
326	C₂×C₄	—	268	2	no	—
327	C₂×C₄	—	268	2	no	—
328	C₂×C₄	—	268	2	no	—
329	C₂×C₄	—	268	2	no	—
330	C₂×C₄	—	268	4	no	—
331	C₂×C₄	—	268	4	no	—
332	C₂×C₄	—	134	2	no	—
333	C₂×C₄	—	134	2	no	—
334	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
335	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
336	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
337	C₂×C₄	C₂×D₅₃₆	1	2	yes	—
338	C₂×C₄	#14524065	1	2	yes	—
339	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
341	C₂×C₄	C₂×#11761628	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	—	268	4	no	—
348	C₈	M₁₆×D₆₇	1	2	yes	complemented
349	C₈	C₂×D₅₃₆	1	4	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	268	2	no	—
353	C₂²	—	268	2	no	—
354	C₂²	—	268	2	no	—
355	C₂²	—	268	2	no	—
356	C₂²	—	268	2	no	—
357	C₂²	—	536	8	no	—
358	C₂²	—	134	4	no	—
359	C₂²	C₄×D₅₃₆	1	2	yes	—
360	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	268	2	no	—
365	C₄	—	268	2	no	—
366	C₄	C₄×D₅₃₆	1	2	yes	—
367	C₄	C₂×M₁₆×D₆₇	1	1	yes	characteristic
368	C₄	#16864162	1	1	yes	characteristic
369	C₄	C₂²×D₅₃₆	1	1	yes	characteristic
370	C₄	C₂×#14524065	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	268	4	no	—
373	C₂	—	536	2	no	—
374	C₂	M₁₆×D₂₆₈	1	1	yes	characteristic
375	C₂	C₂×C₄×D₅₃₆	1	1	yes	characteristic
376	C₂	#22569127	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×M₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂²×D₅₃₆	C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₈×M₁₆	D₆₇
hypocenter	C₆₇	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
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×D₂₆₈	C₂	semidirect
3. #22559095	C₂	semidirect
4. #22559040	C₂	semidirect
5. C₈×D₅₃₆	C₂	semidirect
6. #22558968	C₂	semidirect
7. #22558635	C₂	semidirect
8. C₈×M₁₆×C₆₇	C₂	semidirect
18. #16863475	C₂²	semidirect
20. C₈×D₂₆₈	C₂²	semidirect
25. #16863149	C₂²	semidirect
26. #16863149	C₂²	semidirect
27. #16863125	C₂²	semidirect
28. #16863125	C₂²	semidirect
32. #322×C₆₇	C₂²	semidirect
33. C₈²×C₆₇	C₂²	semidirect
92. D₅₃₆	M₁₆	direct (N × H)
108. M₁₆×C₆₇	D₈	semidirect
146. D₂₆₈	C₂×M₁₆	semidirect
158. C₈×C₆₇	C₂×M₁₆	semidirect
159. C₈×C₆₇	C₂×D₈	semidirect
196. C₈×M₁₆	D₆₇	semidirect
197. C₆₇	M₁₆×D₈	semidirect
221. #322	C₂×D₆₇	semidirect
222. C₈²	C₂×D₆₇	semidirect
288. M₁₆	D₅₃₆	direct (N × H)
348. C₈	M₁₆×D₆₇	semidirect
349. C₈	C₂×D₅₃₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅₃₆	2
M₁₆×D₂₆₈	2
#22559095	2
#22559040	2
C₈×D₅₃₆	2
#22558968	2
#22558635	2
C₈×M₁₆×C₆₇	2
M₁₆×D₈	67

Subgroups — M16×D536 #30827255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×D₅₃₆ #30827255