Subgroups — #483703

Order 512.

428 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#33505	C₂	1	1	yes	maximal, characteristic
2	#33498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#137	C₂	1	1	yes	maximal, characteristic
4	#12060	C₂	1	1	yes	maximal, characteristic, complemented
5	#12059	C₂	1	1	yes	maximal, characteristic, complemented
6	#12058	C₂	1	1	yes	maximal, characteristic, complemented
7	#12056	C₂	1	1	yes	maximal, characteristic, complemented
8	#12053	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₆×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#12051	C₂	1	1	yes	maximal, characteristic, complemented
11	#12050	C₂	1	1	yes	maximal, characteristic, complemented
12	#12017	C₂	1	1	yes	maximal, characteristic, complemented
13	#11615	C₂	1	1	yes	maximal, characteristic
14	#11607	C₂	1	1	yes	maximal, characteristic, complemented
15	#11409	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈×#41	C₂²	1	1	yes	characteristic
17	C₂×C₈×Q₈	C₂²	1	1	yes	characteristic
18	C₄×#137	C₄	1	1	yes	characteristic
19	#2183	—	2	1	no	—
20	#2183	—	2	1	no	—
21	#2183	C₂²	1	1	yes	characteristic
22	#2183	C₂²	1	1	yes	characteristic
23	Q₈×C₁₆	C₂²	1	1	yes	characteristic
24	Q₈×C₁₆	C₂²	1	1	yes	characteristic
25	Q₈×C₁₆	C₂²	1	1	yes	characteristic
26	Q₈×C₁₆	C₂²	1	1	yes	characteristic
27	#2169	—	2	1	no	—
28	#2169	—	2	1	no	—
29	#2169	C₂²	1	1	yes	characteristic
30	#2169	C₂²	1	1	yes	characteristic
31	#2163	—	2	1	no	—
32	#2163	C₂²	1	1	yes	characteristic
33	#2162	—	2	1	no	—
34	#2162	—	2	1	no	—
35	#2162	C₂²	1	1	yes	characteristic
36	#2150	—	2	1	no	—
37	#2150	C₂²	1	1	yes	characteristic
38	C₄×M₃₂	C₂²	1	1	yes	characteristic
39	#1579	C₄	1	1	yes	characteristic
40	#1579	C₄	1	1	yes	characteristic
41	SD₁₆⋊C₈	C₄	1	1	yes	characteristic
42	SD₁₆⋊C₈	C₄	1	1	yes	characteristic
43	C₈×Q₁₆	C₂²	1	1	yes	characteristic
44	C₈×Q₁₆	C₂²	1	1	yes	characteristic
45	C₈×SD₁₆	C₂²	1	1	yes	characteristic
46	C₈×SD₁₆	C₂²	1	1	yes	characteristic
47	#1565	C₄	1	1	yes	characteristic
48	#1479	C₄	1	1	yes	characteristic
49	#1477	C₄	1	1	yes	characteristic
50	C₈×M₁₆	C₂²	1	1	yes	characteristic
51	#1370	C₂²	1	1	yes	characteristic
52	#1370	C₂²	1	1	yes	characteristic
53	#1367	C₂²	1	1	yes	characteristic
54	#1367	C₂²	1	1	yes	characteristic
55	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic
56	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic
57	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic
58	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic
59	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic
60	Q₈⋊C₁₆	C₂²	1	1	yes	characteristic
61	D₄⋊C₁₆	C₂²	1	1	yes	characteristic
62	D₄⋊C₁₆	C₂²	1	1	yes	characteristic
63	#1312	C₂²	1	1	yes	characteristic
64	#1312	C₂²	1	1	yes	characteristic
65	#1311	C₂²	1	1	yes	characteristic
66	C₈×C₁₆	C₂²	1	1	yes	characteristic
67	C₂×#137	C₈	1	1	yes	characteristic
68	C₄×#41	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
70	C₂×M₃₂	—	2	1	no	—
71	C₂×M₃₂	—	2	1	no	—
72	C₂×M₃₂	—	2	1	no	—
73	C₂×M₃₂	—	2	1	no	—
74	C₈×Q₈	—	2	1	no	—
75	C₈×Q₈	—	2	1	no	—
76	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
77	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
78	C₈×Q₈	C₂×C₄	1	1	yes	characteristic
79	C₈×Q₈	C₂³	1	1	yes	characteristic
80	C₈×Q₈	C₂³	1	1	yes	characteristic
81	C₈×Q₈	C₂³	1	1	yes	characteristic
82	#441	C₈	1	1	yes	characteristic
83	#441	C₈	1	1	yes	characteristic
84	#440	C₈	1	1	yes	characteristic
85	#440	C₈	1	1	yes	characteristic
86	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
88	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
89	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
90	C₈×D₄	—	2	1	no	—
91	C₈×D₄	—	2	1	no	—
92	C₈×D₄	C₂×C₄	1	1	yes	characteristic
93	C₈×D₄	C₂³	1	1	yes	characteristic
94	#431	—	2	1	no	—
95	#431	C₂×C₄	1	1	yes	characteristic
96	#431	C₂×C₄	1	1	yes	characteristic
97	#428	C₈	1	1	yes	characteristic
98	C₂×C₄⋊C₈	—	2	1	no	—
99	C₂×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
100	#419	C₈	1	1	yes	characteristic
101	#417	C₈	1	1	yes	characteristic
102	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄×C₈	—	2	1	no	—
104	C₂×C₄×C₈	—	2	1	no	—
105	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
106	C₄⋊C₁₆	—	2	1	no	—
107	C₄⋊C₁₆	—	2	1	no	—
108	C₄⋊C₁₆	—	2	1	no	—
109	C₄⋊C₁₆	—	2	1	no	—
110	C₄⋊C₁₆	—	2	1	no	—
111	C₄⋊C₁₆	—	2	1	no	—
112	C₄⋊C₁₆	—	2	1	no	—
113	C₄⋊C₁₆	D₄	1	1	yes	characteristic
114	C₄⋊C₁₆	D₄	1	1	yes	characteristic
115	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
116	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
117	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
118	C₄⋊C₁₆	C₂³	1	1	yes	characteristic
119	C₂²⋊C₁₆	—	2	1	no	—
120	C₂²⋊C₁₆	—	2	1	no	—
121	C₂²⋊C₁₆	—	2	1	no	—
122	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
123	C₂²⋊C₁₆	D₄	1	1	yes	characteristic
124	#346	—	2	1	no	—
125	#346	—	2	1	no	—
126	#346	—	2	1	no	—
127	#346	—	2	1	no	—
128	C₄×C₁₆	—	2	1	no	—
129	C₄×C₁₆	—	2	1	no	—
130	C₄×C₁₆	—	2	1	no	—
131	C₄×C₁₆	—	2	1	no	—
132	C₄×C₁₆	C₂³	1	1	yes	characteristic
133	C₄×C₁₆	C₂³	1	1	yes	characteristic
134	C₄×C₁₆	C₂³	1	1	yes	characteristic
135	C₄×C₁₆	C₂³	1	1	yes	characteristic
136	#335	C₂×C₄	1	1	yes	characteristic
137	#335	C₂×C₄	1	1	yes	characteristic
138	#334	C₂×C₄	1	1	yes	characteristic
139	#334	C₂×C₄	1	1	yes	characteristic
140	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
141	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
142	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
143	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
144	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
145	Q₈⋊C₈	C₂×C₄	1	1	yes	characteristic
146	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
147	D₄⋊C₈	C₂×C₄	1	1	yes	characteristic
148	#322	C₂×C₄	1	1	yes	characteristic
149	#322	C₂×C₄	1	1	yes	characteristic
150	C₈²	C₂³	1	1	yes	characteristic
151	C₈²	C₂³	1	1	yes	characteristic
152	C₂×#41	C₂×C₈	1	1	yes	characteristic
153	C₂²×Q₈	C₂×C₈	1	1	yes	characteristic
154	#137	—	2	4	no	—
155	C₂×Q₁₆	C₂×C₈	1	1	yes	characteristic
156	C₂×Q₁₆	C₂×C₈	1	1	yes	characteristic
157	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
158	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
159	C₂×M₁₆	C₂×C₈	1	1	yes	characteristic
160	C₂×M₁₆	C₂×C₈	1	1	yes	characteristic
161	C₂²×C₈	—	2	1	no	—
162	C₂²×C₈	—	2	1	no	—
163	C₂²×C₈	—	2	1	no	—
164	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₈	#41	1	1	yes	characteristic
166	C₄×Q₈	—	2	1	no	—
167	C₄×Q₈	—	2	1	no	—
168	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
169	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
170	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
171	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
172	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
173	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
174	C₄×D₄	—	2	1	no	—
175	C₄×D₄	—	2	1	no	—
176	C₄×D₄	C₂×C₈	1	1	yes	characteristic
177	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
178	#117	—	2	1	no	—
179	#117	C₂×C₈	1	1	yes	characteristic
180	C₂×C₄⋊C₄	—	2	1	no	—
181	C₂×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
182	C₂×C₄²	—	2	1	no	—
183	C₂×C₄²	—	2	1	no	—
184	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
185	M₃₂	—	4	2	no	—
186	M₃₂	—	8	1	no	—
187	M₃₂	—	8	1	no	—
188	M₃₂	—	8	1	no	—
189	C₂×C₁₆	—	2	1	no	—
190	C₂×C₁₆	—	2	1	no	—
191	C₂×C₁₆	—	2	1	no	—
192	C₂×C₁₆	—	2	1	no	—
193	C₂×C₁₆	—	2	1	no	—
194	C₂×C₁₆	—	2	1	no	—
195	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
196	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
197	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
198	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
199	#107	C₂×C₈	1	1	yes	characteristic
200	#107	C₂×C₈	1	1	yes	characteristic
201	#106	C₂×C₈	1	1	yes	characteristic
202	#106	C₂×C₈	1	1	yes	characteristic
203	C₄⋊C₈	—	2	1	no	—
204	C₄⋊C₈	—	2	1	no	—
205	C₄⋊C₈	—	2	1	no	—
206	C₄⋊C₈	—	2	1	no	—
207	C₄⋊C₈	—	2	1	no	—
208	C₄⋊C₈	—	2	1	no	—
209	C₄⋊C₈	—	2	1	no	—
210	C₄⋊C₈	—	2	1	no	—
211	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
213	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
214	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
215	#103	C₂×C₈	1	1	yes	characteristic
216	#103	C₂×C₈	1	1	yes	characteristic
217	#103	C₂×C₈	1	1	yes	characteristic
218	#103	C₂×C₈	1	1	yes	characteristic
219	#103	C₂×C₈	1	1	yes	characteristic
220	#103	C₂×C₈	1	1	yes	characteristic
221	#102	C₂×C₈	1	1	yes	characteristic
222	#102	C₂×C₈	1	1	yes	characteristic
223	C₂²⋊C₈	—	2	1	no	—
224	C₂²⋊C₈	—	2	1	no	—
225	C₂²⋊C₈	—	2	1	no	—
226	C₂²⋊C₈	—	2	1	no	—
227	#97	C₂×C₈	1	1	yes	characteristic
228	#97	C₂×C₈	1	1	yes	characteristic
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	2	1	no	—
234	C₄×C₈	—	2	1	no	—
235	C₄×C₈	—	2	1	no	—
236	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
237	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
238	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
239	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
240	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
241	C₄×C₈	C₂×D₄	1	1	yes	characteristic
242	C₄×C₈	#41	1	1	yes	characteristic
243	C₄×C₈	C₂⁴	1	1	yes	characteristic
244	#41	—	2	2	no	—
245	#41	—	4	1	no	—
246	C₂×Q₈	—	2	1	no	—
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	—	4	1	no	—
249	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
250	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
251	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₈	1	1	yes	characteristic
261	C₂²×C₄	#131	1	1	yes	characteristic
262	Q₁₆	—	2	2	no	—
263	Q₁₆	M₃₂	1	4	yes	complemented
264	SD₁₆	—	2	2	no	—
265	SD₁₆	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	4	1	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	4	1	no	—
277	C₂×C₈	—	4	1	no	—
278	C₂×C₈	—	4	1	no	—
279	C₂×C₈	—	8	1	no	—
280	C₂×C₈	—	8	1	no	—
281	C₂×C₈	C₄×D₄	1	1	yes	characteristic
282	C₂×C₈	C₄×D₄	1	1	yes	characteristic
283	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
284	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
285	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
286	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
287	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₈	C₂×#41	1	1	yes	characteristic
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	1	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
297	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
298	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
299	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
300	C₂²⋊C₄	—	2	1	no	—
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	C₄×D₄	1	1	yes	characteristic
311	C₄²	C₂²×C₈	1	1	yes	characteristic
312	C₄²	#131	1	1	yes	characteristic
313	C₄²	C₂³×C₄	1	1	yes	characteristic
314	C₁₆	—	2	2	no	—
315	C₁₆	—	2	1	no	—
316	C₁₆	—	2	1	no	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	4	1	no	—
320	C₁₆	—	4	1	no	—
321	C₁₆	—	4	1	no	—
322	C₁₆	—	4	1	no	—
323	C₁₆	—	4	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₈×D₄	1	1	yes	characteristic
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	2	1	no	—
330	Q₈	—	4	2	no	—
331	Q₈	C₂×M₃₂	1	2	yes	—
332	Q₈	C₂×M₃₂	1	2	yes	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	4	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	C₈×D₄	1	1	yes	characteristic
355	C₂×C₄	C₈×D₄	1	1	yes	characteristic
356	C₂×C₄	C₈×D₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
358	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
359	C₂×C₄	C₂×#131	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₈	—	4	1	no	—
372	C₈	C₂×M₃₂	1	2	yes	—
373	C₈	#577	1	1	yes	characteristic
374	C₈	#578	1	1	yes	characteristic
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	#2947	1	1	yes	characteristic
394	C₄	#2956	1	1	yes	characteristic
395	C₄	C₂²×M₃₂	1	1	yes	characteristic
396	C₄	#3407	1	1	yes	characteristic
397	C₂	—	4	1	no	—
398	C₂	—	8	1	no	—
399	C₂	#17853	1	1	yes	characteristic
400	C₂	D₄×M₃₂	1	1	yes	characteristic
401	C₂	#33441	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₄
commutator	C₂×C₄	C₂³×C₈
Frattini, cosocle	C₄×C₈	C₂⁴
socle	C₂²	C₂×C₈×D₄
prime radical	C₂×#41	C₂×C₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ #2162 ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #33498	C₂	semidirect
4. #12060	C₂	semidirect
5. #12059	C₂	semidirect
6. #12058	C₂	semidirect
7. #12056	C₂	semidirect
8. #12053	C₂	semidirect
9. C₁₆×Q₁₆	C₂	semidirect
10. #12051	C₂	semidirect
11. #12050	C₂	semidirect
12. #12017	C₂	semidirect
14. #11607	C₂	semidirect
15. #11409	C₂	semidirect
263. Q₁₆	M₃₂	semidirect

Maximal subgroups

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

subgroup	index
#33505	2
#33498	2
C₈×#137	2
#12060	2
#12059	2
#12058	2
#12056	2
#12053	2
C₁₆×Q₁₆	2
#12051	2
#12050	2
#12017	2
#11615	2
#11607	2
#11409	2