Subgroups — Q₁₆×#13083557 #36525883

Order 22784.

638 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#13083557	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26019150	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019148	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019102	C₂	1	2	yes	maximal, complemented
6	#26019099	C₂	1	2	yes	maximal, complemented
7	Q₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019009	C₂	1	1	yes	maximal, characteristic
9	#26018679	C₂	1	2	yes	maximal
10	C₈×#13083557	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₈₉	C₂²	1	2	yes	—
14	#19151728	—	2	2	no	—
15	#19151728	C₂²	1	2	yes	—
16	#19151725	—	2	2	no	—
17	#19151725	C₂²	1	2	yes	—
18	Q₈×#10623494	C₂²	1	2	yes	—
19	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic
21	#19151692	C₄	1	1	yes	characteristic
22	C₄×#13083564	C₂²	1	2	yes	—
23	#19151690	C₄	1	2	yes	—
24	#19151649	C₂²	1	1	yes	characteristic
25	#107×D₈₉	C₄	1	1	yes	characteristic
26	#19151620	—	2	2	no	—
27	#19151620	C₂²	1	2	yes	—
28	#103×D₈₉	C₄	1	2	yes	—
29	C₄×#13083557	—	2	2	no	—
30	C₄×#13083557	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic
33	#19151350	C₂²	1	2	yes	—
34	#19151330	C₂²	1	2	yes	—
35	Q₈⋊#10623494	C₂²	1	2	yes	—
36	#19151328	C₂²	1	2	yes	—
37	#19151320	C₂²	1	1	yes	characteristic
38	#19151319	C₂²	1	1	yes	characteristic
39	C₈×#10623494	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	#335×C₈₉	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₈₉	C₂×C₄	1	2	yes	—
46	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083564	C₂×C₄	1	2	yes	—
48	Q₁₆×D₈₉	—	2	4	no	—
49	C₂×#13083557	—	2	2	no	—
50	C₂×#13083557	D₄	1	1	yes	characteristic
51	C₂×#13083557	D₄	1	1	yes	characteristic
52	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	Q₈×Dic₈₉	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₇₈	—	2	2	no	—
56	C₄×Dic₁₇₈	C₂³	1	2	yes	—
57	#15667977	—	2	2	no	—
58	#15667977	C₂×C₄	1	2	yes	—
59	C₄⋊C₄×D₈₉	—	2	2	no	—
60	C₄⋊C₄×D₈₉	C₂×C₄	1	2	yes	—
61	C₄²×D₈₉	—	2	2	no	—
62	C₄²×D₈₉	C₂³	1	1	yes	characteristic
63	#15667946	C₂×C₄	1	1	yes	characteristic
64	#15667945	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	—	2	2	no	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	#15667941	—	2	2	no	—
68	#15667941	—	2	2	no	—
69	#15667941	—	2	1	no	—
70	#15667941	—	2	2	no	—
71	#15667937	C₂×C₄	1	2	yes	—
72	#15667936	C₂×C₄	1	2	yes	—
73	#15667935	C₂×C₄	1	2	yes	—
74	#15667924	—	2	1	no	—
75	#15667922	—	2	2	no	—
76	#15667922	—	2	2	no	—
77	#15667922	D₄	1	1	yes	characteristic
78	#15667922	D₄	1	1	yes	characteristic
79	C₄×#10623494	—	2	2	no	—
80	C₄×#10623494	C₂³	1	1	yes	characteristic
81	C₄×#10623494	C₂³	1	1	yes	characteristic
82	C₄×#10623494	C₂³	1	1	yes	characteristic
83	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
87	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	—	2	2	no	—
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	#103×C₈₉	C₂×C₄	1	2	yes	—
91	C₄×C₈×C₈₉	—	2	2	no	—
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×Dic₁₇₈	—	2	2	no	—
96	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
97	Q₈×D₈₉	—	2	4	no	—
98	Q₈×D₈₉	—	4	2	no	—
99	C₂×C₄×D₈₉	—	2	2	no	—
100	C₂×C₄×D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
104	Dic₃₅₆	—	2	2	no	—
105	#13083564	—	2	4	no	—
106	#13083557	—	2	2	no	—
107	#13083557	—	4	4	no	—
108	#13083557	Q₁₆	1	4	yes	direct product factor
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
112	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
113	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
114	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
115	C₈×D₈₉	—	2	2	no	—
116	C₈×D₈₉	—	4	1	no	—
117	C₄⋊Dic₈₉	—	2	2	no	—
118	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
119	#13083553	—	2	2	no	—
120	#13083553	—	2	2	no	—
121	#13083553	—	2	2	no	—
122	C₄×Dic₈₉	—	2	2	no	—
123	C₄×Dic₈₉	—	2	2	no	—
124	C₄×Dic₈₉	—	2	2	no	—
125	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₈₉	#41	1	1	yes	characteristic
128	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
129	Q₁₆×C₈₉	M₁₆	1	4	yes	complemented
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₈₉	—	2	2	no	—
137	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
138	C₄²×C₈₉	—	2	2	no	—
139	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₈₉	—	2	2	no	—
142	Q₈×C₈₉	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
148	C₂×Dic₈₉	—	2	2	no	—
149	C₂×Dic₈₉	—	2	2	no	—
150	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
153	C₄×D₈₉	—	2	1	no	—
154	C₄×D₈₉	—	2	1	no	—
155	C₄×D₈₉	—	4	1	no	—
156	C₄×D₈₉	—	4	4	no	—
157	C₄×D₈₉	—	8	2	no	—
158	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
159	C₄×D₈₉	#135	1	2	yes	—
160	Dic₁₇₈	—	2	2	no	—
161	Dic₁₇₈	—	2	2	no	—
162	Dic₁₇₈	—	4	4	no	—
163	C₈×C₈₉	—	2	1	no	—
164	C₈×C₈₉	—	2	1	no	—
165	C₈×C₈₉	—	4	1	no	—
166	C₈×C₈₉	—	4	2	no	—
167	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
168	C₈×C₈₉	C₂×Q₁₆	1	2	yes	complemented
169	#10623494	—	2	1	no	—
170	#10623494	—	2	1	no	—
171	#10623494	—	2	1	no	—
172	#10623494	—	4	1	no	—
173	#10623494	—	4	2	no	—
174	#10623494	C₂×Q₁₆	1	2	yes	complemented
175	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
176	C₂×D₈₉	—	2	1	no	—
177	C₂×D₈₉	—	2	1	no	—
178	C₂×D₈₉	C₄×Q₁₆	1	2	yes	—
179	C₄×C₈₉	—	2	4	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	4	2	no	—
182	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
183	C₄×C₈₉	#568	1	1	yes	characteristic
184	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
185	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
186	Dic₈₉	—	2	1	no	—
187	Dic₈₉	—	2	1	no	—
188	Dic₈₉	—	4	2	no	—
189	Dic₈₉	—	4	2	no	—
190	Dic₈₉	C₄×Q₁₆	1	2	yes	—
191	M₁₆×Q₁₆	—	89	1	no	maximal, Sylow
192	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
193	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
194	C₂×C₈₉	#2957	1	1	yes	characteristic
195	D₈₉	—	2	2	no	—
196	Q₈×M₁₆	—	89	2	no	—
197	C₂×C₄×Q₁₆	—	89	1	no	—
198	#1591	—	89	1	no	—
199	#1591	—	89	1	no	—
200	#1584	—	89	2	no	—
201	#1584	—	89	2	no	—
202	C₈×Q₁₆	—	89	1	no	—
203	C₈×Q₁₆	D₈₉	1	1	yes	characteristic, complemented
204	#1567	—	89	1	no	—
205	#1487	—	89	2	no	—
206	C₈×M₁₆	—	89	1	no	—
207	C₈₉	M₁₆×Q₁₆	1	1	yes	characteristic, complemented, Sylow
208	C₂²×Q₁₆	—	89	1	no	—
209	C₂×C₄×Q₈	—	89	2	no	—
210	#446	—	89	2	no	—
211	#446	—	89	2	no	—
212	#446	—	178	2	no	—
213	#446	—	178	2	no	—
214	C₈×Q₈	—	89	2	no	—
215	C₈×Q₈	C₂×D₈₉	1	2	yes	—
216	C₄×Q₁₆	—	89	1	no	—
217	C₄×Q₁₆	—	89	2	no	—
218	C₄×Q₁₆	—	89	1	no	—
219	C₄×Q₁₆	—	89	2	no	—
220	C₄×Q₁₆	—	89	1	no	—
221	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
222	#431	—	89	1	no	—
223	C₂×#107	—	89	1	no	—
224	#423	—	89	2	no	—
225	#423	—	178	2	no	—
226	C₂×#103	—	89	2	no	—
227	C₄×M₁₆	—	89	1	no	—
228	C₄×M₁₆	—	178	2	no	—
229	C₂×C₄×C₈	—	89	1	no	—
230	#335	—	89	2	no	—
231	#335	—	89	1	no	—
232	#335	C₂×D₈₉	1	1	yes	characteristic
233	Q₈⋊C₈	—	89	2	no	—
234	Q₈⋊C₈	—	89	2	no	—
235	Q₈⋊C₈	—	89	2	no	—
236	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
237	#322	—	89	1	no	—
238	#322	—	89	1	no	—
239	C₈²	—	89	1	no	—
240	C₈²	C₂×D₈₉	1	1	yes	characteristic
241	C₂²×Q₈	—	89	2	no	—
242	C₂×Q₁₆	—	89	2	no	—
243	C₂×Q₁₆	—	89	1	no	—
244	C₂×Q₁₆	—	178	4	no	—
245	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
246	C₂×M₁₆	—	89	1	no	—
247	C₂×M₁₆	—	89	1	no	—
248	C₂×M₁₆	—	178	2	no	—
249	C₂²×C₈	—	89	1	no	—
250	C₂²×C₈	—	89	1	no	—
251	C₄×Q₈	—	89	2	no	—
252	C₄×Q₈	—	89	2	no	—
253	C₄×Q₈	—	89	2	no	—
254	C₄×Q₈	—	178	2	no	—
255	C₄×Q₈	—	178	2	no	—
256	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
257	C₂×C₄⋊C₄	—	89	2	no	—
258	C₂×C₄⋊C₄	—	178	2	no	—
259	C₂×C₄²	—	89	1	no	—
260	C₂×C₄²	—	178	2	no	—
261	#107	—	89	1	no	—
262	#107	—	89	2	no	—
263	#107	C₄×D₈₉	1	1	yes	characteristic
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	89	2	no	—
266	C₄⋊C₈	—	178	2	no	—
267	C₄⋊C₈	—	178	2	no	—
268	C₄⋊C₈	—	178	1	no	—
269	C₄⋊C₈	—	178	2	no	—
270	C₄⋊C₈	—	178	2	no	—
271	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
272	#103	—	89	2	no	—
273	#103	—	89	2	no	—
274	#103	—	89	2	no	—
275	#103	C₄×D₈₉	1	2	yes	—
276	C₂²⋊C₈	—	178	1	no	—
277	#97	—	89	1	no	—
278	#97	—	89	1	no	—
279	#97	—	178	2	no	—
280	#97	—	178	2	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	89	1	no	—
283	C₄×C₈	—	89	1	no	—
284	C₄×C₈	—	89	1	no	—
285	C₄×C₈	—	89	1	no	—
286	C₄×C₈	—	89	1	no	—
287	C₄×C₈	—	178	2	no	—
288	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₂×Q₈	—	89	2	no	—
292	C₂×Q₈	—	356	2	no	—
293	C₂×Q₈	—	178	2	no	—
294	C₂×Q₈	—	178	4	no	—
295	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
296	C₂²×C₄	—	89	1	no	—
297	C₂²×C₄	—	89	1	no	—
298	C₂²×C₄	—	89	1	no	—
299	C₂²×C₄	—	178	2	no	—
300	C₂²×C₄	—	178	2	no	—
301	Q₁₆	—	178	4	no	—
302	Q₁₆	—	178	2	no	—
303	Q₁₆	#13083557	1	4	yes	direct product factor
304	M₁₆	—	89	4	no	—
305	M₁₆	—	356	4	no	—
306	M₁₆	—	178	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	89	1	no	—
310	C₂×C₈	—	89	1	no	—
311	C₂×C₈	—	89	1	no	—
312	C₂×C₈	—	89	1	no	—
313	C₂×C₈	—	356	1	no	—
314	C₂×C₈	—	178	2	no	—
315	C₂×C₈	—	178	1	no	—
316	C₂×C₈	—	178	2	no	—
317	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
318	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
319	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
320	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	89	2	no	—
323	C₄⋊C₄	—	178	2	no	—
324	C₄⋊C₄	—	178	2	no	—
325	C₄⋊C₄	—	178	2	no	—
326	C₄⋊C₄	—	178	2	no	—
327	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
328	C₄²	—	2	2	no	—
329	C₄²	—	89	1	no	—
330	C₄²	—	89	1	no	—
331	C₄²	—	89	1	no	—
332	C₄²	—	178	2	no	—
333	C₄²	—	178	2	no	—
334	C₄²	—	178	2	no	—
335	C₄²	C₂³×D₈₉	1	1	yes	characteristic
336	C₂³	—	89	1	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	356	4	no	—
339	Q₈	—	178	2	no	—
340	Q₈	—	178	2	no	—
341	Q₈	C₂×#13083557	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	89	1	no	—
345	C₂×C₄	—	89	2	no	—
346	C₂×C₄	—	89	2	no	—
347	C₂×C₄	—	89	1	no	—
348	C₂×C₄	—	89	1	no	—
349	C₂×C₄	—	356	4	no	—
350	C₂×C₄	—	356	1	no	—
351	C₂×C₄	—	178	2	no	—
352	C₂×C₄	—	178	2	no	—
353	C₂×C₄	—	178	1	no	—
354	C₂×C₄	—	178	1	no	—
355	C₂×C₄	—	712	2	no	—
356	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	2	no	—
363	C₈	—	89	2	no	—
364	C₈	—	356	1	no	—
365	C₈	—	356	2	no	—
366	C₈	—	178	1	no	—
367	C₈	—	178	1	no	—
368	C₈	—	178	1	no	—
369	C₈	C₂×#13083557	1	2	yes	—
370	C₈	Q₁₆×D₈₉	1	2	yes	complemented
371	C₂²	—	89	2	no	—
372	C₂²	—	178	1	no	—
373	C₂²	—	178	1	no	—
374	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	89	2	no	—
379	C₄	—	356	2	no	—
380	C₄	—	356	2	no	—
381	C₄	—	178	1	no	—
382	C₄	—	178	1	no	—
383	C₄	C₂²×#13083557	1	1	yes	characteristic
384	C₄	#19152363	1	1	yes	characteristic
385	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
386	C₄	#135×D₈₉	1	1	yes	characteristic
387	C₂	—	178	2	no	—
388	C₂	D₄×#13083557	1	1	yes	characteristic
389	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
390	C₂	#26029164	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×Q₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×Q₁₆	D₈₉
hypocenter	C₈₉	M₁₆×Q₁₆
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #26019150	C₂	semidirect
4. #26019148	C₂	semidirect
5. #26019102	C₂	semidirect
6. #26019099	C₂	semidirect
7. Q₁₆×#10623494	C₂	semidirect
11. C₈×Q₁₆×C₈₉	C₂	semidirect
108. #13083557	Q₁₆	direct (N × H)
129. Q₁₆×C₈₉	M₁₆	semidirect
168. C₈×C₈₉	C₂×Q₁₆	semidirect
174. #10623494	C₂×Q₁₆	semidirect
203. C₈×Q₁₆	D₈₉	semidirect
207. C₈₉	M₁₆×Q₁₆	semidirect
303. Q₁₆	#13083557	direct (N × H)
370. C₈	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#13083557	2
C₄×Q₁₆×D₈₉	2
#26019150	2
#26019148	2
#26019102	2
#26019099	2
Q₁₆×#10623494	2
#26019009	2
#26018679	2
C₈×#13083557	2
C₈×Q₁₆×C₈₉	2
M₁₆×Q₁₆	89

Subgroups — Q16×#13083557 #36525883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#13083557 #36525883