Subgroups — Q₁₆×#11745659 #28560144

Order 15104.

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×#11745659	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#21422994	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422992	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422946	C₂	1	2	yes	maximal, complemented
6	#21422943	C₂	1	2	yes	maximal, complemented
7	Q₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422853	C₂	1	1	yes	maximal, characteristic
9	#21422523	C₂	1	2	yes	maximal
10	C₈×#11745659	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₉	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₅₉	C₂²	1	2	yes	—
14	#16837532	—	2	2	no	—
15	#16837532	C₂²	1	2	yes	—
16	#16837529	—	2	2	no	—
17	#16837529	C₂²	1	2	yes	—
18	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
19	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₅₉	C₄	1	1	yes	characteristic
21	#16837496	C₄	1	1	yes	characteristic
22	C₄×#11745672	C₂²	1	2	yes	—
23	#16837494	C₄	1	2	yes	—
24	#16837453	C₂²	1	1	yes	characteristic
25	#107×D₅₉	C₄	1	1	yes	characteristic
26	#16837424	—	2	2	no	—
27	#16837424	C₂²	1	2	yes	—
28	#103×D₅₉	C₄	1	2	yes	—
29	C₄×#11745659	—	2	2	no	—
30	C₄×#11745659	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
32	#16837155	C₂²	1	1	yes	characteristic
33	#16837154	C₂²	1	2	yes	—
34	#16837134	C₂²	1	2	yes	—
35	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
36	#16837132	C₂²	1	2	yes	—
37	#16837124	C₂²	1	1	yes	characteristic
38	#16837123	C₂²	1	1	yes	characteristic
39	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#335	C₂²	1	1	yes	characteristic
43	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₅₉	C₂×C₄	1	2	yes	—
46	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#11745672	C₂×C₄	1	2	yes	—
48	Q₁₆×D₅₉	—	2	4	no	—
49	C₂×#11745659	—	2	2	no	—
50	C₂×#11745659	D₄	1	1	yes	characteristic
51	C₂×#11745659	D₄	1	1	yes	characteristic
52	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
54	Q₈×Dic₅₉	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₁₈	—	2	2	no	—
56	C₄×Dic₁₁₈	C₂³	1	2	yes	—
57	#14273692	—	2	2	no	—
58	#14273692	C₂×C₄	1	2	yes	—
59	C₄⋊C₄×D₅₉	—	2	2	no	—
60	C₄⋊C₄×D₅₉	C₂×C₄	1	2	yes	—
61	C₄²×D₅₉	—	2	2	no	—
62	C₄²×D₅₉	C₂³	1	1	yes	characteristic
63	#14273661	C₂×C₄	1	1	yes	characteristic
64	#14273660	C₂×C₄	1	2	yes	—
65	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
66	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
67	Dic₅₉⋊C₈	—	2	2	no	—
68	Dic₅₉⋊C₈	—	2	2	no	—
69	Dic₅₉⋊C₈	—	2	1	no	—
70	Dic₅₉⋊C₈	—	2	2	no	—
71	#14273652	C₂×C₄	1	2	yes	—
72	#14273651	C₂×C₄	1	2	yes	—
73	#14273650	C₂×C₄	1	2	yes	—
74	(C₂×D₅₉)⋊C₈	—	2	1	no	—
75	#14273637	—	2	2	no	—
76	#14273637	—	2	2	no	—
77	#14273637	D₄	1	1	yes	characteristic
78	#14273637	D₄	1	1	yes	characteristic
79	C₄×C₅₉⋊C₈	—	2	2	no	—
80	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
87	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₅₉	—	2	2	no	—
89	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
90	#103×C₅₉	C₂×C₄	1	2	yes	—
91	C₄×C₈×C₅₉	—	2	2	no	—
92	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
96	Q₈×D₅₉	—	2	4	no	—
97	Q₈×D₅₉	—	4	2	no	—
98	C₂×C₄×D₅₉	—	2	2	no	—
99	C₂×C₄×D₅₉	—	2	2	no	—
100	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
103	C₂×Dic₁₁₈	—	2	2	no	—
104	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
105	Q₁₆×C₅₉	M₁₆	1	4	yes	complemented
106	C₂×C₈×C₅₉	—	2	2	no	—
107	C₂×C₈×C₅₉	—	2	1	no	—
108	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₄⋊C₄×C₅₉	—	2	2	no	—
113	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
114	C₄²×C₅₉	—	2	2	no	—
115	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
116	#11745672	—	2	4	no	—
117	C₄⋊Dic₅₉	—	2	2	no	—
118	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
119	Dic₅₉⋊C₄	—	2	2	no	—
120	Dic₅₉⋊C₄	—	2	2	no	—
121	Dic₅₉⋊C₄	—	2	2	no	—
122	C₄×Dic₅₉	—	2	2	no	—
123	C₄×Dic₅₉	—	2	2	no	—
124	C₄×Dic₅₉	—	2	2	no	—
125	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₅₉	#41	1	1	yes	characteristic
128	C₂×C₅₉⋊C₈	—	2	2	no	—
129	C₂×C₅₉⋊C₈	—	2	1	no	—
130	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
134	Dic₂₃₆	—	2	2	no	—
135	#11745659	—	2	2	no	—
136	#11745659	—	4	4	no	—
137	#11745659	Q₁₆	1	4	yes	direct product factor
138	C₈×D₅₉	—	2	2	no	—
139	C₈×D₅₉	—	4	1	no	—
140	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₅₉	—	2	2	no	—
142	Q₈×C₅₉	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	2	2	no	—
145	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
148	C₂×Dic₅₉	—	2	2	no	—
149	C₂×Dic₅₉	—	2	2	no	—
150	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
151	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
153	C₄×D₅₉	—	2	1	no	—
154	C₄×D₅₉	—	2	1	no	—
155	C₄×D₅₉	—	4	1	no	—
156	C₄×D₅₉	—	4	4	no	—
157	C₄×D₅₉	—	8	2	no	—
158	C₄×D₅₉	C₂×Q₁₆	1	2	yes	—
159	C₄×D₅₉	#135	1	2	yes	—
160	Dic₁₁₈	—	2	2	no	—
161	Dic₁₁₈	—	2	2	no	—
162	Dic₁₁₈	—	4	4	no	—
163	C₈×C₅₉	—	2	1	no	—
164	C₈×C₅₉	—	2	1	no	—
165	C₈×C₅₉	—	4	1	no	—
166	C₈×C₅₉	—	4	2	no	—
167	C₈×C₅₉	C₂×M₁₆	1	2	yes	—
168	C₈×C₅₉	C₂×Q₁₆	1	2	yes	complemented
169	C₅₉⋊C₈	—	2	1	no	—
170	C₅₉⋊C₈	—	2	1	no	—
171	C₅₉⋊C₈	—	2	1	no	—
172	C₅₉⋊C₈	—	4	1	no	—
173	C₅₉⋊C₈	—	4	2	no	—
174	C₅₉⋊C₈	C₂×Q₁₆	1	2	yes	complemented
175	M₁₆×Q₁₆	—	59	1	no	maximal, Sylow
176	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂×D₅₉	—	2	1	no	—
178	C₂×D₅₉	—	2	1	no	—
179	C₂×D₅₉	C₄×Q₁₆	1	2	yes	—
180	C₄×C₅₉	—	2	4	no	—
181	C₄×C₅₉	—	2	1	no	—
182	C₄×C₅₉	—	4	2	no	—
183	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
184	C₄×C₅₉	#568	1	1	yes	characteristic
185	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
186	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
187	Dic₅₉	—	2	1	no	—
188	Dic₅₉	—	2	1	no	—
189	Dic₅₉	—	4	2	no	—
190	Dic₅₉	—	4	2	no	—
191	Dic₅₉	C₄×Q₁₆	1	2	yes	—
192	Q₈×M₁₆	—	59	2	no	—
193	C₂×C₄×Q₁₆	—	59	1	no	—
194	#1591	—	59	1	no	—
195	#1591	—	59	1	no	—
196	#1584	—	59	2	no	—
197	#1584	—	59	2	no	—
198	C₈×Q₁₆	—	59	1	no	—
199	C₈×Q₁₆	D₅₉	1	1	yes	characteristic, complemented
200	#1567	—	59	1	no	—
201	#1487	—	59	2	no	—
202	C₈×M₁₆	—	59	1	no	—
203	C₂×C₅₉	D₄×M₁₆	1	1	yes	characteristic
204	C₂×C₅₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
205	C₂×C₅₉	#2957	1	1	yes	characteristic
206	D₅₉	—	2	2	no	—
207	C₂²×Q₁₆	—	59	1	no	—
208	C₂×C₄×Q₈	—	59	2	no	—
209	#446	—	59	2	no	—
210	#446	—	59	2	no	—
211	#446	—	118	2	no	—
212	#446	—	118	2	no	—
213	C₈×Q₈	—	59	2	no	—
214	C₈×Q₈	C₂×D₅₉	1	2	yes	—
215	C₄×Q₁₆	—	59	1	no	—
216	C₄×Q₁₆	—	59	2	no	—
217	C₄×Q₁₆	—	59	1	no	—
218	C₄×Q₁₆	—	59	2	no	—
219	C₄×Q₁₆	—	59	1	no	—
220	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
221	#431	—	59	1	no	—
222	C₂×#107	—	59	1	no	—
223	#423	—	59	2	no	—
224	#423	—	118	2	no	—
225	C₂×#103	—	59	2	no	—
226	C₄×M₁₆	—	59	1	no	—
227	C₄×M₁₆	—	118	2	no	—
228	C₂×C₄×C₈	—	59	1	no	—
229	#335	—	59	2	no	—
230	#335	—	59	1	no	—
231	#335	C₂×D₅₉	1	1	yes	characteristic
232	Q₈⋊C₈	—	59	2	no	—
233	Q₈⋊C₈	—	59	2	no	—
234	Q₈⋊C₈	—	59	2	no	—
235	Q₈⋊C₈	C₂×D₅₉	1	2	yes	—
236	#322	—	59	1	no	—
237	#322	—	59	1	no	—
238	C₈²	—	59	1	no	—
239	C₈²	C₂×D₅₉	1	1	yes	characteristic
240	C₅₉	M₁₆×Q₁₆	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	—	59	2	no	—
242	C₂×Q₁₆	—	59	2	no	—
243	C₂×Q₁₆	—	59	1	no	—
244	C₂×Q₁₆	—	118	4	no	—
245	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
246	C₂×M₁₆	—	59	1	no	—
247	C₂×M₁₆	—	59	1	no	—
248	C₂×M₁₆	—	118	2	no	—
249	C₂²×C₈	—	59	1	no	—
250	C₂²×C₈	—	59	1	no	—
251	C₄×Q₈	—	59	2	no	—
252	C₄×Q₈	—	59	2	no	—
253	C₄×Q₈	—	59	2	no	—
254	C₄×Q₈	—	118	2	no	—
255	C₄×Q₈	—	118	2	no	—
256	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
257	C₂×C₄⋊C₄	—	59	2	no	—
258	C₂×C₄⋊C₄	—	118	2	no	—
259	C₂×C₄²	—	59	1	no	—
260	C₂×C₄²	—	118	2	no	—
261	#107	—	59	1	no	—
262	#107	—	59	2	no	—
263	#107	C₄×D₅₉	1	1	yes	characteristic
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	59	2	no	—
266	C₄⋊C₈	—	118	2	no	—
267	C₄⋊C₈	—	118	2	no	—
268	C₄⋊C₈	—	118	1	no	—
269	C₄⋊C₈	—	118	2	no	—
270	C₄⋊C₈	—	118	2	no	—
271	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
272	#103	—	59	2	no	—
273	#103	—	59	2	no	—
274	#103	—	59	2	no	—
275	#103	C₄×D₅₉	1	2	yes	—
276	C₂²⋊C₈	—	118	1	no	—
277	#97	—	59	1	no	—
278	#97	—	59	1	no	—
279	#97	—	118	2	no	—
280	#97	—	118	2	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	59	1	no	—
283	C₄×C₈	—	59	1	no	—
284	C₄×C₈	—	59	1	no	—
285	C₄×C₈	—	59	1	no	—
286	C₄×C₈	—	59	1	no	—
287	C₄×C₈	—	118	2	no	—
288	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
291	C₂×Q₈	—	59	2	no	—
292	C₂×Q₈	—	118	2	no	—
293	C₂×Q₈	—	118	4	no	—
294	C₂×Q₈	—	236	2	no	—
295	C₂×Q₈	C₂×C₄×D₅₉	1	2	yes	—
296	C₂²×C₄	—	59	1	no	—
297	C₂²×C₄	—	59	1	no	—
298	C₂²×C₄	—	59	1	no	—
299	C₂²×C₄	—	118	2	no	—
300	C₂²×C₄	—	118	2	no	—
301	Q₁₆	—	118	4	no	—
302	Q₁₆	—	118	2	no	—
303	Q₁₆	#11745659	1	4	yes	direct product factor
304	M₁₆	—	59	4	no	—
305	M₁₆	—	118	2	no	—
306	M₁₆	—	236	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	59	1	no	—
310	C₂×C₈	—	59	1	no	—
311	C₂×C₈	—	59	1	no	—
312	C₂×C₈	—	59	1	no	—
313	C₂×C₈	—	118	2	no	—
314	C₂×C₈	—	118	2	no	—
315	C₂×C₈	—	118	1	no	—
316	C₂×C₈	—	236	1	no	—
317	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
318	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
319	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
320	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	59	2	no	—
323	C₄⋊C₄	—	118	2	no	—
324	C₄⋊C₄	—	118	2	no	—
325	C₄⋊C₄	—	118	2	no	—
326	C₄⋊C₄	—	118	2	no	—
327	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
328	C₄²	—	2	2	no	—
329	C₄²	—	59	1	no	—
330	C₄²	—	59	1	no	—
331	C₄²	—	59	1	no	—
332	C₄²	—	118	2	no	—
333	C₄²	—	118	2	no	—
334	C₄²	—	118	2	no	—
335	C₄²	C₂³×D₅₉	1	1	yes	characteristic
336	C₂³	—	59	1	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	118	2	no	—
339	Q₈	—	118	2	no	—
340	Q₈	—	236	4	no	—
341	Q₈	C₂×#11745659	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	59	1	no	—
345	C₂×C₄	—	59	2	no	—
346	C₂×C₄	—	59	2	no	—
347	C₂×C₄	—	59	1	no	—
348	C₂×C₄	—	59	1	no	—
349	C₂×C₄	—	118	1	no	—
350	C₂×C₄	—	118	1	no	—
351	C₂×C₄	—	118	2	no	—
352	C₂×C₄	—	118	2	no	—
353	C₂×C₄	—	472	2	no	—
354	C₂×C₄	—	236	1	no	—
355	C₂×C₄	—	236	4	no	—
356	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
358	C₂×C₄	#41×D₅₉	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	—	59	2	no	—
364	C₈	—	118	1	no	—
365	C₈	—	118	1	no	—
366	C₈	—	118	1	no	—
367	C₈	—	236	1	no	—
368	C₈	—	236	2	no	—
369	C₈	C₂×#11745659	1	2	yes	—
370	C₈	Q₁₆×D₅₉	1	2	yes	complemented
371	C₂²	—	59	2	no	—
372	C₂²	—	118	1	no	—
373	C₂²	—	118	1	no	—
374	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	59	2	no	—
379	C₄	—	118	1	no	—
380	C₄	—	118	1	no	—
381	C₄	—	236	2	no	—
382	C₄	—	236	2	no	—
383	C₄	C₂²×#11745659	1	1	yes	characteristic
384	C₄	#16838167	1	1	yes	characteristic
385	C₄	C₂×Q₁₆×D₅₉	1	1	yes	characteristic
386	C₄	#135×D₅₉	1	1	yes	characteristic
387	C₂	—	118	2	no	—
388	C₂	D₄×#11745659	1	1	yes	characteristic
389	C₂	C₄×Q₁₆×D₅₉	1	1	yes	characteristic
390	C₂	#21433008	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₈×Q₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₈×Q₁₆	D₅₉
hypocenter	C₅₉	M₁₆×Q₁₆
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
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. #21422994	C₂	semidirect
4. #21422992	C₂	semidirect
5. #21422946	C₂	semidirect
6. #21422943	C₂	semidirect
7. Q₁₆×C₅₉⋊C₈	C₂	semidirect
11. C₈×Q₁₆×C₅₉	C₂	semidirect
105. Q₁₆×C₅₉	M₁₆	semidirect
137. #11745659	Q₁₆	direct (N × H)
168. C₈×C₅₉	C₂×Q₁₆	semidirect
174. C₅₉⋊C₈	C₂×Q₁₆	semidirect
199. C₈×Q₁₆	D₅₉	semidirect
240. C₅₉	M₁₆×Q₁₆	semidirect
303. Q₁₆	#11745659	direct (N × H)
370. C₈	Q₁₆×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#11745659	2
C₄×Q₁₆×D₅₉	2
#21422994	2
#21422992	2
#21422946	2
#21422943	2
Q₁₆×C₅₉⋊C₈	2
#21422853	2
#21422523	2
C₈×#11745659	2
C₈×Q₁₆×C₅₉	2
M₁₆×Q₁₆	59

Subgroups — Q16×#11745659 #28560144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×#11745659 #28560144