Subgroups — #29833594

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₁₆×D₂₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#11758185	C₂	1	1	yes	maximal, characteristic, complemented
4	#21447638	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×C₂²⋊D₆₁	C₂	1	2	yes	maximal, complemented
6	#21447636	C₂	1	2	yes	maximal, complemented
7	#21447617	C₂	1	1	yes	maximal, characteristic, complemented
8	#21447616	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16839541	C₂	1	2	yes	maximal, complemented
10	C₂²⋊C₁₆×D₆₁	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₆₁	C₂²	1	2	yes	—
13	C₄×D₄×D₆₁	C₄	1	1	yes	characteristic
14	C₂²×#11758185	C₂²	1	2	yes	complemented
15	C₂×C₁₆×D₆₁	C₂²	1	2	yes	complemented
16	C₂×C₁₆×D₆₁	C₂²	1	2	yes	complemented
17	C₈×D₂₄₄	C₂²	1	1	yes	characteristic
18	D₄×#92418	C₄	1	1	yes	characteristic
19	#16839827	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₆₁	C₂²	1	2	yes	—
21	#16839825	C₄	1	2	yes	—
22	C₄⋊C₈×D₆₁	C₄	1	1	yes	characteristic
23	C₂²⋊C₈×D₆₁	C₄	1	2	yes	—
24	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
25	C₄⋊#11758185	C₂²	1	1	yes	characteristic, complemented
26	#16839580	C₂²	1	1	yes	characteristic, complemented
27	#16839580	C₂²	1	1	yes	characteristic, complemented
28	C₂²⋊#11758185	C₂²	1	2	yes	complemented
29	#16839541	C₂²	1	1	yes	characteristic
30	#16839541	C₂²	1	2	yes	—
31	#16839541	C₂²	1	1	yes	characteristic
32	#16839541	C₂²	1	2	yes	complemented
33	#16839541	C₂²	1	2	yes	complemented
34	C₄×#11758185	C₂²	1	1	yes	characteristic, complemented
35	C₁₆×Dic₆₁	C₂²	1	2	yes	complemented
36	C₂²×C₁₆×C₆₁	C₂²	1	2	yes	complemented
37	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₆₁	C₈	1	1	yes	characteristic
42	C₂²×C₄×D₆₁	C₂×C₄	1	2	yes	—
43	C₂²×#92418	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₆₁	—	4	2	no	—
45	C₂×C₈×D₆₁	—	4	2	no	—
46	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₆₁	C₂³	1	2	yes	—
51	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
52	D₄×Dic₆₁	C₈	1	1	yes	characteristic
53	#14519739	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
55	#14519737	C₈	1	2	yes	—
56	C₄⋊C₄×D₆₁	C₈	1	1	yes	characteristic
57	C₂²⋊C₄×D₆₁	C₈	1	2	yes	—
58	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×#11758185	—	4	2	no	—
60	C₂×#11758185	C₂³	1	2	yes	—
61	C₂×#11758185	C₂³	1	1	yes	characteristic
62	C₂×#11758185	C₂³	1	1	yes	characteristic
63	C₁₆×D₆₁	—	4	2	no	—
64	C₁₆×D₆₁	—	4	2	no	—
65	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
66	#14519706	C₂×C₄	1	2	yes	—
67	C₂²⋊#92418	C₂×C₄	1	2	yes	—
68	#14519689	C₂×C₄	1	2	yes	—
69	#14519689	C₂×C₄	1	2	yes	—
70	C₄×#92418	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
74	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₆×C₆₁	—	4	2	no	—
76	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
79	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂³×D₆₁	C₂×C₈	1	2	yes	—
83	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
85	C₂×C₂²⋊D₆₁	C₂×C₈	1	2	yes	—
86	C₂²×Dic₆₁	C₂×C₈	1	2	yes	—
87	D₄×D₆₁	C₁₆	1	8	yes	complemented
88	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₆₁	—	4	2	no	—
90	C₂×C₄×D₆₁	—	4	2	no	—
91	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
92	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
93	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₆₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₆₁	—	2	2	no	—
98	C₂×C₈×C₆₁	—	2	2	no	—
99	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
103	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
104	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²⋊Dic₆₁	C₂×C₈	1	2	yes	—
106	#11758198	C₂×C₈	1	2	yes	—
107	#11758198	C₂×C₈	1	2	yes	—
108	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
109	#11758196	C₂×C₈	1	2	yes	—
110	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
111	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
112	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×#92418	—	4	2	no	—
114	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
115	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
116	C₂×#92418	C₂²×C₄	1	2	yes	—
117	C₈×D₆₁	—	2	2	no	—
118	C₈×D₆₁	—	2	2	no	—
119	C₈×D₆₁	—	2	1	no	—
120	C₈×D₆₁	—	2	1	no	—
121	C₈×D₆₁	—	4	2	no	—
122	C₈×D₆₁	—	4	2	no	—
123	C₈×D₆₁	—	4	1	no	—
124	C₁₆×C₆₁	—	2	1	no	—
125	C₁₆×C₆₁	—	2	2	no	—
126	C₁₆×C₆₁	—	2	1	no	—
127	#11758185	—	2	1	no	—
128	#11758185	—	2	2	no	—
129	#11758185	—	2	1	no	—
130	C₂³×C₆₁	C₂²×C₈	1	2	yes	—
131	C₂²×D₆₁	—	4	2	no	—
132	C₂²×D₆₁	—	4	2	no	—
133	C₂²×D₆₁	C₂×C₁₆	1	8	yes	complemented
134	C₂²×D₆₁	C₂²×C₈	1	2	yes	—
135	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
136	D₄×C₆₁	C₂×C₁₆	1	4	yes	complemented
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
143	C₂²⋊D₆₁	C₂×C₁₆	1	8	yes	complemented
144	C₂×Dic₆₁	—	4	2	no	—
145	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₆₁	C₂²×C₈	1	2	yes	—
148	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
149	D₂₄₄	C₂×C₁₆	1	4	yes	complemented
150	C₄×D₆₁	—	2	1	no	—
151	C₄×D₆₁	—	2	2	no	—
152	C₄×D₆₁	—	2	1	no	—
153	C₄×D₆₁	—	2	2	no	—
154	C₄×D₆₁	—	4	2	no	—
155	C₄×D₆₁	—	4	2	no	—
156	C₄×D₆₁	—	4	1	no	—
157	C₄×D₆₁	C₂×C₁₆	1	4	yes	complemented
158	C₈×C₆₁	—	2	2	no	—
159	C₈×C₆₁	—	2	1	no	—
160	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
162	#92418	—	2	1	no	—
163	#92418	—	2	2	no	—
164	#92418	—	2	1	no	—
165	#33486	—	61	1	no	maximal, Sylow
166	C₂²×C₆₁	—	2	2	no	—
167	C₂²×C₆₁	—	2	2	no	—
168	C₂²×C₆₁	C₂²×C₁₆	1	4	yes	—
169	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
170	C₂×D₆₁	—	2	1	no	—
171	C₂×D₆₁	—	2	2	no	—
172	C₂×D₆₁	—	2	1	no	—
173	C₂×D₆₁	—	2	2	no	—
174	C₂×D₆₁	—	4	8	no	—
175	C₂×D₆₁	C₂²×C₁₆	1	2	yes	—
176	C₂×D₆₁	C₂²×C₁₆	1	4	yes	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	2	no	—
179	C₄×C₆₁	C₂²×C₁₆	1	2	yes	—
180	C₄×C₆₁	#518	1	1	yes	characteristic
181	C₄×C₆₁	#568	1	1	yes	characteristic
182	Dic₆₁	—	2	1	no	—
183	Dic₆₁	—	2	1	no	—
184	Dic₆₁	—	2	2	no	—
185	Dic₆₁	C₂²×C₁₆	1	2	yes	—
186	C₂×C₈×D₄	—	61	1	no	—
187	D₄×C₁₆	—	61	2	no	—
188	D₄×C₁₆	—	61	1	no	—
189	D₄×C₁₆	—	61	1	no	—
190	D₄×C₁₆	—	61	2	no	—
191	D₄×C₁₆	—	61	1	no	—
192	D₄×C₁₆	D₆₁	1	1	yes	characteristic, complemented
193	#2162	—	61	1	no	—
194	#2162	—	61	1	no	—
195	C₂×C₂²⋊C₁₆	—	61	2	no	—
196	C₂×C₂²⋊C₁₆	—	61	2	no	—
197	C₂×C₆₁	—	2	4	no	—
198	C₂×C₆₁	#2972	1	1	yes	characteristic
199	C₂×C₆₁	C₂³×C₁₆	1	1	yes	characteristic
200	C₂×C₆₁	#3407	1	1	yes	characteristic
201	D₆₁	—	2	2	no	—
202	D₆₁	—	2	4	no	—
203	C₂³×C₈	—	61	2	no	—
204	C₂×C₄×D₄	—	61	1	no	—
205	C₂²×C₁₆	—	61	2	no	—
206	C₂²×C₁₆	—	61	2	no	—
207	C₂²×C₁₆	—	61	2	no	—
208	C₂²×C₁₆	C₂×D₆₁	1	2	yes	complemented
209	C₈×D₄	—	61	2	no	—
210	C₈×D₄	—	61	1	no	—
211	C₈×D₄	—	61	1	no	—
212	C₈×D₄	—	61	2	no	—
213	C₈×D₄	—	61	1	no	—
214	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
215	C₂×C₄⋊C₈	—	61	1	no	—
216	C₂×C₂²⋊C₈	—	61	2	no	—
217	C₂×C₄×C₈	—	61	1	no	—
218	C₄⋊C₁₆	—	61	1	no	—
219	C₄⋊C₁₆	—	61	1	no	—
220	C₄⋊C₁₆	—	61	1	no	—
221	C₄⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
222	C₂²⋊C₁₆	—	61	2	no	—
223	C₂²⋊C₁₆	—	61	2	no	—
224	C₂²⋊C₁₆	—	61	1	no	—
225	C₂²⋊C₁₆	—	61	1	no	—
226	C₂²⋊C₁₆	—	61	2	no	—
227	C₂²⋊C₁₆	—	61	2	no	—
228	C₂²⋊C₁₆	C₂×D₆₁	1	2	yes	complemented
229	C₄×C₁₆	—	61	2	no	—
230	C₄×C₁₆	—	61	1	no	—
231	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
232	C₆₁	#33486	1	1	yes	characteristic, complemented, Sylow
233	C₂²×D₄	—	61	1	no	—
234	C₂³×C₄	—	61	2	no	—
235	C₂²×C₈	—	61	2	no	—
236	C₂²×C₈	—	61	1	no	—
237	C₂²×C₈	—	61	2	no	—
238	C₂²×C₈	—	61	2	no	—
239	C₂²×C₈	—	61	2	no	—
240	C₂²×C₈	—	61	1	no	—
241	C₂²×C₈	—	244	2	no	—
242	C₂²×C₈	—	244	2	no	—
243	C₂²×C₈	C₂²×D₆₁	1	2	yes	—
244	C₄×D₄	—	61	1	no	—
245	C₄×D₄	—	61	2	no	—
246	C₄×D₄	—	61	1	no	—
247	C₄×D₄	—	61	2	no	—
248	C₄×D₄	—	61	1	no	—
249	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	61	1	no	—
251	C₂×C₂²⋊C₄	—	61	2	no	—
252	C₂×C₄²	—	61	1	no	—
253	C₂×C₁₆	—	4	2	no	—
254	C₂×C₁₆	—	61	1	no	—
255	C₂×C₁₆	—	61	2	no	—
256	C₂×C₁₆	—	61	1	no	—
257	C₂×C₁₆	—	244	2	no	—
258	C₂×C₁₆	—	244	2	no	—
259	C₂×C₁₆	—	244	2	no	—
260	C₂×C₁₆	C₂²×D₆₁	1	2	yes	—
261	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
263	C₄⋊C₈	—	61	2	no	—
264	C₄⋊C₈	—	61	1	no	—
265	C₄⋊C₈	C₄×D₆₁	1	1	yes	characteristic
266	C₂²⋊C₈	—	61	2	no	—
267	C₂²⋊C₈	—	61	2	no	—
268	C₂²⋊C₈	—	61	2	no	—
269	C₂²⋊C₈	C₄×D₆₁	1	2	yes	—
270	C₄×C₈	—	61	1	no	—
271	C₄×C₈	—	61	1	no	—
272	C₄×C₈	—	61	1	no	—
273	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
274	C₂⁴	—	61	2	no	—
275	C₂×D₄	—	61	2	no	—
276	C₂×D₄	—	61	8	no	—
277	C₂×D₄	—	61	1	no	—
278	C₂×D₄	C₈×D₆₁	1	1	yes	characteristic
279	C₂²×C₄	—	61	1	no	—
280	C₂²×C₄	—	61	2	no	—
281	C₂²×C₄	—	61	2	no	—
282	C₂²×C₄	—	61	1	no	—
283	C₂²×C₄	—	61	1	no	—
284	C₂²×C₄	—	61	2	no	—
285	C₂²×C₄	—	61	2	no	—
286	C₂²×C₄	—	244	2	no	—
287	C₂²×C₄	—	244	2	no	—
288	C₂²×C₄	C₂×C₄×D₆₁	1	2	yes	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	61	1	no	—
292	C₂×C₈	—	61	1	no	—
293	C₂×C₈	—	61	2	no	—
294	C₂×C₈	—	122	2	no	—
295	C₂×C₈	—	122	1	no	—
296	C₂×C₈	—	122	2	no	—
297	C₂×C₈	—	122	1	no	—
298	C₂×C₈	—	244	1	no	—
299	C₂×C₈	—	244	2	no	—
300	C₂×C₈	—	244	2	no	—
301	C₂×C₈	—	244	2	no	—
302	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
303	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
304	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
305	C₄⋊C₄	—	61	2	no	—
306	C₄⋊C₄	—	61	1	no	—
307	C₄⋊C₄	C₈×D₆₁	1	1	yes	characteristic
308	C₂²⋊C₄	—	61	2	no	—
309	C₂²⋊C₄	—	61	2	no	—
310	C₂²⋊C₄	—	61	2	no	—
311	C₂²⋊C₄	C₈×D₆₁	1	2	yes	—
312	C₄²	—	61	1	no	—
313	C₄²	—	61	1	no	—
314	C₄²	—	61	1	no	—
315	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
316	C₁₆	—	2	1	no	—
317	C₁₆	—	2	2	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	122	1	no	—
320	C₁₆	—	122	2	no	—
321	C₁₆	—	122	1	no	—
322	C₂³	—	61	2	no	—
323	C₂³	—	61	1	no	—
324	C₂³	—	61	8	no	—
325	C₂³	—	244	2	no	—
326	C₂³	—	244	2	no	—
327	C₂³	C₂×C₈×D₆₁	1	2	yes	—
328	D₄	—	61	8	no	—
329	D₄	—	61	4	no	—
330	D₄	C₁₆×D₆₁	1	4	yes	complemented
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	61	1	no	—
334	C₂×C₄	—	61	4	no	—
335	C₂×C₄	—	61	1	no	—
336	C₂×C₄	—	61	1	no	—
337	C₂×C₄	—	61	2	no	—
338	C₂×C₄	—	122	1	no	—
339	C₂×C₄	—	122	2	no	—
340	C₂×C₄	—	122	1	no	—
341	C₂×C₄	—	122	2	no	—
342	C₂×C₄	—	244	1	no	—
343	C₂×C₄	—	244	2	no	—
344	C₂×C₄	—	244	2	no	—
345	C₂×C₄	—	244	2	no	—
346	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₆₁	1	2	yes	—
348	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	1	no	—
352	C₈	—	122	2	no	—
353	C₈	—	122	1	no	—
354	C₈	—	122	1	no	—
355	C₈	#14519822	1	1	yes	characteristic
356	C₈	#14519823	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	61	2	no	—
360	C₂²	—	61	4	no	—
361	C₂²	—	122	1	no	—
362	C₂²	—	122	2	no	—
363	C₂²	—	122	1	no	—
364	C₂²	—	122	2	no	—
365	C₂²	—	244	8	no	—
366	C₂²	C₂×C₁₆×D₆₁	1	4	yes	—
367	C₂²	C₂²×C₈×D₆₁	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	61	2	no	—
371	C₄	—	122	1	no	—
372	C₄	—	122	2	no	—
373	C₄	—	122	1	no	—
374	C₄	C₂×C₁₆×D₆₁	1	2	yes	—
375	C₄	#16840234	1	1	yes	characteristic
376	C₄	#16840527	1	1	yes	characteristic
377	C₂	—	2	4	no	—
378	C₂	—	122	2	no	—
379	C₂	—	122	4	no	—
380	C₂	#21454840	1	1	yes	characteristic
381	C₂	C₂²×C₁₆×D₆₁	1	1	yes	characteristic
382	C₂	#21458920	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₁
commutator	C₂×C₆₁	C₂³×C₁₆
Fitting	D₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂³×C₈
prime radical	C₂×D₄×D₆₁	C₈
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	D₄×C₁₆	D₆₁
hypocenter	C₆₁	#33486
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₁₆×D₂₄₄	C₂	semidirect
3. D₄×#11758185	C₂	semidirect
4. #21447638	C₂	semidirect
5. C₁₆×C₂²⋊D₆₁	C₂	semidirect
6. #21447636	C₂	semidirect
7. #21447617	C₂	semidirect
8. #21447616	C₂	semidirect
9. C₂×#16839541	C₂	semidirect
10. C₂²⋊C₁₆×D₆₁	C₂	semidirect
11. D₄×C₁₆×C₆₁	C₂	semidirect
14. C₂²×#11758185	C₂²	semidirect
15. C₂×C₁₆×D₆₁	C₂²	semidirect
16. C₂×C₁₆×D₆₁	C₂²	semidirect
25. C₄⋊#11758185	C₂²	semidirect
26. #16839580	C₂²	semidirect
27. #16839580	C₂²	semidirect
28. C₂²⋊#11758185	C₂²	semidirect
32. #16839541	C₂²	semidirect
33. #16839541	C₂²	semidirect
34. C₄×#11758185	C₂²	semidirect
35. C₁₆×Dic₆₁	C₂²	semidirect
36. C₂²×C₁₆×C₆₁	C₂²	semidirect
38. C₆₁×C₄⋊C₁₆	C₂²	semidirect
39. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₆₁	C₂²	semidirect
87. D₄×D₆₁	C₁₆	semidirect
133. C₂²×D₆₁	C₂×C₁₆	semidirect
136. D₄×C₆₁	C₂×C₁₆	semidirect
143. C₂²⋊D₆₁	C₂×C₁₆	semidirect
149. D₂₄₄	C₂×C₁₆	semidirect
157. C₄×D₆₁	C₂×C₁₆	semidirect
192. D₄×C₁₆	D₆₁	semidirect
208. C₂²×C₁₆	C₂×D₆₁	semidirect
221. C₄⋊C₁₆	C₂×D₆₁	semidirect
228. C₂²⋊C₁₆	C₂×D₆₁	semidirect
231. C₄×C₁₆	C₂×D₆₁	semidirect
232. C₆₁	#33486	semidirect
330. D₄	C₁₆×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄×D₆₁	2
C₁₆×D₂₄₄	2
D₄×#11758185	2
#21447638	2
C₁₆×C₂²⋊D₆₁	2
#21447636	2
#21447617	2
#21447616	2
C₂×#16839541	2
C₂²⋊C₁₆×D₆₁	2
D₄×C₁₆×C₆₁	2
#33486	61