Subgroups — #29833264

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21458922	C₂	1	1	yes	maximal, characteristic, complemented
2	#21458921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16839877	C₂	1	1	yes	maximal, characteristic
4	#21447658	C₂	1	4	yes	maximal, complemented
5	#21447653	C₂	1	4	yes	maximal, complemented
6	C₂×#16839582	C₂	1	1	yes	maximal, characteristic, complemented
7	#21447446	C₂	1	1	yes	maximal, characteristic, complemented
8	M₃₂×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14519797	C₄	1	1	yes	characteristic
11	C₂×#14519783	C₂²	1	1	yes	characteristic
12	#16840180	C₂²	1	4	yes	complemented
13	#16840179	—	2	2	no	—
14	#16840179	C₂²	1	4	yes	complemented
15	#16840178	—	2	2	no	—
16	C₂×#14519717	—	2	2	no	—
17	C₂×#14519717	C₂²	1	1	yes	characteristic
18	C₂×#14519717	C₂²	1	1	yes	characteristic
19	M₃₂×D₆₁	—	2	2	no	—
20	#16839877	C₄	1	2	yes	—
21	#16839877	C₄	1	2	yes	—
22	#16839877	C₂²	1	2	yes	—
23	#16839877	C₂²	1	2	yes	—
24	C₂×#14519712	C₄	1	1	yes	characteristic
25	C₂×#14519704	C₄	1	1	yes	characteristic
26	C₂×#14519703	C₄	1	1	yes	characteristic
27	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
28	#16839582	C₂²	1	2	yes	complemented
29	#16839582	C₂²	1	2	yes	complemented
30	#16839545	C₂²	1	4	yes	complemented
31	#16839537	C₂²	1	2	yes	complemented
32	C₁₆×Dic₆₁	C₂²	1	2	yes	complemented
33	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#350	C₂²	1	4	yes	complemented
37	C₂×#11758222	C₂×C₄	1	1	yes	characteristic
38	#14519797	C₈	1	2	yes	—
39	#14519797	C₈	1	2	yes	—
40	#14519797	C₂×C₄	1	2	yes	—
41	#14519797	C₂×C₄	1	2	yes	—
42	C₂×#11758202	C₈	1	1	yes	characteristic
43	C₂×#11758200	C₈	1	1	yes	characteristic
44	C₂×#11758201	C₈	1	1	yes	characteristic
45	C₂×#11758199	C₈	1	1	yes	characteristic
46	#14519783	—	2	1	no	—
47	#14519783	—	2	1	no	—
48	#14519783	C₂×C₄	1	2	yes	—
49	#14519783	C₂³	1	2	yes	—
50	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
51	C₂×#11758189	—	2	1	no	—
52	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₆₁	—	2	1	no	—
54	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
55	#14519717	—	2	1	no	—
56	#14519717	—	2	4	no	—
57	#14519717	D₄	1	2	yes	—
58	#14519717	D₄	1	2	yes	—
59	#14519717	C₂³	1	2	yes	—
60	#14519716	—	2	4	no	—
61	C₂×#11758185	—	2	1	no	—
62	C₂×#11758185	—	2	4	no	—
63	C₂×#11758185	C₂³	1	2	yes	—
64	C₁₆×D₆₁	—	2	4	no	—
65	#14519712	C₂×C₄	1	2	yes	—
66	#14519712	C₂×C₄	1	2	yes	—
67	#14519704	C₂×C₄	1	2	yes	—
68	#14519704	C₂×C₄	1	2	yes	—
69	#14519703	C₂×C₄	1	2	yes	—
70	#14519703	C₂×C₄	1	2	yes	—
71	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
74	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
75	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
76	#131×C₆₁	—	2	1	no	—
77	#131×C₆₁	—	2	1	no	—
78	#131×C₆₁	C₂×C₄	1	2	yes	—
79	#131×C₆₁	C₂³	1	2	yes	—
80	C₂×M₁₆×C₆₁	—	2	1	no	—
81	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₆₁	—	2	1	no	—
83	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
84	M₃₂×C₆₁	—	2	1	no	—
85	M₃₂×C₆₁	—	2	1	no	—
86	M₃₂×C₆₁	—	2	1	no	—
87	M₃₂×C₆₁	C₂³	1	2	yes	—
88	C₂×C₁₆×C₆₁	—	2	1	no	—
89	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
90	#41×C₆₁	—	2	1	no	—
91	#41×C₆₁	—	2	1	no	—
92	#41×C₆₁	C₂×C₈	1	2	yes	—
93	#41×C₆₁	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₆₁	—	2	1	no	—
96	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₆₁	—	2	1	no	—
100	C₂²×Dic₆₁	—	2	1	no	—
101	#11758222	—	2	1	no	—
102	#11758222	—	2	1	no	—
103	#11758222	C₂×C₈	1	2	yes	—
104	#11758222	C₂²×C₄	1	2	yes	—
105	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₆₁	—	2	1	no	—
107	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
108	M₁₆×C₆₁	—	2	1	no	—
109	M₁₆×C₆₁	—	2	2	no	—
110	M₁₆×C₆₁	—	2	2	no	—
111	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
119	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
120	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
121	#11758202	C₂×C₈	1	2	yes	—
122	#11758202	C₂×C₈	1	2	yes	—
123	#11758201	C₂×C₈	1	2	yes	—
124	#11758201	C₂×C₈	1	2	yes	—
125	#11758200	C₂×C₈	1	2	yes	—
126	#11758200	C₂×C₈	1	2	yes	—
127	#11758199	C₂×C₈	1	2	yes	—
128	#11758199	C₂×C₈	1	2	yes	—
129	C₄×Dic₆₁	—	2	1	no	—
130	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
132	#11758194	—	2	1	no	—
133	#11758194	C₂²×C₄	1	2	yes	—
134	C₂×#92418	—	2	1	no	—
135	C₂×#92418	C₂×C₈	1	1	yes	characteristic
136	C₂×#92418	C₂×C₈	1	1	yes	characteristic
137	C₂×#92418	C₂×C₈	1	1	yes	characteristic
138	C₂×#92418	C₂×C₈	1	1	yes	characteristic
139	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
140	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
141	#11758189	—	2	2	no	—
142	#11758189	—	2	2	no	—
143	C₈×D₆₁	—	2	2	no	—
144	C₈×D₆₁	—	2	2	no	—
145	C₁₆×C₆₁	—	2	2	no	—
146	C₁₆×C₆₁	—	2	2	no	—
147	#11758185	—	2	2	no	—
148	#11758185	C₂×D₄	1	4	yes	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	#131	1	1	yes	characteristic
151	C₂²×D₆₁	—	2	1	no	—
152	Q₈×C₆₁	—	2	1	no	—
153	Q₈×C₆₁	C₂²×C₈	1	2	yes	—
154	D₄×C₆₁	—	2	2	no	—
155	D₄×C₆₁	—	2	2	no	—
156	D₄×C₆₁	—	2	1	no	—
157	D₄×C₆₁	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₆₁	#131	1	1	yes	characteristic
166	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
167	C₂²⋊D₆₁	—	2	2	no	—
168	C₂²⋊D₆₁	—	2	2	no	—
169	C₂×Dic₆₁	—	2	1	no	—
170	C₂×Dic₆₁	—	2	1	no	—
171	C₂×Dic₆₁	—	2	1	no	—
172	C₂×Dic₆₁	—	4	2	no	—
173	D₂₄₄	—	2	1	no	—
174	D₂₄₄	C₂²×C₈	1	2	yes	—
175	C₄×D₆₁	—	2	2	no	—
176	C₄×D₆₁	—	2	2	no	—
177	Dic₁₂₂	—	2	1	no	—
178	Dic₁₂₂	C₂²×C₈	1	2	yes	—
179	C₈×C₆₁	—	2	2	no	—
180	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
181	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
182	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
184	#92418	—	2	2	no	—
185	#92418	C₂²×C₈	1	1	yes	characteristic
186	#92418	C₂²×C₈	1	1	yes	characteristic
187	#92418	C₂²×C₈	1	1	yes	characteristic
188	#92418	C₂²×C₈	1	1	yes	characteristic
189	#33443	—	61	1	no	maximal, Sylow
190	C₂²×C₆₁	—	2	2	no	—
191	C₂²×C₆₁	—	4	1	no	—
192	C₂²×C₆₁	—	8	1	no	—
193	C₂²×C₆₁	C₈×D₄	1	1	yes	characteristic
194	C₂²×C₆₁	C₈×D₄	1	1	yes	characteristic
195	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
196	C₂×D₆₁	—	2	2	no	—
197	C₂×D₆₁	—	8	1	no	—
198	C₄×C₆₁	—	2	2	no	—
199	C₄×C₆₁	C₈×D₄	1	1	yes	characteristic
200	C₄×C₆₁	C₈×D₄	1	1	yes	characteristic
201	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
203	Dic₆₁	—	2	2	no	—
204	Dic₆₁	—	2	2	no	—
205	Dic₆₁	—	4	1	no	—
206	#3407	—	61	1	no	—
207	#3407	—	61	1	no	—
208	C₂×#443	—	61	1	no	—
209	#2171	—	61	4	no	—
210	#2170	—	61	4	no	—
211	C₂×#364	—	61	1	no	—
212	#2117	—	61	1	no	—
213	#2117	D₆₁	1	1	yes	characteristic, complemented
214	C₄×M₃₂	—	61	1	no	—
215	C₂×C₆₁	—	2	1	no	—
216	C₂×C₆₁	—	2	1	no	—
217	C₂×C₆₁	—	2	1	no	—
218	C₂×C₆₁	—	4	2	no	—
219	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
220	D₆₁	—	4	2	no	—
221	C₂×#135	—	61	1	no	—
222	C₂×#131	—	61	1	no	—
223	C₂×#131	C₂×D₆₁	1	1	yes	characteristic
224	#504	—	61	4	no	—
225	#504	—	61	4	no	—
226	#504	—	122	2	no	—
227	#504	—	122	2	no	—
228	C₂×M₃₂	—	61	1	no	—
229	C₂×M₃₂	—	61	1	no	—
230	C₂×M₃₂	—	122	2	no	—
231	C₂×M₃₂	—	122	2	no	—
232	C₂×M₃₂	C₂×D₆₁	1	1	yes	characteristic
233	C₂×M₃₂	C₂×D₆₁	1	1	yes	characteristic
234	#443	—	61	2	no	—
235	#443	—	61	2	no	—
236	#443	—	61	2	no	—
237	#443	—	61	2	no	—
238	C₂×#108	—	61	1	no	—
239	C₂×#104	—	61	1	no	—
240	C₂×#104	—	61	1	no	—
241	C₂×C₄×C₈	—	61	1	no	—
242	#364	—	61	2	no	—
243	#364	—	61	2	no	—
244	#350	—	61	4	no	—
245	#350	C₂×D₆₁	1	4	yes	complemented
246	#346	—	61	2	no	—
247	C₄×C₁₆	—	61	2	no	—
248	C₆₁	#33443	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	61	1	no	—
250	C₂×#41	C₄×D₆₁	1	1	yes	characteristic
251	#135	—	61	2	no	—
252	#135	—	61	2	no	—
253	#135	—	61	2	no	—
254	#135	—	61	2	no	—
255	C₂×Q₁₆	—	61	1	no	—
256	C₂×SD₁₆	—	61	1	no	—
257	C₂×SD₁₆	—	61	1	no	—
258	C₂×D₈	—	61	1	no	—
259	#131	—	2	1	no	—
260	#131	—	2	1	no	—
261	#131	—	61	2	no	—
262	#131	—	61	2	no	—
263	#131	—	122	1	no	—
264	#131	—	122	1	no	—
265	#131	C₄×D₆₁	1	2	yes	—
266	#131	C₂²×D₆₁	1	2	yes	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	61	1	no	—
269	C₂×M₁₆	—	122	1	no	—
270	C₂×M₁₆	C₄×D₆₁	1	1	yes	characteristic
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	61	1	no	—
273	C₂²×C₈	—	122	1	no	—
274	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
275	C₂×C₄²	—	61	1	no	—
276	M₃₂	—	2	1	no	—
277	M₃₂	—	2	1	no	—
278	M₃₂	—	2	1	no	—
279	M₃₂	—	61	2	no	—
280	M₃₂	—	61	2	no	—
281	M₃₂	—	61	2	no	—
282	M₃₂	—	122	4	no	—
283	M₃₂	—	122	4	no	—
284	M₃₂	—	122	1	no	—
285	M₃₂	C₂²×D₆₁	1	2	yes	—
286	C₂×C₁₆	—	2	1	no	—
287	C₂×C₁₆	—	61	2	no	—
288	C₂×C₁₆	—	122	4	no	—
289	C₂×C₁₆	—	122	4	no	—
290	C₂×C₁₆	—	122	1	no	—
291	C₂×C₁₆	C₂²×D₆₁	1	2	yes	—
292	#108	—	61	2	no	—
293	#108	—	61	2	no	—
294	#104	—	61	2	no	—
295	#104	—	61	2	no	—
296	#104	—	61	2	no	—
297	#104	—	61	2	no	—
298	C₄×C₈	—	61	1	no	—
299	C₄×C₈	—	61	1	no	—
300	C₄×C₈	—	61	1	no	—
301	C₄×C₈	—	61	1	no	—
302	#41	—	2	1	no	—
303	#41	—	2	1	no	—
304	#41	—	61	2	no	—
305	#41	—	61	2	no	—
306	#41	—	122	1	no	—
307	#41	—	122	1	no	—
308	#41	C₈×D₆₁	1	2	yes	—
309	#41	C₂×C₄×D₆₁	1	2	yes	—
310	C₂×Q₈	—	61	1	no	—
311	C₂×Q₈	C₈×D₆₁	1	1	yes	characteristic
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	61	1	no	—
314	C₂×D₄	—	122	1	no	—
315	C₂×D₄	C₈×D₆₁	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	122	1	no	—
318	C₂²×C₄	—	122	1	no	—
319	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
320	Q₁₆	—	61	2	no	—
321	Q₁₆	—	61	2	no	—
322	SD₁₆	—	61	2	no	—
323	SD₁₆	—	61	2	no	—
324	SD₁₆	—	61	2	no	—
325	SD₁₆	—	61	2	no	—
326	D₈	—	61	2	no	—
327	D₈	—	61	2	no	—
328	M₁₆	—	2	1	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	61	2	no	—
332	M₁₆	—	122	1	no	—
333	M₁₆	—	122	2	no	—
334	M₁₆	—	122	2	no	—
335	M₁₆	C₂×C₄×D₆₁	1	2	yes	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	61	1	no	—
340	C₂×C₈	—	61	1	no	—
341	C₂×C₈	—	61	1	no	—
342	C₂×C₈	—	61	1	no	—
343	C₂×C₈	—	61	1	no	—
344	C₂×C₈	—	61	1	no	—
345	C₂×C₈	—	122	1	no	—
346	C₂×C₈	—	122	2	no	—
347	C₂×C₈	—	122	2	no	—
348	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
349	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
350	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
351	C₂×C₈	#11758224	1	1	yes	characteristic
352	C₂×C₈	#11758224	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
354	C₄²	—	61	1	no	—
355	C₄²	—	61	1	no	—
356	C₄²	—	122	1	no	—
357	C₁₆	—	2	2	no	—
358	C₁₆	—	2	2	no	—
359	C₁₆	—	61	4	no	—
360	C₁₆	—	122	2	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	122	1	no	—
363	C₂³	#14519785	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	61	2	no	—
366	Q₈	—	122	1	no	—
367	Q₈	C₂×C₈×D₆₁	1	2	yes	—
368	D₄	—	2	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	2	1	no	—
371	D₄	—	61	2	no	—
372	D₄	—	122	2	no	—
373	D₄	—	122	2	no	—
374	D₄	—	122	1	no	—
375	D₄	C₂×C₈×D₆₁	1	2	yes	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	122	1	no	—
380	C₂×C₄	—	122	1	no	—
381	C₂×C₄	—	122	2	no	—
382	C₂×C₄	—	122	2	no	—
383	C₂×C₄	—	122	1	no	—
384	C₂×C₄	—	244	2	no	—
385	C₂×C₄	#14519737	1	1	yes	characteristic
386	C₂×C₄	#14519737	1	1	yes	characteristic
387	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
388	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
389	C₂×C₄	#14519785	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	61	1	no	—
393	C₈	—	61	1	no	—
394	C₈	—	61	1	no	—
395	C₈	—	61	1	no	—
396	C₈	—	122	2	no	—
397	C₈	#14519737	1	1	yes	characteristic
398	C₈	#14519737	1	1	yes	characteristic
399	C₈	C₂×D₄×D₆₁	1	1	yes	characteristic
400	C₈	C₂×#11758224	1	1	yes	characteristic
401	C₂²	—	2	2	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	122	2	no	—
405	C₂²	—	488	1	no	—
406	C₂²	#16839825	1	1	yes	characteristic
407	C₂²	#16839825	1	1	yes	characteristic
408	C₂²	C₂×#14519785	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	122	2	no	—
411	C₄	—	122	2	no	—
412	C₄	—	244	1	no	—
413	C₄	#16839825	1	1	yes	characteristic
414	C₄	#16839825	1	1	yes	characteristic
415	C₄	C₂×#14519737	1	1	yes	characteristic
416	C₄	C₂²×C₈×D₆₁	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	4	2	no	—
421	C₂	—	244	2	no	—
422	C₂	C₂×#16839825	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₆₁
commutator	C₄×C₆₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₆₁
Fitting	C₆₁×#2117	C₂
socle	C₂×C₆₁	C₂×C₈×D₄
prime radical	C₂×#14519797	C₄
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	#2117	D₆₁
hypocenter	C₆₁	#33443
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2117

Complements

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

N	H ≅ G/N	type
1. #21458922	C₂	semidirect
2. #21458921	C₂	semidirect
4. #21447658	C₂	semidirect
5. #21447653	C₂	semidirect
6. C₂×#16839582	C₂	semidirect
7. #21447446	C₂	semidirect
8. M₃₂×Dic₆₁	C₂	semidirect
9. C₆₁×#2117	C₂	semidirect
12. #16840180	C₂²	semidirect
14. #16840179	C₂²	semidirect
28. #16839582	C₂²	semidirect
29. #16839582	C₂²	semidirect
30. #16839545	C₂²	semidirect
31. #16839537	C₂²	semidirect
32. C₁₆×Dic₆₁	C₂²	semidirect
36. C₆₁×#350	C₂²	semidirect
213. #2117	D₆₁	semidirect
245. #350	C₂×D₆₁	semidirect
248. C₆₁	#33443	semidirect

Maximal subgroups

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

subgroup	index
#21458922	2
#21458921	2
C₂×#16839877	2
#21447658	2
#21447653	2
C₂×#16839582	2
#21447446	2
M₃₂×Dic₆₁	2
C₆₁×#2117	2
#33443	61