Subgroups — #29573839

Order 15616.

556 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#21445796	C₂	1	1	yes	maximal, characteristic
3	C₄×#14519689	C₂	1	1	yes	maximal, characteristic
4	C₂×#16839514	C₂	1	1	yes	maximal, characteristic, complemented
5	#21443654	C₂	1	1	yes	maximal, characteristic, complemented
6	#21443653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₆₁	—	2	1	no	—
9	C₂×C₄²×D₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
12	C₂×#14519706	—	2	1	no	—
13	C₄⋊C₈×D₆₁	—	2	2	no	—
14	C₄⋊C₈×D₆₁	—	2	2	no	—
15	C₂×#14519689	—	2	1	no	—
16	C₂×#14519689	C₄	1	1	yes	characteristic
17	C₂×#14519689	C₄	1	1	yes	characteristic
18	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
19	#16839516	—	2	1	no	—
20	#16839516	C₄	1	1	yes	characteristic
21	#16839516	C₄	1	1	yes	characteristic
22	#16839514	—	2	2	no	—
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#335	—	2	2	no	—
27	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₆₁	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₆₁	Q₈	1	1	yes	characteristic
30	C₂²×#92418	—	2	1	no	—
31	C₂²×#92418	—	2	1	no	—
32	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
33	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×D₆₁	—	2	4	no	—
35	C₂×C₈×D₆₁	—	4	2	no	—
36	C₂×C₈×D₆₁	—	4	2	no	—
37	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₆₁	Q₈	1	1	yes	characteristic
40	C₄²×D₆₁	—	2	1	no	—
41	C₄²×D₆₁	—	2	1	no	—
42	C₄²×D₆₁	—	2	1	no	—
43	C₄²×D₆₁	—	2	1	no	—
44	C₄⋊#92418	—	2	1	no	—
45	C₄⋊#92418	—	2	1	no	—
46	C₄⋊#92418	—	2	1	no	—
47	C₄⋊#92418	D₄	1	2	yes	—
48	#14519706	—	2	4	no	—
49	#14519689	—	2	2	no	—
50	#14519689	—	4	2	no	—
51	#14519689	C₈	1	4	yes	complemented
52	C₄×#92418	—	2	1	no	—
53	C₄×#92418	—	2	1	no	—
54	C₂²×C₈×C₆₁	—	2	1	no	—
55	C₂²×C₈×C₆₁	—	2	1	no	—
56	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₆₁	—	2	1	no	—
60	C₄⋊C₈×C₆₁	—	2	1	no	—
61	C₄⋊C₈×C₆₁	—	2	1	no	—
62	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
63	C₄×C₈×C₆₁	—	2	1	no	—
64	C₄×C₈×C₆₁	—	2	1	no	—
65	C₂³×D₆₁	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
69	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×D₆₁	—	2	1	no	—
73	C₂×C₄×D₆₁	—	2	1	no	—
74	C₂×C₄×D₆₁	—	2	1	no	—
75	C₂×C₄×D₆₁	—	2	1	no	—
76	C₂×C₄×D₆₁	—	2	1	no	—
77	C₂×C₄×D₆₁	—	2	1	no	—
78	C₂×C₄×D₆₁	—	2	1	no	—
79	C₂×C₄×D₆₁	—	2	1	no	—
80	C₂×C₄×D₆₁	—	2	2	no	—
81	C₂×C₄×D₆₁	—	2	1	no	—
82	C₂×C₄×D₆₁	—	2	1	no	—
83	C₂×C₄×D₆₁	—	4	1	no	—
84	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
85	C₂×C₄×D₆₁	M₁₆	1	2	yes	—
86	C₂×C₄×D₆₁	D₈	1	2	yes	—
87	C₂×C₄×D₆₁	Q₁₆	1	2	yes	—
88	C₂×C₈×C₆₁	—	2	1	no	—
89	C₂×C₈×C₆₁	—	2	1	no	—
90	C₂×C₈×C₆₁	—	2	1	no	—
91	C₂×C₈×C₆₁	—	2	2	no	—
92	C₂×C₈×C₆₁	—	2	1	no	—
93	C₂×C₈×C₆₁	—	2	1	no	—
94	C₂×C₈×C₆₁	—	4	1	no	—
95	C₂×C₈×C₆₁	—	4	1	no	—
96	C₂×C₈×C₆₁	—	4	1	no	—
97	C₂×C₈×C₆₁	—	4	1	no	—
98	C₂×C₈×C₆₁	—	4	1	no	—
99	C₂×C₈×C₆₁	C₂×C₈	1	2	yes	complemented
100	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₆₁	#41	1	1	yes	characteristic
103	C₄²×C₆₁	#41	1	1	yes	characteristic
104	C₄×Dic₆₁	—	2	1	no	—
105	C₄×Dic₆₁	—	2	1	no	—
106	C₄×Dic₆₁	—	2	1	no	—
107	C₄×Dic₆₁	—	2	1	no	—
108	C₄×Dic₆₁	—	2	1	no	—
109	C₄×Dic₆₁	—	2	1	no	—
110	C₂×#92418	—	2	1	no	—
111	C₂×#92418	—	2	1	no	—
112	C₂×#92418	—	2	1	no	—
113	C₂×#92418	—	2	2	no	—
114	C₂×#92418	—	2	1	no	—
115	C₂×#92418	—	2	1	no	—
116	C₂×#92418	—	4	1	no	—
117	C₂×#92418	—	4	1	no	—
118	C₂×#92418	—	4	1	no	—
119	C₂×#92418	—	4	1	no	—
120	C₂×#92418	—	4	1	no	—
121	C₂×#92418	C₂×C₈	1	2	yes	complemented
122	C₈×D₆₁	—	4	8	no	—
123	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₆₁	—	2	1	no	—
125	C₂²×D₆₁	—	2	1	no	—
126	C₂²×D₆₁	—	2	1	no	—
127	C₂²×D₆₁	—	2	1	no	—
128	C₂²×D₆₁	C₄⋊C₈	1	2	yes	—
129	C₂²×D₆₁	#107	1	2	yes	—
130	C₂²×D₆₁	#108	1	2	yes	—
131	C₂×C₄×C₆₁	—	2	1	no	—
132	C₂×C₄×C₆₁	—	2	1	no	—
133	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
136	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
139	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
141	C₂×C₄×C₆₁	#131	1	1	yes	characteristic
142	C₂×C₄×C₆₁	#131	1	1	yes	characteristic
143	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
145	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
147	C₂×Dic₆₁	—	2	1	no	—
148	C₂×Dic₆₁	—	2	1	no	—
149	C₂×Dic₆₁	—	2	1	no	—
150	C₂×Dic₆₁	—	2	1	no	—
151	C₂×Dic₆₁	—	2	1	no	—
152	C₂×Dic₆₁	—	2	1	no	—
153	C₂×Dic₆₁	—	2	1	no	—
154	C₂×Dic₆₁	C₄⋊C₈	1	2	yes	—
155	C₂×Dic₆₁	#107	1	2	yes	—
156	C₄×D₆₁	—	2	2	no	—
157	C₄×D₆₁	—	2	2	no	—
158	C₄×D₆₁	—	2	2	no	—
159	C₄×D₆₁	—	2	2	no	—
160	C₄×D₆₁	—	2	2	no	—
161	C₄×D₆₁	—	2	2	no	—
162	C₄×D₆₁	—	2	2	no	—
163	C₄×D₆₁	—	2	2	no	—
164	C₄×D₆₁	—	4	2	no	—
165	C₄×D₆₁	—	4	2	no	—
166	C₈×C₆₁	—	2	2	no	—
167	C₈×C₆₁	—	4	1	no	—
168	C₈×C₆₁	—	4	2	no	—
169	C₈×C₆₁	—	8	1	no	—
170	#92418	—	2	2	no	—
171	#92418	—	4	1	no	—
172	#92418	—	4	2	no	—
173	#92418	—	8	1	no	—
174	#8829	—	61	1	no	maximal, Sylow
175	C₂²×C₆₁	#385	1	1	yes	characteristic
176	C₂²×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
177	C₂²×C₆₁	#424	1	1	yes	characteristic
178	C₂²×C₆₁	C₂×#107	1	1	yes	characteristic
179	C₂²×C₆₁	#428	1	1	yes	characteristic
180	C₂²×C₆₁	C₂×#108	1	1	yes	characteristic
181	C₂²×C₆₁	#430	1	1	yes	characteristic
182	C₂×D₆₁	—	2	2	no	—
183	C₂×D₆₁	—	2	2	no	—
184	C₂×D₆₁	—	2	2	no	—
185	C₂×D₆₁	—	2	2	no	—
186	C₂×D₆₁	—	2	2	no	—
187	C₂×D₆₁	—	2	2	no	—
188	C₂×D₆₁	#335	1	4	yes	complemented
189	C₄×C₆₁	—	2	1	no	—
190	C₄×C₆₁	—	2	1	no	—
191	C₄×C₆₁	C₈×D₄	1	1	yes	characteristic
192	C₄×C₆₁	C₈×D₄	1	1	yes	characteristic
193	C₄×C₆₁	#435	1	1	yes	characteristic
194	C₄×C₆₁	#435	1	1	yes	characteristic
195	C₄×C₆₁	#447	1	1	yes	characteristic
196	C₄×C₆₁	#451	1	1	yes	characteristic
197	C₄×C₆₁	#480	1	1	yes	characteristic
198	C₄×C₆₁	#484	1	1	yes	characteristic
199	Dic₆₁	—	2	2	no	—
200	Dic₆₁	—	2	2	no	—
201	Dic₆₁	—	4	1	no	—
202	C₂²×C₄⋊C₈	—	61	1	no	—
203	#1797	—	61	1	no	—
204	C₄×C₂²⋊C₈	—	61	1	no	—
205	C₂×#335	—	61	1	no	—
206	C₂×#335	D₆₁	1	1	yes	characteristic, complemented
207	#1277	—	61	1	no	—
208	#1277	—	61	1	no	—
209	C₂×C₆₁	C₂×#335	1	1	yes	characteristic
210	C₂×C₆₁	#1565	1	1	yes	characteristic
211	C₂×C₆₁	#1571	1	1	yes	characteristic
212	C₂×C₆₁	#1573	1	1	yes	characteristic
213	C₂×C₆₁	#1850	1	1	yes	characteristic
214	C₂×C₆₁	#1852	1	1	yes	characteristic
215	C₂×C₆₁	#1855	1	1	yes	characteristic
216	D₆₁	—	2	4	no	—
217	C₂³×C₈	—	122	1	no	—
218	C₂²×C₄²	—	61	1	no	—
219	C₂×C₄⋊C₈	—	61	1	no	—
220	C₂×C₄⋊C₈	—	61	1	no	—
221	C₂×C₄⋊C₈	—	122	2	no	—
222	C₂×C₄⋊C₈	—	122	1	no	—
223	C₂×C₄⋊C₈	—	122	2	no	—
224	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	—	61	1	no	—
227	C₂×C₂²⋊C₈	—	61	1	no	—
228	C₂×C₂²⋊C₈	—	122	1	no	—
229	C₂×C₄×C₈	—	61	1	no	—
230	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
231	#336	—	61	1	no	—
232	#336	—	61	1	no	—
233	#336	—	122	1	no	—
234	#335	—	2	2	no	—
235	#335	—	122	2	no	—
236	C₆₁	#8829	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	—	61	1	no	—
238	C₂³×C₄	—	61	1	no	—
239	C₂³×C₄	—	61	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	61	1	no	—
243	C₂²×C₈	—	61	1	no	—
244	C₂²×C₈	—	122	4	no	—
245	C₂²×C₈	—	122	1	no	—
246	C₂²×C₈	—	122	1	no	—
247	C₂²×C₈	—	244	2	no	—
248	C₂²×C₈	—	244	2	no	—
249	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
250	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
251	C₂×C₄²	—	61	1	no	—
252	C₂×C₄²	—	61	1	no	—
253	C₂×C₄²	—	61	1	no	—
254	C₂×C₄²	—	122	1	no	—
255	C₂×C₄²	—	122	1	no	—
256	C₂×C₄²	—	122	1	no	—
257	C₂×C₄²	—	122	1	no	—
258	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	61	2	no	—
263	C₄⋊C₈	—	122	4	no	—
264	C₄⋊C₈	—	122	1	no	—
265	C₄⋊C₈	—	122	1	no	—
266	C₄⋊C₈	—	122	1	no	—
267	C₄⋊C₈	C₂²⋊D₆₁	1	2	yes	—
268	C₂²⋊C₈	—	61	4	no	—
269	C₂²⋊C₈	—	122	2	no	—
270	C₂²⋊C₈	—	244	2	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	122	1	no	—
274	C₄×C₈	—	122	1	no	—
275	C₂⁴	—	61	1	no	—
276	C₂²×C₄	—	61	1	no	—
277	C₂²×C₄	—	61	1	no	—
278	C₂²×C₄	—	61	2	no	—
279	C₂²×C₄	—	61	2	no	—
280	C₂²×C₄	—	61	2	no	—
281	C₂²×C₄	—	61	2	no	—
282	C₂²×C₄	—	61	1	no	—
283	C₂²×C₄	—	122	2	no	—
284	C₂²×C₄	—	122	1	no	—
285	C₂²×C₄	—	122	1	no	—
286	C₂²×C₄	—	122	1	no	—
287	C₂²×C₄	—	122	1	no	—
288	C₂²×C₄	—	122	1	no	—
289	C₂²×C₄	—	122	1	no	—
290	C₂²×C₄	—	122	1	no	—
291	C₂²×C₄	—	122	1	no	—
292	C₂²×C₄	—	122	1	no	—
293	C₂²×C₄	—	122	1	no	—
294	C₂²×C₄	—	244	1	no	—
295	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
297	C₂²×C₄	Q₈×D₆₁	1	1	yes	characteristic
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	61	2	no	—
310	C₂×C₈	—	122	1	no	—
311	C₂×C₈	—	122	1	no	—
312	C₂×C₈	—	122	1	no	—
313	C₂×C₈	—	122	2	no	—
314	C₂×C₈	—	122	1	no	—
315	C₂×C₈	—	122	1	no	—
316	C₂×C₈	—	244	8	no	—
317	C₂×C₈	—	244	1	no	—
318	C₂×C₈	—	244	1	no	—
319	C₂×C₈	—	244	1	no	—
320	C₂×C₈	—	244	1	no	—
321	C₂×C₈	—	244	1	no	—
322	C₂×C₈	C₈×D₆₁	1	2	yes	complemented
323	C₄²	—	122	1	no	—
324	C₄²	—	122	1	no	—
325	C₄²	—	122	1	no	—
326	C₄²	—	122	1	no	—
327	C₄²	—	122	1	no	—
328	C₄²	—	122	1	no	—
329	C₄²	#11758222	1	1	yes	characteristic
330	C₄²	D₄×D₆₁	1	1	yes	characteristic
331	C₄²	#11758226	1	1	yes	characteristic
332	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
333	C₂³	—	61	2	no	—
334	C₂³	—	61	2	no	—
335	C₂³	—	61	2	no	—
336	C₂³	—	122	1	no	—
337	C₂³	—	122	1	no	—
338	C₂³	—	122	1	no	—
339	C₂³	—	122	1	no	—
340	C₂³	C₄⋊C₄×D₆₁	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	61	2	no	—
344	C₂×C₄	—	61	2	no	—
345	C₂×C₄	—	122	1	no	—
346	C₂×C₄	—	122	1	no	—
347	C₂×C₄	—	122	1	no	—
348	C₂×C₄	—	122	1	no	—
349	C₂×C₄	—	122	2	no	—
350	C₂×C₄	—	122	2	no	—
351	C₂×C₄	—	122	2	no	—
352	C₂×C₄	—	122	2	no	—
353	C₂×C₄	—	122	2	no	—
354	C₂×C₄	—	122	2	no	—
355	C₂×C₄	—	122	2	no	—
356	C₂×C₄	—	122	2	no	—
357	C₂×C₄	—	122	1	no	—
358	C₂×C₄	—	122	1	no	—
359	C₂×C₄	—	122	1	no	—
360	C₂×C₄	—	244	2	no	—
361	C₂×C₄	—	244	2	no	—
362	C₂×C₄	C₄×C₂²⋊D₆₁	1	1	yes	characteristic
363	C₂×C₄	#14519739	1	1	yes	characteristic
364	C₂×C₄	#14519745	1	1	yes	characteristic
365	C₂×C₄	#14519753	1	1	yes	characteristic
366	C₂×C₄	#14519755	1	1	yes	characteristic
367	C₂×C₄	#14519762	1	1	yes	characteristic
368	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
369	C₂×C₄	M₁₆×D₆₁	1	1	yes	characteristic
370	C₂×C₄	#14519783	1	1	yes	characteristic
371	C₂×C₄	#14519785	1	1	yes	characteristic
372	C₂×C₄	D₈×D₆₁	1	1	yes	characteristic
373	C₂×C₄	Q₁₆×D₆₁	1	1	yes	characteristic
374	C₂×C₄	#14519801	1	1	yes	characteristic
375	C₂×C₄	#14519809	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	8	1	no	—
380	C₈	—	122	2	no	—
381	C₈	—	488	1	no	—
382	C₈	—	244	1	no	—
383	C₈	—	244	2	no	—
384	C₂²	—	61	4	no	—
385	C₂²	—	122	2	no	—
386	C₂²	—	122	2	no	—
387	C₂²	—	122	2	no	—
388	C₂²	—	122	2	no	—
389	C₂²	—	122	2	no	—
390	C₂²	—	122	2	no	—
391	C₂²	#16839633	1	1	yes	characteristic
392	C₂²	C₄⋊C₈×D₆₁	1	1	yes	characteristic
393	C₂²	#16839787	1	1	yes	characteristic
394	C₂²	#107×D₆₁	1	1	yes	characteristic
395	C₂²	#16839803	1	1	yes	characteristic
396	C₂²	#108×D₆₁	1	1	yes	characteristic
397	C₂²	#16839809	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	122	2	no	—
401	C₄	—	122	2	no	—
402	C₄	—	244	1	no	—
403	C₄	C₈×C₂²⋊D₆₁	1	1	yes	characteristic
404	C₄	#16839827	1	1	yes	characteristic
405	C₄	#16839831	1	1	yes	characteristic
406	C₄	#16839832	1	1	yes	characteristic
407	C₄	#16839894	1	1	yes	characteristic
408	C₄	#16839916	1	1	yes	characteristic
409	C₄	#16840077	1	1	yes	characteristic
410	C₄	#16840099	1	1	yes	characteristic
411	C₂	—	122	4	no	—
412	C₂	#335×D₆₁	1	1	yes	characteristic
413	C₂	#21444570	1	1	yes	characteristic
414	C₂	#21444592	1	1	yes	characteristic
415	C₂	#21444603	1	1	yes	characteristic
416	C₂	#21445995	1	1	yes	characteristic
417	C₂	#21446005	1	1	yes	characteristic
418	C₂	#21446022	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₂×C₆₁×#335	C₂
socle	C₂³×C₆₁	C₂×C₄⋊C₄
prime radical	C₂³×D₆₁	C₄⋊C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₂×#335	D₆₁
hypocenter	C₆₁	#8829
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
4. C₂×#16839514	C₂	semidirect
5. #21443654	C₂	semidirect
6. #21443653	C₂	semidirect
7. C₂×C₆₁×#335	C₂	semidirect
51. #14519689	C₈	semidirect
99. C₂×C₈×C₆₁	C₂×C₈	semidirect
121. C₂×#92418	C₂×C₈	semidirect
188. C₂×D₆₁	#335	semidirect
206. C₂×#335	D₆₁	semidirect
236. C₆₁	#8829	semidirect
322. C₂×C₈	C₈×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×D₆₁	2
#21445796	2
C₄×#14519689	2
C₂×#16839514	2
#21443654	2
#21443653	2
C₂×C₆₁×#335	2
#8829	61