Subgroups — C₂×#21443678 #29569789

Order 15616.

702 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839786	C₂	1	1	yes	maximal, characteristic
2	C₂×#16839628	C₂	1	1	yes	maximal, characteristic
3	#21443678	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11758194	—	2	1	no	—
6	C₂²×C₄⋊Dic₆₁	—	2	1	no	—
7	#16839786	—	2	1	no	—
8	#16839786	—	2	1	no	—
9	#16839786	C₄	1	2	yes	complemented
10	#16839786	C₂²	1	2	yes	—
11	C₂×C₄⋊#92418	—	2	1	no	—
12	C₂×C₄⋊#92418	C₄	1	2	yes	complemented
13	#16839628	—	2	1	no	—
14	#16839628	—	2	1	no	—
15	#16839628	C₄	1	2	yes	—
16	#16839628	C₂²	1	2	yes	—
17	C₂×#14519684	—	2	1	no	—
18	C₂×#14519684	C₄	1	2	yes	—
19	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#431	—	2	1	no	—
21	C₆₁×#431	—	2	1	no	—
22	C₆₁×#431	C₄	1	2	yes	complemented
23	C₆₁×#431	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
26	C₂×C₄×C₈×C₆₁	C₄	1	2	yes	complemented
27	C₂³×Dic₆₁	—	2	2	no	—
28	C₂×#11758194	—	2	2	no	—
29	C₂×#11758194	—	2	2	no	—
30	C₂×#11758194	—	4	2	no	—
31	C₂×#11758194	—	4	2	no	—
32	C₂²×#92418	—	2	2	no	—
33	C₂×C₄⋊Dic₆₁	—	2	2	no	—
34	C₂×C₄⋊Dic₆₁	—	2	2	no	—
35	C₂×C₄⋊Dic₆₁	—	4	2	no	—
36	C₂×C₄⋊Dic₆₁	—	4	2	no	—
37	C₄⋊#92418	—	2	2	no	—
38	C₄⋊#92418	—	2	2	no	—
39	C₄⋊#92418	—	2	2	no	—
40	C₄⋊#92418	C₂×C₄	1	4	yes	complemented
41	#14519684	—	2	2	no	—
42	#14519684	—	2	2	no	—
43	#14519684	—	2	2	no	—
44	#14519684	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₆₁	—	2	2	no	—
49	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
60	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₆₁	—	2	2	no	—
62	C₄⋊C₈×C₆₁	—	2	2	no	—
63	C₂²⋊C₈×C₆₁	—	2	2	no	—
64	C₂²⋊C₈×C₆₁	—	2	2	no	—
65	C₄×C₈×C₆₁	—	2	2	no	—
66	C₄×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
67	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₆₁	—	4	2	no	—
69	C₂²×C₄×C₆₁	—	4	2	no	—
70	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	D₈	1	2	yes	—
86	C₂²×C₄×C₆₁	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₆₁	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₆₁	Q₁₆	1	2	yes	—
89	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₆₁	—	2	4	no	—
93	C₂²×Dic₆₁	—	4	4	no	—
94	C₂²×Dic₆₁	—	4	4	no	—
95	C₂²×Dic₆₁	—	4	4	no	—
96	C₂×C₈×C₆₁	—	2	4	no	—
97	C₂×C₈×C₆₁	—	4	4	no	—
98	C₄²×C₆₁	C₄²	1	1	yes	characteristic
99	C₄²×C₆₁	C₄²	1	1	yes	characteristic
100	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
114	C₄⋊Dic₆₁	—	4	4	no	—
115	C₄⋊Dic₆₁	—	4	2	no	—
116	C₄⋊Dic₆₁	—	4	2	no	—
117	#11758194	—	4	4	no	—
118	#11758194	—	4	2	no	—
119	#11758194	—	4	2	no	—
120	C₂×#92418	—	2	4	no	—
121	C₂×#92418	—	4	4	no	—
122	C₂³×C₆₁	—	2	2	no	—
123	C₂³×C₆₁	—	2	2	no	—
124	C₂³×C₆₁	#95	1	1	yes	characteristic
125	C₂³×C₆₁	#95	1	1	yes	characteristic
126	C₂³×C₆₁	#102	1	2	yes	—
127	C₂³×C₆₁	#103	1	2	yes	—
128	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₆₁	—	2	2	no	—
130	C₂×C₄×C₆₁	—	2	2	no	—
131	C₂×C₄×C₆₁	—	2	2	no	—
132	C₂×C₄×C₆₁	—	2	2	no	—
133	C₂×C₄×C₆₁	—	4	1	no	—
134	C₂×C₄×C₆₁	—	4	1	no	—
135	C₂×C₄×C₆₁	—	4	1	no	—
136	C₂×C₄×C₆₁	—	4	1	no	—
137	C₂×C₄×C₆₁	—	4	1	no	—
138	C₂×C₄×C₆₁	—	4	1	no	—
139	C₂×C₄×C₆₁	—	4	1	no	—
140	C₂×C₄×C₆₁	—	4	1	no	—
141	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₁	#102	1	2	yes	—
148	C₂×C₄×C₆₁	#102	1	2	yes	—
149	C₂×C₄×C₆₁	#102	1	2	yes	—
150	C₂×C₄×C₆₁	#103	1	2	yes	—
151	C₂×C₄×C₆₁	#103	1	2	yes	—
152	C₂×C₄×C₆₁	#103	1	2	yes	—
153	C₂×C₄×C₆₁	#106	1	2	yes	—
154	C₂×C₄×C₆₁	#106	1	2	yes	—
155	C₂×C₄×C₆₁	#107	1	2	yes	—
156	C₂×C₄×C₆₁	#107	1	2	yes	—
157	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
167	C₂×Dic₆₁	—	4	4	no	—
168	C₂×Dic₆₁	—	4	4	no	—
169	C₂×Dic₆₁	—	4	4	no	—
170	C₂×Dic₆₁	—	8	8	no	—
171	C₈×C₆₁	—	4	4	no	—
172	#92418	—	4	4	no	—
173	C₂×#1286	—	61	1	no	maximal, Sylow
174	C₂²×C₆₁	—	2	4	no	—
175	C₂²×C₆₁	—	2	4	no	—
176	C₂²×C₆₁	—	2	1	no	—
177	C₂²×C₆₁	—	2	1	no	—
178	C₂²×C₆₁	—	2	1	no	—
179	C₂²×C₆₁	—	2	1	no	—
180	C₂²×C₆₁	H(3,ℤ/4)	1	2	yes	—
181	C₂²×C₆₁	#340	1	2	yes	—
182	C₂²×C₆₁	#340	1	2	yes	—
183	C₂²×C₆₁	#344	1	2	yes	—
184	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
185	C₂²×C₆₁	C₂×#102	1	1	yes	characteristic
186	C₂²×C₆₁	C₂×#103	1	1	yes	characteristic
187	C₄×C₆₁	—	2	1	no	—
188	C₄×C₆₁	—	2	1	no	—
189	C₄×C₆₁	—	2	1	no	—
190	C₄×C₆₁	—	2	1	no	—
191	C₄×C₆₁	—	2	1	no	—
192	C₄×C₆₁	—	2	1	no	—
193	C₄×C₆₁	—	2	1	no	—
194	C₄×C₆₁	—	2	1	no	—
195	C₄×C₆₁	#340	1	2	yes	—
196	C₄×C₆₁	#340	1	2	yes	—
197	C₄×C₆₁	C₂×#102	1	1	yes	characteristic
198	C₄×C₆₁	C₂×#103	1	1	yes	characteristic
199	C₄×C₆₁	C₂×#106	1	1	yes	characteristic
200	C₄×C₆₁	C₂×#107	1	1	yes	characteristic
201	Dic₆₁	—	8	4	no	—
202	C₂×#431	D₆₁	1	1	yes	characteristic
203	C₂×#423	—	61	1	no	—
204	C₂×#382	—	61	1	no	—
205	#1286	—	61	4	no	—
206	C₂×C₆₁	—	2	1	no	—
207	C₂×C₆₁	—	2	2	no	—
208	C₂×C₆₁	—	2	1	no	—
209	C₂×C₆₁	#1286	1	4	yes	complemented
210	C₂×C₆₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
211	C₂×C₆₁	C₂×#340	1	1	yes	characteristic
212	C₂×C₆₁	C₂×#344	1	1	yes	characteristic
213	C₂²×M₁₆	—	122	1	no	—
214	C₂²×C₄⋊C₄	—	122	1	no	—
215	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
216	#431	—	2	1	no	—
217	#431	—	2	1	no	—
218	#431	Dic₆₁	1	2	yes	complemented
219	#431	C₂×D₆₁	1	2	yes	—
220	#423	—	61	2	no	—
221	#423	—	61	2	no	—
222	#423	—	122	1	no	—
223	#423	—	122	1	no	—
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄⋊C₈	—	61	2	no	—
226	C₂×C₄⋊C₈	—	122	1	no	—
227	C₂×C₂²⋊C₈	—	2	1	no	—
228	C₂×C₄×C₈	Dic₆₁	1	2	yes	complemented
229	#382	—	61	2	no	—
230	#382	—	61	2	no	—
231	#382	—	122	1	no	—
232	#382	—	122	1	no	—
233	C₂×#95	—	61	2	no	—
234	C₂×#95	—	122	1	no	—
235	C₆₁	C₂×#1286	1	1	yes	characteristic, complemented, Sylow
236	C₂³×C₄	—	122	2	no	—
237	C₂³×C₄	C₄×D₆₁	1	1	yes	characteristic
238	C₂³×C₄	D₂₄₄	1	1	yes	characteristic
239	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
240	C₂×M₁₆	—	122	2	no	—
241	C₂×M₁₆	—	122	2	no	—
242	C₂×M₁₆	—	244	2	no	—
243	C₂×M₁₆	—	244	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	122	2	no	—
246	C₂×C₄⋊C₄	—	122	2	no	—
247	C₂×C₄⋊C₄	—	122	2	no	—
248	C₂×C₄⋊C₄	—	244	2	no	—
249	C₂×C₄⋊C₄	—	244	2	no	—
250	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
251	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
254	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
255	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
256	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
257	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	61	4	no	—
265	C₄⋊C₈	—	122	2	no	—
266	C₄⋊C₈	—	122	2	no	—
267	C₄⋊C₈	—	122	2	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	2	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×Dic₆₁	1	4	yes	complemented
272	#95	—	61	4	no	—
273	#95	—	122	2	no	—
274	#95	—	122	2	no	—
275	#95	—	122	2	no	—
276	C₂⁴	#11758198	1	1	yes	characteristic
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	122	4	no	—
280	C₂²×C₄	—	244	4	no	—
281	C₂²×C₄	—	244	4	no	—
282	C₂²×C₄	—	244	4	no	—
283	C₂²×C₄	#11758190	1	2	yes	—
284	C₂²×C₄	#11758190	1	2	yes	—
285	C₂²×C₄	D₄₈₈	1	2	yes	—
286	C₂²×C₄	Dic₂₄₄	1	2	yes	—
287	C₂²×C₄	C₄×Dic₆₁	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₆₁	1	1	yes	characteristic
289	C₂²×C₄	#11758196	1	1	yes	characteristic
290	C₂²×C₄	#11758196	1	1	yes	characteristic
291	C₂²×C₄	#11758196	1	1	yes	characteristic
292	C₂²×C₄	#11758196	1	1	yes	characteristic
293	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
294	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
295	C₂²×C₄	#11758198	1	1	yes	characteristic
296	C₂²×C₄	#11758198	1	1	yes	characteristic
297	C₂²×C₄	#11758198	1	1	yes	characteristic
298	C₂²×C₄	#11758198	1	1	yes	characteristic
299	C₂²×C₄	#11758198	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
305	M₁₆	—	244	4	no	—
306	M₁₆	—	244	2	no	—
307	M₁₆	—	244	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	4	no	—
310	C₂×C₈	—	122	4	no	—
311	C₂×C₈	—	244	4	no	—
312	C₄⋊C₄	—	244	4	no	—
313	C₄⋊C₄	—	244	2	no	—
314	C₄⋊C₄	—	244	2	no	—
315	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
316	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
317	C₄²	#11758196	1	1	yes	characteristic
318	C₄²	#11758196	1	1	yes	characteristic
319	C₄²	#11758196	1	1	yes	characteristic
320	C₄²	#11758196	1	1	yes	characteristic
321	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
322	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
323	C₄²	#11758198	1	1	yes	characteristic
324	C₄²	#11758198	1	1	yes	characteristic
325	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
326	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
327	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
329	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
330	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	#14519684	1	1	yes	characteristic
334	C₂³	#14519684	1	1	yes	characteristic
335	C₂³	#14519699	1	2	yes	—
336	C₂³	#14519702	1	2	yes	—
337	C₂³	C₂×#11758198	1	1	yes	characteristic
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	488	8	no	—
351	C₂×C₄	—	244	4	no	—
352	C₂×C₄	—	244	4	no	—
353	C₂×C₄	—	244	4	no	—
354	C₂×C₄	#14519684	1	1	yes	characteristic
355	C₂×C₄	#14519684	1	1	yes	characteristic
356	C₂×C₄	#14519684	1	1	yes	characteristic
357	C₂×C₄	#14519684	1	1	yes	characteristic
358	C₂×C₄	#14519684	1	1	yes	characteristic
359	C₂×C₄	#14519684	1	1	yes	characteristic
360	C₂×C₄	#14519699	1	2	yes	—
361	C₂×C₄	#14519699	1	2	yes	—
362	C₂×C₄	#14519699	1	2	yes	—
363	C₂×C₄	#14519702	1	2	yes	—
364	C₂×C₄	#14519702	1	2	yes	—
365	C₂×C₄	#14519702	1	2	yes	—
366	C₂×C₄	#14519709	1	2	yes	—
367	C₂×C₄	#14519709	1	2	yes	—
368	C₂×C₄	#14519711	1	2	yes	—
369	C₂×C₄	#14519711	1	2	yes	—
370	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
372	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
373	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
374	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄₈₈	1	1	yes	characteristic
377	C₂×C₄	C₂×#11758190	1	1	yes	characteristic
378	C₂×C₄	C₂×#11758190	1	1	yes	characteristic
379	C₂×C₄	C₂×Dic₂₄₄	1	1	yes	characteristic
380	C₈	—	4	4	no	—
381	C₈	—	244	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	#16839518	1	2	yes	—
389	C₂²	#16839525	1	2	yes	—
390	C₂²	#16839525	1	2	yes	—
391	C₂²	#16839533	1	2	yes	—
392	C₂²	C₂×#14519684	1	1	yes	characteristic
393	C₂²	C₂×#14519699	1	1	yes	characteristic
394	C₂²	C₂×#14519702	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	488	4	no	—
404	C₄	#16839525	1	2	yes	—
405	C₄	#16839525	1	2	yes	—
406	C₄	C₂×#14519699	1	1	yes	characteristic
407	C₄	C₂×#14519702	1	1	yes	characteristic
408	C₄	C₂×#14519709	1	1	yes	characteristic
409	C₄	C₂×#14519711	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	2	no	—
413	C₂	#21443678	1	4	yes	direct product factor
414	C₂	C₂×#16839518	1	1	yes	characteristic
415	C₂	C₂×#16839525	1	1	yes	characteristic
416	C₂	C₂×#16839533	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14519684
commutator	C₂×C₄×C₆₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₂×C₆₁×#431	C₂
socle	C₂³×C₆₁	#95
prime radical	C₂⁴×C₆₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₂×#431	D₆₁
hypocenter	C₆₁	C₂×#1286
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #21443678	C₂	direct (N × H)
9. #16839786	C₄	semidirect
12. C₂×C₄⋊#92418	C₄	semidirect
22. C₆₁×#431	C₄	semidirect
26. C₂×C₄×C₈×C₆₁	C₄	semidirect
40. C₄⋊#92418	C₂×C₄	semidirect
66. C₄×C₈×C₆₁	C₂×C₄	semidirect
209. C₂×C₆₁	#1286	semidirect
218. #431	Dic₆₁	semidirect
228. C₂×C₄×C₈	Dic₆₁	semidirect
235. C₆₁	C₂×#1286	semidirect
271. C₄×C₈	C₂×Dic₆₁	semidirect
413. C₂	#21443678	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16839786	2
C₂×#16839628	2
#21443678	2
C₂×C₆₁×#431	2
C₂×#1286	61

Subgroups — C2×#21443678 #29569789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21443678 #29569789