Subgroups — C₂×#21443655 #29569504

Order 15616.

782 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11758194	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#92418	C₂	1	1	yes	maximal, characteristic
3	#21443655	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11758194	C₄	1	2	yes	—
6	C₂³×#92418	—	2	1	no	—
7	C₄×#11758194	—	2	1	no	—
8	C₄×#11758194	—	2	1	no	—
9	C₄×#11758194	C₄	1	2	yes	—
10	C₄×#11758194	C₂²	1	2	yes	—
11	C₂×#14519688	—	2	1	no	—
12	C₂×C₄×#92418	—	2	1	no	—
13	C₂×C₄×#92418	—	2	1	no	—
14	C₂×C₄×#92418	—	2	1	no	—
15	C₂×C₄×#92418	—	2	1	no	—
16	C₂×C₄×#92418	C₄	1	2	yes	—
17	C₂×C₄×#92418	C₄	1	2	yes	—
18	C₂×C₄×#92418	C₂²	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	—
23	C₆₁×#431	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₁	C₄	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
26	C₂×C₄×C₈×C₆₁	—	2	1	no	—
27	C₂×#11758194	—	2	2	no	—
28	C₂×#11758194	—	2	4	no	—
29	C₂×#11758194	C₈	1	8	yes	complemented
30	C₂×#11758194	C₂×C₄	1	4	yes	—
31	C₂²×#92418	—	2	8	no	—
32	C₂²×#92418	—	2	2	no	—
33	C₂²×#92418	—	2	2	no	—
34	C₂²×#92418	—	2	2	no	—
35	C₂²×#92418	—	2	2	no	—
36	#14519688	—	2	2	no	—
37	#14519688	—	2	2	no	—
38	C₄×#92418	—	2	2	no	—
39	C₄×#92418	—	2	2	no	—
40	C₄×#92418	—	2	2	no	—
41	C₄×#92418	—	2	2	no	—
42	C₄×#92418	—	2	2	no	—
43	C₄×#92418	C₂×C₄	1	4	yes	—
44	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	Q₈	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	—	2	2	no	—
48	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
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	D₄	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	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₆₁	—	2	2	no	—
61	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
62	C₂²⋊C₈×C₆₁	—	2	2	no	—
63	C₂²⋊C₈×C₆₁	—	2	2	no	—
64	C₄×C₈×C₆₁	—	2	2	no	—
65	C₄×C₈×C₆₁	—	2	2	no	—
66	C₂⁴×C₆₁	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₆₁	—	2	4	no	—
68	C₂²×C₄×C₆₁	—	2	4	no	—
69	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₄⋊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	C₂×C₈	1	4	yes	—
85	C₂²×C₄×C₆₁	M₁₆	1	4	yes	—
86	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₈×C₆₁	—	2	4	no	—
90	C₂×C₈×C₆₁	—	4	4	no	—
91	C₄²×C₆₁	C₄²	1	1	yes	characteristic
92	C₄²×C₆₁	C₄²	1	1	yes	characteristic
93	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
107	#11758194	—	2	8	no	—
108	#11758194	—	2	4	no	—
109	#11758194	C₂×C₈	1	8	yes	complemented
110	C₂×#92418	—	2	8	no	—
111	C₂×#92418	—	2	8	no	—
112	C₂×#92418	—	2	8	no	—
113	C₂×#92418	—	2	8	no	—
114	C₂×#92418	—	2	4	no	—
115	C₂×#92418	—	2	4	no	—
116	C₂³×C₆₁	—	2	2	no	—
117	C₂³×C₆₁	—	2	2	no	—
118	C₂³×C₆₁	#95	1	1	yes	characteristic
119	C₂³×C₆₁	#95	1	1	yes	characteristic
120	C₂³×C₆₁	C₄⋊C₈	1	4	yes	—
121	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	2	no	—
127	C₂×C₄×C₆₁	—	2	2	no	—
128	C₂×C₄×C₆₁	—	2	2	no	—
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	#95	1	1	yes	characteristic
133	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
134	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
135	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
136	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
137	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
138	C₂×C₄×C₆₁	C₄×C₈	1	2	yes	—
139	C₂×C₄×C₆₁	C₄×C₈	1	2	yes	—
140	C₂×C₄×C₆₁	#97	1	2	yes	—
141	C₂×C₄×C₆₁	#97	1	2	yes	—
142	C₂×C₄×C₆₁	C₂²⋊C₈	1	4	yes	—
143	C₂×C₄×C₆₁	C₂²⋊C₈	1	4	yes	—
144	C₂×C₄×C₆₁	#104	1	4	yes	—
145	C₂×C₄×C₆₁	C₄⋊C₈	1	4	yes	—
146	C₂×C₄×C₆₁	#108	1	4	yes	—
147	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
154	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
155	C₈×C₆₁	—	4	4	no	—
156	#92418	—	2	8	no	—
157	#92418	—	2	8	no	—
158	C₂×#1278	—	61	1	no	maximal, Sylow
159	C₂²×C₆₁	—	2	1	no	—
160	C₂²×C₆₁	—	2	1	no	—
161	C₂²×C₆₁	—	2	1	no	—
162	C₂²×C₆₁	—	2	1	no	—
163	C₂²×C₆₁	—	2	8	no	—
164	C₂²×C₆₁	#336	1	2	yes	—
165	C₂²×C₆₁	#336	1	2	yes	—
166	C₂²×C₆₁	#339	1	2	yes	—
167	C₂²×C₆₁	#341	1	2	yes	—
168	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
169	C₂²×C₆₁	C₂×C₄⋊C₈	1	2	yes	—
170	C₄×C₆₁	—	2	1	no	—
171	C₄×C₆₁	—	2	1	no	—
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	2	1	no	—
174	C₄×C₆₁	#336	1	2	yes	—
175	C₄×C₆₁	#336	1	2	yes	—
176	C₄×C₆₁	#339	1	2	yes	—
177	C₄×C₆₁	#341	1	2	yes	—
178	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
179	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
180	C₄×C₆₁	C₂×C₂²⋊C₈	1	2	yes	—
181	C₄×C₆₁	C₂×#104	1	2	yes	—
182	C₄×C₆₁	C₂×#108	1	2	yes	—
183	C₂×#431	D₆₁	1	1	yes	characteristic
184	C₂×C₄×M₁₆	—	61	1	no	—
185	C₂²×C₄×C₈	—	61	1	no	—
186	#1278	—	61	4	no	—
187	C₂×C₆₁	—	2	2	no	—
188	C₂×C₆₁	—	2	2	no	—
189	C₂×C₆₁	#1278	1	4	yes	complemented
190	C₂×C₆₁	C₂×#336	1	1	yes	characteristic
191	C₂×C₆₁	C₂×#339	1	1	yes	characteristic
192	C₂×C₆₁	C₂×#341	1	1	yes	characteristic
193	C₂²×M₁₆	—	61	2	no	—
194	C₂³×C₈	—	122	1	no	—
195	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
196	#431	—	2	1	no	—
197	#431	—	2	1	no	—
198	#431	Dic₆₁	1	2	yes	—
199	#431	C₂×D₆₁	1	2	yes	—
200	C₂×C₄⋊C₈	Dic₆₁	1	2	yes	—
201	C₂×C₂²⋊C₈	—	2	1	no	—
202	C₄×M₁₆	—	61	2	no	—
203	C₄×M₁₆	—	61	2	no	—
204	C₄×M₁₆	—	122	1	no	—
205	C₄×M₁₆	—	122	1	no	—
206	C₂×#97	—	122	1	no	—
207	C₂×C₄×C₈	—	2	1	no	—
208	C₂×C₄×C₈	—	61	2	no	—
209	C₂×C₄×C₈	—	61	2	no	—
210	C₂×C₄×C₈	—	61	2	no	—
211	C₂×C₄×C₈	—	122	1	no	—
212	C₂×C₄×C₈	—	122	1	no	—
213	C₂×C₄×C₈	—	122	1	no	—
214	C₂×C₄×C₈	—	122	1	no	—
215	C₆₁	C₂×#1278	1	1	yes	characteristic, complemented, Sylow
216	C₂³×C₄	Dic₁₂₂	1	1	yes	characteristic
217	C₂³×C₄	C₄×D₆₁	1	1	yes	characteristic
218	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
219	C₂×M₁₆	—	61	8	no	—
220	C₂×M₁₆	—	61	4	no	—
221	C₂×M₁₆	—	122	4	no	—
222	C₂×M₁₆	—	122	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	122	8	no	—
225	C₂²×C₈	—	122	2	no	—
226	C₂²×C₈	—	122	2	no	—
227	C₂²×C₈	—	122	2	no	—
228	C₂²×C₈	—	122	2	no	—
229	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₆₁	1	1	yes	characteristic
233	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
234	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
236	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
238	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
240	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	C₂×Dic₆₁	1	4	yes	—
243	C₂²⋊C₈	—	2	2	no	—
244	C₂²⋊C₈	—	2	2	no	—
245	#97	—	122	2	no	—
246	#97	—	122	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	61	4	no	—
250	C₄×C₈	—	122	2	no	—
251	C₄×C₈	—	122	2	no	—
252	C₄×C₈	—	122	2	no	—
253	C₄×C₈	—	122	2	no	—
254	C₄×C₈	—	122	2	no	—
255	C₂⁴	#11758196	1	1	yes	characteristic
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	C₈×D₆₁	1	4	yes	—
259	C₂²×C₄	#11758189	1	4	yes	—
260	C₂²×C₄	C₄×Dic₆₁	1	1	yes	characteristic
261	C₂²×C₄	C₄×Dic₆₁	1	1	yes	characteristic
262	C₂²×C₄	#11758196	1	1	yes	characteristic
263	C₂²×C₄	#11758196	1	1	yes	characteristic
264	C₂²×C₄	#11758196	1	1	yes	characteristic
265	C₂²×C₄	#11758196	1	1	yes	characteristic
266	C₂²×C₄	#11758196	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
269	C₂²×C₄	#11758198	1	1	yes	characteristic
270	C₂²×C₄	#11758198	1	1	yes	characteristic
271	C₂²×C₄	#11758198	1	1	yes	characteristic
272	C₂²×C₄	#11758198	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
278	M₁₆	—	61	8	no	—
279	M₁₆	—	122	8	no	—
280	M₁₆	—	122	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₂×C₈	—	122	8	no	—
284	C₂×C₈	—	122	8	no	—
285	C₂×C₈	—	122	8	no	—
286	C₂×C₈	—	122	8	no	—
287	C₂×C₈	—	122	4	no	—
288	C₂×C₈	—	122	4	no	—
289	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
290	C₄²	C₄×Dic₆₁	1	1	yes	characteristic
291	C₄²	#11758196	1	1	yes	characteristic
292	C₄²	#11758196	1	1	yes	characteristic
293	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
294	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
295	C₄²	#11758198	1	1	yes	characteristic
296	C₄²	#11758198	1	1	yes	characteristic
297	C₄²	#11758198	1	1	yes	characteristic
298	C₄²	#11758198	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
300	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
302	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
303	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
304	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	#14519684	1	1	yes	characteristic
308	C₂³	#14519684	1	1	yes	characteristic
309	C₂³	#14519706	1	4	yes	—
310	C₂³	C₂×#11758196	1	1	yes	characteristic
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	#14519684	1	1	yes	characteristic
322	C₂×C₄	#14519684	1	1	yes	characteristic
323	C₂×C₄	#14519684	1	1	yes	characteristic
324	C₂×C₄	#14519684	1	1	yes	characteristic
325	C₂×C₄	#14519684	1	1	yes	characteristic
326	C₂×C₄	#14519684	1	1	yes	characteristic
327	C₂×C₄	C₈×Dic₆₁	1	2	yes	—
328	C₂×C₄	C₈×Dic₆₁	1	2	yes	—
329	C₂×C₄	#14519687	1	2	yes	—
330	C₂×C₄	#14519687	1	2	yes	—
331	C₂×C₄	#14519689	1	4	yes	—
332	C₂×C₄	#14519689	1	4	yes	—
333	C₂×C₄	#14519704	1	4	yes	—
334	C₂×C₄	#14519706	1	4	yes	—
335	C₂×C₄	#14519712	1	4	yes	—
336	C₂×C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
337	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
338	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
340	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
342	C₂×C₄	C₂×C₈×D₆₁	1	2	yes	—
343	C₂×C₄	C₂×#11758189	1	2	yes	—
344	C₈	—	4	4	no	—
345	C₈	—	122	8	no	—
346	C₈	—	122	8	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	#16839516	1	2	yes	—
353	C₂²	#16839516	1	2	yes	—
354	C₂²	#16839521	1	2	yes	—
355	C₂²	#16839526	1	2	yes	—
356	C₂²	C₂×#14519684	1	1	yes	characteristic
357	C₂²	C₂×#14519706	1	2	yes	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#16839516	1	2	yes	—
363	C₄	#16839516	1	2	yes	—
364	C₄	#16839521	1	2	yes	—
365	C₄	#16839526	1	2	yes	—
366	C₄	C₂×C₈×Dic₆₁	1	1	yes	characteristic
367	C₄	C₂×#14519687	1	1	yes	characteristic
368	C₄	C₂×#14519689	1	2	yes	—
369	C₄	C₂×#14519704	1	2	yes	—
370	C₄	C₂×#14519712	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	#21443655	1	4	yes	direct product factor
374	C₂	C₂×#16839516	1	1	yes	characteristic
375	C₂	C₂×#16839521	1	1	yes	characteristic
376	C₂	C₂×#16839526	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²⋊D₆₁
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₂×C₆₁×#431	C₂
socle	C₂³×C₆₁	#95
prime radical	C₂⁴×C₆₁	C₄⋊C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₂×#431	D₆₁
hypocenter	C₆₁	C₂×#1278
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #21443655	C₂	direct (N × H)
29. C₂×#11758194	C₈	semidirect
109. #11758194	C₂×C₈	semidirect
189. C₂×C₆₁	#1278	semidirect
215. C₆₁	C₂×#1278	semidirect
373. C₂	#21443655	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×C₄×#11758194	2
C₂²×C₄×#92418	2
#21443655	2
C₂×C₆₁×#431	2
C₂×#1278	61

Subgroups — C2×#21443655 #29569504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21443655 #29569504