Subgroups — C₂×#21460652 #30596126

Order 15616.

782 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840778	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#92420	C₂	1	1	yes	maximal, characteristic
3	#21460652	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×#92420	—	2	1	no	—
6	#16840778	—	2	1	no	—
7	#16840778	—	2	1	no	—
8	#16840778	C₄	1	2	yes	—
9	#16840778	C₂²	1	2	yes	—
10	C₂×C₄⋊#92420	C₄	1	2	yes	—
11	C₂×C₂²⋊#92420	—	2	1	no	—
12	C₂×C₄×#92420	—	2	1	no	—
13	C₂×C₄×#92420	—	2	1	no	—
14	C₂×C₄×#92420	—	2	1	no	—
15	C₂×C₄×#92420	—	2	1	no	—
16	C₂×C₄×#92420	C₄	1	2	yes	—
17	C₂×C₄×#92420	C₄	1	2	yes	—
18	C₂×C₄×#92420	C₂²	1	2	yes	—
19	C₂²×#11758194	C₄	1	1	yes	characteristic
20	C₂²×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
21	M₁₆×Dic₆₁	—	2	1	no	—
22	M₁₆×Dic₆₁	—	2	1	no	—
23	M₁₆×Dic₆₁	C₄	1	2	yes	—
24	M₁₆×Dic₆₁	C₂²	1	2	yes	—
25	C₂×#14519687	—	2	1	no	—
26	C₂×C₈×Dic₆₁	—	2	1	no	—
27	C₂²×M₁₆×C₆₁	C₄	1	1	yes	characteristic
28	C₂²×#92420	—	2	8	no	—
29	C₂²×#92420	—	2	2	no	—
30	C₂²×#92420	—	2	2	no	—
31	C₂²×#92420	—	2	2	no	—
32	C₂²×#92420	—	2	2	no	—
33	C₄⋊#92420	—	2	2	no	—
34	C₄⋊#92420	C₂×C₄	1	4	yes	—
35	C₂²⋊#92420	—	2	2	no	—
36	C₂²⋊#92420	—	2	2	no	—
37	C₄×#92420	—	2	2	no	—
38	C₄×#92420	—	2	2	no	—
39	C₄×#92420	—	2	2	no	—
40	C₄×#92420	—	2	2	no	—
41	C₄×#92420	—	2	2	no	—
42	C₄×#92420	C₂×C₄	1	4	yes	—
43	C₂³×Dic₆₁	D₄	1	1	yes	characteristic
44	C₂³×Dic₆₁	Q₈	1	1	yes	characteristic
45	C₂×#11758194	—	2	1	no	—
46	C₂×#11758194	—	2	2	no	—
47	C₂×#11758194	C₈	1	4	yes	complemented
48	C₂×#11758194	C₂×C₄	1	2	yes	—
49	C₂²×#92418	—	2	1	no	—
50	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₆₁	Q₈	1	1	yes	characteristic
61	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
62	#14519687	—	2	2	no	—
63	#14519687	—	2	2	no	—
64	C₈×Dic₆₁	—	2	2	no	—
65	C₈×Dic₆₁	—	2	2	no	—
66	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
67	C₂×M₁₆×C₆₁	—	2	1	no	—
68	C₂×M₁₆×C₆₁	—	2	2	no	—
69	C₂×M₁₆×C₆₁	C₈	1	4	yes	complemented
70	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₆₁	—	2	1	no	—
72	C₂⁴×C₆₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₄²	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	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₆₁	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₆₁	M₁₆	1	2	yes	—
81	C₂²×C₄×C₆₁	M₁₆	1	2	yes	—
82	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×Dic₆₁	—	2	4	no	—
84	C₂²×Dic₆₁	—	2	4	no	—
85	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
97	C₂×#92420	—	2	8	no	—
98	C₂×#92420	—	2	8	no	—
99	C₂×#92420	—	2	8	no	—
100	C₂×#92420	—	2	4	no	—
101	C₂×#92420	—	2	4	no	—
102	C₂×#92420	—	4	4	no	—
103	M₁₆×C₆₁	—	2	4	no	—
104	M₁₆×C₆₁	—	2	2	no	—
105	M₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
106	C₂×C₈×C₆₁	—	2	4	no	—
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
109	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
110	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
113	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
123	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
124	#11758194	—	2	4	no	—
125	#11758194	—	2	2	no	—
126	#11758194	C₂×C₈	1	4	yes	complemented
127	C₂×#92418	—	2	4	no	—
128	C₂×#92418	—	2	2	no	—
129	C₂³×C₆₁	—	2	2	no	—
130	C₂³×C₆₁	—	2	2	no	—
131	C₂³×C₆₁	#95	1	1	yes	characteristic
132	C₂³×C₆₁	#95	1	1	yes	characteristic
133	C₂³×C₆₁	C₄⋊C₈	1	2	yes	—
134	C₂³×C₆₁	C₄⋊C₈	1	2	yes	—
135	C₂³×C₆₁	C₂×C₄⋊C₄	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	2	yes	—
143	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
144	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
145	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
146	C₂×C₄×C₆₁	C₄⋊C₈	1	2	yes	—
147	C₂×C₄×C₆₁	C₄⋊C₈	1	2	yes	—
148	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
154	C₂×Dic₆₁	—	2	2	no	—
155	C₂×Dic₆₁	—	2	2	no	—
156	C₂×Dic₆₁	—	2	2	no	—
157	C₂×Dic₆₁	—	2	2	no	—
158	C₂×Dic₆₁	—	2	2	no	—
159	C₂×Dic₆₁	—	2	2	no	—
160	C₂×Dic₆₁	—	2	2	no	—
161	C₂×Dic₆₁	—	2	2	no	—
162	C₂×Dic₆₁	—	2	2	no	—
163	C₂×Dic₆₁	—	2	2	no	—
164	C₂×Dic₆₁	#95	1	1	yes	characteristic
165	C₂×Dic₆₁	#95	1	1	yes	characteristic
166	C₂×Dic₆₁	#95	1	1	yes	characteristic
167	C₂×Dic₆₁	#95	1	1	yes	characteristic
168	C₂×Dic₆₁	#104	1	4	yes	—
169	C₂×Dic₆₁	#108	1	4	yes	—
170	C₂×Dic₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×Dic₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	#92420	—	2	8	no	—
175	#92420	—	4	4	no	—
176	C₈×C₆₁	—	2	4	no	—
177	#92418	—	2	4	no	—
178	C₂×#1278	—	61	1	no	maximal, Sylow
179	C₂²×C₆₁	—	2	1	no	—
180	C₂²×C₆₁	—	2	1	no	—
181	C₂²×C₆₁	—	2	1	no	—
182	C₂²×C₆₁	—	2	1	no	—
183	C₂²×C₆₁	—	2	4	no	—
184	C₂²×C₆₁	—	2	4	no	—
185	C₂²×C₆₁	#336	1	2	yes	—
186	C₂²×C₆₁	#336	1	2	yes	—
187	C₂²×C₆₁	#339	1	2	yes	—
188	C₂²×C₆₁	#341	1	2	yes	—
189	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
190	C₂²×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
191	C₂²×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
192	C₄×C₆₁	#336	1	2	yes	—
193	C₄×C₆₁	#336	1	2	yes	—
194	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
195	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
196	C₄×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
197	C₄×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
198	Dic₆₁	—	2	1	no	—
199	Dic₆₁	—	2	1	no	—
200	Dic₆₁	—	2	1	no	—
201	Dic₆₁	—	2	1	no	—
202	Dic₆₁	#339	1	2	yes	—
203	Dic₆₁	#341	1	2	yes	—
204	Dic₆₁	C₂×#104	1	2	yes	—
205	Dic₆₁	C₂×#108	1	2	yes	—
206	C₂×#431	—	61	1	no	—
207	C₂×C₄×M₁₆	—	61	1	no	—
208	C₂²×C₄×C₈	—	61	1	no	—
209	#1278	—	61	4	no	—
210	C₂×C₆₁	—	2	2	no	—
211	C₂×C₆₁	—	2	1	no	—
212	C₂×C₆₁	—	2	1	no	—
213	C₂×C₆₁	#1278	1	4	yes	complemented
214	C₂×C₆₁	C₂×#336	1	1	yes	characteristic
215	C₂×C₆₁	C₂×#339	1	1	yes	characteristic
216	C₂×C₆₁	C₂×#341	1	1	yes	characteristic
217	C₂²×M₁₆	—	61	1	no	—
218	C₂²×M₁₆	#6923	1	1	yes	characteristic
219	C₂³×C₈	—	122	1	no	—
220	C₂²×C₄²	—	61	1	no	—
221	#431	—	61	2	no	—
222	#431	—	61	2	no	—
223	#431	—	122	1	no	—
224	#431	—	122	1	no	—
225	C₂×C₄⋊C₈	—	61	2	no	—
226	C₂×C₂²⋊C₈	—	122	1	no	—
227	C₄×M₁₆	—	61	2	no	—
228	C₄×M₁₆	—	61	2	no	—
229	C₄×M₁₆	—	122	1	no	—
230	C₄×M₁₆	—	122	1	no	—
231	C₂×#97	—	122	1	no	—
232	C₂×C₄×C₈	—	61	2	no	—
233	C₂×C₄×C₈	—	61	2	no	—
234	C₂×C₄×C₈	—	61	2	no	—
235	C₂×C₄×C₈	—	122	1	no	—
236	C₂×C₄×C₈	—	122	1	no	—
237	C₂×C₄×C₈	—	122	1	no	—
238	C₂×C₄×C₈	—	122	1	no	—
239	C₂×C₄×C₈	—	122	1	no	—
240	C₆₁	C₂×#1278	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₄	—	61	1	no	—
242	C₂³×C₄	—	61	1	no	—
243	C₂³×C₄	C₂×#6923	1	1	yes	characteristic
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂×M₁₆	—	61	4	no	—
247	C₂×M₁₆	—	61	2	no	—
248	C₂×M₁₆	—	122	2	no	—
249	C₂×M₁₆	—	122	1	no	—
250	C₂×M₁₆	#92420	1	4	yes	complemented
251	C₂×M₁₆	C₂×#6923	1	2	yes	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	122	2	no	—
254	C₂²×C₈	—	122	2	no	—
255	C₂²×C₈	—	122	2	no	—
256	C₂²×C₈	—	122	8	no	—
257	C₂²×C₈	—	122	1	no	—
258	C₂²×C₈	—	122	2	no	—
259	C₂×C₄²	—	61	1	no	—
260	C₂×C₄²	—	61	1	no	—
261	C₂×C₄²	—	61	1	no	—
262	C₂×C₄²	—	61	1	no	—
263	C₂×C₄²	—	61	1	no	—
264	C₂×C₄²	—	61	1	no	—
265	C₂×C₄²	—	61	1	no	—
266	C₂×C₄²	—	61	1	no	—
267	C₂×C₄²	—	61	1	no	—
268	C₂×C₄²	—	61	1	no	—
269	C₂×C₄²	—	61	1	no	—
270	C₂×C₄²	—	61	1	no	—
271	C₄⋊C₈	—	61	4	no	—
272	C₄⋊C₈	—	122	2	no	—
273	C₂²⋊C₈	—	122	2	no	—
274	C₂²⋊C₈	—	122	2	no	—
275	#97	—	122	2	no	—
276	#97	—	122	2	no	—
277	C₄×C₈	—	61	4	no	—
278	C₄×C₈	—	122	2	no	—
279	C₄×C₈	—	122	2	no	—
280	C₄×C₈	—	122	2	no	—
281	C₄×C₈	—	122	2	no	—
282	C₄×C₈	—	122	2	no	—
283	C₄×C₈	—	122	2	no	—
284	C₄×C₈	—	122	2	no	—
285	C₂⁴	C₄⋊#6923	1	1	yes	characteristic
286	C₂²×C₄	—	61	1	no	—
287	C₂²×C₄	—	61	1	no	—
288	C₂²×C₄	—	61	1	no	—
289	C₂²×C₄	—	61	1	no	—
290	C₂²×C₄	—	61	1	no	—
291	C₂²×C₄	—	61	1	no	—
292	C₂²×C₄	—	61	1	no	—
293	C₂²×C₄	—	61	1	no	—
294	C₂²×C₄	—	61	1	no	—
295	C₂²×C₄	—	61	1	no	—
296	C₂²×C₄	—	61	1	no	—
297	C₂²×C₄	—	61	1	no	—
298	C₂²×C₄	—	122	4	no	—
299	C₂²×C₄	—	122	4	no	—
300	C₂²×C₄	D₆₁⋊C₈	1	2	yes	—
301	C₂²×C₄	#11758213	1	2	yes	—
302	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
303	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
304	C₂²×C₄	C₄⋊#6923	1	1	yes	characteristic
305	C₂²×C₄	C₂×#92420	1	2	yes	—
306	C₂²×C₄	#11758217	1	2	yes	—
307	C₂²×C₄	C₂²⋊#6923	1	1	yes	characteristic
308	C₂²×C₄	C₂²⋊#6923	1	1	yes	characteristic
309	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	2	no	—
312	M₁₆	—	61	4	no	—
313	M₁₆	—	122	4	no	—
314	M₁₆	—	122	2	no	—
315	M₁₆	C₂×#92420	1	4	yes	complemented
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	122	4	no	—
319	C₂×C₈	—	122	8	no	—
320	C₂×C₈	—	122	8	no	—
321	C₂×C₈	—	122	8	no	—
322	C₂×C₈	—	122	4	no	—
323	C₂×C₈	—	122	2	no	—
324	C₂×C₈	—	122	4	no	—
325	C₂×C₈	—	244	4	no	—
326	C₄²	—	61	1	no	—
327	C₄²	—	61	1	no	—
328	C₄²	—	61	1	no	—
329	C₄²	—	61	1	no	—
330	C₄²	—	61	1	no	—
331	C₄²	—	61	1	no	—
332	C₄²	—	61	1	no	—
333	C₄²	—	61	1	no	—
334	C₄²	—	61	1	no	—
335	C₄²	—	61	1	no	—
336	C₄²	—	61	1	no	—
337	C₄²	—	61	1	no	—
338	C₄²	—	61	1	no	—
339	C₄²	—	61	1	no	—
340	C₄²	—	61	1	no	—
341	C₄²	—	61	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	(C₂×#6923)⋊C₄	1	1	yes	characteristic
345	C₂³	(C₂×#6923)⋊C₄	1	1	yes	characteristic
346	C₂³	C₄⋊#92420	1	2	yes	—
347	C₂³	#14519844	1	2	yes	—
348	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
349	C₂×C₄	—	61	4	no	—
350	C₂×C₄	—	61	4	no	—
351	C₂×C₄	—	61	1	no	—
352	C₂×C₄	—	61	1	no	—
353	C₂×C₄	—	61	1	no	—
354	C₂×C₄	—	61	1	no	—
355	C₂×C₄	—	61	1	no	—
356	C₂×C₄	—	61	1	no	—
357	C₂×C₄	—	61	1	no	—
358	C₂×C₄	—	61	1	no	—
359	C₂×C₄	—	122	2	no	—
360	C₂×C₄	—	122	2	no	—
361	C₂×C₄	—	122	2	no	—
362	C₂×C₄	—	122	2	no	—
363	C₂×C₄	—	122	2	no	—
364	C₂×C₄	—	122	2	no	—
365	C₂×C₄	—	122	2	no	—
366	C₂×C₄	—	122	2	no	—
367	C₂×C₄	—	122	2	no	—
368	C₂×C₄	—	122	2	no	—
369	C₂×C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₄×#92420	1	2	yes	—
372	C₂×C₄	C₄×#92420	1	2	yes	—
373	C₂×C₄	#14519832	1	2	yes	—
374	C₂×C₄	#14519832	1	2	yes	—
375	C₂×C₄	C₂²⋊#92420	1	2	yes	—
376	C₂×C₄	C₂²⋊#92420	1	2	yes	—
377	C₂×C₄	#14519834	1	2	yes	—
378	C₂×C₄	#14519834	1	2	yes	—
379	C₂×C₄	C₄⋊#92420	1	2	yes	—
380	C₂×C₄	#14519844	1	2	yes	—
381	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
382	C₂×C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
383	C₂×C₄	C₂²×#92420	1	1	yes	characteristic
384	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
385	C₂×C₄	C₂×#11758217	1	1	yes	characteristic
386	C₂×C₄	C₂×#11758213	1	1	yes	characteristic
387	C₈	—	2	4	no	—
388	C₈	—	122	8	no	—
389	C₈	—	122	4	no	—
390	C₈	—	244	4	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	#16840628	1	2	yes	—
398	C₂²	#16840628	1	2	yes	—
399	C₂²	#16840634	1	2	yes	—
400	C₂²	#16840637	1	2	yes	—
401	C₂²	C₂×(C₂×#6923)⋊C₄	1	1	yes	characteristic
402	C₂²	C₂×C₄⋊#92420	1	1	yes	characteristic
403	C₂²	C₂×#14519844	1	1	yes	characteristic
404	C₄	—	61	2	no	—
405	C₄	—	61	2	no	—
406	C₄	—	61	2	no	—
407	C₄	—	61	2	no	—
408	C₄	—	122	1	no	—
409	C₄	—	122	1	no	—
410	C₄	—	122	1	no	—
411	C₄	—	122	1	no	—
412	C₄	#16840628	1	2	yes	—
413	C₄	#16840628	1	2	yes	—
414	C₄	C₂×C₄×#92420	1	1	yes	characteristic
415	C₄	C₂×#14519832	1	1	yes	characteristic
416	C₄	C₂×C₂²⋊#92420	1	1	yes	characteristic
417	C₄	C₂×#14519834	1	1	yes	characteristic
418	C₂	—	2	1	no	—
419	C₂	—	2	1	no	—
420	C₂	—	2	2	no	—
421	C₂	#21460652	1	4	yes	direct product factor
422	C₂	C₂×#16840628	1	1	yes	characteristic
423	C₂	C₂×#16840634	1	1	yes	characteristic
424	C₂	C₂×#16840637	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#6923
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#6923
Fitting	C₂²×M₁₆×C₆₁	C₄
socle	C₂³×C₆₁	#95
prime radical	C₂⁴×C₆₁	C₄⋊C₄
cosocle	C₂×C₄×Dic₆₁	C₂³
hypercenter	C₂²×M₁₆	#6923
hypocenter	C₆₁	C₂×#1278
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #21460652	C₂	direct (N × H)
47. C₂×#11758194	C₈	semidirect
69. C₂×M₁₆×C₆₁	C₈	semidirect
105. M₁₆×C₆₁	C₂×C₈	semidirect
126. #11758194	C₂×C₈	semidirect
213. C₂×C₆₁	#1278	semidirect
240. C₆₁	C₂×#1278	semidirect
250. C₂×M₁₆	#92420	semidirect
315. M₁₆	C₂×#92420	semidirect
421. C₂	#21460652	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×#16840778	2
C₂²×C₄×#92420	2
#21460652	2
C₂×M₁₆×Dic₆₁	2
C₂×#1278	61

Subgroups — C2×#21460652 #30596126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21460652 #30596126