Subgroups — #30596132

Order 15616.

666 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×#16840778	C₂	1	1	yes	maximal, characteristic
2	C₂×#16840778	C₂	1	1	yes	maximal, characteristic
3	#21460652	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×Dic₆₁	C₂	1	1	yes	maximal, characteristic
5	#16840778	—	2	1	no	—
6	#16840778	—	2	1	no	—
7	#16840778	—	2	1	no	—
8	#16840778	—	2	1	no	—
9	#16840778	C₄	1	2	yes	—
10	#16840778	C₄	1	2	yes	—
11	#16840778	C₄	1	2	yes	—
12	#16840778	C₂²	1	2	yes	—
13	C₂×C₄⋊#92420	—	2	1	no	—
14	C₂×C₄⋊#92420	C₄	1	2	yes	—
15	C₂×C₂²⋊#92420	—	2	1	no	—
16	C₂×C₂²⋊#92420	—	2	1	no	—
17	C₂×C₄×#92420	—	2	1	no	—
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	2	no	—
29	C₂²×#92420	—	2	2	no	—
30	C₄⋊#92420	—	2	2	no	—
31	C₄⋊#92420	—	2	2	no	—
32	C₄⋊#92420	—	2	2	no	—
33	C₄⋊#92420	C₂×C₄	1	4	yes	—
34	C₂²⋊#92420	—	2	2	no	—
35	C₂²⋊#92420	—	2	2	no	—
36	C₂²⋊#92420	—	2	2	no	—
37	C₂²⋊#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	C₂×C₄	1	4	yes	—
42	C₂³×Dic₆₁	D₄	1	1	yes	characteristic
43	C₂³×Dic₆₁	Q₈	1	1	yes	characteristic
44	C₂×#11758194	—	2	1	no	—
45	C₂×#11758194	—	2	2	no	—
46	C₂×#11758194	C₈	1	4	yes	complemented
47	C₂×#11758194	C₂×C₄	1	2	yes	—
48	C₂²×#92418	—	2	1	no	—
49	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
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	D₄	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	Q₈	1	1	yes	characteristic
60	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
61	#14519687	—	2	2	no	—
62	#14519687	—	2	2	no	—
63	C₈×Dic₆₁	—	2	2	no	—
64	C₈×Dic₆₁	—	2	2	no	—
65	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
66	C₂×M₁₆×C₆₁	—	2	1	no	—
67	C₂×M₁₆×C₆₁	—	2	2	no	—
68	C₂×M₁₆×C₆₁	C₈	1	4	yes	complemented
69	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₆₁	—	2	1	no	—
71	C₂⁴×C₆₁	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₄²	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	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₆₁	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₆₁	M₁₆	1	2	yes	—
80	C₂²×C₄×C₆₁	M₁₆	1	2	yes	—
81	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×Dic₆₁	—	4	2	no	—
83	C₂²×Dic₆₁	—	4	2	no	—
84	C₂²×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
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	C₄⋊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	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
96	C₂×#92420	—	2	4	no	—
97	C₂×#92420	—	2	4	no	—
98	C₂×#92420	—	4	4	no	—
99	C₂×#92420	—	4	4	no	—
100	M₁₆×C₆₁	—	2	4	no	—
101	M₁₆×C₆₁	—	2	2	no	—
102	M₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
103	C₂×C₈×C₆₁	—	2	4	no	—
104	C₂×C₈×C₆₁	—	2	2	no	—
105	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
106	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
107	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₄×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₄×Dic₆₁	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
116	C₄×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
118	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
120	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
121	#11758194	—	2	4	no	—
122	#11758194	—	2	2	no	—
123	#11758194	C₂×C₈	1	4	yes	complemented
124	C₂×#92418	—	2	4	no	—
125	C₂×#92418	—	2	2	no	—
126	C₂³×C₆₁	—	4	1	no	—
127	C₂³×C₆₁	—	4	1	no	—
128	C₂³×C₆₁	#95	1	1	yes	characteristic
129	C₂³×C₆₁	#95	1	1	yes	characteristic
130	C₂³×C₆₁	C₄⋊C₈	1	2	yes	—
131	C₂³×C₆₁	C₄⋊C₈	1	2	yes	—
132	C₂³×C₆₁	C₂×C₄⋊C₄	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	C₄×C₈	1	2	yes	—
136	C₂×C₄×C₆₁	C₄×C₈	1	2	yes	—
137	C₂×C₄×C₆₁	#97	1	2	yes	—
138	C₂×C₄×C₆₁	#97	1	2	yes	—
139	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
140	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
141	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
142	C₂×C₄×C₆₁	C₂²⋊C₈	1	2	yes	—
143	C₂×C₄×C₆₁	C₄⋊C₈	1	2	yes	—
144	C₂×C₄×C₆₁	C₄⋊C₈	1	2	yes	—
145	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
151	C₂×Dic₆₁	—	2	2	no	—
152	C₂×Dic₆₁	—	2	2	no	—
153	C₂×Dic₆₁	—	2	2	no	—
154	C₂×Dic₆₁	—	2	2	no	—
155	C₂×Dic₆₁	—	2	2	no	—
156	C₂×Dic₆₁	—	2	2	no	—
157	C₂×Dic₆₁	—	4	1	no	—
158	C₂×Dic₆₁	—	4	1	no	—
159	C₂×Dic₆₁	—	4	1	no	—
160	C₂×Dic₆₁	—	4	1	no	—
161	C₂×Dic₆₁	—	4	1	no	—
162	C₂×Dic₆₁	—	4	1	no	—
163	C₂×Dic₆₁	#95	1	1	yes	characteristic
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×Dic₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	#92420	—	4	4	no	—
172	#92420	—	4	4	no	—
173	C₈×C₆₁	—	2	4	no	—
174	#92418	—	2	4	no	—
175	#7882	—	61	1	no	maximal, Sylow
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	—	2	1	no	—
181	C₂²×C₆₁	—	2	1	no	—
182	C₂²×C₆₁	—	4	2	no	—
183	C₂²×C₆₁	—	4	2	no	—
184	C₂²×C₆₁	#336	1	2	yes	—
185	C₂²×C₆₁	#336	1	2	yes	—
186	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
187	C₂²×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
188	C₂²×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
189	C₄×C₆₁	#336	1	2	yes	—
190	C₄×C₆₁	#336	1	2	yes	—
191	C₄×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
192	C₄×C₆₁	C₂×#97	1	1	yes	characteristic
193	C₄×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
194	C₄×C₆₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
195	Dic₆₁	—	2	1	no	—
196	Dic₆₁	—	2	1	no	—
197	Dic₆₁	—	2	1	no	—
198	Dic₆₁	—	2	1	no	—
199	Dic₆₁	—	2	1	no	—
200	Dic₆₁	—	2	1	no	—
201	Dic₆₁	#421	1	2	yes	—
202	Dic₆₁	#430	1	2	yes	—
203	C₂×#431	—	61	1	no	—
204	C₂×#431	—	61	1	no	—
205	C₂×C₄×M₁₆	—	61	1	no	—
206	#1278	—	61	4	no	—
207	C₂×C₆₁	—	2	2	no	—
208	C₂×C₆₁	—	2	2	no	—
209	C₂×C₆₁	—	2	1	no	—
210	C₂×C₆₁	—	2	1	no	—
211	C₂×C₆₁	C₂×#336	1	1	yes	characteristic
212	C₂×C₆₁	#1733	1	1	yes	characteristic
213	C₂×C₆₁	#1738	1	1	yes	characteristic
214	C₂²×M₁₆	—	61	1	no	—
215	C₂²×M₁₆	#6923	1	1	yes	characteristic
216	C₂²×C₄²	—	61	1	no	—
217	#431	—	61	2	no	—
218	#431	—	61	2	no	—
219	#431	—	61	2	no	—
220	#431	—	61	2	no	—
221	#431	—	122	1	no	—
222	#431	—	122	1	no	—
223	#431	—	122	1	no	—
224	#431	—	122	1	no	—
225	C₂×C₄⋊C₈	—	61	2	no	—
226	C₂×C₄⋊C₈	—	122	1	no	—
227	C₂×C₂²⋊C₈	—	122	1	no	—
228	C₂×C₂²⋊C₈	—	122	1	no	—
229	C₄×M₁₆	—	61	2	no	—
230	C₄×M₁₆	—	61	2	no	—
231	C₄×M₁₆	—	122	1	no	—
232	C₄×M₁₆	—	122	1	no	—
233	C₂×#97	—	122	1	no	—
234	C₂×C₄×C₈	—	61	2	no	—
235	C₂×C₄×C₈	—	122	1	no	—
236	C₂×C₄×C₈	—	122	1	no	—
237	C₆₁	#7882	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₄	—	61	1	no	—
239	C₂³×C₄	—	61	1	no	—
240	C₂³×C₄	C₂×#6923	1	1	yes	characteristic
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	61	4	no	—
244	C₂×M₁₆	—	61	2	no	—
245	C₂×M₁₆	—	122	2	no	—
246	C₂×M₁₆	—	122	1	no	—
247	C₂×M₁₆	#92420	1	4	yes	complemented
248	C₂×M₁₆	C₂×#6923	1	2	yes	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	122	1	no	—
251	C₂²×C₈	—	122	2	no	—
252	C₂²×C₈	—	122	2	no	—
253	C₂×C₄²	—	61	1	no	—
254	C₂×C₄²	—	61	1	no	—
255	C₂×C₄²	—	61	1	no	—
256	C₂×C₄²	—	61	1	no	—
257	C₂×C₄²	—	61	1	no	—
258	C₂×C₄²	—	61	1	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	C₄⋊C₈	—	61	4	no	—
266	C₄⋊C₈	—	122	2	no	—
267	C₄⋊C₈	—	122	2	no	—
268	C₄⋊C₈	—	122	2	no	—
269	C₂²⋊C₈	—	122	2	no	—
270	C₂²⋊C₈	—	122	2	no	—
271	C₂²⋊C₈	—	122	2	no	—
272	C₂²⋊C₈	—	122	2	no	—
273	#97	—	122	2	no	—
274	#97	—	122	2	no	—
275	C₄×C₈	—	61	4	no	—
276	C₄×C₈	—	122	2	no	—
277	C₄×C₈	—	122	2	no	—
278	C₄×C₈	—	122	2	no	—
279	C₄×C₈	—	122	2	no	—
280	C₄×C₈	—	122	2	no	—
281	C₂⁴	C₄⋊#6923	1	1	yes	characteristic
282	C₂²×C₄	—	61	1	no	—
283	C₂²×C₄	—	61	1	no	—
284	C₂²×C₄	—	61	1	no	—
285	C₂²×C₄	—	61	1	no	—
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	—	244	2	no	—
295	C₂²×C₄	—	244	2	no	—
296	C₂²×C₄	D₆₁⋊C₈	1	2	yes	—
297	C₂²×C₄	#11758213	1	2	yes	—
298	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
299	C₂²×C₄	C₄×#6923	1	1	yes	characteristic
300	C₂²×C₄	C₄⋊#6923	1	1	yes	characteristic
301	C₂²×C₄	C₂×#92420	1	2	yes	—
302	C₂²×C₄	#11758217	1	2	yes	—
303	C₂²×C₄	C₂²⋊#6923	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊#6923	1	1	yes	characteristic
305	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	61	4	no	—
309	M₁₆	—	122	4	no	—
310	M₁₆	—	122	2	no	—
311	M₁₆	C₂×#92420	1	4	yes	complemented
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	122	4	no	—
315	C₂×C₈	—	122	2	no	—
316	C₂×C₈	—	122	4	no	—
317	C₂×C₈	—	122	4	no	—
318	C₂×C₈	—	244	4	no	—
319	C₂×C₈	—	244	4	no	—
320	C₄²	—	61	1	no	—
321	C₄²	—	61	1	no	—
322	C₄²	—	61	1	no	—
323	C₄²	—	61	1	no	—
324	C₄²	—	61	1	no	—
325	C₄²	—	61	1	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	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	(C₂×#6923)⋊C₄	1	1	yes	characteristic
339	C₂³	(C₂×#6923)⋊C₄	1	1	yes	characteristic
340	C₂³	C₄⋊#92420	1	2	yes	—
341	C₂³	#14519844	1	2	yes	—
342	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
343	C₂×C₄	—	61	1	no	—
344	C₂×C₄	—	61	1	no	—
345	C₂×C₄	—	61	1	no	—
346	C₂×C₄	—	61	1	no	—
347	C₂×C₄	—	61	1	no	—
348	C₂×C₄	—	61	1	no	—
349	C₂×C₄	—	61	1	no	—
350	C₂×C₄	—	61	1	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	—	244	1	no	—
358	C₂×C₄	—	244	1	no	—
359	C₂×C₄	—	244	1	no	—
360	C₂×C₄	—	244	1	no	—
361	C₂×C₄	—	244	1	no	—
362	C₂×C₄	—	244	1	no	—
363	C₂×C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	(C₂×#6923)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₄×#92420	1	2	yes	—
366	C₂×C₄	C₄×#92420	1	2	yes	—
367	C₂×C₄	#14519832	1	2	yes	—
368	C₂×C₄	#14519832	1	2	yes	—
369	C₂×C₄	C₂²⋊#92420	1	2	yes	—
370	C₂×C₄	C₂²⋊#92420	1	2	yes	—
371	C₂×C₄	#14519834	1	2	yes	—
372	C₂×C₄	#14519834	1	2	yes	—
373	C₂×C₄	C₄⋊#92420	1	2	yes	—
374	C₂×C₄	#14519844	1	2	yes	—
375	C₂×C₄	C₂×C₄×#6923	1	1	yes	characteristic
376	C₂×C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
377	C₂×C₄	C₂²×#92420	1	1	yes	characteristic
378	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
379	C₂×C₄	C₂×#11758217	1	1	yes	characteristic
380	C₂×C₄	C₂×#11758213	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	122	4	no	—
383	C₈	—	244	4	no	—
384	C₈	—	244	4	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	#16840628	1	2	yes	—
394	C₂²	#16840628	1	2	yes	—
395	C₂²	C₂×(C₂×#6923)⋊C₄	1	1	yes	characteristic
396	C₂²	C₂×C₄⋊#92420	1	1	yes	characteristic
397	C₂²	C₂×#14519844	1	1	yes	characteristic
398	C₄	—	61	2	no	—
399	C₄	—	61	2	no	—
400	C₄	—	122	1	no	—
401	C₄	—	122	1	no	—
402	C₄	—	122	1	no	—
403	C₄	—	122	1	no	—
404	C₄	—	122	1	no	—
405	C₄	—	122	1	no	—
406	C₄	#16840628	1	2	yes	—
407	C₄	#16840628	1	2	yes	—
408	C₄	C₂×C₄×#92420	1	1	yes	characteristic
409	C₄	C₂×#14519832	1	1	yes	characteristic
410	C₄	C₂×C₂²⋊#92420	1	1	yes	characteristic
411	C₄	C₂×#14519834	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	2	no	—
415	C₂	—	2	2	no	—
416	C₂	C₂×#16840628	1	1	yes	characteristic
417	C₂	#21461501	1	1	yes	characteristic
418	C₂	#21461512	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#6923
commutator	C₄×C₆₁	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#6923
Fitting	C₂²×M₁₆×C₆₁	C₄
socle	C₂²×C₆₁	C₂×#95
prime radical	C₂⁴×C₆₁	C₄⋊C₄
cosocle	C₂×C₄×Dic₆₁	C₂³
hypercenter	C₂²×M₁₆	#6923
hypocenter	C₆₁	#7882
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×M₁₆

Complements

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

N	H ≅ G/N	type
3. #21460652	C₂	semidirect
46. C₂×#11758194	C₈	semidirect
68. C₂×M₁₆×C₆₁	C₈	semidirect
102. M₁₆×C₆₁	C₂×C₈	semidirect
123. #11758194	C₂×C₈	semidirect
237. C₆₁	#7882	semidirect
247. C₂×M₁₆	#92420	semidirect
311. M₁₆	C₂×#92420	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16840778	2
#21460652	2
C₂×M₁₆×Dic₆₁	2
#7882	61