Subgroups — #30624490

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462236	C₂	1	2	yes	maximal, complemented
2	#21462200	C₂	1	2	yes	maximal, complemented
3	#21462199	C₂	1	2	yes	maximal, complemented
4	#21462197	C₂	1	2	yes	maximal, complemented
5	#21462182	C₂	1	1	yes	maximal, characteristic, complemented
6	#21462181	C₂	1	1	yes	maximal, characteristic, complemented
7	#21462177	C₂	1	1	yes	maximal, characteristic, complemented
8	#21462153	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16840683	C₂	1	1	yes	maximal, characteristic, complemented
10	D₆₁⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#11758224	C₂	1	1	yes	maximal, characteristic
12	C₂×#14519851	C₂²	1	2	yes	—
13	C₂×D₆₁⋊C₁₆	C₂²	1	2	yes	—
14	C₂²×#11758187	C₂²	1	2	yes	—
15	#16840683	C₂²	1	1	yes	characteristic
16	#16840683	C₂²	1	1	yes	characteristic
17	#16840683	C₂²	1	1	yes	characteristic
18	#16840683	C₂²	1	2	yes	—
19	#16840683	C₂²	1	2	yes	—
20	#16840683	C₂²	1	1	yes	characteristic
21	C₄⋊#11758187	C₂²	1	2	yes	—
22	#16840657	C₂²	1	2	yes	—
23	C₂²⋊#11758187	C₂²	1	2	yes	—
24	C₂²⋊#11758187	C₂²	1	2	yes	—
25	#16840651	C₂²	1	2	yes	—
26	#16840650	C₂²	1	2	yes	—
27	#16840648	C₂²	1	2	yes	—
28	C₄×#11758224	C₄	1	1	yes	characteristic
29	C₈×Dic₁₂₂	C₄	1	1	yes	characteristic
30	#16839886	C₂²	1	1	yes	characteristic
31	D₄×#92418	C₂²	1	1	yes	characteristic
32	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
33	C₈×C₂²⋊D₆₁	C₄	1	1	yes	characteristic
34	#16839825	C₂²	1	1	yes	characteristic
35	#16839825	C₂²	1	1	yes	characteristic
36	#16839814	C₄	1	1	yes	characteristic
37	#16839812	C₄	1	1	yes	characteristic
38	#16839812	C₄	1	1	yes	characteristic
39	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₆₁	C₄	1	1	yes	characteristic
43	#14519851	—	4	2	no	—
44	D₆₁⋊C₁₆	—	4	2	no	—
45	C₂×#11758187	—	4	2	no	—
46	C₂×#11758187	C₂³	1	2	yes	—
47	C₂×#11758187	C₂³	1	2	yes	—
48	C₂×#11758187	C₂³	1	2	yes	—
49	C₂×#11758187	C₂³	1	2	yes	—
50	C₂×#11758224	C₈	1	1	yes	characteristic
51	C₂²×#92418	C₂³	1	1	yes	characteristic
52	C₂²×#92418	C₂³	1	1	yes	characteristic
53	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
55	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
56	#14519742	C₈	1	1	yes	characteristic
57	D₄×Dic₆₁	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
60	#14519737	C₈	1	1	yes	characteristic
61	#14519737	C₈	1	1	yes	characteristic
62	#14519735	C₈	1	1	yes	characteristic
63	#14519733	C₈	1	1	yes	characteristic
64	#14519733	C₈	1	1	yes	characteristic
65	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
69	#14519706	C₂×C₄	1	1	yes	characteristic
70	#14519706	C₂×C₄	1	1	yes	characteristic
71	#14519706	C₂×C₄	1	1	yes	characteristic
72	#14519706	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
74	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
75	#14519689	C₂×C₄	1	1	yes	characteristic
76	#14519689	C₂×C₄	1	1	yes	characteristic
77	C₄×#92418	C₂³	1	1	yes	characteristic
78	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
84	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
85	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
98	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
99	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
100	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
101	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
102	#11758224	—	2	4	no	—
103	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
107	C₂×C₈×C₆₁	—	4	1	no	—
108	C₂×C₈×C₆₁	—	4	1	no	—
109	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
114	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
115	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
116	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
118	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
119	#11758198	C₂×C₈	1	1	yes	characteristic
120	#11758198	C₂×C₈	1	1	yes	characteristic
121	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
122	#11758196	C₂×C₈	1	1	yes	characteristic
123	#11758196	C₂×C₈	1	1	yes	characteristic
124	#11758196	C₂×C₈	1	1	yes	characteristic
125	#11758196	C₂×C₈	1	1	yes	characteristic
126	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×#92418	—	2	1	no	—
136	C₂×#92418	—	2	1	no	—
137	C₂×#92418	—	2	1	no	—
138	C₂×#92418	—	2	1	no	—
139	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
140	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
141	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
142	C₂×#92418	C₂⁴	1	1	yes	characteristic
143	C₈×D₆₁	—	2	1	no	—
144	C₈×D₆₁	—	2	1	no	—
145	C₈×D₆₁	—	4	1	no	—
146	#11758187	—	2	2	no	—
147	#11758187	—	2	2	no	—
148	#11758187	—	2	2	no	—
149	#11758187	—	2	2	no	—
150	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
151	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
152	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
153	D₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
163	C₂²⋊D₆₁	—	2	2	no	—
164	C₂²⋊D₆₁	M₃₂	1	4	yes	complemented
165	C₂×Dic₆₁	—	2	2	no	—
166	C₂×Dic₆₁	—	2	2	no	—
167	C₂×Dic₆₁	—	2	2	no	—
168	C₂×Dic₆₁	—	2	2	no	—
169	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
170	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₆₁	—	2	2	no	—
177	C₄×D₆₁	—	2	1	no	—
178	C₄×D₆₁	—	2	1	no	—
179	C₄×D₆₁	—	2	2	no	—
180	Dic₁₂₂	—	2	2	no	—
181	C₈×C₆₁	—	2	1	no	—
182	C₈×C₆₁	—	2	1	no	—
183	C₈×C₆₁	—	2	1	no	—
184	C₈×C₆₁	—	2	1	no	—
185	#92418	—	2	1	no	—
186	#92418	—	2	1	no	—
187	#92418	—	2	1	no	—
188	#92418	H(5,𝔽₂)	1	1	yes	characteristic
189	#92418	2₋¹⁺⁴	1	1	yes	characteristic
190	#33504	—	61	1	no	maximal, Sylow
191	C₂²×C₆₁	—	2	1	no	—
192	C₂²×C₆₁	—	2	1	no	—
193	C₂²×C₆₁	—	2	1	no	—
194	C₂²×C₆₁	—	2	1	no	—
195	C₂²×C₆₁	—	2	1	no	—
196	C₂²×C₆₁	C₂×M₃₂	1	2	yes	—
197	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
198	C₂×D₆₁	—	2	1	no	—
199	C₂×D₆₁	—	2	1	no	—
200	C₂×D₆₁	C₂×M₃₂	1	2	yes	—
201	C₄×C₆₁	—	2	1	no	—
202	C₄×C₆₁	—	2	1	no	—
203	C₄×C₆₁	—	2	1	no	—
204	C₄×C₆₁	—	2	1	no	—
205	C₄×C₆₁	#520	1	1	yes	characteristic
206	C₄×C₆₁	#568	1	1	yes	characteristic
207	Dic₆₁	—	2	1	no	—
208	Dic₆₁	—	2	1	no	—
209	Dic₆₁	—	2	1	no	—
210	Dic₆₁	—	2	1	no	—
211	Dic₆₁	—	2	1	no	—
212	Dic₆₁	C₂×M₃₂	1	2	yes	—
213	Dic₆₁	#504	1	2	yes	—
214	C₈×#41	—	61	1	no	—
215	#2183	—	61	2	no	—
216	#2168	—	61	2	no	—
217	#2168	—	61	2	no	—
218	D₄×C₁₆	—	61	2	no	—
219	#2163	—	61	1	no	—
220	#2163	—	61	1	no	—
221	#2162	—	61	1	no	—
222	#2150	—	61	1	no	—
223	C₂×C₄⋊C₁₆	—	61	1	no	—
224	C₂×C₄⋊C₁₆	—	61	1	no	—
225	C₂×C₆₁	—	2	2	no	—
226	C₂×C₆₁	—	4	1	no	—
227	C₂×C₆₁	#2988	1	1	yes	characteristic
228	C₂×C₆₁	C₂²×M₃₂	1	1	yes	characteristic
229	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
230	D₆₁	—	2	2	no	—
231	C₄×#41	—	61	1	no	—
232	C₂×M₃₂	—	61	2	no	—
233	C₂²×C₁₆	—	61	2	no	—
234	C₂²×C₁₆	—	61	2	no	—
235	C₈×Q₈	—	61	1	no	—
236	C₈×Q₈	—	61	1	no	—
237	C₈×D₄	—	61	1	no	—
238	C₈×D₄	—	61	1	no	—
239	C₈×D₄	—	61	1	no	—
240	C₈×D₄	—	61	1	no	—
241	C₈×D₄	—	61	1	no	—
242	C₈×D₄	#6923	1	1	yes	characteristic
243	#431	—	61	1	no	—
244	#431	—	61	1	no	—
245	#431	—	61	1	no	—
246	C₂×C₄×C₈	—	61	1	no	—
247	C₂×C₄×C₈	—	61	1	no	—
248	C₂×C₄×C₈	—	61	1	no	—
249	C₄⋊C₁₆	—	61	1	no	—
250	C₄⋊C₁₆	—	61	1	no	—
251	C₄⋊C₁₆	—	61	1	no	—
252	C₄⋊C₁₆	—	61	2	no	—
253	C₄⋊C₁₆	—	61	2	no	—
254	C₄⋊C₁₆	—	61	2	no	—
255	C₄⋊C₁₆	—	61	1	no	—
256	C₂²⋊C₁₆	—	61	2	no	—
257	C₂²⋊C₁₆	—	61	2	no	—
258	C₂²⋊C₁₆	—	61	2	no	—
259	#346	—	61	2	no	—
260	#346	—	61	2	no	—
261	C₄×C₁₆	—	61	2	no	—
262	C₆₁	#33504	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	61	1	no	—
264	C₂²×C₈	—	61	1	no	—
265	C₂²×C₈	—	61	1	no	—
266	C₂²×C₈	—	61	1	no	—
267	C₂²×C₈	—	61	1	no	—
268	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
269	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
270	C₄×Q₈	—	61	1	no	—
271	C₄×Q₈	—	61	1	no	—
272	C₄×D₄	—	61	1	no	—
273	C₄×D₄	—	61	1	no	—
274	C₄×D₄	—	61	1	no	—
275	C₄×D₄	—	61	1	no	—
276	C₄×D₄	—	61	1	no	—
277	C₄×D₄	C₂×#6923	1	1	yes	characteristic
278	#117	—	61	1	no	—
279	#117	—	61	1	no	—
280	#117	—	61	1	no	—
281	C₂×C₄²	—	61	1	no	—
282	C₂×C₄²	—	61	1	no	—
283	C₂×C₄²	—	61	1	no	—
284	M₃₂	—	244	2	no	—
285	C₂×C₁₆	—	61	2	no	—
286	C₂×C₁₆	—	61	2	no	—
287	C₂×C₁₆	—	61	2	no	—
288	C₂×C₁₆	—	61	2	no	—
289	C₂×C₁₆	—	244	2	no	—
290	C₂×C₁₆	—	244	2	no	—
291	C₄⋊C₈	—	61	1	no	—
292	C₄⋊C₈	—	61	1	no	—
293	C₄⋊C₈	—	61	1	no	—
294	C₄⋊C₈	—	61	1	no	—
295	C₄⋊C₈	—	61	1	no	—
296	C₄⋊C₈	C₂×#6923	1	1	yes	characteristic
297	C₂²⋊C₈	—	61	1	no	—
298	C₂²⋊C₈	—	61	1	no	—
299	C₂²⋊C₈	—	61	1	no	—
300	C₂²⋊C₈	—	61	1	no	—
301	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic
302	C₂²⋊C₈	C₂×#6923	1	1	yes	characteristic
303	C₄×C₈	—	61	1	no	—
304	C₄×C₈	—	61	1	no	—
305	C₄×C₈	—	61	1	no	—
306	C₄×C₈	—	61	1	no	—
307	C₄×C₈	—	61	1	no	—
308	C₄×C₈	—	61	1	no	—
309	C₄×C₈	—	61	1	no	—
310	C₄×C₈	—	61	1	no	—
311	C₄×C₈	—	61	1	no	—
312	C₄×C₈	C₂×#6923	1	1	yes	characteristic
313	#41	—	122	4	no	—
314	C₂×Q₈	—	61	1	no	—
315	C₂×D₄	—	61	1	no	—
316	C₂×D₄	—	61	1	no	—
317	C₂×D₄	D₆₁⋊C₈	1	1	yes	characteristic
318	C₂²×C₄	—	61	1	no	—
319	C₂²×C₄	—	61	1	no	—
320	C₂²×C₄	—	61	1	no	—
321	C₂²×C₄	—	61	1	no	—
322	C₂²×C₄	—	61	1	no	—
323	C₂²×C₄	—	61	1	no	—
324	C₂²×C₄	—	61	1	no	—
325	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
326	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	61	1	no	—
330	C₂×C₈	—	61	1	no	—
331	C₂×C₈	—	61	1	no	—
332	C₂×C₈	—	61	1	no	—
333	C₂×C₈	—	122	1	no	—
334	C₂×C₈	—	122	1	no	—
335	C₂×C₈	—	122	1	no	—
336	C₂×C₈	—	122	1	no	—
337	C₂×C₈	—	122	1	no	—
338	C₂×C₈	—	122	1	no	—
339	C₂×C₈	—	244	1	no	—
340	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
341	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
342	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
343	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
344	C₄⋊C₄	—	61	1	no	—
345	C₄⋊C₄	—	61	1	no	—
346	C₄⋊C₄	—	61	1	no	—
347	C₄⋊C₄	—	61	1	no	—
348	C₄⋊C₄	—	61	1	no	—
349	C₄⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
350	C₂²⋊C₄	—	61	1	no	—
351	C₂²⋊C₄	—	61	1	no	—
352	C₂²⋊C₄	—	61	1	no	—
353	C₂²⋊C₄	—	61	1	no	—
354	C₂²⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
355	C₂²⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
356	C₄²	—	61	1	no	—
357	C₄²	—	61	1	no	—
358	C₄²	—	61	1	no	—
359	C₄²	—	61	1	no	—
360	C₄²	—	61	1	no	—
361	C₄²	—	61	1	no	—
362	C₄²	—	61	1	no	—
363	C₄²	—	61	1	no	—
364	C₄²	—	61	1	no	—
365	C₄²	C₂²×#6923	1	1	yes	characteristic
366	C₁₆	—	122	2	no	—
367	C₁₆	—	122	2	no	—
368	C₁₆	—	122	2	no	—
369	C₁₆	—	122	2	no	—
370	C₂³	—	61	1	no	—
371	C₂³	C₂×D₆₁⋊C₈	1	1	yes	characteristic
372	C₂³	C₂×D₆₁⋊C₈	1	1	yes	characteristic
373	Q₈	—	122	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	61	4	no	—
376	D₄	—	122	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	61	1	no	—
382	C₂×C₄	—	61	1	no	—
383	C₂×C₄	—	61	1	no	—
384	C₂×C₄	—	61	1	no	—
385	C₂×C₄	—	61	1	no	—
386	C₂×C₄	—	61	1	no	—
387	C₂×C₄	—	61	1	no	—
388	C₂×C₄	—	122	2	no	—
389	C₂×C₄	—	122	2	no	—
390	C₂×C₄	—	122	2	no	—
391	C₂×C₄	—	122	2	no	—
392	C₂×C₄	—	122	2	no	—
393	C₂×C₄	—	122	2	no	—
394	C₂×C₄	—	122	1	no	—
395	C₂×C₄	—	122	1	no	—
396	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
397	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
398	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
399	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
400	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	61	1	no	—
406	C₈	—	61	1	no	—
407	C₈	—	122	1	no	—
408	C₈	—	122	1	no	—
409	C₈	—	122	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	61	2	no	—
416	C₂²	—	122	1	no	—
417	C₂²	—	122	1	no	—
418	C₂²	D₆₁⋊M₃₂	1	2	yes	—
419	C₂²	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	61	2	no	—
425	C₄	—	61	2	no	—
426	C₄	—	122	1	no	—
427	C₄	—	122	1	no	—
428	C₄	—	122	1	no	—
429	C₄	—	122	1	no	—
430	C₄	—	122	1	no	—
431	C₄	#16840831	1	1	yes	characteristic
432	C₄	#16840840	1	1	yes	characteristic
433	C₂	—	2	2	no	—
434	C₂	—	4	1	no	—
435	C₂	—	122	2	no	—
436	C₂	#21462735	1	1	yes	characteristic
437	C₂	C₂×D₆₁⋊M₃₂	1	1	yes	characteristic
438	C₂	D₆₁⋊#504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₈
Fitting	C₈×D₄×C₆₁	C₄
prime radical	C₂×#11758224	C₈
cosocle	C₂×#92418	C₂⁴
hypercenter	C₈×D₄	#6923
hypocenter	C₆₁	#33504
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #21462236	C₂	semidirect
2. #21462200	C₂	semidirect
3. #21462199	C₂	semidirect
4. #21462197	C₂	semidirect
5. #21462182	C₂	semidirect
6. #21462181	C₂	semidirect
7. #21462177	C₂	semidirect
8. #21462153	C₂	semidirect
9. C₂×#16840683	C₂	semidirect
10. D₆₁⋊(C₄⋊C₁₆)	C₂	semidirect
164. C₂²⋊D₆₁	M₃₂	semidirect
262. C₆₁	#33504	semidirect

Maximal subgroups

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

subgroup	index
#21462236	2
#21462200	2
#21462199	2
#21462197	2
#21462182	2
#21462181	2
#21462177	2
#21462153	2
C₂×#16840683	2
D₆₁⋊(C₄⋊C₁₆)	2
C₈×#11758224	2
#33504	61