Subgroups — #29648607

Order 15616.

1178 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454452	C₂	1	1	yes	maximal, characteristic
2	#21454452	C₂	1	1	yes	maximal, characteristic
3	#21444536	C₂	1	4	yes	maximal, complemented
4	#21444504	C₂	1	4	yes	maximal, complemented
5	#21444491	C₂	1	4	yes	maximal, complemented
6	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
7	#16839819	—	2	1	no	—
8	#16839819	—	2	1	no	—
9	#16839819	C₂²	1	2	yes	—
10	#16839819	C₂²	1	2	yes	—
11	#16839815	—	2	1	no	—
12	#16839815	—	2	1	no	—
13	#16839815	C₂²	1	2	yes	—
14	#16839815	C₂²	1	2	yes	—
15	#16839786	C₂²	1	2	yes	—
16	#16839786	C₂²	1	2	yes	—
17	#16839726	—	2	1	no	—
18	#16839726	—	2	1	no	—
19	C₄×#11758194	—	2	1	no	—
20	C₄×#11758194	—	2	1	no	—
21	#16839508	C₂²	1	16	yes	complemented
22	C₂³×Q₈×C₆₁	—	2	1	no	—
23	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
24	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
26	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
27	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
28	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
29	C₂×C₄⋊Q₈×C₆₁	C₄	1	2	yes	—
30	C₂×C₄⋊Q₈×C₆₁	C₄	1	2	yes	—
31	C₂×C₄⋊Q₈×C₆₁	C₄	1	2	yes	—
32	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
34	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
36	C₂²×C₄⋊C₄×C₆₁	C₄	1	2	yes	—
37	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#11758194	—	2	2	no	—
39	C₂×#11758194	—	2	2	no	—
40	C₄⋊#92418	—	2	2	no	—
41	C₄⋊#92418	—	2	2	no	—
42	C₄⋊#92418	C₂³	1	4	yes	—
43	C₄⋊#92418	C₂³	1	4	yes	—
44	C₂²⋊#92418	—	2	2	no	—
45	C₂²⋊#92418	—	2	2	no	—
46	C₂²⋊#92418	—	2	2	no	—
47	C₂²⋊#92418	—	2	2	no	—
48	#14519688	—	2	2	no	—
49	#14519688	—	2	2	no	—
50	C₄×#92418	—	2	2	no	—
51	C₄×#92418	—	2	2	no	—
52	C₂²×Q₈×C₆₁	—	2	2	no	—
53	C₂²×Q₈×C₆₁	—	2	2	no	—
54	C₂²×Q₈×C₆₁	—	2	2	no	—
55	C₂²×Q₈×C₆₁	—	2	2	no	—
56	C₂²×Q₈×C₆₁	—	2	2	no	—
57	C₂²×Q₈×C₆₁	—	2	2	no	—
58	C₂²×Q₈×C₆₁	—	4	8	no	—
59	C₂³×C₄×C₆₁	—	2	2	no	—
60	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₆₁	—	2	2	no	—
64	C₄⋊Q₈×C₆₁	—	2	2	no	—
65	C₄⋊Q₈×C₆₁	—	2	2	no	—
66	C₄⋊Q₈×C₆₁	—	2	2	no	—
67	C₄⋊Q₈×C₆₁	—	2	2	no	—
68	C₄⋊Q₈×C₆₁	—	2	2	no	—
69	C₄⋊Q₈×C₆₁	—	2	2	no	—
70	C₄⋊Q₈×C₆₁	—	2	2	no	—
71	C₄⋊Q₈×C₆₁	—	2	2	no	—
72	C₄⋊Q₈×C₆₁	—	2	2	no	—
73	C₄⋊Q₈×C₆₁	—	2	2	no	—
74	C₄⋊Q₈×C₆₁	—	2	2	no	—
75	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
76	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
77	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
78	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
90	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
91	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×Q₈×C₆₁	—	2	4	no	—
105	C₂×Q₈×C₆₁	—	2	4	no	—
106	C₂×Q₈×C₆₁	—	2	4	no	—
107	C₂×Q₈×C₆₁	—	2	4	no	—
108	C₂×Q₈×C₆₁	—	4	8	no	—
109	C₂×Q₈×C₆₁	—	4	8	no	—
110	C₂×Q₈×C₆₁	—	4	8	no	—
111	C₂×Q₈×C₆₁	—	4	8	no	—
112	C₂×Q₈×C₆₁	—	4	8	no	—
113	C₂×Q₈×C₆₁	—	4	8	no	—
114	C₂²×C₄×C₆₁	—	2	4	no	—
115	C₂²×C₄×C₆₁	—	2	4	no	—
116	C₂²×C₄×C₆₁	—	2	4	no	—
117	C₂²×C₄×C₆₁	—	2	4	no	—
118	C₂²×C₄×C₆₁	—	2	4	no	—
119	C₂²×C₄×C₆₁	—	2	4	no	—
120	C₂²×C₄×C₆₁	—	4	8	no	—
121	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₆₁	—	2	4	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	4	no	—
142	C₄⋊C₄×C₆₁	—	2	4	no	—
143	C₄⋊C₄×C₆₁	—	2	4	no	—
144	C₄⋊C₄×C₆₁	—	2	4	no	—
145	C₄⋊C₄×C₆₁	—	2	4	no	—
146	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
147	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
148	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
149	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
150	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
151	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
152	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
153	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
163	#11758194	—	4	4	no	—
164	#11758194	—	4	4	no	—
165	C₂×#92418	—	2	4	no	—
166	C₂×#92418	—	2	4	no	—
167	C₂³×C₆₁	—	2	2	no	—
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	Q₈×C₆₁	—	4	8	no	—
174	Q₈×C₆₁	—	4	8	no	—
175	Q₈×C₆₁	—	4	8	no	—
176	Q₈×C₆₁	—	4	8	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	8	no	—
193	C₂×C₄×C₆₁	—	4	8	no	—
194	C₂×C₄×C₆₁	—	4	8	no	—
195	C₂×C₄×C₆₁	—	4	8	no	—
196	C₂×C₄×C₆₁	#101	1	4	yes	—
197	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
207	C₂×C₄×C₆₁	#137	1	4	yes	—
208	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
211	#92418	—	4	4	no	—
212	#92418	—	4	4	no	—
213	#17742	—	61	1	no	maximal, Sylow
214	C₂²×C₆₁	—	2	8	no	—
215	C₂²×C₆₁	—	2	1	no	—
216	C₂²×C₆₁	—	2	1	no	—
217	C₂²×C₆₁	—	2	1	no	—
218	C₂²×C₆₁	—	2	1	no	—
219	C₂²×C₆₁	—	2	1	no	—
220	C₂²×C₆₁	—	2	1	no	—
221	C₂²×C₆₁	C₂×#101	1	2	yes	—
222	C₂²×C₆₁	#418	1	2	yes	—
223	C₂²×C₆₁	#419	1	2	yes	—
224	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
225	C₄×C₆₁	—	2	1	no	—
226	C₄×C₆₁	—	2	1	no	—
227	C₄×C₆₁	—	2	1	no	—
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	2	1	no	—
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	—	4	8	no	—
232	C₄×C₆₁	C₂×#101	1	2	yes	—
233	C₄×C₆₁	C₂×#101	1	2	yes	—
234	C₄×C₆₁	#418	1	2	yes	—
235	C₄×C₆₁	#419	1	2	yes	—
236	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
237	C₄×C₆₁	C₂×#137	1	2	yes	—
238	C₂²×C₄⋊Q₈	D₆₁	1	1	yes	characteristic
239	#2920	—	61	1	no	—
240	#2920	—	61	1	no	—
241	#1556	—	61	4	no	—
242	#1549	—	61	4	no	—
243	#1546	—	61	4	no	—
244	C₂×C₆₁	—	2	2	no	—
245	C₂×C₆₁	—	2	2	no	—
246	C₂×C₆₁	—	2	2	no	—
247	C₂×C₆₁	C₂²×#101	1	1	yes	characteristic
248	C₂×C₆₁	C₂×#418	1	1	yes	characteristic
249	C₂×C₆₁	C₂×#419	1	1	yes	characteristic
250	C₂³×Q₈	—	2	1	no	—
251	C₂×C₄⋊Q₈	—	2	1	no	—
252	C₂×C₄⋊Q₈	—	2	1	no	—
253	C₂×C₄⋊Q₈	—	2	1	no	—
254	C₂×C₄⋊Q₈	—	2	1	no	—
255	C₂×C₄⋊Q₈	—	2	1	no	—
256	C₂×C₄⋊Q₈	—	2	1	no	—
257	C₂×C₄⋊Q₈	Dic₆₁	1	2	yes	—
258	C₂×C₄⋊Q₈	Dic₆₁	1	2	yes	—
259	C₂×C₄⋊Q₈	Dic₆₁	1	2	yes	—
260	C₂×C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
261	C₂×C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
262	C₂×C₄⋊Q₈	C₂×D₆₁	1	2	yes	—
263	C₂²×C₄⋊C₄	—	2	1	no	—
264	C₂²×C₄⋊C₄	Dic₆₁	1	2	yes	—
265	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
266	#432	—	61	2	no	—
267	#432	—	61	2	no	—
268	#432	—	122	1	no	—
269	#432	—	122	1	no	—
270	#431	—	61	2	no	—
271	#431	—	61	2	no	—
272	#431	—	122	1	no	—
273	#431	—	122	1	no	—
274	#423	—	61	2	no	—
275	#423	—	61	2	no	—
276	#407	—	122	1	no	—
277	#407	—	122	1	no	—
278	C₄×M₁₆	—	122	1	no	—
279	C₄×M₁₆	—	122	1	no	—
280	#332	—	61	16	no	—
281	C₆₁	#17742	1	1	yes	characteristic, complemented, Sylow
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×Q₈	—	2	2	no	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	—	4	8	no	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	C₂×Dic₆₁	1	1	yes	characteristic
291	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
292	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
293	C₂×M₁₆	—	122	2	no	—
294	C₂×M₁₆	—	122	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	C₂×Dic₆₁	1	4	yes	—
308	C₄⋊Q₈	C₂×Dic₆₁	1	4	yes	—
309	C₄⋊Q₈	C₂×Dic₆₁	1	4	yes	—
310	C₄⋊Q₈	C₂²×D₆₁	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
321	C₂×C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
322	C₂×C₄⋊C₄	C₂×Dic₆₁	1	4	yes	—
323	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
324	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
325	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
326	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
327	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
328	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
329	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
330	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
331	C₂×C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
335	C₄⋊C₈	—	61	4	no	—
336	C₄⋊C₈	—	61	4	no	—
337	C₄⋊C₈	—	122	2	no	—
338	C₄⋊C₈	—	122	2	no	—
339	C₂²⋊C₈	—	122	2	no	—
340	C₂²⋊C₈	—	122	2	no	—
341	C₂²⋊C₈	—	122	2	no	—
342	C₂²⋊C₈	—	122	2	no	—
343	#97	—	122	2	no	—
344	#97	—	122	2	no	—
345	C₄×C₈	—	122	2	no	—
346	C₄×C₈	—	122	2	no	—
347	C₂⁴	C₂²⋊Dic₆₁	1	1	yes	characteristic
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	4	no	—
351	C₂×Q₈	—	2	4	no	—
352	C₂×Q₈	—	4	8	no	—
353	C₂×Q₈	—	4	8	no	—
354	C₂×Q₈	—	4	8	no	—
355	C₂×Q₈	—	4	8	no	—
356	C₂×Q₈	—	4	8	no	—
357	C₂×Q₈	—	4	8	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	4	8	no	—
365	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
367	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
370	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
371	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
373	C₂²×C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
374	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
375	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
376	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
383	M₁₆	—	244	4	no	—
384	M₁₆	—	244	4	no	—
385	C₂×C₈	—	122	4	no	—
386	C₂×C₈	—	122	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	C₂²×Dic₆₁	1	8	yes	—
395	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
396	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
397	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
398	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
399	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
400	C₄²	C₂²⋊Dic₆₁	1	1	yes	characteristic
401	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
402	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
403	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
404	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
405	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
406	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
407	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
409	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
410	C₄²	C₂³×D₆₁	1	1	yes	characteristic
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
415	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
416	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
417	Q₈	—	4	8	no	—
418	Q₈	—	4	8	no	—
419	Q₈	—	4	8	no	—
420	Q₈	—	4	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	#14519696	1	4	yes	—
441	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
442	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
443	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
444	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
445	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
446	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
447	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
448	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
449	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
450	C₂×C₄	#14519803	1	4	yes	—
451	C₂×C₄	#14519808	1	4	yes	—
452	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
455	C₈	—	244	4	no	—
456	C₈	—	244	4	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	C₂×#14519696	1	2	yes	—
465	C₂²	#16839767	1	2	yes	—
466	C₂²	#16839771	1	2	yes	—
467	C₂²	C₂²×C₂²⋊Dic₆₁	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	8	no	—
475	C₄	C₂×#14519696	1	2	yes	—
476	C₄	C₂×#14519696	1	2	yes	—
477	C₄	#16839767	1	2	yes	—
478	C₄	#16839771	1	2	yes	—
479	C₄	C₂×#14519803	1	2	yes	—
480	C₄	C₂×#14519808	1	2	yes	—
481	C₂	—	2	2	no	—
482	C₂	—	2	2	no	—
483	C₂	—	2	2	no	—
484	C₂	C₂²×#14519696	1	1	yes	characteristic
485	C₂	C₂×#16839767	1	1	yes	characteristic
486	C₂	C₂×#16839771	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₄²	C₂³×D₆₁
Fitting	C₂²×C₄⋊Q₈×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₆₁	C₂²⋊C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₂²×C₄⋊Q₈	D₆₁
hypocenter	C₆₁	#17742
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂²×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #21444536	C₂	semidirect
4. #21444504	C₂	semidirect
5. #21444491	C₂	semidirect
21. #16839508	C₂²	semidirect
281. C₆₁	#17742	semidirect

Maximal subgroups

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

subgroup	index
#21454452	2
#21444536	2
#21444504	2
#21444491	2
C₂²×C₄⋊Q₈×C₆₁	2
#17742	61