Subgroups — #29649180

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 392 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	C₂×#16839786	C₂	1	1	yes	maximal, characteristic
3	#21444608	C₂	1	4	yes	maximal, complemented
4	#21444604	C₂	1	4	yes	maximal, complemented
5	#21444578	C₂	1	2	yes	maximal, complemented
6	#21444575	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11758194	—	2	1	no	—
9	#16839819	—	2	1	no	—
10	#16839819	C₂²	1	2	yes	—
11	#16839815	—	2	1	no	—
12	#16839815	C₂²	1	2	yes	—
13	#16839786	—	2	1	no	—
14	#16839786	—	2	1	no	—
15	#16839786	C₂²	1	2	yes	—
16	#16839786	C₂²	1	2	yes	—
17	#16839786	C₂²	1	1	yes	characteristic
18	#16839786	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#92418	—	2	1	no	—
20	C₂×C₄⋊#92418	C₂²	1	2	yes	—
21	#16839726	—	2	1	no	—
22	C₄×#11758194	—	2	1	no	—
23	#16839515	C₂²	1	8	yes	complemented
24	#16839513	C₂²	1	8	yes	complemented
25	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#431	C₄	1	2	yes	—
27	C₆₁×#431	C₄	1	2	yes	—
28	C₆₁×#431	C₂²	1	2	yes	—
29	C₆₁×#431	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₆₁	C₄	1	2	yes	—
31	C₂×C₂²⋊C₈×C₆₁	C₄	1	2	yes	—
32	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
33	C₂×#11758194	—	2	1	no	—
34	C₂×#11758194	—	2	1	no	—
35	C₂×#11758194	—	2	2	no	—
36	C₂×#11758194	—	2	2	no	—
37	C₂×#11758194	—	4	4	no	—
38	C₂²×#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	1	no	—
43	C₄⋊#92418	—	2	1	no	—
44	C₄⋊#92418	C₂³	1	2	yes	—
45	C₄⋊#92418	C₂³	1	4	yes	—
46	C₄⋊#92418	C₂³	1	2	yes	—
47	C₂²⋊#92418	—	2	2	no	—
48	C₂²⋊#92418	—	2	2	no	—
49	#14519688	—	2	2	no	—
50	C₄×#92418	—	2	2	no	—
51	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₁	Q₈	1	1	yes	characteristic
54	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
62	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
63	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
64	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
68	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
69	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
70	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
71	C₄×C₈×C₆₁	C₂×C₄	1	4	yes	—
72	C₄×C₈×C₆₁	C₂³	1	4	yes	—
73	C₂⁴×C₆₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	—	2	4	no	—
75	C₂²×C₄×C₆₁	—	2	2	no	—
76	C₂²×C₄×C₆₁	—	2	2	no	—
77	C₂²×C₄×C₆₁	—	4	2	no	—
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	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₈×C₆₁	—	4	4	no	—
97	C₂×C₈×C₆₁	C₂²×C₄	1	8	yes	—
98	C₄²×C₆₁	C₄⋊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	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
111	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
114	#11758194	—	4	4	no	—
115	#11758194	—	4	2	no	—
116	#11758194	—	4	4	no	—
117	#11758194	—	4	2	no	—
118	C₂×#92418	—	2	2	no	—
119	C₂×#92418	—	2	2	no	—
120	C₂×#92418	—	2	4	no	—
121	C₂×#92418	—	4	4	no	—
122	C₂³×C₆₁	—	2	2	no	—
123	C₂³×C₆₁	—	2	2	no	—
124	C₂³×C₆₁	—	4	1	no	—
125	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
133	C₂×C₄×C₆₁	—	2	1	no	—
134	C₂×C₄×C₆₁	—	2	1	no	—
135	C₂×C₄×C₆₁	—	2	1	no	—
136	C₂×C₄×C₆₁	—	2	1	no	—
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	2	no	—
141	C₂×C₄×C₆₁	—	2	2	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	4	1	no	—
144	C₂×C₄×C₆₁	—	4	1	no	—
145	C₂×C₄×C₆₁	—	4	1	no	—
146	C₂×C₄×C₆₁	#108	1	4	yes	—
147	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂×C₄⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₆₁	#137	1	2	yes	—
158	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
161	C₈×C₆₁	—	2	8	no	—
162	#92418	—	4	4	no	—
163	#92418	—	4	2	no	—
164	#92418	—	4	2	no	—
165	#17817	—	61	1	no	maximal, Sylow
166	C₂²×C₆₁	—	2	1	no	—
167	C₂²×C₆₁	—	2	1	no	—
168	C₂²×C₆₁	—	2	1	no	—
169	C₂²×C₆₁	—	2	1	no	—
170	C₂²×C₆₁	—	2	1	no	—
171	C₂²×C₆₁	—	2	1	no	—
172	C₂²×C₆₁	—	2	1	no	—
173	C₂²×C₆₁	—	4	4	no	—
174	C₂²×C₆₁	#428	1	2	yes	—
175	C₂²×C₆₁	C₂×#108	1	2	yes	—
176	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	2	1	no	—
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	1	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	#428	1	2	yes	—
185	C₄×C₆₁	C₂×#108	1	2	yes	—
186	C₄×C₆₁	C₂×#108	1	2	yes	—
187	C₄×C₆₁	#568	1	2	yes	—
188	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₄×C₆₁	C₂×#137	1	1	yes	characteristic
190	#2920	—	61	1	no	—
191	C₂×#431	D₆₁	1	1	yes	characteristic
192	C₂×#423	—	61	1	no	—
193	#1574	—	61	4	no	—
194	#1573	—	61	4	no	—
195	#1567	—	61	2	no	—
196	#1566	—	61	2	no	—
197	C₂×C₆₁	—	2	2	no	—
198	C₂×C₆₁	—	2	2	no	—
199	C₂×C₆₁	—	4	1	no	—
200	C₂×C₆₁	#2905	1	1	yes	characteristic
201	C₂×C₆₁	C₂×#428	1	1	yes	characteristic
202	C₂×C₆₁	C₂²×#108	1	1	yes	characteristic
203	C₂²×M₁₆	—	122	1	no	—
204	C₂²×C₄²	C₂×D₆₁	1	1	yes	characteristic
205	#432	—	61	2	no	—
206	#432	—	122	1	no	—
207	#431	—	61	2	no	—
208	#431	—	122	1	no	—
209	#431	Dic₆₁	1	2	yes	—
210	#431	Dic₆₁	1	2	yes	—
211	#431	C₂×D₆₁	1	2	yes	—
212	#431	C₂×D₆₁	1	2	yes	—
213	#423	—	61	1	no	—
214	#423	—	61	2	no	—
215	#423	—	61	1	no	—
216	#423	—	61	2	no	—
217	#423	—	122	1	no	—
218	#423	—	122	1	no	—
219	C₂×C₄⋊C₈	—	61	2	no	—
220	C₂×C₄⋊C₈	—	122	1	no	—
221	C₂×C₄⋊C₈	Dic₆₁	1	2	yes	—
222	#407	—	122	1	no	—
223	C₂×C₂²⋊C₈	Dic₆₁	1	2	yes	—
224	C₄×M₁₆	—	122	1	no	—
225	C₂×C₄×C₈	C₂×D₆₁	1	2	yes	—
226	#335	—	61	8	no	—
227	#334	—	61	8	no	—
228	C₆₁	#17817	1	1	yes	characteristic, complemented, Sylow
229	C₂³×C₄	Dic₁₂₂	1	1	yes	characteristic
230	C₂³×C₄	D₂₄₄	1	1	yes	characteristic
231	C₂³×C₄	C₂×Dic₆₁	1	1	yes	characteristic
232	C₂×M₁₆	—	122	2	no	—
233	C₂×M₁₆	—	122	2	no	—
234	C₂×M₁₆	—	122	1	no	—
235	C₂×M₁₆	—	122	1	no	—
236	C₂×M₁₆	—	244	4	no	—
237	C₂²×C₈	—	122	2	no	—
238	C₂²×C₈	C₂×Dic₆₁	1	4	yes	—
239	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
240	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
241	C₂×C₄²	Dic₁₂₂	1	1	yes	characteristic
242	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
243	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
244	C₂×C₄²	D₂₄₄	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₆₁	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
251	C₄⋊C₈	—	61	2	no	—
252	C₄⋊C₈	—	61	4	no	—
253	C₄⋊C₈	—	61	2	no	—
254	C₄⋊C₈	—	122	2	no	—
255	C₄⋊C₈	—	122	2	no	—
256	C₄⋊C₈	—	122	2	no	—
257	C₄⋊C₈	—	122	1	no	—
258	C₄⋊C₈	—	122	1	no	—
259	C₄⋊C₈	C₂×Dic₆₁	1	4	yes	—
260	C₄⋊C₈	C₂×Dic₆₁	1	4	yes	—
261	C₂²⋊C₈	—	122	2	no	—
262	C₂²⋊C₈	—	122	2	no	—
263	C₂²⋊C₈	C₂×Dic₆₁	1	4	yes	—
264	C₂²⋊C₈	C₂×Dic₆₁	1	4	yes	—
265	#97	—	122	2	no	—
266	C₄×C₈	—	122	2	no	—
267	C₄×C₈	C₂×Dic₆₁	1	4	yes	—
268	C₄×C₈	C₂²×D₆₁	1	4	yes	—
269	C₂⁴	C₄⋊Dic₆₁	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊Dic₆₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
284	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
285	C₂²×C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
292	M₁₆	—	244	4	no	—
293	M₁₆	—	244	2	no	—
294	M₁₆	—	244	2	no	—
295	M₁₆	—	244	4	no	—
296	C₂×C₈	—	4	4	no	—
297	C₂×C₈	—	122	2	no	—
298	C₂×C₈	—	122	2	no	—
299	C₂×C₈	—	122	4	no	—
300	C₂×C₈	—	244	4	no	—
301	C₂×C₈	C₂²×Dic₆₁	1	8	yes	—
302	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
303	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
304	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
305	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
306	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
307	C₄²	C₄⋊Dic₆₁	1	1	yes	characteristic
308	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
309	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
310	C₄²	C₂×Dic₁₂₂	1	1	yes	characteristic
311	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
312	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
313	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
314	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
315	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
316	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
317	C₄²	C₂³×D₆₁	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
322	C₂³	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
323	C₂³	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	#14519713	1	4	yes	—
343	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
347	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
352	C₂×C₄	#14519805	1	2	yes	—
353	C₂×C₄	#14519810	1	2	yes	—
354	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
356	C₂×C₄	C₂²×Dic₁₂₂	1	1	yes	characteristic
357	C₈	—	2	8	no	—
358	C₈	—	244	4	no	—
359	C₈	—	244	2	no	—
360	C₈	—	244	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	4	no	—
369	C₂²	#16839804	1	2	yes	—
370	C₂²	C₂×#14519713	1	2	yes	—
371	C₂²	C₂²×C₄⋊Dic₆₁	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	#16839804	1	2	yes	—
380	C₄	C₂×#14519713	1	2	yes	—
381	C₄	C₂×#14519713	1	2	yes	—
382	C₄	#16840529	1	2	yes	—
383	C₄	C₂×#14519805	1	1	yes	characteristic
384	C₄	C₂×#14519810	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	#21454383	1	1	yes	characteristic
389	C₂	C₂×#16839804	1	1	yes	characteristic
390	C₂	C₂²×#14519713	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₄₄
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₄²	C₂³×D₆₁
Fitting	C₂×C₆₁×#431	C₂
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₆₁	C₄⋊C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₂×#431	D₆₁
hypocenter	C₆₁	#17817
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #21444608	C₂	semidirect
4. #21444604	C₂	semidirect
5. #21444578	C₂	semidirect
6. #21444575	C₂	semidirect
23. #16839515	C₂²	semidirect
24. #16839513	C₂²	semidirect
228. C₆₁	#17817	semidirect

Maximal subgroups

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

subgroup	index
#21454452	2
C₂×#16839786	2
#21444608	2
#21444604	2
#21444578	2
#21444575	2
C₂×C₆₁×#431	2
#17817	61