Subgroups — #29693946

Order 15616.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454736	C₂	1	1	yes	maximal, characteristic, complemented
2	#21454671	C₂	1	1	yes	maximal, characteristic, complemented
3	#21446730	C₂	1	1	yes	maximal, characteristic, complemented
4	#21446718	C₂	1	1	yes	maximal, characteristic, complemented
5	#21446352	C₂	1	2	yes	maximal, complemented
6	#21446347	C₂	1	2	yes	maximal, complemented
7	#21446308	C₂	1	2	yes	maximal, complemented
8	#21446301	C₂	1	2	yes	maximal, complemented
9	#21445943	C₂	1	1	yes	maximal, characteristic, complemented
10	#21445574	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3155	C₂	1	1	yes	maximal, characteristic
12	#16840529	C₂²	1	2	yes	—
13	#16840237	C₂²	1	2	yes	—
14	#16839884	—	2	2	no	—
15	#16839879	—	2	2	no	—
16	#16839874	—	2	2	no	—
17	D₈×Dic₆₁	—	2	2	no	—
18	C₂×#14519713	C₂²	1	1	yes	characteristic
19	#16839800	C₂²	1	1	yes	characteristic
20	#16839779	C₂²	1	2	yes	—
21	#16839779	C₂²	1	2	yes	—
22	#16839767	C₂²	1	2	yes	—
23	#16839767	C₂²	1	2	yes	—
24	C₂×#14519694	C₂²	1	2	yes	—
25	#16839736	C₂²	1	2	yes	—
26	#16839717	C₂²	1	1	yes	characteristic
27	#16839717	C₂²	1	1	yes	characteristic
28	#16839533	C₂²	1	2	yes	—
29	#16839520	C₂²	1	1	yes	characteristic
30	#16839519	C₂²	1	1	yes	characteristic
31	#16839518	C₂²	1	2	yes	—
32	#16839518	C₂²	1	1	yes	characteristic
33	#16839518	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
35	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
36	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#535	C₂²	1	2	yes	—
38	C₆₁×#496	C₄	1	4	yes	complemented
39	C₆₁×#495	C₄	1	2	yes	complemented
40	C₆₁×#493	C₄	1	2	yes	complemented
41	C₆₁×#405	C₂²	1	1	yes	characteristic
42	#14519784	—	2	4	no	—
43	#14519784	—	4	2	no	—
44	C₂×#11758194	—	4	2	no	—
45	C₂×#11758194	C₂³	1	1	yes	characteristic
46	C₂×#11758194	C₂³	1	2	yes	—
47	C₂×#11758194	C₂³	1	1	yes	characteristic
48	D₄×Dic₆₁	—	2	4	no	—
49	D₄×Dic₆₁	—	4	2	no	—
50	#14519736	C₂³	1	1	yes	characteristic
51	#14519736	C₂³	1	2	yes	—
52	#14519736	C₂³	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₆₁	—	4	2	no	—
54	#14519713	—	2	1	no	—
55	#14519713	—	2	1	no	—
56	#14519711	—	2	1	no	—
57	#14519709	—	2	1	no	—
58	#14519704	—	2	4	no	—
59	#14519704	—	4	2	no	—
60	#14519698	—	2	4	no	—
61	#14519698	—	4	2	no	—
62	#14519694	—	4	2	no	—
63	#14519692	—	4	2	no	—
64	#14519687	—	2	1	no	—
65	#14519687	D₄	1	2	yes	complemented
66	C₈×Dic₆₁	—	2	1	no	—
67	C₈×Dic₆₁	D₄	1	2	yes	complemented
68	C₂×#41×C₆₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
70	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
71	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
72	#135×C₆₁	—	2	1	no	—
73	#135×C₆₁	—	2	1	no	—
74	#135×C₆₁	—	2	1	no	—
75	#135×C₆₁	—	2	1	no	—
76	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×SD₁₆×C₆₁	C₂×C₄	1	2	yes	complemented
78	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
79	C₂×D₈×C₆₁	—	2	1	no	—
80	C₂×D₈×C₆₁	—	2	1	no	—
81	C₂×D₈×C₆₁	—	2	1	no	—
82	C₂×D₈×C₆₁	—	2	1	no	—
83	C₂×D₈×C₆₁	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₆₁	C₂×C₄	1	2	yes	—
85	C₂×D₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×D₈×C₆₁	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	#127×C₆₁	C₂×C₄	1	4	yes	complemented
90	#124×C₆₁	C₂×C₄	1	4	yes	complemented
91	#121×C₆₁	—	4	2	no	—
92	#120×C₆₁	—	4	2	no	—
93	#117×C₆₁	C₂³	1	1	yes	characteristic
94	#97×C₆₁	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	complemented
96	C₂⁴×C₆₁	—	2	2	no	—
97	#41×C₆₁	—	2	2	no	—
98	#41×C₆₁	—	2	2	no	—
99	#41×C₆₁	—	2	2	no	—
100	#41×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	—	2	2	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	2	no	—
108	C₂×D₄×C₆₁	—	4	4	no	—
109	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
110	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₆₁	—	2	2	no	—
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₆₁	—	4	4	no	—
114	Q₁₆×C₆₁	—	2	1	no	—
115	Q₁₆×C₆₁	—	2	1	no	—
116	SD₁₆×C₆₁	—	2	2	no	—
117	SD₁₆×C₆₁	—	2	2	no	—
118	SD₁₆×C₆₁	—	4	4	no	—
119	D₈×C₆₁	—	2	2	no	—
120	D₈×C₆₁	—	2	2	no	—
121	D₈×C₆₁	—	2	2	no	—
122	D₈×C₆₁	—	2	2	no	—
123	D₈×C₆₁	—	2	1	no	—
124	D₈×C₆₁	—	2	1	no	—
125	D₈×C₆₁	—	4	4	no	—
126	M₁₆×C₆₁	—	2	1	no	—
127	M₁₆×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
134	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₂²⋊C₄×C₆₁	—	2	1	no	—
137	C₂²⋊C₄×C₆₁	—	4	4	no	—
138	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
139	C₂²⋊Dic₆₁	—	2	1	no	—
140	C₂²⋊Dic₆₁	—	2	1	no	—
141	C₂²⋊Dic₆₁	—	2	2	no	—
142	C₂²⋊Dic₆₁	—	4	4	no	—
143	C₄⋊Dic₆₁	—	2	1	no	—
144	C₄⋊Dic₆₁	—	2	2	no	—
145	C₄⋊Dic₆₁	—	2	1	no	—
146	C₄×Dic₆₁	—	2	1	no	—
147	C₄×Dic₆₁	—	2	2	no	—
148	C₄×Dic₆₁	C₂×D₄	1	2	yes	—
149	#11758194	—	2	1	no	—
150	#11758194	—	2	1	no	—
151	#11758194	—	2	2	no	—
152	#11758194	—	2	1	no	—
153	#11758194	—	2	2	no	—
154	#11758194	—	2	1	no	—
155	#11758194	—	4	4	no	—
156	C₂×#92418	—	2	1	no	—
157	C₂×#92418	—	2	2	no	—
158	C₂×#92418	—	4	4	no	—
159	C₂×#92418	C₂×D₄	1	2	yes	—
160	C₂³×C₆₁	—	2	4	no	—
161	C₂³×C₆₁	—	2	2	no	—
162	C₂³×C₆₁	—	4	2	no	—
163	C₂³×C₆₁	—	4	2	no	—
164	C₂³×C₆₁	—	16	2	no	—
165	C₂³×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
166	Q₈×C₆₁	—	2	2	no	—
167	Q₈×C₆₁	—	2	2	no	—
168	D₄×C₆₁	—	2	4	no	—
169	D₄×C₆₁	—	2	2	no	—
170	D₄×C₆₁	—	2	2	no	—
171	D₄×C₆₁	—	2	4	no	—
172	D₄×C₆₁	—	4	2	no	—
173	D₄×C₆₁	—	4	2	no	—
174	D₄×C₆₁	—	4	2	no	—
175	D₄×C₆₁	—	4	2	no	—
176	D₄×C₆₁	—	16	4	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×Dic₆₁	—	2	2	no	—
188	C₂×Dic₆₁	—	4	2	no	—
189	C₂×Dic₆₁	—	4	1	no	—
190	C₂×Dic₆₁	—	16	4	no	—
191	C₈×C₆₁	—	2	2	no	—
192	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
193	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
194	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
195	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
196	#92418	—	2	2	no	—
197	#92418	—	4	2	no	—
198	#92418	—	4	1	no	—
199	#22286	—	61	1	no	maximal, Sylow
200	C₂²×C₆₁	—	4	1	no	—
201	C₂²×C₆₁	—	4	2	no	—
202	C₂²×C₆₁	—	4	4	no	—
203	C₂²×C₆₁	—	8	2	no	—
204	C₂²×C₆₁	—	8	4	no	—
205	C₂²×C₆₁	—	8	4	no	—
206	C₂²×C₆₁	—	16	2	no	—
207	C₂²×C₆₁	#518	1	1	yes	characteristic
208	C₂²×C₆₁	#535	1	1	yes	characteristic
209	C₂²×C₆₁	#540	1	1	yes	characteristic
210	C₄×C₆₁	—	4	2	no	—
211	C₄×C₆₁	—	4	2	no	—
212	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₆₁	#518	1	1	yes	characteristic
214	C₄×C₆₁	#535	1	1	yes	characteristic
215	C₄×C₆₁	#540	1	1	yes	characteristic
216	Dic₆₁	—	4	2	no	—
217	Dic₆₁	—	8	1	no	—
218	Dic₆₁	—	8	2	no	—
219	#3155	D₆₁	1	1	yes	characteristic
220	#2957	—	61	1	no	—
221	#2948	—	61	1	no	—
222	#1978	—	61	1	no	—
223	#1976	—	61	1	no	—
224	#1911	—	61	2	no	—
225	#1910	—	61	2	no	—
226	#1904	—	61	2	no	—
227	#1903	—	61	2	no	—
228	#1833	—	61	1	no	—
229	#1747	—	61	1	no	—
230	C₂×C₆₁	—	2	1	no	—
231	C₂×C₆₁	—	2	1	no	—
232	C₂×C₆₁	—	2	1	no	—
233	C₂×C₆₁	—	8	2	no	—
234	C₂×C₆₁	—	8	4	no	—
235	C₂×C₆₁	#2328	1	1	yes	characteristic
236	C₂×AGL(1,ℤ/8)	C₂×D₆₁	1	2	yes	—
237	C₂×#135	C₂×D₆₁	1	1	yes	characteristic
238	C₂²×D₈	C₂×D₆₁	1	1	yes	characteristic
239	#568	—	61	2	no	—
240	#535	C₂×D₆₁	1	2	yes	—
241	#518	—	61	2	no	—
242	#496	Dic₆₁	1	4	yes	complemented
243	#495	Dic₆₁	1	2	yes	complemented
244	#493	Dic₆₁	1	2	yes	complemented
245	#444	—	122	2	no	—
246	#443	—	122	2	no	—
247	#442	—	122	2	no	—
248	C₄×D₈	—	122	2	no	—
249	C₂×#108	—	61	1	no	—
250	#427	—	61	1	no	—
251	#421	—	61	2	no	—
252	#421	—	61	2	no	—
253	#418	—	61	2	no	—
254	#418	—	61	2	no	—
255	C₂×#100	—	61	2	no	—
256	#410	—	61	2	no	—
257	#405	—	61	1	no	—
258	#405	—	61	1	no	—
259	#405	C₂×D₆₁	1	1	yes	characteristic
260	#344	—	61	2	no	—
261	#338	—	61	1	no	—
262	H(3,ℤ/4)	—	61	1	no	—
263	H(3,ℤ/4)	—	61	2	no	—
264	H(3,ℤ/4)	—	61	1	no	—
265	H(3,ℤ/4)	—	61	1	no	—
266	C₆₁	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	C₂²×D₆₁	1	2	yes	—
268	C₂²×D₄	C₂²×D₆₁	1	2	yes	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	AGL(1,ℤ/8)	—	4	2	no	—
271	#135	—	2	1	no	—
272	#135	—	2	1	no	—
273	#135	—	2	1	no	—
274	#135	—	2	1	no	—
275	C₂×Q₁₆	C₂×Dic₆₁	1	1	yes	characteristic, complemented
276	C₂×SD₁₆	C₂×Dic₆₁	1	2	yes	complemented
277	C₂×SD₁₆	C₂×Dic₆₁	1	4	yes	complemented
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	C₂×Dic₆₁	1	2	yes	—
283	C₂×D₈	C₂×Dic₆₁	1	2	yes	—
284	C₂×D₈	C₂×Dic₆₁	1	1	yes	characteristic, complemented
285	C₂×D₈	C₂×Dic₆₁	1	4	yes	complemented
286	#131	—	122	4	no	—
287	#131	—	244	2	no	—
288	C₂×M₁₆	—	61	1	no	—
289	C₂×M₁₆	—	61	2	no	—
290	C₂×M₁₆	—	61	1	no	—
291	C₂×M₁₆	—	244	2	no	—
292	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
294	#127	C₂×Dic₆₁	1	4	yes	complemented
295	#124	C₂×Dic₆₁	1	4	yes	complemented
296	#121	—	4	2	no	—
297	#120	—	4	2	no	—
298	C₄×D₄	—	122	4	no	—
299	C₄×D₄	—	244	2	no	—
300	#117	—	61	1	no	—
301	#117	—	61	2	no	—
302	#117	—	61	1	no	—
303	#117	C₂²×D₆₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	244	2	no	—
305	#108	—	122	1	no	—
306	#108	—	122	1	no	—
307	#107	—	122	1	no	—
308	#106	—	122	1	no	—
309	#104	—	122	4	no	—
310	#104	—	244	2	no	—
311	#102	—	122	4	no	—
312	#102	—	244	2	no	—
313	#100	—	244	2	no	—
314	#99	—	244	2	no	—
315	#97	—	61	2	no	—
316	#97	—	122	1	no	—
317	#97	C₂×Dic₆₁	1	2	yes	complemented
318	C₄×C₈	—	61	2	no	—
319	C₄×C₈	—	122	1	no	—
320	C₄×C₈	C₂×Dic₆₁	1	2	yes	complemented
321	C₂⁴	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	C₂²×Dic₆₁	1	4	yes	—
335	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	244	4	no	—
338	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	1	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	4	4	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	2	1	no	—
349	D₈	—	2	1	no	—
350	D₈	—	4	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	122	1	no	—
354	M₁₆	—	122	1	no	—
355	M₁₆	—	122	2	no	—
356	M₁₆	—	122	1	no	—
357	M₁₆	—	122	2	no	—
358	M₁₆	—	122	1	no	—
359	M₁₆	—	244	4	no	—
360	C₂×C₈	—	61	2	no	—
361	C₂×C₈	—	122	1	no	—
362	C₂×C₈	—	122	2	no	—
363	C₂×C₈	—	244	4	no	—
364	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
365	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
366	C₂×C₈	#11758224	1	1	yes	characteristic
367	C₂×C₈	#11758224	1	1	yes	characteristic
368	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
369	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
370	C₂×C₈	C₂²×Dic₆₁	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	122	1	no	—
373	C₄⋊C₄	—	122	2	no	—
374	C₄⋊C₄	—	122	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	122	1	no	—
378	C₂²⋊C₄	—	122	1	no	—
379	C₂²⋊C₄	—	122	2	no	—
380	C₂²⋊C₄	—	244	4	no	—
381	C₄²	—	61	2	no	—
382	C₄²	—	122	1	no	—
383	C₄²	—	122	2	no	—
384	C₄²	C₂²×Dic₆₁	1	2	yes	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	16	2	no	—
390	C₂³	#14519822	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	16	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	122	2	no	—
407	C₂×C₄	—	976	4	no	—
408	C₂×C₄	—	244	2	no	—
409	C₂×C₄	—	244	1	no	—
410	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
412	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
413	C₂×C₄	#14519822	1	1	yes	characteristic
414	C₂×C₄	#14519822	1	1	yes	characteristic
415	C₂×C₄	#14519822	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	122	2	no	—
418	C₈	—	244	2	no	—
419	C₈	—	244	1	no	—
420	C₈	D₄×Dic₆₁	1	1	yes	characteristic
421	C₈	D₄×Dic₆₁	1	1	yes	characteristic
422	C₈	D₄×Dic₆₁	1	1	yes	characteristic
423	C₈	D₄×Dic₆₁	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	#16840237	1	1	yes	characteristic
432	C₂²	#16840325	1	1	yes	characteristic
433	C₂²	#16840366	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	488	2	no	—
437	C₄	—	488	1	no	—
438	C₄	—	244	2	no	—
439	C₄	C₂×D₄×Dic₆₁	1	1	yes	characteristic
440	C₄	#16840237	1	1	yes	characteristic
441	C₄	#16840325	1	1	yes	characteristic
442	C₄	#16840366	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	#21448545	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21448545
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting, prime radical	C₆₁×#3155	C₂
socle	C₂×C₆₁	#2328
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#3155	D₆₁
hypocenter	C₆₁	#22286
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3155

Complements

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

N	H ≅ G/N	type
1. #21454736	C₂	semidirect
2. #21454671	C₂	semidirect
3. #21446730	C₂	semidirect
4. #21446718	C₂	semidirect
5. #21446352	C₂	semidirect
6. #21446347	C₂	semidirect
7. #21446308	C₂	semidirect
8. #21446301	C₂	semidirect
9. #21445943	C₂	semidirect
10. #21445574	C₂	semidirect
38. C₆₁×#496	C₄	semidirect
39. C₆₁×#495	C₄	semidirect
40. C₆₁×#493	C₄	semidirect
65. #14519687	D₄	semidirect
67. C₈×Dic₆₁	D₄	semidirect
76. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
77. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
78. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
85. C₂×D₈×C₆₁	C₂×C₄	semidirect
86. C₂×D₈×C₆₁	C₂×C₄	semidirect
89. #127×C₆₁	C₂×C₄	semidirect
90. #124×C₆₁	C₂×C₄	semidirect
94. #97×C₆₁	C₂×C₄	semidirect
95. C₄×C₈×C₆₁	C₂×C₄	semidirect
242. #496	Dic₆₁	semidirect
243. #495	Dic₆₁	semidirect
244. #493	Dic₆₁	semidirect
266. C₆₁	#22286	semidirect
275. C₂×Q₁₆	C₂×Dic₆₁	semidirect
276. C₂×SD₁₆	C₂×Dic₆₁	semidirect
277. C₂×SD₁₆	C₂×Dic₆₁	semidirect
284. C₂×D₈	C₂×Dic₆₁	semidirect
285. C₂×D₈	C₂×Dic₆₁	semidirect
294. #127	C₂×Dic₆₁	semidirect
295. #124	C₂×Dic₆₁	semidirect
317. #97	C₂×Dic₆₁	semidirect
320. C₄×C₈	C₂×Dic₆₁	semidirect

Maximal subgroups

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

subgroup	index
#21454736	2
#21454671	2
#21446730	2
#21446718	2
#21446352	2
#21446347	2
#21446308	2
#21446301	2
#21445943	2
#21445574	2
C₆₁×#3155	2
#22286	61