Subgroups — #29702523

Order 15616.

892 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839879	C₂	1	2	yes	maximal, complemented
2	#21454563	C₂	1	1	yes	maximal, characteristic, complemented
3	#21454387	C₂	1	1	yes	maximal, characteristic, complemented
4	#21446648	C₂	1	1	yes	maximal, characteristic, complemented
5	#21446595	C₂	1	1	yes	maximal, characteristic, complemented
6	#21446525	C₂	1	2	yes	maximal, complemented
7	#21446148	C₂	1	2	yes	maximal, complemented
8	#21446096	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14519704	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic
12	C₂×#14519784	C₂²	1	2	yes	—
13	C₂×#14519784	C₂²	1	2	yes	—
14	#16839879	—	2	8	no	—
15	#16839840	—	2	1	no	—
16	#16839834	—	2	2	no	—
17	D₄×#92418	—	2	1	no	—
18	C₂×#14519713	C₂²	1	2	yes	—
19	#16839789	—	2	2	no	—
20	#16839789	C₂²	1	2	yes	—
21	#16839786	—	2	1	no	—
22	#16839786	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#92418	—	2	1	no	—
24	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
25	C₂×#14519704	C₂²	1	1	yes	characteristic
26	C₂×#14519704	C₂²	1	2	yes	—
27	C₂×#14519704	C₂²	1	2	yes	—
28	C₂×#14519704	C₂²	1	1	yes	characteristic
29	#16839729	C₂²	1	2	yes	—
30	C₄×#11758194	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₆₁	C₂²	1	2	yes	—
32	C₄²×Dic₆₁	C₂²	1	1	yes	characteristic
33	#16839527	C₂²	1	2	yes	—
34	#16839521	C₂²	1	1	yes	characteristic
35	#16839521	C₂²	1	1	yes	characteristic
36	#16839516	C₂²	1	2	yes	—
37	C₂×#135×C₆₁	C₂²	1	2	yes	—
38	C₆₁×#532	C₂²	1	1	yes	characteristic
39	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#464	C₄	1	2	yes	complemented
41	C₆₁×#463	C₄	1	2	yes	complemented
42	C₆₁×#462	C₄	1	1	yes	characteristic, complemented
43	C₆₁×#461	C₄	1	1	yes	characteristic, complemented
44	C₆₁×#460	C₄	1	1	yes	characteristic, complemented
45	C₆₁×#459	C₄	1	1	yes	characteristic, complemented
46	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₆₁×#416	C₂²	1	2	yes	—
48	#14519784	—	2	4	no	—
49	#14519784	—	2	4	no	—
50	#14519784	—	4	2	no	—
51	#14519784	—	4	2	no	—
52	C₂×#11758194	—	2	2	no	—
53	C₂×#11758194	—	2	2	no	—
54	C₂×#11758194	C₂³	1	1	yes	characteristic
55	C₂×#11758194	C₂³	1	2	yes	—
56	C₂×#11758194	C₂³	1	1	yes	characteristic
57	C₂²×#92418	—	2	2	no	—
58	C₂²×#92418	—	2	2	no	—
59	C₂²×#92418	C₂³	1	2	yes	—
60	C₂×C₄×Dic₆₁	—	2	1	no	—
61	C₂×C₄×Dic₆₁	—	2	1	no	—
62	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
64	#14519713	—	2	4	no	—
65	C₄⋊#92418	—	2	1	no	—
66	C₄⋊#92418	—	2	1	no	—
67	C₄⋊#92418	—	2	2	no	—
68	C₄⋊#92418	—	2	2	no	—
69	C₄⋊#92418	D₄	1	1	yes	characteristic
70	C₄⋊#92418	D₄	1	1	yes	characteristic
71	C₄⋊#92418	D₄	1	2	yes	—
72	#14519704	—	2	2	no	—
73	#14519704	—	2	4	no	—
74	#14519704	—	4	2	no	—
75	#14519704	D₄	1	4	yes	complemented
76	C₂²⋊#92418	—	2	2	no	—
77	C₂²⋊#92418	—	2	2	no	—
78	#14519688	—	2	1	no	—
79	C₄×#92418	—	2	1	no	—
80	C₈×Dic₆₁	—	2	4	no	—
81	C₂×#41×C₆₁	C₂³	1	2	yes	—
82	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
83	#135×C₆₁	—	2	4	no	—
84	#135×C₆₁	—	2	4	no	—
85	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
86	C₂×SD₁₆×C₆₁	C₂×C₄	1	2	yes	—
87	C₂×SD₁₆×C₆₁	C₂×C₄	1	2	yes	—
88	C₂×D₈×C₆₁	C₂×C₄	1	2	yes	—
89	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
90	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
91	#127×C₆₁	C₂×C₄	1	1	yes	characteristic
92	#124×C₆₁	C₂×C₄	1	2	yes	—
93	#121×C₆₁	—	2	1	no	—
94	#121×C₆₁	—	2	1	no	—
95	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
97	C₄×D₄×C₆₁	—	2	1	no	—
98	C₄×D₄×C₆₁	—	2	1	no	—
99	C₄×D₄×C₆₁	—	2	1	no	—
100	C₄×D₄×C₆₁	—	2	1	no	—
101	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
103	#117×C₆₁	—	2	1	no	—
104	#117×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	—	2	1	no	—
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
109	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
110	#103×C₆₁	C₂×C₄	1	2	yes	—
111	#103×C₆₁	C₂×C₄	1	2	yes	—
112	#102×C₆₁	C₂×C₄	1	2	yes	—
113	#102×C₆₁	C₂×C₄	1	2	yes	—
114	#41×C₆₁	—	2	1	no	—
115	#41×C₆₁	—	2	1	no	—
116	#41×C₆₁	—	2	2	no	—
117	#41×C₆₁	—	2	2	no	—
118	#41×C₆₁	—	2	2	no	—
119	#41×C₆₁	—	2	2	no	—
120	#41×C₆₁	C₂×D₄	1	2	yes	—
121	#41×C₆₁	#41	1	2	yes	—
122	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
123	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	2	2	no	—
126	C₂×D₄×C₆₁	—	2	1	no	—
127	C₂×D₄×C₆₁	—	2	1	no	—
128	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	—	2	1	no	—
131	C₂²×C₄×C₆₁	—	2	1	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
137	C₂²×Dic₆₁	—	2	1	no	—
138	C₂²×Dic₆₁	—	2	1	no	—
139	Q₁₆×C₆₁	—	2	4	no	—
140	SD₁₆×C₆₁	—	2	4	no	—
141	SD₁₆×C₆₁	—	2	4	no	—
142	D₈×C₆₁	—	2	4	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	1	no	—
150	C₄⋊C₄×C₆₁	—	2	1	no	—
151	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²⋊C₄×C₆₁	—	2	1	no	—
154	C₂²⋊C₄×C₆₁	—	2	1	no	—
155	C₂²⋊C₄×C₆₁	—	2	1	no	—
156	C₂²⋊C₄×C₆₁	—	2	2	no	—
157	C₂²⋊C₄×C₆₁	—	2	2	no	—
158	C₄²×C₆₁	—	2	1	no	—
159	C₄²×C₆₁	—	2	1	no	—
160	C₄²×C₆₁	—	2	1	no	—
161	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₄×Dic₆₁	—	2	4	no	—
166	C₄×Dic₆₁	—	2	1	no	—
167	C₄×Dic₆₁	—	2	1	no	—
168	C₄×Dic₆₁	—	2	1	no	—
169	C₄×Dic₆₁	—	4	2	no	—
170	C₄×Dic₆₁	C₂×D₄	1	2	yes	—
171	#11758194	—	2	1	no	—
172	#11758194	—	2	2	no	—
173	#11758194	—	2	1	no	—
174	#11758194	—	2	2	no	—
175	#11758194	—	2	1	no	—
176	#11758194	—	4	4	no	—
177	#11758194	—	4	4	no	—
178	#11758194	C₂×D₄	1	2	yes	—
179	C₂×#92418	—	2	2	no	—
180	C₂×#92418	—	2	1	no	—
181	C₂×#92418	—	2	2	no	—
182	C₂×#92418	—	2	1	no	—
183	C₂×#92418	—	2	2	no	—
184	C₂×#92418	—	4	4	no	—
185	C₂×#92418	—	4	4	no	—
186	C₂×#92418	C₂×D₄	1	2	yes	—
187	C₂×#92418	C₂×D₄	1	2	yes	—
188	C₂³×C₆₁	—	2	1	no	—
189	C₂³×C₆₁	—	2	2	no	—
190	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
191	Q₈×C₆₁	—	2	1	no	—
192	Q₈×C₆₁	—	2	2	no	—
193	Q₈×C₆₁	—	2	2	no	—
194	Q₈×C₆₁	C₄×D₄	1	2	yes	—
195	D₄×C₆₁	—	2	2	no	—
196	D₄×C₆₁	—	2	2	no	—
197	D₄×C₆₁	—	2	2	no	—
198	D₄×C₆₁	—	2	1	no	—
199	D₄×C₆₁	—	2	2	no	—
200	D₄×C₆₁	—	4	2	no	—
201	D₄×C₆₁	—	4	2	no	—
202	D₄×C₆₁	—	4	2	no	—
203	D₄×C₆₁	—	8	1	no	—
204	D₄×C₆₁	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₆₁	—	2	1	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	2	2	no	—
208	C₂×C₄×C₆₁	—	2	2	no	—
209	C₂×C₄×C₆₁	—	2	1	no	—
210	C₂×C₄×C₆₁	—	2	1	no	—
211	C₂×C₄×C₆₁	—	2	2	no	—
212	C₂×C₄×C₆₁	—	4	1	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	—	4	2	no	—
215	C₂×C₄×C₆₁	—	4	2	no	—
216	C₂×C₄×C₆₁	—	8	1	no	—
217	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂×Dic₆₁	—	2	2	no	—
228	C₂×Dic₆₁	—	2	2	no	—
229	C₂×Dic₆₁	—	2	2	no	—
230	C₂×Dic₆₁	—	2	2	no	—
231	C₂×Dic₆₁	—	4	1	no	—
232	C₂×Dic₆₁	—	4	1	no	—
233	C₈×C₆₁	—	2	2	no	—
234	C₈×C₆₁	—	2	2	no	—
235	#92418	—	2	2	no	—
236	#92418	—	2	2	no	—
237	#92418	—	2	2	no	—
238	#92418	—	4	2	no	—
239	#92418	—	4	1	no	—
240	#23015	—	61	1	no	maximal, Sylow
241	C₂²×C₆₁	—	2	1	no	—
242	C₂²×C₆₁	—	2	1	no	—
243	C₂²×C₆₁	—	2	2	no	—
244	C₂²×C₆₁	—	4	1	no	—
245	C₂²×C₆₁	—	4	1	no	—
246	C₂²×C₆₁	—	4	2	no	—
247	C₂²×C₆₁	—	4	2	no	—
248	C₂²×C₆₁	—	4	2	no	—
249	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₆₁	#547	1	1	yes	characteristic
251	C₂²×C₆₁	#553	1	1	yes	characteristic
252	C₄×C₆₁	—	2	2	no	—
253	C₄×C₆₁	—	2	1	no	—
254	C₄×C₆₁	—	2	1	no	—
255	C₄×C₆₁	—	2	1	no	—
256	C₄×C₆₁	—	4	2	no	—
257	C₄×C₆₁	—	4	1	no	—
258	C₄×C₆₁	—	4	1	no	—
259	C₄×C₆₁	#443	1	2	yes	complemented
260	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
261	C₄×C₆₁	#520	1	1	yes	characteristic
262	C₄×C₆₁	D₄²	1	1	yes	characteristic
263	C₄×C₆₁	#548	1	1	yes	characteristic
264	Dic₆₁	—	2	4	no	—
265	Dic₆₁	—	4	2	no	—
266	#3035	D₆₁	1	1	yes	characteristic
267	C₂×#443	—	61	2	no	—
268	#2935	—	61	1	no	—
269	#2906	—	61	1	no	—
270	#1962	—	61	1	no	—
271	#1950	—	61	1	no	—
272	#1937	—	61	2	no	—
273	#1876	—	61	2	no	—
274	#1866	—	61	2	no	—
275	C₄×C₄⋊C₈	—	61	1	no	—
276	C₄×#104	—	61	1	no	—
277	C₂×C₆₁	—	2	1	no	—
278	C₂×C₆₁	—	2	1	no	—
279	C₂×C₆₁	—	4	2	no	—
280	C₂×C₆₁	—	8	2	no	—
281	C₂×C₆₁	#2361	1	1	yes	characteristic
282	C₂×C₆₁	C₂×#443	1	1	yes	characteristic
283	C₂×C₆₁	#2956	1	1	yes	characteristic
284	C₂×#135	C₂×D₆₁	1	2	yes	—
285	C₂×#131	—	61	2	no	—
286	C₂×#131	—	61	2	no	—
287	#532	C₂×D₆₁	1	1	yes	characteristic
288	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
289	#464	Dic₆₁	1	2	yes	complemented
290	#463	Dic₆₁	1	2	yes	complemented
291	#462	Dic₆₁	1	1	yes	characteristic, complemented
292	#461	Dic₆₁	1	1	yes	characteristic, complemented
293	#460	Dic₆₁	1	1	yes	characteristic, complemented
294	#459	Dic₆₁	1	1	yes	characteristic, complemented
295	#443	—	122	8	no	—
296	#436	—	122	1	no	—
297	#435	—	122	2	no	—
298	C₈×D₄	—	122	1	no	—
299	C₂×#108	—	61	2	no	—
300	#424	—	61	2	no	—
301	#424	—	122	2	no	—
302	#423	—	61	1	no	—
303	#423	—	122	1	no	—
304	C₂×C₄⋊C₈	—	61	1	no	—
305	C₂×C₄⋊C₈	—	122	1	no	—
306	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
307	C₂×#104	—	61	1	no	—
308	C₂×#104	—	61	1	no	—
309	C₂×#104	—	61	2	no	—
310	C₂×#104	—	61	2	no	—
311	#416	C₂×D₆₁	1	2	yes	—
312	#408	—	61	2	no	—
313	C₄×M₁₆	—	61	1	no	—
314	C₂×C₄×C₈	—	61	2	no	—
315	C₄³	—	61	1	no	—
316	#341	—	61	2	no	—
317	#339	—	61	1	no	—
318	#339	—	61	1	no	—
319	#336	—	61	2	no	—
320	C₆₁	#23015	1	1	yes	characteristic, complemented, Sylow
321	C₂×#41	C₂²×D₆₁	1	2	yes	—
322	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
323	#135	—	2	4	no	—
324	#135	—	2	4	no	—
325	C₂×Q₁₆	C₂×Dic₆₁	1	2	yes	—
326	C₂×SD₁₆	C₂×Dic₆₁	1	2	yes	—
327	C₂×SD₁₆	C₂×Dic₆₁	1	2	yes	—
328	C₂×D₈	C₂×Dic₆₁	1	2	yes	—
329	#131	—	122	4	no	—
330	#131	—	122	4	no	—
331	#131	—	244	2	no	—
332	#131	—	244	2	no	—
333	C₂×M₁₆	—	61	1	no	—
334	C₂×M₁₆	—	61	2	no	—
335	C₂×M₁₆	—	61	1	no	—
336	C₂×M₁₆	—	122	2	no	—
337	C₂×M₁₆	—	122	2	no	—
338	C₂²×C₈	—	61	2	no	—
339	C₂²×C₈	—	122	2	no	—
340	C₂²×C₈	—	122	2	no	—
341	C₂²×C₈	C₂²×D₆₁	1	2	yes	—
342	C₄⋊Q₈	C₂×Dic₆₁	1	1	yes	characteristic
343	#127	C₂×Dic₆₁	1	1	yes	characteristic
344	#124	C₂×Dic₆₁	1	2	yes	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
348	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
354	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
355	#117	—	2	1	no	—
356	#117	C₂²×D₆₁	1	1	yes	characteristic
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	—	61	1	no	—
359	C₂×C₄²	—	61	1	no	—
360	C₂×C₄²	—	122	1	no	—
361	C₂×C₄²	—	122	1	no	—
362	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
363	#108	—	122	4	no	—
364	C₄⋊C₈	—	61	1	no	—
365	C₄⋊C₈	—	61	1	no	—
366	C₄⋊C₈	—	61	2	no	—
367	C₄⋊C₈	—	122	2	no	—
368	C₄⋊C₈	—	122	2	no	—
369	C₄⋊C₈	—	122	1	no	—
370	C₄⋊C₈	—	122	1	no	—
371	C₄⋊C₈	C₂×Dic₆₁	1	1	yes	characteristic
372	C₄⋊C₈	C₂×Dic₆₁	1	1	yes	characteristic
373	C₄⋊C₈	C₂×Dic₆₁	1	2	yes	—
374	#104	—	61	4	no	—
375	#104	—	122	4	no	—
376	#104	—	122	2	no	—
377	#104	—	244	2	no	—
378	#103	C₂×Dic₆₁	1	2	yes	—
379	#103	C₂×Dic₆₁	1	2	yes	—
380	#102	C₂×Dic₆₁	1	2	yes	—
381	#102	C₂×Dic₆₁	1	2	yes	—
382	C₂²⋊C₈	—	122	2	no	—
383	C₂²⋊C₈	—	122	2	no	—
384	#97	—	122	1	no	—
385	C₄×C₈	—	122	4	no	—
386	C₄×C₈	—	122	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	D₄×D₆₁	1	2	yes	—
394	#41	#11758224	1	2	yes	—
395	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
396	C₂×Q₈	C₂²×Dic₆₁	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
402	C₂×D₄	C₂²×Dic₆₁	1	1	yes	characteristic
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	122	1	no	—
408	C₂²×C₄	—	122	1	no	—
409	C₂²×C₄	#11758224	1	1	yes	characteristic
410	C₂²×C₄	#11758224	1	1	yes	characteristic
411	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
412	Q₁₆	—	2	4	no	—
413	SD₁₆	—	2	4	no	—
414	SD₁₆	—	2	4	no	—
415	D₈	—	2	4	no	—
416	M₁₆	—	61	2	no	—
417	M₁₆	—	122	1	no	—
418	M₁₆	—	122	2	no	—
419	M₁₆	—	122	1	no	—
420	M₁₆	—	122	2	no	—
421	M₁₆	—	122	1	no	—
422	M₁₆	—	244	4	no	—
423	M₁₆	—	244	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	61	2	no	—
427	C₂×C₈	—	61	2	no	—
428	C₂×C₈	—	122	2	no	—
429	C₂×C₈	—	122	1	no	—
430	C₂×C₈	—	122	2	no	—
431	C₂×C₈	—	122	1	no	—
432	C₂×C₈	—	122	2	no	—
433	C₂×C₈	—	244	4	no	—
434	C₂×C₈	—	244	4	no	—
435	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
436	C₂×C₈	C₂²×Dic₆₁	1	2	yes	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
442	C₄⋊C₄	C₂²×Dic₆₁	1	1	yes	characteristic
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	61	2	no	—
452	C₄²	—	122	4	no	—
453	C₄²	—	122	1	no	—
454	C₄²	—	122	1	no	—
455	C₄²	—	122	1	no	—
456	C₄²	—	244	2	no	—
457	C₄²	D₄×D₆₁	1	1	yes	characteristic
458	C₄²	D₄×D₆₁	1	1	yes	characteristic
459	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
460	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×#11758224	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	D₄×Dic₆₁	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	1	no	—
477	D₄	D₄×Dic₆₁	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	8	1	no	—
490	C₂×C₄	—	122	2	no	—
491	C₂×C₄	—	122	2	no	—
492	C₂×C₄	—	122	2	no	—
493	C₂×C₄	—	122	2	no	—
494	C₂×C₄	—	244	1	no	—
495	C₂×C₄	—	244	1	no	—
496	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
497	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
498	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
499	C₂×C₄	D₄×Dic₆₁	1	1	yes	characteristic
500	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
501	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
502	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
504	C₂×C₄	#14519823	1	1	yes	characteristic
505	C₂×C₄	#14519824	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₈	—	122	2	no	—
509	C₈	—	122	2	no	—
510	C₈	—	122	2	no	—
511	C₈	—	244	2	no	—
512	C₈	—	244	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	C₂×D₄×Dic₆₁	1	1	yes	characteristic
522	C₂²	#16840412	1	1	yes	characteristic
523	C₂²	#16840464	1	1	yes	characteristic
524	C₄	—	2	1	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	122	4	no	—
532	C₄	—	244	2	no	—
533	C₄	#16839879	1	2	yes	complemented
534	C₄	C₂×D₄×Dic₆₁	1	1	yes	characteristic
535	C₄	#16840245	1	1	yes	characteristic
536	C₄	#16840396	1	1	yes	characteristic
537	C₄	#16840418	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	2	no	—
542	C₂	#21448839	1	1	yes	characteristic
543	C₂	C₂×#16839879	1	1	yes	characteristic
544	C₂	#21454729	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting, prime radical	C₆₁×#3035	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#3035	D₆₁
hypocenter	C₆₁	#23015
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. C₂×#16839879	C₂	semidirect
2. #21454563	C₂	semidirect
3. #21454387	C₂	semidirect
4. #21446648	C₂	semidirect
5. #21446595	C₂	semidirect
6. #21446525	C₂	semidirect
7. #21446148	C₂	semidirect
8. #21446096	C₂	semidirect
9. C₄⋊C₈×Dic₆₁	C₂	semidirect
10. C₄×#14519704	C₂	semidirect
40. C₆₁×#464	C₄	semidirect
41. C₆₁×#463	C₄	semidirect
42. C₆₁×#462	C₄	semidirect
43. C₆₁×#461	C₄	semidirect
44. C₆₁×#460	C₄	semidirect
45. C₆₁×#459	C₄	semidirect
75. #14519704	D₄	semidirect
259. C₄×C₆₁	#443	semidirect
289. #464	Dic₆₁	semidirect
290. #463	Dic₆₁	semidirect
291. #462	Dic₆₁	semidirect
292. #461	Dic₆₁	semidirect
293. #460	Dic₆₁	semidirect
294. #459	Dic₆₁	semidirect
320. C₆₁	#23015	semidirect
533. C₄	#16839879	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839879	2
#21454563	2
#21454387	2
#21446648	2
#21446595	2
#21446525	2
#21446148	2
#21446096	2
C₄⋊C₈×Dic₆₁	2
C₄×#14519704	2
C₆₁×#3035	2
#23015	61