Subgroups — #29662461

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21456405	C₂	1	1	yes	maximal, characteristic, complemented
2	#21455607	C₂	1	2	yes	maximal
3	#21445277	C₂	1	2	yes	maximal, complemented
4	#21445270	C₂	1	2	yes	maximal, complemented
5	#21445223	C₂	1	1	yes	maximal, characteristic, complemented
6	#21445218	C₂	1	1	yes	maximal, characteristic, complemented
7	#21445189	C₂	1	1	yes	maximal, characteristic, complemented
8	#21445184	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16839515	C₂	1	1	yes	maximal, characteristic, complemented
10	#21444474	C₂	1	2	yes	maximal, complemented
11	C₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
12	#16840319	C₂²	1	2	yes	—
13	#16840167	C₂²	1	1	yes	characteristic
14	#16840142	C₂²	1	1	yes	characteristic
15	#16840113	C₂²	1	2	yes	—
16	#16840069	—	2	2	no	—
17	#16840062	—	2	2	no	—
18	#16840057	C₂²	1	2	yes	—
19	#16840052	C₂²	1	2	yes	—
20	#16840047	C₂²	1	2	yes	—
21	#16840042	C₂²	1	2	yes	—
22	#16840003	—	2	1	no	—
23	#16840003	—	2	1	no	—
24	C₄×Dic₂₄₄	—	2	1	no	—
25	C₄×Dic₂₄₄	—	2	1	no	—
26	#16839798	—	2	2	no	—
27	C₂×C₄⋊#92418	C₂²	1	2	yes	—
28	#16839758	—	2	2	no	—
29	#16839515	C₂²	1	1	yes	characteristic
30	#16839515	C₂²	1	1	yes	characteristic
31	#16839515	C₂²	1	2	yes	—
32	#16839510	C₂²	1	2	yes	—
33	#16839510	C₂²	1	2	yes	—
34	#16839509	C₂²	1	2	yes	—
35	#16839509	C₂²	1	2	yes	—
36	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₆₁	—	2	1	no	—
40	C₈×D₄×C₆₁	—	2	1	no	—
41	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#431	—	2	1	no	—
44	C₆₁×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₆₁	—	2	1	no	—
46	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₄₄	—	2	1	no	—
48	C₂×Dic₂₄₄	—	2	1	no	—
49	C₂²×#92418	—	2	2	no	—
50	#14519777	C₂³	1	2	yes	—
51	#14519777	C₂³	1	2	yes	—
52	#14519769	—	2	2	no	—
53	#14519756	—	2	2	no	—
54	#14519756	—	2	2	no	—
55	C₄×Dic₁₂₂	—	2	2	no	—
56	C₄×Dic₁₂₂	—	2	2	no	—
57	#14519736	—	2	2	no	—
58	#14519711	—	2	1	no	—
59	#14519711	—	2	1	no	—
60	#14519710	—	2	2	no	—
61	#14519710	—	2	2	no	—
62	#14519708	—	2	2	no	—
63	#14519708	—	2	2	no	—
64	C₄⋊#92418	—	2	2	no	—
65	C₄⋊#92418	C₂³	1	2	yes	—
66	C₄⋊#92418	C₂³	1	2	yes	—
67	#14519702	—	2	2	no	—
68	#14519702	—	2	2	no	—
69	#14519701	—	2	2	no	—
70	#14519701	—	2	2	no	—
71	#14519698	—	2	2	no	—
72	#14519698	—	2	2	no	—
73	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₆₁	—	2	1	no	—
75	C₂²×C₈×C₆₁	—	2	1	no	—
76	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
78	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
79	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₄×D₄×C₆₁	—	2	1	no	—
81	C₄×D₄×C₆₁	—	2	1	no	—
82	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
83	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
84	#117×C₆₁	—	2	1	no	—
85	#117×C₆₁	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	—	2	1	no	—
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₁	—	2	1	no	—
89	C₄⋊C₈×C₆₁	—	2	1	no	—
90	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₆₁	—	2	1	no	—
93	C₂²⋊C₈×C₆₁	—	2	1	no	—
94	C₂²⋊C₈×C₆₁	—	2	1	no	—
95	C₄×C₈×C₆₁	—	2	1	no	—
96	C₄×C₈×C₆₁	—	2	1	no	—
97	C₄×C₈×C₆₁	—	2	1	no	—
98	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	#41×C₆₁	—	2	2	no	—
103	#41×C₆₁	Q₁₆	1	4	yes	complemented
104	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₆₁	—	2	1	no	—
106	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
113	C₂×Dic₁₂₂	—	2	2	no	—
114	C₂×Dic₁₂₂	—	2	2	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	4	1	no	—
119	C₂×C₈×C₆₁	—	4	2	no	—
120	C₂×C₈×C₆₁	—	4	2	no	—
121	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₆₁	—	2	1	no	—
130	C₂²⋊C₄×C₆₁	—	2	1	no	—
131	C₂²⋊C₄×C₆₁	—	2	1	no	—
132	C₄²×C₆₁	—	2	1	no	—
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	1	no	—
135	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₆₁	#41	1	1	yes	characteristic
138	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₆₁	—	4	2	no	—
140	C₄⋊Dic₆₁	—	2	2	no	—
141	C₄⋊Dic₆₁	—	2	2	no	—
142	C₄⋊Dic₆₁	—	2	2	no	—
143	C₄⋊Dic₆₁	—	2	2	no	—
144	#11758196	—	4	2	no	—
145	#11758196	—	4	2	no	—
146	C₄×Dic₆₁	—	4	2	no	—
147	C₂×#92418	—	2	2	no	—
148	C₂×#92418	—	2	2	no	—
149	C₂×#92418	—	4	4	no	—
150	Dic₂₄₄	—	4	2	no	—
151	Dic₂₄₄	—	4	2	no	—
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	#121	1	1	yes	characteristic
154	Q₈×C₆₁	—	2	1	no	—
155	Q₈×C₆₁	C₂×Q₁₆	1	2	yes	—
156	D₄×C₆₁	—	2	4	no	—
157	D₄×C₆₁	—	2	1	no	—
158	D₄×C₆₁	C₂×Q₁₆	1	2	yes	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	4	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	1	no	—
169	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
173	C₂×C₄×C₆₁	#135	1	2	yes	—
174	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₆₁	—	4	2	no	—
178	C₂×Dic₆₁	—	4	2	no	—
179	Dic₁₂₂	—	4	2	no	—
180	Dic₁₂₂	—	4	2	no	—
181	Dic₁₂₂	—	8	2	no	—
182	C₈×C₆₁	—	2	1	no	—
183	C₈×C₆₁	—	2	1	no	—
184	C₈×C₆₁	—	2	1	no	—
185	C₈×C₆₁	—	4	1	no	—
186	C₈×C₆₁	—	4	1	no	—
187	C₈×C₆₁	#135	1	2	yes	—
188	#92418	—	4	2	no	—
189	#92418	—	4	2	no	—
190	#19126	—	61	1	no	maximal, Sylow
191	C₂²×C₆₁	—	2	1	no	—
192	C₂²×C₆₁	—	2	1	no	—
193	C₂²×C₆₁	—	2	2	no	—
194	C₂²×C₆₁	—	4	1	no	—
195	C₂²×C₆₁	—	4	1	no	—
196	C₂²×C₆₁	#467	1	2	yes	—
197	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	2	2	no	—
200	C₄×C₆₁	—	2	1	no	—
201	C₄×C₆₁	—	2	1	no	—
202	C₄×C₆₁	—	4	1	no	—
203	C₄×C₆₁	—	4	1	no	—
204	C₄×C₆₁	#467	1	2	yes	—
205	C₄×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
206	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
207	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
208	C₄×C₆₁	#575	1	1	yes	characteristic
209	Dic₆₁	—	8	2	no	—
210	Dic₆₁	—	8	2	no	—
211	#3170	—	61	1	no	—
212	#3076	—	61	2	no	—
213	C₈×#41	D₆₁	1	1	yes	characteristic
214	#1684	—	61	2	no	—
215	#1683	—	61	2	no	—
216	#1676	—	61	1	no	—
217	#1675	—	61	1	no	—
218	#1670	—	61	1	no	—
219	#1669	—	61	1	no	—
220	C₂×#335	—	61	1	no	—
221	#1542	—	61	2	no	—
222	C₂×C₆₁	—	2	2	no	—
223	C₂×C₆₁	—	4	2	no	—
224	C₂×C₆₁	#3035	1	1	yes	characteristic
225	C₂×C₆₁	C₂×#467	1	1	yes	characteristic
226	C₂×C₆₁	#3067	1	1	yes	characteristic
227	#533	—	61	2	no	—
228	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
229	#500	—	61	1	no	—
230	#494	—	61	1	no	—
231	#487	—	61	2	no	—
232	#479	—	122	2	no	—
233	#478	—	122	2	no	—
234	#477	—	61	2	no	—
235	#476	—	61	2	no	—
236	#475	—	61	2	no	—
237	#474	—	61	2	no	—
238	#467	—	122	1	no	—
239	#467	—	122	1	no	—
240	C₈×Q₈	C₂×D₆₁	1	1	yes	characteristic
241	C₈×Q₈	C₂×D₆₁	1	1	yes	characteristic
242	C₄×Q₁₆	—	122	1	no	—
243	C₄×Q₁₆	—	122	1	no	—
244	C₈×D₄	—	2	1	no	—
245	C₈×D₄	—	2	1	no	—
246	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
247	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
248	#431	—	2	1	no	—
249	#431	C₂×D₆₁	1	1	yes	characteristic
250	#427	—	122	2	no	—
251	C₂×C₄⋊C₈	—	61	2	no	—
252	#416	—	122	2	no	—
253	C₂×C₄×C₈	—	2	1	no	—
254	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
255	#335	—	61	1	no	—
256	#335	—	61	1	no	—
257	#335	—	61	2	no	—
258	#333	—	61	2	no	—
259	#333	—	61	2	no	—
260	#332	—	61	2	no	—
261	#332	—	61	2	no	—
262	C₆₁	#19126	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	D₂₄₄	1	1	yes	characteristic
264	C₂×Q₁₆	—	122	1	no	—
265	C₂×Q₁₆	—	122	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	122	2	no	—
269	C₂²×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
271	C₄⋊Q₈	—	61	2	no	—
272	C₄⋊Q₈	—	61	2	no	—
273	#125	—	122	2	no	—
274	C₂²⋊Q₈	—	122	2	no	—
275	C₂²⋊Q₈	—	122	2	no	—
276	C₄×Q₈	—	122	2	no	—
277	C₄×Q₈	—	122	2	no	—
278	C₄×Q₈	D₂₄₄	1	1	yes	characteristic
279	C₄×Q₈	C₂²×D₆₁	1	1	yes	characteristic
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	D₂₄₄	1	1	yes	characteristic
283	C₄×D₄	C₂²×D₆₁	1	1	yes	characteristic
284	#117	—	2	1	no	—
285	#117	—	122	2	no	—
286	#117	D₂₄₄	1	1	yes	characteristic
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
289	#107	—	122	1	no	—
290	#107	—	122	1	no	—
291	#107	—	122	2	no	—
292	#107	—	122	2	no	—
293	#106	—	122	2	no	—
294	#106	—	122	2	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	61	2	no	—
298	C₄⋊C₈	—	61	2	no	—
299	C₄⋊C₈	—	122	2	no	—
300	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
301	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
302	#103	—	122	2	no	—
303	#103	—	122	2	no	—
304	#103	—	122	2	no	—
305	#103	—	122	2	no	—
306	#102	—	122	2	no	—
307	#102	—	122	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
315	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
318	#41	—	2	2	no	—
319	#41	Dic₂₄₄	1	4	yes	complemented
320	C₂×Q₈	—	122	2	no	—
321	C₂×Q₈	—	122	2	no	—
322	C₂×Q₈	C₂×D₂₄₄	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×D₂₄₄	1	1	yes	characteristic
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
329	C₂²×C₄	#11758222	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
331	Q₁₆	—	244	2	no	—
332	Q₁₆	—	244	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	122	2	no	—
340	C₂×C₈	—	122	2	no	—
341	C₂×C₈	—	244	4	no	—
342	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	122	2	no	—
349	C₄⋊C₄	—	122	2	no	—
350	C₄⋊C₄	—	122	2	no	—
351	C₄⋊C₄	—	122	2	no	—
352	C₄⋊C₄	—	244	2	no	—
353	C₄⋊C₄	—	244	2	no	—
354	C₄⋊C₄	C₂×D₂₄₄	1	1	yes	characteristic
355	C₄⋊C₄	C₂×D₂₄₄	1	1	yes	characteristic
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	244	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	244	2	no	—
364	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
365	C₄²	#11758222	1	1	yes	characteristic
366	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
367	C₄²	C₂³×D₆₁	1	1	yes	characteristic
368	C₂³	—	2	1	no	—
369	C₂³	#14519751	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	—	488	2	no	—
372	Q₈	—	244	2	no	—
373	Q₈	—	244	2	no	—
374	Q₈	C₂×Dic₂₄₄	1	2	yes	—
375	D₄	—	2	4	no	—
376	D₄	—	2	1	no	—
377	D₄	C₂×Dic₂₄₄	1	2	yes	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	244	2	no	—
389	C₂×C₄	—	244	2	no	—
390	C₂×C₄	#14519751	1	1	yes	characteristic
391	C₂×C₄	#14519751	1	1	yes	characteristic
392	C₂×C₄	#14519751	1	1	yes	characteristic
393	C₂×C₄	C₂×Dic₂₄₄	1	2	yes	—
394	C₂×C₄	#14519799	1	2	yes	—
395	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
397	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₈	—	244	2	no	—
404	C₈	—	244	2	no	—
405	C₈	#14519797	1	2	yes	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	#16840003	1	2	yes	—
412	C₂²	C₂×#14519751	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	488	2	no	—
420	C₄	—	488	2	no	—
421	C₄	#16840003	1	2	yes	—
422	C₄	C₂²×Dic₂₄₄	1	1	yes	characteristic
423	C₄	C₂×#14519797	1	1	yes	characteristic
424	C₄	C₂×#14519799	1	1	yes	characteristic
425	C₄	#16840560	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	#21455274	1	1	yes	characteristic
429	C₂	C₂×#16840003	1	1	yes	characteristic
430	C₂	#21455539	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14519751
commutator, cosocle	C₄²×C₆₁	C₂⁴
Frattini	C₄²	C₂³×D₆₁
Fitting	C₈×#41×C₆₁	C₂
socle	C₂²×C₆₁	C₂×#121
prime radical	C₂×#41×C₆₁	D₄
hypercenter	C₈×#41	D₆₁
hypocenter	C₆₁	#19126
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #21456405	C₂	semidirect
3. #21445277	C₂	semidirect
4. #21445270	C₂	semidirect
5. #21445223	C₂	semidirect
6. #21445218	C₂	semidirect
7. #21445189	C₂	semidirect
8. #21445184	C₂	semidirect
9. C₂×#16839515	C₂	semidirect
10. #21444474	C₂	semidirect
103. #41×C₆₁	Q₁₆	semidirect
262. C₆₁	#19126	semidirect
319. #41	Dic₂₄₄	semidirect

Maximal subgroups

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

subgroup	index
#21456405	2
#21455607	2
#21445277	2
#21445270	2
#21445223	2
#21445218	2
#21445189	2
#21445184	2
C₂×#16839515	2
#21444474	2
C₈×#41×C₆₁	2
#19126	61