Subgroups — #30615428

Order 15616.

718 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	#21462500	C₂	1	2	yes	maximal
2	#21461760	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461759	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461745	C₂	1	2	yes	maximal, complemented
5	#21461700	C₂	1	2	yes	maximal
6	#21461699	C₂	1	2	yes	maximal
7	#21461639	C₂	1	2	yes	maximal, complemented
8	C₄×#14519848	C₂	1	2	yes	maximal, complemented
9	#405×D₆₁	C₂	1	1	yes	maximal, characteristic
10	#16840787	—	2	4	no	—
11	#16840786	—	2	4	no	—
12	C₂×#14519848	C₂²	1	2	yes	—
13	C₂×#14519848	C₂²	1	2	yes	—
14	C₂×#14519848	C₂²	1	2	yes	—
15	C₂×#14519847	C₂²	1	2	yes	—
16	#16840767	C₂²	1	2	yes	—
17	#16840766	C₂²	1	2	yes	—
18	#16840733	C₂²	1	4	yes	—
19	C₄×#11758213	C₂²	1	4	yes	—
20	#16840638	C₂²	1	4	yes	—
21	#16840638	C₂²	1	4	yes	—
22	C₂×M₁₆×D₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
24	#117×D₆₁	C₂²	1	1	yes	characteristic
25	#16839720	C₄	1	1	yes	characteristic
26	#16839719	C₄	1	1	yes	characteristic
27	#16839719	C₄	1	1	yes	characteristic
28	#16839718	C₄	1	1	yes	characteristic
29	#16839717	C₄	1	1	yes	characteristic
30	#16839716	C₄	1	1	yes	characteristic
31	#16839716	C₄	1	1	yes	characteristic
32	#97×D₆₁	C₂²	1	1	yes	characteristic
33	#97×D₆₁	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#405	C₄	1	1	yes	characteristic
37	C₂×#11758213	C₂³	1	4	yes	—
38	C₂×#11758213	C₂³	1	4	yes	—
39	#14519848	—	2	4	no	—
40	#14519848	—	2	4	no	—
41	#14519848	—	2	4	no	—
42	#14519847	—	2	4	no	—
43	#14519844	—	2	4	no	—
44	C₄⋊#92420	—	2	4	no	—
45	#14519834	—	2	4	no	—
46	C₂²⋊#92420	—	2	4	no	—
47	#14519832	—	2	4	no	—
48	C₄×#92420	—	2	4	no	—
49	C₂²×C₄×D₆₁	C₂³	1	1	yes	characteristic
50	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
51	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
52	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
53	M₁₆×D₆₁	—	2	2	no	—
54	M₁₆×D₆₁	—	2	2	no	—
55	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₆₁	—	2	2	no	—
57	C₂×C₈×D₆₁	—	2	2	no	—
58	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
64	#14519736	C₂×C₄	1	1	yes	characteristic
65	#14519735	D₄	1	2	yes	—
66	#14519734	C₂×C₄	1	1	yes	characteristic
67	#14519734	C₂×C₄	1	1	yes	characteristic
68	#14519733	D₄	1	2	yes	—
69	C₄⋊C₄×D₆₁	Q₈	1	2	yes	—
70	C₂²⋊C₄×D₆₁	Q₈	1	2	yes	—
71	C₄²×D₆₁	C₂³	1	1	yes	characteristic
72	C₄²×D₆₁	C₂³	1	1	yes	characteristic
73	#14519688	C₂×C₄	1	1	yes	characteristic
74	#14519688	C₂×C₄	1	1	yes	characteristic
75	#14519687	C₂×C₄	1	1	yes	characteristic
76	#14519687	C₂×C₄	1	1	yes	characteristic
77	#14519687	C₂×C₄	1	1	yes	characteristic
78	#14519687	C₂×C₄	1	1	yes	characteristic
79	C₄×#92418	C₂×C₄	1	1	yes	characteristic
80	C₄×#92418	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
87	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
88	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
89	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂³×D₆₁	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₆₁	—	2	1	no	—
96	C₂×C₄×D₆₁	—	2	1	no	—
97	C₂×C₄×D₆₁	—	2	1	no	—
98	C₂×C₄×D₆₁	—	2	1	no	—
99	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₆₁	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₄×D₆₁	C₂×Q₈	1	2	yes	—
103	C₂×C₄×D₆₁	C₂×Q₈	1	2	yes	—
104	C₂×C₄×D₆₁	C₂⁴	1	1	yes	characteristic
105	C₂×#92420	—	2	4	no	—
106	C₂×#92420	—	2	4	no	—
107	#11758213	—	2	4	no	—
108	#11758213	—	2	4	no	—
109	#11758213	—	2	4	no	—
110	#11758213	—	2	4	no	—
111	M₁₆×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₄⋊C₄×C₆₁	C₄⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₆₁	C₄⋊C₄	1	2	yes	—
119	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²⋊Dic₆₁	C₄⋊C₄	1	2	yes	—
122	#11758198	C₄⋊C₄	1	2	yes	—
123	#11758198	C₄⋊C₄	1	2	yes	—
124	C₄⋊Dic₆₁	C₄⋊C₄	1	2	yes	—
125	#11758196	C₄⋊C₄	1	2	yes	—
126	#11758196	C₄⋊C₄	1	2	yes	—
127	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₆₁	C₂×D₄	1	2	yes	—
130	C₄×Dic₆₁	C₂×D₄	1	2	yes	—
131	#11758194	—	2	2	no	—
132	C₂×#92418	—	2	2	no	—
133	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
134	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
135	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
136	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
137	#11758189	—	2	2	no	—
138	#11758189	—	2	2	no	—
139	C₈×D₆₁	—	2	1	no	—
140	C₈×D₆₁	—	2	1	no	—
141	C₈×D₆₁	—	2	1	no	—
142	C₈×D₆₁	—	2	1	no	—
143	C₈×D₆₁	—	2	2	no	—
144	C₈×D₆₁	—	2	2	no	—
145	C₈×D₆₁	#41	1	2	yes	—
146	C₈×D₆₁	#41	1	2	yes	—
147	C₈×D₆₁	#41	1	2	yes	—
148	C₈×D₆₁	#41	1	2	yes	—
149	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×D₆₁	—	2	1	no	—
151	C₂²×D₆₁	—	2	1	no	—
152	C₂²×D₆₁	—	4	2	no	—
153	C₂²×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂²×D₆₁	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₆₁	—	2	1	no	—
162	C₂×Dic₆₁	—	2	1	no	—
163	C₂×Dic₆₁	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×Dic₆₁	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×Dic₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
167	C₄×D₆₁	—	2	1	no	—
168	C₄×D₆₁	—	2	1	no	—
169	C₄×D₆₁	—	2	1	no	—
170	C₄×D₆₁	—	2	1	no	—
171	C₄×D₆₁	—	2	1	no	—
172	C₄×D₆₁	—	2	1	no	—
173	C₄×D₆₁	—	4	2	no	—
174	C₄×D₆₁	—	4	2	no	—
175	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
176	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
177	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
178	C₄×D₆₁	C₂×#41	1	1	yes	characteristic
179	#92420	—	4	4	no	—
180	#92420	—	4	4	no	—
181	C₈×C₆₁	—	2	1	no	—
182	C₈×C₆₁	—	2	1	no	—
183	C₈×C₆₁	#117	1	2	yes	—
184	C₈×C₆₁	#117	1	2	yes	—
185	#92418	—	2	1	no	—
186	#92418	—	2	1	no	—
187	#92418	#117	1	2	yes	—
188	#92418	#117	1	2	yes	—
189	#20828	—	61	1	no	maximal, Sylow
190	C₂²×C₆₁	—	2	2	no	—
191	C₂²×C₆₁	—	2	1	no	—
192	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂×D₆₁	—	2	2	no	—
194	C₂×D₆₁	—	2	2	no	—
195	C₂×D₆₁	—	2	1	no	—
196	C₂×D₆₁	—	4	2	no	—
197	C₂×D₆₁	—	4	2	no	—
198	C₂×D₆₁	#533	1	1	yes	characteristic
199	C₂×D₆₁	#533	1	1	yes	characteristic
200	C₄×C₆₁	—	2	2	no	—
201	C₄×C₆₁	—	2	2	no	—
202	C₄×C₆₁	—	2	1	no	—
203	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
204	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
205	Dic₆₁	—	2	2	no	—
206	Dic₆₁	—	2	2	no	—
207	Dic₆₁	—	2	1	no	—
208	Dic₆₁	#532	1	1	yes	characteristic
209	Dic₆₁	#532	1	1	yes	characteristic
210	#2921	—	61	2	no	—
211	C₂×#405	—	61	1	no	—
212	#1848	—	61	1	no	—
213	#1848	—	61	1	no	—
214	#1838	—	61	2	no	—
215	#1811	—	61	2	no	—
216	#1810	—	61	2	no	—
217	#1778	—	61	2	no	—
218	C₄×#108	—	61	2	no	—
219	C₂×C₆₁	—	4	1	no	—
220	C₂×C₆₁	#2285	1	1	yes	characteristic
221	C₂×C₆₁	#2916	1	2	yes	—
222	D₆₁	—	2	1	no	—
223	D₆₁	—	2	1	no	—
224	D₆₁	—	4	1	no	—
225	C₂²×M₁₆	—	61	1	no	—
226	C₂³×C₈	—	61	1	no	—
227	C₂×#117	—	61	1	no	—
228	#433	—	122	4	no	—
229	#433	—	122	4	no	—
230	C₂×#108	—	61	2	no	—
231	C₂×#108	—	61	2	no	—
232	C₂×#108	—	61	2	no	—
233	C₂×#108	—	61	2	no	—
234	#423	—	61	2	no	—
235	#423	—	61	2	no	—
236	#407	—	61	4	no	—
237	#405	—	61	1	no	—
238	#405	—	61	1	no	—
239	#405	—	61	1	no	—
240	#405	—	61	1	no	—
241	#405	—	61	1	no	—
242	#405	—	61	1	no	—
243	#405	—	61	1	no	—
244	#405	#6923	1	1	yes	characteristic
245	C₄×M₁₆	—	61	4	no	—
246	C₂×#97	—	61	1	no	—
247	C₂×#97	—	61	1	no	—
248	C₂×C₄×C₈	—	61	1	no	—
249	C₂×C₄×C₈	—	61	1	no	—
250	#341	—	61	4	no	—
251	#341	—	61	4	no	—
252	C₆₁	#20828	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₄	—	61	1	no	—
254	C₂×M₁₆	—	61	1	no	—
255	C₂×M₁₆	—	61	1	no	—
256	C₂×M₁₆	—	61	1	no	—
257	C₂×M₁₆	—	61	4	no	—
258	C₂×M₁₆	—	61	4	no	—
259	C₂×M₁₆	—	122	2	no	—
260	C₂×M₁₆	—	122	2	no	—
261	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
262	C₂²×C₈	—	61	1	no	—
263	C₂²×C₈	—	61	1	no	—
264	C₂²×C₈	—	61	1	no	—
265	C₂²×C₈	—	61	1	no	—
266	C₂²×C₈	—	61	1	no	—
267	C₂²×C₈	—	61	1	no	—
268	C₂²×C₈	—	61	1	no	—
269	C₂²×C₈	—	122	2	no	—
270	C₂²×C₈	—	122	2	no	—
271	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
272	#117	—	61	1	no	—
273	#117	—	61	2	no	—
274	#117	—	61	2	no	—
275	#117	—	61	1	no	—
276	#117	—	61	1	no	—
277	#117	C₂×#6923	1	1	yes	characteristic
278	C₂×C₄⋊C₄	—	61	2	no	—
279	C₂×C₂²⋊C₄	—	61	2	no	—
280	C₂×C₄²	—	61	1	no	—
281	C₂×C₄²	—	61	1	no	—
282	#108	—	122	4	no	—
283	#108	—	122	4	no	—
284	#108	—	122	4	no	—
285	#108	—	122	4	no	—
286	C₄⋊C₈	—	122	4	no	—
287	C₄⋊C₈	—	122	4	no	—
288	C₂²⋊C₈	—	122	4	no	—
289	C₂²⋊C₈	—	122	4	no	—
290	#97	—	61	1	no	—
291	#97	—	61	1	no	—
292	#97	—	61	1	no	—
293	#97	—	61	1	no	—
294	#97	—	61	1	no	—
295	#97	—	61	1	no	—
296	#97	—	122	4	no	—
297	#97	C₂×#6923	1	1	yes	characteristic
298	#97	C₂×#6923	1	1	yes	characteristic
299	C₄×C₈	—	61	1	no	—
300	C₄×C₈	—	61	1	no	—
301	C₄×C₈	—	61	1	no	—
302	C₄×C₈	—	61	1	no	—
303	C₄×C₈	—	61	1	no	—
304	C₄×C₈	—	61	1	no	—
305	C₄×C₈	—	122	4	no	—
306	C₄×C₈	C₂×#6923	1	1	yes	characteristic
307	C₄×C₈	C₂×#6923	1	1	yes	characteristic
308	C₂⁴	—	61	1	no	—
309	C₂²×C₄	—	61	1	no	—
310	C₂²×C₄	—	61	1	no	—
311	C₂²×C₄	—	61	1	no	—
312	C₂²×C₄	—	61	1	no	—
313	C₂²×C₄	—	61	1	no	—
314	C₂²×C₄	—	61	2	no	—
315	C₂²×C₄	—	61	2	no	—
316	C₂²×C₄	—	122	1	no	—
317	C₂²×C₄	—	122	1	no	—
318	C₂²×C₄	—	122	1	no	—
319	C₂²×C₄	—	122	1	no	—
320	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
321	M₁₆	—	2	2	no	—
322	M₁₆	—	122	2	no	—
323	M₁₆	—	122	2	no	—
324	M₁₆	—	122	2	no	—
325	M₁₆	—	122	4	no	—
326	M₁₆	—	122	4	no	—
327	M₁₆	—	122	4	no	—
328	M₁₆	—	122	4	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	61	1	no	—
331	C₂×C₈	—	61	1	no	—
332	C₂×C₈	—	61	2	no	—
333	C₂×C₈	—	61	2	no	—
334	C₂×C₈	—	61	2	no	—
335	C₂×C₈	—	61	2	no	—
336	C₂×C₈	—	61	1	no	—
337	C₂×C₈	—	61	1	no	—
338	C₂×C₈	—	122	2	no	—
339	C₂×C₈	—	122	1	no	—
340	C₂×C₈	—	122	1	no	—
341	C₂×C₈	—	122	1	no	—
342	C₂×C₈	—	122	1	no	—
343	C₂×C₈	—	122	2	no	—
344	C₂×C₈	—	122	2	no	—
345	C₂×C₈	—	122	4	no	—
346	C₂×C₈	—	122	4	no	—
347	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
348	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
349	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
350	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
351	C₄⋊C₄	—	61	2	no	—
352	C₄⋊C₄	—	61	2	no	—
353	C₄⋊C₄	—	61	2	no	—
354	C₄⋊C₄	C₄⋊#6923	1	2	yes	—
355	C₂²⋊C₄	—	61	2	no	—
356	C₂²⋊C₄	—	61	2	no	—
357	C₂²⋊C₄	—	61	2	no	—
358	C₂²⋊C₄	C₄⋊#6923	1	2	yes	—
359	C₄²	—	61	2	no	—
360	C₄²	—	61	2	no	—
361	C₄²	—	61	1	no	—
362	C₄²	—	61	1	no	—
363	C₄²	C₂²×#6923	1	1	yes	characteristic
364	C₄²	C₂²×#6923	1	1	yes	characteristic
365	C₂³	—	61	1	no	—
366	C₂³	—	61	1	no	—
367	C₂³	—	122	1	no	—
368	C₂³	—	122	1	no	—
369	C₂³	—	244	2	no	—
370	C₂³	C₂×C₄⋊#6923	1	1	yes	characteristic
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	61	1	no	—
374	C₂×C₄	—	61	1	no	—
375	C₂×C₄	—	61	1	no	—
376	C₂×C₄	—	61	1	no	—
377	C₂×C₄	—	61	1	no	—
378	C₂×C₄	—	61	2	no	—
379	C₂×C₄	—	61	2	no	—
380	C₂×C₄	—	61	1	no	—
381	C₂×C₄	—	122	1	no	—
382	C₂×C₄	—	122	1	no	—
383	C₂×C₄	—	122	1	no	—
384	C₂×C₄	—	122	1	no	—
385	C₂×C₄	—	122	1	no	—
386	C₂×C₄	—	122	1	no	—
387	C₂×C₄	—	122	1	no	—
388	C₂×C₄	—	122	1	no	—
389	C₂×C₄	—	244	2	no	—
390	C₂×C₄	—	244	2	no	—
391	C₂×C₄	C₂×C₄⋊#6923	1	2	yes	—
392	C₂×C₄	C₂×C₄⋊#6923	1	2	yes	—
393	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
394	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	61	2	no	—
398	C₈	—	61	2	no	—
399	C₈	—	122	1	no	—
400	C₈	—	122	1	no	—
401	C₈	—	244	4	no	—
402	C₈	—	244	4	no	—
403	C₈	#14519856	1	2	yes	—
404	C₈	#14519856	1	2	yes	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	61	1	no	—
408	C₂²	—	61	1	no	—
409	C₂²	—	122	2	no	—
410	C₂²	—	122	2	no	—
411	C₂²	—	122	1	no	—
412	C₂²	—	244	2	no	—
413	C₂²	—	244	2	no	—
414	C₂²	C₂²×C₄⋊#6923	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	61	1	no	—
419	C₄	—	61	1	no	—
420	C₄	—	122	2	no	—
421	C₄	—	122	2	no	—
422	C₄	—	122	1	no	—
423	C₄	C₂×#14519856	1	1	yes	characteristic
424	C₄	C₂×#14519856	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	122	1	no	—
427	C₂	—	122	1	no	—
428	C₂	—	244	1	no	—
429	C₂	#21462268	1	1	yes	characteristic
430	C₂	#21462481	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#405	C₄
socle	C₂²×C₆₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₆₁	C₂×Q₈
cosocle	C₂×C₄×D₆₁	C₂⁴
hypercenter	#405	#6923
hypocenter	C₆₁	#20828
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
2. #21461760	C₂	semidirect
3. #21461759	C₂	semidirect
4. #21461745	C₂	semidirect
7. #21461639	C₂	semidirect
8. C₄×#14519848	C₂	semidirect
252. C₆₁	#20828	semidirect

Maximal subgroups

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

subgroup	index
#21462500	2
#21461760	2
#21461759	2
#21461745	2
#21461700	2
#21461699	2
#21461639	2
C₄×#14519848	2
#405×D₆₁	2
#20828	61