Finite Group Databasebeta

← #29573395

Subgroups — #29573395

Order 15616.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445887C211yesmaximal, characteristic
2#21444046C211yesmaximal, characteristic
3#21443697C212yesmaximal
4#21443697C212yesmaximal
5C61×#2283C211yesmaximal, characteristic
6C2×C22⋊#92418C2212yes—
7C2×#14519684—21no—
8C2×#14519684—21no—
9C2×#14519684C2212yes—
10#16839517—21no—
11#16839517—21no—
12C22×C42×C61C2211yescharacteristic
13C61×#383—21no—
14C61×#382C411yescharacteristic, complemented
15C61×#382C411yescharacteristic, complemented
16C61×#381—21no—
17C61×#380C2211yescharacteristic
18C61×#380C2211yescharacteristic
19C4×C4⋊C4×C61C411yescharacteristic, complemented
20C4×C4⋊C4×C61C411yescharacteristic, complemented
21C4×C22⋊C4×C61—21no—
22C61×#376—21no—
23C23×Dic61—22no—
24C22×#92418—22no—
25C22⋊#92418—24no—
26#14519684—24no—
27#14519684—24no—
28#14519684—42no—
29C23×C4×C61D411yescharacteristic
30C23×C4×C61D411yescharacteristic
31C23×C4×C61C2311yescharacteristic
32C2×C4⋊C4×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61C2×C411yescharacteristic
34C2×C4⋊C4×C61C2×C411yescharacteristic
35C2×C4⋊C4×C61C2×C411yescharacteristic
36C2×C22⋊C4×C61—21no—
37C2×C22⋊C4×C61—21no—
38C2×C42×C61—24no—
39C2×C42×C61—21no—
40C2×C42×C61—21no—
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45#95×C61—21no—
46#95×C61—21no—
47#95×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53C24×C61C2×D411yescharacteristic
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4114yes—
74C22×Dic61—24no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—42no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C42×C61—22no—
89C42×C61—22no—
90C42×C61—22no—
91C42×C61—22no—
92C42×C61—42no—
93C42×C61—42no—
94C2×#92418—42no—
95C2×#92418—42no—
96C2×#92418—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61C2×C22⋊C411yescharacteristic
102C23×C61#12312yes—
103C23×C61#13512yes—
104C23×C61AGL(1,ℤ/8)11yescharacteristic
105C23×C61#13711yescharacteristic
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—44no—
122C2×C4×C61—44no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61#10412yes—
138C2×C4×C61#11712yes—
139C2×C4×C61#12312yes—
140C2×Dic61—44no—
141C2×Dic61—44no—
142C2×Dic61—44no—
143C2×Dic61—82no—
144C2×Dic61—82no—
145C2×Dic61—82no—
146C2×Dic61—82no—
147#92418—82no—
148#8714—611nomaximal, Sylow
149C22×C61—22no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61#38111yescharacteristic
158C22×C61#41011yescharacteristic
159C22×C61#41011yescharacteristic
160C22×C61#41611yescharacteristic
161C22×C61#41711yescharacteristic
162C22×C61C2×#10411yescharacteristic
163C22×C61#42111yescharacteristic
164C22×C61#48212yes—
165C22×C61#48512yes—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—22no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—81no—
173C4×C61—81no—
174C4×C61—81no—
175C4×C61—81no—
176Dic61—84no—
177#2283D6111yescharacteristic
178#1817—611no—
179#1434—611no—
180#1294—612no—
181#1294—612no—
182C2×C61—22no—
183C2×C61—22no—
184C2×C61#150011yescharacteristic
185C2×C61#150911yescharacteristic
186C2×C61#151211yescharacteristic
187C2×C61#152111yescharacteristic
188C2×C61#182011yescharacteristic
189C2×C61#182511yescharacteristic
190C2×C61#182611yescharacteristic
191C22×C42C2×D6111yescharacteristic
192C2×C22⋊C8—612no—
193#383—21no—
194#382Dic6111yescharacteristic, complemented
195#382Dic6111yescharacteristic, complemented
196#381—21no—
197#380C2×D6111yescharacteristic
198#380C2×D6111yescharacteristic
199C4×C4⋊C4Dic6111yescharacteristic, complemented
200C4×C4⋊C4Dic6111yescharacteristic, complemented
201C4×C22⋊C4—21no—
202#376—21no—
203C2×#95—612no—
204C2×#95—1221no—
205C2×#95—1221no—
206#336—1221no—
207#336—1221no—
208C61#871411yescharacteristic, complemented, Sylow
209C23×C4—1222no—
210C23×C4C22⋊D6111yescharacteristic
211C23×C4C22⋊D6111yescharacteristic
212C23×C4C22×D6111yescharacteristic
213C22×C8—1222no—
214C2×C4⋊C4C2×Dic6111yescharacteristic
215C2×C4⋊C4C2×Dic6111yescharacteristic
216C2×C4⋊C4C2×Dic6111yescharacteristic
217C2×C4⋊C4C2×Dic6111yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—24no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42C2×Dic6111yescharacteristic
224C2×C42C2×Dic6111yescharacteristic
225C2×C42C22⋊D6111yescharacteristic
226C2×C42C22⋊D6111yescharacteristic
227C22⋊C8—1224no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—1224no—
237#95—1224no—
238#95—2442no—
239C24C2×C22⋊D6111yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1224no—
254C22×C4—2442no—
255C22×C4—2442no—
256C22×C4—2442no—
257C22×C4—2442no—
258C22×C4—2442no—
259C22×C4—2442no—
260C22×C4C22⋊Dic6111yescharacteristic
261C22×C4C22⋊Dic6111yescharacteristic
262C22×C4C22⋊Dic6111yescharacteristic
263C22×C4C22⋊Dic6111yescharacteristic
264C22×C4#1175822214yes—
265C22×C4C22×Dic6111yescharacteristic
266C22×C4C2×C22⋊D6111yescharacteristic
267C2×C8—2442no—
268C2×C8—2442no—
269C2×C8—2442no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C22⋊Dic6111yescharacteristic
288C23#1451976012yes—
289C23#1451979712yes—
290C23#1451980211yescharacteristic
291C23#1451980711yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—4882no—
324C2×C4—4882no—
325C2×C4—4882no—
326C2×C4—4882no—
327C2×C4—2444no—
328C2×C4—2444no—
329C2×C4—2444no—
330C2×C4#1451970412yes—
331C2×C4#1451973612yes—
332C2×C4#1451976012yes—
333C8—4882no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22#1683962511yescharacteristic
343C22#1683973611yescharacteristic
344C22#1683973611yescharacteristic
345C22#1683975811yescharacteristic
346C22#1683976311yescharacteristic
347C22C2×#1451970411yescharacteristic
348C22#1683977911yescharacteristic
349C22#1684008612yes—
350C22#1684010312yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—4884no—
362C2—22no—
363C2—22no—
364C2#2144430511yescharacteristic
365C2#2144434411yescharacteristic
366C2#2144435711yescharacteristic
367C2#2144439611yescharacteristic
368C2#2144589611yescharacteristic
369C2#2144591411yescharacteristic
370C2#2144591811yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2283C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#2283D61
hypocenterC61#8714
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2283

Complements

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

NH ≅ G/Ntype
14. C61×#382C4semidirect
15. C61×#382C4semidirect
19. C4×C4⋊C4×C61C4semidirect
20. C4×C4⋊C4×C61C4semidirect
194. #382Dic61semidirect
195. #382Dic61semidirect
199. C4×C4⋊C4Dic61semidirect
200. C4×C4⋊C4Dic61semidirect
208. C61#8714semidirect

Maximal subgroups

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

subgroupindex
#214458872
#214440462
#214436972
C61×#22832
#871461