Finite Group Databasebeta

← #29568709

Subgroups — #29568709

Order 15616.

366 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454201C211yesmaximal, characteristic
2#21445936C211yesmaximal, characteristic
3#21443644C212yesmaximal
4#21443643C212yesmaximal
5C61×#1831C211yesmaximal, characteristic
6C2×C4⋊#92418—21no—
7#16839668C411yescharacteristic
8#16839668C411yescharacteristic
9#16839668C2211yescharacteristic
10#16839660C411yescharacteristic
11#16839660C411yescharacteristic
12#16839660C2211yescharacteristic
13#16839646—21no—
14#16839646—21no—
15#16839646—21no—
16#16839630—21no—
17#16839517—21no—
18#16839517C2212yes—
19C2×C4⋊C8×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×#92418—22no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C4⋊#92418—42no—
32#14519684—21no—
33#14519684—21no—
34#14519684—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41C22×C8×C61—22no—
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—42no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22×C411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C2×Dic122—22no—
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C2×C8×C61—42no—
67C42×C61—22no—
68C42×C61—21no—
69C42×C61—21no—
70C42×C61—41no—
71C42×C61—41no—
72C42×C61—41no—
73C42×C61—41no—
74C42×C61SD1612yes—
75C42×C61Q1612yes—
76C4⋊Dic61—22no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—42no—
80#11758196—42no—
81#11758196—41no—
82#11758196—41no—
83C2×#92418—42no—
84C2×#92418—42no—
85C2×#92418—42no—
86C23×C61C2×C22⋊C411yescharacteristic
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61#10312yes—
104C2×C4×C61#10312yes—
105C2×C4×C61#13112yes—
106C2×C4×C61C2×SD1611yescharacteristic
107C2×C4×C61C2×Q1611yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C2×C4×C61#13711yescharacteristic
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122Dic122—82no—
123C8×C61—82no—
124#92418—82no—
125#7733—611nomaximal, Sylow
126C22×C61#40811yescharacteristic
127C22×C61#41011yescharacteristic
128C22×C61#41311yescharacteristic
129C22×C61C2×#10311yescharacteristic
130C22×C61#41711yescharacteristic
131C22×C61#42111yescharacteristic
132C22×C61#42111yescharacteristic
133C4×C61—22no—
134C4×C61—22no—
135C4×C61—22no—
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142Dic61—81no—
143Dic61—81no—
144Dic61—81no—
145Dic61—81no—
146#2863—611no—
147#1831—611no—
148#1831D6111yescharacteristic
149#1272—612no—
150#1271—612no—
151C2×C61#147311yescharacteristic
152C2×C61#148111yescharacteristic
153C2×C61#149511yescharacteristic
154C2×C61#151211yescharacteristic
155C2×C61#151811yescharacteristic
156C2×C61#153511yescharacteristic
157C2×C61#155011yescharacteristic
158C2×C4⋊C8—21no—
159C2×C4⋊C8—1221no—
160#391—611no—
161#391—611no—
162#391—611no—
163#389—611no—
164#389—611no—
165#389—611no—
166#387—1221no—
167#387—1221no—
168#387—1221no—
169#383—1221no—
170C43C2×D6111yescharacteristic
171#336—21no—
172#336—612no—
173#336—1221no—
174#336C2×D6112yes—
175C61#773311yescharacteristic, complemented, Sylow
176C22×Q8—611no—
177C22×C8—22no—
178C22×C8—1222no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4—1221no—
185C2×C42C4×D6111yescharacteristic
186C2×C42C4×D6111yescharacteristic
187C2×C42D24411yescharacteristic
188C2×C42D24411yescharacteristic
189C2×C42C22⋊D6111yescharacteristic
190C2×C42C22⋊D6111yescharacteristic
191C2×C42C22×D6111yescharacteristic
192C4⋊C8—42no—
193C4⋊C8—2442no—
194#95—1221no—
195#95—1221no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203C2×Q8—1222no—
204C2×Q8—2441no—
205C2×Q8—2441no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4#1175819811yescharacteristic
211C22×C4#1175819811yescharacteristic
212C22×C4#1175819811yescharacteristic
213C22×C4#1175819811yescharacteristic
214C22×C4C2×C4×D6111yescharacteristic
215C22×C4C2×D24411yescharacteristic
216C22×C4C2×C22⋊D6111yescharacteristic
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—2442no—
221C2×C8—2442no—
222C2×C8—2442no—
223C4⋊C4—1222no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C42—21no—
231C42—22no—
232C42—21no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42#1175819012yes—
238C42Dic24412yes—
239C23C2×#1175819811yescharacteristic
240Q8—4882no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4#1451970212yes—
270C2×C4#1451970212yes—
271C2×C4#1451978512yes—
272C2×C4C2×#1175819011yescharacteristic
273C2×C4C2×Dic24411yescharacteristic
274C2×C4#1451980311yescharacteristic
275C2×C4#1451980811yescharacteristic
276C8—82no—
277C8—4882no—
278C22#1683973011yescharacteristic
279C22#1683973511yescharacteristic
280C22#1683974411yescharacteristic
281C22C2×#1451970211yescharacteristic
282C22#1683976111yescharacteristic
283C22#1683977811yescharacteristic
284C22#1683978011yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—41no—
294C4—4881no—
295C4—4881no—
296C4—4881no—
297C4—4881no—
298C2#2144418911yescharacteristic
299C2#2144422311yescharacteristic
300C2#2144428211yescharacteristic
301C2#2144435511yescharacteristic
302C2#2144438411yescharacteristic
303C2#2144445111yescharacteristic
304C2#2144450711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1831C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1831D61
hypocenterC61#7733
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
175. C61#7733semidirect

Maximal subgroups

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

subgroupindex
#214542012
#214459362
#214436442
#214436432
C61×#18312
#773361