Finite Group Databasebeta

← #29568358

Subgroups — #29568358

Order 15616.

370 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454206C211yesmaximal, characteristic
2#21445962C211yesmaximal, characteristic
3#21443643C212yesmaximal
4#21443641C212yesmaximal
5C61×#1744C211yesmaximal, characteristic
6#16839660C411yescharacteristic
7#16839660C411yescharacteristic
8#16839660C2211yescharacteristic
9#16839660C2211yescharacteristic
10#16839646—21no—
11#16839646—21no—
12#16839646—21no—
13#16839646—21no—
14#16839628C411yescharacteristic
15#16839628C411yescharacteristic
16#16839517—21no—
17#16839517—21no—
18#16839517C2212yes—
19C2×C4×C8×C61—21no—
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336C2212yes—
23C22×#92418—22no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32#14519684—21no—
33#14519684—21no—
34#14519684—21no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40C22×C8×C61—22no—
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61D411yescharacteristic
45C2×C42×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61C2311yescharacteristic
48C4×C8×C61—24no—
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22×C411yescharacteristic
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C2×C8×C61—24no—
61C2×C8×C61—42no—
62C2×C8×C61—42no—
63C42×C61—22no—
64C42×C61—22no—
65C42×C61—22no—
66C42×C61—22no—
67C42×C61—22no—
68C42×C61—41no—
69C42×C61—41no—
70C4⋊Dic61—22no—
71C4⋊Dic61—22no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74#11758196—42no—
75#11758196—42no—
76#11758196—42no—
77#11758196—42no—
78C2×#92418—42no—
79C2×#92418—42no—
80C2×#92418—42no—
81C23×C61C2×C22⋊C411yescharacteristic
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
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#10112yes—
99C2×C4×C61#10412yes—
100C2×C4×C61#13112yes—
101C2×C4×C61#13512yes—
102C2×C4×C61#13512yes—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C8×C61—44no—
116#92418—82no—
117#7657—611nomaximal, Sylow
118C22×C61#40811yescharacteristic
119C22×C61#41011yescharacteristic
120C22×C61C2×#10111yescharacteristic
121C22×C61#41611yescharacteristic
122C22×C61#41611yescharacteristic
123C22×C61C2×#10411yescharacteristic
124C22×C61#42111yescharacteristic
125C4×C61—22no—
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—41no—
131C4×C61—41no—
132Dic61—81no—
133Dic61—81no—
134Dic61—81no—
135Dic61—81no—
136#2864—611no—
137#1839—611no—
138#1744D6111yescharacteristic
139#1271—612no—
140#1271—612no—
141C2×C61#147011yescharacteristic
142C2×C61#148211yescharacteristic
143C2×C61#149411yescharacteristic
144C2×C61#150011yescharacteristic
145C2×C61#152111yescharacteristic
146C2×C61#153111yescharacteristic
147C2×C61#154411yescharacteristic
148C2×C4×C8—21no—
149#389—611no—
150#389—611no—
151#389—611no—
152#389—611no—
153#387—1221no—
154#387—1221no—
155#387—1221no—
156#387—1221no—
157#382—611no—
158#382—611no—
159C43C2×D6111yescharacteristic
160#336—21no—
161#336—612no—
162#336—1221no—
163#336—1221no—
164#336C2×D6112yes—
165C61#765711yescharacteristic, complemented, Sylow
166C22×C8—22no—
167C22×C8—1222no—
168C2×C4⋊C4—611no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4—1221no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4—1221no—
176C2×C42C4×D6111yescharacteristic
177C2×C42C4×D6111yescharacteristic
178C2×C42D24411yescharacteristic
179C2×C42D24411yescharacteristic
180C2×C42C22⋊D6111yescharacteristic
181C2×C42C22⋊D6111yescharacteristic
182C2×C42C22×D6111yescharacteristic
183C4×C8—24no—
184#95—1221no—
185#95—1221no—
186#95—1221no—
187#95—1221no—
188#95—1221no—
189#95—1221no—
190#95—1221no—
191#95—1221no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1221no—
196C22×C4#1175819811yescharacteristic
197C22×C4#1175819811yescharacteristic
198C22×C4#1175819811yescharacteristic
199C22×C4#1175819811yescharacteristic
200C22×C4C2×C4×D6111yescharacteristic
201C22×C4C2×D24411yescharacteristic
202C22×C4C2×C22⋊D6111yescharacteristic
203C2×C8—24no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—2442no—
207C2×C8—2442no—
208C2×C8—2442no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C4⋊C4—2442no—
214C4⋊C4—2442no—
215C4⋊C4—2442no—
216C4⋊C4—2442no—
217C42—22no—
218C42—22no—
219C42—22no—
220C42—22no—
221C42—22no—
222C42—41no—
223C42—41no—
224C23C2×#1175819811yescharacteristic
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451969512yes—
254C2×C4#1451970512yes—
255C2×C4#1451978312yes—
256C2×C4#1451979712yes—
257C2×C4#1451979912yes—
258C8—44no—
259C8—4882no—
260C22#1683972811yescharacteristic
261C22#1683973511yescharacteristic
262C22C2×#1451969511yescharacteristic
263C22#1683975611yescharacteristic
264C22#1683975911yescharacteristic
265C22C2×#1451970511yescharacteristic
266C22#1683977811yescharacteristic
267C4—22no—
268C4—22no—
269C4—22no—
270C4—22no—
271C4—22no—
272C4—41no—
273C4—41no—
274C4—4881no—
275C4—4881no—
276C4—4881no—
277C4—4881no—
278C2#2144417411yescharacteristic
279C2#2144422511yescharacteristic
280C2#2144428011yescharacteristic
281C2#2144430311yescharacteristic
282C2#2144439711yescharacteristic
283C2#2144443311yescharacteristic
284C2#2144448311yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1744C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1744D61
hypocenterC61#7657
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
165. C61#7657semidirect

Maximal subgroups

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

subgroupindex
#214542062
#214459622
#214436432
#214436412
C61×#17442
#765761