Finite Group Databasebeta

← #29577848

Subgroups — #29577848

Order 15616.

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

normal subgroups only

This group has 518 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#21448422C211yesmaximal, characteristic
2#21445918C212yesmaximal
3#21444149C211yesmaximal, characteristic
4#21443671C212yesmaximal
5C61×#2484C211yesmaximal, characteristic
6#16839726C2212yes—
7#16839648—24no—
8#16839625—21no—
9#16839622—21no—
10C4×C22⋊Dic61C2212yes—
11#16839521—24no—
12#16839488—22no—
13C2×#117×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C61×#400C412yescomplemented
16C61×#398C412yescomplemented
17C61×#387—22no—
18C61×#385—21no—
19C61×#381—21no—
20C61×#381C2211yescharacteristic
21C2×#11758194—22no—
22C2×C4⋊Dic61—22no—
23C2×C22⋊Dic61—22no—
24C2×C4×Dic61D414yes—
25C22⋊#92418—22no—
26C22⋊#92418—22no—
27#14519684—22no—
28#14519684—24no—
29#14519684—22no—
30C23×C4×C61D411yescharacteristic
31C23×C4×C61D411yescharacteristic
32C23×C4×C61C2311yescharacteristic
33#117×C61—22no—
34#117×C61—22no—
35C2×C4⋊C4×C61—22no—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61—22no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C412yes—
41C2×C4⋊C4×C61D412yes—
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C42×C61—21no—
45#95×C61—22no—
46#95×C61—22no—
47#95×C61—22no—
48#95×C61—21no—
49#95×C61C2×C412yes—
50C24×C61C2×D411yescharacteristic
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—21no—
55C22×C4×C61—22no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—42no—
59C22×C4×C61—42no—
60C22×C4×C61—42no—
61C22×C4×C61C22⋊C412yes—
62C22×C4×C61C22⋊C412yes—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D412yes—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61#4112yes—
67C22×Dic61—24no—
68C4⋊C4×C61—24no—
69C4⋊C4×C61—24no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—44no—
73C22⋊C4×C61—42no—
74C22⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C42×C61—42no—
77C22⋊Dic61—44no—
78C4⋊Dic61—82no—
79C4×Dic61—44no—
80#11758194—44no—
81C2×#92418—42no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—41no—
85C23×C61C2×C22⋊C411yescharacteristic
86C23×C61#12011yescharacteristic
87C23×C61#12311yescharacteristic
88C2×C4×C61—24no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61—81no—
108C2×C4×C61C4×D412yes—
109C2×C4×C61#12112yes—
110C2×Dic61—44no—
111C2×Dic61—44no—
112C2×Dic61—44no—
113#92418—82no—
114#9482—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—44no—
123C22×C61#38611yescharacteristic
124C22×C61#42112yes—
125C22×C61#45812yes—
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—42no—
129C4×C61—42no—
130C4×C61—82no—
131C4×C61—81no—
132C4×C61—81no—
133Dic61—84no—
134#2484D6111yescharacteristic
135#2313—611no—
136#1826—612no—
137#1463—611no—
138#1284—612no—
139C2×C61—22no—
140C2×C61—22no—
141C2×C61—41no—
142C2×C61#189011yescharacteristic
143C2×C61#189711yescharacteristic
144C2×C61#191211yescharacteristic
145C2×#117C2×D6111yescharacteristic
146C22×C4⋊C4C2×D6111yescharacteristic
147#407—612no—
148#400Dic6112yescomplemented
149#398Dic6112yescomplemented
150#387—22no—
151#387—1224no—
152#385—21no—
153#381—21no—
154#381—1221no—
155#381C2×D6111yescharacteristic
156#380—1221no—
157C4×C22⋊C4—612no—
158#339—1224no—
159#324—1222no—
160C61#948211yescharacteristic, complemented, Sylow
161C23×C4C22⋊D6111yescharacteristic
162C23×C4C22⋊D6111yescharacteristic
163C23×C4C22×D6111yescharacteristic
164C2×M16—1222no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4C2×Dic6111yescharacteristic
172C2×C4⋊C4C2×Dic6111yescharacteristic
173C2×C4⋊C4C2×Dic6112yes—
174C2×C4⋊C4C22⋊D6112yes—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—1222no—
178C2×C42—21no—
179C2×C42—614no—
180C22⋊C8—1222no—
181C22⋊C8—1222no—
182#95—22no—
183#95—22no—
184#95—22no—
185#95—21no—
186#95—1222no—
187#95—1224no—
188#95—1222no—
189#95C2×Dic6112yes—
190C24C2×C22⋊D6111yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—1224no—
202C22×C4C22⋊Dic6112yes—
203C22×C4C22⋊Dic6112yes—
204C22×C4D4×D6112yes—
205C22×C4#1175822412yes—
206C22×C4C22×Dic6111yescharacteristic
207C22×C4C2×C22⋊D6111yescharacteristic
208M16—2444no—
209C2×C8—2442no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—4882no—
216C22⋊C4—42no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—2444no—
220C42—42no—
221C42—2444no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×C22⋊Dic6111yescharacteristic
226C23#1451974511yescharacteristic
227C23#1451975811yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—2444no—
249C2×C4—2444no—
250C2×C4—2444no—
251C2×C4D4×Dic6112yes—
252C2×C4#1451974912yes—
253C8—4882no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#1683964211yescharacteristic
263C22#1683977912yes—
264C22#1683995112yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—82no—
270C4—81no—
271C4—81no—
272C4—4884no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2#2144623311yescharacteristic
277C2#2144626811yescharacteristic
278C2#2144635711yescharacteristic
subgroupG/H
centerC22#16839642
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2484C2
socleC22×C61#386
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#2484D61
hypocenterC61#9482
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
15. C61×#400C4semidirect
16. C61×#398C4semidirect
148. #400Dic61semidirect
149. #398Dic61semidirect
160. C61#9482semidirect

Maximal subgroups

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

subgroupindex
#214484222
#214459182
#214441492
#214436712
C61×#24842
#948261