Finite Group Databasebeta

← #30594759

Subgroups — #30594759

Order 15616.

338 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461945C211yesmaximal, characteristic
2#21461682C211yesmaximal, characteristic
3#21444156C211yesmaximal, characteristic
4C2×#14519844C411yescharacteristic, complemented
5C2×#14519836C412yes—
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×#14519832C411yescharacteristic, complemented
9#16840704—21no—
10#16840640—21no—
11C2×#14519739C2211yescharacteristic
12#16839724—21no—
13#16839488C411yescharacteristic, complemented
14#16839485—21no—
15C61×#324C411yescharacteristic, complemented
16C22×#92420—21no—
17C22×#92420—21no—
18C2×C4⋊#6923—41no—
19C2×C22⋊#6923—22no—
20#14519844—41no—
21#14519836—42no—
22#14519834—42no—
23#14519834—42no—
24#14519832—41no—
25(C2×#6923)⋊C4—41no—
26C22×D244C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C2×#11758189—41no—
30#14519739—41no—
31#14519739—41no—
32C2×#11758198D411yescharacteristic
33C2×#11758198Q811yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C22⋊#92418—21no—
36#14519689—41no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C22⋊C8×C61—21no—
39C23×D61C22⋊C411yescharacteristic
40C23×D61C4⋊C411yescharacteristic
41C22×#6923—42no—
42C22×C4×C61C4211yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C4⋊C411yescharacteristic
45C22×Dic61C22⋊C411yescharacteristic
46C22×Dic61C4⋊C411yescharacteristic
47C2×D244—21no—
48C2×D244—21no—
49C2×D244—41no—
50C2×D244—41no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57C2×C4×D61—41no—
58C2×C4×D61—41no—
59C22⋊#6923—42no—
60C22⋊#6923—42no—
61C2×#92420—22no—
62C2×#92420—41no—
63C2×#92420—41no—
64C2×#92420—41no—
65C2×#92420—41no—
66C2×#92420—41no—
67C4⋊#6923—81no—
68C4⋊#6923—81no—
69C2×C8×C61—41no—
70C4⋊C4×C61—41no—
71#11758198—41no—
72#11758198—41no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C2×#92418—41no—
76#11758189—81no—
77#11758189—81no—
78C23×C61#9511yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—41no—
85C22×D61—41no—
86C22×D61—41no—
87C22×D61—41no—
88C22×D61#10011yescharacteristic
89C22×D61#10111yescharacteristic
90C2×#6923—82no—
91C2×#6923—82no—
92C2×#6923—82no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61#9911yescharacteristic
105C2×Dic61#9911yescharacteristic
106D244—42no—
107D244—42no—
108C4×D61—41no—
109C4×D61—41no—
110C4×D61—41no—
111C4×D61—41no—
112C4×D61—81no—
113C4×D61—81no—
114#92420—42no—
115#92420—81no—
116C8×C61—81no—
117#92418—81no—
118#7322—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61#34211yescharacteristic
122C22×C61#34311yescharacteristic
123C22×C61#34411yescharacteristic
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—42no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—81no—
135C2×D61—81no—
136#6923—162no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61—41no—
140Dic61—21no—
141Dic61—41no—
142Dic61#35311yescharacteristic
143Dic61#35411yescharacteristic
144#1955—611no—
145#1799—611no—
146#1465—611no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#130511yescharacteristic
150C2×C61#139311yescharacteristic
151C2×C61#139511yescharacteristic
152D61—41no—
153D61—41no—
154D61—81no—
155C2×C4×D4—611no—
156C2×C4⋊C8—611no—
157C2×#99—612no—
158#407—1221no—
159C2×C22⋊C8—1221no—
160C2×C22⋊C8—1221no—
161C2×#97—611no—
162#380—1221no—
163#342—1221no—
164#324—611no—
165#324#692311yescharacteristic, complemented
166#323—1221no—
167C61#732211yescharacteristic, complemented, Sylow
168C22×D4—611no—
169C23×C4—611no—
170C23×C4—611no—
171C2×M16—2441no—
172C22×C8—1221no—
173C22×C8—1221no—
174C4×D4—2441no—
175C4×D4—2441no—
176C2×C4⋊C4—2441no—
177C2×C4⋊C4C2×#692311yescharacteristic
178C2×C22⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—1222no—
181C2×C42—611no—
182C4⋊C8—2441no—
183#99—2442no—
184C22⋊C8—21no—
185C22⋊C8—1221no—
186C22⋊C8—2441no—
187C22⋊C8—2442no—
188C22⋊C8—2442no—
189#97—2441no—
190#95—2441no—
191C24—611no—
192C24—611no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4—2441no—
196C2×D4—2441no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—1221no—
200C22×C4—1221no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—2441no—
204C22×C4—2441no—
205C22×C4—2441no—
206C22×C4—2441no—
207C22×C4—2442no—
208C22×C4C4×#692311yescharacteristic
209C22×C4C4⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211M16—4881no—
212M16—4881no—
213C2×C8—41no—
214C2×C8—1222no—
215C2×C8—2441no—
216C2×C8—2441no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8—2441no—
220C2×C8—2441no—
221C4⋊C4—41no—
222C4⋊C4—4881no—
223C4⋊C4—4881no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C22⋊C4—2442no—
227C22⋊C4—2442no—
228C42—1221no—
229C42—1221no—
230C23—611no—
231C23—611no—
232C23—1221no—
233C23—1221no—
234C23—1221no—
235C23—1221no—
236C23—1221no—
237C23—2441no—
238C23—2441no—
239C23—2441no—
240C23—2441no—
241C23(C2×#6923)⋊C411yescharacteristic
242D4—2442no—
243D4—2442no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—4881no—
257C2×C4—4881no—
258C2×C4—4882no—
259C2×C4—4882no—
260C2×C4—4882no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2441no—
266C8—81no—
267C8—4881no—
268C8—4881no—
269C8—2442no—
270C22—21no—
271C22—21no—
272C22—1221no—
273C22—1221no—
274C22—4881no—
275C22—4881no—
276C22—2442no—
277C22—2441no—
278C22—2441no—
279C22—2441no—
280C22—2441no—
281C22—2441no—
282C22—2441no—
283C22—2441no—
284C22#1684063911yescharacteristic
285C22#1684064111yescharacteristic
286C22#1684064411yescharacteristic
287C4—41no—
288C4—41no—
289C4—41no—
290C4—611no—
291C4—611no—
292C4—1221no—
293C4—9762no—
294C4—2441no—
295C2—21no—
296C2—21no—
297C2—4881no—
298C2—2441no—
299C2—2441no—
300C2#2146072111yescharacteristic
301C2#2146091211yescharacteristic
302C2#2146092111yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC22×D244C2×C4
cosocleC2×#14519739C22
hypercenter#324#6923
hypocenterC61#7322
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
4. C2×#14519844C4semidirect
8. C2×#14519832C4semidirect
13. #16839488C4semidirect
15. C61×#324C4semidirect
165. #324#6923semidirect
167. C61#7322semidirect

Maximal subgroups

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

subgroupindex
#214619452
#214616822
#214441562
#732261