Finite Group Databasebeta

← #30594392

Subgroups — #30594392

Order 15616.

380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461794C211yesmaximal, characteristic
2#21461566C211yesmaximal, characteristic
3#21444138C211yesmaximal, characteristic
4C23×#92420C411yescharacteristic, complemented
5C2×#14519835C412yes—
6C2×#14519834—21no—
7C2×C22⋊#92420C411yescharacteristic, complemented
8C4×C22⋊#6923—21no—
9#16840640—21no—
10#16840628—21no—
11C2×#14519737C2211yescharacteristic
12#16839812—21no—
13#16839486C411yescharacteristic, complemented
14#16839485—21no—
15C61×#323C411yescharacteristic, complemented
16C22×#92420—21no—
17C22×#92420—21no—
18C22×#92420—42no—
19C22×#92420—41no—
20C2×C22⋊#6923—22no—
21C2×C4×#6923—41no—
22#14519835—22no—
23#14519835C814yescomplemented
24#14519834—42no—
25C22⋊#92420—41no—
26(C2×#6923)⋊C4—41no—
27C22×C22⋊D61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C22×C4×D61D411yescharacteristic
30#14519737—41no—
31#14519737—41no—
32C2×#11758196Q811yescharacteristic
33C2×#11758198D411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35#14519706—41no—
36C22⋊#92418—21no—
37C8×Dic61—41no—
38C2×C22⋊C4×C61C2×C411yescharacteristic
39C22⋊C8×C61—21no—
40C24×C61C4211yescharacteristic
41C23×D61C22⋊C411yescharacteristic
42C22×#6923—42no—
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C4⋊C411yescharacteristic
45C2×C22⋊D61—41no—
46C2×C22⋊D61—41no—
47C2×C22⋊D61C2×C812yes—
48C2×C22⋊D61M1612yes—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61—41no—
52C22×Dic61—41no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C4⋊C411yescharacteristic
55C22×Dic61C4⋊C411yescharacteristic
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—41no—
59C2×C4×D61—41no—
60C22⋊#6923—24no—
61C22⋊#6923—42no—
62C2×#92420—22no—
63C2×#92420—41no—
64C2×#92420—42no—
65C2×#92420—41no—
66C2×#92420—42no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×#92420—41no—
70C4×#6923—81no—
71C4×#6923—81no—
72C2×C8×C61—41no—
73C22⋊C4×C61—41no—
74#11758198—41no—
75#11758196—41no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C2×#92418—41no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—41no—
82C23×C61—41no—
83C23×C61#9511yescharacteristic
84C23×C61C4×C811yescharacteristic
85C23×C61#9711yescharacteristic
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—41no—
89C22×D61—41no—
90C22×D61C22⋊C812yes—
91C2×#6923—44no—
92C2×#6923—82no—
93C2×#6923—82no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C22⋊D61—42no—
99C22⋊D61—42no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—42no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61#9911yescharacteristic
110C2×Dic61#9911yescharacteristic
111C2×Dic61C4⋊C812yes—
112C4×D61—41no—
113C4×D61—41no—
114C4×D61—81no—
115#92420—42no—
116#92420—81no—
117C8×C61—81no—
118#92418—81no—
119#7204—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—42no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61#33611yescharacteristic
130C22×C61#34211yescharacteristic
131C22×C61#34411yescharacteristic
132C2×D61—22no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C2×D61—81no—
137#6923—84no—
138C4×C61—41no—
139C4×C61—41no—
140Dic61—22no—
141Dic61—21no—
142Dic61—41no—
143Dic61AΣL(1,𝔽16)11yescharacteristic
144Dic61#35211yescharacteristic
145#1869—611no—
146C4×#99—611no—
147#1460—611no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61—41no—
151C2×C61—41no—
152C2×C61#128211yescharacteristic
153C2×C61#139011yescharacteristic
154C2×C61#139111yescharacteristic
155D61—42no—
156C23×C8—611no—
157C2×C4×D4—611no—
158#431—1221no—
159C2×#99—612no—
160C2×C22⋊C8—611no—
161C2×C22⋊C8—1221no—
162C4×C22⋊C4—1221no—
163#342—1221no—
164#336—1221no—
165#323—611no—
166#323—1221no—
167#323#692311yescharacteristic, complemented
168C61#720411yescharacteristic, complemented, Sylow
169C22×D4—611no—
170C23×C4—611no—
171C23×C4—611no—
172C22×C8—1221no—
173C22×C8—1221no—
174C22×C8—2442no—
175C22×C8—2441no—
176C4×D4—2441no—
177C4×D4—2441no—
178C2×C4⋊C4—611no—
179C2×C22⋊C4—611no—
180C2×C22⋊C4—1222no—
181C2×C22⋊C4C2×#692311yescharacteristic
182C2×C42—611no—
183C2×C42—2441no—
184C4⋊C8—2441no—
185#99—614no—
186#99—1222no—
187C22⋊C8—21no—
188C22⋊C8—1221no—
189C22⋊C8—2442no—
190C22⋊C8—2441no—
191C4×C8—2441no—
192#95—2441no—
193C24—611no—
194C24C4×#692311yescharacteristic
195C2×D4—612no—
196C2×D4—612no—
197C2×D4—2441no—
198C2×D4—2441no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4—2441no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4—2441no—
210C22×C4—2442no—
211C22×C4C4⋊#692311yescharacteristic
212C22×C4C22⋊#692311yescharacteristic
213C2×C8—41no—
214C2×C8—1222no—
215C2×C8—2441no—
216C2×C8—2441no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8—2441no—
220C2×C8—2441no—
221C2×C8—2442no—
222C2×C8—2442no—
223C4⋊C4—2441no—
224C22⋊C4—41no—
225C22⋊C4—1224no—
226C22⋊C4—2441no—
227C22⋊C4—2442no—
228C42—1221no—
229C42—1221no—
230C42—4881no—
231C42—4881no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—612no—
237C23—1221no—
238C23—1221no—
239C23—2441no—
240C23—2441no—
241C23(C2×#6923)⋊C411yescharacteristic
242C23C8×#692311yescharacteristic
243C23#1451983111yescharacteristic
244D4—2442no—
245D4—2442no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—611no—
251C2×C4—612no—
252C2×C4—611no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—4881no—
259C2×C4—4882no—
260C2×C4—4882no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4—2442no—
266C2×C4—2444no—
267C2×C4—2441no—
268C8—81no—
269C8—4881no—
270C8—4881no—
271C8—2442no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—41no—
281C22—1222no—
282C22—4881no—
283C22—2442no—
284C22—2441no—
285C22—2441no—
286C22(C2×#6923)⋊C811yescharacteristic
287C22#1684063911yescharacteristic
288C22#1684064511yescharacteristic
289C4—41no—
290C4—41no—
291C4—611no—
292C4—611no—
293C4—1221no—
294C4—1222no—
295C4—4884no—
296C4—2441no—
297C2—21no—
298C2—21no—
299C2—41no—
300C2—41no—
301C2—2442no—
302C2#2146066011yescharacteristic
303C2#2146090511yescharacteristic
304C2#2146090611yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC23×C61C4×C8
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
prime radicalC22×C22⋊D61C2×C4
cosocleC2×#14519737C22
hypercenter#323#6923
hypocenterC61#7204
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
4. C23×#92420C4semidirect
7. C2×C22⋊#92420C4semidirect
13. #16839486C4semidirect
15. C61×#323C4semidirect
23. #14519835C8semidirect
167. #323#6923semidirect
168. C61#7204semidirect

Maximal subgroups

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

subgroupindex
#214617942
#214615662
#214441382
#720461