Finite Group Databasebeta

← #30594555

Subgroups — #30594555

Order 15616.

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

normal subgroups only

This group has 344 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#21461678C211yesmaximal, characteristic
2#21461519C211yesmaximal, characteristic
3#21444132C211yesmaximal, characteristic
4C2×#14519856—21no—
5C2×#14519844C411yescharacteristic, complemented
6C2×C4⋊#92420C411yescharacteristic, complemented
7C2×#14519834—21no—
8#16840640—21no—
9#16840640C412yes—
10#16840628—21no—
11C2×#14519735C2211yescharacteristic
12#16839812—21no—
13#16839488C411yescharacteristic, complemented
14#16839485—21no—
15C61×#324C411yescharacteristic, complemented
16C22×#92420—21no—
17C22×#92420—21no—
18#14519856—22no—
19#14519856—22no—
20#14519856—41no—
21#14519856—41no—
22C2×C4⋊#6923—41no—
23C2×C22⋊#6923—22no—
24C2×C4×#6923—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519834—41no—
28#14519834—41no—
29C22×C4×D61D411yescharacteristic
30#14519735—41no—
31#14519735—41no—
32C2×C4⋊Dic61Q811yescharacteristic
33C2×#11758198C2×C411yescharacteristic
34C2×#11758198D411yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37#14519706—41no—
38C22⋊#92418—21no—
39C8×Dic61—41no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C22⋊C8×C61—21no—
42C23×D61C22⋊C411yescharacteristic
43C22×#6923—42no—
44C22×C4×C61C4211yescharacteristic
45C22×C4×C61C22⋊C411yescharacteristic
46C22×C4×C61C4⋊C411yescharacteristic
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C4⋊C411yescharacteristic
49C22×Dic61C4⋊C411yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61D811yescharacteristic
55C2×C4×D61SD1611yescharacteristic
56C2×C4×D61SD1611yescharacteristic
57C2×C4×D61Q1611yescharacteristic
58C22⋊#6923—24no—
59C22⋊#6923—42no—
60C2×#92420—41no—
61C2×#92420—41no—
62C2×#92420—41no—
63C2×#92420—41no—
64C2×#92420—41no—
65C2×#92420—41no—
66C4⋊#6923—42no—
67C4⋊#6923—42no—
68C4×#6923—42no—
69C4×#6923—42no—
70C2×C8×C61—41no—
71C4⋊C4×C61—41no—
72#11758198—41no—
73#11758198—41no—
74C4⋊Dic61—41no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C2×#92418—41no—
80C23×C61#9511yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—41no—
84C22×D61—41no—
85C22×D61#10211yescharacteristic
86C22×D61#10311yescharacteristic
87C2×#6923—44no—
88C2×#6923—82no—
89C2×#6923—82no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#10611yescharacteristic
97C2×C4×C61#10711yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61#9911yescharacteristic
103C2×Dic61#9911yescharacteristic
104C2×Dic61#10211yescharacteristic
105C2×Dic61#10311yescharacteristic
106C2×Dic61#10411yescharacteristic
107C2×Dic61#10411yescharacteristic
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—21no—
115C4×D61—21no—
116#92420—81no—
117#92420—81no—
118C8×C61—81no—
119#92418—81no—
120#7252—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#33911yescharacteristic
124C22×C61#34011yescharacteristic
125C22×C61#34211yescharacteristic
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—81no—
133#6923—84no—
134C4×C61—21no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138Dic61—41no—
139Dic61—41no—
140Dic61#32711yescharacteristic
141Dic61#32711yescharacteristic
142Dic61#32811yescharacteristic
143Dic61#32811yescharacteristic
144#1798—611no—
145#1740—611no—
146#1458—611no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#129411yescharacteristic
150C2×C61#139111yescharacteristic
151C2×C61#139511yescharacteristic
152D61—41no—
153D61—41no—
154C2×#117—611no—
155C2×#117—1221no—
156#431—1221no—
157C2×C4⋊C8—611no—
158C2×C4⋊C8—611no—
159C2×C22⋊C8—1221no—
160#342—612no—
161#342—1221no—
162#336—1221no—
163#324—611no—
164#324#692311yescharacteristic, complemented
165#323—1221no—
166C61#725211yescharacteristic, complemented, Sylow
167C23×C4—611no—
168C22×C8—1221no—
169C22×C8—1221no—
170#117—1222no—
171#117—1222no—
172#117—2441no—
173#117—2441no—
174#117—2441no—
175#117—2441no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—2441no—
178C2×C4⋊C4C2×#692311yescharacteristic
179C2×C22⋊C4—611no—
180C2×C22⋊C4—611no—
181C2×C22⋊C4—1222no—
182C2×C42—611no—
183C2×C42—611no—
184C2×C42—2441no—
185C4⋊C8—2441no—
186C4⋊C8—2441no—
187C4⋊C8—2441no—
188C22⋊C8—21no—
189C22⋊C8—1221no—
190C22⋊C8—2441no—
191C22⋊C8—2441no—
192C4×C8—2441no—
193C24—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—2442no—
206C22×C4C4×#692311yescharacteristic
207C22×C4C4⋊#692311yescharacteristic
208C22×C4C22⋊#692311yescharacteristic
209C2×C8—41no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8—2441no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8—2441no—
217C4⋊C4—41no—
218C4⋊C4—2441no—
219C4⋊C4—2442no—
220C4⋊C4—2442no—
221C22⋊C4—1224no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2442no—
225C42—1221no—
226C42—1221no—
227C42—1221no—
228C42—1221no—
229C42—2442no—
230C42—2442no—
231C23—611no—
232C23—611no—
233C23—1221no—
234C23—1221no—
235C23—2441no—
236C23—2441no—
237C23(C2×#6923)⋊C411yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—4882no—
261C2×C4—4882no—
262C2×C4—2444no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4#1451984511yescharacteristic
266C2×C4#1451984611yescharacteristic
267C8—81no—
268C8—4881no—
269C8—4881no—
270C8—4881no—
271C22—21no—
272C22—21no—
273C22—1221no—
274C22—1221no—
275C22—4881no—
276C22—2441no—
277C22—2441no—
278C22—2441no—
279C22—2441no—
280C22#1684063411yescharacteristic
281C22#1684063611yescharacteristic
282C22#1684063911yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—611no—
288C4—611no—
289C4—611no—
290C4—611no—
291C4—4884no—
292C4—2441no—
293C4—2441no—
294C2—21no—
295C2—21no—
296C2—2441no—
297C2—2441no—
298C2#2146069411yescharacteristic
299C2#2146090611yescharacteristic
300C2#2146092111yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC23×D61C22⋊C4
cosocleC2×#14519735C22
hypercenter#324#6923
hypocenterC61#7252
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
5. C2×#14519844C4semidirect
6. C2×C4⋊#92420C4semidirect
13. #16839488C4semidirect
15. C61×#324C4semidirect
164. #324#6923semidirect
166. C61#7252semidirect

Maximal subgroups

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

subgroupindex
#214616782
#214615192
#214441322
#725261