Finite Group Databasebeta

← #30605161

Subgroups — #30605161

Order 15616.

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

normal subgroups only

This group has 382 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#21461716C211yesmaximal, characteristic
2#21461072C211yesmaximal, characteristic
3#21460815C214yesmaximal
4#21451643C211yesmaximal, characteristic
5#16840782—21no—
6#16840705—21no—
7#16840640—21no—
8#16840640C2212yes—
9#16840608—21no—
10#16840606C2212yes—
11C2×#14519777C411yescharacteristic, complemented
12C2×#14519734C2211yescharacteristic
13#16839702C412yescomplemented
14#16839699C2212yes—
15#16839683—21no—
16#16839675—21no—
17#16839661—21no—
18#16839619—21no—
19C61×#382C411yescharacteristic, complemented
20C2×C22⋊#6923—22no—
21#14519844—41no—
22C22⋊#92420—22no—
23#14519832—41no—
24(C2×#6923)⋊C4—41no—
25(C2×#6923)⋊C4—41no—
26C22×Dic122—21no—
27C22×C4×D61D411yescharacteristic
28#14519777—41no—
29#14519777—41no—
30#14519734—41no—
31#14519734—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—22no—
34C2×C4⋊Dic61C2×C412yes—
35C2×#11758196C2×C411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×#11758198—22no—
38C2×#11758198D411yescharacteristic
39C2×#11758198C2311yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41#14519684—22no—
42#14519684—22no—
43C2×C4⋊C4×C61—21no—
44C2×C42×C61C2×C411yescharacteristic
45#95×C61—21no—
46#95×C61C2×C412yes—
47C23×D61C2×D411yescharacteristic
48C22×#6923—42no—
49C22×C4×C61—22no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C2×C4×D61—22no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—41no—
61C2×Dic122—42no—
62C2×Dic122—82no—
63C22⋊#6923—42no—
64C22⋊#6923—42no—
65C2×#92420—42no—
66C4⋊C4×C61—42no—
67C42×C61—21no—
68C42×C61—21no—
69#11758198—41no—
70#11758198—41no—
71#11758198—82no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74C4⋊Dic61—42no—
75C4⋊Dic61—82no—
76#11758196—41no—
77#11758196—41no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C23×C61C2×C22⋊C411yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—41no—
84C22×D61—41no—
85C22×D61#13712yes—
86C2×#6923—82no—
87C2×#6923—82no—
88C2×#6923—82no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61#9911yescharacteristic
99C2×C4×C61#9911yescharacteristic
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C4×D61—42no—
111C4×D61—42no—
112Dic122—84no—
113#92420—82no—
114#11813—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C2×#9911yescharacteristic
118C22×C61#41911yescharacteristic
119C22×C61#42111yescharacteristic
120C2×D61—22no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61—81no—
125#6923—162no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61—82no—
131Dic61—41no—
132Dic61—41no—
133Dic61—41no—
134Dic61—82no—
135#2628—611no—
136#1820—611no—
137#1464—611no—
138#1352—614no—
139C2×C61—21no—
140C2×C61—21no—
141C2×C61#151111yescharacteristic
142C2×C61#212311yescharacteristic
143C2×C61#212811yescharacteristic
144D61—42no—
145C2×C4⋊Q8—611no—
146C2×#117—611no—
147#432—1221no—
148#400—612no—
149#399—612no—
150#395—1221no—
151#393—1221no—
152#389—1221no—
153#382#692311yescharacteristic, complemented
154#381—1221no—
155#380—1221no—
156#342—612no—
157#342—1221no—
158#324—1221no—
159#323—612no—
160C61#1181311yescharacteristic, complemented, Sylow
161C22×Q8—1221no—
162C23×C4—611no—
163C4⋊Q8—2441no—
164C4⋊Q8—2441no—
165#117—2441no—
166#117—2441no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—611no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1222no—
172C2×C4⋊C4—1221no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4—611no—
175C2×C22⋊C4—1222no—
176C2×C22⋊C4—1222no—
177C2×C42—611no—
178C2×C42C2×#692311yescharacteristic
179C4⋊C8—2441no—
180C22⋊C8—1222no—
181#97—2441no—
182#95—21no—
183#95—1222no—
184#95—1222no—
185#95—2441no—
186#95—2441no—
187#95C2×#692312yes—
188C24—611no—
189C2×Q8—4882no—
190C2×Q8—2442no—
191C22×C4—22no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1222no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1222no—
199C22×C4—2441no—
200C22×C4—2442no—
201C22×C4C22⋊#692311yescharacteristic
202C22×C4C22⋊#692311yescharacteristic
203C22×C4C22×#692311yescharacteristic
204C2×C8—2442no—
205C4⋊C4—42no—
206C4⋊C4—4882no—
207C4⋊C4—2441no—
208C4⋊C4—2441no—
209C4⋊C4—2442no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C22⋊C4—4882no—
213C22⋊C4—2441no—
214C22⋊C4—2441no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C42—21no—
218C42—21no—
219C42—1221no—
220C42—1221no—
221C23—612no—
222C23—1221no—
223C23—1221no—
224C23—2441no—
225C23—2441no—
226C23C2×C22⋊#692311yescharacteristic
227Q8—4884no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1221no—
241C2×C4—1221no—
242C2×C4—4882no—
243C2×C4—4882no—
244C2×C4—4882no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4#1451983611yescharacteristic
253C2×C4#1451983611yescharacteristic
254C8—4882no—
255C22—21no—
256C22—21no—
257C22—1222no—
258C22—4881no—
259C22—2442no—
260C22—2441no—
261C22—2441no—
262C22C2×#1451983611yescharacteristic
263C22#1684075511yescharacteristic
264C22#1684076011yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—82no—
270C4—9762no—
271C4—4882no—
272C4—2441no—
273C4—2441no—
274C4—2441no—
275C2—21no—
276C2—21no—
277C2—2442no—
278C2#2146122711yescharacteristic
279C2#2146208311yescharacteristic
280C2#2146210011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radicalC23×D61C2×D4
cosocleC2×#11758198C23
hypercenter#382#6923
hypocenterC61#11813
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
11. C2×#14519777C4semidirect
13. #16839702C4semidirect
19. C61×#382C4semidirect
153. #382#6923semidirect
160. C61#11813semidirect

Maximal subgroups

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

subgroupindex
#214617162
#214610722
#214608152
#214516432
#1181361