Finite Group Databasebeta

← #30604322

Subgroups — #30604322

Order 15616.

462 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461081C211yesmaximal, characteristic, complemented
2#21461061C211yesmaximal, characteristic, complemented
3#21460747C214yesmaximal, complemented
4#21450822C211yesmaximal, characteristic
5#16840783—21no—
6#16840779—21no—
7#16840608—21no—
8#16840608—21no—
9#16840607C2212yes—
10#16840607C2212yes—
11C2×#14519764C412yes—
12C2×C4×Dic122C2211yescharacteristic
13#16839676—21no—
14#16839676—21no—
15#16839665—21no—
16#16839665—21no—
17#16839665C2212yes—
18C4×C4⋊Dic61C411yescharacteristic
19C2×#127×C61C411yescharacteristic
20#14519844—41no—
21C4⋊#92420—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24#14519832—41no—
25C4×#92420—41no—
26C22×Dic122C2×C411yescharacteristic
27#14519764—44no—
28C4×Dic122—41no—
29C4×Dic122—41no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2311yescharacteristic
32C2×#11758196D411yescharacteristic
33C2×#11758196D411yescharacteristic
34C2×C22⋊Dic61—22no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—22no—
38C2×C4×Dic61C2×C412yes—
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61D411yescharacteristic
41#14519684—21no—
42C22×D4×C61—21no—
43C22×D4×C61—21no—
44C22×D4×C61C2×C412yes—
45#127×C61—41no—
46#127×C61—41no—
47C2×C42×C61C2×C411yescharacteristic
48C24×C61—22no—
49C2×D4×C61—24no—
50C2×D4×C61—42no—
51C2×D4×C61—42no—
52C2×D4×C61—42no—
53C2×D4×C61—42no—
54C2×D4×C61—42no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C2×D4×C61—82no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—22no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—41no—
69C2×#92420—42no—
70C2×#92420—42no—
71C42×C61—21no—
72C42×C61—21no—
73C22⋊Dic61—44no—
74C22⋊Dic61—44no—
75C22⋊Dic61—82no—
76C22⋊Dic61—82no—
77C4⋊Dic61—41no—
78C4⋊Dic61—42no—
79#11758196—41no—
80#11758196—41no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C4×Dic61—42no—
86C23×C61—42no—
87C23×C61—42no—
88C23×C61—42no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61—42no—
92C23×C61—42no—
93C23×C61C2×C22⋊C411yescharacteristic
94D4×C61—84no—
95D4×C61—82no—
96D4×C61—84no—
97D4×C61—82no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61#9911yescharacteristic
104C2×C4×C61#9911yescharacteristic
105C2×C4×C61#13112yes—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61#10012yes—
119Dic122—44no—
120#92420—82no—
121#92420—82no—
122#11567—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—82no—
126C22×C61—82no—
127C22×C61—82no—
128C22×C61—82no—
129C22×C61—82no—
130C22×C61—82no—
131C22×C61—82no—
132C22×C61#40811yescharacteristic
133C22×C61C2×#9911yescharacteristic
134C22×C61C2×#10011yescharacteristic
135C4×C61—21no—
136C4×C61—22no—
137C4×C61—41no—
138C4×C61#35512yes—
139Dic61—22no—
140Dic61—41no—
141Dic61—41no—
142Dic61—41no—
143Dic61—82no—
144#2548—611no—
145#1467—611no—
146#1461—611no—
147#1318—614no—
148C2×C61—21no—
149C2×C61—21no—
150C2×C61—162no—
151C2×C61#147111yescharacteristic
152C2×C61#212811yescharacteristic
153C2×C61C2×#35511yescharacteristic
154C2×#127#692311yescharacteristic
155C2×#124—612no—
156C2×C4×Q8—611no—
157#432—1221no—
158#431—1221no—
159#394—1221no—
160#394—1221no—
161#390—612no—
162#390—1221no—
163#390—1221no—
164C4×C4⋊C4—611no—
165#324—612no—
166#324—612no—
167#324—1221no—
168#324—1221no—
169C61#1156711yescharacteristic, complemented, Sylow
170C22×Q8—611no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4C2×#692312yes—
174#127—41no—
175#127—41no—
176#124—2444no—
177C4×Q8—2441no—
178C4×Q8—2441no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1221no—
183C2×C22⋊C4—1222no—
184C2×C22⋊C4—1222no—
185C2×C22⋊C4—1222no—
186C2×C22⋊C4—1222no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—612no—
190C2×C42C2×#692311yescharacteristic
191C4⋊C8—2441no—
192C4⋊C8—2441no—
193C22⋊C8—1222no—
194C22⋊C8—1222no—
195#97—2441no—
196C4×C8—2441no—
197#95—1221no—
198C24—22no—
199C2×Q8—1222no—
200C2×Q8—1222no—
201C2×Q8—2441no—
202C2×D4—24no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—82no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—1222no—
216C22×C4C22⋊#692311yescharacteristic
217C22×C4C22⋊#692311yescharacteristic
218C22×C4C22×#692311yescharacteristic
219C2×C8—2442no—
220C2×C8—2442no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2442no—
225C22⋊C4—4882no—
226C22⋊C4—4882no—
227C22⋊C4—2444no—
228C22⋊C4—2444no—
229C42—21no—
230C42—21no—
231C42—1221no—
232C42—1221no—
233C42—1221no—
234C42—1221no—
235C42—2442no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23C2×C22⋊#692311yescharacteristic
244Q8—2444no—
245D4—84no—
246D4—82no—
247D4—84no—
248D4—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—612no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—2442no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4#1451983511yescharacteristic
268C2×C4#1451983511yescharacteristic
269C2×C4#1451986412yes—
270C8—4882no—
271C8—4882no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22#1684073611yescharacteristic
282C22C2×#1451983511yescharacteristic
283C22D61⋊#10011yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—1222no—
288C4—4882no—
289C4—2441no—
290C4—2441no—
291C4—2441no—
292C4#1684067012yes—
293C2—21no—
294C2—21no—
295C2—162no—
296C2#2146109411yescharacteristic
297C2#2146209811yescharacteristic
298C2C2×#1684067011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC22×C61C2×#99
cosocleC2×C4⋊Dic61C23
hypercenterC2×#127#6923
hypocenterC61#11567
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21461081C2semidirect
2. #21461061C2semidirect
3. #21460747C2semidirect
169. C61#11567semidirect

Maximal subgroups

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

subgroupindex
#214610812
#214610612
#214607472
#214508222
#1156761