Finite Group Databasebeta

← #30599280

Subgroups — #30599280

Order 15616.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461546C211yesmaximal, characteristic
2#21461546C211yesmaximal, characteristic
3#21460695C214yesmaximal, complemented
4#21448224C211yesmaximal, characteristic
5C2×#14519834—21no—
6C2×#14519834—21no—
7C2×#14519832C2212yes—
8C2×#14519832C2212yes—
9#16840628—21no—
10#16840628—21no—
11C2×#14519735C412yes—
12C2×C42×D61C2211yescharacteristic
13#16839632C411yescharacteristic
14#16839627C2212yes—
15#16839619—21no—
16#16839619—21no—
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61—21no—
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519834—24no—
23#14519834—24no—
24#14519832—24no—
25#14519832—24no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519735—44no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61C2×C412yes—
33C2×#11758198—22no—
34C2×C4×Dic61—22no—
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61C2311yescharacteristic
38C42×D61—24no—
39#14519684—22no—
40#14519684—22no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61C2×C412yes—
44C2×C42×C61C2×C411yescharacteristic
45C23×D61C22⋊C411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C2×D411yescharacteristic
53C22×Dic61C2×D411yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—41no—
62C2×C4×D61—41no—
63C2×#92420—24no—
64C2×#92420—24no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—42no—
72C42×C61—22no—
73#11758198—44no—
74C4⋊Dic61—42no—
75C4⋊Dic61—42no—
76C4⋊Dic61—42no—
77C4×Dic61—22no—
78C4×Dic61—22no—
79C4×Dic61—44no—
80C4×Dic61#4114yes—
81C23×C61C2×C22⋊C411yescharacteristic
82C22×D61—21no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61#10012yes—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61#10412yes—
99C2×C4×C61#10412yes—
100C2×C4×C61#11712yes—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61#10112yes—
111C2×Dic61#12312yes—
112C2×Dic61#12312yes—
113C4×D61—28no—
114C4×D61—44no—
115C4×D61—44no—
116#92420—44no—
117#92420—44no—
118#8722—611nomaximal, Sylow
119C22×C61#38111yescharacteristic
120C22×C61C2×#10011yescharacteristic
121C22×C61C2×#10111yescharacteristic
122C22×C61C2×#10411yescharacteristic
123C22×C61C2×#10411yescharacteristic
124C22×C61#42111yescharacteristic
125C22×C61#42111yescharacteristic
126C2×D61—22no—
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C4×C61—22no—
134C4×C61—22no—
135C4×C61—22no—
136C4×C61—82no—
137Dic61—22no—
138Dic61—22no—
139Dic61—22no—
140Dic61—82no—
141#2285—611no—
142#1749—611no—
143#1749—611no—
144#1295—614no—
145C2×C61#152611yescharacteristic
146C2×C61#153011yescharacteristic
147C2×C61#153011yescharacteristic
148C2×C61#153711yescharacteristic
149C2×C61#182111yescharacteristic
150C2×C61#182611yescharacteristic
151C2×C61#182611yescharacteristic
152D61—42no—
153C2×#117—612no—
154C22×C42—611no—
155C2×C22⋊C8—1221no—
156C2×C22⋊C8—1221no—
157C2×#97—612no—
158C2×#97—612no—
159#384—611no—
160#384#692311yescharacteristic
161#382—612no—
162#380—1221no—
163#380—1221no—
164C4×C4⋊C4—1221no—
165C4×C4⋊C4—1221no—
166#336—1221no—
167#336—1221no—
168C61#872211yescharacteristic, complemented, Sylow
169C23×C4—611no—
170C23×C4—611no—
171C23×C4—611no—
172C22×C8—1222no—
173C22×C8—1222no—
174#117—2444no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4C2×#692312yes—
181C2×C22⋊C4—1222no—
182C2×C42—611no—
183C2×C42—611no—
184C2×C42—611no—
185C2×C42—1224no—
186C2×C42—1222no—
187C2×C42C2×#692311yescharacteristic
188C22⋊C8—1224no—
189C22⋊C8—1224no—
190#97—1224no—
191#97—1224no—
192#95—1222no—
193#95—1222no—
194C24—611no—
195C22×C4—22no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—1222no—
200C22×C4—1222no—
201C22×C4—1222no—
202C22×C4—1222no—
203C22×C4—1222no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—1222no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22×#692311yescharacteristic
212C2×C8—1224no—
213C2×C8—1224no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—2442no—
222C4⋊C4—2442no—
223C4⋊C4—2442no—
224C22⋊C4—2444no—
225C42—22no—
226C42—614no—
227C42—1222no—
228C42—1222no—
229C42—2444no—
230C23—612no—
231C23—1221no—
232C23—1221no—
233C23—1221no—
234C23—1221no—
235C23—1221no—
236C23—1221no—
237C23C2×C22⋊#692311yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—612no—
248C2×C4—612no—
249C2×C4—612no—
250C2×C4—1228no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—2444no—
258C2×C4—2444no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4#1451984112yes—
263C2×C4#1451984212yes—
264C2×C4#1451985612yes—
265C8—2444no—
266C8—2444no—
267C22—1222no—
268C22—1222no—
269C22—1222no—
270C22—2441no—
271C22—2441no—
272C22—2441no—
273C22—2441no—
274C22#1684070511yescharacteristic
275C22D61⋊#10011yescharacteristic
276C22D61⋊#10111yescharacteristic
277C22C2×#1451984111yescharacteristic
278C22C2×#1451984211yescharacteristic
279C22#1684076011yescharacteristic
280C22#1684076111yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—82no—
285C4—1222no—
286C4—1222no—
287C4—1222no—
288C4—4882no—
289C2—2442no—
290C2#2146127711yescharacteristic
291C2#2146128911yescharacteristic
292C2#2146129011yescharacteristic
293C2#2146131111yescharacteristic
294C2#2146171911yescharacteristic
295C2#2146172511yescharacteristic
296C2#2146172611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8722
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #21460695C2semidirect
168. C61#8722semidirect

Maximal subgroups

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

subgroupindex
#214615462
#214606952
#214482242
#872261