Finite Group Databasebeta

← #30605288

Subgroups — #30605288

Order 15616.

382 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461717C211yesmaximal, characteristic
2#21461053C211yesmaximal, characteristic
3#21460816C212yesmaximal
4#21460800C212yesmaximal
5#21451520C211yesmaximal, characteristic
6#16840779—21no—
7#16840705—21no—
8#16840640—21no—
9#16840640C2212yes—
10#16840607—21no—
11#16840606C2212yes—
12C2×#14519768C411yescharacteristic, complemented
13C2×#14519735C2211yescharacteristic
14#16839697C2211yescharacteristic
15#16839692C411yescharacteristic, complemented
16#16839689C2211yescharacteristic
17#16839659—21no—
18#16839651—21no—
19#16839649—21no—
20#16839636—21no—
21#16839607C411yescharacteristic, complemented
22C61×#400C411yescharacteristic, complemented
23C2×C22⋊#6923—22no—
24#14519844—41no—
25C22⋊#92420—22no—
26C4×#92420—41no—
27(C2×#6923)⋊C4—41no—
28(C2×#6923)⋊C4—41no—
29C22×C4×D61D411yescharacteristic
30#14519768—41no—
31#14519768—41no—
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198D411yescharacteristic
43C2×#11758198C2311yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53#95×C61—21no—
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56C23×D61C2×D411yescharacteristic
57C22×#6923—42no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×C4×D61—22no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—41no—
72C22⋊#6923—42no—
73C22⋊#6923—42no—
74C2×#92420—42no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77#11758198—41no—
78#11758198—41no—
79#11758198—42no—
80#11758198—42no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85#11758196—42no—
86#11758196—42no—
87#11758196—42no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—42no—
93C23×C61C2×C22⋊C411yescharacteristic
94C22×D61—21no—
95C22×D61—21no—
96C22×D61—41no—
97C22×D61—41no—
98C22×D61#13512yes—
99C2×#6923—82no—
100C2×#6923—82no—
101C2×#6923—82no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—22no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61#9911yescharacteristic
128C2×Dic61#9911yescharacteristic
129C4×D61—42no—
130C4×D61—42no—
131#92420—82no—
132#11846—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61C2×#9911yescharacteristic
136C22×C61#41611yescharacteristic
137C22×C61#42111yescharacteristic
138C2×D61—22no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—42no—
142C2×D61—81no—
143#6923—162no—
144C4×C61—41no—
145C4×C61—41no—
146C4×C61—41no—
147C4×C61—81no—
148C4×C61—81no—
149Dic61—21no—
150Dic61—21no—
151Dic61—42no—
152Dic61—41no—
153Dic61—41no—
154Dic61—81no—
155#2611—611no—
156#1820—611no—
157#1458—611no—
158#1352—612no—
159#1344—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61#151611yescharacteristic
163C2×C61#212311yescharacteristic
164C2×C61#212611yescharacteristic
165D61—42no—
166C2×#125—611no—
167C2×#117—611no—
168#431—1221no—
169#400#692311yescharacteristic, complemented
170#399—611no—
171#398—611no—
172#397—611no—
173#389—1221no—
174#388—1221no—
175#387—1221no—
176#385—1221no—
177#381—1221no—
178#376—611no—
179#342—612no—
180#342—1221no—
181#324—1221no—
182#323—612no—
183C61#1184611yescharacteristic, complemented, Sylow
184C23×C4—611no—
185#125—2441no—
186#125—2441no—
187#117—2441no—
188#117—2441no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4C2×#692311yescharacteristic
196C2×C4⋊C4C2×#692311yescharacteristic
197C2×C22⋊C4—611no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—1221no—
200C2×C22⋊C4—1221no—
201C2×C22⋊C4—1222no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—1221no—
205C4⋊C8—2441no—
206C22⋊C8—1222no—
207C4×C8—2441no—
208#95—21no—
209#95—21no—
210#95—611no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—2441no—
215#95—2441no—
216#95C2×#692311yescharacteristic
217C24—611no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—1222no—
226C22×C4—1221no—
227C22×C4—1221no—
228C22×C4—2441no—
229C22×C4—2442no—
230C22×C4C22⋊#692311yescharacteristic
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233C2×C8—2442no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2442no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2442no—
242C4⋊C4—2442no—
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C22⋊C4—2442no—
246C22⋊C4—2442no—
247C22⋊C4—2442no—
248C22⋊C4—2442no—
249C42—1221no—
250C42—1221no—
251C42—1221no—
252C42—1221no—
253C42—2442no—
254C23—612no—
255C23—1221no—
256C23—1221no—
257C23—2441no—
258C23—2441no—
259C23C2×C22⋊#692311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—611no—
274C2×C4—611no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1222no—
278C2×C4—1221no—
279C2×C4—1221no—
280C2×C4—4882no—
281C2×C4—4882no—
282C2×C4—4882no—
283C2×C4—2442no—
284C2×C4—2442no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C8—4882no—
293C22—21no—
294C22—21no—
295C22—1222no—
296C22—4881no—
297C22—2442no—
298C22—2441no—
299C22—2441no—
300C22D61⋊#9911yescharacteristic
301C22#1684075211yescharacteristic
302C22#1684076111yescharacteristic
303C4—41no—
304C4—41no—
305C4—41no—
306C4—81no—
307C4—81no—
308C4—1221no—
309C4—1221no—
310C4—9762no—
311C4—4881no—
312C4—2442no—
313C4—2441no—
314C4—2441no—
315C2—21no—
316C2—21no—
317C2—2442no—
318C2#2146124611yescharacteristic
319C2#2146208211yescharacteristic
320C2#2146209111yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC23×D61C2×D4
cosocleC2×#11758198C23
hypercenter#400#6923
hypocenterC61#11846
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
12. C2×#14519768C4semidirect
15. #16839692C4semidirect
21. #16839607C4semidirect
22. C61×#400C4semidirect
169. #400#6923semidirect
183. C61#11846semidirect

Maximal subgroups

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

subgroupindex
#214617172
#214610532
#214608162
#214608002
#214515202
#1184661