Finite Group Databasebeta

← #30605298

Subgroups — #30605298

Order 15616.

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

normal subgroups only

This group has 376 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#21461721C211yesmaximal, characteristic
2#21461051C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21451397C211yesmaximal, characteristic
6#16840779—21no—
7#16840732—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840605—21no—
12C2×#14519742C411yescharacteristic
13C2×#14519733C2211yescharacteristic
14#16839693C2211yescharacteristic
15#16839683C2211yescharacteristic
16#16839674C411yescharacteristic
17#16839655—21no—
18#16839645—21no—
19#16839644—21no—
20#16839634—21no—
21#16839629C411yescharacteristic
22C61×#397C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C22⋊#92420—22no—
26C22⋊#92420—41no—
27C22⋊#92420—41no—
28C4×#92420—41no—
29C22×Dic122C2×C411yescharacteristic
30C23×Dic61D411yescharacteristic
31#14519742—41no—
32#14519742—41no—
33#14519733—41no—
34#14519733—41no—
35C2×C4⋊Dic61—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196D411yescharacteristic
39C2×#11758196C2311yescharacteristic
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61D411yescharacteristic
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C22⋊C4×C61—21no—
53C2×C22⋊C4×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—22no—
65C22×Dic61—21no—
66C22×Dic61—41no—
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C2×Dic122—41no—
72C2×Dic122—42no—
73#11758217—42no—
74#11758217—42no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—41no—
78C22⋊C4×C61—41no—
79C22⋊C4×C61—42no—
80C22⋊Dic61—41no—
81C22⋊Dic61—42no—
82C4⋊Dic61—42no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—42no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—42no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61C2×C22⋊C411yescharacteristic
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#9911yescharacteristic
126C2×Dic61#9911yescharacteristic
127C2×Dic61#13512yes—
128Dic122—42no—
129Dic122—42no—
130#92420—82no—
131#92420—82no—
132#11849—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—42no—
136C22×C61—41no—
137C22×C61—41no—
138C22×C61—41no—
139C22×C61—81no—
140C22×C61C2×#9911yescharacteristic
141C22×C61#41611yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—81no—
146C4×C61—81no—
147Dic61—22no—
148Dic61—21no—
149Dic61—21no—
150Dic61—41no—
151Dic61—42no—
152Dic61—41no—
153Dic61—81no—
154#2599—611no—
155#1822—611no—
156#1458—611no—
157#1354—612no—
158#1346—612no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61—81no—
162C2×C61#151611yescharacteristic
163C2×C61#212011yescharacteristic
164C2×C61#213511yescharacteristic
165C2×C4×Q8—611no—
166C2×#117—611no—
167#431—1221no—
168#407—1221no—
169#398—611no—
170#397#692311yescharacteristic
171#395—611no—
172#393—611no—
173#388—1221no—
174#387—1221no—
175#387—1221no—
176#385—1221no—
177#383—611no—
178#343—612no—
179#343—1221no—
180#324—612no—
181#323—1221no—
182C61#1184911yescharacteristic, complemented, Sylow
183C22×Q8—611no—
184C23×C4—611no—
185C2×M16—1222no—
186C4×Q8—2441no—
187C4×Q8—2441no—
188#117—2441no—
189#117—2441no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4—1221no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4C2×#692311yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—1221no—
199C2×C22⋊C4C2×#692311yescharacteristic
200C2×C42—611no—
201C2×C42—611no—
202C2×C42—1221no—
203C4⋊C8—2441no—
204C22⋊C8—1222no—
205C22⋊C8—2441no—
206C22⋊C8—2441no—
207C4×C8—2441no—
208#95—21no—
209#95—611no—
210#95—1221no—
211#95—1221no—
212#95—1221no—
213#95—1221no—
214#95—1221no—
215#95C2×#692311yescharacteristic
216C24C22⋊#692311yescharacteristic
217C2×Q8—2441no—
218C2×Q8—2442no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—1221no—
226C22×C4—1221no—
227C22×C4—1222no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—2441no—
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233M16—2442no—
234M16—2442no—
235C2×C8—2442no—
236C2×C8—2442no—
237C4⋊C4—41no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2442no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C4⋊C4—2442no—
244C22⋊C4—41no—
245C22⋊C4—42no—
246C22⋊C4—2441no—
247C22⋊C4—2442no—
248C42—1221no—
249C42—1221no—
250C42—1221no—
251C42—1221no—
252C42—2442no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×C22⋊#692311yescharacteristic
259Q8—2442no—
260Q8—2442no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—612no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1222no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—2442no—
282C2×C4—2442no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C8—4882no—
291C8—4882no—
292C22—21no—
293C22—21no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22D61⋊#9911yescharacteristic
300C22#1684075211yescharacteristic
301C22#1684076011yescharacteristic
302C4—41no—
303C4—41no—
304C4—81no—
305C4—81no—
306C4—1222no—
307C4—1221no—
308C4—1221no—
309C4—4881no—
310C4—2441no—
311C4—2442no—
312C4—2441no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2#2146124411yescharacteristic
317C2#2146207311yescharacteristic
318C2#2146212211yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#397C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenter#397#6923
hypocenterC61#11849
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460803C2semidirect
182. C61#11849semidirect

Maximal subgroups

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

subgroupindex
#214617212
#214610512
#214608192
#214608032
#214513972
#1184961