Finite Group Databasebeta

← #30595931

Subgroups — #30595931

Order 15616.

346 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 84 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#21461747C211yesmaximal, characteristic
2#21461747C211yesmaximal, characteristic
3#21460640C212yesmaximal
4#21460638C212yesmaximal
5#21454202C211yesmaximal, characteristic
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12#16839668C411yescharacteristic
13#16839667C411yescharacteristic
14#16839667C2211yescharacteristic
15#16839661C411yescharacteristic
16#16839658C2211yescharacteristic
17#16839648—21no—
18#16839645—21no—
19#16839643—21no—
20#16839629—21no—
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C22×Dic122C2×C411yescharacteristic
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61C2311yescharacteristic
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61C2×C411yescharacteristic
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C42×C61C2×C411yescharacteristic
47#95×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22×C411yescharacteristic
53C22×Dic61—21no—
54C22×Dic61—21no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C2×Dic122—22no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61—41no—
72C4⋊Dic61—22no—
73C4⋊Dic61—42no—
74#11758196—42no—
75C4×Dic61—22no—
76C4×Dic61—22no—
77C4×Dic61—22no—
78C4×Dic61—41no—
79C4×Dic61—41no—
80C4×Dic61—41no—
81C23×C61C2×C22⋊C411yescharacteristic
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61#13112yes—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61#13512yes—
114C2×Dic61#13712yes—
115Dic122—82no—
116#92420—82no—
117#92420—82no—
118#7729—611nomaximal, Sylow
119C22×C61#40811yescharacteristic
120C22×C61#41011yescharacteristic
121C22×C61#41311yescharacteristic
122C22×C61#41611yescharacteristic
123C22×C61#41911yescharacteristic
124C22×C61#42111yescharacteristic
125C22×C61#42111yescharacteristic
126C4×C61—22no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61—81no—
130C4×C61—81no—
131Dic61—22no—
132Dic61—22no—
133Dic61—41no—
134Dic61—41no—
135Dic61—81no—
136Dic61—81no—
137#2863—611no—
138#1839—611no—
139#1839—611no—
140#1272—612no—
141#1271—612no—
142C2×C61#147311yescharacteristic
143C2×C61#148211yescharacteristic
144C2×C61#149711yescharacteristic
145C2×C61#151511yescharacteristic
146C2×C61#152111yescharacteristic
147C2×C61#153511yescharacteristic
148C2×C61#155411yescharacteristic
149#391—611no—
150#391—611no—
151#391—611no—
152#389—611no—
153#389—611no—
154#389#692311yescharacteristic
155#387—1221no—
156#387—1221no—
157#387—1221no—
158#383—1221no—
159C43—611no—
160#336—612no—
161#336—612no—
162#336—1221no—
163#336—1221no—
164#336—1221no—
165#336—1221no—
166C61#772911yescharacteristic, complemented, Sylow
167C22×Q8—611no—
168C22×C8—1222no—
169C22×C8—1222no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—1221no—
173C2×C4⋊C4—1221no—
174C2×C4⋊C4C2×#692311yescharacteristic
175C2×C4⋊C4C2×#692311yescharacteristic
176C2×C42—611no—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—611no—
180C2×C42—611no—
181C2×C42—611no—
182C2×C42C2×#692311yescharacteristic
183#95—21no—
184#95—1221no—
185#95—1221no—
186#95—1221no—
187#95—1221no—
188#95—1221no—
189#95—1221no—
190#95—1221no—
191#95—1221no—
192C2×Q8—1222no—
193C2×Q8—2441no—
194C2×Q8—2441no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4C22⋊#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205C22×C4C22×#692311yescharacteristic
206C2×C8—2442no—
207C2×C8—2442no—
208C2×C8—2442no—
209C2×C8—2442no—
210C2×C8—2442no—
211C2×C8—2442no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—1222no—
216C4⋊C4—2442no—
217C4⋊C4—2442no—
218C42—41no—
219C42—1222no—
220C42—1222no—
221C42—1222no—
222C42—2441no—
223C42—2441no—
224C42—2441no—
225C23C2×C22⋊#692311yescharacteristic
226Q8—4882no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—612no—
242C2×C4—612no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4#1451986512yes—
260C8—4882no—
261C8—4882no—
262C22#1684073711yescharacteristic
263C22#1684074111yescharacteristic
264C22#1684074911yescharacteristic
265C22#1684075211yescharacteristic
266C22#1684075511yescharacteristic
267C22#1684075911yescharacteristic
268C22#1684076011yescharacteristic
269C4—22no—
270C4—41no—
271C4—41no—
272C4—81no—
273C4—81no—
274C4—1222no—
275C4—1222no—
276C4—4881no—
277C4—4881no—
278C4—2441no—
279C4—2441no—
280C2#2146110211yescharacteristic
281C2#2146113311yescharacteristic
282C2#2146118311yescharacteristic
283C2#2146124111yescharacteristic
284C2#2146126111yescharacteristic
285C2#2146130411yescharacteristic
286C2#2146134511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#389#6923
hypocenterC61#7729
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
166. C61#7729semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606402
#214606382
#214542022
#772961