Finite Group Databasebeta

← #30595817

Subgroups — #30595817

Order 15616.

378 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 90 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#21461734C211yesmaximal, characteristic
2#21461604C211yesmaximal, characteristic
3#21460638C212yesmaximal
4#21460637C212yesmaximal
5#21454205C211yesmaximal, characteristic
6C2×#14519844—21no—
7C2×C4⋊#92420—21no—
8C2×#14519832—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12#16839661C2211yescharacteristic
13#16839660C411yescharacteristic
14#16839658C2211yescharacteristic
15#16839648—21no—
16#16839647—21no—
17#16839644—21no—
18#16839643—21no—
19#16839627C411yescharacteristic
20#16839627C411yescharacteristic
21C42×Dic61C2211yescharacteristic
22C61×#389C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25#14519844—24no—
26C4⋊#92420—42no—
27#14519832—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C42×C61C2×C411yescharacteristic
50#95×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C22⋊C411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C22×Dic61C2×D411yescharacteristic
62C2×#92420—24no—
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—42no—
66C2×#92420—42no—
67C2×#92420—42no—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—41no—
71C42×C61—22no—
72C4⋊Dic61—22no—
73C4⋊Dic61—41no—
74C4⋊Dic61—41no—
75C4⋊Dic61—41no—
76#11758196—42no—
77#11758196—41no—
78#11758196—41no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—21no—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C23×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61—21no—
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—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61#10412yes—
102C2×C4×C61#13112yes—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61#10112yes—
119C2×Dic61AGL(1,ℤ/8)11yescharacteristic
120C2×Dic61AGL(1,ℤ/8)11yescharacteristic
121C2×Dic61#13711yescharacteristic
122C2×Dic61#13711yescharacteristic
123#92420—44no—
124#92420—82no—
125#7697—611nomaximal, Sylow
126C22×C61#40811yescharacteristic
127C22×C61#41011yescharacteristic
128C22×C61C2×#10111yescharacteristic
129C22×C61#41711yescharacteristic
130C22×C61#41711yescharacteristic
131C22×C61C2×#10411yescharacteristic
132C22×C61#42111yescharacteristic
133C4×C61—22no—
134C4×C61—22no—
135C4×C61—41no—
136C4×C61—81no—
137C4×C61—81no—
138Dic61—21no—
139Dic61—21no—
140Dic61—21no—
141Dic61—21no—
142Dic61—22no—
143Dic61—41no—
144Dic61—81no—
145Dic61—81no—
146#2864—611no—
147#1831—611no—
148#1767—611no—
149#1271—612no—
150#1271—612no—
151C2×C61#147011yescharacteristic
152C2×C61#148311yescharacteristic
153C2×C61#149511yescharacteristic
154C2×C61#150911yescharacteristic
155C2×C61#151211yescharacteristic
156C2×C61#153111yescharacteristic
157C2×C61#156111yescharacteristic
158C2×C4⋊C8—1221no—
159C2×C4⋊C8—1221no—
160C2×#97—1221no—
161#389—611no—
162#389—611no—
163#389—611no—
164#389#692311yescharacteristic
165#387—1221no—
166#387—1221no—
167#387—1221no—
168#387—1221no—
169#382—611no—
170#382—611no—
171C43—611no—
172#336—612no—
173#336—612no—
174#336—1221no—
175C61#769711yescharacteristic, complemented, Sylow
176C22×C8—1222no—
177C22×C8—1222no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C4⋊C4C2×#692311yescharacteristic
185C2×C4⋊C4C2×#692311yescharacteristic
186C2×C42—611no—
187C2×C42—611no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42C2×#692311yescharacteristic
193C4⋊C8—1224no—
194C4⋊C8—2442no—
195#97—2442no—
196#95—21no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4C22⋊#692311yescharacteristic
213C22×C4C22⋊#692311yescharacteristic
214C22×C4C22×#692311yescharacteristic
215C2×C8—1224no—
216C2×C8—2442no—
217C2×C8—2442no—
218C2×C8—2442no—
219C2×C8—2442no—
220C2×C8—2442no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—1222no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2442no—
231C42—22no—
232C42—1221no—
233C42—1221no—
234C42—1222no—
235C42—1221no—
236C42—1221no—
237C42—1222no—
238C42—2441no—
239C42—2441no—
240C23C2×C22⋊#692311yescharacteristic
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—612no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4#1451984212yes—
275C2×C4#1451986412yes—
276C8—4882no—
277C8—2444no—
278C22#1684073511yescharacteristic
279C22#1684074111yescharacteristic
280C22D61⋊#10111yescharacteristic
281C22#1684075311yescharacteristic
282C22#1684075311yescharacteristic
283C22C2×#1451984211yescharacteristic
284C22#1684076011yescharacteristic
285C4—22no—
286C4—22no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—1222no—
291C4—1221no—
292C4—1221no—
293C4—1221no—
294C4—1221no—
295C4—4881no—
296C4—4881no—
297C4—2441no—
298C2#2146109111yescharacteristic
299C2#2146113611yescharacteristic
300C2#2146117411yescharacteristic
301C2#2146122311yescharacteristic
302C2#2146123011yescharacteristic
303C2#2146129311yescharacteristic
304C2#2146135911yescharacteristic
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#7697
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
175. C61#7697semidirect

Maximal subgroups

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

subgroupindex
#214617342
#214616042
#214606382
#214606372
#214542052
#769761