Finite Group Databasebeta

← #30605698

Subgroups — #30605698

Order 15616.

314 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462153C211yesmaximal, characteristic, complemented
2#21461373C211yesmaximal, characteristic, complemented
3#21460835C212yesmaximal, complemented
4#21460831C212yesmaximal, complemented
5#21456384C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840765—21no—
8#16840683—21no—
9#16840683C2212yes—
10#16840624C2212yes—
11#16840623—21no—
12#16840293—21no—
13#16840163C2211yescharacteristic
14#16840145C2211yescharacteristic
15#16840115—21no—
16#16840003C411yescharacteristic
17#16839989—21no—
18#16839856C411yescharacteristic
19#16839853—21no—
20D8×Dic61C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758217—41no—
24#14519851—42no—
25C2×#11758187—22no—
26#14519844—41no—
27C4⋊#92420—22no—
28C2×Dic244C2×C411yescharacteristic
29C2×#11758200—21no—
30C22×#92418D411yescharacteristic
31#14519770—41no—
32#14519768—21no—
33#14519764—21no—
34#14519758—41no—
35#14519756—21no—
36#14519742—21no—
37D4×Dic61—21no—
38D4×Dic61—41no—
39#14519733—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519702—21no—
44#14519700—21no—
45#14519698—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#121×C61—21no—
53#107×C61C2×C411yescharacteristic
54#102×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×Dic61—41no—
59C22×Dic61D811yescharacteristic
60C22×Dic61SD1611yescharacteristic
61C2×Dic122—21no—
62#11758217—82no—
63C2×#92420—42no—
64D8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22×C411yescharacteristic
68C4⋊C4×C61—21no—
69C22⋊C4×C61—41no—
70C22⋊Dic61—41no—
71C22⋊Dic61—41no—
72C22⋊Dic61—41no—
73C22⋊Dic61—41no—
74#11758200—41no—
75#11758200—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78#11758196—41no—
79#11758196—41no—
80#11758196—41no—
81C4×Dic61—41no—
82C4×Dic61C22⋊C411yescharacteristic
83C4×Dic61D811yescharacteristic
84C4×Dic61SD1611yescharacteristic
85C4×Dic61C2×D411yescharacteristic
86C2×#92418—21no—
87C2×#92418—21no—
88C2×#92418C22⋊C411yescharacteristic
89C2×#92418C2×D411yescharacteristic
90Dic244—41no—
91#11758187—42no—
92C23×C61—41no—
93C23×C61#10211yescharacteristic
94D4×C61—41no—
95D4×C61—41no—
96D4×C61—82no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61#10211yescharacteristic
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×Dic61—22no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—82no—
107C2×Dic61#10211yescharacteristic
108C2×Dic61#10211yescharacteristic
109C2×Dic61C2×D811yescharacteristic
110C2×Dic61C2×SD1611yescharacteristic
111Dic122—41no—
112Dic122—41no—
113#92420—82no—
114C8×C61—21no—
115C8×C61—21no—
116#92418—21no—
117#92418AGL(1,ℤ/8)11yescharacteristic
118#92418#13711yescharacteristic
119#11980—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—81no—
124C22×C61—81no—
125C22×C61—81no—
126C22×C61C2×#10211yescharacteristic
127C4×C61—21no—
128C4×C61—81no—
129C4×C61#41311yescharacteristic
130C4×C61#41711yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—81no—
135Dic61—81no—
136Dic61#36012yes—
137#3168—611no—
138#2150—611no—
139#1566—611no—
140#1363—612no—
141#1360—612no—
142C2×C61—41no—
143C2×C61—161no—
144C2×C61#154711yescharacteristic
145C2×C61#214311yescharacteristic
146C2×C61C2×#36011yescharacteristic
147#529—1221no—
148C2×M32—1221no—
149#499—611no—
150#495—611no—
151#488—1221no—
152#467—611no—
153#466#692311yescharacteristic
154#465—1221no—
155C4×Q16—611no—
156C4×SD16—1221no—
157C4×D8—611no—
158#423—1221no—
159C2×C4×C8—611no—
160C4⋊C16—612no—
161C4⋊C16—1221no—
162#334—612no—
163#334—1221no—
164C61#1198011yescharacteristic, complemented, Sylow
165C2×Q16—611no—
166C2×SD16—1221no—
167C2×D8C2×#692311yescharacteristic
168C2×M16—2441no—
169C22×C8—611no—
170C22×C8C2×#692311yescharacteristic
171#126—2441no—
172#125—1221no—
173#124—1221no—
174#123—2441no—
175C22⋊Q8—1221no—
176#121—21no—
177C4×Q8—1221no—
178C4×D4—1221no—
179C4×D4—2441no—
180#117—2441no—
181C2×C42—611no—
182M32—2442no—
183C2×C16—1222no—
184#107—611no—
185#107C2×#692311yescharacteristic
186#106—1221no—
187C4⋊C8—1222no—
188C4⋊C8—2441no—
189#103—1221no—
190#103—1221no—
191#102—21no—
192#102—1221no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—611no—
196C4×C8—611no—
197C2×Q8—1221no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—2441no—
203C22×C4C22⋊#692311yescharacteristic
204Q16—2441no—
205SD16—2441no—
206SD16—2441no—
207D8—41no—
208M16—4882no—
209C2×C8—41no—
210C2×C8—611no—
211C2×C8—611no—
212C2×C8—1221no—
213C2×C8—1221no—
214C2×C8—2442no—
215C2×C8C22⋊#692311yescharacteristic
216C2×C8C22×#692311yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—1221no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C22⋊C4—41no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C22⋊C4—2441no—
227C22⋊C4—2441no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—611no—
232C42—2441no—
233C16—2442no—
234C23—41no—
235C23#1451983911yescharacteristic
236Q8—2441no—
237Q8—2441no—
238D4—41no—
239D4—41no—
240D4—82no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—1222no—
249C2×C4—4882no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451983911yescharacteristic
254C2×C4C2×C22⋊#692311yescharacteristic
255C8—21no—
256C8—21no—
257C8—611no—
258C8—611no—
259C8—1221no—
260C8—4882no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22C2×#1451983911yescharacteristic
268C4—21no—
269C4—81no—
270C4—612no—
271C4—1221no—
272C4—1221no—
273C4—1221no—
274C4—4881no—
275C4—4881no—
276C4#1684074911yescharacteristic
277C4#1684075311yescharacteristic
278C2—41no—
279C2—161no—
280C2#2146133111yescharacteristic
281C2#2146213411yescharacteristic
282C2D61⋊#36011yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
Fitting, prime radicalC61×#466C4
socleC22×C61C2×#102
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11980
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #21462153C2semidirect
2. #21461373C2semidirect
3. #21460835C2semidirect
4. #21460831C2semidirect
164. C61#11980semidirect

Maximal subgroups

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

subgroupindex
#214621532
#214613732
#214608352
#214608312
#214563842
#1198061