Finite Group Databasebeta

← #30605696

Subgroups — #30605696

Order 15616.

306 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461381C211yesmaximal, characteristic, complemented
3#21460835C212yesmaximal, complemented
4#21460832C212yesmaximal, complemented
5#21456390C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840783—21no—
8#16840683—21no—
9#16840683C2212yes—
10#16840625—21no—
11#16840624C2212yes—
12#16840298—21no—
13#16840163C2211yescharacteristic
14#16840147C2211yescharacteristic
15#16840118—21no—
16#16839998C411yescharacteristic
17#16839993—21no—
18Q16×Dic61C411yescharacteristic
19#16839847—21no—
20#16839844C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#467C411yescharacteristic
23#14519851—42no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26C22⋊#92420—41no—
27#14519832—41no—
28C2×#11758201—21no—
29C2×D488C2×C411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519772—41no—
32#14519768—21no—
33#14519766—21no—
34#14519761—41no—
35#14519751—21no—
36Q8×Dic61—21no—
37#14519739—21no—
38#14519737—41no—
39#14519735—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519708—21no—
43#14519701—21no—
44#14519699—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×Q16×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52C22⋊Q8×C61—21no—
53#107×C61C2×C411yescharacteristic
54#103×C61—21no—
55C2×Q8×C61—21no—
56C22×C4×C61C22⋊C411yescharacteristic
57C2×C22⋊D61—41no—
58C22×Dic61D811yescharacteristic
59C22×Dic61SD1611yescharacteristic
60C2×D244—21no—
61C2×C4×D61—41no—
62C2×#92420—42no—
63Q16×C61—41no—
64C2×C8×C61—41no—
65C2×C8×C61C22⋊C411yescharacteristic
66C2×C8×C61C22×C411yescharacteristic
67C4⋊C4×C61—21no—
68C4⋊C4×C61—41no—
69C22⋊C4×C61—41no—
70#11758201—41no—
71#11758201—41no—
72#11758198—41no—
73#11758198—41no—
74#11758198—41no—
75#11758198—41no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79#11758196—41no—
80C4×Dic61—41no—
81C4×Dic61C22⋊C411yescharacteristic
82C4×Dic61D811yescharacteristic
83C4×Dic61SD1611yescharacteristic
84C4×Dic61C2×D411yescharacteristic
85C2×#92418—21no—
86C2×#92418—21no—
87C2×#92418C22⋊C411yescharacteristic
88C2×#92418C2×D411yescharacteristic
89D488—41no—
90#11758187—42no—
91C23×C61#10211yescharacteristic
92C22×D61—41no—
93Q8×C61—41no—
94Q8×C61—41no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61#10211yescharacteristic
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C22⋊D61—82no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61#10211yescharacteristic
106C2×Dic61#10211yescharacteristic
107C2×Dic61C2×D811yescharacteristic
108C2×Dic61C2×SD1611yescharacteristic
109D244—41no—
110D244—41no—
111C4×D61—82no—
112#92420—82no—
113C8×C61—21no—
114C8×C61—21no—
115#92418—21no—
116#92418AGL(1,ℤ/8)11yescharacteristic
117#92418#13711yescharacteristic
118#11979—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61C2×#10211yescharacteristic
123C2×D61—81no—
124C2×D61—81no—
125C2×D61—81no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61—81no—
129C4×C61#41311yescharacteristic
130C4×C61#41711yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—21no—
135Dic61—81no—
136#3168—611no—
137#2150—611no—
138#1568—611no—
139#1363—612no—
140#1360—612no—
141C2×C61—41no—
142C2×C61#154711yescharacteristic
143C2×C61#214311yescharacteristic
144C2×C61#214511yescharacteristic
145D61—161no—
146#529—1221no—
147C2×M32—1221no—
148#499—611no—
149#495—611no—
150#488—1221no—
151#467#692311yescharacteristic
152#466—611no—
153#465—1221no—
154C4×Q16—611no—
155C4×SD16—1221no—
156C4×D8—611no—
157#432—1221no—
158C2×C4×C8—611no—
159C4⋊C16—612no—
160C4⋊C16—1221no—
161#335—1221no—
162#334—612no—
163C61#1197911yescharacteristic, complemented, Sylow
164C2×Q16C2×#692311yescharacteristic
165C2×SD16—1221no—
166C2×D8—611no—
167C22×C8—611no—
168C22×C8C2×#692311yescharacteristic
169#126—2441no—
170#125—1221no—
171#124—1221no—
172#123—2441no—
173C22⋊Q8—21no—
174#121—1221no—
175C4×Q8—1221no—
176C4×D4—1221no—
177C4×D4—2441no—
178#117—2441no—
179C2×C42—611no—
180M32—2442no—
181C2×C16—1222no—
182#107—611no—
183#107C2×#692311yescharacteristic
184#106—1221no—
185C4⋊C8—1222no—
186#103—21no—
187#103—1221no—
188#102—1221no—
189#102—1221no—
190C22⋊C8—2441no—
191#97—2441no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—611no—
196C2×Q8—21no—
197C2×D4—1221no—
198C2×D4—2441no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—2441no—
202C22×C4C22⋊#692311yescharacteristic
203Q16—41no—
204SD16—2441no—
205SD16—2441no—
206D8—2441no—
207C2×C8—41no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1221no—
211C2×C8—1221no—
212C2×C8—2442no—
213C2×C8C22⋊#692311yescharacteristic
214C2×C8C22×#692311yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—41no—
217C4⋊C4—1221no—
218C4⋊C4—2441no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C22⋊C4—41no—
222C22⋊C4—2441no—
223C22⋊C4—2441no—
224C22⋊C4—2441no—
225C22⋊C4—2441no—
226C42—611no—
227C42—611no—
228C42—611no—
229C42—611no—
230C42—2441no—
231C16—2442no—
232C23—2441no—
233C23#1451983911yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—4882no—
237D4—2441no—
238D4—2441no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—4882no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4#1451983911yescharacteristic
252C2×C4C2×C22⋊#692311yescharacteristic
253C8—21no—
254C8—21no—
255C8—611no—
256C8—611no—
257C8—1221no—
258C8—4882no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—4881no—
263C22—4881no—
264C22—4881no—
265C22C2×#1451983911yescharacteristic
266C4—21no—
267C4—81no—
268C4—81no—
269C4—1221no—
270C4—1221no—
271C4—1221no—
272C4—1221no—
273C4—4881no—
274C4#1684074911yescharacteristic
275C4#1684075311yescharacteristic
276C2—41no—
277C2—9761no—
278C2#2146133111yescharacteristic
279C2#2146213311yescharacteristic
280C2#2146214111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#467C4
socleC22×C61C2×#102
prime radical#16839998C4
cosocleC8×Dic61C23
hypercenter#467#6923
hypocenterC61#11979
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #21462153C2semidirect
2. #21461381C2semidirect
3. #21460835C2semidirect
4. #21460832C2semidirect
163. C61#11979semidirect

Maximal subgroups

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

subgroupindex
#214621532
#214613812
#214608352
#214608322
#214563902
#1197961