Finite Group Databasebeta

← #30605625

Subgroups — #30605625

Order 15616.

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

normal subgroups only

This group has 340 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#21462181C211yesmaximal, characteristic, complemented
2#21461368C211yesmaximal, characteristic, complemented
3#21460837C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456393C211yesmaximal, characteristic
6#16840778—21no—
7#16840683C2212yes—
8C22⋊#11758187—21no—
9#16840651—21no—
10#16840626C2212yes—
11#16840624—21no—
12#16840307—21no—
13#16840166C2211yescharacteristic
14#16840137C2211yescharacteristic
15#16840107—21no—
16#16839998C411yescharacteristic
17#16839996—21no—
18D8×Dic61C411yescharacteristic
19#16839844C411yescharacteristic
20#16839842—21no—
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758187—22no—
24C4⋊#92420—22no—
25C22⋊#92420—41no—
26C4×#92420—41no—
27C2×#11758224—41no—
28C2×D488C2×C411yescharacteristic
29C2×#11758199—21no—
30C22×#92418D411yescharacteristic
31#14519776—21no—
32#14519773—21no—
33#14519763—41no—
34#14519751—21no—
35#14519749—41no—
36D4×Dic61—21no—
37#14519739—21no—
38#14519737—41no—
39C2×C4×Dic61D411yescharacteristic
40#14519711C2×C411yescharacteristic
41#14519710—21no—
42#14519699—21no—
43#14519698—21no—
44#14519697—21no—
45C8×Dic61C2×C411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51#121×C61—21no—
52#107×C61C2×C411yescharacteristic
53#102×C61—21no—
54C2×D4×C61—21no—
55C2×D4×C61—41no—
56C22×C4×C61C22⋊C411yescharacteristic
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60C22×Dic61—41no—
61C22×Dic61D811yescharacteristic
62C22×Dic61SD1611yescharacteristic
63#11758224—84no—
64C2×D244—21no—
65C2×C4×D61—41no—
66C2×Dic122—41no—
67C2×#92420—42no—
68D8×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61C22⋊C411yescharacteristic
71C2×C8×C61C22×C411yescharacteristic
72C4⋊C4×C61—21no—
73C22⋊C4×C61—41no—
74C22⋊Dic61—41no—
75#11758199—42no—
76#11758198—41no—
77#11758198—41no—
78C4⋊Dic61—21no—
79#11758196—41no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61D811yescharacteristic
82C4×Dic61SD1611yescharacteristic
83C4×Dic61C2×D411yescharacteristic
84C2×#92418—22no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87D488—41no—
88#11758187—42no—
89C23×C61—41no—
90C23×C61#10211yescharacteristic
91C22×D61—41no—
92D4×C61—41no—
93D4×C61—41no—
94D4×C61—82no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61#10211yescharacteristic
99C2×C4×C61C2×C22⋊C411yescharacteristic
100C22⋊D61—82no—
101C22⋊D61—82no—
102C22⋊D61—82no—
103C2×Dic61—22no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—82no—
107C2×Dic61#10211yescharacteristic
108C2×Dic61#10211yescharacteristic
109C2×Dic61C2×D811yescharacteristic
110C2×Dic61C2×SD1611yescharacteristic
111D244—41no—
112D244—41no—
113C4×D61—82no—
114Dic122—82no—
115#92420—82no—
116C8×C61—21no—
117C8×C61—21no—
118#92418—21no—
119#92418#13512yes—
120#11951—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—81no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61C2×#10211yescharacteristic
128C2×D61—81no—
129C2×D61—81no—
130C2×D61—81no—
131C4×C61—21no—
132C4×C61—81no—
133C4×C61#41311yescharacteristic
134C4×C61#41611yescharacteristic
135Dic61—21no—
136Dic61—21no—
137Dic61—21no—
138Dic61—81no—
139Dic61#50912yes—
140#3169—611no—
141#2163—611no—
142#1564—611no—
143#1364—612no—
144#1361—612no—
145C2×C61—41no—
146C2×C61—161no—
147C2×C61#154011yescharacteristic
148C2×C61#214011yescharacteristic
149C2×C61#214811yescharacteristic
150D61—161no—
151#532—1221no—
152#500—611no—
153#493—611no—
154#486—1221no—
155#466—611no—
156#466—1221no—
157#466#692311yescharacteristic
158C4×D8—611no—
159C4×D8—611no—
160C4×D8—1221no—
161#431—1221no—
162C2×C4×C8—611no—
163C4⋊C16—612no—
164C22⋊C16—1221no—
165#346—1221no—
166#335—612no—
167#334—1221no—
168C61#1195111yescharacteristic, complemented, Sylow
169C2×#41—2441no—
170C2×D8—611no—
171C2×D8—1221no—
172C2×D8C2×#692311yescharacteristic
173C22×C8—611no—
174C22×C8C2×#692311yescharacteristic
175C4⋊Q8—1221no—
176#127—1221no—
177#124—2441no—
178#121—21no—
179#121—1221no—
180#121—2441no—
181C4×D4—1221no—
182C4×D4—1221no—
183C4×D4—2441no—
184C2×C42—611no—
185C2×C16—1222no—
186#107—611no—
187#107—1221no—
188#107C2×#692311yescharacteristic
189C4⋊C8—1222no—
190#102—21no—
191#102—1221no—
192#102—1221no—
193#102—1221no—
194C22⋊C8—2441no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—611no—
199C4×C8—2441no—
200#41—4884no—
201C2×Q8—2441no—
202C2×D4—21no—
203C2×D4—41no—
204C2×D4—1221no—
205C2×D4—2441no—
206C2×D4—2441no—
207C2×D4—2441no—
208C22×C4—611no—
209C22×C4—611no—
210C22×C4—2441no—
211C22×C4—2441no—
212C22×C4C22⋊#692311yescharacteristic
213D8—41no—
214D8—2441no—
215D8—2442no—
216C2×C8—41no—
217C2×C8—611no—
218C2×C8—611no—
219C2×C8—1222no—
220C2×C8—2442no—
221C2×C8C22⋊#692311yescharacteristic
222C2×C8C22×#692311yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—1221no—
225C4⋊C4—2441no—
226C22⋊C4—41no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C42—611no—
231C42—611no—
232C42—611no—
233C42—611no—
234C16—2442no—
235C23—41no—
236C23—2441no—
237C23#1451983911yescharacteristic
238Q8—4882no—
239D4—41no—
240D4—41no—
241D4—82no—
242D4—4882no—
243D4—4882no—
244D4—4882no—
245D4—2441no—
246D4—2441no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—611no—
253C2×C4—611no—
254C2×C4—1222no—
255C2×C4—4882no—
256C2×C4—4882no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4#1451983911yescharacteristic
260C2×C4C2×C22⋊#692311yescharacteristic
261C8—21no—
262C8—21no—
263C8—612no—
264C8—1221no—
265C8—4882no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—81no—
270C22—81no—
271C22—81no—
272C22—4881no—
273C22—4881no—
274C22—4881no—
275C22C2×#1451983911yescharacteristic
276C4—21no—
277C4—81no—
278C4—612no—
279C4—1221no—
280C4—1221no—
281C4—1221no—
282C4—4881no—
283C4#1684074911yescharacteristic
284C4#1684075211yescharacteristic
285C2—41no—
286C2—161no—
287C2—9761no—
288C2#2146131711yescharacteristic
289C2#2146212811yescharacteristic
290C2#2146214611yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#466C4
socleC22×C61C2×#102
prime radical#21456393C2
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11951
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. #21462181C2semidirect
2. #21461368C2semidirect
3. #21460837C2semidirect
4. #21460833C2semidirect
168. C61#11951semidirect

Maximal subgroups

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

subgroupindex
#214621812
#214613682
#214608372
#214608332
#214563932
#1195161