Finite Group Databasebeta

← #30605642

Subgroups — #30605642

Order 15616.

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

normal subgroups only

This group has 404 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#21462178C211yesmaximal, characteristic, complemented
2#21461375C211yesmaximal, characteristic, complemented
3#21460832C214yesmaximal, complemented
4#21456248C211yesmaximal, characteristic
5#16840766—21no—
6#16840683C2212yes—
7#16840657—21no—
8C4×#11758187—21no—
9#16840624—21no—
10#16840624C2212yes—
11C2×#14519800—21no—
12C2×#14519800C412yes—
13#16840313—21no—
14#16840147—21no—
15#16840147C2212yes—
16#16840139C411yescharacteristic
17#16840136—21no—
18C4×C8×D61C2211yescharacteristic
19C61×#494C411yescharacteristic
20C2×#11758213—41no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23C4⋊#92420—41no—
24C2×#11758226—22no—
25#14519800—44no—
26#14519800—44no—
27C2×#11758201—22no—
28C2×#11758201—22no—
29C2×D488—21no—
30C2×D488C2×C412yes—
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519774—21no—
34#14519766—22no—
35#14519752—41no—
36#14519752—41no—
37#14519739—41no—
38#14519739—41no—
39C42×D61D411yescharacteristic
40C4×#92418D411yescharacteristic
41C8×Dic61D411yescharacteristic
42C8×Dic61C2311yescharacteristic
43C2×Q16×C61—21no—
44C2×Q16×C61C2×C412yes—
45C4⋊Q8×C61—21no—
46C4×C8×C61C2×C411yescharacteristic
47C2×Q8×C61—22no—
48#11758226—44no—
49#11758226—44no—
50C2×D244—22no—
51C2×D244—42no—
52C2×D244—41no—
53C2×D244—41no—
54C2×C4×D61—42no—
55C2×C4×D61C22⋊C411yescharacteristic
56C2×C4×D61D811yescharacteristic
57C2×C4×D61SD1611yescharacteristic
58C2×#92420—42no—
59#11758213—82no—
60Q16×C61—42no—
61Q16×C61—42no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22×C411yescharacteristic
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61C22⋊C411yescharacteristic
67#11758201—44no—
68#11758201—44no—
69#11758198—42no—
70#11758198—42no—
71C4×Dic61D811yescharacteristic
72C4×Dic61SD1611yescharacteristic
73C4×Dic61C2×D411yescharacteristic
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C2×D411yescharacteristic
76D488—42no—
77D488—42no—
78C8×D61—22no—
79C8×D61—22no—
80#11758187—42no—
81C22×D61—42no—
82C22×D61#10211yescharacteristic
83Q8×C61—42no—
84Q8×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61#10211yescharacteristic
87C2×C4×C61#10211yescharacteristic
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×Dic61#10211yescharacteristic
90C2×Dic61C2×D811yescharacteristic
91C2×Dic61C2×SD1611yescharacteristic
92D244—42no—
93D244—42no—
94D244—84no—
95D244—82no—
96D244—82no—
97C4×D61—22no—
98C4×D61—22no—
99C4×D61—21no—
100C4×D61—21no—
101C4×D61—84no—
102#92420—82no—
103C8×C61—21no—
104C8×C61—21no—
105#92418#10012yes—
106#92418AGL(1,ℤ/8)12yes—
107#11958—611nomaximal, Sylow
108C22×C61C2×#10211yescharacteristic
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—21no—
112C2×D61—82no—
113C2×D61—82no—
114C2×D61—82no—
115C4×C61—82no—
116C4×C61#35912yes—
117C4×C61#36012yes—
118C4×C61C2×#10011yescharacteristic
119C4×C61#41811yescharacteristic
120Dic61—21no—
121Dic61—21no—
122Dic61—21no—
123#3147—611no—
124#2162—611no—
125#1566—611no—
126#1360—614no—
127C2×C61#154511yescharacteristic
128C2×C61C2×#35911yescharacteristic
129C2×C61C2×#36011yescharacteristic
130D61—41no—
131D61—162no—
132C2×#135—612no—
133C2×#135—1221no—
134#532—1221no—
135#495—612no—
136#495—1221no—
137#494#692311yescharacteristic
138#493—611no—
139#492—1221no—
140#423—1221no—
141C2×C4×C8—611no—
142C4⋊C16—612no—
143C22⋊C16—1221no—
144C4×C16—1221no—
145#334—612no—
146#334—1221no—
147C61#1195811yescharacteristic, complemented, Sylow
148C2×#41—1222no—
149#135—2444no—
150#135—2444no—
151C2×Q16—21no—
152C2×Q16C2×#692312yes—
153C2×SD16—1222no—
154C2×SD16—1222no—
155C2×D8—612no—
156C2×D8—1221no—
157C2×M16—2441no—
158C22×C8—611no—
159C22×C8—611no—
160C4⋊Q8—21no—
161#127—1221no—
162#124—1222no—
163#121—2441no—
164#121—2441no—
165C4×D4—2441no—
166C4×D4—2441no—
167C2×C42—611no—
168C2×C16—1222no—
169C4⋊C8—1222no—
170C4⋊C8—2441no—
171C4×C8—611no—
172C4×C8—611no—
173C4×C8—611no—
174C4×C8C2×#692311yescharacteristic
175#41—2444no—
176#41—2444no—
177C2×Q8—22no—
178C2×D4—1222no—
179C2×D4—2442no—
180C2×D4—2441no—
181C2×D4—2441no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—2442no—
186Q16—42no—
187Q16—42no—
188SD16—2444no—
189SD16—2444no—
190D8—2442no—
191D8—2442no—
192M16—4882no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—1222no—
196C2×C8—1222no—
197C2×C8—2442no—
198C2×C8C22⋊#692311yescharacteristic
199C2×C8C22×#692311yescharacteristic
200C4⋊C4—41no—
201C4⋊C4—41no—
202C22⋊C4—2442no—
203C22⋊C4—2442no—
204C42—611no—
205C42—611no—
206C42—611no—
207C42C22⋊#692311yescharacteristic
208C16—2442no—
209C23—611no—
210C23—2442no—
211Q8—42no—
212Q8—42no—
213D4—4884no—
214D4—4882no—
215D4—4882no—
216D4—2442no—
217D4—2442no—
218C2×C4—42no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—4884no—
227C2×C4#1451983911yescharacteristic
228C2×C4#1451983911yescharacteristic
229C2×C4C2×C22⋊#692311yescharacteristic
230C8—21no—
231C8—21no—
232C8—612no—
233C8—612no—
234C8—4882no—
235C22—1221no—
236C22—1221no—
237C22—1221no—
238C22—4882no—
239C22—4882no—
240C22—4882no—
241C22C2×#1451983911yescharacteristic
242C4—82no—
243C4—1221no—
244C4—1221no—
245C4—1221no—
246C4#1684067712yes—
247C4#1684067912yes—
248C4D61⋊#10011yescharacteristic
249C4#1684075411yescharacteristic
250C2—9762no—
251C2—2441no—
252C2#2146132711yescharacteristic
253C2C2×#1684067711yescharacteristic
254C2C2×#1684067911yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#494C4
socleC22×C61C2×#102
prime radical#21456248C2
cosocleC8×Dic61C23
hypercenter#494#6923
hypocenterC61#11958
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. #21461375C2semidirect
3. #21460832C2semidirect
147. C61#11958semidirect

Maximal subgroups

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

subgroupindex
#214621782
#214613752
#214608322
#214562482
#1195861