Finite Group Databasebeta

← #30605641

Subgroups — #30605641

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#21460831C214yesmaximal, complemented
4#21456246C211yesmaximal, characteristic
5#16840766—21no—
6#16840683C2212yes—
7#16840657—21no—
8C4×#11758187—21no—
9#16840624—21no—
10#16840624C2212yes—
11C2×#14519796—21no—
12C2×#14519796C412yes—
13#16840310—21no—
14#16840145—21no—
15#16840145C2212yes—
16#16840142C411yescharacteristic
17#16840134—21no—
18C4×C8×D61C2211yescharacteristic
19C61×#493C411yescharacteristic
20C2×#11758213—41no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23C4⋊#92420—41no—
24C2×#11758224—22no—
25#14519796—44no—
26#14519796—44no—
27C2×Dic244—21no—
28C2×Dic244C2×C412yes—
29C2×#11758200—22no—
30C2×#11758200—22no—
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519777—21no—
34#14519764—22no—
35#14519748—41no—
36#14519748—41no—
37D4×Dic61—41no—
38D4×Dic61—41no—
39C42×D61D411yescharacteristic
40C4×#92418D411yescharacteristic
41C8×Dic61D411yescharacteristic
42C8×Dic61C2311yescharacteristic
43C2×D8×C61—21no—
44C2×D8×C61C2×C412yes—
45#127×C61—21no—
46C4×C8×C61C2×C411yescharacteristic
47C2×D4×C61—22no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C2×C22⋊D61—42no—
51C22×Dic61—42no—
52#11758224—44no—
53#11758224—44no—
54C2×C4×D61C22⋊C411yescharacteristic
55C2×C4×D61D811yescharacteristic
56C2×C4×D61SD1611yescharacteristic
57C2×Dic122—22no—
58C2×#92420—42no—
59#11758213—82no—
60D8×C61—42no—
61D8×C61—42no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22×C411yescharacteristic
64C42×C61C22⋊C411yescharacteristic
65C22⋊Dic61—42no—
66C22⋊Dic61—42no—
67#11758200—44no—
68#11758200—44no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71C4×Dic61D811yescharacteristic
72C4×Dic61SD1611yescharacteristic
73C4×Dic61C2×D411yescharacteristic
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C2×D411yescharacteristic
76Dic244—42no—
77Dic244—42no—
78C8×D61—22no—
79C8×D61—22no—
80#11758187—42no—
81C23×C61—42no—
82C22×D61#10211yescharacteristic
83D4×C61—42no—
84D4×C61—42no—
85D4×C61—82no—
86D4×C61—82no—
87C2×C4×C61#10211yescharacteristic
88C2×C4×C61#10211yescharacteristic
89C2×C4×C61C2×C22⋊C411yescharacteristic
90C22⋊D61—84no—
91C2×Dic61—42no—
92C2×Dic61—84no—
93C2×Dic61#10211yescharacteristic
94C2×Dic61C2×D811yescharacteristic
95C2×Dic61C2×SD1611yescharacteristic
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—21no—
99C4×D61—21no—
100Dic122—42no—
101Dic122—42no—
102#92420—82no—
103C8×C61—21no—
104C8×C61—21no—
105#92418#10012yes—
106#92418AGL(1,ℤ/8)12yes—
107#11958—611nomaximal, Sylow
108C22×C61—82no—
109C22×C61—82no—
110C22×C61—82no—
111C22×C61C2×#10211yescharacteristic
112C2×D61—21no—
113C2×D61—21no—
114C2×D61—21no—
115C4×C61#35912yes—
116C4×C61#36012yes—
117C4×C61C2×#10011yescharacteristic
118C4×C61#41811yescharacteristic
119Dic61—21no—
120Dic61—21no—
121Dic61—21no—
122Dic61—82no—
123#3147—611no—
124#2162—611no—
125#1566—611no—
126#1360—614no—
127C2×C61—162no—
128C2×C61#154511yescharacteristic
129C2×C61C2×#35911yescharacteristic
130C2×C61C2×#36011yescharacteristic
131D61—41no—
132C2×#135—612no—
133C2×#135—1221no—
134#532—1221no—
135#495—612no—
136#495—1221no—
137#494—611no—
138#493#692311yescharacteristic
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—612no—
152C2×Q16—1221no—
153C2×SD16—1222no—
154C2×SD16—1222no—
155C2×D8—21no—
156C2×D8C2×#692312yes—
157C2×M16—2441no—
158C22×C8—611no—
159C22×C8—611no—
160C4⋊Q8—1221no—
161#127—21no—
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—1222no—
178C2×D4—22no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4—2442no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—2442no—
186Q16—2442no—
187Q16—2442no—
188SD16—2444no—
189SD16—2444no—
190D8—42no—
191D8—42no—
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—2441no—
201C4⋊C4—2441no—
202C22⋊C4—2442no—
203C22⋊C4—2442no—
204C42—611no—
205C42—611no—
206C42—611no—
207C42C22⋊#692311yescharacteristic
208C16—2442no—
209C23—42no—
210C23—611no—
211Q8—2442no—
212Q8—2442no—
213D4—42no—
214D4—42no—
215D4—82no—
216D4—82no—
217D4—4884no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—4884no—
226C2×C4—2442no—
227C2×C4#1451983911yescharacteristic
228C2×C4#1451983911yescharacteristic
229C2×C4C2×C22⋊#692311yescharacteristic
230C8—21no—
231C8—21no—
232C8—612no—
233C8—612no—
234C8—4882no—
235C22—82no—
236C22—82no—
237C22—82no—
238C22—1221no—
239C22—1221no—
240C22—1221no—
241C22C2×#1451983911yescharacteristic
242C4—1221no—
243C4—1221no—
244C4—1221no—
245C4—4882no—
246C4#1684067612yes—
247C4#1684067812yes—
248C4D61⋊#10011yescharacteristic
249C4#1684075411yescharacteristic
250C2—162no—
251C2—2441no—
252C2#2146132711yescharacteristic
253C2C2×#1684067611yescharacteristic
254C2C2×#1684067811yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#493C4
socleC22×C61C2×#102
prime radical#21456246C2
cosocleC8×Dic61C23
hypercenter#493#6923
hypocenterC61#11958
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. #21461375C2semidirect
3. #21460831C2semidirect
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
#214608312
#214562462
#1195861