Finite Group Databasebeta

← #30599293

Subgroups — #30599293

Order 15616.

514 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461675C212yesmaximal
2#21460697C214yesmaximal, complemented
3#21448222C211yesmaximal, characteristic
4C2×#14519844C2214yes—
5C2×C22⋊#92420—22no—
6#16840628—22no—
7C2×#14519736C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839631C2212yes—
10#16839627C412yes—
11#16839620—22no—
12C4×#11758196—22no—
13C2×#117×C61C411yescharacteristic
14C22×#92420—24no—
15#14519844—28no—
16C22⋊#92420—44no—
17C23×Dic61D412yes—
18#14519736—42no—
19C2×C4⋊Dic61C2×C412yes—
20C2×#11758196—22no—
21C2×#11758196—22no—
22C2×C22⋊Dic61—21no—
23C2×C4×Dic61—24no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61D412yes—
27C2×C4×Dic61C2311yescharacteristic
28#14519684—24no—
29C23×C4×C61C2×C411yescharacteristic
30#117×C61—42no—
31C2×C4⋊C4×C61C2×C412yes—
32C2×C22⋊C4×C61—21no—
33C2×C42×C61—21no—
34C24×C61C22⋊C411yescharacteristic
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61C22⋊C411yescharacteristic
40C22×C4×C61C22×C411yescharacteristic
41C22×Dic61—24no—
42C22×Dic61—24no—
43C22×Dic61—22no—
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61C22⋊C412yes—
47C22×Dic61C2×D412yes—
48C2×#92420—44no—
49C2×#92420—44no—
50C2×#92420—44no—
51C4⋊C4×C61—42no—
52C22⋊C4×C61—42no—
53C42×C61—42no—
54C22⋊Dic61—42no—
55C4⋊Dic61—42no—
56#11758196—44no—
57#11758196—42no—
58#11758196—42no—
59C4×Dic61—22no—
60C4×Dic61—24no—
61C4×Dic61—42no—
62C4×Dic61#4114yes—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61#10012yes—
68C23×C61C2×C22⋊C411yescharacteristic
69C2×C4×C61—28no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61—42no—
77C2×C4×C61#10112yes—
78C2×C4×C61#11712yes—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—44no—
83C2×Dic61—44no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61#12314yes—
88C2×Dic61#13514yes—
89C2×Dic61AGL(1,ℤ/8)12yes—
90C2×Dic61#13712yes—
91#92420—84no—
92#8729—611nomaximal, Sylow
93C22×C61—24no—
94C22×C61—22no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—42no—
98C22×C61#38111yescharacteristic
99C22×C61C2×#10011yescharacteristic
100C22×C61C2×#10111yescharacteristic
101C22×C61#41612yes—
102C22×C61#41712yes—
103C4×C61—22no—
104C4×C61—22no—
105C4×C61—82no—
106Dic61—42no—
107Dic61—82no—
108Dic61#48214yes—
109Dic61#48514yes—
110#2285—611no—
111#1797—612no—
112#1296—614no—
113C2×C61—42no—
114C2×C61#154411yescharacteristic
115C2×C61#155112yes—
116C2×C61#156111yescharacteristic
117C2×C61#182111yescharacteristic
118C2×C61#182512yes—
119C2×#117—611no—
120C2×#117#692311yescharacteristic
121C22×C42—611no—
122C2×C4⋊C8—614no—
123C2×C22⋊C8—1222no—
124#384—612no—
125#382—612no—
126#380—1222no—
127C4×C4⋊C4—1222no—
128#336—1222no—
129C61#872911yescharacteristic, complemented, Sylow
130C23×C4—612no—
131C23×C4C2×#692311yescharacteristic
132C22×C8—1224no—
133#117—42no—
134#117—2442no—
135C2×C4⋊C4—612no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4—1222no—
138C2×C4⋊C4C2×#692312yes—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—1221no—
141C2×C42—21no—
142C2×C42—611no—
143C2×C42—612no—
144C2×C42—611no—
145C2×C42—1224no—
146C2×C42—1221no—
147C4⋊C8—1228no—
148C22⋊C8—2444no—
149#95—1224no—
150C24C22⋊#692311yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—1222no—
158C22×C4—1224no—
159C22×C4—1224no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4C22⋊#692311yescharacteristic
163C22×C4C22×#692311yescharacteristic
164C2×C8—2444no—
165C2×C8—2444no—
166C2×C8—2444no—
167C4⋊C4—42no—
168C4⋊C4—2442no—
169C4⋊C4—2444no—
170C4⋊C4—2442no—
171C4⋊C4—2442no—
172C22⋊C4—42no—
173C22⋊C4—2442no—
174C42—42no—
175C42—614no—
176C42—1224no—
177C42—1222no—
178C42—2442no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23—22no—
183C23#1451983712yes—
184C23C2×C22⋊#692311yescharacteristic
185C2×C4—28no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—614no—
194C2×C4—614no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—2444no—
201C2×C4—2444no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4#1451983812yes—
206C2×C4#1451985612yes—
207C8—4884no—
208C22—24no—
209C22—22no—
210C22—41no—
211C22—41no—
212C22—42no—
213C22#1684070511yescharacteristic
214C22C2×#1451983711yescharacteristic
215C22C2×#1451983811yescharacteristic
216C22#1684075212yes—
217C22#1684075312yes—
218C4—22no—
219C4—22no—
220C4—82no—
221C4—614no—
222C4—614no—
223C4—4882no—
224C4—2442no—
225C2—42no—
226C2#2146132411yescharacteristic
227C2#2146133812yes—
228C2#2146135811yescharacteristic
229C2#2146171811yescharacteristic
230C2#2146172412yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8729
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460697C2semidirect
129. C61#8729semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214606972
#214482222
#872961