Finite Group Databasebeta

← #30594769

Subgroups — #30594769

Order 15616.

374 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 58 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#21461067C212yesmaximal
2#21444086C211yesmaximal, characteristic
3#16840732—22no—
4#16840607—22no—
5#16840607C414yescomplemented
6C22×C4⋊Dic61C2211yescharacteristic
7C2×#14519684—22no—
8C2×#14519684C411yescharacteristic
9C2×#95×C61C411yescharacteristic
10C2×#11758217—42no—
11C22⋊#92420—24no—
12C22⋊#92420—42no—
13C23×Dic61—21no—
14C23×Dic61D412yes—
15C2×C4⋊Dic61—41no—
16C2×C4⋊Dic61—41no—
17C2×C4⋊Dic61C2×C412yes—
18C2×C4⋊Dic61D411yescharacteristic
19C2×C4⋊Dic61Q811yescharacteristic
20#14519684—44no—
21#14519684—41no—
22C23×C4×C61—21no—
23C23×C4×C61C2×C411yescharacteristic
24#95×C61—41no—
25C24×C61C22⋊C411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61—22no—
29C22×C4×C61—42no—
30C22×C4×C61—42no—
31C22×C4×C61—41no—
32C22×C4×C61—42no—
33C22×C4×C61—41no—
34C22×C4×C61C4211yescharacteristic
35C22×C4×C61C4⋊C411yescharacteristic
36C22×Dic61—22no—
37C22×Dic61—22no—
38C22×Dic61—22no—
39C22×Dic61—42no—
40C22×Dic61—42no—
41C22×Dic61—42no—
42C22×Dic61—41no—
43C22×Dic61—42no—
44C22×Dic61—41no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C4⋊C412yes—
47#11758217—82no—
48#11758217—82no—
49C2×#92420—44no—
50C4⋊Dic61—42no—
51C4⋊Dic61—41no—
52C4⋊Dic61—41no—
53C23×C61—22no—
54C23×C61—21no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61#9511yescharacteristic
59C23×C61#9911yescharacteristic
60C23×C61#9911yescharacteristic
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—44no—
68C2×C4×C61—42no—
69C2×C4×C61—82no—
70C2×C4×C61—81no—
71C2×C4×C61—81no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—42no—
75C2×Dic61—42no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—44no—
79C2×Dic61—42no—
80C2×Dic61—82no—
81C2×Dic61—82no—
82C2×Dic61—81no—
83C2×Dic61—81no—
84#92420—84no—
85#7326—611nomaximal, Sylow
86C22×C61—22no—
87C22×C61—22no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61#34211yescharacteristic
97C22×C61#34412yes—
98C22×C61#35311yescharacteristic
99C22×C61#35411yescharacteristic
100C22×C61#35511yescharacteristic
101C22×C61#35611yescharacteristic
102C4×C61—41no—
103C4×C61—41no—
104C4×C61—82no—
105Dic61—42no—
106Dic61—42no—
107Dic61—82no—
108#1463—612no—
109#1445—611no—
110C2×C61—21no—
111C2×C61—21no—
112C2×C61—22no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61#130611yescharacteristic
116C2×C61#139311yescharacteristic
117C2×C61#139411yescharacteristic
118C22×C4⋊C4—611no—
119#407—1222no—
120C2×#95—611no—
121C2×#95—1222no—
122C2×#95#692311yescharacteristic
123#324—614no—
124#324—1222no—
125C61#732611yescharacteristic, complemented, Sylow
126C23×C4—21no—
127C23×C4—612no—
128C23×C4—1221no—
129C23×C4C2×#692311yescharacteristic
130C2×M16—2442no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4—2441no—
135C2×C4⋊C4—2441no—
136C22⋊C8—1224no—
137C22⋊C8—2442no—
138#95—41no—
139#95—2441no—
140#95—2444no—
141C24C22⋊#692311yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—41no—
148C22×C4—42no—
149C22×C4—41no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—1222no—
153C22×C4—1222no—
154C22×C4—1222no—
155C22×C4—2442no—
156C22×C4—2442no—
157C22×C4—2441no—
158C22×C4—2441no—
159C22×C4—2442no—
160C22×C4—2442no—
161C22×C4C4×#692311yescharacteristic
162C22×C4C4⋊#692311yescharacteristic
163M16—4882no—
164M16—4882no—
165C2×C8—2444no—
166C4⋊C4—2442no—
167C4⋊C4—2441no—
168C4⋊C4—2441no—
169C23—22no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23(C2×#6923)⋊C411yescharacteristic
175C23#1451983511yescharacteristic
176C23#1451983611yescharacteristic
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—4882no—
191C2×C4—4881no—
192C2×C4—4881no—
193C2×C4—4882no—
194C2×C4—2444no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C8—4884no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—22no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1684064011yescharacteristic
212C22#1684064312yes—
213C22#1684066711yescharacteristic
214C22#1684066911yescharacteristic
215C22#1684067011yescharacteristic
216C22#1684067211yescharacteristic
217C4—41no—
218C4—41no—
219C4—82no—
220C4—4882no—
221C4—2442no—
222C4—2442no—
223C2—21no—
224C2—21no—
225C2—22no—
226C2—21no—
227C2—21no—
228C2#2146072211yescharacteristic
229C2#2146091311yescharacteristic
230C2#2146091711yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC22×C61#342
prime radicalC24×C61C22⋊C4
cosocleC22×C4⋊Dic61C22
hypercenterC2×#95#6923
hypocenterC61#7326
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
5. #16840607C4semidirect
125. C61#7326semidirect

Maximal subgroups

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

subgroupindex
#214610672
#214440862
#732661