Finite Group Databasebeta

← #30595636

Subgroups — #30595636

Order 15616.

490 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 96 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#21461710C212yesmaximal
2#21460638C214yesmaximal, complemented
3#21448301C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840628—22no—
6#16840628C2214yes—
7C2×#14519736C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839658C412yes—
10#16839658C2212yes—
11#16839634—22no—
12C4×#11758196—22no—
13C2×#117×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—44no—
16C23×Dic61D412yes—
17#14519736—24no—
18C2×C4⋊Dic61C2×C412yes—
19C2×#11758196—22no—
20C2×#11758196—22no—
21C2×C22⋊Dic61—21no—
22C2×C4×Dic61—21no—
23C2×C4×Dic61—42no—
24C2×C4×Dic61C2×C411yescharacteristic
25C2×C4×Dic61D412yes—
26C2×C4×Dic61C2311yescharacteristic
27#14519684—22no—
28#14519684—22no—
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—22no—
43C22×Dic61—24no—
44C22×Dic61—42no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C2×D412yes—
47C2×#92420—44no—
48C2×#92420—44no—
49C2×#92420—44no—
50C4⋊C4×C61—42no—
51C22⋊C4×C61—42no—
52C42×C61—42no—
53C22⋊Dic61—24no—
54C4⋊Dic61—22no—
55C4⋊Dic61M1614yes—
56#11758196—44no—
57#11758196—44no—
58C4×Dic61—24no—
59C4×Dic61—41no—
60C4×Dic61—42no—
61C4×Dic61—41no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61—22no—
65C23×C61—22no—
66C23×C61#9912yes—
67C23×C61C2×C22⋊C411yescharacteristic
68C2×C4×C61—28no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61—42no—
76C2×C4×C61#10112yes—
77C2×C4×C61C2×M1612yes—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—24no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—48no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61#13514yes—
88#92420—84no—
89#7646—611nomaximal, Sylow
90C22×C61—22no—
91C22×C61—24no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—42no—
95C22×C61#40711yescharacteristic
96C22×C61C2×#9911yescharacteristic
97C22×C61C2×#10111yescharacteristic
98C22×C61#41612yes—
99C22×C61#42112yes—
100C4×C61—22no—
101C4×C61—22no—
102C4×C61—82no—
103Dic61—24no—
104Dic61—44no—
105Dic61—42no—
106#2296—611no—
107#1817—612no—
108#1271—614no—
109C2×C61—42no—
110C2×C61#146311yescharacteristic
111C2×C61#148812yes—
112C2×C61#151612yes—
113C2×C61#153711yescharacteristic
114C2×C61#154411yescharacteristic
115C2×#117—611no—
116C2×#117#692311yescharacteristic
117C22×C42—611no—
118C2×C22⋊C8—1222no—
119#389—612no—
120#389—612no—
121#385—1222no—
122C4×C4⋊C4—1222no—
123#336—614no—
124#336—1222no—
125C61#764611yescharacteristic, complemented, Sylow
126C23×C4—612no—
127C23×C4C2×#692311yescharacteristic
128C22×C8—1224no—
129#117—42no—
130#117—1224no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—1222no—
133C2×C4⋊C4—1222no—
134C2×C4⋊C4C2×#692312yes—
135C2×C22⋊C4—21no—
136C2×C22⋊C4—1221no—
137C2×C42—21no—
138C2×C42—612no—
139C2×C42—611no—
140C2×C42—611no—
141C2×C42—1221no—
142C2×C42—2442no—
143C22⋊C8—2444no—
144#95—1222no—
145#95—1222no—
146C24C22⋊#692311yescharacteristic
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—1224no—
154C22×C4—1224no—
155C22×C4—1222no—
156C22×C4—2442no—
157C22×C4C22⋊#692311yescharacteristic
158C22×C4C22×#692311yescharacteristic
159C2×C8—2444no—
160C2×C8—2444no—
161C2×C8—2444no—
162C4⋊C4—42no—
163C4⋊C4—614no—
164C4⋊C4—1222no—
165C4⋊C4—2444no—
166C4⋊C4—2444no—
167C22⋊C4—42no—
168C22⋊C4—1224no—
169C42—42no—
170C42—1224no—
171C42—2442no—
172C42—2441no—
173C42—2441no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23#1451983512yes—
179C23C2×C22⋊#692311yescharacteristic
180C2×C4—28no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—614no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1224no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—2448no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4#1451983812yes—
199C2×C4D61⋊M1612yes—
200C8—4884no—
201C22—22no—
202C22—24no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22#1684073411yescharacteristic
207C22C2×#1451983511yescharacteristic
208C22C2×#1451983811yescharacteristic
209C22#1684075212yes—
210C22#1684075912yes—
211C4—22no—
212C4—22no—
213C4—82no—
214C4—1224no—
215C4—2444no—
216C4—2442no—
217C2—42no—
218C2#2146106911yescharacteristic
219C2#2146115212yes—
220C2#2146124512yes—
221C2#2146131011yescharacteristic
222C2#2146132411yescharacteristic
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#7646
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. #21460638C2semidirect
125. C61#7646semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214606382
#214483012
#764661