Finite Group Databasebeta

← #30599310

Subgroups — #30599310

Order 15616.

514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C2×#16840607C212yesmaximal
2#21460662C214yesmaximal
3#21448175C211yesmaximal, characteristic
4C2×C22⋊#92420C2214yes—
5#16840607—22no—
6#16840607—22no—
7C2×#14519736C411yescharacteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C4⋊C4×Dic61—22no—
10C4×C4⋊Dic61—22no—
11C22⋊C4×Dic61C412yes—
12C22⋊C4×Dic61C2212yes—
13C2×#117×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—24no—
16C22⋊#92420—24no—
17C23×Dic61C2×C411yescharacteristic
18C23×Dic61C2311yescharacteristic
19#14519736—24no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61—24no—
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61D412yes—
24C2×C22⋊Dic61C2×C412yes—
25C2×C4×Dic61—21no—
26C2×C4×Dic61—22no—
27C2×C4×Dic61—22no—
28#14519684—22no—
29#14519684—22no—
30C23×C4×C61C2×C411yescharacteristic
31#117×C61—22no—
32#117×C61C814yescomplemented
33C2×C4⋊C4×C61—21no—
34C2×C22⋊C4×C61C2×C412yes—
35C2×C42×C61—21no—
36C24×C61C22×C411yescharacteristic
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C2×C812yes—
43C22×C4×C61M1612yes—
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61—81no—
47C22×Dic61—81no—
48C22×Dic61C22⋊C412yes—
49C22×Dic61C2×D412yes—
50C22×Dic61#4114yes—
51C2×#92420—44no—
52C2×#92420—84no—
53C4⋊C4×C61—24no—
54C22⋊C4×C61—22no—
55C22⋊C4×C61C2×C814yes—
56C42×C61—24no—
57C22⋊Dic61—22no—
58C22⋊Dic61M1614yes—
59C4⋊Dic61—24no—
60C4⋊Dic61—24no—
61C4⋊Dic61—24no—
62C4×Dic61—24no—
63C4×Dic61—82no—
64C4×Dic61—82no—
65C23×C61—41no—
66C23×C61—41no—
67C23×C61C2×C22⋊C411yescharacteristic
68C23×C61#11712yes—
69C23×C61C22×C811yescharacteristic
70C23×C61C2×M1611yescharacteristic
71C23×C61C2×M1612yes—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—24no—
77C2×C4×C61—24no—
78C2×C4×C61—24no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61C22⋊C812yes—
82C2×C4×C61C22⋊C812yes—
83C2×Dic61—22no—
84C2×Dic61—24no—
85C2×Dic61—42no—
86C2×Dic61—44no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—82no—
91C2×Dic61#12314yes—
92#92420—84no—
93#8735—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—42no—
101C22×C61#38111yescharacteristic
102C22×C61C2×C22⋊C811yescharacteristic
103C22×C61#40711yescharacteristic
104C22×C61#43112yes—
105C22×C61#43212yes—
106C4×C61—22no—
107C4×C61—22no—
108C4×C61—44no—
109Dic61—24no—
110Dic61—44no—
111Dic61—42no—
112#2274—611no—
113C2×#324—612no—
114#1282—614no—
115C2×C61—21no—
116C2×C61—21no—
117C2×C61—22no—
118C2×C61—22no—
119C2×C61#181711yescharacteristic
120C2×C61#182811yescharacteristic
121C2×C61#183011yescharacteristic
122C2×#117—611no—
123C2×#117#692311yescharacteristic
124C22×C4⋊C4—611no—
125C2×C22⋊C8—614no—
126C4×C4⋊C4—1222no—
127C4×C4⋊C4—1222no—
128C4×C22⋊C4—612no—
129C4×C22⋊C4—612no—
130#324—1222no—
131#324—1222no—
132C61#873511yescharacteristic, complemented, Sylow
133C23×C4—611no—
134C23×C4—611no—
135C23×C4C2×#692311yescharacteristic
136C22×C8—1224no—
137#117—22no—
138#117—1224no—
139#117#9242014yescomplemented
140C2×C4⋊C4—21no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—1224no—
144C2×C4⋊C4—1221no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4C2×#692312yes—
147C2×C42—21no—
148C2×C42—1221no—
149C2×C42—1222no—
150C2×C42—1222no—
151C22⋊C8—1224no—
152C22⋊C8—1224no—
153#95—1222no—
154#95—1222no—
155C24C22×#692311yescharacteristic
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—612no—
160C22×C4—614no—
161C22×C4—612no—
162C22×C4—1222no—
163C22×C4—1222no—
164C22×C4—4881no—
165C22×C4—4881no—
166C22×C4C2×#9242012yes—
167C22×C4#1175821712yes—
168C22×C4C22⋊#692311yescharacteristic
169C22×C4C22⋊#692311yescharacteristic
170C2×C8—4884no—
171C2×C8—2444no—
172C4⋊C4—24no—
173C4⋊C4—1224no—
174C4⋊C4—1224no—
175C4⋊C4—1224no—
176C22⋊C4—22no—
177C22⋊C4—614no—
178C22⋊C4—1222no—
179C22⋊C4C2×#9242014yes—
180C42—24no—
181C42—1224no—
182C42—4882no—
183C42—4882no—
184C23—41no—
185C23—41no—
186C23C2×C22⋊#692311yescharacteristic
187C23#1451985612yes—
188C23C22×#9242011yescharacteristic
189C23C2×#1175821711yescharacteristic
190C23D61⋊M1612yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—614no—
201C2×C4—1222no—
202C2×C4—1224no—
203C2×C4—4882no—
204C2×C4—2442no—
205C2×C4—2444no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4—2442no—
209C2×C4C22⋊#9242012yes—
210C2×C4C22⋊#9242012yes—
211C8—4884no—
212C22—21no—
213C22—22no—
214C22—21no—
215C22—22no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22#1684070511yescharacteristic
220C22C2×C22⋊#9242011yescharacteristic
221C22#1684073411yescharacteristic
222C22#1684077812yes—
223C22#1684078212yes—
224C4—22no—
225C4—22no—
226C4—44no—
227C4—1224no—
228C4—2444no—
229C4—2442no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2#2146170911yescharacteristic
235C2#2146173111yescharacteristic
236C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61#381
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8735
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
32. #117×C61C8semidirect
132. C61#8735semidirect
139. #117#92420semidirect

Maximal subgroups

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

subgroupindex
C2×#168406072
#214606622
#214481752
#873561