Finite Group Databasebeta

← #30599222

Subgroups — #30599222

Order 15616.

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

normal subgroups only

This group has 530 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#21461710C212yesmaximal
2#21460657C214yesmaximal
3C2×#16839627C211yesmaximal, characteristic
4C2×C22⋊#92420C2214yes—
5#16840628—22no—
6#16840628—22no—
7C22×C4⋊Dic61C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839627—22no—
10#16839627—22no—
11C2×#14519684C412yes—
12C2×#14519684C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16C23×Dic61C2×C411yescharacteristic
17C23×Dic61C2×C412yes—
18C23×Dic61C2311yescharacteristic
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61—42no—
22C2×C4×Dic61—24no—
23C2×C4×Dic61D412yes—
24C2×C4×Dic61D412yes—
25#14519684—24no—
26#14519684—24no—
27C23×C4×C61C2×C412yes—
28C23×C4×C61C2×C411yescharacteristic
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—42no—
32C24×C61C22×C411yescharacteristic
33C22×C4×C61—22no—
34C22×C4×C61—22no—
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—24no—
38C22×C4×C61—42no—
39C22×C4×C61—42no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×Dic61—22no—
43C22×Dic61—22no—
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61—24no—
47C22×Dic61—41no—
48C22×Dic61—41no—
49C22×Dic61—42no—
50C22×Dic61—42no—
51C22×Dic61C22⋊C412yes—
52C22×Dic61C2×D412yes—
53C22×Dic61#4114yes—
54C2×#92420—44no—
55C2×#92420—44no—
56C2×#92420—44no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C4⋊Dic61—42no—
60C4⋊Dic61—42no—
61C4×Dic61—24no—
62C4×Dic61—24no—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61C2×C22⋊C411yescharacteristic
68C23×C61#11712yes—
69C23×C61#13112yes—
70C23×C61#13112yes—
71C2×C4×C61—28no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—84no—
80C2×C4×C61#10012yes—
81C2×C4×C61#10112yes—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—44no—
88C2×Dic61—44no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—84no—
93C2×Dic61#12314yes—
94#92420—84no—
95#8703—611nomaximal, Sylow
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61#38111yescharacteristic
103C22×C61#40811yescharacteristic
104C22×C61#40811yescharacteristic
105C22×C61#41011yescharacteristic
106C22×C61#41011yescharacteristic
107C22×C61C2×#10011yescharacteristic
108C22×C61C2×#10111yescharacteristic
109C22×C61#43314yes—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—82no—
113Dic61—24no—
114Dic61—42no—
115Dic61—82no—
116C2×#382—611no—
117#1817—612no—
118#1280—614no—
119C2×C61—24no—
120C2×C61#146911yescharacteristic
121C2×C61#146911yescharacteristic
122C2×C61#147011yescharacteristic
123C2×C61#147011yescharacteristic
124C2×C61#181811yescharacteristic
125C2×C61#182011yescharacteristic
126C2×C61#182111yescharacteristic
127C22×C4⋊C4—611no—
128C22×C4⋊C4#692311yescharacteristic
129C22×C42—611no—
130C2×C22⋊C8—614no—
131#382—1222no—
132#382—1222no—
133C2×#95—612no—
134C2×#95—612no—
135#336—1222no—
136#336—1222no—
137C61#870311yescharacteristic, complemented, Sylow
138C23×C4—611no—
139C23×C4—611no—
140C23×C4—612no—
141C23×C4C2×#692312yes—
142C23×C4C2×#692311yescharacteristic
143C22×C8—1224no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—42no—
147C2×C4⋊C4—1221no—
148C2×C4⋊C4—1221no—
149C2×C4⋊C4—2442no—
150C2×C42—612no—
151C2×C42—612no—
152C2×C42—1224no—
153C22⋊C8—1228no—
154#95—1224no—
155#95—1224no—
156C24C22×#692311yescharacteristic
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—24no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—612no—
165C22×C4—614no—
166C22×C4—612no—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—1224no—
171C22×C4—1222no—
172C22×C4—2441no—
173C22×C4—2441no—
174C22×C4—2442no—
175C22×C4—2442no—
176C22×C4C22⋊#692311yescharacteristic
177C22×C4C22⋊#692311yescharacteristic
178C2×C8—2444no—
179C2×C8—2444no—
180C2×C8—2444no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—2442no—
184C4⋊C4—2442no—
185C42—1224no—
186C42—1224no—
187C23—21no—
188C23—21no—
189C23—21no—
190C23—21no—
191C23C2×C22⋊#692311yescharacteristic
192C23#1451985612yes—
193C23#1451986412yes—
194C23#1451986512yes—
195C2×C4—28no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—84no—
204C2×C4—614no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—4884no—
211C2×C4—2444no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2444no—
216C2×C4#1451983712yes—
217C2×C4#1451983812yes—
218C8—4884no—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22#1684070511yescharacteristic
226C22#1684073611yescharacteristic
227C22#1684073711yescharacteristic
228C22#1684074211yescharacteristic
229C22#1684074311yescharacteristic
230C22C2×#1451983711yescharacteristic
231C22C2×#1451983811yescharacteristic
232C22#1684078714yes—
233C4—22no—
234C4—22no—
235C4—82no—
236C4—1224no—
237C4—4882no—
238C4—2442no—
239C2—24no—
240C2#2146108911yescharacteristic
241C2#2146109011yescharacteristic
242C2#2146109211yescharacteristic
243C2#2146109311yescharacteristic
244C2#2146171311yescharacteristic
245C2#2146171711yescharacteristic
246C2#2146171811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8703
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
137. C61#8703semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214606572
C2×#168396272
#870361