Finite Group Databasebeta

← #30599372

Subgroups — #30599372

Order 15616.

474 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461066C212yesmaximal
2#21460720C214yesmaximal, complemented
3#21448414C211yesmaximal, characteristic
4#16840732C2214yes—
5#16840606—22no—
6#16840606—22no—
7C22×#11758198C2211yescharacteristic
8#16839653—22no—
9#16839651—22no—
10#16839620C2212yes—
11#16839617C412yes—
12C4×C22⋊Dic61C411yescharacteristic
13C4×C22⋊C4×C61C411yescharacteristic
14C2×#11758217—24no—
15C22⋊#92420—24no—
16C22⋊#92420—24no—
17C24×D61C2×C411yescharacteristic
18C23×Dic61C2311yescharacteristic
19C2×#11758196—22no—
20C2×C22⋊Dic61C2×C412yes—
21C2×#11758198—24no—
22C2×#11758198—22no—
23C2×#11758198—22no—
24C2×#11758198D412yes—
25C2×#11758198D412yes—
26C2×C4×Dic61—21no—
27#14519684—21no—
28#14519684—22no—
29C23×C4×C61C2×C411yescharacteristic
30C2×C22⋊C4×C61C2×C412yes—
31C2×C42×C61—21no—
32#95×C61—21no—
33C24×C61C22×C411yescharacteristic
34C23×D61—22no—
35C23×D61—42no—
36C23×D61—81no—
37C23×D61—81no—
38C23×D61C22⋊C412yes—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—81no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×Dic61—22no—
45C22×Dic61—81no—
46C22×Dic61C2×D412yes—
47C22×Dic61#4114yes—
48#11758217—84no—
49C2×#92420—44no—
50C22⋊C4×C61—42no—
51C42×C61—81no—
52C22⋊Dic61—42no—
53#11758198—24no—
54#11758198—24no—
55#11758198—82no—
56#11758198—82no—
57#11758196—82no—
58C4×Dic61—81no—
59C23×C61—22no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61C2×C22⋊C411yescharacteristic
63C23×C61#11712yes—
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—44no—
67C22×D61—42no—
68C22×D61—42no—
69C22×D61—82no—
70C22×D61—82no—
71C22×D61—88no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61—82no—
80C2×Dic61—42no—
81C2×Dic61—44no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61#12314yes—
86#92420—84no—
87#8759—611nomaximal, Sylow
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—22no—
91C22×C61—22no—
92C22×C61—22no—
93C22×C61—44no—
94C22×C61#38111yescharacteristic
95C22×C61#41312yes—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—88no—
100C2×D61—84no—
101C4×C61—41no—
102C4×C61—41no—
103C4×C61—82no—
104Dic61—24no—
105Dic61—82no—
106#2312—611no—
107#1462—612no—
108#1305—614no—
109C2×C61—22no—
110C2×C61—42no—
111C2×C61#182211yescharacteristic
112C2×C61#182811yescharacteristic
113C2×C61#182911yescharacteristic
114D61—82no—
115C22×C22⋊C4—611no—
116#407—614no—
117#388—1222no—
118#388—1222no—
119#380—612no—
120#379—612no—
121C4×C22⋊C4—611no—
122C4×C22⋊C4#692311yescharacteristic
123#323—1222no—
124#323—1222no—
125C61#875911yescharacteristic, complemented, Sylow
126C25—611no—
127C23×C4—611no—
128C23×C4C2×#692311yescharacteristic
129C2×M16—1224no—
130C2×C4⋊C4—1222no—
131C2×C22⋊C4—612no—
132C2×C22⋊C4—612no—
133C2×C22⋊C4—612no—
134C2×C22⋊C4—1224no—
135C2×C22⋊C4—1222no—
136C2×C22⋊C4—1222no—
137C2×C22⋊C4C2×#692312yes—
138C2×C42—21no—
139C2×C42—1221no—
140C22⋊C8—1224no—
141C22⋊C8—1224no—
142#95—21no—
143#95—1222no—
144#95—1221no—
145C24—612no—
146C24—1222no—
147C24—4881no—
148C24—4881no—
149C24—2442no—
150C24C22×#692311yescharacteristic
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—81no—
154C22×C4—612no—
155C22×C4—614no—
156C22×C4—1222no—
157C22×C4—4881no—
158C22×C4C22⋊#692311yescharacteristic
159C22×C4C22⋊#692311yescharacteristic
160M16—4884no—
161C2×C8—2444no—
162C4⋊C4—4882no—
163C22⋊C4—42no—
164C22⋊C4—1224no—
165C22⋊C4—1224no—
166C22⋊C4—4882no—
167C22⋊C4—4882no—
168C22⋊C4—2442no—
169C42—81no—
170C42—4881no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—1224no—
175C23—1222no—
176C23—4882no—
177C23—4882no—
178C23—4888no—
179C23—2442no—
180C23—2442no—
181C23—2444no—
182C23C2×C22⋊#692311yescharacteristic
183C23#1451985612yes—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—82no—
192C2×C4—614no—
193C2×C4—2442no—
194C2×C4—2444no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4—2442no—
198C8—4884no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—44no—
205C22—4884no—
206C22—4888no—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22#1684070511yescharacteristic
211C22#1684074812yes—
212C4—41no—
213C4—41no—
214C4—82no—
215C4—1224no—
216C4—4882no—
217C2—22no—
218C2—42no—
219C2—4882no—
220C2#2146172011yescharacteristic
221C2#2146173111yescharacteristic
222C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC24×D61C2×C4
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8759
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460720C2semidirect
125. C61#8759semidirect

Maximal subgroups

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

subgroupindex
#214610662
#214607202
#214484142
#875961