Finite Group Databasebeta

← #30599366

Subgroups — #30599366

Order 15616.

438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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#21460720C214yesmaximal
3#21448435C211yesmaximal, characteristic
4#16840732C2214yes—
5#16840607—22no—
6#16840607—22no—
7C2×#14519736C411yescharacteristic
8C22×C4⋊Dic61C2211yescharacteristic
9#16839660—22no—
10#16839658—22no—
11#16839620C412yes—
12#16839620C2212yes—
13C2×#117×C61C411yescharacteristic
14C2×#11758217—24no—
15C22⋊#92420—24no—
16C22⋊#92420—24no—
17C23×Dic61C2×C411yescharacteristic
18C23×Dic61C2311yescharacteristic
19#14519736—42no—
20C2×C4⋊Dic61—24no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61D412yes—
24C2×#11758196—22no—
25C2×#11758196—22no—
26C2×C22⋊Dic61C2×C412yes—
27C2×C4×Dic61—21no—
28#14519684—22no—
29#14519684—22no—
30C23×C4×C61C2×C411yescharacteristic
31#117×C61—42no—
32C2×C4⋊C4×C61—21no—
33C2×C22⋊C4×C61C2×C412yes—
34C2×C42×C61—21no—
35C24×C61C22×C411yescharacteristic
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×Dic61—22no—
43C22×Dic61—22no—
44C22×Dic61—81no—
45C22×Dic61—81no—
46C22×Dic61C22⋊C412yes—
47C22×Dic61C2×D412yes—
48C22×Dic61#4114yes—
49#11758217—84no—
50C2×#92420—44no—
51C4⋊C4×C61—42no—
52C22⋊C4×C61—42no—
53C42×C61—42no—
54C22⋊Dic61—42no—
55C4⋊Dic61—24no—
56C4⋊Dic61—24no—
57C4⋊Dic61—42no—
58#11758196—82no—
59#11758196—82no—
60C4×Dic61—42no—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61—41no—
64C23×C61—41no—
65C23×C61C2×C22⋊C411yescharacteristic
66C23×C61#11712yes—
67C2×C4×C61—28no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61#10012yes—
76C2×C4×C61#10112yes—
77C2×Dic61—22no—
78C2×Dic61—42no—
79C2×Dic61—44no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—82no—
85C2×Dic61#12314yes—
86#92420—84no—
87#8757—611nomaximal, Sylow
88C22×C61—21no—
89C22×C61—21no—
90C22×C61—22no—
91C22×C61—22no—
92C22×C61—22no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61#38111yescharacteristic
96C22×C61C2×#10011yescharacteristic
97C22×C61C2×#10111yescharacteristic
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—82no—
101Dic61—24no—
102Dic61—42no—
103Dic61—82no—
104#2316—611no—
105#1463—612no—
106#1305—614no—
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—42no—
110C2×C61#182111yescharacteristic
111C2×C61#182811yescharacteristic
112C2×C61#183011yescharacteristic
113C2×#117—611no—
114C2×#117#692311yescharacteristic
115C22×C4⋊C4—611no—
116#407—614no—
117#389—1222no—
118#389—1222no—
119#380—612no—
120#380—612no—
121#324—1222no—
122#324—1222no—
123C61#875711yescharacteristic, complemented, Sylow
124C23×C4—611no—
125C23×C4—611no—
126C23×C4C2×#692311yescharacteristic
127C2×M16—1224no—
128#117—42no—
129#117—2442no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—1224no—
134C2×C4⋊C4—1222no—
135C2×C4⋊C4—1222no—
136C2×C4⋊C4—1221no—
137C2×C22⋊C4—612no—
138C2×C22⋊C4C2×#692312yes—
139C2×C42—21no—
140C2×C42—1221no—
141C22⋊C8—1224no—
142C22⋊C8—1224no—
143#95—1222no—
144#95—1222no—
145C24C22×#692311yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—612no—
151C22×C4—614no—
152C22×C4—612no—
153C22×C4—1222no—
154C22×C4—1222no—
155C22×C4—4881no—
156C22×C4—4881no—
157C22×C4C22⋊#692311yescharacteristic
158C22×C4C22⋊#692311yescharacteristic
159M16—4884no—
160C2×C8—2444no—
161C4⋊C4—42no—
162C4⋊C4—1224no—
163C4⋊C4—1224no—
164C4⋊C4—4882no—
165C4⋊C4—4882no—
166C4⋊C4—2442no—
167C22⋊C4—42no—
168C22⋊C4—2442no—
169C42—42no—
170C42—2442no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊#692311yescharacteristic
176C23#1451985612yes—
177C2×C4—28no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—614no—
186C2×C4—1222no—
187C2×C4—4882no—
188C2×C4—2442no—
189C2×C4—2444no—
190C2×C4—2442no—
191C2×C4—2442no—
192C2×C4—2442no—
193C2×C4—2442no—
194C2×C4#1451983712yes—
195C2×C4#1451983812yes—
196C8—4884no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—42no—
203C22—42no—
204C22#1684070511yescharacteristic
205C22C2×#1451983711yescharacteristic
206C22C2×#1451983811yescharacteristic
207C4—22no—
208C4—22no—
209C4—82no—
210C4—1224no—
211C4—4882no—
212C4—2442no—
213C2—21no—
214C2—21no—
215C2—42no—
216C2#2146171811yescharacteristic
217C2#2146173111yescharacteristic
218C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8757
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
123. C61#8757semidirect

Maximal subgroups

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

subgroupindex
#214610672
#214607202
#214484352
#875761