Finite Group Databasebeta

← #30603896

Subgroups — #30603896

Order 15616.

434 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461050C212yesmaximal
2#21460760C214yesmaximal, complemented
3#21448443C211yesmaximal, characteristic
4#16840778—22no—
5#16840607C2214yes—
6#16840605—22no—
7C2×#14519736C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839658—22no—
10#16839635—22no—
11#16839631C412yes—
12#16839627C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14C4⋊#92420—42no—
15C22⋊#92420—24no—
16C4×#92420—42no—
17#14519736—22no—
18#14519736—42no—
19#14519736C814yescomplemented
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61C2×C411yescharacteristic
22C2×C4⋊Dic61C2311yescharacteristic
23C2×#11758196—24no—
24C2×C22⋊Dic61—21no—
25C2×C22⋊Dic61D412yes—
26C2×C4×Dic61C2×C412yes—
27C2×C4×Dic61D412yes—
28#14519684—24no—
29C23×C4×C61—21no—
30C23×C4×C61C2×C411yescharacteristic
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61—42no—
33C2×C4⋊C4×C61C2×C412yes—
34C24×C61C22⋊C411yescharacteristic
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—42no—
39C22×C4×C61—82no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C2×C812yes—
42C22×C4×C61M1612yes—
43C22×C4×C61C22×C411yescharacteristic
44C22×Dic61—22no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C2×D412yes—
47C2×#92420—44no—
48C4⋊C4×C61—42no—
49C4⋊C4×C61—42no—
50C22⋊Dic61—24no—
51C22⋊Dic61—42no—
52C4⋊Dic61—24no—
53C4⋊Dic61—41no—
54C4⋊Dic61—41no—
55#11758196—84no—
56C4×Dic61—22no—
57C4×Dic61—22no—
58C4×Dic61—22no—
59C4×Dic61C2×C814yes—
60C23×C61—21no—
61C23×C61—21no—
62C23×C61—41no—
63C23×C61—41no—
64C23×C61C22⋊C812yes—
65C23×C61C2×C22⋊C411yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—24no—
69C2×C4×C61—24no—
70C2×C4×C61—44no—
71C2×C4×C61—42no—
72C2×C4×C61—84no—
73C2×C4×C61C22⋊C812yes—
74C2×C4×C61#9912yes—
75C2×C4×C61#10112yes—
76C2×C4×C61C22×C811yescharacteristic
77C2×C4×C61C2×M1611yescharacteristic
78C2×Dic61—24no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85#92420—84no—
86#11449—611nomaximal, Sylow
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—22no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61C2×C22⋊C811yescharacteristic
95C22×C61C2×#9911yescharacteristic
96C22×C61C2×#10111yescharacteristic
97C4×C61—21no—
98C4×C61—21no—
99C4×C61—82no—
100C4×C61#32414yes—
101Dic61—44no—
102Dic61—42no—
103Dic61—42no—
104#2317—611no—
105#1458—612no—
106#1324—614no—
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—42no—
110C2×C61C2×#32411yescharacteristic
111C2×C61#212911yescharacteristic
112C2×C61#213411yescharacteristic
113C2×#117—611no—
114C2×#117—611no—
115C22×C4⋊C4#692311yescharacteristic
116#431—1222no—
117#389—1222no—
118#385—1222no—
119#384—612no—
120#382—612no—
121#324—614no—
122#323—1222no—
123C61#1144911yescharacteristic, complemented, Sylow
124C23×C4—21no—
125C23×C4C2×#692311yescharacteristic
126#117—614no—
127#117—1222no—
128#117—2442no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—611no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—1221no—
134C2×C4⋊C4—1224no—
135C2×C4⋊C4C2×#692312yes—
136C2×C22⋊C4—612no—
137C2×C22⋊C4—1221no—
138C2×C42—612no—
139C2×C42—612no—
140C4⋊C8—2442no—
141C22⋊C8—1224no—
142C4×C8—2442no—
143#95—1224no—
144C24C22⋊#692311yescharacteristic
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—82no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—1222no—
153C22×C4D61⋊C812yes—
154C22×C4#1175821312yes—
155C22×C4C22⋊#692311yescharacteristic
156C22×C4C22×#692311yescharacteristic
157C2×C8—2444no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—1224no—
161C4⋊C4—4884no—
162C4⋊C4—2441no—
163C4⋊C4—2441no—
164C22⋊C4—1224no—
165C22⋊C4—2442no—
166C42—614no—
167C42—1222no—
168C42—1222no—
169C42—1222no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23#1451983412yes—
175C23C2×C22⋊#692311yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—44no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4—1224no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4—2442no—
190C2×C4#1451983412yes—
191C2×C4#1451983512yes—
192C2×C4#1451983812yes—
193C2×C4C2×D61⋊C811yescharacteristic
194C2×C4C2×#1175821311yescharacteristic
195C8—4884no—
196C22—21no—
197C22—21no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22C2×#1451983411yescharacteristic
204C22C2×#1451983511yescharacteristic
205C22C2×#1451983811yescharacteristic
206C4—21no—
207C4—21no—
208C4—82no—
209C4—2444no—
210C4—2442no—
211C4—2442no—
212C4#1684060814yes—
213C2—21no—
214C2—21no—
215C2—42no—
216C2C2×#1684060811yescharacteristic
217C2#2146210111yescharacteristic
218C2#2146211811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11449
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460760C2semidirect
19. #14519736C8semidirect
123. C61#11449semidirect

Maximal subgroups

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

subgroupindex
#214610502
#214607602
#214484432
#1144961