Finite Group Databasebeta

← #30604128

Subgroups — #30604128

Order 15616.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461070C212yesmaximal
2#21460760C214yesmaximal, complemented
3#21448443C211yesmaximal, characteristic
4#16840782—22no—
5#16840607C2214yes—
6#16840605—22no—
7C2×#14519736C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839658—22no—
10#16839635—22no—
11#16839631C412yes—
12#16839627C2212yes—
13C22×C4⋊C4×C61C411yescharacteristic
14#14519844—42no—
15C22⋊#92420—24no—
16#14519832—42no—
17#14519736—24no—
18#14519736—42no—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61C2×C411yescharacteristic
21C2×C4⋊Dic61C2311yescharacteristic
22C2×#11758196—24no—
23C2×C22⋊Dic61—21no—
24C2×C22⋊Dic61D412yes—
25C2×C4×Dic61C2×C412yes—
26C2×C4×Dic61D412yes—
27#14519684—24no—
28C23×C4×C61—21no—
29C23×C4×C61C2×C411yescharacteristic
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—42no—
32C2×C4⋊C4×C61C2×C412yes—
33C24×C61C22⋊C411yescharacteristic
34C22×C4×C61—22no—
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×C61C22×C411yescharacteristic
42C22×Dic61—22no—
43C22×Dic61C22⋊C412yes—
44C22×Dic61C2×D412yes—
45C2×#92420—44no—
46C4⋊C4×C61—42no—
47C4⋊C4×C61—42no—
48C22⋊Dic61—24no—
49C22⋊Dic61—42no—
50C4⋊Dic61—24no—
51C4⋊Dic61—41no—
52C4⋊Dic61—41no—
53#11758196—84no—
54C4×Dic61—22no—
55C4×Dic61—22no—
56C4×Dic61—22no—
57C4×Dic61M1614yes—
58C23×C61—21no—
59C23×C61—21no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61#10112yes—
63C23×C61C2×C22⋊C411yescharacteristic
64C2×C4×C61—28no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—44no—
70C2×C4×C61—42no—
71C2×C4×C61—84no—
72C2×C4×C61#9912yes—
73C2×C4×C61C2×M1612yes—
74C2×Dic61—24no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81#92420—84no—
82#11515—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—22no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61#40711yescharacteristic
91C22×C61C2×#9911yescharacteristic
92C22×C61C2×#10111yescharacteristic
93C4×C61—22no—
94C4×C61—22no—
95C4×C61—82no—
96Dic61—44no—
97Dic61—42no—
98Dic61—42no—
99#2317—611no—
100#1464—612no—
101#1324—614no—
102C2×C61—21no—
103C2×C61—21no—
104C2×C61—42no—
105C2×C61#146311yescharacteristic
106C2×C61#212911yescharacteristic
107C2×C61#213411yescharacteristic
108C2×#117—611no—
109C2×#117—611no—
110C22×C4⋊C4#692311yescharacteristic
111#432—1222no—
112#389—1222no—
113#385—1222no—
114#384—612no—
115#382—612no—
116#324—614no—
117#323—1222no—
118C61#1151511yescharacteristic, complemented, Sylow
119C23×C4—21no—
120C23×C4C2×#692311yescharacteristic
121#117—1224no—
122#117—2442no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—611no—
126C2×C4⋊C4—611no—
127C2×C4⋊C4—1221no—
128C2×C4⋊C4—1224no—
129C2×C4⋊C4C2×#692312yes—
130C2×C22⋊C4—612no—
131C2×C22⋊C4—1221no—
132C2×C42—612no—
133C2×C42—612no—
134C4⋊C8—2442no—
135C22⋊C8—1224no—
136#97—2442no—
137#95—1224no—
138C24C22⋊#692311yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—82no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—1222no—
148C22×C4C22⋊#692311yescharacteristic
149C22×C4C22×#692311yescharacteristic
150C2×C8—2444no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—1224no—
154C4⋊C4—4884no—
155C4⋊C4—2441no—
156C4⋊C4—2441no—
157C22⋊C4—1224no—
158C22⋊C4—2442no—
159C42—614no—
160C42—1222no—
161C42—1222no—
162C42—1222no—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#1451983812yes—
168C23C2×C22⋊#692311yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—44no—
175C2×C4—42no—
176C2×C4—84no—
177C2×C4—1224no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—2442no—
181C2×C4—2442no—
182C2×C4—2442no—
183C2×C4—2442no—
184C2×C4#1451983512yes—
185C2×C4D61⋊M1612yes—
186C8—4884no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22#1684073411yescharacteristic
195C22C2×#1451983511yescharacteristic
196C22C2×#1451983811yescharacteristic
197C4—22no—
198C4—22no—
199C4—82no—
200C4—2444no—
201C4—2442no—
202C4—2442no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2#2146106911yescharacteristic
207C2#2146210111yescharacteristic
208C2#2146211811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11515
LCSG ▷ C22×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
118. C61#11515semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607602
#214484432
#1151561