Finite Group Databasebeta

← #30599279

Subgroups — #30599279

Order 15616.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461545C212yesmaximal
2#21460695C214yesmaximal, complemented
3#21448222C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5C2×#14519832C2214yes—
6#16840628—22no—
7C2×#14519736C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839631C412yes—
10#16839627C2212yes—
11#16839620—22no—
12C4×#11758196—22no—
13C2×#117×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16#14519832—28no—
17C23×Dic61D412yes—
18#14519736—42no—
19C2×C4⋊Dic61C2×C412yes—
20C2×#11758196—22no—
21C2×#11758196—22no—
22C2×C22⋊Dic61—21no—
23C2×C4×Dic61—24no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61D412yes—
27C2×C4×Dic61C2311yescharacteristic
28#14519684—24no—
29C23×C4×C61C2×C411yescharacteristic
30#117×C61—42no—
31C2×C4⋊C4×C61C2×C412yes—
32C2×C22⋊C4×C61—21no—
33C2×C42×C61—21no—
34C24×C61C22⋊C411yescharacteristic
35C22×C4×C61—22no—
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61C22⋊C411yescharacteristic
40C22×C4×C61C22×C411yescharacteristic
41C22×Dic61—24no—
42C22×Dic61—24no—
43C22×Dic61—22no—
44C22×Dic61—42no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C2×D412yes—
47C2×#92420—28no—
48C2×#92420—44no—
49C2×#92420—44no—
50C4⋊C4×C61—42no—
51C22⋊C4×C61—42no—
52C42×C61—42no—
53C22⋊Dic61—42no—
54C4⋊Dic61—42no—
55#11758196—44no—
56#11758196—44no—
57C4×Dic61—22no—
58C4×Dic61—24no—
59C4×Dic61—42no—
60C4×Dic61#4114yes—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61—22no—
64C23×C61—22no—
65C23×C61#10012yes—
66C23×C61C2×C22⋊C411yescharacteristic
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#10112yes—
76C2×C4×C61#11712yes—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—48no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61#10414yes—
86C2×Dic61#12314yes—
87#92420—48no—
88#8722—611nomaximal, Sylow
89C22×C61—22no—
90C22×C61—24no—
91C22×C61—41no—
92C22×C61—42no—
93C22×C61—41no—
94C22×C61#38111yescharacteristic
95C22×C61C2×#10011yescharacteristic
96C22×C61C2×#10111yescharacteristic
97C22×C61C2×#10412yes—
98C22×C61#42112yes—
99C4×C61—22no—
100C4×C61—22no—
101C4×C61—82no—
102Dic61—24no—
103Dic61—24no—
104Dic61—82no—
105#2285—611no—
106#1749—612no—
107#1295—614no—
108C2×C61—42no—
109C2×C61#152611yescharacteristic
110C2×C61#153012yes—
111C2×C61#153711yescharacteristic
112C2×C61#182111yescharacteristic
113C2×C61#182612yes—
114C2×#117—611no—
115C2×#117#692311yescharacteristic
116C22×C42—611no—
117C2×C22⋊C8—1222no—
118C2×#97—614no—
119#384—612no—
120#382—612no—
121#380—1222no—
122C4×C4⋊C4—1222no—
123#336—1222no—
124C61#872211yescharacteristic, complemented, Sylow
125C23×C4—612no—
126C23×C4C2×#692311yescharacteristic
127C22×C8—1224no—
128#117—42no—
129#117—2442no—
130C2×C4⋊C4—612no—
131C2×C4⋊C4—1222no—
132C2×C4⋊C4—1222no—
133C2×C4⋊C4C2×#692312yes—
134C2×C22⋊C4—21no—
135C2×C22⋊C4—1221no—
136C2×C42—21no—
137C2×C42—611no—
138C2×C42—612no—
139C2×C42—611no—
140C2×C42—1224no—
141C2×C42—1221no—
142C22⋊C8—1228no—
143#97—1228no—
144#95—1224no—
145C24C22⋊#692311yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—1224no—
153C22×C4—1224no—
154C22×C4—1222no—
155C22×C4—2442no—
156C22×C4C22⋊#692311yescharacteristic
157C22×C4C22×#692311yescharacteristic
158C2×C8—1228no—
159C2×C8—2444no—
160C2×C8—2444no—
161C4⋊C4—42no—
162C4⋊C4—2442no—
163C4⋊C4—2444no—
164C4⋊C4—2444no—
165C22⋊C4—42no—
166C22⋊C4—2442no—
167C42—42no—
168C42—614no—
169C42—1224no—
170C42—1222no—
171C42—2442no—
172C23—21no—
173C23—21no—
174C23—22no—
175C23—22no—
176C23#1451983712yes—
177C23C2×C22⋊#692311yescharacteristic
178C2×C4—28no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—614no—
187C2×C4—614no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—2448no—
193C2×C4—2442no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4#1451983812yes—
197C2×C4#1451985612yes—
198C8—2448no—
199C22—24no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—42no—
204C22#1684070511yescharacteristic
205C22C2×#1451983711yescharacteristic
206C22C2×#1451983811yescharacteristic
207C22D61⋊#10412yes—
208C22#1684075912yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—1224no—
213C4—1224no—
214C4—4882no—
215C2—42no—
216C2#2146127611yescharacteristic
217C2#2146128812yes—
218C2#2146131011yescharacteristic
219C2#2146171811yescharacteristic
220C2#2146172712yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8722
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
124. C61#8722semidirect

Maximal subgroups

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

subgroupindex
#214615452
#214606952
#214482222
#872261