Finite Group Databasebeta

← #30599267

Subgroups — #30599267

Order 15616.

554 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 112 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
3C2×#16839627C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5C2×#14519832C2214yes—
6#16840628—22no—
7C22×C4⋊Dic61C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839627—22no—
10#16839627C412yes—
11#16839627C2212yes—
12C2×#14519684—22no—
13C22×C4⋊C4×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16#14519832—28no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—42no—
21C2×C4⋊Dic61C2×C412yes—
22C2×C4×Dic61—24no—
23C2×C4×Dic61C2×C411yescharacteristic
24C2×C4×Dic61D412yes—
25C2×C4×Dic61C2311yescharacteristic
26#14519684—24no—
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—44no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22×C411yescharacteristic
42C22×Dic61—24no—
43C22×Dic61—24no—
44C22×Dic61—22no—
45C22×Dic61—42no—
46C22×Dic61—44no—
47C22×Dic61—42no—
48C22×Dic61C22⋊C412yes—
49C22×Dic61C2×D412yes—
50C2×#92420—28no—
51C2×#92420—44no—
52C2×#92420—44no—
53C4⋊C4×C61—42no—
54C4⋊C4×C61—42no—
55C4⋊Dic61—42no—
56C4⋊Dic61—42no—
57C4×Dic61—22no—
58C4×Dic61—24no—
59C4×Dic61#4114yes—
60C23×C61—21no—
61C23×C61—21no—
62C23×C61—22no—
63C23×C61#10012yes—
64C23×C61#10414yes—
65C23×C61C2×C22⋊C411yescharacteristic
66C2×C4×C61—28no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—42no—
72C2×C4×C61—44no—
73C2×C4×C61—84no—
74C2×C4×C61#10112yes—
75C2×C4×C61#11712yes—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—48no—
82C2×Dic61—42no—
83C2×Dic61—44no—
84C2×Dic61—84no—
85C2×Dic61#12314yes—
86#92420—48no—
87#8718—611nomaximal, Sylow
88C22×C61—22no—
89C22×C61—24no—
90C22×C61—24no—
91C22×C61—22no—
92C22×C61#32914yes—
93C22×C61#38111yescharacteristic
94C22×C61C2×#10011yescharacteristic
95C22×C61C2×#10111yescharacteristic
96C22×C61C2×#10412yes—
97C22×C61#42112yes—
98C4×C61—22no—
99C4×C61—22no—
100C4×C61—82no—
101Dic61—24no—
102Dic61—42no—
103Dic61—82no—
104C2×#382—611no—
105#1749—612no—
106#1295—614no—
107C2×C61—24no—
108C2×C61C2×#32911yescharacteristic
109C2×C61#152812yes—
110C2×C61#153311yescharacteristic
111C2×C61#182111yescharacteristic
112C2×C61#182612yes—
113C22×C4⋊C4—611no—
114C22×C4⋊C4#692311yescharacteristic
115C22×C42—611no—
116C2×C22⋊C8—1222no—
117C2×#97—614no—
118#382—612no—
119#382—612no—
120#382—1222no—
121C2×#95—1222no—
122#336—1222no—
123C61#871811yescharacteristic, complemented, Sylow
124C23×C4—21no—
125C23×C4—612no—
126C23×C4—1221no—
127C23×C4C2×#692311yescharacteristic
128C22×C8—1224no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—1221no—
133C2×C4⋊C4—2442no—
134C2×C4⋊C4C2×#692312yes—
135C2×C42—611no—
136C2×C42—612no—
137C2×C42—611no—
138C2×C42—1224no—
139C22⋊C8—1228no—
140#97—1228no—
141#95—1224no—
142#95—1224no—
143C24C22⋊#692311yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—44no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—1224no—
153C22×C4—1224no—
154C22×C4—1222no—
155C22×C4—2442no—
156C22×C4—2444no—
157C22×C4—2442no—
158C22×C4C22⋊#692311yescharacteristic
159C22×C4C22×#692311yescharacteristic
160C2×C8—1228no—
161C2×C8—2444no—
162C2×C8—2444no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—2442no—
166C4⋊C4—2442no—
167C42—614no—
168C42—1224no—
169C42—1222no—
170C23—21no—
171C23—21no—
172C23—22no—
173C23#1451983712yes—
174C23#1451984114yes—
175C23C2×C22⋊#692311yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—44no—
183C2×C4—84no—
184C2×C4—614no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—4884no—
191C2×C4—2448no—
192C2×C4—2442no—
193C2×C4—2444no—
194C2×C4#1451983812yes—
195C2×C4#1451985612yes—
196C8—2448no—
197C22—24no—
198C22—22no—
199C22—22no—
200C22—24no—
201C22#1684061714yes—
202C22#1684070511yescharacteristic
203C22C2×#1451983711yescharacteristic
204C22C2×#1451983811yescharacteristic
205C22C2×#1451984112yes—
206C22#1684076112yes—
207C4—22no—
208C4—22no—
209C4—82no—
210C4—1224no—
211C4—4882no—
212C4—2442no—
213C2—24no—
214C2C2×#1684061711yescharacteristic
215C2#2146128112yes—
216C2#2146130011yescharacteristic
217C2#2146171811yescharacteristic
218C2#2146172512yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8718
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
123. C61#8718semidirect

Maximal subgroups

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

subgroupindex
#214615452
#214606952
C2×#168396272
#871861