Finite Group Databasebeta

← #30594745

Subgroups — #30594745

Order 15616.

484 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 50 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#21461648C212yesmaximal
2#21445736C211yesmaximal, characteristic
3C2×#14519836—22no—
4C2×#14519835—22no—
5#16840705C414yescomplemented
6C22×#11758222C2211yescharacteristic
7C2×#14519691—22no—
8#16839625C411yescharacteristic, complemented
9C61×#381C411yescharacteristic, complemented
10C2×C22⋊#6923—24no—
11#14519836—44no—
12#14519835—42no—
13#14519835—42no—
14(C2×#6923)⋊C4—44no—
15C2×#11758222—44no—
16C2×#11758222—41no—
17C2×#11758222—41no—
18C22×Dic122Q811yescharacteristic
19C22×D244D411yescharacteristic
20C22×C22⋊D61D412yes—
21C22×C4×D61C2×C412yes—
22C2×C22⋊Dic61—21no—
23#14519691—44no—
24#14519684—41no—
25C23×C4×C61C2×C411yescharacteristic
26C2×C22⋊C4×C61—21no—
27#95×C61—41no—
28C24×C61C22⋊C411yescharacteristic
29C23×D61C22⋊C412yes—
30C22×#6923—44no—
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—42no—
34C22×C4×C61—41no—
35C22×C4×C61C4211yescharacteristic
36C22×C4×C61C4⋊C411yescharacteristic
37C2×C22⋊D61—22no—
38C2×C22⋊D61—22no—
39C2×C22⋊D61—24no—
40C2×C22⋊D61—42no—
41C22×Dic61—41no—
42C22×Dic61C4⋊C412yes—
43#11758222—48no—
44#11758222—48no—
45C2×D244—24no—
46C2×D244—41no—
47C2×C4×D61—24no—
48C2×C4×D61—42no—
49C2×C4×D61—42no—
50C2×Dic122—42no—
51C2×Dic122—41no—
52C22⋊#6923—44no—
53C22⋊#6923—44no—
54C22⋊C4×C61—42no—
55C22⋊Dic61—42no—
56C23×C61—22no—
57C23×C61—81no—
58C23×C61#9511yescharacteristic
59C23×C61#9911yescharacteristic
60C23×C61#9911yescharacteristic
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—82no—
64C22×D61#9914yes—
65C2×#6923—84no—
66C2×#6923—88no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—42no—
72C2×C4×C61—42no—
73C2×C4×C61—81no—
74C2×C4×C61—82no—
75C22⋊D61—44no—
76C22⋊D61—44no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—81no—
81C2×Dic61—82no—
82D244—44no—
83C4×D61—48no—
84Dic122—44no—
85#7318—611nomaximal, Sylow
86C22×C61—21no—
87C22×C61—21no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—82no—
92C22×C61#34212yes—
93C22×C61#34211yescharacteristic
94C2×D61—24no—
95C2×D61—44no—
96C2×D61—82no—
97C2×D61—82no—
98#6923—164no—
99C4×C61—41no—
100C4×C61—41no—
101C4×C61—161no—
102Dic61—42no—
103Dic61—161no—
104#1782—612no—
105#1782—611no—
106C2×C61—22no—
107C2×C61—21no—
108C2×C61—41no—
109C2×C61—41no—
110C2×C61#130411yescharacteristic
111D61—44no—
112C22×#41—611no—
113C2×#99—1222no—
114C2×#99—1222no—
115C2×#99—1222no—
116#381—614no—
117#381—611no—
118#381#692311yescharacteristic, complemented
119C61#731811yescharacteristic, complemented, Sylow
120C2×#41—2441no—
121C2×#41—2441no—
122C2×#41—2444no—
123C22×Q8—611no—
124C22×D4—612no—
125C22×D4—611no—
126C23×C4—612no—
127C23×C4C2×#692311yescharacteristic
128C2×C22⋊C4—21no—
129C2×C22⋊C4—1224no—
130C2×C22⋊C4—1221no—
131#99—2444no—
132#99—2442no—
133#99—2442no—
134#99—2444no—
135#95—41no—
136#95—2441no—
137#95—2444no—
138C24—612no—
139C24C22⋊#692311yescharacteristic
140#41—2448no—
141#41—2448no—
142C2×Q8—2442no—
143C2×Q8—2441no—
144C2×D4—1224no—
145C2×D4—1224no—
146C2×D4—1222no—
147C2×D4—1222no—
148C2×D4—2441no—
149C2×D4—2442no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—42no—
153C22×C4—41no—
154C22×C4—612no—
155C22×C4—1224no—
156C22×C4—2442no—
157C22×C4—2442no—
158C22×C4—2444no—
159C22×C4—2441no—
160C22×C4C4×#692311yescharacteristic
161C22×C4C4⋊#692311yescharacteristic
162C22⋊C4—42no—
163C22⋊C4—2442no—
164C22⋊C4—2444no—
165C22⋊C4—2444no—
166C23—22no—
167C23—81no—
168C23—614no—
169C23—1222no—
170C23—1222no—
171C23—4882no—
172C23(C2×#6923)⋊C411yescharacteristic
173C23#1451983511yescharacteristic
174C23#1451983611yescharacteristic
175Q8—2444no—
176D4—2444no—
177D4—2444no—
178D4—2444no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—81no—
186C2×C4—82no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—4881no—
191C2×C4—4882no—
192C2×C4—4884no—
193C2×C4—4888no—
194C2×C4—2448no—
195C22—21no—
196C22—21no—
197C22—41no—
198C22—41no—
199C22—41no—
200C22—82no—
201C22—1224no—
202C22—4882no—
203C22—4882no—
204C22—2444no—
205C22#1684063912yes—
206C22#1684064011yescharacteristic
207C4—41no—
208C4—41no—
209C4—161no—
210C4—9761no—
211C4—9764no—
212C4—2442no—
213C2—21no—
214C2—22no—
215C2—41no—
216C2—41no—
217C2—2444no—
218C2#2146071811yescharacteristic
subgroupG/H
centerC2#21460718
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC61×#381C4
socleC2×C61#1304
prime radical, cosocleC22×#11758222C22
hypercenter#381#6923
hypocenterC61#7318
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
5. #16840705C4semidirect
8. #16839625C4semidirect
9. C61×#381C4semidirect
118. #381#6923semidirect
119. C61#7318semidirect

Maximal subgroups

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

subgroupindex
#214616482
#214457362
#731861