Finite Group Databasebeta

← #30594747

Subgroups — #30594747

Order 15616.

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

normal subgroups only

This group has 456 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#21461655C212yesmaximal
2#21445736C211yesmaximal, characteristic
3C2×#14519838—22no—
4C2×#14519837—22no—
5#16840734C414yescomplemented
6C22×#11758222C2211yescharacteristic
7C2×#14519691—22no—
8#16839625C411yescharacteristic
9C61×#381C411yescharacteristic
10C2×#11758217—24no—
11#14519838—44no—
12#14519837—42no—
13#14519837—42no—
14#14519834—44no—
15C2×#11758222—44no—
16C2×#11758222—41no—
17C2×#11758222—41no—
18C22×Dic122D411yescharacteristic
19C22×D244Q811yescharacteristic
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×D61C4⋊C412yes—
30C22×C4×C61—21no—
31C22×C4×C61—21no—
32C22×C4×C61—42no—
33C22×C4×C61—41no—
34C22×C4×C61C4211yescharacteristic
35C22×C4×C61C4⋊C411yescharacteristic
36C2×C22⋊D61—22no—
37C2×C22⋊D61—22no—
38C2×C22⋊D61—24no—
39C2×C22⋊D61—42no—
40C22×Dic61—41no—
41C22×Dic61C22⋊C412yes—
42#11758222—48no—
43#11758222—48no—
44C2×D244—42no—
45C2×D244—41no—
46C2×C4×D61—24no—
47C2×C4×D61—42no—
48C2×C4×D61—42no—
49C2×Dic122—24no—
50C2×Dic122—41no—
51#11758217—44no—
52#11758217—44no—
53C2×#92420—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—22no—
64C22×D61—82no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—81no—
72C2×C4×C61—82no—
73C22⋊D61—44no—
74C22⋊D61—44no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—81no—
78C2×Dic61—82no—
79C2×Dic61#9914yes—
80D244—44no—
81C4×D61—48no—
82Dic122—44no—
83#92420—84no—
84#7319—611nomaximal, Sylow
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—41no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—82no—
91C22×C61#34212yes—
92C22×C61#34211yescharacteristic
93C2×D61—44no—
94C2×D61—42no—
95C2×D61—82no—
96C2×D61—82no—
97C4×C61—41no—
98C4×C61—41no—
99C4×C61—161no—
100Dic61—24no—
101Dic61—161no—
102#1785—612no—
103#1782—611no—
104C2×C61—22no—
105C2×C61—21no—
106C2×C61—41no—
107C2×C61—41no—
108C2×C61#130411yescharacteristic
109D61—82no—
110C22×#41—611no—
111C2×#101—1222no—
112C2×#100—1222no—
113C2×#99—1222no—
114#407—614no—
115#381—611no—
116#381#692311yescharacteristic
117C61#731911yescharacteristic, complemented, Sylow
118C2×#41—2441no—
119C2×#41—2441no—
120C2×#41—2444no—
121C22×Q8—611no—
122C22×D4—612no—
123C22×D4—611no—
124C23×C4—612no—
125C23×C4C2×#692311yescharacteristic
126C2×M16—1224no—
127C2×C22⋊C4—21no—
128C2×C22⋊C4—1221no—
129#101—2444no—
130#100—2442no—
131#100—2442no—
132#99—2444no—
133C22⋊C8—2444no—
134#95—41no—
135#95—2441no—
136C24—612no—
137C24C22⋊#692311yescharacteristic
138#41—2448no—
139#41—2448no—
140C2×Q8—1224no—
141C2×Q8—2441no—
142C2×D4—1224no—
143C2×D4—1222no—
144C2×D4—1222no—
145C2×D4—2442no—
146C2×D4—2441no—
147C2×D4—2442no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—42no—
151C22×C4—41no—
152C22×C4—612no—
153C22×C4—1224no—
154C22×C4—2442no—
155C22×C4—2442no—
156C22×C4—2441no—
157C22×C4C4×#692311yescharacteristic
158C22×C4C4⋊#692311yescharacteristic
159M16—2444no—
160M16—2444no—
161C2×C8—2444no—
162C22⋊C4—42no—
163C22⋊C4—2442no—
164C23—22no—
165C23—81no—
166C23—1222no—
167C23—1222no—
168C23—1222no—
169C23—4882no—
170C23(C2×#6923)⋊C411yescharacteristic
171C23#1451983511yescharacteristic
172C23#1451983611yescharacteristic
173Q8—2444no—
174D4—2444no—
175D4—2444no—
176D4—2444no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—82no—
185C2×C4—614no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—4881no—
189C2×C4—4882no—
190C2×C4—2448no—
191C8—4884no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22—82no—
198C22—4882no—
199C22—4882no—
200C22—2444no—
201C22—2442no—
202C22#1684063912yes—
203C22#1684064011yescharacteristic
204C4—41no—
205C4—41no—
206C4—161no—
207C4—1224no—
208C4—9761no—
209C2—21no—
210C2—22no—
211C2—41no—
212C2—41no—
213C2—4882no—
214C2#2146071811yescharacteristic
subgroupG/H
centerC2#21460718
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC61×#381C4
socleC2×C61#1304
prime radical, cosocleC22×#11758222C22
hypercenter#381#6923
hypocenterC61#7319
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. #16840734C4semidirect
117. C61#7319semidirect

Maximal subgroups

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

subgroupindex
#214616552
#214457362
#731961