Finite Group Databasebeta

← #30594592

Subgroups — #30594592

Order 15616.

336 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 68 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#21462047C211yesmaximal, characteristic
2#21461695C211yesmaximal, characteristic
3#341×D61C211yesmaximal, characteristic
4C2×#14519852—21no—
5C2×#14519845C412yes—
6#16840704—21no—
7#16840657C412yescomplemented
8C22⋊#11758187—21no—
9#16840636—21no—
10C2×M16×D61—21no—
11C22×C8×D61C2211yescharacteristic
12#16839527C411yescharacteristic, complemented
13#16839526—21no—
14C61×#341C411yescharacteristic, complemented
15C2×C4⋊#6923—22no—
16C2×C22⋊#6923—41no—
17#14519852—42no—
18C2×#11758187—22no—
19#14519845—42no—
20(C2×#6923)⋊C4—41no—
21C22×C4×D61D411yescharacteristic
22C2×#11758194—21no—
23C2×#11758189—41no—
24M16×D61—24no—
25M16×D61—42no—
26C22×#92418D411yescharacteristic
27C2×C8×D61—42no—
28C2×C8×D61—41no—
29C2×C8×D61C2×C411yescharacteristic
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32C2×C8×D61Q811yescharacteristic
33C2×M16×C61—21no—
34C22×C8×C61C2×C411yescharacteristic
35C23×D61SD1611yescharacteristic
36C22×#6923—42no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×Dic61Q1611yescharacteristic
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61C22⋊C411yescharacteristic
42C2×C4×D61C4⋊C411yescharacteristic
43C2×C4×D61D811yescharacteristic
44C2×C4×D61SD1611yescharacteristic
45C22⋊#6923—82no—
46C4⋊#6923—42no—
47C4⋊#6923—42no—
48M16×C61—22no—
49M16×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61—41no—
52C2×C8×C61C4211yescharacteristic
53C2×C8×C61C4⋊C411yescharacteristic
54#11758194—22no—
55#11758194—41no—
56C2×#92418—41no—
57C2×#92418—41no—
58C2×#92418C22⋊C411yescharacteristic
59C2×#92418C4⋊C411yescharacteristic
60#11758189—44no—
61C8×D61—22no—
62C8×D61—22no—
63C8×D61—41no—
64C8×D61—41no—
65C8×D61—44no—
66#11758187—42no—
67C23×C61#10311yescharacteristic
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—41no—
71C22×D61#10211yescharacteristic
72C22×D61#10611yescharacteristic
73C2×#6923—82no—
74C2×#6923—82no—
75C2×#6923—82no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61#9511yescharacteristic
79C2×C4×C61#10211yescharacteristic
80C2×Dic61—22no—
81C2×Dic61#10311yescharacteristic
82C2×Dic61#10711yescharacteristic
83C4×D61—22no—
84C4×D61—21no—
85C4×D61—21no—
86C4×D61—22no—
87C4×D61#9912yes—
88C4×D61#10412yes—
89C8×C61—21no—
90C8×C61—21no—
91C8×C61—42no—
92#92418—21no—
93#92418—21no—
94#92418—42no—
95#7263—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—21no—
99C22×C61#34011yescharacteristic
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—21no—
104C2×D61—44no—
105C2×D61#32712yes—
106C2×D61#36512yes—
107#6923—162no—
108C4×C61—21no—
109C4×C61#33911yescharacteristic
110C4×C61#34211yescharacteristic
111Dic61—21no—
112Dic61#32812yes—
113#2112—611no—
114#1807—611no—
115C2×#341—611no—
116C2×C61—41no—
117C2×C61#129411yescharacteristic
118C2×C61#138311yescharacteristic
119C2×C61#138911yescharacteristic
120D61—22no—
121D61—22no—
122C22×M16—1221no—
123C23×C8—611no—
124C2×M32—1221no—
125C2×#106—612no—
126#380—1221no—
127C22⋊C16—612no—
128C22⋊C16—1221no—
129#341—611no—
130#341—1221no—
131#341#692311yescharacteristic, complemented
132#340—1221no—
133C61#726311yescharacteristic, complemented, Sylow
134C23×C4—611no—
135C2×M16—21no—
136C2×M16—1224no—
137C2×M16—1221no—
138C2×M16—2441no—
139C2×M16—2442no—
140C22×C8—611no—
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—611no—
144C22×C8—611no—
145C22×C8—2442no—
146C22×C8—2441no—
147C22×C8C2×#692311yescharacteristic
148C2×C4⋊C4—1222no—
149C2×C22⋊C4—2441no—
150M32—2442no—
151C2×C16—1222no—
152#106—2442no—
153#95—2441no—
154C24—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—1222no—
161C22×C4—1222no—
162C22×C4—2442no—
163C22×C4C22⋊#692311yescharacteristic
164M16—22no—
165M16—41no—
166M16—1222no—
167M16—2444no—
168M16—2441no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—611no—
172C2×C8—611no—
173C2×C8—1222no—
174C2×C8—1222no—
175C2×C8—2441no—
176C2×C8—2441no—
177C2×C8—2444no—
178C2×C8—2441no—
179C2×C8—2441no—
180C2×C8C4×#692311yescharacteristic
181C2×C8C4⋊#692311yescharacteristic
182C4⋊C4—2442no—
183C4⋊C4—2442no—
184C22⋊C4—4882no—
185C16—2442no—
186C23—611no—
187C23—611no—
188C23—1222no—
189C23—1222no—
190C23—2441no—
191C23#1451984011yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—611no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—611no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—4882no—
204C2×C4—4882no—
205C2×C4—4882no—
206C2×C4(C2×#6923)⋊C411yescharacteristic
207C2×C4#1451983911yescharacteristic
208C8—21no—
209C8—21no—
210C8—42no—
211C8—1221no—
212C8—1221no—
213C8—2442no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—612no—
218C22—612no—
219C22—1221no—
220C22—1221no—
221C22—1221no—
222C22—1221no—
223C22—2444no—
224C22#1684063511yescharacteristic
225C4—21no—
226C4—612no—
227C4—1221no—
228C4—9762no—
229C4#1684063311yescharacteristic
230C4#1684063911yescharacteristic
231C2—41no—
232C2—1222no—
233C2—1222no—
234C2#2146069311yescharacteristic
235C2#2146088511yescharacteristic
236C2#2146089911yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#341C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenter#341#6923
hypocenterC61#7263
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
7. #16840657C4semidirect
12. #16839527C4semidirect
14. C61×#341C4semidirect
131. #341#6923semidirect
133. C61#7263semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214616952
#341×D612
#726361