Finite Group Databasebeta

← #30594590

Subgroups — #30594590

Order 15616.

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

normal subgroups only

This group has 352 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#21461695C211yesmaximal, characteristic
2#21461505C211yesmaximal, characteristic
3#21447428C211yesmaximal, characteristic
4C2×#14519856—21no—
5C2×#14519845C412yescomplemented
6#16840704—21no—
7#16840636—21no—
8#16840636—21no—
9#16840636C412yescomplemented
10C22×C8×D61C2211yescharacteristic
11C2×#14519716—21no—
12C22⋊#11758185C411yescharacteristic, complemented
13#16839541—21no—
14C61×C22⋊C16C411yescharacteristic, complemented
15#14519856—24no—
16#14519856—42no—
17C2×C4⋊#6923—22no—
18C2×C4⋊#6923—22no—
19C2×C22⋊#6923—41no—
20C2×C22⋊#6923—41no—
21C2×C4×#6923—41no—
22#14519845—42no—
23(C2×#6923)⋊C4—41no—
24C22×C4×D61D411yescharacteristic
25C22×#92418Q811yescharacteristic
26C2×C8×D61—42no—
27C2×C8×D61C2×C411yescharacteristic
28C2×C8×D61C2×C411yescharacteristic
29C2×C8×D61D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31#14519716—42no—
32C2×#11758185—21no—
33C22×C8×C61C2×C411yescharacteristic
34C2×C16×C61—21no—
35C23×D61D811yescharacteristic
36C22×#6923—42no—
37C22×#6923—42no—
38C22×C4×C61C4⋊C411yescharacteristic
39C22×Dic61Q1611yescharacteristic
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61C22⋊C411yescharacteristic
43C2×C4×D61C22⋊C411yescharacteristic
44C2×C4×D61SD1611yescharacteristic
45C2×C4×D61SD1611yescharacteristic
46C22⋊#6923—44no—
47C22⋊#6923—82no—
48C4⋊#6923—24no—
49C4⋊#6923—42no—
50C4⋊#6923—42no—
51C4⋊#6923—42no—
52C4×#6923—44no—
53C2×C8×C61—41no—
54C2×C8×C61C4211yescharacteristic
55C2×C8×C61C22⋊C411yescharacteristic
56C2×#92418—41no—
57C2×#92418C4⋊C411yescharacteristic
58C2×#92418C4⋊C411yescharacteristic
59C8×D61—22no—
60C8×D61—22no—
61C8×D61—41no—
62C8×D61—41no—
63C16×C61—41no—
64#11758185—41no—
65C23×C61#10711yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—41no—
69C22×D61#10211yescharacteristic
70C22×D61#10211yescharacteristic
71C2×#6923—44no—
72C2×#6923—82no—
73C2×#6923—82no—
74C2×#6923—82no—
75C2×#6923—82no—
76C2×#6923—82no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61#9511yescharacteristic
80C2×C4×C61#10611yescharacteristic
81C2×Dic61—22no—
82C2×Dic61#10311yescharacteristic
83C2×Dic61#10311yescharacteristic
84C4×D61—22no—
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—22no—
88C4×D61#9912yes—
89C4×D61#10412yes—
90C8×C61—21no—
91C8×C61—21no—
92#92418—21no—
93#92418—21no—
94#7262—611nomaximal, Sylow
95C22×C61—21no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#34011yescharacteristic
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—44no—
104C2×D61#32712yes—
105C2×D61#36012yes—
106#6923—84no—
107#6923—162no—
108C4×C61—21no—
109C4×C61#33911yescharacteristic
110C4×C61#34211yescharacteristic
111Dic61—21no—
112Dic61#32812yes—
113#2112—611no—
114#1807—611no—
115#1735—611no—
116C2×C61—41no—
117C2×C61#129411yescharacteristic
118C2×C61#138411yescharacteristic
119C2×C61#138611yescharacteristic
120D61—22no—
121D61—22no—
122C23×C8—611no—
123C2×#117—1221no—
124C2×M32—1221no—
125C2×#106—612no—
126#380—1221no—
127C22⋊C16—611no—
128C22⋊C16—1221no—
129C22⋊C16#692311yescharacteristic, complemented
130#340—612no—
131#340—1221no—
132#340—1221no—
133C61#726211yescharacteristic, complemented, Sylow
134C23×C4—611no—
135C22×C8—611no—
136C22×C8—611no—
137C22×C8—611no—
138C22×C8—611no—
139C22×C8—611no—
140C22×C8—2442no—
141C22×C8C2×#692311yescharacteristic
142#117—1224no—
143#117—2442no—
144C2×C4⋊C4—1222no—
145C2×C4⋊C4—1222no—
146C2×C22⋊C4—2441no—
147C2×C22⋊C4—2441no—
148C2×C42—2441no—
149M32—2442no—
150C2×C16—21no—
151C2×C16—1221no—
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×C4—2442no—
164C22×C4C4⋊#692311yescharacteristic
165C2×C8—41no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—1222no—
169C2×C8—1222no—
170C2×C8—2441no—
171C2×C8—2441no—
172C2×C8—2441no—
173C2×C8C4×#692311yescharacteristic
174C2×C8C22⋊#692311yescharacteristic
175C4⋊C4—1224no—
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C4⋊C4—2442no—
179C22⋊C4—4882no—
180C22⋊C4—2444no—
181C42—2444no—
182C16—41no—
183C16—2441no—
184C23—611no—
185C23—611no—
186C23—1222no—
187C23—1222no—
188C23—2441no—
189C23#1451984611yescharacteristic
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—611no—
193C2×C4—612no—
194C2×C4—612no—
195C2×C4—611no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—4882no—
202C2×C4—4882no—
203C2×C4—4882no—
204C2×C4—4882no—
205C2×C4—4882no—
206C2×C4—2444no—
207C2×C4(C2×#6923)⋊C411yescharacteristic
208C2×C4#1451984511yescharacteristic
209C8—21no—
210C8—21no—
211C8—1221no—
212C8—1221no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—612no—
217C22—612no—
218C22—1221no—
219C22—1221no—
220C22—1221no—
221C22—1221no—
222C22—2444no—
223C22#1684063611yescharacteristic
224C4—21no—
225C4—612no—
226C4—1221no—
227C4—9762no—
228C4—4884no—
229C4#1684063411yescharacteristic
230C4#1684063911yescharacteristic
231C2—41no—
232C2—1222no—
233C2—1222no—
234C2#2146069411yescharacteristic
235C2#2146088711yescharacteristic
236C2#2146089111yescharacteristic
subgroupG/H
centerC22#16840636
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×C22⋊C16C4
socleC22×C61#340
prime radicalC23×D61D8
cosocleC22×C8×D61C22
hypercenterC22⋊C16#6923
hypocenterC61#7262
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
5. C2×#14519845C4semidirect
9. #16840636C4semidirect
12. C22⋊#11758185C4semidirect
14. C61×C22⋊C16C4semidirect
129. C22⋊C16#6923semidirect
133. C61#7262semidirect

Maximal subgroups

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

subgroupindex
#214616952
#214615052
#214474282
#726261