Finite Group Databasebeta

← #30594581

Subgroups — #30594581

Order 15616.

342 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461696C211yesmaximal, characteristic
2#21461511C211yesmaximal, characteristic
3C22⋊C16×D61C211yesmaximal, characteristic
4C2×D61⋊M16—21no—
5C2×#14519846C412yes—
6#16840704—21no—
7#16840638—21no—
8#16840638C412yescomplemented
9#16840636—21no—
10C22×C8×D61C2211yescharacteristic
11C2×C16×D61—21no—
12C22⋊#11758185C411yescharacteristic, complemented
13#16839541—21no—
14C61×C22⋊C16C411yescharacteristic, complemented
15C2×#11758213—22no—
16D61⋊M16—24no—
17D61⋊M16—42no—
18C2×#11758217—41no—
19C2×D61⋊C8—41no—
20C2×C4⋊#6923—22no—
21C2×C22⋊#6923—41no—
22#14519846—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
31C2×#11758185—21no—
32C16×D61—42no—
33C22×C8×C61C2×C411yescharacteristic
34C2×C16×C61—21no—
35C23×D61SD1611yescharacteristic
36C22×#6923—42no—
37C22×C4×C61C4⋊C411yescharacteristic
38C22×Dic61SD1611yescharacteristic
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61C22⋊C411yescharacteristic
42C2×C4×D61C22⋊C411yescharacteristic
43C2×C4×D61D811yescharacteristic
44C2×C4×D61Q1611yescharacteristic
45C22⋊#6923—82no—
46#11758217—44no—
47C2×#92420—42no—
48C4⋊#6923—42no—
49C4⋊#6923—42no—
50#11758213—24no—
51#11758213—42no—
52D61⋊C8—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#10611yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—21no—
69C22×D61—21no—
70C22×D61#10211yescharacteristic
71C22×D61#10311yescharacteristic
72C2×#6923—82no—
73C2×#6923—82no—
74C2×#6923—82no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61#9511yescharacteristic
78C2×C4×C61#10711yescharacteristic
79C2×Dic61—22no—
80C2×Dic61#10211yescharacteristic
81C2×Dic61#10311yescharacteristic
82C4×D61—22no—
83C4×D61—21no—
84C4×D61—21no—
85C4×D61—22no—
86C4×D61#9912yes—
87C4×D61#10412yes—
88#92420—44no—
89C8×C61—21no—
90C8×C61—21no—
91#92418—21no—
92#92418—21no—
93#7259—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61#34011yescharacteristic
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61#32712yes—
104C2×D61#35912yes—
105C2×D61#36111yescharacteristic
106C2×D61#36211yescharacteristic
107#6923—162no—
108C4×C61—21no—
109C4×C61#33911yescharacteristic
110C4×C61#34211yescharacteristic
111Dic61—21no—
112Dic61#32812yes—
113C2×C22⋊C16—611no—
114#1808—611no—
115C2×#341—611no—
116C2×C61—41no—
117C2×C61#129411yescharacteristic
118C2×C61#138211yescharacteristic
119C2×C61#138711yescharacteristic
120D61—41no—
121D61#134912yes—
122D61#135012yes—
123C22×M16—1221no—
124C23×C8—611no—
125C22×C16—1221no—
126C2×#107—612no—
127#380—1221no—
128C22⋊C16—611no—
129C22⋊C16—1221no—
130C22⋊C16#692311yescharacteristic, complemented
131#341—612no—
132#341—1221no—
133#340—1221no—
134C61#725911yescharacteristic, complemented, Sylow
135C23×C4—611no—
136C2×M16—1222no—
137C2×M16—1224no—
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—
150C2×C16—21no—
151C2×C16—1221no—
152C2×C16—2442no—
153#107—2442no—
154#95—2441no—
155C24—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—611no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—1222no—
162C22×C4—1222no—
163C22×C4—2442no—
164C22×C4C4⋊#692311yescharacteristic
165M16—1224no—
166M16—2442no—
167M16—2444no—
168C2×C8—41no—
169C2×C8—611no—
170C2×C8—611no—
171C2×C8—1222no—
172C2×C8—1222no—
173C2×C8—2441no—
174C2×C8—2441no—
175C2×C8—2441no—
176C2×C8—2442no—
177C2×C8—2444no—
178C2×C8C4×#692311yescharacteristic
179C2×C8C22⋊#692311yescharacteristic
180C4⋊C4—2442no—
181C4⋊C4—2442no—
182C22⋊C4—4882no—
183C16—41no—
184C16—2441no—
185C23—611no—
186C23—611no—
187C23—1221no—
188C23—1222no—
189C23—1222no—
190C23—1221no—
191C23#1451984511yescharacteristic
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#1451984611yescharacteristic
208C8—21no—
209C8—21no—
210C8—1221no—
211C8—1221no—
212C8—2444no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—612no—
217C22—611no—
218C22—611no—
219C22—612no—
220C22—1221no—
221C22—1221no—
222C22—1221no—
223C22—2442no—
224C22—2442no—
225C22#1684063611yescharacteristic
226C4—21no—
227C4—612no—
228C4—1221no—
229C4—9762no—
230C4#1684063411yescharacteristic
231C4#1684063911yescharacteristic
232C2—41no—
233C2—612no—
234C2—612no—
235C2—2441no—
236C2#2146069411yescharacteristic
237C2#2146088111yescharacteristic
238C2#2146089411yescharacteristic
subgroupG/H
centerC22#16840636
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×C22⋊C16C4
socleC22×C61#340
prime radicalC23×D61SD16
cosocleC22×C8×D61C22
hypercenterC22⋊C16#6923
hypocenterC61#7259
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
8. #16840638C4semidirect
12. C22⋊#11758185C4semidirect
14. C61×C22⋊C16C4semidirect
130. C22⋊C16#6923semidirect
134. C61#7259semidirect

Maximal subgroups

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

subgroupindex
#214616962
#214615112
C22⋊C16×D612
#725961