Finite Group Databasebeta

← #30599277

Subgroups — #30599277

Order 15616.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461546C212yesmaximal
2#21460695C214yesmaximal, complemented
3#21448224C211yesmaximal, characteristic
4C2×#14519834—22no—
5C2×#14519832C2214yes—
6#16840628—22no—
7C2×#14519735C412yes—
8C2×C42×D61C2211yescharacteristic
9#16839632C411yescharacteristic
10#16839627C2212yes—
11#16839619—22no—
12C4⋊C4×Dic61—22no—
13C61×#384C411yescharacteristic
14C22×#92420—24no—
15#14519834—28no—
16#14519832—28no—
17C22×C4×D61C2×C411yescharacteristic
18C22×C4×D61D412yes—
19#14519735—44no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×#11758198—22no—
23C2×C4×Dic61—22no—
24C2×C4×Dic61D412yes—
25C2×C4×Dic61C2311yescharacteristic
26C42×D61—24no—
27#14519684—24no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61C2×C412yes—
30C2×C42×C61C2×C411yescharacteristic
31C23×D61C22⋊C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61C22⋊C412yes—
34C22×C4×C61C22×C411yescharacteristic
35C22×Dic61—22no—
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C2×D412yes—
38C2×C4×D61—22no—
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61—24no—
42C2×C4×D61—24no—
43C2×C4×D61—42no—
44C2×#92420—28no—
45C2×#92420—44no—
46C2×#92420—44no—
47C4⋊C4×C61—42no—
48C4⋊C4×C61—44no—
49C42×C61—22no—
50#11758198—44no—
51C4⋊Dic61—44no—
52C4⋊Dic61—42no—
53C4×Dic61—24no—
54C4×Dic61—44no—
55C4×Dic61#4114yes—
56C23×C61C2×C22⋊C411yescharacteristic
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—22no—
60C22×D61—22no—
61C22×D61#10112yes—
62C2×C4×C61—22no—
63C2×C4×C61—21no—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61—42no—
67C2×C4×C61—44no—
68C2×C4×C61#10414yes—
69C2×C4×C61#11712yes—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—42no—
75C2×Dic61—44no—
76C2×Dic61#10012yes—
77C2×Dic61#12314yes—
78C4×D61—28no—
79C4×D61—48no—
80#92420—48no—
81#8721—611nomaximal, Sylow
82C22×C61#38111yescharacteristic
83C22×C61C2×#10011yescharacteristic
84C22×C61C2×#10111yescharacteristic
85C22×C61C2×#10412yes—
86C22×C61#42112yes—
87C2×D61—22no—
88C2×D61—24no—
89C2×D61—41no—
90C2×D61—42no—
91C2×D61—41no—
92C4×C61—22no—
93C4×C61—24no—
94C4×C61—82no—
95Dic61—22no—
96Dic61—24no—
97Dic61—82no—
98#2285—611no—
99#1749—612no—
100#1295—614no—
101C2×C61#152511yescharacteristic
102C2×C61#153112yes—
103C2×C61#153611yescharacteristic
104C2×C61#182111yescharacteristic
105C2×C61#182612yes—
106D61—42no—
107C2×#117—612no—
108C22×C42—611no—
109C2×C22⋊C8—1222no—
110C2×#97—614no—
111#384—611no—
112#384#692311yescharacteristic
113#382—612no—
114#380—1222no—
115C4×C4⋊C4—1222no—
116#336—1222no—
117C61#872111yescharacteristic, complemented, Sylow
118C23×C4—611no—
119C23×C4—612no—
120C22×C8—1224no—
121#117—2444no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—1222no—
125C2×C4⋊C4C2×#692312yes—
126C2×C22⋊C4—1222no—
127C2×C42—611no—
128C2×C42—612no—
129C2×C42—1224no—
130C2×C42—1222no—
131C2×C42C2×#692311yescharacteristic
132C22⋊C8—1228no—
133#97—1228no—
134#95—1224no—
135C24—611no—
136C22×C4—22no—
137C22×C4—612no—
138C22×C4—611no—
139C22×C4—1222no—
140C22×C4—1224no—
141C22×C4—1222no—
142C22×C4—1222no—
143C22×C4—1224no—
144C22×C4—1222no—
145C22×C4—2442no—
146C22×C4C22⋊#692312yes—
147C22×C4C22×#692311yescharacteristic
148C2×C8—1228no—
149C2×C8—2444no—
150C2×C8—2444no—
151C4⋊C4—42no—
152C4⋊C4—44no—
153C4⋊C4—2442no—
154C4⋊C4—2444no—
155C22⋊C4—2444no—
156C42—22no—
157C42—614no—
158C42—1224no—
159C42—2444no—
160C23—612no—
161C23—1221no—
162C23—1221no—
163C23—1222no—
164C23—1222no—
165C23C2×C22⋊#692311yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—44no—
172C2×C4—614no—
173C2×C4—612no—
174C2×C4—1228no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—2448no—
180C2×C4—2442no—
181C2×C4—2444no—
182C2×C4#1451984114yes—
183C2×C4#1451985612yes—
184C8—2448no—
185C22—1224no—
186C22—1222no—
187C22—2441no—
188C22—2441no—
189C22—2442no—
190C22#1684070511yescharacteristic
191C22D61⋊#10011yescharacteristic
192C22D61⋊#10111yescharacteristic
193C22C2×#1451984112yes—
194C22#1684076112yes—
195C4—22no—
196C4—24no—
197C4—82no—
198C4—1222no—
199C4—1224no—
200C4—4882no—
201C2—2442no—
202C2#2146127411yescharacteristic
203C2#2146129212yes—
204C2#2146130911yescharacteristic
205C2#2146171911yescharacteristic
206C2#2146172512yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8721
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
117. C61#8721semidirect

Maximal subgroups

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

subgroupindex
#214615462
#214606952
#214482242
#872161