Finite Group Databasebeta

← #30599286

Subgroups — #30599286

Order 15616.

630 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 132 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#21461676C212yesmaximal
2#21460697C214yesmaximal, complemented
3#384×D61C211yesmaximal, characteristic
4C2×#14519844C2214yes—
5C2×#14519834—22no—
6#16840628—22no—
7C2×C4⋊C4×D61—22no—
8C2×C4⋊C4×D61C412yes—
9C2×C42×D61C2211yescharacteristic
10#16839632C411yescharacteristic
11#16839631—22no—
12#16839631C2212yes—
13C61×#384C411yescharacteristic
14C22×#92420—24no—
15#14519844—28no—
16#14519834—44no—
17C22×C4×D61—22no—
18C22×C4×D61C2×C411yescharacteristic
19C22×C4×D61D412yes—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61C2×C412yes—
22C2×#11758196—22no—
23C2×#11758196—24no—
24C4⋊C4×D61—44no—
25C4⋊C4×D61—48no—
26C2×C4×Dic61D412yes—
27C2×C4×Dic61C2311yescharacteristic
28C42×D61—24no—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61C2×C412yes—
31C2×C42×C61C2×C411yescharacteristic
32C23×D61C22⋊C411yescharacteristic
33C22×C4×C61—22no—
34C22×C4×C61C22⋊C412yes—
35C22×C4×C61C22×C411yescharacteristic
36C22×Dic61—22no—
37C22×Dic61C22⋊C411yescharacteristic
38C22×Dic61C2×D412yes—
39C2×C4×D61—22no—
40C2×C4×D61—22no—
41C2×C4×D61—22no—
42C2×C4×D61—24no—
43C2×C4×D61—24no—
44C2×C4×D61—48no—
45C2×C4×D61—44no—
46C2×C4×D61SD1614yes—
47C2×C4×D61Q1614yes—
48C2×#92420—44no—
49C2×#92420—44no—
50C2×#92420—44no—
51C4⋊C4×C61—44no—
52C4⋊C4×C61—42no—
53C42×C61—22no—
54C4⋊Dic61—44no—
55C4⋊Dic61—42no—
56#11758196—44no—
57#11758196—48no—
58C4×Dic61—24no—
59C4×Dic61#4114yes—
60C23×C61C2×C22⋊C411yescharacteristic
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—22no—
64C22×D61#10012yes—
65C22×D61#10314yes—
66C2×C4×C61—22no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—22no—
70C2×C4×C61—42no—
71C2×C4×C61—44no—
72C2×C4×C61#10314yes—
73C2×C4×C61#11712yes—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—42no—
77C2×Dic61—44no—
78C2×Dic61#10112yes—
79C2×Dic61#12314yes—
80C2×Dic61C2×SD1612yes—
81C2×Dic61C2×Q1612yes—
82C2×Dic61AGL(1,ℤ/8)14yes—
83C4×D61—28no—
84C4×D61—28no—
85C4×D61—28no—
86C4×D61—88no—
87#92420—84no—
88#8725—611nomaximal, Sylow
89C22×C61#38111yescharacteristic
90C22×C61C2×#10011yescharacteristic
91C22×C61C2×#10111yescharacteristic
92C22×C61C2×#10312yes—
93C22×C61#41812yes—
94C2×D61—24no—
95C2×D61—22no—
96C2×D61—22no—
97C2×D61—24no—
98C2×D61#33314yes—
99C4×C61—22no—
100C4×C61—24no—
101C4×C61—82no—
102Dic61—22no—
103Dic61—82no—
104Dic61#48114yes—
105Dic61#48414yes—
106C2×#384—611no—
107#1797—612no—
108#1296—614no—
109C2×C61C2×#33311yescharacteristic
110C2×C61#154912yes—
111C2×C61#155511yescharacteristic
112C2×C61#182111yescharacteristic
113C2×C61#182412yes—
114D61—24no—
115C22×C4⋊C4—612no—
116C22×C4⋊C4—1222no—
117C22×C42—611no—
118C2×C4⋊C8—614no—
119C2×C22⋊C8—1222no—
120#384—612no—
121#384—611no—
122#384—1222no—
123#384#692311yescharacteristic
124#336—1222no—
125C61#872511yescharacteristic, complemented, Sylow
126C23×C4—612no—
127C23×C4—611no—
128C23×C4—1222no—
129C22×C8—1224no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—612no—
132C2×C4⋊C4—1222no—
133C2×C4⋊C4—1224no—
134C2×C4⋊C4—1222no—
135C2×C4⋊C4—2444no—
136C2×C4⋊C4—2448no—
137C2×C4⋊C4C2×#692312yes—
138C2×C42—611no—
139C2×C42—612no—
140C2×C42—1224no—
141C2×C42C2×#692311yescharacteristic
142C4⋊C8—1228no—
143C22⋊C8—2444no—
144C24—611no—
145C22×C4—22no—
146C22×C4—612no—
147C22×C4—611no—
148C22×C4—614no—
149C22×C4—614no—
150C22×C4—1224no—
151C22×C4—1224no—
152C22×C4—1222no—
153C22×C4—1222no—
154C22×C4—1222no—
155C22×C4—1222no—
156C22×C4—2444no—
157C22×C4—2448no—
158C22×C4C22⋊#692312yes—
159C22×C4C22×#692311yescharacteristic
160C2×C8—2444no—
161C2×C8—2444no—
162C2×C8—2444no—
163C4⋊C4—42no—
164C4⋊C4—44no—
165C4⋊C4—2442no—
166C4⋊C4—2444no—
167C4⋊C4—2448no—
168C4⋊C4—2444no—
169C42—22no—
170C42—614no—
171C42—1224no—
172C23—612no—
173C23—614no—
174C23—1221no—
175C23—1221no—
176C23—1222no—
177C23C2×C22⋊#692311yescharacteristic
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—44no—
184C2×C4—614no—
185C2×C4—612no—
186C2×C4—612no—
187C2×C4—614no—
188C2×C4—612no—
189C2×C4—1228no—
190C2×C4—1228no—
191C2×C4—1228no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—4888no—
195C2×C4—2442no—
196C2×C4—2444no—
197C2×C4#1451984014yes—
198C2×C4#1451985612yes—
199C8—4884no—
200C22—614no—
201C22—1224no—
202C22—1222no—
203C22—1222no—
204C22—1224no—
205C22#1684070511yescharacteristic
206C22D61⋊#10011yescharacteristic
207C22D61⋊#10111yescharacteristic
208C22C2×#1451984012yes—
209C22#1684075412yes—
210C4—22no—
211C4—24no—
212C4—82no—
213C4—614no—
214C4—614no—
215C4—1222no—
216C4—4882no—
217C2—1224no—
218C2D61⋊#33311yescharacteristic
219C2#2146133512yes—
220C2#2146134711yescharacteristic
221C2#2146171911yescharacteristic
222C2#2146172312yes—
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#8725
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. #21460697C2semidirect
125. C61#8725semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214606972
#384×D612
#872561