Finite Group Databasebeta

← #30599359

Subgroups — #30599359

Order 15616.

566 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461653C212yesmaximal
2#21460722C214yesmaximal
3#21448403C211yesmaximal, characteristic
4C2×#14519838—22no—
5C2×#14519838—22no—
6#16840732C2214yes—
7C23×Dic122C2211yescharacteristic
8C2×#14519736C411yescharacteristic
9#16839668—22no—
10#16839667—22no—
11#16839623C412yes—
12#16839623C2212yes—
13C2×#117×C61C411yescharacteristic
14C2×#11758217—24no—
15#14519838—44no—
16#14519838—44no—
17C22⋊#92420—28no—
18C22×Dic122—24no—
19C22×Dic122—42no—
20C22×Dic122—42no—
21C22×Dic122D412yes—
22C22×Dic122D412yes—
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2311yescharacteristic
25#14519736—42no—
26C2×C4⋊Dic61—21no—
27C2×C22⋊Dic61C2×C412yes—
28C2×C4×Dic61—21no—
29#14519684—24no—
30#14519684—24no—
31C23×C4×C61C2×C411yescharacteristic
32#117×C61—42no—
33C2×C4⋊C4×C61—21no—
34C2×C22⋊C4×C61C2×C412yes—
35C2×C42×C61—21no—
36C24×C61C22×C411yescharacteristic
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C22⋊C411yescharacteristic
43C22×Dic61—22no—
44C22×Dic61—22no—
45C22×Dic61—41no—
46C22×Dic61—41no—
47C22×Dic61—41no—
48C22×Dic61—41no—
49C22×Dic61C22⋊C412yes—
50C22×Dic61C2×D412yes—
51C22×Dic61#4114yes—
52C2×Dic122—24no—
53C2×Dic122—24no—
54C2×Dic122—24no—
55C2×Dic122—24no—
56C2×Dic122—42no—
57C2×Dic122—42no—
58C2×Dic122—416no—
59#11758217—44no—
60#11758217—44no—
61C2×#92420—44no—
62C4⋊C4×C61—42no—
63C22⋊C4×C61—42no—
64C42×C61—42no—
65C22⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4×Dic61—42no—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—42no—
71C23×C61C2×C22⋊C411yescharacteristic
72C23×C61#11712yes—
73C2×C4×C61—28no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—44no—
79C2×C4×C61—42no—
80C2×C4×C61#9912yes—
81C2×C4×C61#9912yes—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—44no—
88C2×Dic61—44no—
89C2×Dic61—44no—
90C2×Dic61—42no—
91C2×Dic61#12314yes—
92Dic122—48no—
93Dic122—48no—
94#92420—84no—
95#8754—611nomaximal, Sylow
96C22×C61—22no—
97C22×C61—22no—
98C22×C61—24no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61#38111yescharacteristic
102C22×C61C2×#9911yescharacteristic
103C22×C61C2×#9911yescharacteristic
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—82no—
107Dic61—24no—
108Dic61—42no—
109Dic61—82no—
110#2310—611no—
111#1784—612no—
112#1306—614no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—42no—
116C2×C61#181911yescharacteristic
117C2×C61#183012yes—
118C23×Q8—611no—
119C2×#117—611no—
120C2×#117#692311yescharacteristic
121C2×#101—1222no—
122C2×#101—1222no—
123#407—614no—
124#391—1222no—
125#391—1222no—
126#381—612no—
127#381—612no—
128C61#875411yescharacteristic, complemented, Sylow
129C22×Q8—612no—
130C22×Q8—612no—
131C22×Q8—1224no—
132C22×Q8—2442no—
133C22×Q8—2442no—
134C23×C4—611no—
135C23×C4—611no—
136C23×C4C2×#692311yescharacteristic
137C2×M16—1224no—
138#117—42no—
139#117—2442no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—1221no—
142C2×C22⋊C4—612no—
143C2×C22⋊C4C2×#692312yes—
144C2×C42—21no—
145C2×C42—1221no—
146#101—2444no—
147#101—2444no—
148C22⋊C8—1228no—
149#95—1224no—
150#95—1224no—
151C24C22×#692311yescharacteristic
152C2×Q8—1224no—
153C2×Q8—1224no—
154C2×Q8—1224no—
155C2×Q8—1224no—
156C2×Q8—2442no—
157C2×Q8—2442no—
158C2×Q8—24416no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—612no—
164C22×C4—614no—
165C22×C4—612no—
166C22×C4—1222no—
167C22×C4—1222no—
168C22×C4—2441no—
169C22×C4—2441no—
170C22×C4—2441no—
171C22×C4—2441no—
172C22×C4C22⋊#692311yescharacteristic
173C22×C4C22⋊#692311yescharacteristic
174M16—2444no—
175M16—2444no—
176C2×C8—2444no—
177C4⋊C4—42no—
178C4⋊C4—2442no—
179C22⋊C4—42no—
180C22⋊C4—2442no—
181C42—42no—
182C42—2442no—
183C23—21no—
184C23—21no—
185C23—42no—
186C23C2×C22⋊#692311yescharacteristic
187C23#1451985612yes—
188Q8—2448no—
189Q8—2448no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—44no—
196C2×C4—42no—
197C2×C4—614no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—2444no—
204C2×C4—2444no—
205C2×C4—2442no—
206C2×C4—2444no—
207C2×C4#1451983512yes—
208C2×C4#1451983612yes—
209C8—4884no—
210C22—22no—
211C22—22no—
212C22—24no—
213C22—42no—
214C22—42no—
215C22#1684070511yescharacteristic
216C22C2×#1451983511yescharacteristic
217C22C2×#1451983611yescharacteristic
218C4—22no—
219C4—22no—
220C4—82no—
221C4—1224no—
222C4—4882no—
223C4—2442no—
224C2—21no—
225C2—21no—
226C2—42no—
227C2#2146171411yescharacteristic
228C2#2146173312yes—
subgroupG/H
centerC22#16840705
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61#381
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8754
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
128. C61#8754semidirect

Maximal subgroups

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

subgroupindex
#214616532
#214607222
#214484032
#875461