Finite Group Databasebeta

← #30595455

Subgroups — #30595455

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#21461709C212yesmaximal
2#21460639C214yesmaximal, complemented
3C2×#16839669C211yesmaximal, characteristic
4C2×C22⋊#92420—22no—
5#16840628—22no—
6#16840628C2214yes—
7C22×C4⋊Dic61C411yescharacteristic
8C22×C4×Dic61C2211yescharacteristic
9#16839669—22no—
10#16839669C412yes—
11#16839669C2212yes—
12C2×#14519684—22no—
13C23×Q8×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—44no—
16C23×Dic61—21no—
17C23×Dic61D412yes—
18C2×C4⋊Dic61—21no—
19C2×C4⋊Dic61—42no—
20C2×C4⋊Dic61C2×C412yes—
21C2×C4×Dic61—42no—
22C2×C4×Dic61C2×C411yescharacteristic
23C2×C4×Dic61D412yes—
24C2×C4×Dic61C2311yescharacteristic
25#14519684—24no—
26#14519684—24no—
27C22×Q8×C61—21no—
28C22×Q8×C61—22no—
29C22×Q8×C61—42no—
30C22×Q8×C61—42no—
31C22×Q8×C61C814yescomplemented
32C22×Q8×C61C2×C412yes—
33C23×C4×C61—21no—
34C23×C4×C61C2×C411yescharacteristic
35C24×C61C22⋊C411yescharacteristic
36C2×Q8×C61—24no—
37C2×Q8×C61—22no—
38C2×Q8×C61—48no—
39C2×Q8×C61—42no—
40C2×Q8×C61—42no—
41C2×Q8×C61—48no—
42C2×Q8×C61—42no—
43C2×Q8×C61—42no—
44C2×Q8×C61C2×C814yes—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—24no—
48C22×C4×C61—22no—
49C22×C4×C61—42no—
50C22×C4×C61—42no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C2×C812yes—
53C22×C4×C61M1612yes—
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—24no—
56C22×Dic61—24no—
57C22×Dic61—22no—
58C22×Dic61—42no—
59C22×Dic61—44no—
60C22×Dic61—42no—
61C22×Dic61C22⋊C412yes—
62C22×Dic61C2×D412yes—
63C2×#92420—44no—
64C2×#92420—44no—
65C2×#92420—44no—
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4×Dic61—41no—
69C4×Dic61—42no—
70C4×Dic61—41no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61C22⋊C812yes—
74C23×C61#9912yes—
75C23×C61#10012yes—
76C23×C61C2×C22⋊C411yescharacteristic
77Q8×C61—48no—
78Q8×C61—44no—
79Q8×C61—44no—
80C2×C4×C61—24no—
81C2×C4×C61—24no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—24no—
87C2×C4×C61—48no—
88C2×C4×C61—42no—
89C2×C4×C61—42no—
90C2×C4×C61C22⋊C812yes—
91C2×C4×C61C22×C811yescharacteristic
92C2×C4×C61C2×M1611yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—48no—
99C2×Dic61—42no—
100C2×Dic61—44no—
101C2×Dic61—84no—
102C2×Dic61#13714yes—
103#92420—84no—
104#7595—611nomaximal, Sylow
105C22×C61—22no—
106C22×C61—24no—
107C22×C61—24no—
108C22×C61—22no—
109C22×C61#32314yes—
110C22×C61C2×C22⋊C811yescharacteristic
111C22×C61C2×#9911yescharacteristic
112C22×C61C2×#10011yescharacteristic
113C22×C61#41912yes—
114C22×C61#42112yes—
115C4×C61—22no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—44no—
119Dic61—24no—
120Dic61—42no—
121Dic61—82no—
122C2×#391—611no—
123#1817—612no—
124#1272—614no—
125C2×C61—24no—
126C2×C61C2×#32311yescharacteristic
127C2×C61#147912yes—
128C2×C61#151112yes—
129C2×C61#153311yescharacteristic
130C2×C61#155811yescharacteristic
131C23×Q8#692311yescharacteristic
132C22×C4⋊C4—611no—
133C22×C42—611no—
134C2×C22⋊C8—1222no—
135#391—612no—
136#391—612no—
137#391—1222no—
138C2×#95—1222no—
139#336—614no—
140#336—1222no—
141C61#759511yescharacteristic, complemented, Sylow
142C22×Q8—22no—
143C22×Q8—21no—
144C22×Q8—42no—
145C22×Q8—42no—
146C22×Q8#9242014yescomplemented
147C22×Q8C2×#692312yes—
148C23×C4—21no—
149C23×C4—612no—
150C23×C4—1221no—
151C23×C4C2×#692311yescharacteristic
152C22×C8—1224no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—2442no—
156C2×C42—612no—
157C2×C42—611no—
158C2×C42—611no—
159C2×C42—2442no—
160C22⋊C8—2444no—
161#95—1224no—
162#95—1224no—
163C24C22⋊#692311yescharacteristic
164C2×Q8—24no—
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—48no—
169C2×Q8—48no—
170C2×Q8—42no—
171C2×Q8—42no—
172C2×Q8C2×#9242014yes—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—22no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—612no—
180C22×C4—612no—
181C22×C4—1224no—
182C22×C4—1224no—
183C22×C4—1222no—
184C22×C4—2442no—
185C22×C4—2444no—
186C22×C4—2442no—
187C22×C4C2×#9242012yes—
188C22×C4#1175821712yes—
189C22×C4C22⋊#692311yescharacteristic
190C22×C4C22×#692311yescharacteristic
191C2×C8—2444no—
192C2×C8—2444no—
193C2×C8—2444no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C42—2442no—
197C42—2441no—
198C42—2441no—
199C23—22no—
200C23—22no—
201C23C22⋊#9242012yes—
202C23#1451983512yes—
203C23#1451983712yes—
204C23C2×C22⋊#692311yescharacteristic
205Q8—44no—
206Q8—48no—
207Q8—44no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—24no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—48no—
218C2×C4—614no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—4884no—
225C2×C4—2448no—
226C2×C4—2442no—
227C2×C4—2444no—
228C2×C4C22⋊#9242012yes—
229C2×C4C22×#9242011yescharacteristic
230C2×C4C2×#1175821711yescharacteristic
231C8—4884no—
232C22—22no—
233C22—22no—
234C22—24no—
235C22—24no—
236C22#1684060514yes—
237C22C2×C22⋊#9242011yescharacteristic
238C22C2×#1451983511yescharacteristic
239C22C2×#1451983711yescharacteristic
240C22#1684075512yes—
241C22#1684076112yes—
242C4—22no—
243C4—21no—
244C4—21no—
245C4—44no—
246C4—1224no—
247C4—4882no—
248C4—2442no—
249C2—24no—
250C2C2×#1684060511yescharacteristic
251C2#2146112112yes—
252C2#2146122912yes—
253C2#2146130011yescharacteristic
254C2#2146135211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC23×Q8×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC23×Q8#6923
hypocenterC61#7595
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
2. #21460639C2semidirect
31. C22×Q8×C61C8semidirect
141. C61#7595semidirect
146. C22×Q8#92420semidirect

Maximal subgroups

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

subgroupindex
#214617092
#214606392
C2×#168396692
#759561