Finite Group Databasebeta

← #30607256

Subgroups — #30607256

Order 15616.

638 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 88 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#21460917C214yesmaximal, complemented
3C2×#16839667C211yesmaximal, characteristic
4C2×#14519838—22no—
5C2×#14519838C2214yes—
6#16840732—22no—
7C23×Dic122C2211yescharacteristic
8C22×C4×Dic61C411yescharacteristic
9#16839667—22no—
10#16839667C412yes—
11#16839667C2212yes—
12C2×#14519684—22no—
13C22×C4⋊C4×C61C411yescharacteristic
14C2×#11758217—24no—
15#14519838—28no—
16#14519838—44no—
17C22⋊#92420—42no—
18C22⋊#92420—42no—
19C22×Dic122—24no—
20C22×Dic122—42no—
21C22×Dic122—41no—
22C22×Dic122—41no—
23C22×Dic122C2×C411yescharacteristic
24C22×Dic122D412yes—
25C22×Dic122C2311yescharacteristic
26C23×Dic61—21no—
27C23×Dic61D412yes—
28C2×C4×Dic61—21no—
29C2×C4×Dic61—42no—
30C2×C4×Dic61C2×C412yes—
31#14519684—24no—
32#14519684—24no—
33C23×C4×C61—21no—
34C23×C4×C61C2×C411yescharacteristic
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—41no—
37C2×C4⋊C4×C61—41no—
38C2×C4⋊C4×C61C2×C412yes—
39C24×C61C22⋊C411yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61—44no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—24no—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—22no—
54C22×Dic61—24no—
55C22×Dic61—42no—
56C22×Dic61—42no—
57C22×Dic61—42no—
58C22×Dic61C22⋊C412yes—
59C22×Dic61C2×D412yes—
60C2×Dic122—24no—
61C2×Dic122—22no—
62C2×Dic122—24no—
63C2×Dic122—41no—
64C2×Dic122—41no—
65C2×Dic122—42no—
66C2×Dic122—41no—
67C2×Dic122—41no—
68C2×Dic122—48no—
69C2×Dic122—48no—
70C2×Dic122#4114yes—
71#11758217—44no—
72#11758217—44no—
73C2×#92420—44no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—42no—
76C4×Dic61—42no—
77C4×Dic61—42no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61#9911yescharacteristic
83C23×C61#9911yescharacteristic
84C23×C61C2×C22⋊C411yescharacteristic
85C2×C4×C61—24no—
86C2×C4×C61—24no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—44no—
92C2×C4×C61—42no—
93C2×C4×C61—82no—
94C2×C4×C61—82no—
95C2×C4×C61#9912yes—
96C2×C4×C61#11712yes—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—24no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—44no—
104C2×Dic61—44no—
105C2×Dic61—48no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61#12314yes—
109Dic122—44no—
110Dic122—48no—
111Dic122—44no—
112#92420—84no—
113#12860—611nomaximal, Sylow
114C22×C61—24no—
115C22×C61—24no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61#35512yes—
123C22×C61#35612yes—
124C22×C61#38111yescharacteristic
125C22×C61C2×#9911yescharacteristic
126C22×C61C2×#9911yescharacteristic
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—82no—
130Dic61—24no—
131Dic61—44no—
132Dic61—42no—
133C2×#391—611no—
134#1784—612no—
135#1394—614no—
136C2×C61—21no—
137C2×C61—22no—
138C2×C61—22no—
139C2×C61—21no—
140C2×C61#181911yescharacteristic
141C2×C61C2×#35511yescharacteristic
142C2×C61C2×#35611yescharacteristic
143C23×Q8—611no—
144C22×C4⋊C4#692311yescharacteristic
145C22×C42—611no—
146C2×#101—614no—
147C2×#101—1222no—
148#407—1222no—
149#391—612no—
150#391—612no—
151#391—1222no—
152C2×#95—1222no—
153C61#1286011yescharacteristic, complemented, Sylow
154C22×Q8—612no—
155C22×Q8—611no—
156C22×Q8—611no—
157C22×Q8—1224no—
158C22×Q8—2441no—
159C22×Q8—2441no—
160C22×Q8—2442no—
161C23×C4—21no—
162C23×C4—612no—
163C23×C4—1221no—
164C23×C4C2×#692311yescharacteristic
165C2×M16—1224no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4C2×#692312yes—
170C2×C42—612no—
171C2×C42—1221no—
172C2×C42—2442no—
173#101—1228no—
174#101—2444no—
175C22⋊C8—2442no—
176C22⋊C8—2442no—
177#95—1224no—
178#95—1224no—
179C24C22⋊#692311yescharacteristic
180C2×Q8—614no—
181C2×Q8—1224no—
182C2×Q8—1224no—
183C2×Q8—1222no—
184C2×Q8—2442no—
185C2×Q8—2441no—
186C2×Q8—2441no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8—2448no—
190C2×Q8—2448no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—44no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—612no—
200C22×C4—612no—
201C22×C4—1224no—
202C22×C4—1224no—
203C22×C4—1222no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—2442no—
207C22×C4—2442no—
208C22×C4—2442no—
209C22×C4C22⋊#692311yescharacteristic
210C22×C4C22×#692311yescharacteristic
211M16—2444no—
212M16—2444no—
213C2×C8—2444no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C42—2442no—
217C42—2442no—
218C23—21no—
219C23—21no—
220C23—22no—
221C23—22no—
222C23#1451983511yescharacteristic
223C23#1451983511yescharacteristic
224C23C2×C22⋊#692311yescharacteristic
225Q8—2444no—
226Q8—2448no—
227Q8—2444no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—44no—
235C2×C4—42no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—614no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1224no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—2444no—
246C2×C4—2444no—
247C2×C4—2448no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4#1451983612yes—
251C2×C4#1451985612yes—
252C8—4884no—
253C22—24no—
254C22—24no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22#1684067012yes—
262C22#1684067212yes—
263C22#1684070511yescharacteristic
264C22C2×#1451983511yescharacteristic
265C22C2×#1451983611yescharacteristic
266C4—22no—
267C4—22no—
268C4—82no—
269C4—1224no—
270C4—2444no—
271C4—2442no—
272C2—21no—
273C2—21no—
274C2—22no—
275C2—22no—
276C2#2146171411yescharacteristic
277C2C2×#1684067011yescharacteristic
278C2C2×#1684067211yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC22×Dic122C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#12860
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21460917C2semidirect
153. C61#12860semidirect

Maximal subgroups

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

subgroupindex
#214616532
#214609172
C2×#168396672
#1286061