Finite Group Databasebeta

← #25012863

Subgroups — #25012863

Order 11008.

638 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 115 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#19134519C212yesmaximal
2#19132722C214yesmaximal, complemented
3C2×C43×#391C211yesmaximal, characteristic
4C2×#13063244—22no—
5C2×#13063244C2214yes—
6#14582863—22no—
7C23×Q8×C43C2211yescharacteristic
8C22×C4⋊C4×C43C411yescharacteristic
9C22×C42×C43C411yescharacteristic
10C43×#391—22no—
11C43×#391C412yes—
12C43×#391C2212yes—
13C2×#95×C43—22no—
14C2×#10621877—24no—
15#13063244—28no—
16#13063244—44no—
17C22⋊(C43⋊C8)—42no—
18C22⋊(C43⋊C8)—42no—
19C22×Q8×C43—24no—
20C22×Q8×C43—41no—
21C22×Q8×C43—41no—
22C22×Q8×C43—42no—
23C22×Q8×C43C2×C411yescharacteristic
24C22×Q8×C43D412yes—
25C22×Q8×C43C2311yescharacteristic
26C23×C4×C43—21no—
27C23×C4×C43—21no—
28C23×C4×C43C2×C411yescharacteristic
29C23×C4×C43D412yes—
30C2×C4⋊C4×C43—21no—
31C2×C4⋊C4×C43—41no—
32C2×C4⋊C4×C43—41no—
33C2×C4⋊C4×C43C2×C412yes—
34C2×C42×C43—21no—
35C2×C42×C43—42no—
36C2×C42×C43C2×C412yes—
37#95×C43—24no—
38#95×C43—24no—
39C24×C43C22⋊C411yescharacteristic
40C2×Q8×C43—24no—
41C2×Q8×C43—22no—
42C2×Q8×C43—24no—
43C2×Q8×C43—41no—
44C2×Q8×C43—41no—
45C2×Q8×C43—42no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43—48no—
49C2×Q8×C43—48no—
50C2×Q8×C43#4114yes—
51C22×C4×C43—22no—
52C22×C4×C43—22no—
53C22×C4×C43—24no—
54C22×C4×C43—24no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—22no—
58C22×C4×C43—22no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—42no—
62C22×C4×C43—42no—
63C22×C4×C43—42no—
64C22×C4×C43—44no—
65C22×C4×C43—41no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C412yes—
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D412yes—
71C4⋊C4×C43—42no—
72C4⋊C4×C43—42no—
73C42×C43—42no—
74C42×C43—42no—
75#10621877—44no—
76#10621877—44no—
77C2×C43⋊C8—44no—
78C23×C43—22no—
79C23×C43—22no—
80C23×C43—21no—
81C23×C43—21no—
82C23×C43#9911yescharacteristic
83C23×C43#9911yescharacteristic
84C23×C43C2×C22⋊C411yescharacteristic
85Q8×C43—44no—
86Q8×C43—48no—
87Q8×C43—44no—
88C2×C4×C43—24no—
89C2×C4×C43—24no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—21no—
96C2×C4×C43—24no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—44no—
101C2×C4×C43—44no—
102C2×C4×C43—48no—
103C2×C4×C43—42no—
104C2×C4×C43—42no—
105C2×C4×C43—44no—
106C2×C4×C43—42no—
107C2×C4×C43—82no—
108C2×C4×C43—82no—
109C2×C4×C43#9912yes—
110C2×C4×C43#11712yes—
111C2×C4×C43#12314yes—
112C43⋊C8—84no—
113#12860—431nomaximal, Sylow
114C22×C43—24no—
115C22×C43—24no—
116C22×C43—21no—
117C22×C43—21no—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—21no—
121C22×C43—21no—
122C22×C43#35512yes—
123C22×C43#35612yes—
124C22×C43#38111yescharacteristic
125C22×C43C2×#9911yescharacteristic
126C22×C43C2×#9911yescharacteristic
127C4×C43—24no—
128C4×C43—22no—
129C4×C43—22no—
130C4×C43—44no—
131C4×C43—42no—
132C4×C43—82no—
133C2×#391D4311yescharacteristic
134#1784—432no—
135#1394—434no—
136C2×C43—21no—
137C2×C43—22no—
138C2×C43—22no—
139C2×C43—21no—
140C2×C43#181911yescharacteristic
141C2×C43C2×#35511yescharacteristic
142C2×C43C2×#35611yescharacteristic
143C23×Q8C2×D4311yescharacteristic
144C22×C4⋊C4Dic4311yescharacteristic
145C22×C42Dic4311yescharacteristic
146C2×#101—434no—
147C2×#101—862no—
148#407—862no—
149#391—22no—
150#391Dic4312yes—
151#391C2×D4312yes—
152C2×#95—22no—
153C43#1286011yescharacteristic, complemented, Sylow
154C22×Q8—24no—
155C22×Q8—41no—
156C22×Q8—41no—
157C22×Q8—42no—
158C22×Q8C2×Dic4311yescharacteristic
159C22×Q8C22⋊D4312yes—
160C22×Q8C22×D4311yescharacteristic
161C23×C4—21no—
162C23×C4—21no—
163C23×C4C2×Dic4311yescharacteristic
164C23×C4C22⋊D4312yes—
165C2×M16—864no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4C2×Dic4312yes—
170C2×C42—21no—
171C2×C42—42no—
172C2×C42C2×Dic4312yes—
173#101—868no—
174#101—1724no—
175C22⋊C8—1722no—
176C22⋊C8—1722no—
177#95—24no—
178#95—24no—
179C24C22⋊Dic4311yescharacteristic
180C2×Q8—24no—
181C2×Q8—22no—
182C2×Q8—24no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—42no—
188C2×Q8—48no—
189C2×Q8—48no—
190C2×Q8#1062189814yes—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—24no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—24no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—44no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4C22⋊Dic4312yes—
208C22×C4C22⋊Dic4311yescharacteristic
209C22×C4C22×Dic4311yescharacteristic
210C22×C4C2×C22⋊D4312yes—
211M16—1724no—
212M16—1724no—
213C2×C8—1724no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C42—42no—
217C42—42no—
218C23—21no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23#1306324011yescharacteristic
223C23#1306324011yescharacteristic
224C23C2×C22⋊Dic4311yescharacteristic
225Q8—44no—
226Q8—48no—
227Q8—44no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—48no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4#1306324012yes—
250C2×C4#1306328412yes—
251C2×C4#1306330814yes—
252C8—3444no—
253C22—24no—
254C22—24no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22#1458269612yes—
262C22#1458269812yes—
263C22#1458276211yescharacteristic
264C22C2×#1306324011yescharacteristic
265C22C2×#1306324011yescharacteristic
266C4—24no—
267C4—22no—
268C4—22no—
269C4—44no—
270C4—42no—
271C4—82no—
272C2—21no—
273C2—22no—
274C2—22no—
275C2—21no—
276C2#1913466911yescharacteristic
277C2C2×#1458269611yescharacteristic
278C2C2×#1458269811yescharacteristic
subgroupG/H
centerC22C2×#13063240
commutatorC22×C4×C43C22×C4
FrattiniC22×Q8C22×D43
FittingC2×C43×#391C2
socleC22×C43C2×#99
prime radicalC24×C43C22⋊C4
cosocleC22×Q8×C43C23
hypercenterC2×#391D43
hypocenterC43#12860
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. #19132722C2semidirect
153. C43#12860semidirect

Maximal subgroups

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

subgroupindex
#191345192
#191327222
C2×C43×#3912
#1286043