Finite Group Databasebeta

← #14640344

Subgroups — #14640344

Order 2816.

730 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 127 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#13068526C212yesmaximal
2C11×C22⋊#95C211yesmaximal, characteristic
3C24×C4×C11C2211yescharacteristic
4C22×C11×C22⋊C4C412yes—
5C2×C11×#95—22no—
6C2×C22⋊(C11⋊C8)—22no—
7C2×C22⋊(C11⋊C8)—22no—
8C2×C22⋊(C11⋊C8)C414yescomplemented
9C25×C11C2×C411yescharacteristic
10C23×C4×C11—22no—
11C23×C4×C11—44no—
12C23×C4×C11—42no—
13C23×C4×C11C2×C412yes—
14C23×C4×C11D411yescharacteristic
15C23×C4×C11D412yes—
16C23×C4×C11Q811yescharacteristic
17C2×C11×C22⋊C4—22no—
18C2×C11×C22⋊C4—42no—
19C2×C11×C22⋊C4—42no—
20C2×C11×C22⋊C4C814yescomplemented
21C22×C11⋊C8—24no—
22C11×#95—44no—
23C22⋊(C11⋊C8)—44no—
24C22⋊(C11⋊C8)—44no—
25C22⋊(C11⋊C8)—44no—
26#7032—111nomaximal, Sylow
27C24×C11—22no—
28C24×C11—21no—
29C24×C11—21no—
30C24×C11—42no—
31C24×C11—42no—
32C24×C11C4211yescharacteristic
33C24×C11C22⋊C411yescharacteristic
34C24×C11C4⋊C411yescharacteristic
35C24×C11C2×C812yes—
36C24×C11M1612yes—
37C22×C4×C11—24no—
38C22×C4×C11—24no—
39C22×C4×C11—24no—
40C22×C4×C11—24no—
41C22×C4×C11—24no—
42C22×C4×C11—42no—
43C22×C4×C11—42no—
44C22×C4×C11—41no—
45C22×C4×C11—42no—
46C22×C4×C11—42no—
47C22×C4×C11—41no—
48C22×C4×C11—416no—
49C22×C4×C11—44no—
50C22×C4×C11—44no—
51C22×C4×C11—42no—
52C22×C4×C11—42no—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C4⋊C412yes—
55C11×C22⋊C4—44no—
56C11×C22⋊C4—44no—
57C2×C11⋊C8—44no—
58C2×C11⋊C8—44no—
59C2×C11⋊C8—44no—
60#1779—112no—
61C22⋊#95D1111yescharacteristic
62C23×C11—22no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—22no—
67C23×C11—22no—
68C23×C11—22no—
69C23×C11—22no—
70C23×C11—21no—
71C23×C11—21no—
72C23×C11—21no—
73C23×C11—21no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—44no—
77C23×C11—44no—
78C23×C11—44no—
79C23×C11—44no—
80C23×C11—44no—
81C23×C11—44no—
82C23×C11#9511yescharacteristic
83C23×C11C4×C811yescharacteristic
84C23×C11#9711yescharacteristic
85C23×C11C22⋊C812yes—
86C23×C11#9912yes—
87C23×C11#10011yescharacteristic
88C23×C11#10111yescharacteristic
89C23×C11C4⋊C812yes—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—44no—
96C2×C4×C11—48no—
97C2×C4×C11—48no—
98C2×C4×C11—44no—
99C2×C4×C11—48no—
100C2×C4×C11—44no—
101C2×C4×C11—82no—
102C2×C4×C11—84no—
103C2×C4×C11—82no—
104C2×C4×C11#9914yes—
105C11⋊C8—84no—
106C24×C4C2×D1111yescharacteristic
107C22×C22⋊C4Dic1112yes—
108C2×C22⋊C8—114no—
109C2×C22⋊C8—222no—
110C2×C22⋊C8—222no—
111C2×#95—22no—
112C22×C11—24no—
113C22×C11—22no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—22no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—24no—
123C22×C11—44no—
124C22×C11—44no—
125C22×C11—44no—
126C22×C11—44no—
127C22×C11—41no—
128C22×C11—41no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—41no—
132C22×C11—41no—
133C22×C11#32312yes—
134C22×C11#32412yes—
135C22×C11#33611yescharacteristic
136C22×C11#34211yescharacteristic
137C22×C11#34212yes—
138C22×C11#34311yescharacteristic
139C22×C11#34412yes—
140C4×C11—24no—
141C4×C11—42no—
142C4×C11—84no—
143C25C2×Dic1111yescharacteristic
144C23×C4—22no—
145C23×C4—44no—
146C23×C4—42no—
147C23×C4Dic2211yescharacteristic
148C23×C4C4×D1112yes—
149C23×C4D4411yescharacteristic
150C23×C4C22⋊D1112yes—
151C22×C8—224no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—42no—
154C2×C22⋊C4—42no—
155C2×C22⋊C4C11⋊C814yescomplemented
156C22⋊C8—444no—
157C22⋊C8—444no—
158C22⋊C8—444no—
159#95—44no—
160C2×C11—22no—
161C2×C11—22no—
162C2×C11—41no—
163C2×C11—41no—
164C2×C11—42no—
165C2×C11#128011yescharacteristic
166C2×C11#128212yes—
167C2×C11#130411yescharacteristic
168C2×C11#130512yes—
169C2×C11#130611yescharacteristic
170C24—21no—
171C24—22no—
172C24—21no—
173C24—42no—
174C24—42no—
175C24C2×C11⋊C812yes—
176C24#431812yes—
177C24C4×Dic1111yescharacteristic
178C24C4⋊Dic1111yescharacteristic
179C24C22⋊Dic1111yescharacteristic
180C22×C4—24no—
181C22×C4—24no—
182C22×C4—24no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—41no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—41no—
190C22×C4—42no—
191C22×C4—416no—
192C22×C4—44no—
193C22×C4—44no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4Dic11⋊C412yes—
197C22×C4(C2×D11)⋊C412yes—
198C2×C8—444no—
199C2×C8—444no—
200C2×C8—444no—
201C22⋊C4—44no—
202C22⋊C4—44no—
203C11#703211yescharacteristic, complemented, Sylow
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—22no—
218C23—44no—
219C23—44no—
220C23—44no—
221C23—44no—
222C23—44no—
223C23—44no—
224C23C4×C11⋊C811yescharacteristic
225C23#6686711yescharacteristic
226C23C4⋊(C11⋊C8)12yes—
227C23C22⋊(C11⋊C8)12yes—
228C23C11⋊#9511yescharacteristic
229C23#6689711yescharacteristic
230C23#6689812yes—
231C23#6690011yescharacteristic
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—48no—
239C2×C4—48no—
240C2×C4—44no—
241C2×C4—48no—
242C2×C4—44no—
243C2×C4—82no—
244C2×C4—84no—
245C2×C4—82no—
246C2×C4#6687014yes—
247C8—884no—
248C22—22no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—24no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—24no—
259C22—44no—
260C22—44no—
261C22—44no—
262C22—44no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22#1062216211yescharacteristic
270C22#1062216312yes—
271C22#1062216411yescharacteristic
272C22#1062216512yes—
273C22#1062216612yes—
274C22#1062216811yescharacteristic
275C22#1062217112yes—
276C4—24no—
277C4—42no—
278C4—84no—
279C2—22no—
280C2—22no—
281C2—41no—
282C2—41no—
283C2—42no—
284C2#1306645911yescharacteristic
285C2#1306646412yes—
286C2C11⋊#130411yescharacteristic
287C2#1306652212yes—
288C2#1306652411yescharacteristic
subgroupG/H
centerC23C11⋊#95
commutatorC23×C11C4×C8
FrattiniC24×C4C2×D11
FittingC11×C22⋊#95C2
socleC23×C11#95
prime radicalC25×C11C2×C4
cosocleC24×C4×C11C22
hypercenterC22⋊#95D11
hypocenterC11#7032
LCSG ▷ C23×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
8. C2×C22⋊(C11⋊C8)C4semidirect
20. C2×C11×C22⋊C4C8semidirect
155. C2×C22⋊C4C11⋊C8semidirect
203. C11#7032semidirect

Maximal subgroups

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

subgroupindex
#130685262
C11×C22⋊#952
#703211