Finite Group Databasebeta

← #14651565

Subgroups — #14651565

Order 2816.

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

normal subgroups only

This group has 576 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#13077645C211yesmaximal, characteristic
2#13072924C211yesmaximal, characteristic
3#13068700C212yesmaximal, complemented
4#13066483C212yesmaximal, complemented
5C11×#1799C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66988—21no—
8C22×C4⋊Dic11C2211yescharacteristic
9C2×C11×#99—21no—
10C11×#380C2212yes—
11#10622825—21no—
12#10622825C2211yescharacteristic
13#10622820—21no—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622624—24no—
16#10622596C412yescomplemented
17#10622566C412yescomplemented
18#10622556—21no—
19#10622541—21no—
20#10622539—21no—
21C11×#342—21no—
22#10622167—24no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4C2×C411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—21no—
37#66988—44no—
38C2×C4⋊Dic11—22no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C412yes—
43C2×Dic11⋊C4—22no—
44C2×#4318—22no—
45C22×C11⋊C8D414yes—
46C11×#99—42no—
47C11×#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95C2×C412yes—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C4⋊(C11⋊C8)—22no—
55#66867—22no—
56#9474—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C24×C11C2×D411yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—21no—
61C2×D4×C11—22no—
62C2×D4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11#4112yes—
75C22×Dic11—22no—
76C22×Dic11—22no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—44no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—42no—
87C42×C11—21no—
88C42×C11—21no—
89C22⋊Dic11—44no—
90C22⋊Dic11—42no—
91C4⋊Dic11—24no—
92C4⋊Dic11—42no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—44no—
96#4318—82no—
97C2×C11⋊C8—24no—
98C2×C11⋊C8—44no—
99#2973—111no—
100#2486—111no—
101#1823—112no—
102#1799D1111yescharacteristic
103#1289—112no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11C2×C22⋊C411yescharacteristic
112C23×C11#12112yes—
113C23×C11AGL(1,ℤ/8)11yescharacteristic
114C23×C11AGL(1,ℤ/8)12yes—
115C23×C11#13711yescharacteristic
116D4×C11—42no—
117D4×C11—42no—
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—81no—
131C2×C4×C11—82no—
132C2×C4×C11—82no—
133C2×C4×C11—82no—
134C2×C4×C11C4×D412yes—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—82no—
144C2×Dic11—82no—
145C11⋊C8—44no—
146C2×#123—221no—
147C2×C4×D4C2×D1111yescharacteristic
148C22×C4⋊C4—111no—
149#435—224no—
150#432—221no—
151C2×#99—21no—
152#407—221no—
153C2×C22⋊C8—112no—
154#398—112no—
155#397—112no—
156#389—221no—
157#381—221no—
158#380—111no—
159#380—221no—
160#380C2×D1112yes—
161#342—21no—
162#340—224no—
163C22×C11—21no—
164C22×C11—22no—
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—41no—
168C22×C11—42no—
169C22×C11—41no—
170C22×C11—42no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—81no—
175C22×C11#38611yescharacteristic
176C22×C11#41711yescharacteristic
177C22×C11#41811yescharacteristic
178C22×C11#46812yes—
179C22×C11#46912yes—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11—162no—
186C4×C11#45812yes—
187Dic11—82no—
188Dic11—82no—
189C22×D4C22⋊D1111yescharacteristic
190C23×C4—221no—
191C23×C4D4411yescharacteristic
192C23×C4C22×D1111yescharacteristic
193C2×M16—222no—
194C22×C8—114no—
195#123—444no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—112no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—222no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C4×D1111yescharacteristic
206C2×C22⋊C4—22no—
207C2×C22⋊C4—222no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4C4×D1111yescharacteristic
210C2×C22⋊C4C22⋊D1111yescharacteristic
211C2×C42D4411yescharacteristic
212C4⋊C8—222no—
213#99—42no—
214C22⋊C8—222no—
215C22⋊C8—222no—
216C22⋊C8—222no—
217#97—222no—
218#95—22no—
219#95—112no—
220#95—222no—
221#95—222no—
222C2×C11—21no—
223C2×C11—22no—
224C2×C11—21no—
225C2×C11—22no—
226C2×C11—81no—
227C2×C11#189011yescharacteristic
228C2×C11#189511yescharacteristic
229C2×C11#190911yescharacteristic
230C24(C2×D11)⋊C411yescharacteristic
231C24C2×C22⋊D1111yescharacteristic
232C2×D4—21no—
233C2×D4—22no—
234C2×D4—21no—
235C2×D4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—441no—
244C22×C4—442no—
245C22×C4—441no—
246C22×C4—442no—
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4(C2×D11)⋊C411yescharacteristic
250C22×C4C2×C4×D1111yescharacteristic
251C22×C4C2×D4411yescharacteristic
252C22×C4D4×D1112yes—
253C22×C4#434112yes—
254M16—882no—
255C2×C8—224no—
256C2×C8—444no—
257C4⋊C4—22no—
258C4⋊C4—44no—
259C4⋊C4—224no—
260C4⋊C4—444no—
261C4⋊C4—442no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—444no—
269C22⋊C4—442no—
270C42—21no—
271C42—21no—
272C11#947411yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×(C2×D11)⋊C411yescharacteristic
281C23#6698511yescharacteristic
282C23#6699212yes—
283C23#6699511yescharacteristic
284C23#6700212yes—
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—442no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—882no—
310C2×C4—882no—
311C2×C4(C22⋊D11)⋊C412yes—
312C2×C4#6693511yescharacteristic
313C2×C4#6693911yescharacteristic
314C8—444no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#1062257111yescharacteristic
328C22#1062257911yescharacteristic
329C22#1062261411yescharacteristic
330C22#1062265212yes—
331C22#1062266212yes—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—162no—
338C4—882no—
339C4—882no—
340C4#1062235512yes—
341C2—22no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2#1306902711yescharacteristic
347C2#1306905211yescharacteristic
348C2#1306913611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1799C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1799D11
hypocenterC11#9474
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13068700C2semidirect
4. #13066483C2semidirect
16. #10622596C4semidirect
17. #10622566C4semidirect
272. C11#9474semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130729242
#130687002
#130664832
C11×#17992
#947411