Finite Group Databasebeta

← #14651518

Subgroups — #14651518

Order 2816.

610 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071219C211yesmaximal, characteristic, complemented
2#13068696C211yesmaximal, characteristic, complemented
3#13067145C212yesmaximal
4#13066469C212yesmaximal, complemented
5C11×#2501C211yesmaximal, characteristic
6C2×C11×#123—21no—
7C2×C11×#123—21no—
8C2×C11×#121C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C11×#399—22no—
11C11×#390C412yescomplemented
12C11×#384C412yescomplemented
13C4×C11×C22⋊C4C2211yescharacteristic
14#10622825—21no—
15#10622824C2212yes—
16C4×C22⋊Dic11—21no—
17#10622820C2212yes—
18#10622594—24no—
19#10622175—24no—
20#10622168—22no—
21C22×D4×C11—21no—
22C22×D4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C11×#123—44no—
27C11×#123—44no—
28C11×#121—22no—
29C11×#121—22no—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C412yes—
36C2×C11×C4⋊C4D412yes—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—22no—
39C2×C11×C22⋊C4—22no—
40C2×C11×C22⋊C4—21no—
41C2×C42×C11C2×C412yes—
42C2×C22⋊Dic11—22no—
43C2×C4⋊Dic11—22no—
44C2×C4×Dic11—22no—
45C2×#4318—22no—
46C11×#95—21no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95D414yes—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53#9464—111nomaximal, Sylow
54C24×C11—21no—
55C24×C11C2×D411yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—42no—
69C22×C4×C11—42no—
70C22×C4×C11—42no—
71C22×C4×C11C22⋊C412yes—
72C22×C4×C11C22⋊C412yes—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C22×C4×C11#4112yes—
77C22×Dic11—24no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—24no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—44no—
82C11×C4⋊C4—44no—
83C11×C22⋊C4—24no—
84C11×C22⋊C4—44no—
85C11×C22⋊C4—44no—
86C11×C22⋊C4—42no—
87C42×C11—42no—
88C22⋊Dic11—44no—
89C4⋊Dic11—82no—
90C4×Dic11—82no—
91#4318—44no—
92C2×C11⋊C8—42no—
93#2501D1111yescharacteristic
94#2313—111no—
95#1821—111no—
96#1510—112no—
97#1284—112no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—41no—
103C23×C11—42no—
104C23×C11—41no—
105C23×C11—42no—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11#12011yescharacteristic
108C23×C11#12311yescharacteristic
109D4×C11—82no—
110D4×C11—82no—
111D4×C11—82no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12112yes—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C11⋊C8—82no—
136C2×#123—21no—
137C2×#123—21no—
138C2×#121C2×D1111yescharacteristic
139C22×C4⋊C4C2×D1111yescharacteristic
140#407—112no—
141#399—22no—
142#390Dic1112yescomplemented
143#387—224no—
144#384Dic1112yescomplemented
145#381—112no—
146#380—221no—
147C4×C22⋊C4—221no—
148C4×C22⋊C4C2×D1111yescharacteristic
149#343—222no—
150#327—224no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—44no—
159C22×C11—82no—
160C22×C11—82no—
161C22×C11—81no—
162C22×C11—81no—
163C22×C11—81no—
164C22×C11#38611yescharacteristic
165C22×C11#41012yes—
166C22×C11#45312yes—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—44no—
170C4×C11—42no—
171C4×C11—42no—
172C4×C11—81no—
173Dic11—84no—
174C22×D4—21no—
175C22×D4C2×Dic1111yescharacteristic
176C23×C4C22⋊D1111yescharacteristic
177C23×C4C22⋊D1111yescharacteristic
178C23×C4C22×D1111yescharacteristic
179C2×M16—222no—
180#123—44no—
181#123—44no—
182#121—22no—
183#121—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—222no—
189C2×C4⋊C4C2×Dic1111yescharacteristic
190C2×C4⋊C4C2×Dic1112yes—
191C2×C4⋊C4C22⋊D1112yes—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—222no—
197C2×C42—222no—
198C2×C42C2×Dic1112yes—
199C22⋊C8—222no—
200C22⋊C8—222no—
201#95—21no—
202#95—114no—
203#95—222no—
204#95—222no—
205#95—222no—
206C2×C11—22no—
207C2×C11—22no—
208C2×C11—41no—
209C2×C11—161no—
210C2×C11#188711yescharacteristic
211C2×C11#189911yescharacteristic
212C2×C11#191211yescharacteristic
213C24—21no—
214C24C2×C22⋊D1111yescharacteristic
215C2×D4—22no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—224no—
231C22×C4C22⋊Dic1112yes—
232C22×C4C22⋊Dic1112yes—
233C22×C4D4×D1112yes—
234C22×C4#434112yes—
235C22×C4C22×Dic1111yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237M16—444no—
238C2×C8—442no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—22no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4—882no—
245C22⋊C4—24no—
246C22⋊C4—44no—
247C22⋊C4—44no—
248C22⋊C4—42no—
249C22⋊C4—444no—
250C42—42no—
251C42—882no—
252C11#946411yescharacteristic, complemented, Sylow
253C23—22no—
254C23—22no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—41no—
260C23—42no—
261C23#6698811yescharacteristic
262C23#6699011yescharacteristic
263C23C2×C22⋊Dic1111yescharacteristic
264D4—82no—
265D4—82no—
266D4—82no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—444no—
286C2×C4—444no—
287C2×C4—444no—
288C2×C4D4×Dic1112yes—
289C2×C4#6699212yes—
290C8—882no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—82no—
300C22—82no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22#1062269012yes—
305C22#1062283311yescharacteristic
306C22#1062285312yes—
307C4—22no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—42no—
312C4—81no—
313C4—884no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—161no—
318C2#1306901511yescharacteristic
319C2#1306907511yescharacteristic
320C2#1306915411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2501C2
socleC22×C11#386
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2501D11
hypocenterC11#9464
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. #13071219C2semidirect
2. #13068696C2semidirect
4. #13066469C2semidirect
11. C11×#390C4semidirect
12. C11×#384C4semidirect
142. #390Dic11semidirect
144. #384Dic11semidirect
252. C11#9464semidirect

Maximal subgroups

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

subgroupindex
#130712192
#130686962
#130671452
#130664692
C11×#25012
#946411