Finite Group Databasebeta

← #14649851

Subgroups — #14649851

Order 2816.

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

normal subgroups only

This group has 578 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#13074358C211yesmaximal, characteristic
2#13067183C212yesmaximal
3C2×#10622166C211yesmaximal, characteristic, complemented
4#13066483C212yesmaximal, complemented
5C11×#2313C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C11×#387—24no—
10C11×#381—21no—
11C11×#380C2212yes—
12C4×C11×C22⋊C4—21no—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2212yes—
16#10622607—22no—
17#10622604C412yescomplemented
18#10622596C412yescomplemented
19#10622166—22no—
20#10622089—24no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C22×D44C2×C411yescharacteristic
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4C2×C412yes—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C22⋊C4—22no—
32C2×C42×C11—22no—
33C2×C22⋊Dic11—21no—
34#66983—22no—
35#66983—22no—
36#66982—44no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11C2×C411yescharacteristic
42C2×Dic11⋊C4—22no—
43C22×C11⋊C8—22no—
44C11×#95—22no—
45C11×#95—24no—
46C11×#95D414yes—
47C11⋊#95—22no—
48C11⋊#95C2×C412yes—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#9206—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C23×D11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—24no—
61C22×C4×C11—81no—
62C22×C4×C11—81no—
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D412yes—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4112yes—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71C2×C22⋊D11—42no—
72C2×C22⋊D11—42no—
73C22×Dic11—21no—
74C22×Dic11—22no—
75C2×D44—22no—
76C2×D44—81no—
77C11×C4⋊C4—24no—
78C11×C4⋊C4—24no—
79C11×C4⋊C4—82no—
80C11×C22⋊C4—42no—
81C11×C22⋊C4—42no—
82C42×C11—82no—
83C22⋊Dic11—42no—
84(C2×D11)⋊C4—44no—
85(C2×D11)⋊C4—42no—
86(C2×D11)⋊C4—82no—
87C4⋊Dic11—22no—
88C4⋊Dic11—81no—
89Dic11⋊C4—44no—
90C2×C11⋊C8—42no—
91C2×C11⋊C8—82no—
92#2618—111no—
93#2313D1111yescharacteristic, complemented
94#1519—112no—
95C2×#324—111no—
96#1289—112no—
97C23×C11—41no—
98C23×C11—41no—
99C23×C11C2×C22⋊C411yescharacteristic
100C23×C11#12011yescharacteristic
101C23×C11#12311yescharacteristic
102C23×C11#13512yes—
103C23×C11AGL(1,ℤ/8)12yes—
104C22×D11—42no—
105C22×D11—42no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—41no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—44no—
122C2×C4×C11—44no—
123C2×C4×C11—44no—
124C2×C4×C11—81no—
125C2×C4×C11C4×D412yes—
126C2×C4×C11#12112yes—
127C22⋊D11—82no—
128C22⋊D11—82no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135D44—82no—
136C11⋊C8—82no—
137C2×#123—221no—
138C2×#121—111no—
139C22×C4⋊C4C2×D1111yescharacteristic
140C2×C22⋊C8—112no—
141#398—112no—
142#396—222no—
143#394—112no—
144#387—24no—
145#386—221no—
146#381—21no—
147#380—111no—
148#380C2×D1112yes—
149C4×C22⋊C4—21no—
150#327—224no—
151#324—222no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—42no—
159C22×C11—42no—
160C22×C11#38611yescharacteristic
161C22×C11#41611yescharacteristic
162C22×C11#41811yescharacteristic
163C22×C11#44912yes—
164C22×C11#48212yes—
165C2×D11—82no—
166C2×D11—82no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—22no—
171C4×C11—22no—
172C4×C11—42no—
173C4×C11—42no—
174C4×C11—84no—
175Dic11—82no—
176Dic11—81no—
177C22×D4—111no—
178C22×D4—221no—
179C23×C4C22⋊D1111yescharacteristic
180C23×C4C22⋊D1111yescharacteristic
181C23×C4C22×D1111yescharacteristic
182C22×C8—222no—
183#123—444no—
184#121—222no—
185#121—222no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—222no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4C4×D1112yes—
193C2×C4⋊C4D4412yes—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—221no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4—221no—
198C2×C22⋊C4—222no—
199C2×C42—22no—
200C22⋊C8—222no—
201C22⋊C8—222no—
202#95—22no—
203#95—24no—
204#95—112no—
205#95—222no—
206#95C22⋊D1114yes—
207C2×C11—21no—
208C2×C11—22no—
209C2×C11—21no—
210C2×C11—22no—
211C2×C11#187511yescharacteristic
212C2×C11#191211yescharacteristic
213C2×C11#191311yescharacteristic
214D11—161no—
215C24—221no—
216C24C2×C22⋊D1111yescharacteristic
217C2×D4—222no—
218C2×D4—441no—
219C2×D4—442no—
220C2×D4—442no—
221C2×D4—441no—
222C2×D4—881no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—81no—
231C22×C4—81no—
232C22×C4—222no—
233C22×C4—221no—
234C22×C4(C2×D11)⋊C412yes—
235C22×C4(C2×D11)⋊C412yes—
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4C2×D4411yescharacteristic
238C22×C4#433912yes—
239C22×C4C2×C22⋊D1112yes—
240C2×C8—442no—
241C2×C8—882no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—82no—
245C4⋊C4—222no—
246C4⋊C4—444no—
247C4⋊C4—881no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—444no—
251C22⋊C4—442no—
252C22⋊C4—442no—
253C22⋊C4—882no—
254C42—82no—
255C11#920611yescharacteristic, complemented, Sylow
256C23—41no—
257C23—41no—
258C23—442no—
259C23—442no—
260C23—441no—
261C23—441no—
262C23—441no—
263C23C2×(C2×D11)⋊C411yescharacteristic
264C23#6698211yescharacteristic
265C23#6700212yes—
266C23#6700312yes—
267C23#6700611yescharacteristic
268D4—882no—
269D4—882no—
270D4—882no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—81no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4C4×C22⋊D1112yes—
294C2×C4#6698312yes—
295C8—882no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—882no—
305C22—882no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22#1062261411yescharacteristic
310C22#1062261511yescharacteristic
311C22#1062261612yes—
312C22#1062282611yescharacteristic
313C22#1062285112yes—
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—84no—
319C4—882no—
320C4—881no—
321C2—22no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—1761no—
326C2#1306893811yescharacteristic
327C2#1306915311yescharacteristic
328C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2313C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#2313D11
hypocenterC11#9206
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. C2×#10622166C2semidirect
4. #13066483C2semidirect
5. C11×#2313C2semidirect
17. #10622604C4semidirect
18. #10622596C4semidirect
93. #2313D11semidirect
255. C11#9206semidirect

Maximal subgroups

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

subgroupindex
#130743582
#130671832
C2×#106221662
#130664832
C11×#23132
#920611