Finite Group Databasebeta

← #14652205

Subgroups — #14652205

Order 2816.

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

normal subgroups only

This group has 376 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#13069444C211yesmaximal, characteristic
2#13067386C211yesmaximal, characteristic, complemented
3#13067266C211yesmaximal, characteristic
4#13067014C211yesmaximal, characteristic
5#13066513C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C4×C11×C4⋊C8C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11—21no—
12C43×C11C2211yescharacteristic
13C2×#66869—21no—
14C2×#66869—21no—
15#10622538C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18C11×#336—21no—
19#10622123C412yescomplemented
20#10622121—22no—
21#10622120C412yescomplemented
22#10622118—22no—
23C2×#4339—21no—
24C22×C8×C11—21no—
25C22×C8×C11—21no—
26C2×C42×C11—21no—
27C2×C42×C11—21no—
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C42×C11C2311yescharacteristic
31#66983—21no—
32#66983—21no—
33C2×#4318—21no—
34#66928—21no—
35#66927C2×C411yescharacteristic
36C4×D44—21no—
37C4×D44—21no—
38#66922C2×C411yescharacteristic
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8C2×C412yes—
42C11×C4⋊C8D412yes—
43C4×C8×C11—42no—
44C22⋊(C11⋊C8)—21no—
45C22⋊(C11⋊C8)—21no—
46#66869—42no—
47#66869—42no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)C2×C412yes—
52C4×C11⋊C8—21no—
53C4×C11⋊C8—21no—
54#9578—111nomaximal, Sylow
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11#4111yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C2×C22⋊D11—41no—
61#4339—41no—
62#4339—41no—
63#4339—41no—
64#4339—41no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—21no—
68C2×C4×D11—41no—
69C2×Dic22—21no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C2×C8×C11—41no—
75C2×C8×C11—41no—
76C42×C11—24no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—42no—
81C42×C11SD1612yes—
82C42×C11C22×C411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11#4111yescharacteristic
85C42×C11#4111yescharacteristic
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90#4318—41no—
91#4318—41no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95#1962—111no—
96C4×C4⋊C8D1111yescharacteristic, complemented
97#1570—111no—
98#1540—111no—
99#1480—111no—
100#1301—111no—
101#1276—111no—
102C23×C11#12311yescharacteristic
103C22×D11—41no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11#11711yescharacteristic
113C2×C4×C11C4×D411yescharacteristic
114C2×C4×C11C4×D411yescharacteristic
115C2×C4×C11#12111yescharacteristic
116C2×C4×C11#12411yescharacteristic
117C2×C4×C11#12611yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11#13511yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122C22⋊D11—81no—
123C22⋊D11—81no—
124C2×Dic11—41no—
125D44—41no—
126D44—41no—
127D44—42no—
128D44—81no—
129C4×D11—81no—
130C4×D11—81no—
131Dic22—41no—
132Dic22—41no—
133C8×C11—42no—
134C8×C11—42no—
135C11⋊C8—42no—
136C11⋊C8—81no—
137C11⋊C8—81no—
138#532—111no—
139#431—111no—
140#431—111no—
141#423—111no—
142C2×C4⋊C8C2×D1111yescharacteristic
143C2×C4⋊C8C2×D1111yescharacteristic
144C2×#104—221no—
145C2×#104—221no—
146C2×C4×C8—21no—
147C43C2×D1111yescharacteristic
148#336—21no—
149#334—222no—
150#332—112no—
151#331—112no—
152D4⋊C8—222no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11#38811yescharacteristic
156C22×C11#48111yescharacteristic
157C22×C11#48211yescharacteristic
158C2×D11—81no—
159C2×D11—81no—
160C2×D11—81no—
161C4×C11—24no—
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—21no—
165C4×C11—42no—
166C4×C11C4×SD1611yescharacteristic
167C4×C11#44211yescharacteristic
168C4×C11#44312yes—
169C4×C11#46011yescharacteristic
170C4×C11#46311yescharacteristic
171Dic11—81no—
172C2×#41—221no—
173C2×M16—221no—
174C22×C8—21no—
175C22×C8—21no—
176C4⋊Q8—111no—
177#127—111no—
178#124—221no—
179#121—221no—
180#121—221no—
181C4×D4—221no—
182C4×D4—221no—
183C2×C42—21no—
184C2×C42—21no—
185C2×C42C22⋊D1111yescharacteristic
186C2×C42C22⋊D1111yescharacteristic
187C2×C42C22×D1111yescharacteristic
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—112no—
191C4⋊C8—221no—
192C4⋊C8—221no—
193C4⋊C8—221no—
194C4⋊C8C4×D1112yes—
195C4⋊C8D4412yes—
196#104—442no—
197#104—442no—
198C22⋊C8—221no—
199C22⋊C8—221no—
200C4×C8—42no—
201C4×C8—221no—
202C4×C8—221no—
203C2×C11—21no—
204C2×C11—21no—
205C2×C11#192611yescharacteristic
206C2×C11#193211yescharacteristic
207C2×C11#193711yescharacteristic
208D11—161no—
209#41—441no—
210#41—441no—
211#41—441no—
212#41—441no—
213C2×Q8—221no—
214C2×D4—221no—
215C2×D4—221no—
216C2×D4—221no—
217C2×D4—441no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—441no—
221C22×C4#433911yescharacteristic
222C22×C4#433911yescharacteristic
223C22×C4C2×C22⋊D1111yescharacteristic
224M16—441no—
225M16—441no—
226C2×C8—22no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—222no—
233C2×C8—441no—
234C2×C8—441no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C22⋊C4—441no—
238C22⋊C4—441no—
239C42—24no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—42no—
244C42#432512yes—
245C42C2×C4×D1111yescharacteristic
246C42C2×D4411yescharacteristic
247C42#433911yescharacteristic
248C42#433911yescharacteristic
249C11#957811yescharacteristic, complemented, Sylow
250C23—441no—
251C23#6698211yescharacteristic
252Q8—441no—
253Q8—441no—
254D4—442no—
255D4—441no—
256D4—441no—
257D4—881no—
258D4—881no—
259D4—881no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—441no—
269C2×C4—881no—
270C2×C4—881no—
271C2×C4#6692511yescharacteristic
272C2×C4C4×D4411yescharacteristic
273C2×C4#6692811yescharacteristic
274C2×C4#6692911yescharacteristic
275C2×C4C4×C22⋊D1111yescharacteristic
276C2×C4#6698311yescharacteristic
277C2×C4#6698511yescharacteristic
278C2×C4C2×#432511yescharacteristic
279C2×C4#6700211yescharacteristic
280C2×C4#6700311yescharacteristic
281C8—42no—
282C8—42no—
283C8—442no—
284C8—881no—
285C8—881no—
286C22—21no—
287C22—21no—
288C22—881no—
289C22—881no—
290C22—881no—
291C22#1062255311yescharacteristic
292C22#1062258111yescharacteristic
293C22#1062261611yescharacteristic
294C4—24no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—42no—
299C4—881no—
300C4#1062231312yes—
301C4#1062262711yescharacteristic
302C4#1062262911yescharacteristic
303C4C4×#432511yescharacteristic
304C4#1062264011yescharacteristic
305C2—21no—
306C2—21no—
307C2—1761no—
308C2#1306924311yescharacteristic
309C2#1306928511yescharacteristic
310C2#1306932011yescharacteristic
subgroupG/H
centerC2×C4#66983
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊C8C2
socleC22×C11#388
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenterC4×C4⋊C8D11
hypocenterC11#9578
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13067386C2semidirect
5. #13066513C2semidirect
6. #13066449C2semidirect
7. C4×C11×C4⋊C8C2semidirect
19. #10622123C4semidirect
21. #10622120C4semidirect
96. C4×C4⋊C8D11semidirect
249. C11#9578semidirect

Maximal subgroups

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

subgroupindex
#130694442
#130673862
#130672662
#130670142
#130665132
#130664492
C4×C11×C4⋊C82
#957811