Finite Group Databasebeta

← #14648095

Subgroups — #14648095

Order 2816.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077284C211yesmaximal, characteristic
2#13068637C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic, complemented
4#13067371C211yesmaximal, characteristic, complemented
5#13066996C211yesmaximal, characteristic
6#13066457C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C4×#4339C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12#10622742—21no—
13#10622735—21no—
14C2×#66869—21no—
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18#10622453—22no—
19#10622448—21no—
20#10622446—21no—
21#10622161—21no—
22#10622122C411yescharacteristic, complemented
23#10622122C411yescharacteristic, complemented
24#10622121C411yescharacteristic, complemented
25#10622121C411yescharacteristic, complemented
26#10622118—22no—
27#10622096—21no—
28#10622096—21no—
29C2×#4339D411yescharacteristic
30C2×C11×M16—21no—
31C2×C11×C4⋊C4—21no—
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C4×C22⋊D11—21no—
35C4×C22⋊D11—21no—
36#66979D411yescharacteristic
37C2×#4318—21no—
38C22×C11⋊C8—21no—
39C22×C11⋊C8—21no—
40C4×D44C2×C411yescharacteristic
41C4×D44Q811yescharacteristic
42#66925—21no—
43C42×D11—21no—
44C4×Dic22C2×C411yescharacteristic
45C4×Dic22Q811yescharacteristic
46C11×C4⋊C8—21no—
47C11×C4⋊C8C2×C411yescharacteristic
48C11×C4⋊C8C2×C411yescharacteristic
49C11×C4⋊C8D412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52C11×#95—21no—
53(C2×D11)⋊C8—22no—
54(C2×D11)⋊C8—22no—
55#66879—22no—
56C8×Dic11—22no—
57#66869—42no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D411yescharacteristic
62C4⋊(C11⋊C8)D411yescharacteristic
63C4×C11⋊C8—21no—
64C4×C11⋊C8C2×C411yescharacteristic
65C4×C11⋊C8C2×C411yescharacteristic
66#8905—111nomaximal, Sylow
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C2×C22⋊D11—21no—
72#4339—21no—
73#4339—21no—
74#4339—21no—
75#4339—21no—
76C2×D44C4⋊C411yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×Dic22C4⋊C411yescharacteristic
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—41no—
88C42×C11—41no—
89C42×C11—41no—
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×Q811yescharacteristic
94C22⋊Dic11—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11C4⋊C411yescharacteristic
98C4⋊Dic11C4⋊C411yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2925—111no—
115#1806—111no—
116#1571—111no—
117#1566—111no—
118#1476—111no—
119#1303D1111yescharacteristic, complemented
120#1279—111no—
121C23×C11#12311yescharacteristic
122C22×D11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C2×C4⋊C411yescharacteristic
130C2×C4×C11C4×D411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11C22⋊Q811yescharacteristic
134C2×C4×C11C22⋊Q811yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C22⋊D11—41no—
140C22⋊D11—41no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144D44—21no—
145D44—21no—
146C4×D11—41no—
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—41no—
150C4×D11—81no—
151Dic22—21no—
152Dic22—21no—
153C8×C11—41no—
154C8×C11—41no—
155C8×C11—42no—
156C11⋊C8—22no—
157C11⋊C8—41no—
158C11⋊C8—41no—
159C11⋊C8—41no—
160C11⋊C8—81no—
161C4×#41—111no—
162#433—222no—
163#432—221no—
164#431—221no—
165#431C2×D1111yescharacteristic
166#423—111no—
167#423C2×D1111yescharacteristic
168C2×C4⋊C8—111no—
169C2×#104—221no—
170#408—221no—
171#405—221no—
172C2×C4×C8—111no—
173C4×C4⋊C4C2×D1111yescharacteristic
174#339—221no—
175#335—221no—
176#335—221no—
177#334—222no—
178Q8⋊C8—111no—
179Q8⋊C8—111no—
180D4⋊C8—111no—
181D4⋊C8—111no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11#38511yescharacteristic
185C22×C11#48211yescharacteristic
186C22×C11#48511yescharacteristic
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—82no—
194C4×C11#42711yescharacteristic
195C4×C11#42811yescharacteristic
196C4×C11#44311yescharacteristic
197C4×C11#44411yescharacteristic
198C4×C11#44911yescharacteristic
199C4×C11#45211yescharacteristic
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203C2×#41—111no—
204C2×M16—21no—
205C2×M16—221no—
206C22×C8—221no—
207C22×C8—221no—
208C4×Q8—111no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213C4×D4—221no—
214#117—111no—
215#117—221no—
216C2×C4⋊C4—21no—
217C2×C42—21no—
218C2×C42—221no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—111no—
222C4⋊C8—111no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C4⋊C8C4×D1111yescharacteristic
227C4⋊C8C4×D1111yescharacteristic
228C4⋊C8D4412yes—
229#104—442no—
230C22⋊C8—21no—
231C22⋊C8—222no—
232C22⋊C8—222no—
233#97—222no—
234C4×C8—21no—
235C4×C8—111no—
236C4×C8—111no—
237C4×C8—222no—
238C4×C8—221no—
239#95—21no—
240C2×C11—21no—
241C2×C11—21no—
242C2×C11#185411yescharacteristic
243C2×C11#186111yescharacteristic
244C2×C11#186611yescharacteristic
245D11—81no—
246#41—221no—
247#41—221no—
248#41—221no—
249#41—221no—
250C2×Q8—111no—
251C2×D4—111no—
252C2×D4—221no—
253C22×C4—41no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4#433911yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4#434111yescharacteristic
260M16—41no—
261M16—41no—
262M16—441no—
263M16—441no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—22no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—442no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—111no—
278C4⋊C4—111no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C42—41no—
285C42—41no—
286C42—221no—
287C42—221no—
288C42—221no—
289C42C2×C4×D1111yescharacteristic
290C42C2×D4411yescharacteristic
291C42D4×D1111yescharacteristic
292C42Q8×D1111yescharacteristic
293C11#890511yescharacteristic, complemented, Sylow
294C23—221no—
295C23#6693611yescharacteristic
296Q8—221no—
297Q8—221no—
298D4—221no—
299D4—221no—
300D4—441no—
301D4—441no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—881no—
316C2×C4C4×D4411yescharacteristic
317C2×C4(C22⋊D11)⋊C411yescharacteristic
318C2×C4#6693511yescharacteristic
319C2×C4C4⋊C4×D1111yescharacteristic
320C2×C4#6694911yescharacteristic
321C2×C4#6695011yescharacteristic
322C2×C4#6696511yescharacteristic
323C2×C4#6696711yescharacteristic
324C2×C4#6696811yescharacteristic
325C2×C4#6697211yescharacteristic
326C8—42no—
327C8—41no—
328C8—41no—
329C8—222no—
330C8—441no—
331C8—441no—
332C8—441no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—441no—
337C22—441no—
338C22—441no—
339C22#1062228111yescharacteristic
340C22#1062239711yescharacteristic
341C22#1062242711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—82no—
346C4—441no—
347C4—441no—
348C4—441no—
349C4#1062239611yescharacteristic
350C4#1062242411yescharacteristic
351C4#1062243611yescharacteristic
352C4#1062243711yescharacteristic
353C4#1062247411yescharacteristic
354C4#1062249311yescharacteristic
355C2—21no—
356C2—21no—
357C2—881no—
358C2#1306881811yescharacteristic
359C2#1306885911yescharacteristic
360C2#1306889211yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#385
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#8905
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
3. #13067391C2semidirect
4. #13067371C2semidirect
6. #13066457C2semidirect
7. C11×#1303C2semidirect
22. #10622122C4semidirect
23. #10622122C4semidirect
24. #10622121C4semidirect
25. #10622121C4semidirect
119. #1303D11semidirect
293. C11#8905semidirect

Maximal subgroups

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

subgroupindex
#130772842
#130686372
#130673912
#130673712
#130669962
#130664572
C11×#13032
#890511