Finite Group Databasebeta

← #14643535

Subgroups — #14643535

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#432C211yesmaximal, characteristic
2D11×#432C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13066473C211yesmaximal, characteristic, complemented
5#13066472C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1285C211yesmaximal, characteristic, complemented
8C2×#66925C412yes—
9C2×C42×D11C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622600—21no—
14#10622589—21no—
15C4×C4⋊Dic11C2211yescharacteristic
16C4×Dic11⋊C4C412yes—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622448—21no—
20#10622448C412yescomplemented
21D11×C4⋊C8—21no—
22D11×C4⋊C8C412yescomplemented
23D11×C22⋊C8—21no—
24D11×C22⋊C8—21no—
25#10622332—21no—
26#10622332—21no—
27#10622318—21no—
28#10622318C412yescomplemented
29D11×#97—21no—
30D11×#97C412yescomplemented
31#10622280—21no—
32#10622263—21no—
33C22×C4×D11C2×C411yescharacteristic
34C22×C4×D11D411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—22no—
42C2×Dic11⋊C4—22no—
43C2×C4×Dic11C2×C412yes—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C8×D11—22no—
48C2×C8×D11—22no—
49#66925—44no—
50C42×D11C2×C411yescharacteristic
51C42×D11C2×C411yescharacteristic
52C42×D11C2×C411yescharacteristic
53C42×D11C2×C411yescharacteristic
54C42×D11D411yescharacteristic
55C42×D11D411yescharacteristic
56C42×D11Q811yescharacteristic
57C42×D11Q811yescharacteristic
58C11×C4⋊C8—21no—
59C11×C4⋊C8C2×C412yes—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63C11×#97C2×C412yes—
64C11×#95—21no—
65C11⋊#95—21no—
66C11⋊#95—22no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69(C2×D11)⋊C8—22no—
70(C2×D11)⋊C8—22no—
71#66879—22no—
72#66879—22no—
73Dic11⋊C8—22no—
74Dic11⋊C8—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)C2×C412yes—
77#66867—21no—
78#66867C2×C412yes—
79#7952—111nomaximal, Sylow
80C23×D11C22⋊C411yescharacteristic
81C22×C4×C11—22no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—22no—
86C22×Dic11C22⋊C411yescharacteristic
87C22×Dic11C22⋊C411yescharacteristic
88C22×Dic11C22⋊C411yescharacteristic
89C2×C4×D11—22no—
90C2×C4×D11—22no—
91C2×C4×D11—42no—
92C2×C4×D11—42no—
93C2×C4×D11C4211yescharacteristic
94C2×C4×D11C4211yescharacteristic
95C2×C4×D11C22⋊C411yescharacteristic
96C2×C4×D11C22⋊C411yescharacteristic
97C2×C4×D11C22⋊C411yescharacteristic
98C2×C4×D11C22⋊C411yescharacteristic
99C2×C4×D11C4⋊C411yescharacteristic
100C2×C4×D11C4⋊C411yescharacteristic
101C2×C4×D11C4⋊C411yescharacteristic
102C2×C4×D11C4⋊C411yescharacteristic
103C2×C4×D11C4⋊C411yescharacteristic
104C2×C4×D11C4⋊C411yescharacteristic
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C11×C4⋊C4—42no—
108C42×C11—42no—
109C42×C11C22×C411yescharacteristic
110C42×C11C22×C411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×Q811yescharacteristic
113(C2×D11)⋊C4—44no—
114C4⋊Dic11—42no—
115Dic11⋊C4—44no—
116Dic11⋊C4—44no—
117C4×Dic11—42no—
118C4×Dic11C4211yescharacteristic
119C4×Dic11C4211yescharacteristic
120C4×Dic11C22⋊C411yescharacteristic
121C4×Dic11C22⋊C411yescharacteristic
122C4×Dic11C22⋊C411yescharacteristic
123C4×Dic11C22⋊C411yescharacteristic
124C4×Dic11C4⋊C411yescharacteristic
125C4×Dic11C4⋊C411yescharacteristic
126C4×Dic11C4⋊C411yescharacteristic
127C4×Dic11C4⋊C411yescharacteristic
128C4×Dic11C4⋊C411yescharacteristic
129C4×Dic11C4⋊C411yescharacteristic
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C8×D11—44no—
133C8×D11—44no—
134C2×#432—111no—
135C2×#432—111no—
136#2285—111no—
137#1285—111no—
138#1285—111no—
139#1285—111no—
140#1285D1111yescharacteristic, complemented
141C23×C11C2×C22⋊C411yescharacteristic
142C22×D11—41no—
143C22×D11—41no—
144C22×D11#9511yescharacteristic
145C22×D11#9511yescharacteristic
146C22×D11#10012yes—
147C22×D11#10112yes—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C2×C4211yescharacteristic
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C2×C4⋊C411yescharacteristic
159C2×C4×C11C2×C4⋊C411yescharacteristic
160C2×C4×C11C2×C4⋊C411yescharacteristic
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—22no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11#9511yescharacteristic
169C2×Dic11#9511yescharacteristic
170C2×Dic11#9511yescharacteristic
171C2×Dic11#9511yescharacteristic
172C2×Dic11#9511yescharacteristic
173C2×Dic11#9511yescharacteristic
174C4×D11—22no—
175C4×D11—22no—
176C4×D11—22no—
177C4×D11—22no—
178C4×D11—22no—
179C4×D11—22no—
180C4×D11—22no—
181C4×D11—22no—
182C4×D11—41no—
183C4×D11—41no—
184C4×D11—41no—
185C4×D11—41no—
186C8×C11—42no—
187C8×C11—42no—
188C11⋊C8—42no—
189C11⋊C8—42no—
190C2×#117—112no—
191C22×C42—111no—
192#432—111no—
193#432—112no—
194#432—111no—
195#432—112no—
196#432—221no—
197#432—221no—
198#432—221no—
199#432—221no—
200#432C2×D1111yescharacteristic
201#432C2×D1111yescharacteristic
202C2×C4⋊C8—112no—
203C2×C4⋊C8—221no—
204C2×C22⋊C8—221no—
205C2×C22⋊C8—221no—
206C2×#97—112no—
207C2×#97—221no—
208#384—221no—
209#382—221no—
210#380—221no—
211#380—221no—
212C4×C4⋊C4—111no—
213C4×C4⋊C4—112no—
214C4×C4⋊C4C2×D1111yescharacteristic
215C22×C11—21no—
216C22×C11—21no—
217C22×C11C2×#9511yescharacteristic
218C22×C11C2×#10011yescharacteristic
219C22×C11C2×#10111yescharacteristic
220C2×D11—21no—
221C2×D11—21no—
222C2×D11—21no—
223C2×D11—21no—
224C2×D11—42no—
225C2×D11—42no—
226C2×D11#34312yes—
227C2×D11#34312yes—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—82no—
234C4×C11#42112yes—
235Dic11—21no—
236Dic11—21no—
237Dic11—21no—
238Dic11—21no—
239Dic11—21no—
240Dic11—82no—
241Dic11H(3,ℤ/4)12yes—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—111no—
245C22×C8—222no—
246C22×C8—222no—
247#117—444no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—222no—
250C2×C4⋊C4—222no—
251C2×C4⋊C4—221no—
252C2×C22⋊C4—222no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—111no—
256C2×C42—111no—
257C2×C42—111no—
258C2×C42—111no—
259C2×C42—111no—
260C2×C42—111no—
261C2×C42—111no—
262C2×C42—111no—
263C2×C42—111no—
264C2×C42—112no—
265C2×C42C4×D1112yes—
266C2×C42C22×D1111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—112no—
269C4⋊C8—222no—
270C4⋊C8—222no—
271C4⋊C8—221no—
272C4⋊C8C4×D1112yes—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—222no—
276C22⋊C8—222no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279#97—21no—
280#97—112no—
281#97—222no—
282#97—222no—
283#97—221no—
284#97C4×D1112yes—
285#95—21no—
286#95—222no—
287#95—221no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11C2×H(3,ℤ/4)11yescharacteristic
291C2×C11#173311yescharacteristic
292C2×C11C2×#34311yescharacteristic
293D11—22no—
294D11—22no—
295C24—111no—
296C22×C4—22no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—111no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4C2×C4×D1111yescharacteristic
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—444no—
325C2×C8—444no—
326C4⋊C4—42no—
327C4⋊C4—442no—
328C4⋊C4—444no—
329C4⋊C4—444no—
330C22⋊C4—444no—
331C42—42no—
332C42—111no—
333C42—111no—
334C42—111no—
335C42—111no—
336C42—111no—
337C42—111no—
338C42—111no—
339C42—111no—
340C42—111no—
341C42—111no—
342C42—111no—
343C42—111no—
344C42—442no—
345C42C2×C4×D1111yescharacteristic
346C42C2×C4×D1111yescharacteristic
347C42D4×D1111yescharacteristic
348C42Q8×D1111yescharacteristic
349C11#795211yescharacteristic, complemented, Sylow
350C23—111no—
351C23—111no—
352C23—112no—
353C23—112no—
354C23—441no—
355C23—441no—
356C23C22⋊C4×D1111yescharacteristic
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—111no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—111no—
368C2×C4—111no—
369C2×C4—111no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4C42×D1111yescharacteristic
390C2×C4C22⋊C4×D1111yescharacteristic
391C2×C4C22⋊C4×D1111yescharacteristic
392C2×C4C4⋊C4×D1111yescharacteristic
393C2×C4C4⋊C4×D1111yescharacteristic
394C2×C4C4⋊C4×D1111yescharacteristic
395C8—42no—
396C8—42no—
397C8—442no—
398C8—442no—
399C22—21no—
400C22—21no—
401C22—112no—
402C22—112no—
403C22—221no—
404C22—221no—
405C22—221no—
406C22—221no—
407C22—442no—
408C22—442no—
409C22D11×#9511yescharacteristic
410C22D11×#10011yescharacteristic
411C22D11×#10111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—82no—
418C4—112no—
419C4—221no—
420C4—221no—
421C4—221no—
422C4—221no—
423C4—221no—
424C4—882no—
425C4#1062243412yes—
426C2—21no—
427C2—21no—
428C2—222no—
429C2—222no—
430C2D11×H(3,ℤ/4)11yescharacteristic
431C2#1306832411yescharacteristic
432C2D11×#34311yescharacteristic
subgroupG/H
centerC22D11×#95
commutatorC2×C4×C11C2×C42
FrattiniC2×C42C22×D11
FittingC11×#1285C2
socleC22×C11C2×#95
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1285D11
hypocenterC11#7952
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
4. #13066473C2semidirect
5. #13066472C2semidirect
6. #13066471C2semidirect
7. C11×#1285C2semidirect
20. #10622448C4semidirect
22. D11×C4⋊C8C4semidirect
28. #10622318C4semidirect
30. D11×#97C4semidirect
140. #1285D11semidirect
349. C11#7952semidirect

Maximal subgroups

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

subgroupindex
D11×#4322
#130710202
#130664732
#130664722
#130664712
C11×#12852
#795211