Finite Group Databasebeta

← #14652905

Subgroups — #14652905

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2C2×#10622176C212yesmaximal, complemented
3C2×#10622175C212yesmaximal
4C4×C11⋊#95C211yesmaximal, characteristic, complemented
5C11×#2850C211yesmaximal, characteristic
6C2×C11×#124C411yescharacteristic, complemented
7C2×C11×C22⋊Q8C2211yescharacteristic
8C2×C11×#121C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C22×C4×Dic11—21no—
11C11×#391C411yescharacteristic, complemented
12C11×#390C411yescharacteristic, complemented
13C11×#388—21no—
14C11×#388—21no—
15C11×#386—21no—
16C11×#386—21no—
17C11×#382C411yescharacteristic, complemented
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C4⋊(C11⋊C8)—21no—
22#10622176—24no—
23#10622175—24no—
24#10622162—21no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—22no—
32C11×#124—42no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—22no—
35C11×#121—22no—
36C11×#121—22no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—42no—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C4×Dic11—24no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11—42no—
54C22×C11⋊C8—22no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11⋊#95—24no—
60C11⋊#95—22no—
61C11⋊#95D414yes—
62C22⋊(C11⋊C8)—22no—
63C22⋊(C11⋊C8)—22no—
64C4⋊(C11⋊C8)—42no—
65#9713—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22×C411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11#4112yes—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—41no—
119C42×C11—41no—
120C4×Dic11—48no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—42no—
124#2850D1111yescharacteristic
125#1797—111no—
126C2×#328—112no—
127C2×#327—112no—
128C4×#95—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11#12112yes—
142C23×C11#13512yes—
143C23×C11AGL(1,ℤ/8)11yescharacteristic
144C23×C11#13711yescharacteristic
145Q8×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—82no—
149C2×C4×C11—24no—
150C2×C4×C11—24no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—44no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11#9912yes—
177C2×C4×C11#10412yes—
178C2×C4×C11#10412yes—
179C2×C4×C11C4×D412yes—
180C2×C4×C11#12411yescharacteristic
181C2×C4×C11#12711yescharacteristic
182C2×Dic11—28no—
183C2×Dic11—44no—
184C2×Dic11—44no—
185C2×Dic11—44no—
186C2×Dic11—44no—
187C2×Dic11—44no—
188C2×Dic11—44no—
189C11⋊C8—82no—
190C2×#124Dic1111yescharacteristic, complemented
191C2×C22⋊Q8C2×D1111yescharacteristic
192C2×#121C2×D1111yescharacteristic
193C22×C42—221no—
194C22×C42C2×D1111yescharacteristic
195C2×C4⋊C8—221no—
196C2×C22⋊C8—112no—
197#391Dic1111yescharacteristic, complemented
198#390Dic1111yescharacteristic, complemented
199#388—21no—
200#388—21no—
201#386—21no—
202#386—21no—
203#382Dic1111yescharacteristic, complemented
204C2×#95—112no—
205C2×#95—221no—
206#336—221no—
207#328—224no—
208#327—224no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11#39011yescharacteristic
225C22×C11C2×#9911yescharacteristic
226C22×C11#41011yescharacteristic
227C22×C11#41611yescharacteristic
228C22×C11#41711yescharacteristic
229C22×C11C2×#10411yescharacteristic
230C22×C11C2×#10411yescharacteristic
231C22×C11#46312yes—
232C22×C11#46412yes—
233C4×C11—22no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—41no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—81no—
243Dic11—48no—
244C22×Q8C2×Dic1111yescharacteristic
245C22×D4—21no—
246C22×D4C2×Dic1111yescharacteristic
247C23×C4—222no—
248C23×C4C22⋊D1111yescharacteristic
249C23×C4C22⋊D1111yescharacteristic
250C23×C4C22×D1111yescharacteristic
251C22×C8—222no—
252#124—42no—
253C22⋊Q8—22no—
254C22⋊Q8—22no—
255#121—22no—
256#121—22no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C2×Dic1111yescharacteristic
259C2×C4⋊C4C2×Dic1111yescharacteristic
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C42—42no—
267C2×C42—224no—
268C2×C42—442no—
269C2×C42—442no—
270C2×C42C2×Dic1111yescharacteristic
271C2×C42C2×Dic1111yescharacteristic
272C2×C42C22⋊D1111yescharacteristic
273C2×C42C22⋊D1111yescharacteristic
274C4⋊C8—442no—
275C22⋊C8—222no—
276C22⋊C8—222no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—114no—
282#95—224no—
283#95—222no—
284C2×C11—22no—
285C2×C11—22no—
286C2×C11—161no—
287C2×C11#150011yescharacteristic
288C2×C11#150111yescharacteristic
289C2×C11#150411yescharacteristic
290C2×C11#150911yescharacteristic
291C2×C11#196211yescharacteristic
292C2×C11#196411yescharacteristic
293C2×C11#198311yescharacteristic
294C24—21no—
295C24C2×C22⋊D1111yescharacteristic
296C2×Q8—22no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×D4—22no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—42no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—41no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—224no—
319C22×C4—224no—
320C22×C4—224no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4C22⋊Dic1111yescharacteristic
326C22×C4C22⋊Dic1111yescharacteristic
327C22×C4C22⋊Dic1111yescharacteristic
328C22×C4C22⋊Dic1111yescharacteristic
329C22×C4D4×D1112yes—
330C22×C4#434112yes—
331C22×C4C22×Dic1111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333C2×C8—442no—
334C2×C8—442no—
335C2×C8—442no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C42—22no—
348C42—22no—
349C42—41no—
350C42—41no—
351C42—448no—
352C11#971311yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23#6699112yes—
365C23#6700211yescharacteristic
366C23#6700312yes—
367C23#6700411yescharacteristic
368C23C2×C22⋊Dic1111yescharacteristic
369Q8—82no—
370D4—82no—
371D4—82no—
372D4—82no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—228no—
401C2×C4—444no—
402C2×C4—444no—
403C2×C4—444no—
404C2×C4—444no—
405C2×C4—444no—
406C2×C4—444no—
407C2×C4#6689812yes—
408C2×C4#6690112yes—
409C2×C4#6690112yes—
410C2×C4D4×Dic1112yes—
411C2×C4#6698911yescharacteristic
412C2×C4#6699311yescharacteristic
413C8—882no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—22no—
421C22—22no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22#1062266712yes—
430C22#1062267012yes—
431C22C2×#6689811yescharacteristic
432C22#1062283411yescharacteristic
433C22#1062284511yescharacteristic
434C22#1062284611yescharacteristic
435C22C2×#6690111yescharacteristic
436C22C2×#6690111yescharacteristic
437C22#1062285311yescharacteristic
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—41no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—448no—
449C2—22no—
450C2—22no—
451C2—161no—
452C2#1306710211yescharacteristic
453C2#1306710711yescharacteristic
454C2#1306712011yescharacteristic
455C2#1306714111yescharacteristic
456C2#1306944511yescharacteristic
457C2#1306945311yescharacteristic
458C2#1306954911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2850C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2850D11
hypocenterC11#9713
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. C2×#10622176C2semidirect
4. C4×C11⋊#95C2semidirect
6. C2×C11×#124C4semidirect
11. C11×#391C4semidirect
12. C11×#390C4semidirect
17. C11×#382C4semidirect
190. C2×#124Dic11semidirect
197. #391Dic11semidirect
198. #390Dic11semidirect
203. #382Dic11semidirect
352. C11#9713semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221762
C2×#106221752
C4×C11⋊#952
C11×#28502
#971311