Finite Group Databasebeta

← #14653858

Subgroups — #14653858

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076966C211yesmaximal, characteristic
2#13068380C211yesmaximal, characteristic
3#13066842C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×C4×Dic11C2211yescharacteristic
9C2×#66941C411yescharacteristic, complemented
10C2×#66931—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×#66879—21no—
20#10622598C411yescharacteristic, complemented
21#10622589C411yescharacteristic, complemented
22#10622586C411yescharacteristic, complemented
23#10622555—21no—
24#10622260—21no—
25#10622259—21no—
26#10622188—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×Dic22—21no—
33C22×C8×C11—21no—
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×C4×Dic11—42no—
46C2×C4×Dic11C2×C411yescharacteristic
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C22×C11⋊C8—21no—
51#66941—42no—
52#66931—42no—
53#66931—42no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8Q812yescomplemented
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11⋊#95—24no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—42no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)Q812yescomplemented
68#66879—42no—
69#9889—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C22×C4×C11—22no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×Q811yescharacteristic
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C22×Dic11—41no—
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C22×Dic11C22⋊C411yescharacteristic
108C22×Dic11C22⋊C411yescharacteristic
109C2×Dic22—42no—
110C2×Dic22—42no—
111C2×Dic22—42no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C22⋊Dic11—41no—
120C22⋊Dic11—41no—
121C4⋊Dic11—41no—
122C4⋊Dic11—41no—
123C4⋊Dic11—42no—
124Dic11⋊C4—42no—
125Dic11⋊C4—42no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128C4×Dic11—22no—
129C4×Dic11—22no—
130C4×Dic11—41no—
131C4×Dic11—41no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—41no—
134C2×C11⋊C8—41no—
135#2857—111no—
136#1749—111no—
137#1434—111no—
138#1294—111no—
139#1294—111no—
140#1294—111no—
141#1294D1111yescharacteristic
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11#12411yescharacteristic
148C23×C11C4⋊Q811yescharacteristic
149C23×C11AGL(1,ℤ/8)11yescharacteristic
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C23×C11#13711yescharacteristic
152C23×C11#13711yescharacteristic
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—81no—
171C2×C4×C11—81no—
172C2×C4×C11—81no—
173C2×C4×C11—81no—
174C2×C4×C11C4×Q811yescharacteristic
175C2×C4×C11C4×Q811yescharacteristic
176C2×C4×C11C22⋊Q811yescharacteristic
177C2×C4×C11C22⋊Q811yescharacteristic
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203C2×Dic11—81no—
204C2×Dic11—81no—
205C2×Dic11#9912yes—
206C2×Dic11#10412yes—
207Dic22—84no—
208C8×C11—42no—
209C11⋊C8—42no—
210C2×C4⋊Q8—111no—
211C2×C22⋊Q8—221no—
212C22×C42—111no—
213C2×C22⋊C8—111no—
214C2×C22⋊C8C2×D1111yescharacteristic
215C2×#97—221no—
216#391—221no—
217#389—111no—
218#389—111no—
219#389—221no—
220#384—111no—
221#380—111no—
222#380—221no—
223#380C2×D1111yescharacteristic
224C2×#95—111no—
225C2×#95—221no—
226C2×#95—221no—
227C2×#95C2×D1111yescharacteristic
228#336—221no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11#39111yescharacteristic
242C22×C11C2×#9911yescharacteristic
243C22×C11#41011yescharacteristic
244C22×C11#41811yescharacteristic
245C22×C11#41911yescharacteristic
246C22×C11C2×#10411yescharacteristic
247C22×C11#42111yescharacteristic
248C22×C11#48911yescharacteristic
249C22×C11#48911yescharacteristic
250C22×C11#50111yescharacteristic
251C22×C11#50111yescharacteristic
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—82no—
257C4×C11—81no—
258C4×C11—81no—
259Dic11—22no—
260Dic11—22no—
261Dic11—41no—
262Dic11—41no—
263Dic11—82no—
264Dic11—81no—
265Dic11—81no—
266C22×Q8—221no—
267C23×C4—21no—
268C23×C4—111no—
269C23×C4—111no—
270C23×C4—221no—
271C23×C4C22×D1111yescharacteristic
272C22×C8—21no—
273C22×C8—221no—
274C4⋊Q8—442no—
275C22⋊Q8—442no—
276C22⋊Q8—442no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4C4×D1111yescharacteristic
285C2×C4⋊C4C4×D1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—221no—
288C2×C42—111no—
289C2×C42—111no—
290C2×C42—111no—
291C2×C42—111no—
292C2×C42—442no—
293C22⋊C8—21no—
294C22⋊C8—112no—
295C22⋊C8—221no—
296C22⋊C8Dic2212yescomplemented
297#97—442no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—221no—
302#95—221no—
303#95—224no—
304#95—221no—
305#95—221no—
306#95—221no—
307#95—442no—
308C2×C11—21no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11#150511yescharacteristic
313C2×C11#150811yescharacteristic
314C2×C11#151011yescharacteristic
315C2×C11#151511yescharacteristic
316C2×C11#198611yescharacteristic
317C2×C11#199311yescharacteristic
318C2×C11#199611yescharacteristic
319C24D4×D1111yescharacteristic
320C2×Q8—442no—
321C2×Q8—442no—
322C2×Q8—442no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—111no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—111no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—222no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—441no—
348C22×C4—441no—
349C22×C4—441no—
350C22×C4—441no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4—441no—
354C22×C4—441no—
355C22×C4C2×Dic2211yescharacteristic
356C22×C4C2×C4×D1111yescharacteristic
357C22×C4#433911yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4#434111yescharacteristic
360C22×C4Q8×D1111yescharacteristic
361C2×C8—22no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—222no—
365C2×C8—441no—
366C2×C8—441no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4—442no—
375C4⋊C4—442no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42—222no—
381C42—222no—
382C42—441no—
383C42—441no—
384C11#988911yescharacteristic, complemented, Sylow
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23C22⋊C4×D1111yescharacteristic
390C23#6693811yescharacteristic
391C23#6694111yescharacteristic
392C23#6696411yescharacteristic
393C23#6696711yescharacteristic
394C23#6696811yescharacteristic
395C23#6697111yescharacteristic
396Q8—884no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—112no—
419C2×C4—112no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—881no—
444C2×C4—881no—
445C2×C4—881no—
446C2×C4—881no—
447C2×C4C4×Dic2211yescharacteristic
448C2×C4#6693111yescharacteristic
449C2×C4#6694011yescharacteristic
450C2×C4#6694911yescharacteristic
451C8—42no—
452C8—442no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22#1062225911yescharacteristic
466C22#1062235311yescharacteristic
467C22D11×#9911yescharacteristic
468C22#1062237811yescharacteristic
469C22#1062238311yescharacteristic
470C22#1062240811yescharacteristic
471C22#1062241511yescharacteristic
472C22D11×#10411yescharacteristic
473C22#1062243411yescharacteristic
474C22#1062246911yescharacteristic
475C22#1062248911yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—82no—
481C4—81no—
482C4—81no—
483C4—222no—
484C4—222no—
485C4—441no—
486C4—441no—
487C4—882no—
488C4—881no—
489C4—881no—
490C2—21no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2#1306712211yescharacteristic
495C2#1306713411yescharacteristic
496C2#1306714311yescharacteristic
497C2#1306716511yescharacteristic
498C2#1306955811yescharacteristic
499C2#1306958711yescharacteristic
500C2#1306959911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9889
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
9. C2×#66941C4semidirect
20. #10622598C4semidirect
21. #10622589C4semidirect
22. #10622586C4semidirect
55. C11×C22⋊C8Q8semidirect
67. C22⋊(C11⋊C8)Q8semidirect
296. C22⋊C8Dic22semidirect
384. C11#9889semidirect

Maximal subgroups

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

subgroupindex
#130769662
#130683802
#130668422
#130664962
#130664952
#130664942
C11×#12942
#988911