Finite Group Databasebeta

← #14653940

Subgroups — #14653940

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076966C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic
3#95×Dic11C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×C4×Dic11—21no—
9C22×C4×Dic11C2211yescharacteristic
10C2×#66941C411yescharacteristic, complemented
11C2×#66931—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×Dic11⋊C8—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—24no—
46C2×C4×Dic11—42no—
47C2×C4×Dic11—42no—
48C2×C4×Dic11—42no—
49C2×C4×Dic11C2×C411yescharacteristic
50C2×C4×Dic11C2×C411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C2×C4×Dic11D411yescharacteristic
53C22×C11⋊C8—21no—
54#66941—42no—
55#66931—42no—
56#66931—42no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95Q812yescomplemented
62C11⋊#95—24no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95Q812yescomplemented
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70Dic11⋊C8—42no—
71#9908—111nomaximal, Sylow
72C24×C11C2×D411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×Q811yescharacteristic
87C22×C4×C11C2×Q811yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—21no—
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
109C22×Dic11SD1612yes—
110C22×Dic11Q1612yes—
111C2×Dic22—42no—
112C2×Dic22—42no—
113C2×Dic22—42no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—41no—
120C11×C22⋊C4—41no—
121C22⋊Dic11—41no—
122C22⋊Dic11—41no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125C4⋊Dic11—42no—
126Dic11⋊C4—42no—
127Dic11⋊C4—42no—
128Dic11⋊C4—42no—
129Dic11⋊C4—42no—
130C4×Dic11—22no—
131C4×Dic11—22no—
132C4×Dic11—41no—
133C4×Dic11—41no—
134C4×Dic11—48no—
135C2×C11⋊C8—41no—
136C2×C11⋊C8—41no—
137C2×C11⋊C8—41no—
138#2857—111no—
139#1797—111no—
140C4×#95—111no—
141#1294—111no—
142#1294—111no—
143#1294—111no—
144#1294D1111yescharacteristic
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11C2×C22⋊C411yescharacteristic
150C23×C11C22⋊Q811yescharacteristic
151C23×C11C22⋊Q811yescharacteristic
152C23×C11C2×SD1611yescharacteristic
153C23×C11C2×Q1611yescharacteristic
154C23×C11AGL(1,ℤ/8)11yescharacteristic
155C23×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—24no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11C4×Q811yescharacteristic
178C2×C4×C11C4×Q811yescharacteristic
179C2×C4×C11#12411yescharacteristic
180C2×C4×C11C4⋊Q811yescharacteristic
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11#9912yes—
206C2×Dic11#10312yes—
207C2×Dic11#10312yes—
208C2×Dic11#10412yes—
209C2×Dic11#10412yes—
210Dic22—84no—
211C8×C11—81no—
212C11⋊C8—81no—
213C2×C4⋊Q8—111no—
214C2×C22⋊Q8—221no—
215C22×C42—111no—
216C22×C42—221no—
217C2×C4⋊C8—221no—
218C2×C22⋊C8—111no—
219C2×C22⋊C8C2×D1111yescharacteristic
220#391—221no—
221#389—111no—
222#389—111no—
223#389—221no—
224#384—111no—
225#380—111no—
226#380—221no—
227#380C2×D1111yescharacteristic
228C2×#95—111no—
229C2×#95—221no—
230C2×#95C2×D1111yescharacteristic
231#336—221no—
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—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11#39111yescharacteristic
245C22×C11C2×#9911yescharacteristic
246C22×C11#41011yescharacteristic
247C22×C11C2×#10311yescharacteristic
248C22×C11#41811yescharacteristic
249C22×C11C2×#10411yescharacteristic
250C22×C11C2×#10411yescharacteristic
251C22×C11#47611yescharacteristic
252C22×C11#47611yescharacteristic
253C22×C11#47711yescharacteristic
254C22×C11#47711yescharacteristic
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—44no—
260C4×C11—81no—
261C4×C11—81no—
262Dic11—22no—
263Dic11—22no—
264Dic11—44no—
265Dic11—41no—
266Dic11—81no—
267Dic11—81no—
268Dic11#32814yes—
269C22×Q8—221no—
270C23×C4—21no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C22×C8—21no—
276C22×C8—221no—
277C4⋊Q8—442no—
278C22⋊Q8—442no—
279C22⋊Q8—442no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4C4×D1111yescharacteristic
288C2×C4⋊C4C4×D1111yescharacteristic
289C2×C22⋊C4—21no—
290C2×C22⋊C4—221no—
291C2×C42—111no—
292C2×C42—111no—
293C2×C42—111no—
294C2×C42—111no—
295C2×C42—224no—
296C2×C42—442no—
297C2×C42—442no—
298C2×C42—442no—
299C4⋊C8—442no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8—221no—
303C22⋊C8—221no—
304#95—21no—
305#95—21no—
306#95—112no—
307#95—221no—
308#95—221no—
309#95—224no—
310#95—221no—
311#95—221no—
312#95Dic2212yescomplemented
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11C2×#32811yescharacteristic
318C2×C11#150311yescharacteristic
319C2×C11#150511yescharacteristic
320C2×C11#150711yescharacteristic
321C2×C11#198711yescharacteristic
322C2×C11#199411yescharacteristic
323C2×C11#199611yescharacteristic
324C24D4×D1111yescharacteristic
325C2×Q8—442no—
326C2×Q8—442no—
327C2×Q8—442no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—111no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4C2×Dic2211yescharacteristic
361C22×C4C2×C4×D1111yescharacteristic
362C22×C4#433911yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4#434111yescharacteristic
365C22×C4Q8×D1111yescharacteristic
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—41no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4—442no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4—442no—
380C4⋊C4—442no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—441no—
384C22⋊C4—441no—
385C42—222no—
386C42—222no—
387C42—441no—
388C42—441no—
389C42—448no—
390C11#990811yescharacteristic, complemented, Sylow
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23#6693111yescharacteristic
396C23C22⋊C4×D1111yescharacteristic
397C23#6694911yescharacteristic
398C23#6696411yescharacteristic
399C23SD16×D1111yescharacteristic
400C23#6696711yescharacteristic
401C23Q16×D1111yescharacteristic
402Q8—884no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—24no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—112no—
425C2×C4—112no—
426C2×C4—112no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—224no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4C4×Dic2211yescharacteristic
454C2×C4#6693811yescharacteristic
455C2×C4#6694011yescharacteristic
456C2×C4#6694111yescharacteristic
457C8—81no—
458C8—881no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22#1062225911yescharacteristic
472C22#1062235311yescharacteristic
473C22D11×#9911yescharacteristic
474C22#1062237411yescharacteristic
475C22#1062238311yescharacteristic
476C22#1062240711yescharacteristic
477C22D11×#10311yescharacteristic
478C22D11×#10411yescharacteristic
479C22D11×#10411yescharacteristic
480C22#1062248311yescharacteristic
481C22#1062248811yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—44no—
487C4—81no—
488C4—81no—
489C4—114no—
490C4—222no—
491C4—222no—
492C4—444no—
493C4—441no—
494C4—881no—
495C4—881no—
496C2—21no—
497C2—21no—
498C2—21no—
499C2—21no—
500C2D11×#32811yescharacteristic
501C2#1306711311yescharacteristic
502C2#1306712211yescharacteristic
503C2#1306713011yescharacteristic
504C2#1306956211yescharacteristic
505C2#1306959111yescharacteristic
506C2#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#9908
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
10. C2×#66941C4semidirect
20. #10622598C4semidirect
21. #10622589C4semidirect
22. #10622586C4semidirect
61. C11×#95Q8semidirect
67. C11⋊#95Q8semidirect
312. #95Dic22semidirect
390. C11#9908semidirect

Maximal subgroups

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

subgroupindex
#130769662
#130685942
#95×Dic112
#130664962
#130664952
#130664942
C11×#12942
#990811