Finite Group Databasebeta

← #14803658

Subgroups — #14803658

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic
2C2×#10622461C211yesmaximal, characteristic
3#13073824C211yesmaximal, characteristic, complemented
4#13071680C211yesmaximal, characteristic
5#13070021C212yesmaximal, complemented
6#13069934C212yesmaximal, complemented
7#13069563C211yesmaximal, characteristic, complemented
8#13068949C212yesmaximal, complemented
9#13068617C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C2×#66946—21no—
14C2×#66927C2211yescharacteristic
15C2×C4×D44C2212yes—
16C2×#66922C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×#66880C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27#10622601—21no—
28#10622598—21no—
29#10622598—21no—
30#10622552C2212yes—
31#10622548C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622542C2212yes—
34#10622461—24no—
35#10622307—24no—
36#10622278—22no—
37#10622269—22no—
38C11×#336C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C22×Dic22—21no—
48C22×Dic22C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11C2312yes—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C2×#4314—24no—
70C2×#4314—24no—
71C2×#4314—42no—
72#66946—44no—
73#66927—22no—
74#66927D414yes—
75C4×D44—24no—
76C4×D44—42no—
77#66922—22no—
78#66922—22no—
79C4×Dic22—22no—
80C4×Dic22—22no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—42no—
83C4×C8×C11—22no—
84C11×#95D412yes—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—21no—
88#66885—24no—
89#66885—24no—
90#66885—24no—
91#66880—22no—
92#66880—22no—
93#25322—111nomaximal, Sylow
94C23×D11—22no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C2×D44—24no—
106C2×D44—24no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—42no—
113C2×D44—42no—
114C2×D44—81no—
115C2×D44—81no—
116C2×D44C2×D414yes—
117C2×C4×D11—44no—
118C2×C4×D11—44no—
119C2×C4×D11—82no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22—21no—
124C2×Dic22—21no—
125C2×Dic22—42no—
126C2×Dic22—81no—
127C2×Dic22—81no—
128C2×Dic22#4112yes—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4SD1614yescomplemented
140C42×C11—22no—
141C42×C11—22no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144(C2×D11)⋊C4—44no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—82no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—42no—
155C4⋊Dic11—82no—
156C4⋊Dic11—82no—
157C4⋊Dic11#4112yes—
158Dic11⋊C4—42no—
159C4×Dic11—42no—
160C4×Dic11—42no—
161#4314—48no—
162C2×#486—111no—
163C2×#460—111no—
164#2567—111no—
165#2366—111no—
166#2071—112no—
167#2055—112no—
168#1987—111no—
169#1939D1111yescharacteristic, complemented
170#1877—112no—
171#1802—112no—
172C4×#103—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—24no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11#12112yes—
189C2×C4×C11#12112yes—
190C2×C4×C11C2×SD1614yes—
191C2×C4×C11C2×SD1612yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214D44—24no—
215D44—24no—
216D44—42no—
217D44—42no—
218D44—48no—
219D44—84no—
220C4×D11—88no—
221Dic22—22no—
222Dic22—22no—
223Dic22—41no—
224Dic22—41no—
225Dic22—84no—
226C8×C11—42no—
227C8×C11—41no—
228C8×C11—41no—
229C22×SD16—112no—
230C2×C4⋊Q8—111no—
231C2×#127—111no—
232C2×C4×Q8—111no—
233C2×C4×D4—112no—
234C2×C4×D4—221no—
235#486—224no—
236#460—224no—
237C2×C4⋊C8C2×D1111yescharacteristic
238C2×C4⋊C8C2×D1112yes—
239C2×#103—111no—
240C2×#103—111no—
241C2×#102—112no—
242C2×#102—112no—
243C2×#102—112no—
244C2×C4×C8C2×D1111yescharacteristic
245#395—222no—
246#391—112no—
247#390—112no—
248#390—221no—
249#389—221no—
250#389—221no—
251#386—222no—
252#384—112no—
253C4×C4⋊C4—111no—
254C4×C4⋊C4C2×D1111yescharacteristic
255#340—112no—
256#340—111no—
257#340—112no—
258#340—111no—
259#336C2×D1112yes—
260C22×C11C2×#12111yescharacteristic
261C22×C11#54611yescharacteristic
262C22×C11#54811yescharacteristic
263C22×C11C22×SD1611yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57611yescharacteristic
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—82no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11—42no—
277C4×C11#46114yes—
278C4×C11#52911yescharacteristic
279C4×C11#54211yescharacteristic
280C4×C11#54611yescharacteristic
281C4×C11#54711yescharacteristic
282Dic11—42no—
283Dic11—42no—
284Dic11—81no—
285Dic11—82no—
286Dic11—81no—
287C22×Q8—111no—
288C22×Q8—221no—
289C22×D4—112no—
290C22×D4—221no—
291C22×D4—221no—
292C23×C4—222no—
293C2×SD16—224no—
294C2×SD16—224no—
295C2×SD16—442no—
296C22×C8C22×D1112yes—
297C22×C8C22×D1111yescharacteristic
298C22×C8C22×D1111yescharacteristic
299C4⋊Q8—222no—
300C4⋊Q8—222no—
301#127—114no—
302#127—222no—
303C4×Q8—222no—
304C4×Q8—222no—
305C4×D4—224no—
306C4×D4—442no—
307C4×D4—444no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4D4411yescharacteristic
317C2×C4⋊C4D4411yescharacteristic
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—221no—
322C2×C42—221no—
323C2×C42C22×D1112yes—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—22no—
326C4⋊C8—42no—
327#103—222no—
328#103—222no—
329#102—224no—
330#102—224no—
331#102—224no—
332C4×C8—22no—
333#95—221no—
334#95—222no—
335#95—222no—
336#95D4412yes—
337C2×C11#242711yescharacteristic
338C2×C11C2×#46111yescharacteristic
339C2×C11#304111yescharacteristic
340C2×C11#329511yescharacteristic
341C2×C11#333311yescharacteristic
342C2×C11#336211yescharacteristic
343C2×C11#337511yescharacteristic
344D11—84no—
345C24—222no—
346C2×Q8—112no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8—221no—
352C2×Q8—442no—
353C2×Q8—881no—
354C2×Q8—881no—
355C2×D4—114no—
356C2×D4—224no—
357C2×D4—224no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—442no—
364C2×D4—442no—
365C2×D4—881no—
366C2×D4—881no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—222no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—444no—
373C22×C4—444no—
374C22×C4—882no—
375C22×C4C2×D4412yes—
376C22×C4C2×D4411yescharacteristic
377C22×C4C2×D4412yes—
378C22×C4C2×D4411yescharacteristic
379C22×C4C23×D1111yescharacteristic
380SD16—448no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C4⋊C4—22no—
391C4⋊C4—112no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—221no—
396C4⋊C4—222no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—442no—
400C4⋊C4—442no—
401C4⋊C4—882no—
402C4⋊C4—882no—
403C4⋊C4#431414yescomplemented
404C22⋊C4—444no—
405C22⋊C4—444no—
406C22⋊C4—882no—
407C42—22no—
408C42—22no—
409C42—442no—
410C42—442no—
411C42D4×D1112yes—
412C42#434312yes—
413C11#2532211yescharacteristic, complemented, Sylow
414C23—224no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—442no—
420C23—442no—
421C23C22×D4411yescharacteristic
422Q8—222no—
423Q8—222no—
424Q8—441no—
425Q8—441no—
426Q8—884no—
427D4—224no—
428D4—224no—
429D4—442no—
430D4—448no—
431D4—442no—
432D4—884no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—888no—
456C2×C4#6694812yes—
457C2×C4#6694812yes—
458C2×C4C2×#431414yes—
459C2×C4C2×#431412yes—
460C2×C4#6696212yes—
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4#6703711yescharacteristic
463C2×C4C2×#434311yescharacteristic
464C2×C4#6704011yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C2×C4#41×D1111yescharacteristic
467C8—42no—
468C8—41no—
469C8—41no—
470C22—444no—
471C22—444no—
472C22—444no—
473C22—882no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22C2×#6694811yescharacteristic
478C22#1062308511yescharacteristic
479C22#1062310711yescharacteristic
480C22C22×#431411yescharacteristic
481C22C2×#6696211yescharacteristic
482C22#1062328311yescharacteristic
483C22#1062328311yescharacteristic
484C4—22no—
485C4—24no—
486C4—42no—
487C4—442no—
488C4—442no—
489C4—882no—
490C4—881no—
491C4—881no—
492C4#1062245414yes—
493C4#1062314311yescharacteristic
494C4#1062316211yescharacteristic
495C4#1062322211yescharacteristic
496C4#1062326411yescharacteristic
497C2—884no—
498C2#1307219111yescharacteristic
499C2C2×#1062245411yescharacteristic
500C2#1307812011yescharacteristic
501C2#1308044111yescharacteristic
502C2#1308095511yescharacteristic
503C2#1308128811yescharacteristic
504C2#1308143211yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1939D11
hypocenterC11#25322
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
3. #13073824C2semidirect
5. #13070021C2semidirect
6. #13069934C2semidirect
7. #13069563C2semidirect
8. #13068949C2semidirect
9. #13068617C2semidirect
10. C4×#66880C2semidirect
11. C11×#1939C2semidirect
139. C11×C4⋊C4SD16semidirect
169. #1939D11semidirect
403. C4⋊C4#4314semidirect
413. C11#25322semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106224612
#130738242
#130716802
#130700212
#130699342
#130695632
#130689492
#130686172
C4×#668802
C11×#19392
#2532211