Finite Group Databasebeta

← #14803647

Subgroups — #14803647

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622307C211yesmaximal, characteristic, complemented
2C2×#10622456C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic, complemented
4#13071680C211yesmaximal, characteristic, complemented
5#13070031C212yesmaximal, complemented
6#13069927C212yesmaximal, complemented
7#13069563C211yesmaximal, characteristic, complemented
8#13068963C212yesmaximal, complemented
9#13068627C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×D88C2212yes—
13C2×#66946—21no—
14C2×#66927C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×C4×D44C2212yes—
17C2×#66922C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C4⋊C8C2212yes—
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66885C2212yes—
24C2×#66885C2211yescharacteristic
25C2×#66885C2212yes—
26C2×#66885C2211yescharacteristic
27#10622601—21no—
28#10622600—21no—
29#10622600—21no—
30#10622552C2212yes—
31#10622552C2212yes—
32#10622549C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34#10622456—24no—
35#10622307—24no—
36#10622286—22no—
37#10622278—22no—
38C11×#336C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11—22no—
49C22×Dic22—21no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4×Dic11—21no—
69C2×D88—24no—
70C2×D88—24no—
71C2×D88—42no—
72#66946—44no—
73#66927—22no—
74#66927D414yes—
75C4×D44—22no—
76C4×D44—22no—
77C4×D44—24no—
78C4×D44—42no—
79#66922—22no—
80#66922—22no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—42no—
83C4×C8×C11—22no—
84C11×#95D412yes—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—24no—
89#66885—24no—
90#66885—24no—
91#66885—22no—
92#66885—22no—
93#25321—111nomaximal, Sylow
94C23×D11—21no—
95C23×D11—22no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C22×Dic11—21no—
105C2×D44—24no—
106C2×D44—24no—
107C2×D44—21no—
108C2×D44—22no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—22no—
112C2×D44—22no—
113C2×D44—22no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—22no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—81no—
120C2×D44—81no—
121C2×D44C2×D414yes—
122C2×D44#4112yes—
123C2×C4×D11—44no—
124C2×C4×D11—44no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—82no—
129C2×Dic22—42no—
130C2×Dic22—81no—
131C2×Dic22—81no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—21no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11C2×D412yes—
146C42×C11#4112yes—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—42no—
150(C2×D11)⋊C4—82no—
151(C2×D11)⋊C4—82no—
152(C2×D11)⋊C4—82no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—42no—
161C4⋊Dic11#4112yes—
162C4×Dic11—42no—
163D88—48no—
164C2×#486—111no—
165C2×#459—111no—
166#2563—111no—
167#2366—111no—
168#2073—112no—
169#2054—112no—
170#1987—111no—
171#1939D1111yescharacteristic, complemented
172#1879—112no—
173#1804—112no—
174C4×#102—111no—
175C23×C11C22×D411yescharacteristic
176C22×D11—24no—
177C22×D11—22no—
178C22×D11—41no—
179C22×D11—42no—
180C22×D11—41no—
181C22×D11—42no—
182C22×D11—41no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—42no—
189C22×D11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11#13512yes—
201C2×C4×C11AGL(1,ℤ/8)12yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11H(5,𝔽2)11yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220D44—22no—
221D44—22no—
222D44—24no—
223D44—24no—
224D44—42no—
225D44—42no—
226D44—41no—
227D44—41no—
228D44—48no—
229D44—84no—
230C4×D11—88no—
231C4×D11—84no—
232Dic22—84no—
233C8×C11—42no—
234C8×C11—41no—
235C8×C11—41no—
236C22×D8—112no—
237C2×C4⋊Q8—111no—
238C2×#127—111no—
239C2×C4×D4—111no—
240C2×C4×D4—112no—
241C2×C4×D4—221no—
242#486—224no—
243#459—224no—
244C2×C4⋊C8C2×D1111yescharacteristic
245C2×C4⋊C8C2×D1112yes—
246C2×#102—111no—
247C2×#102—112no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102—111no—
251C2×C4×C8C2×D1111yescharacteristic
252#393—222no—
253#390—112no—
254#390—112no—
255#390—221no—
256#386—222no—
257#382—112no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4—111no—
261C4×C4⋊C4C2×D1111yescharacteristic
262#340—112no—
263#340—111no—
264#340—112no—
265#340—111no—
266#336C2×D1112yes—
267C22×C11C2×#12111yescharacteristic
268C22×C11#54611yescharacteristic
269C22×C11#54811yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C11#57611yescharacteristic
273C22×C11#57611yescharacteristic
274C2×D11—42no—
275C2×D11—42no—
276C2×D11—44no—
277C2×D11—42no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—82no—
281C2×D11—82no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—82no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11#46314yes—
292C4×C11#52911yescharacteristic
293C4×C11#54211yescharacteristic
294C4×C11#54611yescharacteristic
295C4×C11#54711yescharacteristic
296Dic11—42no—
297Dic11—81no—
298Dic11—81no—
299Dic11—82no—
300C22×Q8—221no—
301C22×D4—112no—
302C22×D4—111no—
303C22×D4—221no—
304C22×D4—221no—
305C23×C4—221no—
306C23×C4—222no—
307C2×D8—224no—
308C2×D8—224no—
309C2×D8—442no—
310C22×C8C22×D1112yes—
311C22×C8C22×D1111yescharacteristic
312C22×C8C22×D1111yescharacteristic
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315#127—114no—
316#127—222no—
317C4×D4—224no—
318C4×D4—222no—
319C4×D4—222no—
320C4×D4—442no—
321C4×D4—444no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4D4411yescharacteristic
328C2×C4⋊C4D4411yescharacteristic
329C2×C22⋊C4—222no—
330C2×C22⋊C4—221no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C42—221no—
336C2×C42C22×D1112yes—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—22no—
339C4⋊C8—42no—
340#102—222no—
341#102—222no—
342#102—224no—
343#102—224no—
344#102—224no—
345C4×C8—22no—
346#95—221no—
347#95—222no—
348#95—222no—
349#95D4412yes—
350C2×C11#242711yescharacteristic
351C2×C11C2×#46311yescharacteristic
352C2×C11#304111yescharacteristic
353C2×C11#330511yescharacteristic
354C2×C11#332511yescharacteristic
355C2×C11#336111yescharacteristic
356C2×C11#336611yescharacteristic
357D11—82no—
358D11—84no—
359C24—221no—
360C24—222no—
361C2×Q8—442no—
362C2×Q8—881no—
363C2×Q8—881no—
364C2×D4—114no—
365C2×D4—112no—
366C2×D4—224no—
367C2×D4—224no—
368C2×D4—221no—
369C2×D4—222no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—222no—
377C2×D4—222no—
378C2×D4—442no—
379C2×D4—442no—
380C2×D4—881no—
381C2×D4—881no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—444no—
387C22×C4—444no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—882no—
392C22×C4C2×D4412yes—
393C22×C4C2×D4412yes—
394C22×C4C2×D4411yescharacteristic
395C22×C4C2×D4411yescharacteristic
396C22×C4C23×D1111yescharacteristic
397D8—448no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—112no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—442no—
418C22⋊C4—444no—
419C22⋊C4—444no—
420C22⋊C4—442no—
421C22⋊C4—882no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C42—22no—
425C42—22no—
426C42—442no—
427C42D4×D1112yes—
428C42#434312yes—
429C11#2532111yescharacteristic, complemented, Sylow
430C23—224no—
431C23—222no—
432C23—441no—
433C23—442no—
434C23—442no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—442no—
439C23—442no—
440C23—441no—
441C23—442no—
442C23—441no—
443C23—442no—
444C23C22×D4411yescharacteristic
445Q8—884no—
446D4—222no—
447D4—224no—
448D4—224no—
449D4—222no—
450D4—442no—
451D4—441no—
452D4—441no—
453D4—442no—
454D4—448no—
455D4—884no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—222no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—888no—
477C2×C4—884no—
478C2×C4#6694812yes—
479C2×C4#6694812yes—
480C2×C4#6695712yes—
481C2×C4#6696112yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4#6703711yescharacteristic
484C2×C4C2×#434311yescharacteristic
485C2×C4#6704011yescharacteristic
486C2×C4#41×D1111yescharacteristic
487C2×C4#41×D1111yescharacteristic
488C8—42no—
489C8—41no—
490C8—41no—
491C22—444no—
492C22—442no—
493C22—444no—
494C22—444no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—882no—
499C22—881no—
500C22—881no—
501C22—882no—
502C22—882no—
503C22—881no—
504C22—882no—
505C22C2×#6694811yescharacteristic
506C22#1062308511yescharacteristic
507C22#1062310711yescharacteristic
508C22C2×#6695711yescharacteristic
509C22C2×#6696111yescharacteristic
510C22#1062328311yescharacteristic
511C22#1062328311yescharacteristic
512C4—22no—
513C4—42no—
514C4—42no—
515C4—442no—
516C4—881no—
517C4—882no—
518C4—881no—
519C4#1062245714yes—
520C4#1062314311yescharacteristic
521C4#1062316211yescharacteristic
522C4#1062322211yescharacteristic
523C4#1062326411yescharacteristic
524C2—884no—
525C2—882no—
526C2#1307219111yescharacteristic
527C2C2×#1062245711yescharacteristic
528C2#1307812011yescharacteristic
529C2#1308056711yescharacteristic
530C2#1308085911yescharacteristic
531C2#1308127811yescharacteristic
532C2#1308132511yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC2×#10622456C2
hypercenter#1939D11
hypocenterC11#25321
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
1. C2×#10622307C2semidirect
3. #13073785C2semidirect
4. #13071680C2semidirect
5. #13070031C2semidirect
6. #13069927C2semidirect
7. #13069563C2semidirect
8. #13068963C2semidirect
9. #13068627C2semidirect
10. C4×#66885C2semidirect
11. C11×#1939C2semidirect
171. #1939D11semidirect
429. C11#25321semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106224562
#130737852
#130716802
#130700312
#130699272
#130695632
#130689632
#130686272
C4×#668852
C11×#19392
#2532111