Finite Group Databasebeta

← #14763136

Subgroups — #14763136

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622332C211yesmaximal, characteristic, complemented
3#13071011C211yesmaximal, characteristic, complemented
4#13069547C212yesmaximal, complemented
5#13069545C212yesmaximal, complemented
6#13069438C212yesmaximal, complemented
7#13069434C212yesmaximal, complemented
8#13068557C211yesmaximal, characteristic, complemented
9#13068556C211yesmaximal, characteristic, complemented
10#13068554C211yesmaximal, characteristic, complemented
11C11×#1788C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14#10623363—24no—
15#10623363C418yescomplemented
16C2×#67000C2211yescharacteristic
17C2×#66997C2211yescharacteristic
18C2×#66993C2211yescharacteristic
19C2×#66992—21no—
20C2×#66992—21no—
21C2×#66989C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23C2×C4×C22⋊D11—21no—
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#102C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66896C2212yes—
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2212yes—
34C2×#66880C2212yes—
35C2×#66879C2212yes—
36C2×Dic11⋊C8C2212yes—
37#10622590C2212yes—
38C4⋊C4×Dic11C2212yes—
39C2×#66874C2212yes—
40C2×#66873C2212yes—
41#10622556—21no—
42C22⋊C4×Dic11—21no—
43#10622332—24no—
44#10622264—21no—
45#10622261—21no—
46C2×C11×#41—22no—
47C2×C11×#41—42no—
48C2×C11×#41—42no—
49C2×C11×#41C2×C414yes—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—21no—
56C22×C22⋊D11—21no—
57C22×C22⋊D11—21no—
58C23×Dic11D411yescharacteristic
59C23×Dic11D411yescharacteristic
60C2×#4339—22no—
61C2×#4339—42no—
62C2×#4339—42no—
63C2×#4339C2×C414yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73#67000—22no—
74#67000C2×C414yes—
75#66997—22no—
76#66997C2×C414yes—
77#66993—22no—
78#66993C2×C414yes—
79#66992—28no—
80#66992—28no—
81#66989—22no—
82#66989C2×C414yes—
83C4×C22⋊D11—28no—
84C4×C22⋊D11—28no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11C2×C414yes—
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D414yes—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2312yes—
98C11×#103—42no—
99C11×#102—42no—
100C11×C22⋊C8—22no—
101C11×#95—21no—
102#66899—42no—
103#66896—42no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108C22⋊(C11⋊C8)—22no—
109#66885—42no—
110#66880—42no—
111#66879—24no—
112Dic11⋊C8—24no—
113#66874—42no—
114#66873—42no—
115#21812—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11C2×D411yescharacteristic
118C23×D11—21no—
119C11×#41—44no—
120C11×#41—44no—
121C11×#41—48no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11C22×C412yes—
126C2×D4×C11—24no—
127C2×D4×C11—21no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11C22×C412yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—44no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—24no—
144C2×C22⋊D11—24no—
145C2×C22⋊D11—44no—
146C2×C22⋊D11—44no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—41no—
152C22×Dic11—41no—
153C22×Dic11—42no—
154C22×Dic11C22⋊C414yes—
155C22×Dic11C22⋊C414yes—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160#4339—44no—
161#4339—44no—
162#4339—48no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44C22×C412yes—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×Dic22—21no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22C22×C412yes—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C22⋊C4—42no—
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—42no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188C4×Dic11—44no—
189C4×Dic11C22⋊C414yes—
190C4×Dic11C22⋊C414yes—
191C4×Dic11C22×C412yes—
192C4×Dic11C22×C412yes—
193C4×Dic11C2×D412yes—
194C4×Dic11C2×D412yes—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×#532—111no—
199C2×#432—111no—
200#2283—111no—
201#1983—112no—
202#1983—112no—
203#1961—112no—
204#1960—112no—
205#1788—111no—
206#1788—111no—
207#1788—111no—
208#1788D1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C2×C22⋊C412yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—41no—
224C22×D11—41no—
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—42no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—48no—
231D4×C11—42no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—48no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11C2×C22⋊C412yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11H(5,𝔽2)12yes—
246C2×C4×C11H(5,𝔽2)12yes—
247C22⋊D11—48no—
248C22⋊D11—48no—
249C22⋊D11—48no—
250C2×Dic11—22no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11C2×C22⋊C412yes—
264C2×Dic11C2×C22⋊C412yes—
265C2×Dic11C2×C22⋊C412yes—
266C2×Dic11C2×C22⋊C412yes—
267D44—22no—
268D44—22no—
269D44—42no—
270C4×D11—48no—
271Dic22—22no—
272Dic22—22no—
273Dic22—42no—
274C8×C11—42no—
275C11⋊C8—42no—
276C22×#41—111no—
277C22×#41C2×D1111yescharacteristic
278#532—118no—
279#532—224no—
280C2×C4⋊Q8—111no—
281C2×#127—111no—
282C2×#124—111no—
283C2×#124—111no—
284C2×#121—221no—
285C2×#121—221no—
286C2×C4×D4—221no—
287C2×C4×D4—221no—
288C22×C42—111no—
289#432—224no—
290C2×C4⋊C8—112no—
291C2×#103—112no—
292C2×#103—112no—
293C2×#103—112no—
294C2×#103C2×D1112yes—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102—112no—
298C2×#102C2×D1112yes—
299C2×C22⋊C8—111no—
300C2×C22⋊C8C2×D1111yescharacteristic
301C2×#97—112no—
302#383—221no—
303#382—112no—
304#381—221no—
305#380—111no—
306#380C2×D1111yescharacteristic
307C4×C4⋊C4—112no—
308C4×C22⋊C4—221no—
309#376—221no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—82no—
319C22×C11—82no—
320C22×C11C22×C22⋊C411yescharacteristic
321C22×C11#53512yes—
322C22×C11#57512yes—
323C22×C11#57511yescharacteristic
324C22×C11#57511yescharacteristic
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—82no—
329C2×D11—82no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—82no—
333C4×C11#51811yescharacteristic
334C4×C11#51811yescharacteristic
335C4×C11#53512yes—
336Dic11—22no—
337Dic11—22no—
338Dic11—22no—
339Dic11—22no—
340Dic11—42no—
341Dic11—82no—
342C2×#41—22no—
343C2×#41—42no—
344C2×#41—42no—
345C2×#41—114no—
346C2×#41—222no—
347C2×#41—442no—
348C2×#41—442no—
349C2×#41C4×D1114yes—
350C22×Q8—111no—
351C22×Q8C22×D1111yescharacteristic
352C22×D4—21no—
353C22×D4—111no—
354C22×D4—221no—
355C22×D4—221no—
356C22×D4—221no—
357C22×D4C22×D1111yescharacteristic
358C23×C4—21no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C22×C8—112no—
364C22×C8C22×D1112yes—
365C4⋊Q8—114no—
366C4⋊Q8—222no—
367#127—114no—
368#127—222no—
369#124—114no—
370#124—114no—
371#124—222no—
372#124—222no—
373#121—228no—
374#121—228no—
375C4×D4—228no—
376C4×D4—228no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C22×D1112yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—114no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—114no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—222no—
394C4⋊C8—224no—
395#103—42no—
396#103—442no—
397#103—442no—
398#103—442no—
399#102—42no—
400#102—442no—
401#102—442no—
402#102—442no—
403C22⋊C8—22no—
404C22⋊C8—222no—
405#97—224no—
406#95—21no—
407#95—222no—
408#95—222no—
409#95—222no—
410#95—221no—
411C2×C11—42no—
412C2×C11—82no—
413C2×C11#230911yescharacteristic
414C2×C11#289611yescharacteristic
415C2×C11#289611yescharacteristic
416C2×C11#321912yes—
417C2×C11#321912yes—
418D11—82no—
419C24—21no—
420C24—221no—
421C24D4×D1111yescharacteristic
422#41—44no—
423#41—44no—
424#41—48no—
425#41—444no—
426#41—444no—
427#41—448no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—112no—
432C2×Q8—221no—
433C2×Q8—222no—
434C2×Q8—222no—
435C2×Q8C2×C4×D1112yes—
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—44no—
441C2×D4—112no—
442C2×D4—224no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—221no—
446C2×D4—222no—
447C2×D4—222no—
448C2×D4—444no—
449C2×D4—442no—
450C2×D4—442no—
451C2×D4—444no—
452C2×D4C2×C4×D1112yes—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—44no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—221no—
466C22×C4—224no—
467C22×C4—222no—
468C22×C4—444no—
469C22×C4—442no—
470C22×C4—441no—
471C22×C4—441no—
472C22×C4C2×C4×D1112yes—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1112yes—
475C22×C4C23×D1111yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C22⋊C4—42no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—442no—
494C42—114no—
495C42—114no—
496C42—112no—
497C42—112no—
498C42—112no—
499C42—112no—
500C42—444no—
501C11#2181211yescharacteristic, complemented, Sylow
502C23—22no—
503C23—21no—
504C23—21no—
505C23—22no—
506C23—22no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—222no—
512C23—442no—
513C23—441no—
514C23—441no—
515C23—442no—
516C23C22⋊C4×D1112yes—
517C23C2×D4×D1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—42no—
521Q8—222no—
522Q8—222no—
523Q8—442no—
524D4—22no—
525D4—22no—
526D4—48no—
527D4—42no—
528D4—222no—
529D4—222no—
530D4—448no—
531D4—448no—
532D4—448no—
533D4—442no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—48no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—448no—
556C2×C4—444no—
557C2×C4—444no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4C22⋊C4×D1112yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4#6703712yes—
566C2×C4#6703712yes—
567C8—42no—
568C8—442no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—442no—
580C22—442no—
581C22—442no—
582C22—882no—
583C22—882no—
584C22C2×C22⋊C4×D1111yescharacteristic
585C22#1062312312yes—
586C22#1062329912yes—
587C22#1062330411yescharacteristic
588C22#1062330811yescharacteristic
589C4—22no—
590C4—42no—
591C4—82no—
592C4—222no—
593C4—222no—
594C4—222no—
595C4—222no—
596C4—442no—
597C4—882no—
598C4#1062301711yescharacteristic
599C4#1062301711yescharacteristic
600C4#1062312312yes—
601C2—42no—
602C2—82no—
603C2—882no—
604C2#1307119711yescharacteristic
605C2#1307713111yescharacteristic
606C2#1307713211yescharacteristic
607C2#1307965112yes—
608C2#1307965712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#21812
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. #13071011C2semidirect
4. #13069547C2semidirect
5. #13069545C2semidirect
6. #13069438C2semidirect
7. #13069434C2semidirect
8. #13068557C2semidirect
9. #13068556C2semidirect
10. #13068554C2semidirect
11. C11×#1788C2semidirect
15. #10623363C4semidirect
208. #1788D11semidirect
501. C11#21812semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106223322
#130710112
#130695472
#130695452
#130694382
#130694342
#130685572
#130685562
#130685542
C11×#17882
#2181211