Finite Group Databasebeta

← #14659270

Subgroups — #14659270

Order 2816.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623276C211yesmaximal, characteristic
2C2×#10622752C211yesmaximal, characteristic
3#13077133C211yesmaximal, characteristic
4C2×#10622194C211yesmaximal, characteristic, complemented
5#13068343C211yesmaximal, characteristic, complemented
6#13068326C211yesmaximal, characteristic, complemented
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15#10623276—22no—
16#10623276—22no—
17#10623276—22no—
18#10623276—22no—
19C2×#66960—22no—
20C2×M16×D11—22no—
21C2×#66954C414yescomplemented
22#10622752—22no—
23#10622752C414yescomplemented
24C2×#66889—22no—
25#10622617C412yescomplemented
26#10622615—22no—
27#10622614C412yescomplemented
28#10622579—22no—
29C11×#344—22no—
30#10622194—22no—
31#10622190—22no—
32#10622161—22no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C2×#4339—21no—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339C2×C412yes—
42C2×#4339C2×C412yes—
43C2×#4339D412yes—
44C2×#4339D412yes—
45C2×#4339D412yes—
46C2×#4339Q812yes—
47C22×D44C2×C411yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2×C411yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16C2×C412yes—
60C2×C11×M16D412yes—
61C2×C11×M16D412yes—
62C22×C8×C11—21no—
63C22×C8×C11C2×C412yes—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117C2×C412yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C22⋊Dic11—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979C2×C412yes—
76C2×C4⋊Dic11—21no—
77C2×C4×Dic11—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318C2×C412yes—
87C2×#4318C2×C412yes—
88C2×#4318D412yes—
89C2×#4318D412yes—
90C22×C11⋊C8—21no—
91C22×C11⋊C8—21no—
92#66960—28no—
93#66960—28no—
94M16×D11—28no—
95M16×D11—28no—
96#66954—28no—
97#66954—28no—
98C2×#4313—24no—
99C2×C8×D11—24no—
100#66889—28no—
101#66874—24no—
102#66873—24no—
103#10778—111nomaximal, Sylow
104C24×C11#4111yescharacteristic
105C23×D11—21no—
106C22×C4×C11—41no—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×Q811yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C2×C22⋊D11—22no—
122C2×C22⋊D11—22no—
123C2×C22⋊D11—22no—
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—22no—
127C22×Dic11—21no—
128C22×Dic11—41no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—22no—
135#4339—22no—
136#4339—22no—
137#4339—22no—
138#4339—22no—
139#4339—22no—
140#4339—22no—
141#4339C22⋊C414yes—
142#4339C22⋊C414yes—
143#4339C4⋊C414yes—
144#4339C4⋊C414yes—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C4212yes—
149C2×D44C22⋊C412yes—
150C2×D44C4⋊C412yes—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C4212yes—
161C2×Dic22C22⋊C412yes—
162C2×Dic22C4⋊C412yes—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—41no—
170C11×M16—41no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—41no—
175C2×C8×C11—41no—
176C2×C8×C11C22⋊C414yes—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—41no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—41no—
181C42×C11—22no—
182C42×C11—41no—
183C22⋊Dic11—22no—
184C22⋊Dic11—41no—
185C4⋊Dic11—22no—
186C4⋊Dic11—41no—
187C4×Dic11—22no—
188C4×Dic11—41no—
189#4318—22no—
190#4318—22no—
191#4318—22no—
192#4318—22no—
193#4318—22no—
194#4318—41no—
195#4318—41no—
196#4318C22⋊C414yes—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—41no—
202C2×C11⋊C8—41no—
203#4313—216no—
204C8×D11—216no—
205C2×#568—111no—
206C2×#421—111no—
207#2896—111no—
208C2×#344—111no—
209C2×#344D1111yescharacteristic, complemented
210#1738—111no—
211#1733—111no—
212C23×C11—81no—
213C23×C11#11711yescharacteristic
214C23×C11C4×D411yescharacteristic
215C23×C11C4×D411yescharacteristic
216C23×C11#12111yescharacteristic
217C23×C11C22⋊Q811yescharacteristic
218C23×C11#12311yescharacteristic
219C23×C11#12311yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—82no—
224C2×C4×C11—42no—
225C2×C4×C11—82no—
226C2×C4×C11C2×C4211yescharacteristic
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11C2×C4⋊C411yescharacteristic
233C2×C4×C11C2×C4⋊C411yescharacteristic
234C2×C4×C11C2×C4⋊C411yescharacteristic
235C2×C4×C11#11711yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11C22⋊Q811yescharacteristic
250C2×C4×C11C22⋊Q811yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11#12311yescharacteristic
253C2×C4×C11#12311yescharacteristic
254C22⋊D11—24no—
255C22⋊D11—24no—
256C22⋊D11—24no—
257C22⋊D11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—42no—
262C2×Dic11—82no—
263D44—22no—
264D44—22no—
265D44—22no—
266D44#9514yes—
267C4×D11—24no—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—24no—
271Dic22—22no—
272Dic22—22no—
273Dic22—22no—
274Dic22#9514yes—
275C8×C11—24no—
276C8×C11—42no—
277C11⋊C8—24no—
278C11⋊C8—42no—
279C22×#41—111no—
280#568—222no—
281#568—222no—
282#568—222no—
283#568—222no—
284C2×#131—114no—
285C2×#131—222no—
286C22×M16—111no—
287C22×M16—111no—
288C22×M16—222no—
289C22×M16C2×D1111yescharacteristic
290C22×M16C2×D1111yescharacteristic
291C2×#117—111no—
292C2×#117C2×D1111yescharacteristic
293#421—114no—
294#421—222no—
295C2×#104—222no—
296#419—112no—
297#418—112no—
298#417—222no—
299#416—222no—
300#344—22no—
301#344—222no—
302#341—222no—
303#339—222no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—41no—
311C22×C11C4×C22⋊C411yescharacteristic
312C22×C11#38011yescharacteristic
313C22×C11#38111yescharacteristic
314C22×C11#38511yescharacteristic
315C22×C11#38511yescharacteristic
316C22×C11#38611yescharacteristic
317C22×C11#38611yescharacteristic
318C2×D11—24no—
319C2×D11—44no—
320C2×D11—82no—
321C2×D11—82no—
322C4×C11—82no—
323C4×C11C2×#9511yescharacteristic
324C4×C11C4×C22⋊C411yescharacteristic
325C4×C11#37911yescharacteristic
326C4×C11#38011yescharacteristic
327C4×C11#38511yescharacteristic
328C4×C11#38511yescharacteristic
329C4×C11#38611yescharacteristic
330C4×C11#38611yescharacteristic
331Dic11—24no—
332Dic11—82no—
333C2×#41—112no—
334C2×#41—112no—
335C2×#41—112no—
336C2×#41—112no—
337C2×#41—112no—
338C2×#41—112no—
339C2×#41—221no—
340C2×#41—221no—
341C2×#41—221no—
342C2×#41—221no—
343C2×#41—221no—
344C2×#41—221no—
345C22×Q8—111no—
346C22×D4—111no—
347C22×D4—221no—
348C23×C4—221no—
349C23×C4C22×D1111yescharacteristic
350#131—228no—
351#131—228no—
352#131—228no—
353#131—228no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—112no—
364C2×M16—112no—
365C2×M16—112no—
366C2×M16—112no—
367C2×M16—228no—
368C2×M16—228no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—224no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C2×M16—221no—
378C2×M16C4×D1112yes—
379C2×M16D4412yes—
380C2×M16C22⋊D1112yes—
381C22×C8—21no—
382C22×C8—221no—
383C22×C8—224no—
384C22×C8—221no—
385C22×C8C4×D1112yes—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—112no—
390#117—221no—
391#117—221no—
392#117—221no—
393#117C4×D1112yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—221no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—221no—
398C2×C42—21no—
399C2×C42—221no—
400#104—228no—
401#103—224no—
402#102—224no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11C22⋊#9511yescharacteristic
411D11—44no—
412C24—221no—
413C24#433911yescharacteristic
414#41—114no—
415#41—114no—
416#41—114no—
417#41—114no—
418#41—222no—
419#41—222no—
420#41—222no—
421#41—222no—
422#41—222no—
423#41—222no—
424#41—222no—
425#41—222no—
426#41—222no—
427#41—222no—
428#41—222no—
429#41—222no—
430C2×Q8—112no—
431C2×Q8—112no—
432C2×Q8—112no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×D4—112no—
437C2×D4—112no—
438C2×D4—112no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C22×C4—41no—
449C22×C4—221no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—441no—
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4C2×D4411yescharacteristic
461C22×C4#433911yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4#434111yescharacteristic
468C22×C4Q8×D1111yescharacteristic
469C22×C4#434311yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—41no—
478M16—41no—
479M16—114no—
480M16—2216no—
481M16—222no—
482M16—222no—
483M16—222no—
484M16—222no—
485M16—222no—
486M16—441no—
487M16—441no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—2216no—
494C2×C8—222no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—222no—
498C2×C8—441no—
499C2×C8—441no—
500C2×C8(C2×D11)⋊C414yes—
501C4⋊C4—22no—
502C4⋊C4—41no—
503C4⋊C4—222no—
504C4⋊C4—441no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—222no—
508C22⋊C4—441no—
509C42—22no—
510C42—41no—
511C42—222no—
512C42—441no—
513C11#1077811yescharacteristic, complemented, Sylow
514C23—81no—
515C23—222no—
516C23—222no—
517C23—222no—
518C23—882no—
519C23#6692511yescharacteristic
520C23C4×D4411yescharacteristic
521C23#6693611yescharacteristic
522C23#6693711yescharacteristic
523C23#6694711yescharacteristic
524C23#6694911yescharacteristic
525C23C4×C22⋊D1111yescharacteristic
526Q8—114no—
527Q8—222no—
528Q8—222no—
529Q8—222no—
530D4—114no—
531D4—224no—
532D4—224no—
533D4—224no—
534D4—224no—
535D4—222no—
536D4—222no—
537D4—222no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—442no—
548C2×C4—882no—
549C2×C4C42×D1111yescharacteristic
550C2×C4C4×D4411yescharacteristic
551C2×C4C22⋊C4×D1111yescharacteristic
552C2×C4C22⋊C4×D1111yescharacteristic
553C2×C4C22⋊C4×D1111yescharacteristic
554C2×C4C22⋊C4×D1111yescharacteristic
555C2×C4(C22⋊D11)⋊C411yescharacteristic
556C2×C4(C22⋊D11)⋊C411yescharacteristic
557C2×C4#6693511yescharacteristic
558C2×C4#6693511yescharacteristic
559C2×C4#6693611yescharacteristic
560C2×C4#6693711yescharacteristic
561C2×C4C4⋊C4×D1111yescharacteristic
562C2×C4C4⋊C4×D1111yescharacteristic
563C2×C4C4⋊C4×D1111yescharacteristic
564C2×C4#6694511yescharacteristic
565C2×C4#6694611yescharacteristic
566C2×C4#6694611yescharacteristic
567C2×C4#6694711yescharacteristic
568C2×C4#6694811yescharacteristic
569C2×C4#6694911yescharacteristic
570C2×C4#6695011yescharacteristic
571C2×C4C2×(C2×D11)⋊C411yescharacteristic
572C2×C4C4×C22⋊D1111yescharacteristic
573C2×C4#6699011yescharacteristic
574C2×C4#6699011yescharacteristic
575C2×C4#6699111yescharacteristic
576C2×C4#6699911yescharacteristic
577C8—24no—
578C8—42no—
579C8—224no—
580C8—442no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—224no—
589C22—444no—
590C22—882no—
591C22—882no—
592C22#1062227711yescharacteristic
593C22#1062227811yescharacteristic
594C22#1062228011yescharacteristic
595C22#1062228111yescharacteristic
596C22C4×(C2×D11)⋊C411yescharacteristic
597C22#1062256911yescharacteristic
598C22#1062260211yescharacteristic
599C4—82no—
600C4—224no—
601C4—882no—
602C4D11×#9511yescharacteristic
603C4#1062227811yescharacteristic
604C4#1062227911yescharacteristic
605C4#1062228111yescharacteristic
606C4#1062256811yescharacteristic
607C4#1062256911yescharacteristic
608C4#1062260011yescharacteristic
609C4#1062260211yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—444no—
618C2(C2×D11)⋊#9511yescharacteristic
subgroupG/H
centerC4#10622568
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#344C2
socleC2×C11C22⋊#95
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#344D11
hypocenterC11#10778
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#10622194C2semidirect
5. #13068343C2semidirect
6. #13068326C2semidirect
7. C2×C11×#344C2semidirect
21. C2×#66954C4semidirect
23. #10622752C4semidirect
25. #10622617C4semidirect
27. #10622614C4semidirect
209. C2×#344D11semidirect
513. C11#10778semidirect

Maximal subgroups

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

subgroupindex
C2×#106232762
C2×#106227522
#130771332
C2×#106221942
#130683432
#130683262
C2×C11×#3442
#1077811