Finite Group Databasebeta

← #14782497

Subgroups — #14782497

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622738C211yesmaximal, characteristic, complemented
2C2×#10622737C211yesmaximal, characteristic, complemented
3C2×#10622745C211yesmaximal, characteristic
4C2×#10622745C211yesmaximal, characteristic
5C2×#10622745C211yesmaximal, characteristic
6#13070016C214yesmaximal, complemented
7#13070013C214yesmaximal, complemented
8C2×C11⋊#338C211yesmaximal, characteristic, complemented
9C2×C11×#430C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#430—22no—
18C11×#430C2214yes—
19C2×C11×#108—22no—
20C2×#66888C2212yes—
21C2×#66888C2212yes—
22C2×#66888C2212yes—
23#10622745—22no—
24#10622745—22no—
25#10622745—22no—
26#10622745—22no—
27#10622745—22no—
28#10622745—22no—
29C2×#66887C2212yes—
30C2×#66887C2212yes—
31C2×#66887C2212yes—
32#10622738—22no—
33#10622738C2214yes—
34#10622737—22no—
35#10622737C2214yes—
36C2×#66886—22no—
37C2×#66883—22no—
38C11⋊#338C2214yes—
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11Q812yes—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339—21no—
50C2×#4339—21no—
51C2×#4339—21no—
52C2×#4339—21no—
53C22×D44C2311yescharacteristic
54C22×C4×D11Q812yes—
55C22×Dic22C2311yescharacteristic
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C2×C11×M16—21no—
67C2×C11×M16D412yes—
68C2×C11×M16D412yes—
69C2×C11×M16D412yes—
70C2×C11×M16D412yes—
71C2×C11×M16C2312yes—
72C2×C11×M16C2312yes—
73C2×C11×M16C2312yes—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C2×#4318—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×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318D412yes—
91C2×#4318D412yes—
92C2×#4318C2312yes—
93C2×#4318C2312yes—
94C2×#4318C2312yes—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C11×#108—28no—
99#66888—24no—
100#66888—24no—
101#66888—24no—
102#66887—24no—
103#66887—24no—
104#66887—24no—
105#66886—28no—
106#66883—28no—
107#23622—111nomaximal, Sylow
108C24×C11C2×Q811yescharacteristic
109C23×D11C2×Q812yes—
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×Q811yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—22no—
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C22×Dic11C2×Q812yes—
131#4339—41no—
132#4339—41no—
133#4339—41no—
134#4339—41no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142#4339—41no—
143#4339—41no—
144#4339—41no—
145#4339—41no—
146#4339—41no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16C2×D414yes—
176C11×M16C2×D414yes—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318—22no—
192#4318—22no—
193#4318—41no—
194#4318—41no—
195#4318—41no—
196#4318—41no—
197#4318C2×D414yes—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—41no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—41no—
206C2×C11⋊C8—41no—
207C2×#430—111no—
208C2×#430—111no—
209C2×#430D1111yescharacteristic, complemented
210C2×#413—111no—
211C2×#413—111no—
212C2×#413—111no—
213#2070—114no—
214#2069—114no—
215C2×#338—111no—
216C23×C11—81no—
217C23×C11C22⋊Q811yescharacteristic
218C23×C11C22⋊Q811yescharacteristic
219C23×C11C22⋊Q811yescharacteristic
220C23×C11C22⋊Q811yescharacteristic
221C23×C11C22⋊Q811yescharacteristic
222C23×C11C22⋊Q811yescharacteristic
223C23×C11C22×Q811yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—82no—
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#12111yescharacteristic
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11C22⋊Q811yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11C22⋊Q811yescharacteristic
246C2×C4×C11#12611yescharacteristic
247C2×C4×C11#12611yescharacteristic
248C2×C4×C11#12611yescharacteristic
249C2×C4×C11#12611yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—42no—
257C22⋊D11—42no—
258C22⋊D11—42no—
259C22⋊D11—42no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267C4×D11—42no—
268C4×D11—42no—
269C4×D11—42no—
270C4×D11—42no—
271Dic22—41no—
272Dic22—41no—
273Dic22—41no—
274Dic22—41no—
275C8×C11—24no—
276C8×C11—24no—
277C8×C11—42no—
278C11⋊C8—24no—
279C11⋊C8—42no—
280C11⋊C8—42no—
281C22×#41—111no—
282C22×M16—111no—
283C22×M16—111no—
284C22×M16—111no—
285C22×M16C2×D1111yescharacteristic
286C22×M16C2×D1111yescharacteristic
287C22×M16C2×D1111yescharacteristic
288#430—22no—
289#430—114no—
290#430—114no—
291#430—222no—
292#430—222no—
293#430C2×D1114yes—
294C2×#108—22no—
295C2×#108—222no—
296C2×#108—222no—
297#413—222no—
298#413—222no—
299#413—222no—
300#413—222no—
301#413—222no—
302#413—222no—
303C2×#101—112no—
304C2×#101—112no—
305C2×#101—112no—
306C2×#100—112no—
307C2×#100—112no—
308C2×#100—112no—
309#338—114no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11#39611yescharacteristic
318C22×C11#39611yescharacteristic
319C22×C11#39611yescharacteristic
320C22×C11#39611yescharacteristic
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11C2×C22⋊Q811yescharacteristic
323C22×C11C2×C22⋊Q811yescharacteristic
324C2×D11—42no—
325C2×D11—82no—
326C2×D11—82no—
327C2×D11—82no—
328C4×C11#39611yescharacteristic
329C4×C11#39611yescharacteristic
330C4×C11#39611yescharacteristic
331C4×C11#39611yescharacteristic
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×#12111yescharacteristic
334C4×C11C2×#12111yescharacteristic
335C4×C11C2×#12611yescharacteristic
336Dic11—42no—
337C2×#41—221no—
338C2×#41—221no—
339C2×#41—221no—
340C2×#41—221no—
341C2×#41—221no—
342C2×#41—221no—
343C2×#41—221no—
344C2×#41—221no—
345C2×#41—221no—
346C2×#41—221no—
347C2×#41—221no—
348C2×#41—221no—
349C22×Q8—111no—
350C22×D4—112no—
351C22×D4—111no—
352C23×C4—112no—
353C23×C4C22×D1111yescharacteristic
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—21no—
364C2×M16—21no—
365C2×M16—112no—
366C2×M16—112no—
367C2×M16—112no—
368C2×M16—112no—
369C2×M16—112no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C2×M16—221no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16D4412yes—
384C2×M16D4412yes—
385C2×M16C22⋊D1112yes—
386C2×M16C22⋊D1112yes—
387C2×M16C22×D1112yes—
388C2×M16C22×D1112yes—
389C2×M16C22×D1112yes—
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—221no—
394C22×C8—221no—
395C22×C8—221no—
396#108—28no—
397#108—228no—
398#108—228no—
399#101—224no—
400#101—224no—
401#101—224no—
402#100—224no—
403#100—224no—
404#100—224no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11—21no—
411C2×C11—21no—
412C2×C11C2×#39611yescharacteristic
413D11—82no—
414C24—112no—
415C24Q8×D1111yescharacteristic
416#41—441no—
417#41—441no—
418#41—441no—
419#41—441no—
420#41—441no—
421#41—441no—
422#41—441no—
423#41—441no—
424#41—441no—
425#41—441no—
426#41—441no—
427#41—441no—
428#41—441no—
429#41—441no—
430#41—441no—
431#41—441no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C22×C4—112no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4C2×D4411yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4#433911yescharacteristic
460C22×C4#433911yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4#434111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4Q8×D1111yescharacteristic
466C22×C4#434311yescharacteristic
467C22×C4#434311yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—41no—
480M16—41no—
481M16—114no—
482M16—222no—
483M16—222no—
484M16—222no—
485M16—222no—
486M16—222no—
487M16—222no—
488M16—222no—
489M16—441no—
490M16—441no—
491M16—441no—
492M16—441no—
493M16C2×D4414yes—
494M16C2×C22⋊D1114yes—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—441no—
510C2×C8—441no—
511C2×C8—441no—
512C2×C8—441no—
513C11#2362211yescharacteristic, complemented, Sylow
514C23—81no—
515C23—222no—
516C23—222no—
517C23—222no—
518C23—882no—
519C23#6694911yescharacteristic
520C23#6694911yescharacteristic
521C23#6695011yescharacteristic
522C23#6695011yescharacteristic
523C23#6699911yescharacteristic
524C23#6699911yescharacteristic
525C23C2×Q8×D1111yescharacteristic
526Q8—441no—
527Q8—441no—
528Q8—441no—
529Q8—441no—
530D4—442no—
531D4—442no—
532D4—442no—
533D4—442no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—441no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4#6694811yescharacteristic
546C2×C4#6694811yescharacteristic
547C2×C4#6694811yescharacteristic
548C2×C4#6694811yescharacteristic
549C2×C4#6694911yescharacteristic
550C2×C4#6694911yescharacteristic
551C2×C4#6695011yescharacteristic
552C2×C4#6695011yescharacteristic
553C2×C4#6695111yescharacteristic
554C2×C4#6695111yescharacteristic
555C2×C4#6695111yescharacteristic
556C2×C4#6695111yescharacteristic
557C2×C4#6698311yescharacteristic
558C2×C4#6698311yescharacteristic
559C2×C4#6698311yescharacteristic
560C2×C4#6698311yescharacteristic
561C2×C4#6699211yescharacteristic
562C2×C4#6699211yescharacteristic
563C2×C4#6699211yescharacteristic
564C2×C4#6699211yescharacteristic
565C2×C4#6699911yescharacteristic
566C2×C4#6699911yescharacteristic
567C2×C4C22×D4411yescharacteristic
568C2×C4C2×#433911yescharacteristic
569C2×C4C2×D4×D1111yescharacteristic
570C2×C4C2×#434111yescharacteristic
571C2×C4C2×#434311yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—24no—
574C8—24no—
575C8—42no—
576C8—224no—
577C8—442no—
578C8—442no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—442no—
587C22—882no—
588C22—882no—
589C22—882no—
590C22#1062260711yescharacteristic
591C22#1062260711yescharacteristic
592C22#1062260711yescharacteristic
593C22#1062260711yescharacteristic
594C22C2×#6694911yescharacteristic
595C22C2×#6695011yescharacteristic
596C22C2×#6699911yescharacteristic
597C4—442no—
598C4#1062260711yescharacteristic
599C4#1062260711yescharacteristic
600C4#1062260711yescharacteristic
601C4#1062260711yescharacteristic
602C4C2×#6694811yescharacteristic
603C4C2×#6695111yescharacteristic
604C4C2×#6698311yescharacteristic
605C4C2×#6699211yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—882no—
614C2C2×#1062260711yescharacteristic
subgroupG/H
centerC4#10622607
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#430C2
socleC2×C11C2×#396
prime radicalC22×#4339C22
hypercenterC2×#430D11
hypocenterC11#23622
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#10622738C2semidirect
2. C2×#10622737C2semidirect
6. #13070016C2semidirect
7. #13070013C2semidirect
8. C2×C11⋊#338C2semidirect
9. C2×C11×#430C2semidirect
209. C2×#430D11semidirect
513. C11#23622semidirect

Maximal subgroups

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

subgroupindex
C2×#106227382
C2×#106227372
C2×#106227452
#130700162
#130700132
C2×C11⋊#3382
C2×C11×#4302
#2362211