Finite Group Databasebeta

← #14782726

Subgroups — #14782726

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622738C211yesmaximal, characteristic, complemented
2#13077136C211yesmaximal, characteristic
3#13077133C211yesmaximal, characteristic
4C2×#10622745C211yesmaximal, characteristic
5#13070082C214yesmaximal, complemented
6#13070075C214yesmaximal, complemented
7C2×#10622194C211yesmaximal, characteristic, complemented
8C2×#10622169C211yesmaximal, characteristic, complemented
9C2×C11×#344C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×#66888C2212yes—
18#10622746—22no—
19#10622745—22no—
20#10622745—22no—
21#10622744C2212yes—
22C2×#66887C2212yes—
23#10622738—22no—
24#10622738C2214yes—
25#10622733C2212yes—
26#10622726—22no—
27C2×#66883—22no—
28#10622617C2212yes—
29#10622615—22no—
30#10622614C2212yes—
31#10622579—22no—
32C11×#344C2214yes—
33#10622194C2214yes—
34#10622169C2214yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339D412yes—
48C2×#4339D412yes—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22C2311yescharacteristic
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×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16D412yes—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C22×C8×C11D412yes—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117C2312yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C22⋊Dic11—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979C2312yes—
78C2×C4⋊Dic11—21no—
79C2×C4×Dic11—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×#4318C2312yes—
91C2×#4318C2312yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94#66888—24no—
95#66887—24no—
96#66885—24no—
97#66883—28no—
98#66880—24no—
99#66874—24no—
100#66873—24no—
101#23652—111nomaximal, Sylow
102C24×C11#4111yescharacteristic
103C23×D11—21no—
104C22×C4×C11—41no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—22no—
120C2×C22⋊D11—22no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11—21no—
126C22×Dic11—41no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—22no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142#4339—41no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C2×D412yes—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C2×D412yes—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—41no—
168C11×M16—41no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11C2×D414yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—41no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—41no—
179C42×C11—22no—
180C42×C11—41no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C4⋊Dic11—22no—
184C4⋊Dic11—41no—
185C4×Dic11—22no—
186C4×Dic11—41no—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318—41no—
192#4318—41no—
193#4318—41no—
194#4318—41no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—41no—
199C2×C11⋊C8—41no—
200C2×C11⋊C8—41no—
201C2×#430—111no—
202#2896—111no—
203#2896—111no—
204C2×#413—111no—
205#2082—114no—
206#2081—114no—
207C2×#344—111no—
208C2×#344D1111yescharacteristic, complemented
209C2×H(3,ℤ/4)—111no—
210C23×C11—81no—
211C23×C11#12311yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12411yescharacteristic
215C23×C11#12611yescharacteristic
216C23×C11#12611yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C22×D11—22no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—82no—
222C2×C4×C11—42no—
223C2×C4×C11—82no—
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#12111yescharacteristic
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12311yescharacteristic
229C2×C4×C11#12311yescharacteristic
230C2×C4×C11#12311yescharacteristic
231C2×C4×C11#12311yescharacteristic
232C2×C4×C11#12311yescharacteristic
233C2×C4×C11#12311yescharacteristic
234C2×C4×C11#12311yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×C4×C11#12311yescharacteristic
237C2×C4×C11#12311yescharacteristic
238C2×C4×C11#12411yescharacteristic
239C2×C4×C11#12411yescharacteristic
240C2×C4×C11#12611yescharacteristic
241C2×C4×C11#12611yescharacteristic
242C2×C4×C11#12611yescharacteristic
243C2×C4×C11#12611yescharacteristic
244C2×C4×C11#12611yescharacteristic
245C2×C4×C11#12611yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—42no—
253C22⋊D11—42no—
254C22⋊D11—42no—
255C22⋊D11—42no—
256C2×Dic11—22no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—42no—
260C2×Dic11—82no—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—42no—
269Dic22—22no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—24no—
274C8×C11—42no—
275C11⋊C8—42no—
276C11⋊C8—42no—
277C22×#41—111no—
278C22×M16—111no—
279C22×M16—111no—
280C22×M16C2×D1111yescharacteristic
281C22×M16C2×D1111yescharacteristic
282C2×#117—111no—
283C2×#117C2×D1111yescharacteristic
284#430—114no—
285#430—222no—
286C2×#108—222no—
287#419—112no—
288#419—112no—
289#418—112no—
290#418—112no—
291#417—222no—
292#417—222no—
293#416—222no—
294#416—222no—
295#413—222no—
296#413—222no—
297C2×#101—112no—
298C2×#100—112no—
299#344—114no—
300#344C2×D1114yes—
301H(3,ℤ/4)—114no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11#39711yescharacteristic
310C22×C11#39711yescharacteristic
311C22×C11#39711yescharacteristic
312C22×C11#39711yescharacteristic
313C22×C11C2×#12311yescharacteristic
314C22×C11C2×#12411yescharacteristic
315C22×C11C2×#12611yescharacteristic
316C2×D11—42no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—82no—
320C4×C11—82no—
321C4×C11#39711yescharacteristic
322C4×C11#39711yescharacteristic
323C4×C11#39711yescharacteristic
324C4×C11#39711yescharacteristic
325C4×C11C2×#12111yescharacteristic
326C4×C11C2×#12311yescharacteristic
327C4×C11C2×#12311yescharacteristic
328C4×C11C2×#12611yescharacteristic
329Dic11—42no—
330Dic11—82no—
331C2×#41—112no—
332C2×#41—112no—
333C2×#41—221no—
334C2×#41—221no—
335C2×#41—221no—
336C2×#41—221no—
337C2×#41—221no—
338C2×#41—221no—
339C2×#41—221no—
340C2×#41—221no—
341C2×#41—221no—
342C2×#41—221no—
343C22×Q8—111no—
344C22×D4—111no—
345C22×D4—221no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—112no—
358C2×M16—112no—
359C2×M16—221no—
360C2×M16—221no—
361C2×M16—221no—
362C2×M16—221no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16D4412yes—
370C2×M16C22×D1112yes—
371C2×M16C22×D1112yes—
372C22×C8—21no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8D4412yes—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—112no—
380#117—221no—
381#117—221no—
382#117—221no—
383#117C22×D1112yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—221no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—221no—
388C2×C42—21no—
389C2×C42—221no—
390#108—228no—
391#103—224no—
392#103—224no—
393#102—224no—
394#102—224no—
395#101—224no—
396#100—224no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11C2×#39711yescharacteristic
405D11—82no—
406C24—221no—
407C24#433911yescharacteristic
408#41—222no—
409#41—222no—
410#41—222no—
411#41—222no—
412#41—222no—
413#41—222no—
414#41—222no—
415#41—222no—
416#41—441no—
417#41—441no—
418#41—441no—
419#41—441no—
420#41—441no—
421#41—441no—
422#41—441no—
423#41—441no—
424C2×Q8—112no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—221no—
429C2×Q8—221no—
430C2×D4—112no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—441no—
441C2×D4—441no—
442C22×C4—41no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4#433911yescharacteristic
454C22×C4#433911yescharacteristic
455C22×C4#433911yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4#434111yescharacteristic
459C22×C4#434111yescharacteristic
460C22×C4#434111yescharacteristic
461C22×C4#434111yescharacteristic
462C22×C4#434311yescharacteristic
463C22×C4#434311yescharacteristic
464C22×C4C23×D1111yescharacteristic
465M16—22no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—41no—
472M16—41no—
473M16—222no—
474M16—222no—
475M16—222no—
476M16—222no—
477M16—441no—
478M16—441no—
479M16—441no—
480M16—441no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—441no—
489C2×C8—441no—
490C2×C8—441no—
491C2×C8—441no—
492C2×C8C2×D4414yes—
493C4⋊C4—22no—
494C4⋊C4—41no—
495C4⋊C4—222no—
496C4⋊C4—441no—
497C22⋊C4—22no—
498C22⋊C4—41no—
499C22⋊C4—222no—
500C22⋊C4—441no—
501C42—22no—
502C42—41no—
503C42—222no—
504C42—441no—
505C11#2365211yescharacteristic, complemented, Sylow
506C23—81no—
507C23—222no—
508C23—441no—
509C23—441no—
510C23—882no—
511C23#6692811yescharacteristic
512C23#6692811yescharacteristic
513C23#6693611yescharacteristic
514C23#6693611yescharacteristic
515C23#6695111yescharacteristic
516C23#6695111yescharacteristic
517C23C2×#433911yescharacteristic
518Q8—222no—
519Q8—222no—
520Q8—441no—
521Q8—441no—
522D4—222no—
523D4—222no—
524D4—442no—
525D4—442no—
526D4—442no—
527D4—442no—
528D4—441no—
529D4—441no—
530C2×C4—42no—
531C2×C4—82no—
532C2×C4—222no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—882no—
541C2×C4#6692811yescharacteristic
542C2×C4#6692811yescharacteristic
543C2×C4#6693611yescharacteristic
544C2×C4#6693611yescharacteristic
545C2×C4#6693611yescharacteristic
546C2×C4#6693611yescharacteristic
547C2×C4#6693611yescharacteristic
548C2×C4#6693611yescharacteristic
549C2×C4#6693911yescharacteristic
550C2×C4#6693911yescharacteristic
551C2×C4#6693911yescharacteristic
552C2×C4#6693911yescharacteristic
553C2×C4#6694811yescharacteristic
554C2×C4#6694811yescharacteristic
555C2×C4#6694811yescharacteristic
556C2×C4#6694811yescharacteristic
557C2×C4#6695111yescharacteristic
558C2×C4#6695111yescharacteristic
559C2×C4#6695111yescharacteristic
560C2×C4#6695111yescharacteristic
561C2×C4#6695111yescharacteristic
562C2×C4#6695111yescharacteristic
563C2×C4C22×D4411yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×#434111yescharacteristic
567C2×C4C2×#434111yescharacteristic
568C2×C4C2×#434311yescharacteristic
569C8—24no—
570C8—42no—
571C8—442no—
572C8—442no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—442no—
581C22—882no—
582C22—882no—
583C22—882no—
584C22#1062228711yescharacteristic
585C22#1062228711yescharacteristic
586C22#1062228711yescharacteristic
587C22#1062228711yescharacteristic
588C22C2×#6692811yescharacteristic
589C22C2×#6693611yescharacteristic
590C22C2×#6695111yescharacteristic
591C4—82no—
592C4—442no—
593C4—882no—
594C4#1062228711yescharacteristic
595C4#1062228711yescharacteristic
596C4#1062228711yescharacteristic
597C4#1062228711yescharacteristic
598C4C2×#6693611yescharacteristic
599C4C2×#6693911yescharacteristic
600C4C2×#6694811yescharacteristic
601C4C2×#6695111yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—882no—
610C2C2×#1062228711yescharacteristic
subgroupG/H
centerC4#10622287
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#344C2
socleC2×C11C2×#397
prime radicalC22×#4339C22
hypercenterC2×#344D11
hypocenterC11#23652
LCSG ▷ C22×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
1. C2×#10622738C2semidirect
5. #13070082C2semidirect
6. #13070075C2semidirect
7. C2×#10622194C2semidirect
8. C2×#10622169C2semidirect
9. C2×C11×#344C2semidirect
208. C2×#344D11semidirect
505. C11#23652semidirect

Maximal subgroups

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

subgroupindex
C2×#106227382
#130771362
#130771332
C2×#106227452
#130700822
#130700752
C2×#106221942
C2×#106221692
C2×C11×#3442
#2365211