Finite Group Databasebeta

← #14781121

Subgroups — #14781121

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic
3#13071208C211yesmaximal, characteristic
4#13069765C212yesmaximal, complemented
5#13069760C212yesmaximal, complemented
6#13069755C212yesmaximal, complemented
7#13069750C212yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×#10622189C211yesmaximal, characteristic, complemented
10#13068312C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10623050—24no—
20#10623050—24no—
21C2×#66943C2212yes—
22C2×#66941C2212yes—
23C2×#66931—22no—
24C2×#66923—21no—
25C2×#66922—21no—
26C11×#416—24no—
27C2×C11×#103C2211yescharacteristic
28C2×C11×#103C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31#10622845—24no—
32#10622843C2212yes—
33C2×#66899C2212yes—
34#10622834C2212yes—
35#10622833—22no—
36C2×#66896C2212yes—
37#10622825—21no—
38#10622825—21no—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41Q814yescomplemented
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—21no—
58C22×Dic22—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11—22no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#117—22no—
65C11×#117D414yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11D412yes—
73#66979—22no—
74#66979—22no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11D411yescharacteristic
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11D414yes—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2312yes—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11C2312yes—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C22×C11⋊C8C2312yes—
93#66943—24no—
94#66943—24no—
95#66941—24no—
96#66941—24no—
97#66931—216no—
98#66923—28no—
99#66922—28no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#102—22no—
103C11×#102—22no—
104#66899—24no—
105#66896—24no—
106C11⋊#95—22no—
107C11⋊#95—22no—
108#23458—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C11×#41—28no—
112C11×#41—28no—
113C11×#41—44no—
114C11×#41—44no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C2×Q812yes—
121C2×D4×C11—24no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11C2×Q812yes—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×Q812yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—42no—
148C22×Dic11—81no—
149C22×Dic11—81no—
150C22×Dic11—81no—
151C22×Dic11—81no—
152C22×Dic11C2×D412yes—
153C22×Dic11C2×D412yes—
154C2×Dic22—28no—
155C2×Dic22—82no—
156C2×Dic22—82no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—44no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C2×D412yes—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—24no—
169C42×C11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—82no—
172C22⋊Dic11—82no—
173C4⋊Dic11—28no—
174C4⋊Dic11—22no—
175C4⋊Dic11—24no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—42no—
181C4⋊Dic11C2×D414yes—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186#4318—44no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×#544—111no—
191C2×#417—111no—
192C2×#416D1111yescharacteristic
193#2311—111no—
194#2026—112no—
195#2025—112no—
196#2024—112no—
197#2023—112no—
198#1736—111no—
199C2×#340—111no—
200#1729—111no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11#12012yes—
213C23×C11C22⋊Q812yes—
214C23×C11#12412yes—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—48no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—48no—
235C2×C4×C11#12012yes—
236C2×C4×C11C22⋊Q814yes—
237C2×C4×C11C22⋊Q812yes—
238C2×C4×C11C22⋊Q814yes—
239C2×C4×C11#12414yes—
240C2×C4×C11#12412yes—
241C2×C4×C11#12414yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×Q811yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—84no—
261C2×Dic11—84no—
262Dic22—88no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—42no—
266C22×#41C2×D1111yescharacteristic
267C22×M16—111no—
268C23×C8C2×D1111yescharacteristic
269#544—224no—
270#544—224no—
271C2×C4⋊Q8—112no—
272C2×C4⋊Q8—221no—
273C2×#125—112no—
274C2×#125—221no—
275C2×C22⋊Q8—222no—
276C2×#117—111no—
277C2×#117C2×D1111yescharacteristic
278C22×C4⋊C4—111no—
279C22×C4⋊C4—111no—
280#417—224no—
281#416—24no—
282C2×#103—112no—
283C2×#103C2×D1111yescharacteristic
284C2×#103C2×D1111yescharacteristic
285C2×#102—112no—
286C2×#102C2×D1111yescharacteristic
287C2×#102C2×D1111yescharacteristic
288#391—112no—
289#390—112no—
290#386—222no—
291#380—221no—
292#380—221no—
293#340—112no—
294#340—112no—
295#340—112no—
296#340—112no—
297#336—112no—
298#336—112no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11#39314yes—
313C22×C11C2×#12011yescharacteristic
314C22×C11C2×C22⋊Q811yescharacteristic
315C22×C11C2×#12411yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57811yescharacteristic
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11#39314yes—
324C4×C11C2×C22⋊Q811yescharacteristic
325C4×C11C2×C22⋊Q811yescharacteristic
326C4×C11C2×#12411yescharacteristic
327C4×C11C2×#12411yescharacteristic
328Dic11—42no—
329Dic11—44no—
330Dic11—42no—
331Dic11—82no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—22no—
337C2×#41Dic2214yescomplemented
338C22×Q8—222no—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—21no—
341C22×D4C22×D1111yescharacteristic
342C23×C4—21no—
343C23×C4—221no—
344C23×C4—221no—
345C23×C4C22×D1111yescharacteristic
346C2×M16—222no—
347C2×M16—222no—
348C2×M16—222no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—112no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C4⋊Q8—228no—
356C4⋊Q8—224no—
357C4⋊Q8—224no—
358#125—228no—
359#125—224no—
360#125—224no—
361C22⋊Q8—2216no—
362#117—22no—
363#117—222no—
364#117—222no—
365#117C22⋊D1114yes—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—112no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—112no—
387#103—22no—
388#103—22no—
389#103—224no—
390#102—22no—
391#102—22no—
392#102—224no—
393#95—222no—
394#95—222no—
395C2×C11—24no—
396C2×C11—82no—
397C2×C11C2×#39311yescharacteristic
398C2×C11#301211yescharacteristic
399C2×C11#301311yescharacteristic
400C2×C11#308311yescharacteristic
401C2×C11#308411yescharacteristic
402C2×C11#313611yescharacteristic
403C2×C11#313711yescharacteristic
404C24—21no—
405C24D4×D1111yescharacteristic
406#41—28no—
407#41—28no—
408#41—44no—
409#41—44no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—228no—
416C2×Q8—882no—
417C2×Q8—882no—
418C2×Q8C2×Dic2212yes—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×Dic2212yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—222no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—442no—
440C22×C4—881no—
441C22×C4—881no—
442C22×C4—881no—
443C22×C4—881no—
444C22×C4C2×Dic2212yes—
445C22×C4#433912yes—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1112yes—
448C22×C4#434112yes—
449C22×C4#434112yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C23×D1111yescharacteristic
452M16—444no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—44no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—114no—
466C4⋊C4—228no—
467C4⋊C4—228no—
468C4⋊C4—228no—
469C4⋊C4—224no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—442no—
476C4⋊C4C2×C22⋊D1112yes—
477C4⋊C4C2×C22⋊D1112yes—
478C22⋊C4—24no—
479C22⋊C4—224no—
480C22⋊C4—882no—
481C22⋊C4—882no—
482C42—24no—
483C42—222no—
484C42—222no—
485C11#2345811yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23#6693112yes—
498C23#6693812yes—
499C23#6699012yes—
500C23C2×D4×D1111yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505Q8—888no—
506D4—22no—
507D4—22no—
508D4—48no—
509D4—41no—
510D4—41no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—48no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—884no—
534C2×C4—884no—
535C2×C4#6693114yes—
536C2×C4#6693112yes—
537C2×C4#6693814yes—
538C2×C4#6693812yes—
539C2×C4#6697714yes—
540C2×C4#6698914yes—
541C2×C4#6699012yes—
542C2×C4C22×Dic2211yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C2×C4C2×#434111yescharacteristic
547C2×C4C22×C22⋊D1111yescharacteristic
548C8—41no—
549C8—41no—
550C8—442no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22#1062256014yes—
565C22C2×#6693111yescharacteristic
566C22C2×#6693811yescharacteristic
567C22#1062330011yescharacteristic
568C22#1062330111yescharacteristic
569C22#1062330111yescharacteristic
570C22#1062330211yescharacteristic
571C22C2×#6699011yescharacteristic
572C4—42no—
573C4—42no—
574C4—42no—
575C4—442no—
576C4—444no—
577C4—442no—
578C4—882no—
579C4#1062256014yes—
580C4C2×#6693111yescharacteristic
581C4C2×#6693811yescharacteristic
582C4C2×#6697711yescharacteristic
583C4C2×#6698911yescharacteristic
584C2—24no—
585C2—82no—
586C2C2×#1062256011yescharacteristic
587C2#1307791611yescharacteristic
588C2#1307792711yescharacteristic
589C2#1307846511yescharacteristic
590C2#1307847611yescharacteristic
591C2#1307897411yescharacteristic
592C2#1307898511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#416D11
hypocenterC11#23458
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
4. #13069765C2semidirect
5. #13069760C2semidirect
6. #13069755C2semidirect
7. #13069750C2semidirect
8. #13068337C2semidirect
9. C2×#10622189C2semidirect
10. #13068312C2semidirect
50. C2×C11×#41Q8semidirect
337. C2×#41Dic22semidirect
485. C11#23458semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106228452
#130712082
#130697652
#130697602
#130697552
#130697502
#130683372
C2×#106221892
#130683122
C2×C11×#4162
#2345811