Finite Group Databasebeta

← #14783648

Subgroups — #14783648

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic, complemented
2C2×D11×#106C211yesmaximal, characteristic, complemented
3C2×#10622384C211yesmaximal, characteristic
4C2×#10622385C211yesmaximal, characteristic
5#13071237C211yesmaximal, characteristic, complemented
6#13071206C211yesmaximal, characteristic
7#13070165C211yesmaximal, characteristic, complemented
8#13070163C211yesmaximal, characteristic, complemented
9#13070160C211yesmaximal, characteristic, complemented
10#13070156C211yesmaximal, characteristic, complemented
11#13070147C211yesmaximal, characteristic, complemented
12#13070137C211yesmaximal, characteristic, complemented
13#13070135C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#2094C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#384C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622602—22no—
37#10622590C2211yescharacteristic
38#10622589C2211yescharacteristic
39#10622587C2211yescharacteristic
40#10622585—22no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622569—22no—
48#10622555—22no—
49#10622549C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622474—24no—
52D11×#106—24no—
53#10622385—24no—
54#10622384—24no—
55C11×#336C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C2×#4341—22no—
63C2×#4341—22no—
64C2×#4341—22no—
65C2×#4341—22no—
66C2×#4341—22no—
67C2×#4341Q814yes—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D412yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4D412yes—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4313—22no—
95C2×#4313—22no—
96C2×#4313D414yes—
97C2×C8×D11—22no—
98C2×C8×D11—22no—
99C2×C8×D11D414yes—
100#66945—22no—
101#66945—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106#66925—22no—
107#66925—22no—
108C11×#106—22no—
109C11×#106—22no—
110C11×#102—22no—
111C11×#102—22no—
112#66896—22no—
113#66896—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118#66882—22no—
119#66881—22no—
120#66880—22no—
121#66880—22no—
122#66874—22no—
123#66874—22no—
124#66872—22no—
125#66872—22no—
126#66872—22no—
127#66871—22no—
128#23738—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11C2×D411yescharacteristic
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11C2×Q812yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C22×Dic11—24no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11C2×D412yes—
153C22×Dic11C2×D411yescharacteristic
154#4341—28no—
155#4341—28no—
156#4341—44no—
157#4341—44no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—82no—
161C2×C4×D11—82no—
162C2×C4×D11C2×D412yes—
163C2×C4×D11C2×D412yes—
164C2×C4×D11C2×Q812yes—
165C2×C4×D11#4112yes—
166C2×C4×D11#4112yes—
167C2×C4×D11#4112yes—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22C2×Q812yes—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—82no—
187C11×C22⋊C4—82no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—82no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199Dic11⋊C4—24no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—82no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8C2×D412yes—
212#4313—28no—
213C8×D11—28no—
214C2×#428—111no—
215C22×#106—111no—
216C2×#417—111no—
217C2×#416—111no—
218#2317—111no—
219#2311—111no—
220#2097—111no—
221#2097—111no—
222#2096—111no—
223#2096—111no—
224#2094—111no—
225#2094D1111yescharacteristic, complemented
226#2092—111no—
227#2092—111no—
228#1729—111no—
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—22no—
237C22×D11C22⋊Q812yes—
238C22×D11#12312yes—
239C22×D11#12712yes—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×Q811yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C22⋊D11—48no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—48no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11C22⋊Q812yes—
274C2×Dic11#12312yes—
275C2×Dic11#12712yes—
276C4×D11—84no—
277C4×D11—84no—
278C4×D11C22⋊Q814yes—
279C4×D11C22⋊Q814yes—
280C4×D11#12314yes—
281C4×D11#12314yes—
282Dic22—22no—
283Dic22—22no—
284Dic22—41no—
285Dic22—41no—
286C8×C11—22no—
287C8×C11—22no—
288C11⋊C8—22no—
289C11⋊C8—22no—
290C22×#41—111no—
291C22×M16—111no—
292C23×C8—111no—
293C2×#117—111no—
294C2×#117—111no—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—111no—
297#428—224no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106—224no—
305C2×#106C2×D1111yescharacteristic
306C2×#106C2×D1111yescharacteristic
307#417—224no—
308#416—224no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102C2×D1111yescharacteristic
316C2×#102C2×D1111yescharacteristic
317#391—111no—
318#391—111no—
319#390—111no—
320#390C2×D1111yescharacteristic
321#389—222no—
322#386—222no—
323#385—222no—
324#384—111no—
325#384C2×D1111yescharacteristic
326#382—111no—
327#382—111no—
328#380—222no—
329#336—111no—
330#336—111no—
331#336—111no—
332#336C2×D1111yescharacteristic
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—82no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11C2×C22⋊Q811yescharacteristic
339C22×C11C2×#12311yescharacteristic
340C22×C11C2×#12711yescharacteristic
341C22×C11#57712yes—
342C22×C11#57712yes—
343C2×D11—24no—
344C2×D11—24no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11#39914yes—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×C22⋊Q811yescharacteristic
353C4×C11C2×C22⋊Q811yescharacteristic
354C4×C11C2×#12311yescharacteristic
355C4×C11C2×#12311yescharacteristic
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360Dic11—81no—
361Dic11#39914yes—
362C2×#41—114no—
363C2×#41—222no—
364C2×#41—222no—
365C2×#41—222no—
366C2×#41—222no—
367C2×#41—222no—
368C22×Q8—111no—
369C22×D4—221no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—111no—
372C23×C4—221no—
373C23×C4—221no—
374C23×C4—221no—
375C2×M16—114no—
376C2×M16—222no—
377C2×M16—222no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—114no—
381C22×C8—222no—
382C22×C8—222no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#117—222no—
386#117—222no—
387#117—222no—
388#117—222no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—112no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—22no—
405C2×C22⋊C4—112no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—222no—
408C2×C42—111no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411#107—222no—
412#107—222no—
413#106—22no—
414#106—22no—
415#106—222no—
416#106—222no—
417#106—222no—
418#106—222no—
419#103—222no—
420#103—222no—
421#103—222no—
422#103—222no—
423#102—22no—
424#102—22no—
425#102—222no—
426#102—222no—
427#95—222no—
428#95—222no—
429#95—222no—
430#95—222no—
431C2×C11—82no—
432C2×C11C2×#39911yescharacteristic
433C2×C11#308412yes—
434C2×C11#309912yes—
435C2×C11#315411yescharacteristic
436C2×C11#315411yescharacteristic
437D11—24no—
438C24—21no—
439C24—111no—
440#41—228no—
441#41—228no—
442#41—444no—
443#41—444no—
444C2×Q8—112no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—224no—
456C2×D4—442no—
457C2×D4—442no—
458C2×D4Q8×D1112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—111no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—224no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—882no—
480C22×C4—882no—
481C22×C4D4×D1112yes—
482C22×C4C23×D1111yescharacteristic
483M16—228no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—228no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8D4×D1112yes—
496C2×C8D4×D1112yes—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—82no—
504C4⋊C4—224no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—882no—
514C22⋊C4—82no—
515C22⋊C4—224no—
516C22⋊C4—442no—
517C22⋊C4—882no—
518C42—21no—
519C42—21no—
520C42—221no—
521C42—221no—
522C42—442no—
523C11#2373811yescharacteristic, complemented, Sylow
524C23—22no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—112no—
530C23—112no—
531C23—112no—
532C23—222no—
533C23—222no—
534C23C2×D4×D1111yescharacteristic
535Q8—222no—
536Q8—222no—
537Q8—441no—
538Q8—441no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—448no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—114no—
557C2×C4—114no—
558C2×C4—114no—
559C2×C4—114no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—448no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—884no—
574C2×C4—884no—
575C2×C4C2×D4×D1111yescharacteristic
576C2×C4C2×D4×D1111yescharacteristic
577C2×C4C2×Q8×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C8—22no—
582C8—22no—
583C8—222no—
584C8—222no—
585C22—44no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—82no—
590C22—114no—
591C22—222no—
592C22—222no—
593C22—224no—
594C22—224no—
595C22D11×C22⋊Q811yescharacteristic
596C22D11×#12311yescharacteristic
597C22D11×#12711yescharacteristic
598C22#1062329312yes—
599C22#1062330612yes—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—114no—
605C4—442no—
606C4—442no—
607C4—881no—
608C4—881no—
609C4—881no—
610C4D11×C22⋊Q811yescharacteristic
611C4D11×C22⋊Q811yescharacteristic
612C4D11×#12311yescharacteristic
613C4D11×#12311yescharacteristic
614C2—82no—
615C2—224no—
616C2D11×#39911yescharacteristic
617C2#1307847312yes—
618C2#1307860612yes—
619C2#1307908511yescharacteristic
620C2#1307908911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2094C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenter#2094D11
hypocenterC11#23738
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. C2×#10622474C2semidirect
2. C2×D11×#106C2semidirect
5. #13071237C2semidirect
7. #13070165C2semidirect
8. #13070163C2semidirect
9. #13070160C2semidirect
10. #13070156C2semidirect
11. #13070147C2semidirect
12. #13070137C2semidirect
13. #13070135C2semidirect
14. #13068311C2semidirect
15. C11×#2094C2semidirect
225. #2094D11semidirect
523. C11#23738semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
C2×D11×#1062
C2×#106223842
C2×#106223852
#130712372
#130712062
#130701652
#130701632
#130701602
#130701562
#130701472
#130701372
#130701352
#130683112
C11×#20942
#2373811