Finite Group Databasebeta

← #14743375

Subgroups — #14743375

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080923C211yesmaximal, characteristic, complemented
2#13080429C211yesmaximal, characteristic, complemented
3#13080334C211yesmaximal, characteristic, complemented
4#13068277C211yesmaximal, characteristic, complemented
5#13068174C211yesmaximal, characteristic, complemented
6#13068051C211yesmaximal, characteristic, complemented
7#13068039C211yesmaximal, characteristic, complemented
8#13067979C211yesmaximal, characteristic, complemented
9#13067900C211yesmaximal, characteristic, complemented
10#13067899C211yesmaximal, characteristic, complemented
11#13067795C211yesmaximal, characteristic, complemented
12#13067704C211yesmaximal, characteristic, complemented
13#13067445C211yesmaximal, characteristic, complemented
14#13067440C211yesmaximal, characteristic, complemented
15C11×#3294C211yesmaximal, characteristic, complemented
16C11×#547C2211yescharacteristic
17D42×C11C2211yescharacteristic
18C2×#67003—21no—
19#10623086C2211yescharacteristic
20#10623082C2211yescharacteristic, complemented
21C11×#486C2211yescharacteristic
22C11×#480—21no—
23C11×#474C2211yescharacteristic
24C11×#466—21no—
25C11×#459C2211yescharacteristic
26C11×#447—21no—
27C4×C11×D8C2211yescharacteristic
28C8×D4×C11C2211yescharacteristic
29C2×C11×#102—21no—
30#10622852—21no—
31#10622830—21no—
32C2×#66896—21no—
33#10622771—21no—
34#10622705C2211yescharacteristic, complemented
35#10622696C2211yescharacteristic, complemented
36#10622692C2211yescharacteristic, complemented
37#10622685C2211yescharacteristic
38#10622683C2211yescharacteristic
39#10622683C2211yescharacteristic
40#10622664—21no—
41#10622660—21no—
42#10622651—21no—
43#10622646—21no—
44#10622632C2211yescharacteristic
45#10622632C2211yescharacteristic, complemented
46C4×#4323C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic, complemented
49#10622620C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622497—21no—
52#10622393—21no—
53#10622384—21no—
54#10622301C2211yescharacteristic, complemented
55#10622294C2211yescharacteristic, complemented
56#10622185C2211yescharacteristic, complemented
57#10622182C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59D4⋊(C11⋊C8)C2211yescharacteristic
60D4⋊(C11⋊C8)C2211yescharacteristic, complemented
61#10622124C2211yescharacteristic, complemented
62#10622121C2211yescharacteristic, complemented
63#10622120C2211yescharacteristic, complemented
64#10622117C2211yescharacteristic, complemented
65#10622095C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C2×C11×#41—21no—
68C22×D4×C11—21no—
69C22×D4×C11—21no—
70C2×#4341—21no—
71C2×#4339—21no—
72C2×C11×D8—21no—
73C2×C11×D8D411yescharacteristic
74C22×C8×C11—21no—
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127C2311yescharacteristic
77C11×#123—41no—
78C11×C22⋊Q8—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121—21no—
82C11×#120—41no—
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C2×C11×C4⋊C4—21no—
87#67003—44no—
88C2×#4326—21no—
89C2×#4326—21no—
90C2×#4325—21no—
91#66991—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95C2×#4323D411yescharacteristic
96#66983—21no—
97C2×C4⋊Dic11—21no—
98#66977—21no—
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101C2×#4313—21no—
102#66950—21no—
103C4⋊C4×D11—21no—
104#66939—41no—
105#66936—41no—
106C4×D44C2311yescharacteristic
107#66922C2311yescharacteristic
108#66922C2311yescharacteristic
109C11×#107—21no—
110C11×#107D411yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#102—21no—
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—21no—
116C11×#102D411yescharacteristic
117C11×#102D411yescharacteristic
118C11×C22⋊C8—21no—
119C4×C8×C11C2311yescharacteristic
120#66899—21no—
121#66896—21no—
122#66896—21no—
123#66896—21no—
124#66896—21no—
125#66896—21no—
126#66896—41no—
127#66896D411yescharacteristic
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130(C2×D11)⋊C8—21no—
131#66880—21no—
132#66880—21no—
133#66874—21no—
134#66874—21no—
135#66873D411yescharacteristic
136#66872—41no—
137#66871—21no—
138#66871—21no—
139#66871D411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19772—111nomaximal, Sylow
146C24×C11—41no—
147C11×#41—42no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—41no—
158C2×D4×C11—81no—
159C2×D4×C11—81no—
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C2×C22⋊D11—41no—
168C2×C22⋊D11—41no—
169C22×Dic11—41no—
170#4341—42no—
171#4341—81no—
172#4339—42no—
173#4339—81no—
174C2×D44C2×D411yescharacteristic
175C2×C4×D11—21no—
176C2×C4×D11—41no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C11×D8—22no—
180C11×D8—81no—
181C2×C8×C11—21no—
182C2×C8×C11—81no—
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—41no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D411yescharacteristic
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—41no—
195C11×C22⋊C4—41no—
196C42×C11C2411yescharacteristic
197C22⋊Dic11—41no—
198#4326—42no—
199#4326—81no—
200#4325—42no—
201#4324—42no—
202#4324—81no—
203#4323—22no—
204#4323—81no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—41no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—41no—
212C4⋊Dic11C2×D411yescharacteristic
213Dic11⋊C4—41no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—42no—
219C2×C11⋊C8—81no—
220C2×C11⋊C8C2×D411yescharacteristic
221C2×C11⋊C8C2×D411yescharacteristic
222#4313—81no—
223#3330—111no—
224#3294—111no—
225#3294D1111yescharacteristic, complemented
226#3283—111no—
227#1720—111no—
228#1701—111no—
229#1681—111no—
230#1679—111no—
231#1669—111no—
232#1654—111no—
233#1654—111no—
234#1639—111no—
235#1625—111no—
236#1581—111no—
237#1580—111no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—41no—
242C23×C11—82no—
243C23×C11—82no—
244C23×C11—161no—
245C22×D11—21no—
246Q8×C11—41no—
247Q8×C11—41no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—21no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—81no—
257D4×C11—82no—
258D4×C11—82no—
259D4×C11—82no—
260D4×C11#13512yescomplemented
261D4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—82no—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C22⋊D11—82no—
277C22⋊D11—82no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—82no—
282D44—21no—
283D44—21no—
284C4×D11—41no—
285C4×D11—41no—
286C4×D11—82no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—41no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C2×#135—221no—
301#547—111no—
302#547—111no—
303#547C2×D1111yescharacteristic
304D42C2×D1111yescharacteristic
305#498—111no—
306#494—111no—
307#487—111no—
308#486—111no—
309#486—111no—
310#486C2×D1111yescharacteristic
311#484—221no—
312#480—21no—
313#480—221no—
314#474—111no—
315#474—111no—
316#474C2×D1111yescharacteristic
317#468—221no—
318#467—221no—
319#466—21no—
320#466—221no—
321#461—111no—
322#461—111no—
323#461—111no—
324#459—111no—
325#459C2×D1111yescharacteristic
326#452—221no—
327#452—221no—
328#449—221no—
329#447—21no—
330#447—221no—
331C4×D8—111no—
332C4×D8C2×D1111yescharacteristic
333#436—111no—
334C8×D4—111no—
335C8×D4—111no—
336C8×D4C2×D1111yescharacteristic
337#417—221no—
338C2×#102—21no—
339C2×#102—221no—
340#335—111no—
341#334—111no—
342#332—111no—
343#332—111no—
344#332—111no—
345#331—111no—
346D4⋊C8—111no—
347D4⋊C8—111no—
348D4⋊C8—111no—
349D4⋊C8—111no—
350#322—111no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—164no—
364C22×C11D4211yescharacteristic
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C4×C11—21no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11C2×#13511yescharacteristic
374C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
375C4×C11#57611yescharacteristic
376C4×C11#57611yescharacteristic
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380C2×#41—21no—
381C2×#41—221no—
382C2×#41—221no—
383C22×D4—21no—
384C22×D4—21no—
385#135—444no—
386C2×Q16—221no—
387C2×Q16—221no—
388C2×SD16—221no—
389C2×SD16—221no—
390C2×SD16—221no—
391C2×D8—21no—
392C2×D8—111no—
393C2×D8—221no—
394C2×D8C22⋊D1111yescharacteristic
395C2×M16—221no—
396C22×C8—21no—
397C22×C8—221no—
398C22×C8—221no—
399C4⋊Q8—111no—
400C4⋊Q8—111no—
401C4⋊Q8C22×D1111yescharacteristic
402#127C22×D1111yescharacteristic
403#123—41no—
404#123—441no—
405#123—441no—
406C22⋊Q8—21no—
407C22⋊Q8—221no—
408C22⋊Q8—221no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—221no—
413#121—221no—
414#120—41no—
415C4×D4—111no—
416C4×D4C22×D1111yescharacteristic
417C4×D4C22×D1111yescharacteristic
418C4×D4C22×D1111yescharacteristic
419C2×C4⋊C4—21no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422#107—21no—
423#107—111no—
424#107—221no—
425#107—221no—
426#107C22⋊D1111yescharacteristic
427#106—441no—
428C4⋊C8—111no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8C22×D1111yescharacteristic
432#103—221no—
433#103—221no—
434#103—221no—
435#103—221no—
436#103—221no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—111no—
442#102—111no—
443#102—221no—
444#102—221no—
445#102—221no—
446#102—221no—
447#102—221no—
448#102—441no—
449#102C22⋊D1111yescharacteristic
450#102C22⋊D1111yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—221no—
453C22⋊C8—221no—
454C22⋊C8—221no—
455C4×C8—111no—
456C4×C8—111no—
457C4×C8C22×D1111yescharacteristic
458C2×C11—42no—
459C2×C11—42no—
460C2×C11—81no—
461C2×C11—161no—
462C2×C11#326411yescharacteristic
463C2×C11#328011yescharacteristic
464C2×C11#328911yescharacteristic
465D11—81no—
466C24—41no—
467#41—42no—
468#41—81no—
469#41—442no—
470#41—442no—
471#41—881no—
472#41—881no—
473C2×Q8—21no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—41no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4—111no—
487C2×D4—441no—
488C2×D4—441no—
489C2×D4D4×D1111yescharacteristic
490C2×D4C2×C22⋊D1111yescharacteristic
491C2×D4C2×C22⋊D1111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—221no—
497C22×C4—441no—
498C22×C4—441no—
499Q16—442no—
500Q16—881no—
501SD16—442no—
502SD16—442no—
503SD16—881no—
504D8—22no—
505D8—81no—
506D8—222no—
507D8—881no—
508M16—881no—
509C2×C8—21no—
510C2×C8—81no—
511C2×C8—111no—
512C2×C8—111no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—442no—
518C2×C8—881no—
519C2×C8C2×C22⋊D1111yescharacteristic
520C2×C8C2×C22⋊D1111yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—111no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—441no—
530C4⋊C4—441no—
531C4⋊C4D4×D1111yescharacteristic
532C4⋊C4C2×C22⋊D1111yescharacteristic
533C4⋊C4C2×C22⋊D1111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—221no—
540C22⋊C4—441no—
541C22⋊C4—441no—
542C42C23×D1111yescharacteristic
543C11#1977211yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—41no—
548C23—82no—
549C23—82no—
550C23—161no—
551C23—221no—
552Q8—41no—
553Q8—41no—
554Q8—441no—
555Q8—441no—
556Q8—441no—
557Q8—441no—
558D4—21no—
559D4—21no—
560D4—21no—
561D4—21no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570D4—221no—
571D4—221no—
572D4—882no—
573D4—882no—
574D4#6696412yes—
575D4#6700312yescomplemented
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—221no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—882no—
593C2×C4—882no—
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4C22×C22⋊D1111yescharacteristic
597C8—21no—
598C8—21no—
599C8—41no—
600C8—221no—
601C8—221no—
602C8—441no—
603C8—441no—
604C8—441no—
605C8—441no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—164no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22D4×C22⋊D1111yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—441no—
629C4—881no—
630C4—881no—
631C4C2×#6696411yescharacteristic
632C4#1062328811yescharacteristic
633C4C2×#6700311yescharacteristic
634C4#1062336611yescharacteristic
635C2—42no—
636C2—42no—
637C2—81no—
638C2—161no—
639C2—881no—
640C2#1308009611yescharacteristic
641C2#1308029711yescharacteristic
642C2#1308038911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3294C2
socleC22×C11D42
hypercenter#3294D11
hypocenterC11#19772
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #13080923C2semidirect
2. #13080429C2semidirect
3. #13080334C2semidirect
4. #13068277C2semidirect
5. #13068174C2semidirect
6. #13068051C2semidirect
7. #13068039C2semidirect
8. #13067979C2semidirect
9. #13067900C2semidirect
10. #13067899C2semidirect
11. #13067795C2semidirect
12. #13067704C2semidirect
13. #13067445C2semidirect
14. #13067440C2semidirect
15. C11×#3294C2semidirect
20. #10623082C22semidirect
34. #10622705C22semidirect
35. #10622696C22semidirect
36. #10622692C22semidirect
45. #10622632C22semidirect
48. D4×C11⋊C8C22semidirect
54. #10622301C22semidirect
55. #10622294C22semidirect
56. #10622185C22semidirect
60. D4⋊(C11⋊C8)C22semidirect
61. #10622124C22semidirect
62. #10622121C22semidirect
63. #10622120C22semidirect
64. #10622117C22semidirect
65. #10622095C22semidirect
66. #10622093C22semidirect
225. #3294D11semidirect
260. D4×C11#135semidirect
543. C11#19772semidirect
575. D4#67003semidirect

Maximal subgroups

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

subgroupindex
#130809232
#130804292
#130803342
#130682772
#130681742
#130680512
#130680392
#130679792
#130679002
#130678992
#130677952
#130677042
#130674452
#130674402
C11×#32942
#1977211