Finite Group Databasebeta

← #14822259

Subgroups — #14822259

Order 2816.

736 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072988C211yesmaximal, characteristic
2#13071645C211yesmaximal, characteristic
3#13069938C211yesmaximal, characteristic, complemented
4#13069814C211yesmaximal, characteristic
5#13069758C211yesmaximal, characteristic, complemented
6#13069625C211yesmaximal, characteristic
7#13069564C211yesmaximal, characteristic, complemented
8#13069308C211yesmaximal, characteristic, complemented
9#13069230C211yesmaximal, characteristic
10#13069203C211yesmaximal, characteristic, complemented
11#13068954C211yesmaximal, characteristic, complemented
12#13068925C211yesmaximal, characteristic
13#13068710C211yesmaximal, characteristic
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1927C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C22×#4326C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622598C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38#10622553—21no—
39C4×(C2×D11)⋊C4C2211yescharacteristic
40C4×C4⋊Dic11—21no—
41#10622542C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622286—21no—
44#10622283—21no—
45#10622283—21no—
46#10622273—21no—
47#10622266—21no—
48#10622259—21no—
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×Dic22—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#66999—22no—
71#66999—41no—
72C2×#4326—22no—
73C2×#4326—41no—
74C2×#4326—41no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4D411yescharacteristic
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66950—22no—
96#66950—22no—
97#66945—22no—
98#66945—41no—
99#66940—22no—
100#66940—41no—
101#66922—22no—
102#66922—41no—
103C11×#106—22no—
104C11×#103—22no—
105C11×#103—22no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119(C2×D11)⋊C8—41no—
120(C2×D11)⋊C8—41no—
121#66880—22no—
122#66880—41no—
123#66879—41no—
124#66874—22no—
125C4⋊(C11⋊C8)—41no—
126#26750—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—42no—
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4#4112yes—
174C11×C4⋊C4#4112yes—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178#4326—44no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—22no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—81no—
185C4⋊Dic11—24no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—42no—
192C4⋊Dic11—42no—
193C4⋊Dic11#4112yes—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#2492—111no—
208#2362—111no—
209#2056—111no—
210#2035—111no—
211#2024—111no—
212#2001—111no—
213#1987—111no—
214#1935—111no—
215#1927D1111yescharacteristic, complemented
216#1924—111no—
217#1920—111no—
218#1878—111no—
219#1873—111no—
220#1825—111no—
221#1763—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11#13712yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287Dic22—84no—
288C8×C11—41no—
289C8×C11—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×Q16—111no—
293C2×C4⋊Q8—111no—
294C2×C22⋊Q8—111no—
295C2×C22⋊Q8—111no—
296C2×C4×Q8—111no—
297C2×#117—111no—
298C2×#106C2×D1111yescharacteristic
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103C2×D1111yescharacteristic
305C2×#103C2×D1111yescharacteristic
306C2×C22⋊C8—111no—
307C2×C22⋊C8—111no—
308C2×#97—111no—
309#400—221no—
310#393—221no—
311#391—111no—
312#391—111no—
313#391—221no—
314#391C2×D1111yescharacteristic
315#389—111no—
316#388—221no—
317#388—221no—
318#388—221no—
319#387—221no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—221no—
323C4×C4⋊C4C2×D1111yescharacteristic
324C4×C22⋊C4—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340C2×D1111yescharacteristic
333#336—111no—
334#336C2×D1111yescharacteristic
335C22×C11#52511yescharacteristic
336C22×C11#54611yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57511yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57811yescharacteristic
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11#52911yescharacteristic
356C4×C11#53811yescharacteristic
357C4×C11#55511yescharacteristic
358C4×C11#55911yescharacteristic
359Dic11—41no—
360Dic11—42no—
361Dic11—41no—
362Dic11—42no—
363Dic11—41no—
364Dic11—81no—
365Dic11—81no—
366C22×Q8—111no—
367C22×Q8—221no—
368C22×Q8C22×D1111yescharacteristic
369C23×C4—111no—
370C2×Q16—222no—
371C2×Q16—441no—
372C2×Q16—441no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C4⋊Q8—222no—
378C4⋊Q8—441no—
379C22⋊Q8—222no—
380C22⋊Q8—222no—
381C22⋊Q8—222no—
382C22⋊Q8—441no—
383C4×Q8—222no—
384C4×Q8—441no—
385#117—222no—
386#117—441no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—21no—
405C2×C42—111no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42C22×D1111yescharacteristic
410#106—22no—
411C4⋊C8—441no—
412#103—22no—
413#103—22no—
414#103—222no—
415#103—222no—
416#103—441no—
417#103—441no—
418C22⋊C8—441no—
419C22⋊C8—441no—
420#97—441no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—111no—
425#95—111no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433C2×C11#245911yescharacteristic
434C2×C11#311611yescharacteristic
435C2×C11#312111yescharacteristic
436C2×C11#331111yescharacteristic
437C2×C11#331211yescharacteristic
438C2×C11#331311yescharacteristic
439C2×C11#333111yescharacteristic
440D11—81no—
441C24—111no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—112no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—442no—
455C2×Q8—442no—
456C2×Q8—881no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477Q16—444no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—112no—
495C4⋊C4—224no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4#433912yes—
506C4⋊C4#434112yes—
507C22⋊C4—224no—
508C22⋊C4—222no—
509C22⋊C4—441no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—881no—
513C42—21no—
514C42—21no—
515C42—42no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—442no—
520C42—881no—
521C11#2675011yescharacteristic, complemented, Sylow
522C23—221no—
523C23—221no—
524C23—221no—
525C23—221no—
526C23—221no—
527C23—221no—
528C23—221no—
529C23C2×D4×D1111yescharacteristic
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—222no—
535Q8—222no—
536Q8—441no—
537Q8—441no—
538Q8—884no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—222no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—221no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4#6696812yes—
582C2×C4C2×#433911yescharacteristic
583C2×C4C2×#434111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#6704211yescharacteristic
587C2×C4#6704211yescharacteristic
588C8—41no—
589C8—41no—
590C8—441no—
591C8—441no—
592C22—441no—
593C22—441no—
594C22—441no—
595C22—441no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22#1062308111yescharacteristic
600C22#1062313711yescharacteristic
601C22#1062318511yescharacteristic
602C22C2×#6696811yescharacteristic
603C22#1062330111yescharacteristic
604C22#1062330811yescharacteristic
605C22#1062331011yescharacteristic
606C4—22no—
607C4—41no—
608C4—42no—
609C4—42no—
610C4—81no—
611C4—81no—
612C4—442no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4—442no—
617C4—881no—
618C4—881no—
619C4#1062305911yescharacteristic
620C4#1062309411yescharacteristic
621C4#1062321211yescharacteristic
622C4#1062323511yescharacteristic
623C2—881no—
624C2#1307255811yescharacteristic
625C2#1307877511yescharacteristic
626C2#1307884211yescharacteristic
627C2#1308065511yescharacteristic
628C2#1308066511yescharacteristic
629C2#1308068711yescharacteristic
630C2#1308093411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1927C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1927D11
hypocenterC11#26750
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
3. #13069938C2semidirect
5. #13069758C2semidirect
7. #13069564C2semidirect
8. #13069308C2semidirect
10. #13069203C2semidirect
11. #13068954C2semidirect
14. #13068445C2semidirect
15. C11×#1927C2semidirect
215. #1927D11semidirect
521. C11#26750semidirect

Maximal subgroups

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

subgroupindex
#130729882
#130716452
#130699382
#130698142
#130697582
#130696252
#130695642
#130693082
#130692302
#130692032
#130689542
#130689252
#130687102
#130684452
C11×#19272
#2675011