Finite Group Databasebeta

← #14827026

Subgroups — #14827026

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071685C211yesmaximal, characteristic
2#13070140C211yesmaximal, characteristic
3#13069931C211yesmaximal, characteristic
4#13069857C211yesmaximal, characteristic
5#13069709C211yesmaximal, characteristic
6#13069476C211yesmaximal, characteristic, complemented
7#13069250C211yesmaximal, characteristic, complemented
8#13069247C211yesmaximal, characteristic, complemented
9#13069205C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068960C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic
13#13068628C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic
15C11×#2514C211yesmaximal, characteristic, complemented
16C22×#4326C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#401—21no—
22C11×#400—21no—
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#383—21no—
29C11×#382C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622603—21no—
35#10622602—21no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622282—21no—
50#10622279—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×#4326—22no—
74C2×#4326—22no—
75C2×#4326—41no—
76C2×#4325—22no—
77C2×#4325—41no—
78C2×#4325—41no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66928—22no—
94#66928—22no—
95C4×D44—22no—
96C4×D44—41no—
97C4×Dic22—22no—
98C4×Dic22—41no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66899—22no—
112#66899—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66874—22no—
117#66874—41no—
118#66874—41no—
119#66873—22no—
120#66873—22no—
121#66873—41no—
122#66872—41no—
123#66871—22no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#27070—111nomaximal, Sylow
127C23×D11—21no—
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×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44#4112yes—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—81no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22#4112yes—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—42no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179#4326—44no—
180#4325—44no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—81no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—42no—
191C4×Dic11—42no—
192C4×Dic11—81no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8#4112yes—
205#2514D1111yescharacteristic, complemented
206#2367—111no—
207#2092—111no—
208#2055—111no—
209#2042—111no—
210#2015—111no—
211#1969—111no—
212#1927—111no—
213#1927—111no—
214#1921—111no—
215#1916—111no—
216#1878—111no—
217#1877—111no—
218#1805—111no—
219C4×#102—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11#13512yes—
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277D44—22no—
278D44—22no—
279D44—41no—
280D44—41no—
281C4×D11—84no—
282Dic22—22no—
283Dic22—22no—
284Dic22—41no—
285Dic22—41no—
286C11⋊C8—22no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C22×Q16—111no—
291C22×SD16—111no—
292C2×#124—111no—
293C2×C4×Q8—111no—
294C2×C4×D4—111no—
295C2×#107—111no—
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×C4×C8—111no—
307#401—21no—
308#400—21no—
309#391—111no—
310#391C2×D1111yescharacteristic
311#391C2×D1111yescharacteristic
312#391C2×D1111yescharacteristic
313#390—111no—
314#389C2×D1111yescharacteristic
315#388—221no—
316#388—221no—
317#387—21no—
318#385—221no—
319#383—21no—
320#382C2×D1111yescharacteristic
321C4×C4⋊C4—111no—
322C4×C4⋊C4C2×D1111yescharacteristic
323C4×C4⋊C4C2×D1111yescharacteristic
324C4×C22⋊C4—221no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336—111no—
330#336—111no—
331#336—111no—
332#336—111no—
333C22×C11#52511yescharacteristic
334C22×C11#54611yescharacteristic
335C22×C11#55011yescharacteristic
336C22×C11C2×#13511yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57711yescharacteristic
339C22×C11#57811yescharacteristic
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#52911yescharacteristic
358C4×C11#53811yescharacteristic
359C4×C11#55111yescharacteristic
360C4×C11#55311yescharacteristic
361Dic11—42no—
362Dic11—42no—
363Dic11—81no—
364C22×Q8—111no—
365C22×Q8C22×D1111yescharacteristic
366C22×D4—111no—
367C23×C4—221no—
368C2×Q16—222no—
369C2×Q16—222no—
370C2×Q16—441no—
371C2×SD16—222no—
372C2×SD16—441no—
373C2×SD16—441no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8—111no—
378#124—222no—
379#124—222no—
380C4×Q8—222no—
381C4×Q8—441no—
382C4×D4—222no—
383C4×D4—441no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22⋊D1111yescharacteristic
389C2×C4⋊C4C22⋊D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—21no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#107—222no—
405#106—441no—
406C4⋊C8—441no—
407#103—222no—
408#103—222no—
409#103—441no—
410#103—441no—
411#103—441no—
412#102—222no—
413#102—222no—
414#102—441no—
415C4×C8—441no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95C22⋊D1111yescharacteristic
430#95C22⋊D1111yescharacteristic
431C2×C11#246711yescharacteristic
432C2×C11#310211yescharacteristic
433C2×C11#312011yescharacteristic
434C2×C11#329611yescharacteristic
435C2×C11#331311yescharacteristic
436C2×C11#339311yescharacteristic
437C2×C11#340111yescharacteristic
438D11—82no—
439C24—221no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×D4—112no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—881no—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C23×D1111yescharacteristic
475Q16—444no—
476SD16—444no—
477C2×C8—112no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—42no—
498C4⋊C4—112no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4—442no—
506C22⋊C4—442no—
507C22⋊C4—881no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—442no—
516C42—881no—
517C11#2707011yescharacteristic, complemented, Sylow
518C23—222no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23C22×C22⋊D1111yescharacteristic
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534D4—222no—
535D4—222no—
536D4—441no—
537D4—441no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—884no—
577C2×C4#6700312yes—
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#41×D1111yescharacteristic
581C2×C4#41×D1111yescharacteristic
582C2×C4#6704211yescharacteristic
583C2×C4#6704211yescharacteristic
584C8—222no—
585C8—441no—
586C8—441no—
587C8—441no—
588C22—442no—
589C22—442no—
590C22—442no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22C2×#6700311yescharacteristic
596C22#1062335311yescharacteristic
597C22#1062335911yescharacteristic
598C22#1062336011yescharacteristic
599C22#1062336511yescharacteristic
600C22#1062336811yescharacteristic
601C22#1062336911yescharacteristic
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—442no—
613C4—442no—
614C4—881no—
615C4#1062323511yescharacteristic
616C4#1062323611yescharacteristic
617C4#1062323711yescharacteristic
618C4#1062324011yescharacteristic
619C2—882no—
620C2#1307266311yescharacteristic
621C2#1307862811yescharacteristic
622C2#1307882411yescharacteristic
623C2#1308044511yescharacteristic
624C2#1308067611yescharacteristic
625C2#1308160011yescharacteristic
626C2#1308168211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2514C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2514D11
hypocenterC11#27070
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2514

Complements

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

NH ≅ G/Ntype
6. #13069476C2semidirect
7. #13069250C2semidirect
8. #13069247C2semidirect
9. #13069205C2semidirect
10. #13069175C2semidirect
11. #13068960C2semidirect
13. #13068628C2semidirect
15. C11×#2514C2semidirect
205. #2514D11semidirect
517. C11#27070semidirect

Maximal subgroups

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

subgroupindex
#130716852
#130701402
#130699312
#130698572
#130697092
#130694762
#130692502
#130692472
#130692052
#130691752
#130689602
#130689532
#130686282
C4×#668732
C11×#25142
#2707011