Finite Group Databasebeta

← #14821819

Subgroups — #14821819

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072951C211yesmaximal, characteristic, complemented
2#13071628C211yesmaximal, characteristic
3#13069932C211yesmaximal, characteristic, complemented
4#13069796C211yesmaximal, characteristic
5#13069760C211yesmaximal, characteristic, complemented
6#13069620C211yesmaximal, characteristic
7#13069570C211yesmaximal, characteristic, complemented
8#13069292C211yesmaximal, characteristic, complemented
9#13069255C211yesmaximal, characteristic, complemented
10#13069222C211yesmaximal, characteristic, complemented
11#13069187C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068922C211yesmaximal, characteristic, complemented
14#13068705C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C2×C4×C22⋊D11—21no—
20C2×#66950C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622823—21no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622569—21no—
41#10622558—21no—
42#10622553—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44#10622549—21no—
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622287—21no—
48#10622272—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C22⋊D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66991—22no—
79#66991—22no—
80C2×#4324—22no—
81C2×#4324—41no—
82C2×#4324—41no—
83C4×C22⋊D11—44no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66950—22no—
101#66950—41no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—41no—
104#66943—22no—
105#66943—41no—
106C11×#102—22no—
107C11×#102—22no—
108C4×C8×C11—41no—
109C11×#95—21no—
110#66896—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120(C2×D11)⋊C8—41no—
121(C2×D11)⋊C8—41no—
122#66880—22no—
123#66880—41no—
124Dic11⋊C8—41no—
125#66874—22no—
126#66871—22no—
127#26721—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11#4112yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—42no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—81no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4#4112yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—42no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C22⋊Dic11—24no—
187C22⋊Dic11—42no—
188C22⋊Dic11—81no—
189#4324—44no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#2489—111no—
215#2361—111no—
216#2055—111no—
217#2033—111no—
218#2025—111no—
219#2000—111no—
220#1989—111no—
221#1933—111no—
222#1928—111no—
223#1923—111no—
224#1918—111no—
225#1877—111no—
226#1872—111no—
227#1824—111no—
228C4×#102D1111yescharacteristic, complemented
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×D411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11#13512yes—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
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—41no—
262C2×C4×C11—84no—
263C2×C4×C11AGL(1,ℤ/8)12yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C22⋊D11—48no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—84no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300Dic22—41no—
301C8×C11—41no—
302C8×C11—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C22×SD16—111no—
306C2×#125—111no—
307C2×C22⋊Q8—111no—
308C2×#121—111no—
309C2×C4×D4—221no—
310C2×C4×D4C2×D1111yescharacteristic
311C22×C4⋊C4—111no—
312C2×#107—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102C2×D1111yescharacteristic
319C2×#102C2×D1111yescharacteristic
320C2×C22⋊C8—111no—
321C2×C22⋊C8—111no—
322C2×C4×C8C2×D1111yescharacteristic
323#400—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#390—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#386—221no—
332#385—221no—
333#382—221no—
334#380—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C22⋊C4—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
346#336—111no—
347#336—111no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11#52511yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C2×#13511yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55511yescharacteristic
377C4×C11#55911yescharacteristic
378Dic11—41no—
379Dic11—42no—
380Dic11—41no—
381Dic11—41no—
382Dic11—81no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8—111no—
386C22×D4—221no—
387C22×D4C22×D1111yescharacteristic
388C23×C4—21no—
389C23×C4—111no—
390C23×C4—221no—
391C2×SD16—222no—
392C2×SD16—441no—
393C2×SD16—441no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#125—222no—
399#125—441no—
400C22⋊Q8—222no—
401C22⋊Q8—441no—
402#121—222no—
403#121—222no—
404C4×D4—22no—
405C4×D4—41no—
406C4×D4—444no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—441no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—21no—
429C2×C42—111no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#107—222no—
433C4⋊C8—441no—
434#103—222no—
435#103—222no—
436#103—441no—
437#102—22no—
438#102—22no—
439#102—441no—
440C22⋊C8—441no—
441C22⋊C8—441no—
442C4×C8—41no—
443#95—21no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453C2×C11—82no—
454C2×C11#245911yescharacteristic
455C2×C11#310511yescharacteristic
456C2×C11#312011yescharacteristic
457C2×C11#330011yescharacteristic
458C2×C11#330111yescharacteristic
459C2×C11#331011yescharacteristic
460C2×C11#333011yescharacteristic
461D11—42no—
462C24—21no—
463C24—111no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—224no—
476C2×D4—442no—
477C2×D4—442no—
478C2×D4#433912yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—881no—
501C22×C4D4×D1111yescharacteristic
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504SD16—444no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—112no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4#433912yes—
533C4⋊C4#433912yes—
534C22⋊C4—42no—
535C22⋊C4—222no—
536C22⋊C4—224no—
537C22⋊C4—222no—
538C22⋊C4—442no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—881no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—221no—
546C42—221no—
547C42—442no—
548C11#2672111yescharacteristic, complemented, Sylow
549C23—22no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—112no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23C2×D4×D1111yescharacteristic
564Q8—441no—
565Q8—441no—
566Q8—441no—
567Q8—441no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4—448no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—884no—
614C2×C4#6696412yes—
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4C2×#433911yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#6704211yescharacteristic
621C8—41no—
622C8—41no—
623C8—441no—
624C8—441no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—222no—
633C22—222no—
634C22—222no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22#1062302111yescharacteristic
640C22#1062307811yescharacteristic
641C22#1062308111yescharacteristic
642C22C2×#6696411yescharacteristic
643C22#1062329311yescharacteristic
644C22D11×#13511yescharacteristic
645C22#1062330211yescharacteristic
646C4—22no—
647C4—42no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—441no—
652C4—442no—
653C4—441no—
654C4—441no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4#1062301011yescharacteristic
659C4#1062306311yescharacteristic
660C4#1062309011yescharacteristic
661C4#1062309111yescharacteristic
662C2—82no—
663C2—442no—
664C2#1307255311yescharacteristic
665C2#1307866111yescharacteristic
666C2#1307882611yescharacteristic
667C2#1308050411yescharacteristic
668C2#1308052311yescharacteristic
669C2#1308063311yescharacteristic
670C2#1308092311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC4×#102D11
hypocenterC11#26721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #13072951C2semidirect
3. #13069932C2semidirect
5. #13069760C2semidirect
7. #13069570C2semidirect
8. #13069292C2semidirect
9. #13069255C2semidirect
10. #13069222C2semidirect
11. #13069187C2semidirect
12. #13068950C2semidirect
13. #13068922C2semidirect
14. #13068705C2semidirect
15. C4×C11×#102C2semidirect
228. C4×#102D11semidirect
548. C11#26721semidirect

Maximal subgroups

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

subgroupindex
#130729512
#130716282
#130699322
#130697962
#130697602
#130696202
#130695702
#130692922
#130692552
#130692222
#130691872
#130689502
#130689222
#130687052
C4×C11×#1022
#2672111