Finite Group Databasebeta

← #14826919

Subgroups — #14826919

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073224C211yesmaximal, characteristic, complemented
2#13070137C211yesmaximal, characteristic, complemented
3#13069933C211yesmaximal, characteristic, complemented
4#13069847C211yesmaximal, characteristic
5#13069704C211yesmaximal, characteristic
6#13069469C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13069194C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2366C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C11×#390—21no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#386—21no—
26C11×#386—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622595—21no—
36#10622591—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49C11⋊#401—21no—
50#10622264—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C22×Dic22C2311yescharacteristic
66C11×#127—22no—
67C11×#127—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C4×D4×C11—41no—
72C4×D4×C11—44no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324—41no—
91C2×#4324—41no—
92C2×#4324—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105#66896—22no—
106#66896—22no—
107#66896—22no—
108#66896—41no—
109#66896—41no—
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⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66874—22no—
122#66874—41no—
123#66872—22no—
124#66871—41no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#27063—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11—21no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11—81no—
145C2×D4×C11—81no—
146C2×D4×C11#4112yes—
147C2×D4×C11#4112yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—81no—
155C22×C4×C11—81no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192#4324—44no—
193#4324—44no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—42no—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8#4112yes—
214#2514—111no—
215#2366D1111yescharacteristic
216#2092—111no—
217#2055—111no—
218#2041—111no—
219#2014—111no—
220#1968—111no—
221#1928—111no—
222#1925—111no—
223#1919—111no—
224#1916—111no—
225#1877—111no—
226#1877—111no—
227#1804—111no—
228C4×#102—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11C22×D411yescharacteristic
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—48no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—84no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—84no—
277C2×C4×C11—84no—
278C2×C4×C11#13512yes—
279C2×C4×C11AGL(1,ℤ/8)12yes—
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298Dic22—41no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C22×SD16—111no—
307C22×SD16—111no—
308C2×#127C2×D1111yescharacteristic
309C2×C4×D4—21no—
310C2×C4×D4C2×D1111yescharacteristic
311C2×C4×D4C2×D1111yescharacteristic
312C2×#107—111no—
313C2×#106—111no—
314C2×C4⋊C8—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C4×C8—111no—
324#401—221no—
325#400—221no—
326#391—111no—
327#391—111no—
328#391—111no—
329#390—21no—
330#390C2×D1111yescharacteristic
331#390C2×D1111yescharacteristic
332#389—111no—
333#387—221no—
334#386—21no—
335#386—21no—
336#383—221no—
337#382—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C4⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348#336—111no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11#52511yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#55011yescharacteristic
366C22×C11C2×#13511yescharacteristic
367C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57711yescharacteristic
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11#52911yescharacteristic
379C4×C11#53811yescharacteristic
380C4×C11#55111yescharacteristic
381C4×C11#55311yescharacteristic
382Dic11—81no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8—111no—
387C22×D4—21no—
388C22×D4—21no—
389C22×D4C22×D1111yescharacteristic
390C22×D4C22×D1111yescharacteristic
391C23×C4—21no—
392C23×C4—21no—
393C2×SD16—222no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—441no—
397C2×SD16—441no—
398C2×SD16—441no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—111no—
403#127—22no—
404#127—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—41no—
408C4×D4—41no—
409C4×D4—44no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22⋊D1111yescharacteristic
415C2×C4⋊C4C22⋊D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C42—21no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429#107—441no—
430#106—222no—
431C4⋊C8—441no—
432#103—222no—
433#103—441no—
434#102—222no—
435#102—222no—
436#102—222no—
437#102—441no—
438#102—441no—
439#102—441no—
440C4×C8—441no—
441#95—21no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95C22⋊D1111yescharacteristic
453#95C22⋊D1111yescharacteristic
454C2×C11—82no—
455C2×C11—82no—
456C2×C11#246711yescharacteristic
457C2×C11#310511yescharacteristic
458C2×C11#312311yescharacteristic
459C2×C11#330411yescharacteristic
460C2×C11#331011yescharacteristic
461C2×C11#339411yescharacteristic
462C2×C11#339711yescharacteristic
463C24—21no—
464C24—21no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4#433912yes—
488C2×D4#433912yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508SD16—444no—
509SD16—444no—
510C2×C8—112no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4#434112yes—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—442no—
549C11#2706311yescharacteristic, complemented, Sylow
550C23—22no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23C22×C22⋊D1111yescharacteristic
565Q8—441no—
566Q8—441no—
567Q8—441no—
568Q8—441no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—48no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—84no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—84no—
602C2×C4—84no—
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—441no—
614C2×C4—441no—
615C2×C4#6698512yes—
616C2×C4#6700312yes—
617C2×C4C2×#433911yescharacteristic
618C2×C4C2×#433911yescharacteristic
619C2×C4C2×#434111yescharacteristic
620C2×C4#6703711yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#6704211yescharacteristic
623C8—222no—
624C8—441no—
625C8—441no—
626C8—441no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22#1062332211yescharacteristic
642C22C2×#6698511yescharacteristic
643C22#1062333711yescharacteristic
644C22C2×#6700311yescharacteristic
645C22#1062336511yescharacteristic
646C22#1062336711yescharacteristic
647C22#1062336711yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—42no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—81no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062306911yescharacteristic
661C4#1062308711yescharacteristic
662C4#1062309111yescharacteristic
663C4#1062309611yescharacteristic
664C2—82no—
665C2—82no—
666C2#1307266111yescharacteristic
667C2#1307866311yescharacteristic
668C2#1307886811yescharacteristic
669C2#1308055511yescharacteristic
670C2#1308063711yescharacteristic
671C2#1308160811yescharacteristic
672C2#1308163211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2366D11
hypocenterC11#27063
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #13073224C2semidirect
2. #13070137C2semidirect
3. #13069933C2semidirect
6. #13069469C2semidirect
7. #13069257C2semidirect
8. #13069233C2semidirect
9. #13069194C2semidirect
10. #13069175C2semidirect
11. #13068950C2semidirect
12. #13068950C2semidirect
13. #13068626C2semidirect
14. C4×#66896C2semidirect
549. C11#27063semidirect

Maximal subgroups

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

subgroupindex
#130732242
#130701372
#130699332
#130698472
#130697042
#130694692
#130692572
#130692332
#130691942
#130691752
#130689502
#130686262
C4×#668962
C11×#23662
#2706311