Finite Group Databasebeta

← #14822227

Subgroups — #14822227

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072982C211yesmaximal, characteristic
2#13071648C211yesmaximal, characteristic, complemented
3#13069931C211yesmaximal, characteristic, complemented
4#13069818C211yesmaximal, characteristic, complemented
5#13069618C211yesmaximal, characteristic
6#13069569C211yesmaximal, characteristic, complemented
7#13069311C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic, complemented
9#13069230C211yesmaximal, characteristic, complemented
10#13069207C211yesmaximal, characteristic, complemented
11#13068969C211yesmaximal, characteristic, complemented
12#13068937C211yesmaximal, characteristic
13#13068709C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C11×#2024C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#67000—21no—
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66948C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26#10622844—21no—
27C2×#66899C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34#10622604—21no—
35#10622603—21no—
36#10622601C2211yescharacteristic
37#10622600C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41#10622552C2211yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622283—21no—
46#10622282—21no—
47#10622268—21no—
48#10622262—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×Q8×C11C2311yescharacteristic
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#67000—44no—
74#66999—22no—
75#66999—22no—
76Q8×Dic11—22no—
77Q8×Dic11—41no—
78C2×#4325—22no—
79C2×#4325—41no—
80C2×#4325—41no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66948—22no—
105#66948—41no—
106#66945—22no—
107#66945—41no—
108C11×#103—22no—
109C11×#103—41no—
110C11×#95—21no—
111C11×#95—21no—
112#66899—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66885—22no—
120#66885—22no—
121(C2×D11)⋊C8—41no—
122(C2×D11)⋊C8—41no—
123#66882—22no—
124#66879—41no—
125#66873—41no—
126C4⋊(C11⋊C8)—41no—
127#26748—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11C2×D411yescharacteristic
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—81no—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—42no—
159C2×D44—42no—
160C2×D44—81no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4#4112yes—
180C42×C11—21no—
181C42×C11—21no—
182#4325—44no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11#4112yes—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
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#2491—111no—
215#2362—111no—
216#2055—111no—
217#2036—111no—
218#2024D1111yescharacteristic, complemented
219#2000—111no—
220#1988—111no—
221#1936—111no—
222#1925—111no—
223#1924—111no—
224#1921—111no—
225#1880—111no—
226#1875—111no—
227#1825—111no—
228#1763—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—84no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11AGL(1,ℤ/8)12yes—
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295D44—84no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C2×C4⋊Q8C2×D1111yescharacteristic
306C2×#124—221no—
307C2×C22⋊Q8—111no—
308C2×#121—111no—
309C2×C4×Q8—111no—
310C2×#117—111no—
311C2×#107—111no—
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103C2×D1111yescharacteristic
315C2×#103C2×D1111yescharacteristic
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×C22⋊C8—111no—
320C2×C22⋊C8—111no—
321C2×#97—111no—
322#394—221no—
323#393—221no—
324#391C2×D1111yescharacteristic
325#390—111no—
326#390—111no—
327#389—111no—
328#388—221no—
329#388—221no—
330#388—221no—
331#387—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—221no—
336C4×C22⋊C4—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11#52511yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11#54611yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11#57511yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57811yescharacteristic
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C4×C11—22no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55511yescharacteristic
377C4×C11#55911yescharacteristic
378Dic11—41no—
379Dic11—42no—
380Dic11—42no—
381Dic11—41no—
382Dic11—41no—
383Dic11—81no—
384C22×Q8—21no—
385C22×Q8C22×D1111yescharacteristic
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—111no—
389C2×SD16—222no—
390C2×SD16—441no—
391C2×SD16—441no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8—22no—
397C4⋊Q8—41no—
398#124—444no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401#121—222no—
402#121—441no—
403C4×Q8—222no—
404C4×Q8—441no—
405#117—222no—
406#117—441no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—111no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42—221no—
432C2×C42C22×D1111yescharacteristic
433#107—222no—
434C4⋊C8—441no—
435#103—22no—
436#103—41no—
437#103—222no—
438#102—222no—
439#102—222no—
440#102—441no—
441C22⋊C8—441no—
442C22⋊C8—441no—
443#97—441no—
444#95—21no—
445#95—21no—
446#95—111no—
447#95—111no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11#245911yescharacteristic
453C2×C11#311511yescharacteristic
454C2×C11#312111yescharacteristic
455C2×C11#331011yescharacteristic
456C2×C11#331311yescharacteristic
457C2×C11#332111yescharacteristic
458C2×C11#333011yescharacteristic
459D11—81no—
460D11—161no—
461C24—111no—
462C24—221no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—81no—
471C2×Q8#434312yes—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—442no—
479C2×D4—442no—
480C2×D4—881no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
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×C4D4×D1111yescharacteristic
498C22×C4D4×D1111yescharacteristic
499C22×C4C23×D1111yescharacteristic
500SD16—444no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—224no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4#434112yes—
529C22⋊C4—224no—
530C22⋊C4—222no—
531C22⋊C4—441no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C22⋊C4—881no—
539C42—21no—
540C42—21no—
541C42—221no—
542C42—221no—
543C42—442no—
544C42—442no—
545C42—442no—
546C42—442no—
547C11#2674811yescharacteristic, complemented, Sylow
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23C2×D4×D1111yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—84no—
568D4—441no—
569D4—441no—
570D4—441no—
571D4—441no—
572D4—884no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
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—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—222no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—222no—
600C2×C4—221no—
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#6696712yes—
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4C2×#434311yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#6704211yescharacteristic
619C8—41no—
620C8—41no—
621C8—441no—
622C8—441no—
623C22—441no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22—881no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22#1062312211yescharacteristic
638C22#1062315811yescharacteristic
639C22#1062320711yescharacteristic
640C22C2×#6696711yescharacteristic
641C22#1062329711yescharacteristic
642C22#1062330611yescharacteristic
643C22#1062330811yescharacteristic
644C4—22no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—81no—
649C4—81no—
650C4—441no—
651C4—442no—
652C4—441no—
653C4—441no—
654C4—442no—
655C4—881no—
656C4#1062315511yescharacteristic
657C4#1062317511yescharacteristic
658C4#1062320111yescharacteristic
659C4#1062321211yescharacteristic
660C2—881no—
661C2—1761no—
662C2#1307255611yescharacteristic
663C2#1307877011yescharacteristic
664C2#1307885011yescharacteristic
665C2#1308064111yescharacteristic
666C2#1308067511yescharacteristic
667C2#1308080111yescharacteristic
668C2#1308092011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#2024D11
hypocenterC11#26748
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. #13071648C2semidirect
3. #13069931C2semidirect
4. #13069818C2semidirect
6. #13069569C2semidirect
7. #13069311C2semidirect
8. #13069237C2semidirect
9. #13069230C2semidirect
10. #13069207C2semidirect
11. #13068969C2semidirect
13. #13068709C2semidirect
14. #13068448C2semidirect
15. C11×#2024C2semidirect
218. #2024D11semidirect
547. C11#26748semidirect

Maximal subgroups

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

subgroupindex
#130729822
#130716482
#130699312
#130698182
#130696182
#130695692
#130693112
#130692372
#130692302
#130692072
#130689692
#130689372
#130687092
#130684482
C11×#20242
#2674811