Finite Group Databasebeta

← #14821906

Subgroups — #14821906

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072964C211yesmaximal, characteristic
2#13071621C211yesmaximal, characteristic, complemented
3#13069935C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic, complemented
5#13069766C211yesmaximal, characteristic, complemented
6#13069621C211yesmaximal, characteristic
7#13069570C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic, complemented
9#13069234C211yesmaximal, characteristic, complemented
10#13069219C211yesmaximal, characteristic, complemented
11#13069206C211yesmaximal, characteristic, complemented
12#13068972C211yesmaximal, characteristic, complemented
13#13068933C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1823C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×#4314C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622823—21no—
25C4×C22⋊Dic11—21no—
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622601C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622591—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622574—21no—
46#10622570—21no—
47#10622288—21no—
48#10622283—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11D411yescharacteristic
76C2×C22⋊Dic11D411yescharacteristic
77#66983—22no—
78#66983—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⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87#66977—22no—
88#66977—22no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4314—22no—
101C2×#4314—41no—
102C2×#4314—41no—
103#66943—22no—
104#66943—41no—
105#66940—22no—
106#66940—41no—
107C11×C22⋊C8—41no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C22⋊(C11⋊C8)—41no—
117#66885—22no—
118#66880—22no—
119Dic11⋊C8—41no—
120C8×Dic11—41no—
121#66874—22no—
122#66874—41no—
123#66873—22no—
124#66873—41no—
125#66871—22no—
126#26727—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
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×C11C2411yescharacteristic
144C2×C22⋊D11—42no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—81no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—81no—
182C22⋊Dic11—24no—
183C22⋊Dic11—22no—
184C22⋊Dic11—22no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11#4112yes—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—81no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C4×Dic11—81no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212#4314—44no—
213#2490—111no—
214#2360—111no—
215#2055—111no—
216#2036—111no—
217#2026—111no—
218#2000—111no—
219#1989—111no—
220#1934—111no—
221#1925—111no—
222#1923—111no—
223#1921—111no—
224#1880—111no—
225#1874—111no—
226#1823D1111yescharacteristic, complemented
227C4×#103—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11#13512yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
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—41no—
262C2×C4×C11—84no—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C22⋊D11—84no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—21no—
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#13712yes—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295Dic22—22no—
296Dic22—22no—
297Dic22—41no—
298Dic22—41no—
299C8×C11—41no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×SD16—111no—
304C2×#125—111no—
305C2×C22⋊Q8—111no—
306C2×#121—111no—
307C2×C4×Q8—111no—
308C22×C4⋊C4C2×D1111yescharacteristic
309C2×#107—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C22⋊C8—111no—
318C2×C22⋊C8C2×D1111yescharacteristic
319C2×C4×C8—111no—
320#397—221no—
321#394—221no—
322#391—111no—
323#390—111no—
324#390—111no—
325#390—221no—
326#389—111no—
327#389—221no—
328#388—221no—
329#387—221no—
330#385—221no—
331#380C2×D1111yescharacteristic
332C4×C4⋊C4—111no—
333C4×C4⋊C4—111no—
334C4×C22⋊C4—111no—
335C4×C22⋊C4—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340C2×D1111yescharacteristic
341#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11#52511yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×#13711yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57711yescharacteristic
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11#52911yescharacteristic
373C4×C11#53811yescharacteristic
374C4×C11#55511yescharacteristic
375C4×C11#55911yescharacteristic
376Dic11—22no—
377Dic11—41no—
378Dic11—42no—
379Dic11—42no—
380Dic11—41no—
381Dic11—42no—
382Dic11—41no—
383C22×Q8—111no—
384C22×D4—111no—
385C22×D4—221no—
386C23×C4—21no—
387C23×C4C22×D1111yescharacteristic
388C2×SD16—222no—
389C2×SD16—441no—
390C2×SD16—441no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#125—222no—
396#125—441no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399#121—222no—
400#121—441no—
401C4×Q8—222no—
402C4×Q8—441no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
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×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431#107—222no—
432C4⋊C8—441no—
433#103—222no—
434#103—222no—
435#103—441no—
436#102—222no—
437#102—222no—
438#102—441no—
439C22⋊C8—41no—
440C22⋊C8—441no—
441C4×C8—441no—
442#95—21no—
443#95—111no—
444#95—111no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450C2×C11—42no—
451C2×C11#245911yescharacteristic
452C2×C11#310811yescharacteristic
453C2×C11#311911yescharacteristic
454C2×C11#329611yescharacteristic
455C2×C11#329711yescharacteristic
456C2×C11#332011yescharacteristic
457C2×C11#333311yescharacteristic
458D11—161no—
459C24—221no—
460C24D4×D1111yescharacteristic
461C2×Q8—112no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—442no—
474C2×D4—442no—
475C2×D4—881no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4D4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498SD16—444no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C4⋊C4—21no—
512C4⋊C4—21no—
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—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—881no—
528C4⋊C4#433912yes—
529C22⋊C4—81no—
530C22⋊C4—222no—
531C22⋊C4—224no—
532C22⋊C4—222no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—881no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C42—881no—
545C11#2672711yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23#6696912yes—
560C23C2×D4×D1111yescharacteristic
561Q8—222no—
562Q8—222no—
563Q8—441no—
564Q8—441no—
565D4—441no—
566D4—441no—
567D4—441no—
568D4—441no—
569D4—884no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
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—84no—
590C2×C4—112no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4C2×#433911yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#6704211yescharacteristic
617C8—41no—
618C8—41no—
619C8—441no—
620C8—441no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22—881no—
634C22—881no—
635C22#1062302111yescharacteristic
636C22#1062318511yescharacteristic
637C22#1062318711yescharacteristic
638C22#1062328811yescharacteristic
639C22C2×#6696911yescharacteristic
640C22D11×#13711yescharacteristic
641C22#1062330911yescharacteristic
642C4—42no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4—81no—
647C4—222no—
648C4—442no—
649C4—441no—
650C4—441no—
651C4—442no—
652C4—441no—
653C4—442no—
654C4#1062305911yescharacteristic
655C4#1062306311yescharacteristic
656C4#1062318811yescharacteristic
657C4#1062319511yescharacteristic
658C2—42no—
659C2—1761no—
660C2#1307255011yescharacteristic
661C2#1307869911yescharacteristic
662C2#1307881811yescharacteristic
663C2#1308044911yescharacteristic
664C2#1308046211yescharacteristic
665C2#1308078811yescharacteristic
666C2#1308095211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1823D11
hypocenterC11#26727
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
2. #13071621C2semidirect
3. #13069935C2semidirect
4. #13069819C2semidirect
5. #13069766C2semidirect
7. #13069570C2semidirect
8. #13069297C2semidirect
9. #13069234C2semidirect
10. #13069219C2semidirect
11. #13069206C2semidirect
12. #13068972C2semidirect
14. #13068435C2semidirect
15. C11×#1823C2semidirect
226. #1823D11semidirect
545. C11#26727semidirect

Maximal subgroups

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

subgroupindex
#130729642
#130716212
#130699352
#130698192
#130697662
#130696212
#130695702
#130692972
#130692342
#130692192
#130692062
#130689722
#130689332
#130684352
C11×#18232
#2672711