Finite Group Databasebeta

← #14811006

Subgroups — #14811006

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622385C211yesmaximal, characteristic
2#13072303C211yesmaximal, characteristic, complemented
3#13071441C211yesmaximal, characteristic
4#13070165C211yesmaximal, characteristic, complemented
5#13069996C211yesmaximal, characteristic, complemented
6#13069992C211yesmaximal, characteristic, complemented
7#13069754C211yesmaximal, characteristic, complemented
8#13068879C211yesmaximal, characteristic, complemented
9#13068863C211yesmaximal, characteristic, complemented
10#13068814C211yesmaximal, characteristic, complemented
11#13068792C211yesmaximal, characteristic, complemented
12#13068638C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14#13068553C211yesmaximal, characteristic
15C2×C11×#476C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C11×#476—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622844—21no—
29#10622843—21no—
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622826—21no—
33C2×C11⋊#95—21no—
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622607—21no—
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622598C2211yescharacteristic
43#10622591—21no—
44#10622590C2211yescharacteristic
45#10622587C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622571—21no—
50#10622556—21no—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622385—24no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C2×#4341—22no—
68C2×#4341—22no—
69C2×#4341—22no—
70C2×#4341—41no—
71C2×#4341—41no—
72C2×#4341Q814yescomplemented
73C22×C4×D11C2311yescharacteristic
74C22×Dic22C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—41no—
79C4×D4×C11—22no—
80C4×D4×C11—41no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88D4×Dic11—22no—
89D4×Dic11—41no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4D411yescharacteristic
94C2×(C2×D11)⋊C4D411yescharacteristic
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—41no—
107#66945—22no—
108#66945—41no—
109C11×#106—22no—
110C11×#106—22no—
111C11×C4⋊C8—22no—
112C11×#102—22no—
113C11×#102D414yes—
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128(C2×D11)⋊C8—22no—
129#66881—41no—
130#66880—22no—
131#66880—41no—
132Dic11⋊C8—41no—
133#66874—22no—
134#66874—41no—
135#66871—41no—
136#25962—111nomaximal, Sylow
137C24×C11—21no—
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11—81no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×Q812yes—
147C2×D4×C11#4112yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—81no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C22×Dic11—24no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—81no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173#4341—28no—
174#4341—44no—
175#4341—44no—
176#4341—44no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×C4×D11C2×Q812yes—
182C2×C4×D11#4112yes—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22C2×Q812yes—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11C2×D412yes—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4C2×D412yes—
202C11×C22⋊C4—42no—
203C42×C11—21no—
204C42×C11—21no—
205C22⋊Dic11—42no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—41no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—81no—
210(C2×D11)⋊C4—81no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—81no—
218Dic11⋊C4—42no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C8×D11—44no—
229C2×#476D1111yescharacteristic, complemented
230C2×#416—111no—
231#2439—111no—
232#2339—111no—
233#2097—111no—
234#2066—111no—
235#2066—111no—
236#2024—111no—
237#1864—111no—
238#1862—111no—
239#1854—111no—
240#1850—111no—
241#1807—111no—
242#1804—111no—
243#1788—111no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11C22⋊Q812yes—
259Q8×C11—84no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—22no—
263D4×C11C22⋊Q814yes—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—84no—
279C2×C4×C11#13512yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×Q811yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C22⋊D11—48no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—22no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—48no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—84no—
309C2×Dic11C22⋊Q812yes—
310C4×D11—22no—
311C4×D11—22no—
312C4×D11—22no—
313C4×D11—22no—
314Dic22—22no—
315Dic22—22no—
316Dic22—41no—
317Dic22—41no—
318C8×C11—22no—
319C8×C11—41no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C22×#41—111no—
323C23×C8—111no—
324C2×C4⋊Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4C2×D1111yescharacteristic
327C2×#117—111no—
328#476—24no—
329C2×#107—111no—
330C2×#106—111no—
331C2×#106C2×D1111yescharacteristic
332C2×#106C2×D1111yescharacteristic
333C2×C4⋊C8—111no—
334C2×C4⋊C8C2×D1111yescharacteristic
335#416—224no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102C2×D1111yescharacteristic
343C2×#102C2×D1111yescharacteristic
344C2×C22⋊C8—111no—
345#396—221no—
346#393—221no—
347#391—111no—
348#391—111no—
349#391—221no—
350#389—111no—
351#389—111no—
352#387—221no—
353#386—221no—
354#386—221no—
355#382—111no—
356#381—221no—
357#380—111no—
358#380—111no—
359C4×C22⋊C4—111no—
360C2×#95—221no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365#336—111no—
366#336—111no—
367C22×C11—24no—
368C22×C11—42no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11C2×C22⋊Q811yescharacteristic
375C22×C11D4211yescharacteristic
376C22×C11#54611yescharacteristic
377C22×C11C2×#13511yescharacteristic
378C22×C11#57511yescharacteristic
379C22×C11#57711yescharacteristic
380C22×C11#57711yescharacteristic
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—41no—
388C4×C11—22no—
389C4×C11—41no—
390C4×C11—42no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11C2×C22⋊Q811yescharacteristic
394C4×C11#54311yescharacteristic
395C4×C11#54611yescharacteristic
396C4×C11#55111yescharacteristic
397Dic11—22no—
398Dic11—42no—
399Dic11—41no—
400Dic11—41no—
401Dic11—81no—
402Dic11—81no—
403Dic11—81no—
404C2×#41—114no—
405C2×#41—222no—
406C2×#41—222no—
407C2×#41—222no—
408C2×#41—441no—
409C2×#41—441no—
410C22×Q8—21no—
411C22×Q8—111no—
412C22×D4—221no—
413C22×D4C22×D1111yescharacteristic
414C23×C4—21no—
415C23×C4—111no—
416C23×C4—221no—
417C23×C4—221no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—222no—
421C22×C8—222no—
422C22×C8—441no—
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—41no—
427C4×D4—22no—
428C4×D4—41no—
429C4×D4—222no—
430C4×D4—441no—
431#117—222no—
432#117—441no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—111no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452#107—441no—
453#106—22no—
454#106—22no—
455#106—441no—
456C4⋊C8—22no—
457C4⋊C8—441no—
458#103—222no—
459#103—222no—
460#103—441no—
461#103—441no—
462#102—22no—
463#102—222no—
464#102—222no—
465#102C22⋊D1114yes—
466C22⋊C8—222no—
467#95—111no—
468#95—111no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479C2×C11—44no—
480C2×C11#243711yescharacteristic
481C2×C11#307611yescharacteristic
482C2×C11#308411yescharacteristic
483C2×C11#326711yescharacteristic
484C2×C11#328211yescharacteristic
485C2×C11#330311yescharacteristic
486C2×C11#331111yescharacteristic
487D11—42no—
488C24—21no—
489C24—111no—
490#41—228no—
491#41—444no—
492#41—444no—
493#41—444no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—81no—
497C2×Q8—112no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—224no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4Q8×D1112yes—
510C2×D4#434312yes—
511C2×D4C2×C22⋊D1112yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4—111no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—224no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—442no—
535C22×C4—442no—
536C22×C4—881no—
537C22×C4D4×D1111yescharacteristic
538C22×C4D4×D1111yescharacteristic
539C22×C4C23×D1111yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—444no—
552C2×C8C2×C22⋊D1112yes—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—442no—
566C4⋊C4—881no—
567C4⋊C4C2×C22⋊D1112yes—
568C22⋊C4—42no—
569C22⋊C4—222no—
570C22⋊C4—441no—
571C22⋊C4—442no—
572C22⋊C4—442no—
573C22⋊C4—881no—
574C22⋊C4—881no—
575C42—21no—
576C42—21no—
577C42—221no—
578C42—221no—
579C42—442no—
580C11#2596211yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—112no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—221no—
595C23C2×D4×D1111yescharacteristic
596Q8—84no—
597Q8—222no—
598Q8—222no—
599Q8—441no—
600Q8—441no—
601D4—22no—
602D4—22no—
603D4—22no—
604D4—448no—
605D4#6699914yes—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—84no—
621C2×C4—112no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—222no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—448no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—884no—
648C2×C4#6696912yes—
649C2×C4#6703711yescharacteristic
650C2×C4C2×Q8×D1111yescharacteristic
651C2×C4C2×#434311yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#6704211yescharacteristic
654C2×C4C22×C22⋊D1111yescharacteristic
655C8—22no—
656C8—41no—
657C8—441no—
658C8—441no—
659C22—24no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—222no—
667C22—222no—
668C22—222no—
669C22—441no—
670C22—441no—
671C22—441no—
672C22—441no—
673C22D11×C22⋊Q811yescharacteristic
674C22#1062316111yescharacteristic
675C22C2×#6696911yescharacteristic
676C22#1062329311yescharacteristic
677C22#1062330411yescharacteristic
678C22#1062330611yescharacteristic
679C22D4×C22⋊D1111yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—81no—
684C4—81no—
685C4—222no—
686C4—441no—
687C4—442no—
688C4—441no—
689C4—881no—
690C4—881no—
691C4—881no—
692C4#1062316511yescharacteristic
693C4#1062316811yescharacteristic
694C4C2×#6699911yescharacteristic
695C4#1062336011yescharacteristic
696C2—44no—
697C2—442no—
698C2#1307227911yescharacteristic
699C2#1307840511yescharacteristic
700C2#1307847311yescharacteristic
701C2#1308013511yescharacteristic
702C2#1308032311yescharacteristic
703C2#1308054111yescharacteristic
704C2#1308064911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenterC2×#476D11
hypocenterC11#25962
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. #13072303C2semidirect
4. #13070165C2semidirect
5. #13069996C2semidirect
6. #13069992C2semidirect
7. #13069754C2semidirect
8. #13068879C2semidirect
9. #13068863C2semidirect
10. #13068814C2semidirect
11. #13068792C2semidirect
12. #13068638C2semidirect
13. #13068624C2semidirect
15. C2×C11×#476C2semidirect
72. C2×#4341Q8semidirect
229. C2×#476D11semidirect
580. C11#25962semidirect

Maximal subgroups

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

subgroupindex
C2×#106223852
#130723032
#130714412
#130701652
#130699962
#130699922
#130697542
#130688792
#130688632
#130688142
#130687922
#130686382
#130686242
#130685532
C2×C11×#4762
#2596211