Finite Group Databasebeta

← #14821811

Subgroups — #14821811

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072982C211yesmaximal, characteristic, complemented
2#13071634C211yesmaximal, characteristic, complemented
3#13069927C211yesmaximal, characteristic, complemented
4#13069801C211yesmaximal, characteristic, complemented
5#13069749C211yesmaximal, characteristic, complemented
6#13069615C211yesmaximal, characteristic
7#13069300C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13069221C211yesmaximal, characteristic, complemented
10#13069190C211yesmaximal, characteristic, complemented
11#13068965C211yesmaximal, characteristic, complemented
12#13068932C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1988C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#67000—21no—
18C22×D88C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66948C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622844—21no—
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622604—21no—
33#10622603—21no—
34#10622601C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622553—21no—
44#10622552C2211yescharacteristic
45#10622552C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622281—21no—
48#10622278—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#67000—44no—
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×(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×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×D88—22no—
100C2×D88—41no—
101C2×D88—41no—
102#66948—22no—
103#66948—22no—
104#66948—22no—
105#66948—41no—
106#66946—22no—
107#66946—41no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—41no—
110C4×D44—44no—
111C11×C4⋊C8—41no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66885—22no—
119#66885—41no—
120(C2×D11)⋊C8—41no—
121(C2×D11)⋊C8—41no—
122C8×Dic11—41no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66873—41no—
127#66871—22no—
128#26720—111nomaximal, Sylow
129C23×D11—21no—
130C23×D11—21no—
131C23×D11C2×D411yescharacteristic
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11—81no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×D44—24no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—42no—
160C2×D44—42no—
161C2×D44—42no—
162C2×D44—42no—
163C2×D44—81no—
164C2×D44#4112yes—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C2×C4×D11—81no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4#4112yes—
190C11×C4⋊C4#4112yes—
191C11×C4⋊C4#4112yes—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—42no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—81no—
205(C2×D11)⋊C4—81no—
206(C2×D11)⋊C4D814yescomplemented
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—42no—
212Dic11⋊C4—42no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222D88—44no—
223#2491—111no—
224#2361—111no—
225#2054—111no—
226#2033—111no—
227#2023—111no—
228#1999—111no—
229#1988D1111yescharacteristic, complemented
230#1934—111no—
231#1925—111no—
232#1923—111no—
233#1918—111no—
234#1879—111no—
235#1874—111no—
236#1823—111no—
237C4×#102—111no—
238C23×C11C22×D411yescharacteristic
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—22no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11C2×D812yes—
260Q8×C11—84no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
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×C11C2×D812yes—
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11C2×D812yes—
300D44—22no—
301D44—22no—
302D44—48no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309D44—84no—
310C4×D11—41no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—41no—
314C4×D11—84no—
315C4×D11—84no—
316C8×C11—41no—
317C8×C11—41no—
318C11⋊C8—41no—
319C11⋊C8—41no—
320C22×D8—111no—
321C2×C4⋊Q8C2×D1111yescharacteristic
322C2×#124—221no—
323C2×#121—111no—
324C2×#121—111no—
325C2×C4×D4—111no—
326C2×C4×D4—221no—
327C22×C4⋊C4—111no—
328C2×#107—111no—
329C2×C4⋊C8C2×D1111yescharacteristic
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×C22⋊C8—111no—
337C2×C22⋊C8—111no—
338C2×C4×C8—111no—
339#394—221no—
340#393—221no—
341#390—111no—
342#390—111no—
343#390—111no—
344#389—111no—
345#388—221no—
346#388—221no—
347#386—221no—
348#385—221no—
349#380—111no—
350C4×C4⋊C4—111no—
351C4×C4⋊C4C2×D1111yescharacteristic
352C4×C22⋊C4—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340C2×D1111yescharacteristic
358#340C2×D1111yescharacteristic
359#340C2×D1111yescharacteristic
360#340C2×D1111yescharacteristic
361#336—111no—
362#336—111no—
363C22×C11#52511yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11C22×D811yescharacteristic
367C22×C11#57511yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57711yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C4×C11—22no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—81no—
397C4×C11#52911yescharacteristic
398C4×C11#53811yescharacteristic
399C4×C11#55511yescharacteristic
400C4×C11#55911yescharacteristic
401Dic11—22no—
402Dic11—41no—
403Dic11—41no—
404Dic11—81no—
405Dic11—81no—
406C22×Q8—21no—
407C22×D4—111no—
408C22×D4—111no—
409C22×D4—221no—
410C22×D4—221no—
411C23×C4—111no—
412C23×C4—221no—
413C23×C4—221no—
414C2×D8—222no—
415C2×D8—441no—
416C2×D8—441no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C4⋊Q8—22no—
422C4⋊Q8—41no—
423#124—444no—
424#121—222no—
425#121—222no—
426#121—222no—
427#121—441no—
428C4×D4—222no—
429C4×D4—444no—
430C4×D4—441no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—441no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C42—21no—
455C2×C42—111no—
456C2×C42—221no—
457C2×C42C22×D1111yescharacteristic
458#107—222no—
459C4⋊C8—41no—
460#102—222no—
461#102—222no—
462#102—222no—
463#102—222no—
464#102—441no—
465#102—441no—
466C22⋊C8—441no—
467C22⋊C8—441no—
468C4×C8—441no—
469#95—21no—
470#95—111no—
471#95—111no—
472#95—221no—
473#95—221no—
474#95—221no—
475C2×C11#245911yescharacteristic
476C2×C11#310011yescharacteristic
477C2×C11#312511yescharacteristic
478C2×C11#329411yescharacteristic
479C2×C11#329411yescharacteristic
480C2×C11#332111yescharacteristic
481C2×C11#332611yescharacteristic
482D11—42no—
483D11—82no—
484D11—161no—
485C24—111no—
486C24—221no—
487C24—221no—
488C2×Q8—42no—
489C2×Q8—42no—
490C2×Q8—81no—
491C2×D4—112no—
492C2×D4—224no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4—442no—
507C2×D4—442no—
508C2×D4—881no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—881no—
529C22×C4—881no—
530C22×C4D4×D1111yescharacteristic
531C22×C4D4×D1111yescharacteristic
532C22×C4C23×D1111yescharacteristic
533D8—444no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4#433912yes—
559C4⋊C4#434312yes—
560C4⋊C4#434312yes—
561C22⋊C4—114no—
562C22⋊C4—224no—
563C22⋊C4—441no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—442no—
570C22⋊C4—442no—
571C22⋊C4—881no—
572C22⋊C4—881no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—221no—
577C42—221no—
578C42—442no—
579C11#2672011yescharacteristic, complemented, Sylow
580C23—112no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—222no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23C2×D4×D1111yescharacteristic
602Q8—84no—
603D4—222no—
604D4—222no—
605D4—448no—
606D4—441no—
607D4—441no—
608D4—441no—
609D4—441no—
610D4—441no—
611D4—441no—
612D4—884no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—112no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—221no—
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—441no—
648C2×C4—441no—
649C2×C4—884no—
650C2×C4—884no—
651C2×C4D8×D1112yes—
652C2×C4C2×#433911yescharacteristic
653C2×C4#6703711yescharacteristic
654C2×C4C2×#434311yescharacteristic
655C2×C4C2×#434311yescharacteristic
656C2×C4#41×D1111yescharacteristic
657C2×C4#6704211yescharacteristic
658C8—41no—
659C8—41no—
660C8—441no—
661C8—441no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22—442no—
670C22—442no—
671C22—442no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22—881no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22#1062302111yescharacteristic
684C22#1062315811yescharacteristic
685C22#1062316111yescharacteristic
686C22C2×D8×D1111yescharacteristic
687C22#1062329311yescharacteristic
688C22#1062330811yescharacteristic
689C22#1062330911yescharacteristic
690C4—22no—
691C4—41no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—81no—
696C4—222no—
697C4—441no—
698C4—441no—
699C4—881no—
700C4—881no—
701C4#1062311111yescharacteristic
702C4#1062311611yescharacteristic
703C4#1062320911yescharacteristic
704C4#1062326511yescharacteristic
705C2—442no—
706C2—882no—
707C2—1761no—
708C2#1307256011yescharacteristic
709C2#1307861811yescharacteristic
710C2#1307890011yescharacteristic
711C2#1308042511yescharacteristic
712C2#1308042611yescharacteristic
713C2#1308079911yescharacteristic
714C2#1308086511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radical#13069615C2
hypercenter#1988D11
hypocenterC11#26720
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. #13072982C2semidirect
2. #13071634C2semidirect
3. #13069927C2semidirect
4. #13069801C2semidirect
5. #13069749C2semidirect
7. #13069300C2semidirect
8. #13069236C2semidirect
9. #13069221C2semidirect
10. #13069190C2semidirect
11. #13068965C2semidirect
12. #13068932C2semidirect
13. #13068701C2semidirect
14. #13068430C2semidirect
15. C11×#1988C2semidirect
206. (C2×D11)⋊C4D8semidirect
229. #1988D11semidirect
579. C11#26720semidirect

Maximal subgroups

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

subgroupindex
#130729822
#130716342
#130699272
#130698012
#130697492
#130696152
#130693002
#130692362
#130692212
#130691902
#130689652
#130689322
#130687012
#130684302
C11×#19882
#2672011