Finite Group Databasebeta

← #14821799

Subgroups — #14821799

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#13072981C211yesmaximal, characteristic, complemented
2#13071636C211yesmaximal, characteristic, complemented
3#13069924C211yesmaximal, characteristic, complemented
4#13069795C211yesmaximal, characteristic, complemented
5#13069750C211yesmaximal, characteristic, complemented
6#13069566C211yesmaximal, characteristic, complemented
7#13069301C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13069190C211yesmaximal, characteristic, complemented
11#13068966C211yesmaximal, characteristic, complemented
12#13068934C211yesmaximal, characteristic, complemented
13#13068703C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#1999C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×#66989—21no—
20C2×D4×Dic11—21no—
21C2×D4×Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66941C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622835—21no—
28#10622834C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31#10622833—21no—
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622825C2211yescharacteristic
37C4×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622598C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622564—21no—
46#10622563—21no—
47#10622560—21no—
48#10622558—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C2×C11×D8—22no—
68C2×C11×D8—41no—
69C2×C11×D8—41no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90#66989—44no—
91D4×Dic11—22no—
92D4×Dic11—41no—
93D4×Dic11—44no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—41no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66941—22no—
110#66941—41no—
111C11×#102—22no—
112C11×#102—22no—
113C11×C22⋊C8—41no—
114#66896—22no—
115#66896—22no—
116#66896—41no—
117#66896—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124C22⋊(C11⋊C8)—41no—
125Dic11⋊C8—41no—
126C8×Dic11—41no—
127#66871—22no—
128#26720—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C2×D4×C11—24no—
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—21no—
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C2×D4×C11—81no—
149C2×D4×C11#4112yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—81no—
169C22×Dic11—81no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C2×Dic22—42no—
175C2×Dic22—42no—
176C2×Dic22—81no—
177C11×D8—44no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4#4112yes—
187C11×C4⋊C4#4112yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—42no—
190C22⋊Dic11—41no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11—81no—
198C22⋊Dic11—81no—
199C22⋊Dic11D814yescomplemented
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223#2491—111no—
224#2361—111no—
225#2054—111no—
226#2033—111no—
227#2023—111no—
228#1999D1111yescharacteristic
229#1988—111no—
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×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11C2×D812yes—
259C23×C11C22×D411yescharacteristic
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—48no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—84no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—22no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
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—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—84no—
312C2×Dic11—84no—
313C2×Dic11C2×D812yes—
314C2×Dic11C2×D812yes—
315Dic22—84no—
316C8×C11—41no—
317C8×C11—41no—
318C11⋊C8—41no—
319C11⋊C8—41no—
320C22×D8C2×D1111yescharacteristic
321C2×C4⋊Q8—111no—
322C2×#124—221no—
323C2×#121C2×D1111yescharacteristic
324C2×#121C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4—221no—
327C22×C4⋊C4—111no—
328C2×#107—111no—
329C2×C4⋊C8—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102C2×D1111yescharacteristic
335C2×#102C2×D1111yescharacteristic
336C2×C22⋊C8—111no—
337C2×C22⋊C8C2×D1111yescharacteristic
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⋊C4—111no—
352C4×C22⋊C4—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340C2×D1111yescharacteristic
361#336—111no—
362#336—111no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—81no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11#52511yescharacteristic
385C22×C11#54611yescharacteristic
386C22×C11#54611yescharacteristic
387C22×C11C22×D811yescharacteristic
388C22×C11#57511yescharacteristic
389C22×C11#57711yescharacteristic
390C22×C11#57711yescharacteristic
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—42no—
394C4×C11#52911yescharacteristic
395C4×C11#53811yescharacteristic
396C4×C11#55511yescharacteristic
397C4×C11#55911yescharacteristic
398Dic11—22no—
399Dic11—22no—
400Dic11—42no—
401Dic11—41no—
402Dic11—41no—
403Dic11—81no—
404Dic11—81no—
405Dic11—81no—
406C22×Q8—221no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4C22×D1111yescharacteristic
410C22×D4C22×D1111yescharacteristic
411C23×C4—221no—
412C23×C4—221no—
413C23×C4C22×D1111yescharacteristic
414C2×D8—22no—
415C2×D8—41no—
416C2×D8—41no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C4⋊Q8—222no—
422C4⋊Q8—441no—
423#124—444no—
424#121—22no—
425#121—22no—
426#121—22no—
427#121—41no—
428C4×D4—222no—
429C4×D4—441no—
430C4×D4—444no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—441no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—111no—
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—111no—
455C2×C42—111no—
456C2×C42—221no—
457C2×C42—221no—
458#107—222no—
459C4⋊C8—441no—
460#102—22no—
461#102—22no—
462#102—222no—
463#102—222no—
464#102—441no—
465#102—441no—
466C22⋊C8—41no—
467C22⋊C8—441no—
468C4×C8—441no—
469#95—111no—
470#95—111no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475C2×C11—42no—
476C2×C11—82no—
477C2×C11—161no—
478C2×C11#245911yescharacteristic
479C2×C11#310011yescharacteristic
480C2×C11#312511yescharacteristic
481C2×C11#329411yescharacteristic
482C2×C11#329411yescharacteristic
483C2×C11#332111yescharacteristic
484C2×C11#332611yescharacteristic
485C24—21no—
486C24—21no—
487C24D4×D1111yescharacteristic
488C2×Q8—442no—
489C2×Q8—442no—
490C2×Q8—881no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—81no—
508C2×D4#434112yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4—881no—
530C22×C4—881no—
531C22×C4D4×D1111yescharacteristic
532C22×C4C23×D1111yescharacteristic
533D8—44no—
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—112no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4#434112yes—
560C4⋊C4#434112yes—
561C22⋊C4—24no—
562C22⋊C4—42no—
563C22⋊C4—114no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—441no—
568C22⋊C4—442no—
569C22⋊C4—442no—
570C22⋊C4—442no—
571C22⋊C4—881no—
572C22⋊C4—881no—
573C42—221no—
574C42—221no—
575C42—221no—
576C42—221no—
577C42—442no—
578C42—442no—
579C11#2672011yescharacteristic, complemented, Sylow
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23D8×D1112yes—
601C23C2×D4×D1111yescharacteristic
602Q8—884no—
603D4—22no—
604D4—22no—
605D4—48no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—41no—
612D4—84no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—112no—
627C2×C4—112no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—222no—
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—441no—
650C2×C4—884no—
651C2×C4—884no—
652C2×C4C2×#434111yescharacteristic
653C2×C4C2×#434111yescharacteristic
654C2×C4C2×#434111yescharacteristic
655C2×C4#6703711yescharacteristic
656C2×C4#6703711yescharacteristic
657C2×C4#41×D1111yescharacteristic
658C8—41no—
659C8—41no—
660C8—441no—
661C8—441no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22#1062311711yescharacteristic
684C22#1062312211yescharacteristic
685C22#1062314111yescharacteristic
686C22C2×D8×D1111yescharacteristic
687C22#1062330111yescharacteristic
688C22#1062330411yescharacteristic
689C22#1062330611yescharacteristic
690C4—42no—
691C4—42no—
692C4—41no—
693C4—222no—
694C4—222no—
695C4—441no—
696C4—442no—
697C4—441no—
698C4—881no—
699C4—881no—
700C4—881no—
701C4#1062312411yescharacteristic
702C4#1062313111yescharacteristic
703C4#1062314711yescharacteristic
704C4#1062324411yescharacteristic
705C2—42no—
706C2—82no—
707C2—161no—
708C2#1307254811yescharacteristic
709C2#1307861111yescharacteristic
710C2#1307889411yescharacteristic
711C2#1308042211yescharacteristic
712C2#1308042411yescharacteristic
713C2#1308079711yescharacteristic
714C2#1308086211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#1999C2
socleC23×C11C22×D4
hypercenter#1999D11
hypocenterC11#26720
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1999

Complements

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

NH ≅ G/Ntype
1. #13072981C2semidirect
2. #13071636C2semidirect
3. #13069924C2semidirect
4. #13069795C2semidirect
5. #13069750C2semidirect
6. #13069566C2semidirect
7. #13069301C2semidirect
8. #13069239C2semidirect
9. #13069219C2semidirect
10. #13069190C2semidirect
11. #13068966C2semidirect
12. #13068934C2semidirect
13. #13068703C2semidirect
14. #102×Dic11C2semidirect
199. C22⋊Dic11D8semidirect
579. C11#26720semidirect

Maximal subgroups

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

subgroupindex
#130729812
#130716362
#130699242
#130697952
#130697502
#130695662
#130693012
#130692392
#130692192
#130691902
#130689662
#130689342
#130687032
#102×Dic112
C11×#19992
#2672011