Finite Group Databasebeta

← #14811007

Subgroups — #14811007

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×#10622697C211yesmaximal, characteristic, complemented
2C2×#10622615C211yesmaximal, characteristic
3#13071447C211yesmaximal, characteristic
4#13070167C211yesmaximal, characteristic, complemented
5#13069994C211yesmaximal, characteristic, complemented
6#13069994C211yesmaximal, characteristic, complemented
7#13069754C211yesmaximal, characteristic, complemented
8#13068876C211yesmaximal, characteristic, complemented
9#13068862C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic, complemented
11#13068796C211yesmaximal, characteristic, complemented
12#13068639C211yesmaximal, characteristic, complemented
13#13068623C211yesmaximal, characteristic, complemented
14#13068554C211yesmaximal, characteristic
15C11×#2439C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C11×#396—21no—
23C11×#393—21no—
24C11×#391—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#382C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622697—24no—
34#10622615—24no—
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622569—21no—
48#10622569—21no—
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622277—21no—
54D11×#95—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—22no—
67C2×#4339—41no—
68C2×#4339—41no—
69C2×#4339Q814yescomplemented
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8—41no—
77C11×#117—22no—
78C11×#117—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×D44—22no—
106C4×D44—22no—
107C4×D44—41no—
108C4×D44—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C22⋊(C11⋊C8)—22no—
122#66874—22no—
123#66874—22no—
124#66874—41no—
125#66874—41no—
126#66873—22no—
127#66873—22no—
128#66873—22no—
129#66873D414yes—
130#66872—22no—
131#66872—22no—
132#66872—41no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—41no—
136#25962—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C23×D11—21no—
139C2×Q8×C11—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11—81no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×Q812yes—
156C22×C4×C11#4112yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—24no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—42no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164#4339—28no—
165#4339—44no—
166#4339—44no—
167#4339—44no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44C2×D412yes—
172C2×D44C2×Q812yes—
173C2×D44#4112yes—
174C2×C4×D11—24no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—42no—
180C2×C4×D11—42no—
181C2×C4×D11—81no—
182C2×C4×D11—81no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22C2×Q812yes—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—81no—
199C11×C4⋊C4C2×D412yes—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—42no—
203C11×C22⋊C4—81no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C42×C11—42no—
209C22⋊Dic11—81no—
210(C2×D11)⋊C4—42no—
211(C2×D11)⋊C4—42no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—44no—
228C2×C11⋊C8C2×D412yes—
229C2×#476—111no—
230C2×#416—111no—
231#2439D1111yescharacteristic, complemented
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—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11C22⋊Q812yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259Q8×C11—84no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11C22⋊Q812yes—
290C2×C4×C11#13512yes—
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×Q811yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C22⋊D11—48no—
298C2×Dic11—22no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307D44—22no—
308D44—22no—
309D44—22no—
310D44C22⋊Q814yes—
311C4×D11—48no—
312C4×D11—84no—
313C4×D11—84no—
314Dic22—22no—
315Dic22—22no—
316Dic22—41no—
317Dic22—41no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C11⋊C8—41no—
321C11⋊C8—41no—
322C22×#41—111no—
323C23×C8—111no—
324C2×C4⋊Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×#117C2×D1111yescharacteristic
328#476—224no—
329C2×#107—111no—
330C2×#106—111no—
331C2×#106—111no—
332C2×#106—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335#416—224no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#102—111no—
344C2×C22⋊C8—111no—
345#396—21no—
346#393—21no—
347#391—21no—
348#391—111no—
349#391—111no—
350#389C2×D1111yescharacteristic
351#389C2×D1111yescharacteristic
352#387—21no—
353#386—221no—
354#386—221no—
355#382C2×D1111yescharacteristic
356#381—221no—
357#380—111no—
358#380C2×D1111yescharacteristic
359C4×C22⋊C4C2×D1111yescharacteristic
360C2×#95—221no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365#336—111no—
366#336—111no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11C2×C22⋊Q811yescharacteristic
375C22×C11D4211yescharacteristic
376C22×C11#54611yescharacteristic
377C22×C11C2×#13511yescharacteristic
378C22×C11#57511yescharacteristic
379C22×C11#57711yescharacteristic
380C22×C11#57711yescharacteristic
381C2×D11—24no—
382C2×D11—42no—
383C2×D11—42no—
384C2×D11—42no—
385C2×D11—42no—
386C2×D11—42no—
387C2×D11—42no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—41no—
391C4×C11—42no—
392C4×C11—41no—
393C4×C11—41no—
394C4×C11—81no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11C2×C22⋊Q811yescharacteristic
398C4×C11#54311yescharacteristic
399C4×C11#54611yescharacteristic
400C4×C11#55111yescharacteristic
401Dic11—42no—
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—111no—
413C22×D4—221no—
414C23×C4—221no—
415C23×C4—221no—
416C23×C4—221no—
417C23×C4C22×D1111yescharacteristic
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—111no—
422C22×C8—222no—
423C22×C8—222no—
424C22×C8—441no—
425C4⋊Q8—22no—
426C4⋊Q8—41no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—441no—
430C4×D4—441no—
431#117—22no—
432#117—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4C22⋊D1111yescharacteristic
448C2×C22⋊C4C22⋊D1111yescharacteristic
449C2×C42—21no—
450C2×C42C22×D1111yescharacteristic
451C2×C42C22×D1111yescharacteristic
452#107—441no—
453#106—222no—
454#106—222no—
455#106—441no—
456C4⋊C8—222no—
457C4⋊C8—441no—
458#103—222no—
459#103—222no—
460#103—441no—
461#103—441no—
462#102—114no—
463#102—222no—
464#102—222no—
465#102—222no—
466C22⋊C8—222no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95C22⋊D1111yescharacteristic
478#95C22⋊D1111yescharacteristic
479C2×C11—42no—
480C2×C11#243711yescharacteristic
481C2×C11#307611yescharacteristic
482C2×C11#308411yescharacteristic
483C2×C11#326711yescharacteristic
484C2×C11#328211yescharacteristic
485C2×C11#330311yescharacteristic
486C2×C11#331111yescharacteristic
487D11—44no—
488C24—221no—
489C24C2×C22⋊D1111yescharacteristic
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—112no—
504C2×D4—112no—
505C2×D4—112no—
506C2×D4—224no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—442no—
511C2×D4—442no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—221no—
521C22×C4—224no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4—881no—
531C22×C4—881no—
532C22×C4Q8×D1112yes—
533C22×C4#434312yes—
534C22×C4C2×C22⋊D1111yescharacteristic
535C22×C4C2×C22⋊D1111yescharacteristic
536C22×C4C2×C22⋊D1111yescharacteristic
537C22×C4C2×C22⋊D1111yescharacteristic
538C22×C4C2×C22⋊D1111yescharacteristic
539C22×C4C23×D1111yescharacteristic
540C2×C8—112no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—444no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—81no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4D4×D1112yes—
568C22⋊C4—22no—
569C22⋊C4—41no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—442no—
573C22⋊C4—442no—
574C22⋊C4—881no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C11#2596211yescharacteristic, complemented, Sylow
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—222no—
588C23—222no—
589C23—222no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23#6699912yes—
595C23C22×C22⋊D1111yescharacteristic
596Q8—84no—
597Q8—222no—
598Q8—222no—
599Q8—441no—
600Q8—441no—
601D4—114no—
602D4—222no—
603D4—222no—
604D4—222no—
605D4—448no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—222no—
636C2×C4—448no—
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—884no—
646C2×C4—884no—
647C2×C4#6699912yes—
648C2×C4#6700312yes—
649C2×C4C2×D4×D1111yescharacteristic
650C2×C4#6703711yescharacteristic
651C2×C4C2×Q8×D1111yescharacteristic
652C2×C4C2×#434311yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#6704211yescharacteristic
655C8—222no—
656C8—441no—
657C8—441no—
658C8—441no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—224no—
667C22—442no—
668C22—442no—
669C22—442no—
670C22—442no—
671C22—442no—
672C22—442no—
673C22D4×C22⋊D1111yescharacteristic
674C22C2×#6699911yescharacteristic
675C22C2×#6700311yescharacteristic
676C22#1062335311yescharacteristic
677C22#1062336011yescharacteristic
678C22#1062336711yescharacteristic
679C22#1062336811yescharacteristic
680C4—22no—
681C4—22no—
682C4—41no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4—442no—
690C4—881no—
691C4—881no—
692C4D11×C22⋊Q811yescharacteristic
693C4#1062316111yescharacteristic
694C4#1062316511yescharacteristic
695C4#1062316811yescharacteristic
696C2—42no—
697C2—444no—
698C2#1307227911yescharacteristic
699C2#1307839811yescharacteristic
700C2#1307847411yescharacteristic
701C2#1308013711yescharacteristic
702C2#1308032411yescharacteristic
703C2#1308053811yescharacteristic
704C2#1308064611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2439C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#2439D11
hypocenterC11#25962
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2439

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
4. #13070167C2semidirect
5. #13069994C2semidirect
6. #13069994C2semidirect
7. #13069754C2semidirect
8. #13068876C2semidirect
9. #13068862C2semidirect
10. #13068815C2semidirect
11. #13068796C2semidirect
12. #13068639C2semidirect
13. #13068623C2semidirect
15. C11×#2439C2semidirect
69. C2×#4339Q8semidirect
231. #2439D11semidirect
580. C11#25962semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106226152
#130714472
#130701672
#130699942
#130697542
#130688762
#130688622
#130688152
#130687962
#130686392
#130686232
#130685542
C11×#24392
#2596211