Finite Group Databasebeta

← #14826906

Subgroups — #14826906

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071680C211yesmaximal, characteristic, complemented
2#13070145C211yesmaximal, characteristic, complemented
3#13069926C211yesmaximal, characteristic, complemented
4#13069850C211yesmaximal, characteristic, complemented
5#13069686C211yesmaximal, characteristic
6#13069481C211yesmaximal, characteristic, complemented
7#13069236C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13069184C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068967C211yesmaximal, characteristic, complemented
12#13068967C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#2512C211yesmaximal, characteristic, complemented
16C2×C11×#126—21no—
17C22×#4323C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C2×#66946—21no—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#397—21no—
24C11×#396—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#388—21no—
30C11×#384C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622601—21no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622552C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622278—21no—
50#10622278—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×D44—21no—
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C11×#126—44no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4323—22no—
86C2×#4323—22no—
87C2×#4323—22no—
88C2×#4323—41no—
89C2×#4323—41no—
90C2×#4323—41no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66946—44no—
105#66927—22no—
106#66927—22no—
107C4×D44—22no—
108C4×D44—22no—
109C4×D44—41no—
110C4×D44—41no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118#66873—22no—
119#66873—22no—
120#66873—22no—
121#66873—41no—
122#66873—41no—
123#66873—41no—
124#66871—22no—
125#66871—41no—
126C4⋊(C11⋊C8)—41no—
127C4×C11⋊C8—41no—
128#27062—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11—21no—
131C23×D11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—42no—
163C2×D44—42no—
164C2×D44—81no—
165C2×D44—81no—
166C2×D44#4112yes—
167C2×D44#4112yes—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4D814yescomplemented
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—81no—
190C11×C22⋊C4—81no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—42no—
198#4323—44no—
199#4323—44no—
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—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11#4112yes—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—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#4112yes—
223#2512D1111yescharacteristic, complemented
224#2366—111no—
225#2093—111no—
226#2054—111no—
227#2041—111no—
228#2011—111no—
229#1970—111no—
230#1925—111no—
231#1925—111no—
232#1918—111no—
233#1916—111no—
234#1879—111no—
235#1879—111no—
236#1802—111no—
237C4×#102—111no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11C22×D411yescharacteristic
246C22×D11—22no—
247C22×D11—22no—
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×D11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
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—21no—
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×C11C2×D812yes—
289C2×C4×C11C2×D812yes—
290C2×C4×C11C2×D812yes—
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C2×Dic11—22no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303D44—22no—
304D44—22no—
305D44—22no—
306D44—22no—
307D44—48no—
308D44—41no—
309D44—41no—
310D44—41no—
311D44—41no—
312D44—84no—
313C4×D11—84no—
314C4×D11—84no—
315C11⋊C8—22no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C22×D8—111no—
320C22×D8—111no—
321C2×#127—111no—
322C2×#126—21no—
323C2×C4×D4—111no—
324C2×C4×D4—111no—
325C2×C4×D4—221no—
326C2×#107—111no—
327C2×#107—111no—
328C2×C4⋊C8—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×C4×C8—111no—
338#397—21no—
339#396—21no—
340#390—111no—
341#390—111no—
342#390—221no—
343#390C2×D1111yescharacteristic
344#390C2×D1111yescharacteristic
345#390C2×D1111yescharacteristic
346#389C2×D1111yescharacteristic
347#388—21no—
348#386—221no—
349#386—221no—
350#384C2×D1111yescharacteristic
351C4×C4⋊C4—111no—
352C4×C4⋊C4C2×D1111yescharacteristic
353C4×C4⋊C4C2×D1111yescharacteristic
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#336—111no—
359#336—111no—
360#336—111no—
361#336—111no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11#52511yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11#55011yescharacteristic
372C22×C11C22×D811yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57711yescharacteristic
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C2×D11—42no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C4×C11—22no—
391C4×C11—22no—
392C4×C11—22no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11#52911yescharacteristic
400C4×C11#53811yescharacteristic
401C4×C11#55111yescharacteristic
402C4×C11#55311yescharacteristic
403Dic11—42no—
404Dic11—81no—
405C22×D4—111no—
406C22×D4—111no—
407C22×D4—221no—
408C22×D4—221no—
409C22×D4C22×D1111yescharacteristic
410C23×C4—221no—
411C23×C4—221no—
412C2×D8—222no—
413C2×D8—222no—
414C2×D8—222no—
415C2×D8—441no—
416C2×D8—441no—
417C2×D8—441no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—111no—
422#127—222no—
423#127—222no—
424#126—44no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—441no—
428C4×D4—441no—
429C4×D4—444no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4C22⋊D1111yescharacteristic
436C2×C4⋊C4C22⋊D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
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×C42—21no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455C2×C42C22×D1111yescharacteristic
456C2×C42C22×D1111yescharacteristic
457#107—222no—
458#107—441no—
459C4⋊C8—441no—
460#102—222no—
461#102—222no—
462#102—222no—
463#102—222no—
464#102—441no—
465#102—441no—
466#102—441no—
467#102—441no—
468C4×C8—441no—
469#95—21no—
470#95—21no—
471#95—221no—
472#95C22⋊D1111yescharacteristic
473#95C22⋊D1111yescharacteristic
474C2×C11—161no—
475C2×C11#246711yescharacteristic
476C2×C11#310011yescharacteristic
477C2×C11#311811yescharacteristic
478C2×C11#329411yescharacteristic
479C2×C11#330911yescharacteristic
480C2×C11#339111yescharacteristic
481C2×C11#340111yescharacteristic
482D11—82no—
483D11—82no—
484C24—21no—
485C24—221no—
486C24—221no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—112no—
494C2×D4—112no—
495C2×D4—224no—
496C2×D4—224no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4—881no—
510C2×D4—881no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—881no—
521C22×C4—881no—
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C2×C22⋊D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529D8—444no—
530D8—444no—
531C2×C8—112no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—41no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—112no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4#432314yescomplemented
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—442no—
578C11#2706211yescharacteristic, complemented, Sylow
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—222no—
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—
600C23C22×C22⋊D1111yescharacteristic
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—222no—
606D4—222no—
607D4—222no—
608D4—222no—
609D4—448no—
610D4—441no—
611D4—441no—
612D4—441no—
613D4—441no—
614D4—884no—
615C2×C4—21no—
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—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—222no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—884no—
646C2×C4—884no—
647C2×C4C2×#432312yes—
648C2×C4C2×#432312yes—
649C2×C4C2×#432312yes—
650C2×C4#41×D1111yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#6704211yescharacteristic
655C2×C4#6704211yescharacteristic
656C8—222no—
657C8—441no—
658C8—441no—
659C8—441no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—442no—
668C22—442no—
669C22—442no—
670C22—442no—
671C22—442no—
672C22—442no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22—881no—
680C22—881no—
681C22C22×#432311yescharacteristic
682C22#1062335311yescharacteristic
683C22#1062335911yescharacteristic
684C22#1062336011yescharacteristic
685C22#1062336511yescharacteristic
686C22#1062336611yescharacteristic
687C22#1062336811yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—442no—
698C4—881no—
699C4#1062323511yescharacteristic
700C4#1062323611yescharacteristic
701C4#1062323711yescharacteristic
702C4#1062324011yescharacteristic
703C2—161no—
704C2—882no—
705C2—882no—
706C2#1307266311yescharacteristic
707C2#1307861211yescharacteristic
708C2#1307879411yescharacteristic
709C2#1308042311yescharacteristic
710C2#1308061611yescharacteristic
711C2#1308158811yescharacteristic
712C2#1308168211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2512C2
socleC23×C11C22×D4
prime radical#13069686C2
hypercenter#2512D11
hypocenterC11#27062
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. #13071680C2semidirect
2. #13070145C2semidirect
3. #13069926C2semidirect
4. #13069850C2semidirect
6. #13069481C2semidirect
7. #13069236C2semidirect
8. #13069233C2semidirect
9. #13069184C2semidirect
10. #13069175C2semidirect
11. #13068967C2semidirect
12. #13068967C2semidirect
13. #13068613C2semidirect
14. C4×#66873C2semidirect
15. C11×#2512C2semidirect
184. C11×C4⋊C4D8semidirect
223. #2512D11semidirect
557. C4⋊C4#4323semidirect
578. C11#27062semidirect

Maximal subgroups

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

subgroupindex
#130716802
#130701452
#130699262
#130698502
#130696862
#130694812
#130692362
#130692332
#130691842
#130691752
#130689672
#130686132
C4×#668732
C11×#25122
#2706211