Finite Group Databasebeta

← #14813923

Subgroups — #14813923

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic
3#13072388C211yesmaximal, characteristic, complemented
4#13071525C211yesmaximal, characteristic
5#13070162C211yesmaximal, characteristic, complemented
6#13070118C211yesmaximal, characteristic, complemented
7#13070037C211yesmaximal, characteristic, complemented
8#13069294C211yesmaximal, characteristic, complemented
9#13069176C211yesmaximal, characteristic, complemented
10#13068947C211yesmaximal, characteristic
11#13068947C211yesmaximal, characteristic
12#13068947C211yesmaximal, characteristic
13#13068872C211yesmaximal, characteristic, complemented
14#13068866C211yesmaximal, characteristic
15C11×#2043C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#389C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622696—24no—
38#10622602—21no—
39#10622600—21no—
40#10622599—21no—
41#10622598C2211yescharacteristic
42#10622596—21no—
43#10622591—21no—
44#10622591—21no—
45#10622590C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622401—24no—
51#10622281—21no—
52D11×#95—21no—
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—22no—
78Q8×Dic11—41no—
79C2×#4325—22no—
80C2×#4325—22no—
81C2×#4325—22no—
82C2×#4325—22no—
83C2×#4325—22no—
84C2×#4325D414yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66946—22no—
102#66946—22no—
103#66946—22no—
104#66946—41no—
105C4×D44—22no—
106C4×D44—41no—
107C11×#103—22no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—41no—
111C11×#95—21no—
112#66899—22no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
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⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66885—22no—
127#66885—22no—
128#66882—41no—
129C8×Dic11—22no—
130#66872—22no—
131C4⋊(C11⋊C8)—22no—
132#26170—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C2×D412yes—
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×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C2×D412yes—
164C2×D44#4112yes—
165C2×D44#4112yes—
166C2×C4×D11—24no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C2×C4×D11—81no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4#4112yes—
188C42×C11—21no—
189C42×C11—21no—
190#4325—28no—
191#4325—44no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—81no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—42no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
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⋊C8C2×D412yes—
217C2×#461—111no—
218C2×C4×SD16—111no—
219#2446—111no—
220#2349—111no—
221#2097—111no—
222#2088—111no—
223#2074—111no—
224#2043D1111yescharacteristic, complemented
225#1933—111no—
226#1916—111no—
227#1877—111no—
228#1877—111no—
229#1877—111no—
230#1863—111no—
231#1862—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11#13512yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11#13712yes—
293D44—22no—
294D44—22no—
295D44—22no—
296D44#12314yes—
297C4×D11—84no—
298C4×D11—84no—
299C4×D11—84no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C22×SD16—111no—
306C2×C4⋊Q8C2×D1111yescharacteristic
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4—111no—
311#461—224no—
312C4×SD16—224no—
313C2×#107—111no—
314C2×#106—111no—
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#103C2×D1111yescharacteristic
321C2×#103C2×D1111yescharacteristic
322C2×#102—111no—
323C2×#102—111no—
324C2×C4×C8—111no—
325#400—221no—
326#398—221no—
327#391—111no—
328#391—111no—
329#391—111no—
330#389—111no—
331#389—111no—
332#389C2×D1111yescharacteristic
333#387—221no—
334#387—221no—
335#385—221no—
336#385—221no—
337#382—111no—
338#380—221no—
339C4×C4⋊C4—111no—
340C2×#95—221no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#336—111no—
346#336—111no—
347#336—111no—
348#336C2×D1111yescharacteristic
349C22×C11#52511yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11C2×#13511yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57711yescharacteristic
356C2×D11—24no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C4×C11—22no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11C2×#12311yescharacteristic
370C4×C11#53911yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55311yescharacteristic
373Dic11—22no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8C22×D1111yescharacteristic
381C22×Q8C22×D1111yescharacteristic
382C22×D4—111no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4—221no—
386C2×SD16—114no—
387C2×SD16—222no—
388C2×SD16—222no—
389C2×SD16—222no—
390C2×SD16—222no—
391C2×SD16—222no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8—22no—
397C4⋊Q8—41no—
398C4×Q8—222no—
399C4×Q8—441no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—441no—
405C4×D4—441no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#107—441no—
427#106—222no—
428C4⋊C8—222no—
429#103—22no—
430#103—22no—
431#103—22no—
432#103—41no—
433#103—222no—
434#103—222no—
435#102—222no—
436#102—222no—
437C4×C8—222no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11#244311yescharacteristic
452C2×C11#310711yescharacteristic
453C2×C11#312311yescharacteristic
454C2×C11#326611yescharacteristic
455C2×C11#328211yescharacteristic
456C2×C11#336011yescharacteristic
457C2×C11#337211yescharacteristic
458D11—44no—
459C24—221no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8D4×D1112yes—
472C2×D4—112no—
473C2×D4—112no—
474C2×D4—112no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—224no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4—881no—
497C22×C4—881no—
498C22×C4D4×D1111yescharacteristic
499C22×C4D4×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501SD16—228no—
502SD16—444no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—112no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—81no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—881no—
532C4⋊C4#434112yes—
533C22⋊C4—224no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C42—21no—
537C42—21no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—442no—
543C11#2617011yescharacteristic, complemented, Sylow
544C23—222no—
545C23—222no—
546C23—222no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23C2×D4×D1111yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558Q8—41no—
559Q8—41no—
560D4—114no—
561D4—222no—
562D4—222no—
563D4—222no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—112no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4—884no—
604C2×C4—884no—
605C2×C4#6697212yes—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—41no—
613C8—41no—
614C8—222no—
615C8—441no—
616C22—224no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22—442no—
623C22#1062312111yescharacteristic
624C22#1062313711yescharacteristic
625C22#1062320811yescharacteristic
626C22#1062329311yescharacteristic
627C22C2×#6697211yescharacteristic
628C22D11×#13711yescharacteristic
629C22#1062330911yescharacteristic
630C4—22no—
631C4—41no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—222no—
637C4—441no—
638C4—441no—
639C4—441no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062314211yescharacteristic
644C4#1062314511yescharacteristic
645C4D11×#12311yescharacteristic
646C4#1062319111yescharacteristic
647C2—444no—
648C2#1307234411yescharacteristic
649C2#1307868611yescharacteristic
650C2#1307886611yescharacteristic
651C2#1308012911yescharacteristic
652C2#1308031611yescharacteristic
653C2#1308127011yescharacteristic
654C2#1308139411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2043D11
hypocenterC11#26170
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
3. #13072388C2semidirect
5. #13070162C2semidirect
6. #13070118C2semidirect
7. #13070037C2semidirect
8. #13069294C2semidirect
9. #13069176C2semidirect
13. #13068872C2semidirect
15. C11×#2043C2semidirect
224. #2043D11semidirect
543. C11#26170semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×#106224012
#130723882
#130715252
#130701622
#130701182
#130700372
#130692942
#130691762
#130689472
#130688722
#130688662
C11×#20432
#2617011