Finite Group Databasebeta

← #14816777

Subgroups — #14816777

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic
2C2×#10622465C211yesmaximal, characteristic
3#13072451C211yesmaximal, characteristic, complemented
4#13071525C211yesmaximal, characteristic
5#13070165C211yesmaximal, characteristic, complemented
6#13070101C211yesmaximal, characteristic, complemented
7#13070008C211yesmaximal, characteristic, complemented
8#13069348C211yesmaximal, characteristic, complemented
9#13069176C211yesmaximal, characteristic, complemented
10#13068951C211yesmaximal, characteristic
11#13068949C211yesmaximal, characteristic
12#13068874C211yesmaximal, characteristic
13#13068871C211yesmaximal, characteristic, complemented
14#13068864C211yesmaximal, characteristic
15C11×#2058C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622843—21no—
26#10622842—21no—
27C2×#66885C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622700—24no—
31#10622602—21no—
32#10622600—21no—
33#10622598C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622597—21no—
36#10622591—21no—
37#10622590C2211yescharacteristic
38#10622587C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622542C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622465—24no—
51#10622281—21no—
52D11×#95—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
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⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314Q814yescomplemented
97#66946—22no—
98#66946—22no—
99#66946—22no—
100#66946—41no—
101#66940—22no—
102#66940—41no—
103C4×D44—22no—
104C4×D44—41no—
105C11×#106—22no—
106C11×#106—41no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66885—22no—
120#66880—41no—
121C8×Dic11—22no—
122#66874—22no—
123#66874—22no—
124#66873—22no—
125#66873D414yes—
126#66871—22no—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#26372—111nomaximal, Sylow
131C23×D11—21no—
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×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C2×D412yes—
153C2×D44C2×Q812yes—
154C2×D44#4112yes—
155C2×C4×D11—24no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C2×Q812yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×Q812yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—81no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4#4112yes—
186C42×C11—21no—
187C42×C11—21no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—81no—
196C4⋊Dic11—81no—
197Dic11⋊C4—22no—
198Dic11⋊C4—22no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C2×D412yes—
212#4314—28no—
213C2×#474—111no—
214C2×C4×SD16—111no—
215#2451—111no—
216#2349—111no—
217#2097—111no—
218#2085—111no—
219#2068—111no—
220#2058D1111yescharacteristic, complemented
221#1942—111no—
222#1916—111no—
223#1877—111no—
224#1877—111no—
225#1864—111no—
226#1863—111no—
227#1862—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—84no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11#13512yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11#13712yes—
282D44—22no—
283D44—22no—
284D44—22no—
285D44C22⋊Q814yes—
286C4×D11—84no—
287C4×D11—84no—
288C4×D11—84no—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293C8×C11—22no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×SD16—111no—
298C2×C4⋊Q8C2×D1111yescharacteristic
299C2×C4×Q8—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—111no—
303#474—224no—
304C4×SD16—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#106C2×D1111yescharacteristic
309C2×#106C2×D1111yescharacteristic
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C4×C8—111no—
318#398—221no—
319#395—221no—
320#391—111no—
321#391—111no—
322#391—221no—
323#389—111no—
324#389—111no—
325#389—111no—
326#389C2×D1111yescharacteristic
327#387—221no—
328#385—221no—
329#385—221no—
330#382—111no—
331#380—221no—
332C4×C4⋊C4—111no—
333C2×#95—221no—
334#340—111no—
335#340—111no—
336#340C2×D1111yescharacteristic
337#340C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11D4×Q811yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57711yescharacteristic
349C2×D11—24no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—22no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C2×C22⋊Q811yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#54711yescharacteristic
365C4×C11#55411yescharacteristic
366Dic11—22no—
367Dic11—41no—
368Dic11—41no—
369Dic11—42no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8—21no—
374C22×Q8—111no—
375C22×D4—111no—
376C23×C4—221no—
377C23×C4—221no—
378C23×C4—221no—
379C2×SD16—114no—
380C2×SD16—222no—
381C2×SD16—222no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C4⋊Q8—22no—
387C4⋊Q8—41no—
388C4×Q8—222no—
389C4×Q8—441no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—441no—
395C4×D4—441no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#107—222no—
418#107—222no—
419#107—222no—
420#106—22no—
421#106—41no—
422C4⋊C8—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—114no—
427#102—222no—
428#102—222no—
429C4×C8—222no—
430#95—21no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11#244911yescharacteristic
443C2×C11#310711yescharacteristic
444C2×C11#311811yescharacteristic
445C2×C11#326611yescharacteristic
446C2×C11#328011yescharacteristic
447C2×C11#338111yescharacteristic
448C2×C11#338511yescharacteristic
449D11—44no—
450C24—221no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8—112no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×D4—112no—
461C2×D4—112no—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—224no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489SD16—228no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8Q8×D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—81no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4D4×D1112yes—
521C4⋊C4#434312yes—
522C22⋊C4—224no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C42—21no—
526C42—21no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—442no—
532C11#2637211yescharacteristic, complemented, Sylow
533C23—222no—
534C23—222no—
535C23—222no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C2×D4×D1111yescharacteristic
541Q8—84no—
542Q8—222no—
543Q8—222no—
544Q8—441no—
545Q8—441no—
546D4—114no—
547D4—222no—
548D4—222no—
549D4—222no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—112no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—884no—
589C2×C4—884no—
590C2×C4—884no—
591C2×C4#6696912yes—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4C2×Q8×D1111yescharacteristic
595C2×C4C2×#434311yescharacteristic
596C2×C4#6704011yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C8—22no—
599C8—41no—
600C8—222no—
601C8—441no—
602C22—224no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22#1062312111yescharacteristic
610C22#1062315811yescharacteristic
611C22#1062325811yescharacteristic
612C22C2×#6696911yescharacteristic
613C22#1062329311yescharacteristic
614C22#1062330511yescharacteristic
615C22D11×#13711yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—81no—
621C4—81no—
622C4—222no—
623C4—441no—
624C4—442no—
625C4—441no—
626C4—441no—
627C4—881no—
628C4—881no—
629C4D11×C22⋊Q811yescharacteristic
630C4#1062316911yescharacteristic
631C4#1062325711yescharacteristic
632C4#1062326111yescharacteristic
633C2—444no—
634C2#1307241811yescharacteristic
635C2#1307869011yescharacteristic
636C2#1307880511yescharacteristic
637C2#1308012911yescharacteristic
638C2#1308029411yescharacteristic
639C2#1308149611yescharacteristic
640C2#1308152311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2058C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2058D11
hypocenterC11#26372
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
3. #13072451C2semidirect
5. #13070165C2semidirect
6. #13070101C2semidirect
7. #13070008C2semidirect
8. #13069348C2semidirect
9. #13069176C2semidirect
13. #13068871C2semidirect
15. C11×#2058C2semidirect
96. C2×#4314Q8semidirect
220. #2058D11semidirect
532. C11#26372semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106224652
#130724512
#130715252
#130701652
#130701012
#130700082
#130693482
#130691762
#130689512
#130689492
#130688742
#130688712
#130688642
C11×#20582
#2637211