Finite Group Databasebeta

← #14812771

Subgroups — #14812771

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073649C211yesmaximal, characteristic, complemented
2#13071564C211yesmaximal, characteristic
3#13070147C211yesmaximal, characteristic
4#13069990C211yesmaximal, characteristic
5#13069986C211yesmaximal, characteristic
6#13069377C211yesmaximal, characteristic, complemented
7#13069376C211yesmaximal, characteristic, complemented
8#13069376C211yesmaximal, characteristic, complemented
9#13069333C211yesmaximal, characteristic, complemented
10#13069203C211yesmaximal, characteristic, complemented
11#13069202C211yesmaximal, characteristic, complemented
12#13068771C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#2094C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C2×#66942—21no—
18C2×#66930—21no—
19C2×C11×#106C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#384C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622597—21no—
34#10622593—21no—
35#10622589C2211yescharacteristic
36#10622589C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622585—21no—
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622558—21no—
45#10622557—21no—
46#10622555—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74D4×Dic11—22no—
75D4×Dic11Q814yes—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66942—44no—
98#66930—44no—
99C11×#106—22no—
100C11×#106—41no—
101C11×#102—22no—
102C11×#102—41no—
103#66896—22no—
104#66896—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112#66881—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116#66872—41no—
117#66872—41no—
118#66872—41no—
119C4⋊(C11⋊C8)—22no—
120#26090—111nomaximal, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11C2×Q812yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—24no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—81no—
161C42×C11—21no—
162C42×C11—21no—
163C22⋊Dic11—24no—
164C22⋊Dic11—42no—
165C22⋊Dic11—81no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—42no—
174C4⋊Dic11C2×Q812yes—
175Dic11⋊C4—22no—
176Dic11⋊C4—42no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182Dic11⋊C4—81no—
183Dic11⋊C4SD1614yes—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11C2×Q812yes—
190C4×Dic11#4112yes—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8#4112yes—
197#2552—111no—
198#2354—111no—
199#2094—111no—
200#2094D1111yescharacteristic
201#2065—111no—
202#2065—111no—
203#1948—111no—
204#1948—111no—
205#1948—111no—
206#1939—111no—
207#1920—111no—
208#1920—111no—
209#1844—111no—
210#1802—111no—
211C4×#102—111no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11C22×D411yescharacteristic
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—41no—
223D4×C11—41no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×SD1612yes—
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—48no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11C22⋊Q812yes—
266C2×Dic11C22⋊Q812yes—
267C2×Dic11C2×SD1612yes—
268C2×Dic11C2×SD1612yes—
269C2×Dic11AGL(1,ℤ/8)12yes—
270C8×C11—22no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C2×#125—221no—
275C2×C4×D4—111no—
276C2×#117—221no—
277C2×#106—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282C2×#106C2×D1111yescharacteristic
283C2×C4⋊C8—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102C2×D1111yescharacteristic
289C2×#102C2×D1111yescharacteristic
290C2×C4×C8—111no—
291#398—221no—
292#398—221no—
293#390—111no—
294#390C2×D1111yescharacteristic
295#389—111no—
296#389—111no—
297#389—221no—
298#388—221no—
299#388—221no—
300#384—111no—
301#384—111no—
302#384—111no—
303#384C2×D1111yescharacteristic
304#380—221no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#336—111no—
316#336C2×D1111yescharacteristic
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11C2×C22⋊Q811yescharacteristic
325C22×C11#54711yescharacteristic
326C22×C11#55011yescharacteristic
327C22×C11C22×SD1611yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57711yescharacteristic
331C4×C11—22no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#53311yescharacteristic
337C4×C11#54411yescharacteristic
338C4×C11#55211yescharacteristic
339C4×C11#55311yescharacteristic
340Dic11—22no—
341Dic11—22no—
342Dic11—41no—
343Dic11—42no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11#47614yes—
348C22×D4C22×D1111yescharacteristic
349C23×C4—221no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354#125—444no—
355C4×D4—114no—
356C4×D4—222no—
357#117—444no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388#106—22no—
389#106—41no—
390#106—222no—
391#106—441no—
392#106—441no—
393#106—441no—
394C4⋊C8—222no—
395C4⋊C8—222no—
396C4⋊C8—222no—
397#102—22no—
398#102—41no—
399#102—222no—
400#102—441no—
401C4×C8—222no—
402#95—111no—
403#95—111no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11—82no—
410C2×C11#244111yescharacteristic
411C2×C11C2×#47611yescharacteristic
412C2×C11#308411yescharacteristic
413C2×C11#333511yescharacteristic
414C2×C11#335411yescharacteristic
415C2×C11#339211yescharacteristic
416C2×C11#339711yescharacteristic
417C24—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4Q8×D1112yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—224no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4D4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—112no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8#434112yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—114no—
462C4⋊C4—112no—
463C4⋊C4—222no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4—442no—
476C4⋊C4—881no—
477C4⋊C4—881no—
478C4⋊C4—881no—
479C22⋊C4—42no—
480C22⋊C4—81no—
481C22⋊C4—224no—
482C22⋊C4—442no—
483C22⋊C4—881no—
484C42—21no—
485C42—21no—
486C42—112no—
487C42—112no—
488C42—221no—
489C42—221no—
490C42—442no—
491C42—442no—
492C42—442no—
493C11#2609011yescharacteristic, complemented, Sylow
494C23—22no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23C2×D4×D1111yescharacteristic
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—222no—
532C2×C4—221no—
533C2×C4—448no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4SD16×D1112yes—
546C2×C4C2×#434111yescharacteristic
547C2×C4#6703711yescharacteristic
548C2×C4C2×Q8×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—22no—
553C8—41no—
554C8—222no—
555C8—441no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22D11×C22⋊Q811yescharacteristic
564C22#1062318611yescharacteristic
565C22#1062324911yescharacteristic
566C22C2×SD16×D1111yescharacteristic
567C22#1062329311yescharacteristic
568C22D11×AGL(1,ℤ/8)11yescharacteristic
569C22#1062330611yescharacteristic
570C4—22no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—114no—
576C4—222no—
577C4—222no—
578C4—442no—
579C4—441no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062315311yescharacteristic
584C4#1062315411yescharacteristic
585C4#1062318111yescharacteristic
586C4#1062319211yescharacteristic
587C2—82no—
588C2#1307232211yescharacteristic
589C2D11×#47611yescharacteristic
590C2#1307847311yescharacteristic
591C2#1308097111yescharacteristic
592C2#1308120411yescharacteristic
593C2#1308159411yescharacteristic
594C2#1308163311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2094C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2094D11
hypocenterC11#26090
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. #13073649C2semidirect
6. #13069377C2semidirect
7. #13069376C2semidirect
8. #13069376C2semidirect
9. #13069333C2semidirect
10. #13069203C2semidirect
11. #13069202C2semidirect
12. #13068771C2semidirect
493. C11#26090semidirect

Maximal subgroups

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

subgroupindex
#130736492
#130715642
#130701472
#130699902
#130699862
#130693772
#130693762
#130693332
#130692032
#130692022
#130687712
#130686142
#102×Dic112
C11×#20942
#2609011