Finite Group Databasebeta

← #14826992

Subgroups — #14826992

Order 2816.

700 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#13073220C211yesmaximal, characteristic
2#13071670C211yesmaximal, characteristic
3#13070167C211yesmaximal, characteristic
4#13069939C211yesmaximal, characteristic
5#13069861C211yesmaximal, characteristic
6#13069717C211yesmaximal, characteristic
7#13069474C211yesmaximal, characteristic
8#13069253C211yesmaximal, characteristic
9#13069248C211yesmaximal, characteristic
10#13069190C211yesmaximal, characteristic
11#13069170C211yesmaximal, characteristic
12#13068958C211yesmaximal, characteristic
13#13068957C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic
15C11×#1805C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66997C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×Dic44C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#382C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622591—21no—
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622587C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622585—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622546—21no—
43C4×Dic11⋊C4—21no—
44C4×Dic11⋊C4C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47C11⋊#401—21no—
48#10622273—21no—
49#10622267—21no—
50#10622264—21no—
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×Q8×C11—22no—
65C4×Q8×C11—41no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#66997—22no—
73#66997—22no—
74C2×#4326—22no—
75C2×#4326—22no—
76C2×#4326—41no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×Dic44—22no—
93C2×Dic44—41no—
94C2×Dic44—41no—
95#66940—22no—
96#66940—41no—
97C11×C4⋊C8—41no—
98C11×#103—41no—
99C11×#103—41no—
100C11×#95—21no—
101C11×#95—21no—
102#66899—22no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
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⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66880—22no—
119#66880—41no—
120C8×Dic11—41no—
121#66874—22no—
122#66874—22no—
123#66874—41no—
124#66872—41no—
125#66871—22no—
126#27067—111nomaximal, Sylow
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22#4112yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4#4112yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176#4326—44no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—42no—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184Dic11⋊C4—22no—
185Dic11⋊C4—22no—
186Dic11⋊C4—42no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8#4112yes—
200Dic44—44no—
201#2514—111no—
202#2365—111no—
203#2097—111no—
204#2056—111no—
205#2043—111no—
206#2016—111no—
207#1969—111no—
208#1927—111no—
209#1927—111no—
210#1918—111no—
211#1916—111no—
212#1878—111no—
213#1878—111no—
214#1805D1111yescharacteristic
215C4×#103—111no—
216C23×C11C22×D411yescharacteristic
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—41no—
220Q8×C11—41no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
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×C11—41no—
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
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×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11#13512yes—
268C2×Dic11#13712yes—
269Dic22—22no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273Dic22—41no—
274Dic22—41no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—41no—
278C8×C11—41no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C22×Q16—111no—
282C22×Q16—111no—
283C2×C4⋊Q8—111no—
284C2×C4×Q8—111no—
285C2×C4×Q8C2×D1111yescharacteristic
286C2×#107—111no—
287C2×#106—111no—
288C2×C4⋊C8C2×D1111yescharacteristic
289C2×#103—111no—
290C2×#103—111no—
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×#103C2×D1111yescharacteristic
296C2×#103C2×D1111yescharacteristic
297C2×C4×C8—111no—
298#401—221no—
299#400—221no—
300#391—111no—
301#391—111no—
302#391—111no—
303#391—111no—
304#391—111no—
305#389—111no—
306#389—221no—
307#387—221no—
308#387—221no—
309#387—221no—
310#383—221no—
311#382C2×D1111yescharacteristic
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—221no—
316#340—111no—
317#340—111no—
318#340C2×D1111yescharacteristic
319#340C2×D1111yescharacteristic
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324C22×C11#52511yescharacteristic
325C22×C11#54611yescharacteristic
326C22×C11#55011yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57811yescharacteristic
330C22×C11#57811yescharacteristic
331C4×C11—42no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#52911yescharacteristic
338C4×C11#53811yescharacteristic
339C4×C11#55111yescharacteristic
340C4×C11#55311yescharacteristic
341Dic11—22no—
342Dic11—22no—
343Dic11—41no—
344Dic11—42no—
345Dic11—41no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349C22×Q8—111no—
350C22×Q8—111no—
351C22×Q8C22×D1111yescharacteristic
352C2×Q16—222no—
353C2×Q16—222no—
354C2×Q16—222no—
355C2×Q16—441no—
356C2×Q16—441no—
357C2×Q16—441no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362C4⋊Q8—222no—
363C4⋊Q8—222no—
364C4×Q8—22no—
365C4×Q8—41no—
366C4×Q8—222no—
367C4×Q8—441no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C42—21no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387#107—222no—
388#106—441no—
389C4⋊C8—41no—
390#103—41no—
391#103—41no—
392#103—222no—
393#103—222no—
394#103—222no—
395#103—222no—
396#103—441no—
397#103—441no—
398C4×C8—441no—
399#95—21no—
400#95—21no—
401#95—111no—
402#95—111no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416C2×C11#246711yescharacteristic
417C2×C11#310811yescharacteristic
418C2×C11#312711yescharacteristic
419C2×C11#330211yescharacteristic
420C2×C11#331211yescharacteristic
421C2×C11#339311yescharacteristic
422C2×C11#339811yescharacteristic
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—112no—
429C2×Q8—221no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8#434312yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456Q16—444no—
457Q16—444no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4#433912yes—
487C42—21no—
488C42—21no—
489C42—42no—
490C42—221no—
491C42—221no—
492C42—221no—
493C42—221no—
494C42—442no—
495C42—442no—
496C42—442no—
497C11#2706711yescharacteristic, complemented, Sylow
498C23C2×D4×D1111yescharacteristic
499Q8—22no—
500Q8—22no—
501Q8—41no—
502Q8—41no—
503Q8—222no—
504Q8—222no—
505Q8—441no—
506Q8—441no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—441no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—222no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4C2×#433911yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4C2×#434311yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C8—41no—
560C8—41no—
561C8—222no—
562C8—441no—
563C22#1062302111yescharacteristic
564C22#1062313011yescharacteristic
565C22#1062315811yescharacteristic
566C22D11×#13511yescharacteristic
567C22#1062330211yescharacteristic
568C22D11×#13711yescharacteristic
569C22#1062331011yescharacteristic
570C4—42no—
571C4—41no—
572C4—41no—
573C4—42no—
574C4—81no—
575C4—81no—
576C4—222no—
577C4—222no—
578C4—442no—
579C4—441no—
580C4—441no—
581C4—881no—
582C4—881no—
583C4—881no—
584C4#1062304511yescharacteristic
585C4#1062305911yescharacteristic
586C4#1062314411yescharacteristic
587C4#1062316811yescharacteristic
588C2#1307267411yescharacteristic
589C2#1307870111yescharacteristic
590C2#1307891811yescharacteristic
591C2#1308052911yescharacteristic
592C2#1308066811yescharacteristic
593C2#1308159911yescharacteristic
594C2#1308165011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socle, prime radicalC23×C11C22×D4
hypercenter#1805D11
hypocenterC11#27067
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
497. C11#27067semidirect

Maximal subgroups

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

subgroupindex
#130732202
#130716702
#130701672
#130699392
#130698612
#130697172
#130694742
#130692532
#130692482
#130691902
#130691702
#130689582
#130689572
#130684352
C11×#18052
#2706711