Finite Group Databasebeta

← #14826979

Subgroups — #14826979

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#13073224C211yesmaximal, characteristic
2#13070164C211yesmaximal, characteristic
3#13069938C211yesmaximal, characteristic
4#13069859C211yesmaximal, characteristic
5#13069716C211yesmaximal, characteristic
6#13069476C211yesmaximal, characteristic
7#13069250C211yesmaximal, characteristic
8#13069247C211yesmaximal, characteristic
9#13069187C211yesmaximal, characteristic
10#13069175C211yesmaximal, characteristic
11#13068957C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic
13#13068631C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic
15C11×#2365C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389—21no—
24C11×#387—21no—
25C11×#387—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622595—21no—
36#10622591—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49C11⋊#401—21no—
50#10622264—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—41no—
86C2×#4326—41no—
87C2×#4326—41no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66899—22no—
105#66899—22no—
106#66899—22no—
107#66899—41no—
108#66899—41no—
109#66899—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—41no—
122#66872—41no—
123#66871—22no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
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—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11#4112yes—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4#4112yes—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C42×C11—42no—
178C42×C11—42no—
179#4326—44no—
180#4326—44no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187Dic11⋊C4—42no—
188C4×Dic11—42no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8#4112yes—
201#2514—111no—
202#2365D1111yescharacteristic
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#1805—111no—
215C4×#103—111no—
216C23×C11C22×D411yescharacteristic
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223Q8×C11—41no—
224Q8×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
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#13512yes—
254C2×C4×C11#13712yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273Dic22—41no—
274Dic22—41no—
275Dic22—41no—
276Dic22—41no—
277C11⋊C8—22no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C22×Q16—111no—
282C22×Q16—111no—
283C2×C4⋊Q8C2×D1111yescharacteristic
284C2×C4×Q8C2×D1111yescharacteristic
285C2×C4×Q8C2×D1111yescharacteristic
286C2×#107—111no—
287C2×#106—111no—
288C2×C4⋊C8—111no—
289C2×#103—111no—
290C2×#103—111no—
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×C4×C8—111no—
298#401—221no—
299#400—221no—
300#391—111no—
301#391—111no—
302#391—111no—
303#391C2×D1111yescharacteristic
304#391C2×D1111yescharacteristic
305#389—21no—
306#389—111no—
307#387—21no—
308#387—21no—
309#387—221no—
310#383—221no—
311#382—111no—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4C2×D1111yescharacteristic
315C4×C4⋊C4C2×D1111yescharacteristic
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
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—22no—
332C4×C11—22no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—81no—
341C4×C11#52911yescharacteristic
342C4×C11#53811yescharacteristic
343C4×C11#55111yescharacteristic
344C4×C11#55311yescharacteristic
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349C22×Q8—111no—
350C22×Q8C22×D1111yescharacteristic
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×C8—111no—
361C22×C8—111no—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×Q8—41no—
367C4×Q8—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22⋊D1111yescharacteristic
377C2×C4⋊C4C22⋊D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C42—21no—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387#107—222no—
388#106—441no—
389C4⋊C8—441no—
390#103—222no—
391#103—222no—
392#103—222no—
393#103—222no—
394#103—441no—
395#103—441no—
396#103—441no—
397#103—441no—
398C4×C8—441no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
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#95C22⋊D1111yescharacteristic
415#95C22⋊D1111yescharacteristic
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—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8#433912yes—
440C2×Q8#433912yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456Q16—444no—
457Q16—444no—
458C2×C8—112no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—442no—
486C4⋊C4#434112yes—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—42no—
495C42—42no—
496C42—442no—
497C11#2706711yescharacteristic, complemented, Sylow
498C23C22×C22⋊D1111yescharacteristic
499Q8—22no—
500Q8—22no—
501Q8—22no—
502Q8—22no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—441no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
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#6699512yes—
552C2×C4#6700312yes—
553C2×C4C2×#433911yescharacteristic
554C2×C4C2×#433911yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C2×C4#6703711yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C2×C4#6704211yescharacteristic
559C8—222no—
560C8—441no—
561C8—441no—
562C8—441no—
563C22#1062332211yescharacteristic
564C22#1062333711yescharacteristic
565C22C2×#6699511yescharacteristic
566C22C2×#6700311yescharacteristic
567C22#1062336511yescharacteristic
568C22#1062336911yescharacteristic
569C22#1062336911yescharacteristic
570C4—22no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—81no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4—881no—
584C4#1062306911yescharacteristic
585C4#1062308711yescharacteristic
586C4#1062309111yescharacteristic
587C4#1062309611yescharacteristic
588C2#1307266111yescharacteristic
589C2#1307869611yescharacteristic
590C2#1307891611yescharacteristic
591C2#1308053311yescharacteristic
592C2#1308066711yescharacteristic
593C2#1308160011yescharacteristic
594C2#1308164311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socle, prime radicalC23×C11C22×D4
hypercenter#2365D11
hypocenterC11#27067
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

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
#130732242
#130701642
#130699382
#130698592
#130697162
#130694762
#130692502
#130692472
#130691872
#130691752
#130689572
#130686312
C4×#668992
C11×#23652
#2706711