Finite Group Databasebeta

← #14826981

Subgroups — #14826981

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#13071672C211yesmaximal, characteristic
2#13070167C211yesmaximal, characteristic
3#13069938C211yesmaximal, characteristic
4#13069862C211yesmaximal, characteristic
5#13069715C211yesmaximal, characteristic
6#13069476C211yesmaximal, characteristic
7#13069250C211yesmaximal, characteristic
8#13069247C211yesmaximal, characteristic
9#13069184C211yesmaximal, characteristic
10#13069175C211yesmaximal, characteristic
11#13068960C211yesmaximal, characteristic
12#13068960C211yesmaximal, characteristic
13#13068628C211yesmaximal, characteristic
14C4×#66874C211yesmaximal, characteristic
15C11×#2514C211yesmaximal, characteristic
16C22×#4326C2211yescharacteristic
17C22×#4326C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#401—21no—
22C11×#400—21no—
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#383—21no—
29C11×#382C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C4⋊C4×Dic11—21no—
35#10622586—21no—
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622267—21no—
50#10622267—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×#4326—22no—
73C2×#4326—22no—
74C2×#4326—22no—
75C2×#4326—41no—
76C2×#4326—41no—
77C2×#4326—41no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66922—22no—
92#66922—22no—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C4×Dic22—41no—
96C4×Dic22—41no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66899—22no—
110#66899—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66874—22no—
117#66874—22no—
118#66874—22no—
119#66874—41no—
120#66874—41no—
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—
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×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
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#4112yes—
159C2×Dic22#4112yes—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176#4326—44no—
177#4326—44no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11#4112yes—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186C4×Dic11—42no—
187C4×Dic11—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#2514D1111yescharacteristic
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#1805—111no—
215C4×#103—111no—
216C23×C11C22×D411yescharacteristic
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—41no—
220Q8×C11—41no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
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—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11#13512yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269Dic22—22no—
270Dic22—22no—
271Dic22—22no—
272Dic22—22no—
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⋊Q8—111no—
284C2×C4×Q8—111no—
285C2×C4×Q8—111no—
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—21no—
299#400—21no—
300#391—111no—
301#391—111no—
302#391C2×D1111yescharacteristic
303#391C2×D1111yescharacteristic
304#391C2×D1111yescharacteristic
305#389—221no—
306#389C2×D1111yescharacteristic
307#387—21no—
308#387—221no—
309#387—221no—
310#383—21no—
311#382C2×D1111yescharacteristic
312C4×C4⋊C4—111no—
313C4×C4⋊C4—221no—
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—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#52911yescharacteristic
342C4×C11#53811yescharacteristic
343C4×C11#55111yescharacteristic
344C4×C11#55311yescharacteristic
345Dic11—42no—
346Dic11—42no—
347Dic11—42no—
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×C8—111no—
361C22×C8—111no—
362C4⋊Q8—222no—
363C4⋊Q8—222no—
364C4×Q8—222no—
365C4×Q8—222no—
366C4×Q8—441no—
367C4×Q8—441no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22⋊D1111yescharacteristic
376C2×C4⋊C4C22⋊D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C42—21no—
381C2×C42—221no—
382C2×C42—221no—
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—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
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—112no—
430C2×Q8—112no—
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—221no—
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—22no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—112no—
480C4⋊C4—224no—
481C4⋊C4—224no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—442no—
495C42—442no—
496C42—442no—
497C11#2706711yescharacteristic, complemented, Sylow
498C23C22×C22⋊D1111yescharacteristic
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—222no—
504Q8—222no—
505Q8—222no—
506Q8—222no—
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—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
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—222no—
540C2×C4—222no—
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#6700312yes—
552C2×C4#6700412yes—
553C2×C4#41×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704211yescharacteristic
558C2×C4#6704211yescharacteristic
559C8—222no—
560C8—441no—
561C8—441no—
562C8—441no—
563C22C2×#6700311yescharacteristic
564C22C2×#6700411yescharacteristic
565C22#1062335911yescharacteristic
566C22#1062336011yescharacteristic
567C22#1062336511yescharacteristic
568C22#1062336911yescharacteristic
569C22#1062336911yescharacteristic
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—442no—
581C4—442no—
582C4—442no—
583C4—881no—
584C4#1062323511yescharacteristic
585C4#1062323611yescharacteristic
586C4#1062323711yescharacteristic
587C4#1062324011yescharacteristic
588C2#1307266311yescharacteristic
589C2#1307869211yescharacteristic
590C2#1307891111yescharacteristic
591C2#1308052711yescharacteristic
592C2#1308066111yescharacteristic
593C2#1308160011yescharacteristic
594C2#1308164711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2514C2
socle, prime radicalC23×C11C22×D4
hypercenter#2514D11
hypocenterC11#27067
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2514

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
#130716722
#130701672
#130699382
#130698622
#130697152
#130694762
#130692502
#130692472
#130691842
#130691752
#130689602
#130686282
C4×#668742
C11×#25142
#2706711