Finite Group Databasebeta

← #14826539

Subgroups — #14826539

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073010C211yesmaximal, characteristic
2#13071620C211yesmaximal, characteristic
3#13070038C211yesmaximal, characteristic, complemented
4#13069998C211yesmaximal, characteristic, complemented
5#13069821C211yesmaximal, characteristic
6#13069815C211yesmaximal, characteristic
7#13069381C211yesmaximal, characteristic, complemented
8#13069341C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic
10#13069200C211yesmaximal, characteristic, complemented
11#13068887C211yesmaximal, characteristic, complemented
12#13068810C211yesmaximal, characteristic
13#13068701C211yesmaximal, characteristic
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#1921C211yesmaximal, characteristic, complemented
16C2×#66950C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622602—21no—
29#10622600C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622590C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622587C2211yescharacteristic
34#10622586—21no—
35#10622586C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622553—21no—
41C4×(C2×D11)⋊C4C2211yescharacteristic
42#10622546—21no—
43#10622541C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622288—21no—
46#10622279—21no—
47C11⋊#401—21no—
48#10622267—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89#66950—22no—
90#66950—22no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11—41no—
93C4×Dic22—22no—
94C4×Dic22—41no—
95C11×#107—22no—
96C11×#95—21no—
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(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—41no—
111#66881—22no—
112#66880—22no—
113#66880—41no—
114Dic11⋊C8—22no—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66872—41no—
119C4×C11⋊C8—41no—
120#27037—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—81no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4#4112yes—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—81no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—22no—
171(C2×D11)⋊C4—22no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—81no—
174C4⋊Dic11—24no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11#4112yes—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—81no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11—81no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8#4112yes—
195#2494—111no—
196#2360—111no—
197#2074—111no—
198#2066—111no—
199#2036—111no—
200#2035—111no—
201#1949—111no—
202#1941—111no—
203#1923—111no—
204#1921D1111yescharacteristic, complemented
205#1920—111no—
206#1865—111no—
207#1853—111no—
208#1823—111no—
209C4×#103—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11#13512yes—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
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#13712yes—
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—84no—
268Dic22—22no—
269Dic22—22no—
270Dic22—41no—
271Dic22—41no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C2×C22⋊Q8—111no—
277C2×C4×Q8—111no—
278C22×C4⋊C4—111no—
279C2×#107C2×D1111yescharacteristic
280C2×#106—111no—
281C2×#106—111no—
282C2×#106—111no—
283C2×C4⋊C8—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×C4×C8—111no—
291#401—221no—
292#397—221no—
293#391—111no—
294#389—111no—
295#389—111no—
296#389—221no—
297#389C2×D1111yescharacteristic
298#388—221no—
299#387—221no—
300#387—221no—
301#385—221no—
302#382—111no—
303#380—111no—
304#380—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4C2×D1111yescharacteristic
307C4×C22⋊C4—111no—
308C4×C22⋊C4—221no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#340C2×D1111yescharacteristic
317#336—111no—
318#336C2×D1111yescharacteristic
319C22×C11#52511yescharacteristic
320C22×C11#54611yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11C2×#13511yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11#57711yescharacteristic
325C22×C11#57711yescharacteristic
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#52911yescharacteristic
340C4×C11#53911yescharacteristic
341C4×C11#55311yescharacteristic
342C4×C11#55611yescharacteristic
343Dic11—41no—
344Dic11—41no—
345Dic11—42no—
346Dic11—41no—
347Dic11—42no—
348Dic11—81no—
349Dic11—81no—
350C22×Q8—111no—
351C23×C4—111no—
352C23×C4—221no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22⋊Q8—222no—
358C22⋊Q8—222no—
359C4×Q8—222no—
360C4×Q8—441no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—441no—
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—111no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C42—21no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—22no—
387#106—222no—
388#106—222no—
389#106—441no—
390C4⋊C8—222no—
391#103—222no—
392#103—222no—
393#103—222no—
394#103—441no—
395C22⋊C8—222no—
396C22⋊C8—441no—
397C4×C8—441no—
398#95—21no—
399#95—21no—
400#95—111no—
401#95—111no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411C2×C11#246611yescharacteristic
412C2×C11#310811yescharacteristic
413C2×C11#312511yescharacteristic
414C2×C11#329611yescharacteristic
415C2×C11#332011yescharacteristic
416C2×C11#333711yescharacteristic
417C2×C11#335611yescharacteristic
418D11—42no—
419C24—111no—
420C2×Q8—112no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—881no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—81no—
469C4⋊C4—112no—
470C4⋊C4—224no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—881no—
480C4⋊C4#433912yes—
481C22⋊C4—222no—
482C22⋊C4—224no—
483C22⋊C4—222no—
484C22⋊C4—442no—
485C22⋊C4—881no—
486C42—21no—
487C42—21no—
488C42—81no—
489C42—221no—
490C42—221no—
491C42—442no—
492C42—881no—
493C11#2703711yescharacteristic, complemented, Sylow
494C23—112no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23C2×D4×D1111yescharacteristic
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
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—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—222no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—221no—
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×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—884no—
549C2×C4#6697112yes—
550C2×C4C2×#433911yescharacteristic
551C2×C4#6704011yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704211yescharacteristic
556C8—41no—
557C8—41no—
558C8—222no—
559C8—441no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22#1062307811yescharacteristic
568C22#1062316211yescharacteristic
569C22#1062318511yescharacteristic
570C22C2×#6697111yescharacteristic
571C22D11×#13511yescharacteristic
572C22#1062330611yescharacteristic
573C22#1062330611yescharacteristic
574C4—22no—
575C4—42no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—441no—
581C4—442no—
582C4—442no—
583C4—441no—
584C4—441no—
585C4—881no—
586C4—881no—
587C4#1062306111yescharacteristic
588C4#1062309911yescharacteristic
589C4#1062322311yescharacteristic
590C4#1062323711yescharacteristic
591C2—442no—
592C2#1307265611yescharacteristic
593C2#1307870011yescharacteristic
594C2#1307889711yescharacteristic
595C2#1308045411yescharacteristic
596C2#1308078511yescharacteristic
597C2#1308100211yescharacteristic
598C2#1308123411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1921D11
hypocenterC11#27037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
3. #13070038C2semidirect
4. #13069998C2semidirect
7. #13069381C2semidirect
8. #13069341C2semidirect
10. #13069200C2semidirect
11. #13068887C2semidirect
14. C4×#66874C2semidirect
15. C11×#1921C2semidirect
204. #1921D11semidirect
493. C11#27037semidirect

Maximal subgroups

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

subgroupindex
#130730102
#130716202
#130700382
#130699982
#130698212
#130698152
#130693812
#130693412
#130692202
#130692002
#130688872
#130688102
#130687012
C4×#668742
C11×#19212
#2703711