Finite Group Databasebeta

← #14771553

Subgroups — #14771553

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic
2#13071500C211yesmaximal, characteristic
3#13071481C211yesmaximal, characteristic
4#13069358C211yesmaximal, characteristic, complemented
5#13069341C211yesmaximal, characteristic, complemented
6#13069207C211yesmaximal, characteristic, complemented
7#13069196C211yesmaximal, characteristic, complemented
8#13069188C211yesmaximal, characteristic, complemented
9#13068709C211yesmaximal, characteristic
10#13068705C211yesmaximal, characteristic
11#13068648C211yesmaximal, characteristic
12#13068512C211yesmaximal, characteristic, complemented
13C4×#66871C211yesmaximal, characteristic, complemented
14#13068396C211yesmaximal, characteristic
15C11×#1920C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66925—21no—
20C2×C11×#106C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26#10622603—21no—
27#10622600C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622598C2211yescharacteristic
30#10622590—21no—
31C4⋊C4×Dic11C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622546—21no—
41#10622541C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622474C418yescomplemented
44#10622283—21no—
45#10622277—21no—
46#10622265—21no—
47#10622261—21no—
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×#4313—22no—
92C2×#4313—22no—
93C2×#4313C2×C414yes—
94#66945—22no—
95#66945C2×C414yes—
96C4⋊C4×D11—22no—
97C4⋊C4×D11C2×C414yes—
98#66925—44no—
99C11×#106C2×C414yes—
100C11×#95—21no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112(C2×D11)⋊C8—22no—
113#66882C2×C414yes—
114#66879—22no—
115#66872—22no—
116#66872C2×C414yes—
117#66871—22no—
118#66871C2×C414yes—
119C4×C11⋊C8—22no—
120#22624—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—24no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11C22×C412yes—
144C2×C4×D11#4112yes—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11C22×C412yes—
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—81no—
158C11×C4⋊C4C22×C412yes—
159C11×C4⋊C4C22×C412yes—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—42no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—22no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—81no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—81no—
175C4⋊Dic11C22×C412yes—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180C4×Dic11—24no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C4×Dic11—42no—
185C4×Dic11—42no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8#4112yes—
191C2×C11⋊C8#4112yes—
192#4313—28no—
193C2×#428—111no—
194#2346—111no—
195#2344—111no—
196#1944—111no—
197#1941—111no—
198#1921—111no—
199#1920D1111yescharacteristic, complemented
200#1919—111no—
201#1918—111no—
202#1825—111no—
203#1824—111no—
204#1809—111no—
205#1776—111no—
206C4×#107—111no—
207#1753—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11C4×D412yes—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—41no—
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×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C4×D412yes—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—48no—
266C8×C11—22no—
267C8×C11—41no—
268C11⋊C8—41no—
269C11⋊C8#11714yescomplemented
270C22×M16—111no—
271C2×#117—111no—
272C2×#117—221no—
273C22×C4⋊C4—111no—
274#428—118no—
275C2×#107—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×#106C2×D1111yescharacteristic
281C2×C22⋊C8—111no—
282C2×#97—111no—
283C2×C4×C8—111no—
284#389—111no—
285#389—111no—
286#389—111no—
287#389C2×D1111yescharacteristic
288#388—221no—
289#388—221no—
290#387—221no—
291#387—221no—
292#382—221no—
293#381—221no—
294#380—111no—
295#380—111no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4C2×D1111yescharacteristic
300C4×C22⋊C4—111no—
301#376—221no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#336—111no—
313#336C2×D1111yescharacteristic
314C22×C11C2×C4×D411yescharacteristic
315C22×C11#54711yescharacteristic
316C22×C11#54711yescharacteristic
317C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C11#57511yescharacteristic
319C22×C11#57711yescharacteristic
320C22×C11#57811yescharacteristic
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—22no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C2×D11—41no—
328C4×C11—22no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11C2×#11711yescharacteristic
335C4×C11#51911yescharacteristic
336C4×C11#55211yescharacteristic
337C4×C11#55211yescharacteristic
338Dic11—22no—
339Dic11—41no—
340Dic11—41no—
341Dic11—42no—
342Dic11—42no—
343Dic11—81no—
344Dic11—81no—
345C23×C4—111no—
346C23×C4—221no—
347C2×M16—114no—
348C2×M16—222no—
349C2×M16—222no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354#117—114no—
355#117—222no—
356#117—444no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42C22×D1111yescharacteristic
384#107—114no—
385#107—114no—
386#107—222no—
387#106—114no—
388#106—222no—
389#106C4×D1114yes—
390C22⋊C8—222no—
391#97—222no—
392C4×C8—222no—
393#95—21no—
394#95—21no—
395#95—111no—
396#95—111no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405C2×C11#234411yescharacteristic
406C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
407C2×C11#294711yescharacteristic
408C2×C11#334311yescharacteristic
409C2×C11#334811yescharacteristic
410C2×C11#335211yescharacteristic
411C2×C11#335411yescharacteristic
412D11—42no—
413C24—111no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—111no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—224no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4D4×D1111yescharacteristic
435C22×C4D4×D1111yescharacteristic
436C22×C4C23×D1111yescharacteristic
437M16—228no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—112no—
444C2×C8—112no—
445C2×C8—112no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8C2×C4×D1112yes—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—81no—
457C4⋊C4—112no—
458C4⋊C4—112no—
459C4⋊C4—224no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—881no—
469C4⋊C4C2×C4×D1112yes—
470C4⋊C4C2×C4×D1112yes—
471C22⋊C4—224no—
472C22⋊C4—222no—
473C22⋊C4—441no—
474C22⋊C4—442no—
475C22⋊C4—881no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—224no—
480C42—221no—
481C42—221no—
482C42—442no—
483C42—442no—
484C42—442no—
485C11#2262411yescharacteristic, complemented, Sylow
486C23—112no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23—221no—
492C23—221no—
493C23C2×D4×D1111yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—112no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—448no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4#6696712yes—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4#6704011yescharacteristic
540C2×C4#41×D1111yescharacteristic
541C2×C4#41×D1111yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—22no—
545C8—41no—
546C8—114no—
547C8—441no—
548C22—222no—
549C22—222no—
550C22—222no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22—441no—
555C22C4×D4×D1111yescharacteristic
556C22#1062316211yescharacteristic
557C22#1062318611yescharacteristic
558C22C2×#6696711yescharacteristic
559C22#1062329911yescharacteristic
560C22#1062330611yescharacteristic
561C22#1062331011yescharacteristic
562C4—22no—
563C4—41no—
564C4—42no—
565C4—42no—
566C4—81no—
567C4—81no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4—442no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4D11×#11711yescharacteristic
576C4#1062310311yescharacteristic
577C4#1062322411yescharacteristic
578C4#1062323911yescharacteristic
579C2—442no—
580C2#1307148211yescharacteristic
581C2C4×#6696711yescharacteristic
582C2#1307745611yescharacteristic
583C2#1308105411yescharacteristic
584C2#1308112911yescharacteristic
585C2#1308118811yescharacteristic
586C2#1308120811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1920C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1920D11
hypocenterC11#22624
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
4. #13069358C2semidirect
5. #13069341C2semidirect
6. #13069207C2semidirect
7. #13069196C2semidirect
8. #13069188C2semidirect
12. #13068512C2semidirect
13. C4×#66871C2semidirect
15. C11×#1920C2semidirect
43. #10622474C4semidirect
199. #1920D11semidirect
269. C11⋊C8#117semidirect
485. C11#22624semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
#130715002
#130714812
#130693582
#130693412
#130692072
#130691962
#130691882
#130687092
#130687052
#130686482
#130685122
C4×#668712
#130683962
C11×#19202
#2262411