Finite Group Databasebeta

← #14771492

Subgroups — #14771492

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622473C211yesmaximal, characteristic
2#13071508C211yesmaximal, characteristic
3#13071505C211yesmaximal, characteristic
4#13069353C211yesmaximal, characteristic, complemented
5#13069351C211yesmaximal, characteristic, complemented
6#13069203C211yesmaximal, characteristic, complemented
7#13069202C211yesmaximal, characteristic, complemented
8#13069200C211yesmaximal, characteristic, complemented
9#13068710C211yesmaximal, characteristic
10#13068709C211yesmaximal, characteristic
11#13068640C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13#13068512C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic
15C11×#1920C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×#66881C2211yescharacteristic
24C2×#66879C2211yescharacteristic
25#10622603—21no—
26#10622600C2211yescharacteristic
27#10622600C2211yescharacteristic
28#10622598C2211yescharacteristic
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11C2211yescharacteristic
31C4⋊C4×Dic11C2211yescharacteristic
32#10622586C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622553—21no—
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×Dic11⋊C4—21no—
41#10622541C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622473C418yescomplemented
44#10622283—21no—
45#10622282—21no—
46#10622264—21no—
47#10622264—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×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
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×C4×Dic11—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×C8×D11—22no—
92C2×C8×D11—22no—
93C2×C8×D11C2×C414yes—
94#66945—22no—
95#66945—22no—
96#66945C2×C414yes—
97#66945C2×C414yes—
98C11×#106C2×C414yes—
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⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111(C2×D11)⋊C8—22no—
112#66881C2×C414yes—
113#66879—22no—
114#66872—22no—
115#66872—22no—
116#66871C2×C414yes—
117#66871C2×C414yes—
118#66867—22no—
119#22620—111nomaximal, Sylow
120C23×D11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11C22×C412yes—
140C2×C4×D11#4112yes—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C22×C412yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4C22×C412yes—
155C11×C4⋊C4C22×C412yes—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—81no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—81no—
164(C2×D11)⋊C4—81no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—42no—
172C4⋊Dic11C22×C412yes—
173C4⋊Dic11C22×C412yes—
174Dic11⋊C4—42no—
175Dic11⋊C4—42no—
176C4×Dic11—24no—
177C4×Dic11—24no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—81no—
181C4×Dic11—81no—
182C4×Dic11—81no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8C22×C412yes—
187C2×C11⋊C8#4112yes—
188C2×C11⋊C8#4112yes—
189C8×D11—28no—
190C2×#427—111no—
191#2347—111no—
192#2347—111no—
193#1943—111no—
194#1943—111no—
195#1920—111no—
196#1920—111no—
197#1920—111no—
198#1920D1111yescharacteristic, complemented
199#1825—111no—
200#1825—111no—
201#1807—111no—
202#1776—111no—
203#1776—111no—
204#1752—111no—
205C23×C11C22×D411yescharacteristic
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11C4×D412yes—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
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×C11C23×C411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11C4×D412yes—
258C4×D11—22no—
259C4×D11—22no—
260C4×D11—22no—
261C4×D11—22no—
262C8×C11—22no—
263C8×C11—41no—
264C11⋊C8—41no—
265C11⋊C8#11714yes—
266C23×C8—111no—
267C2×#117—111no—
268C2×#117—111no—
269#427—118no—
270C2×#107—111no—
271C2×#107—111no—
272C2×#106—111no—
273C2×#106—111no—
274C2×#106—111no—
275C2×#106C2×D1111yescharacteristic
276C2×C22⋊C8—111no—
277C2×#97—111no—
278C2×#97—111no—
279#389—111no—
280#389—111no—
281#389—111no—
282#389C2×D1111yescharacteristic
283#388—221no—
284#388—221no—
285#388—221no—
286#388—221no—
287#383—221no—
288#383—221no—
289#380—111no—
290#380—111no—
291C4×C4⋊C4—111no—
292C4×C4⋊C4—111no—
293C4×C4⋊C4—111no—
294C4×C4⋊C4—221no—
295C4×C4⋊C4—221no—
296C4×C4⋊C4C2×D1111yescharacteristic
297C4×C22⋊C4—111no—
298#340—111no—
299#340—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340C2×D1111yescharacteristic
306#340C2×D1111yescharacteristic
307#340C2×D1111yescharacteristic
308#336—111no—
309#336C2×D1111yescharacteristic
310C22×C11C2×C4×D411yescharacteristic
311C22×C11#54711yescharacteristic
312C22×C11#54711yescharacteristic
313C22×C11#57511yescharacteristic
314C22×C11#57511yescharacteristic
315C22×C11#57711yescharacteristic
316C22×C11#57711yescharacteristic
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—41no—
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11C2×#11711yescharacteristic
331C4×C11#51911yescharacteristic
332C4×C11#55211yescharacteristic
333C4×C11#55211yescharacteristic
334Dic11—22no—
335Dic11—41no—
336Dic11—41no—
337Dic11—42no—
338Dic11—42no—
339Dic11—81no—
340Dic11—81no—
341C23×C4—111no—
342C22×C8—111no—
343C22×C8—114no—
344C22×C8—111no—
345C22×C8—222no—
346C22×C8—222no—
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349#117—114no—
350#117—114no—
351#117—222no—
352#117—222no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C42—21no—
372C2×C42—111no—
373C2×C42—221no—
374C2×C42—221no—
375C2×C42—221no—
376C2×C42—221no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#107—114no—
380#107—114no—
381#106—114no—
382#106—222no—
383#106—222no—
384#106C4×D1114yes—
385C22⋊C8—222no—
386#97—222no—
387#97—222no—
388#95—21no—
389#95—21no—
390#95—111no—
391#95—111no—
392#95—221no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400C2×C11#234411yescharacteristic
401C2×C11#294311yescharacteristic
402C2×C11#295211yescharacteristic
403C2×C11#335011yescharacteristic
404C2×C11#335011yescharacteristic
405C2×C11#335011yescharacteristic
406C2×C11#335011yescharacteristic
407D11—42no—
408C24—111no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—111no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—112no—
435C2×C8—112no—
436C2×C8—112no—
437C2×C8—228no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8C2×C4×D1112yes—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—112no—
450C4⋊C4—112no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—442no—
458C4⋊C4—442no—
459C4⋊C4—442no—
460C4⋊C4C2×C4×D1112yes—
461C4⋊C4C2×C4×D1112yes—
462C22⋊C4—224no—
463C22⋊C4—224no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C22⋊C4—881no—
467C22⋊C4—881no—
468C42—21no—
469C42—21no—
470C42—81no—
471C42—224no—
472C42—224no—
473C42—221no—
474C42—221no—
475C42—881no—
476C42—881no—
477C42—881no—
478C11#2262011yescharacteristic, complemented, Sylow
479C23—112no—
480C23—221no—
481C23—221no—
482C23—221no—
483C23—221no—
484C23—221no—
485C23—221no—
486C23C2×D4×D1111yescharacteristic
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—112no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4C22×C4×D1111yescharacteristic
531C2×C4#6704011yescharacteristic
532C2×C4#41×D1111yescharacteristic
533C2×C4#41×D1111yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—22no—
537C8—41no—
538C8—114no—
539C8—441no—
540C22—222no—
541C22—222no—
542C22—222no—
543C22—441no—
544C22—441no—
545C22—441no—
546C22—441no—
547C22C4×D4×D1111yescharacteristic
548C22#1062316211yescharacteristic
549C22#1062318611yescharacteristic
550C22#1062329311yescharacteristic
551C22#1062330111yescharacteristic
552C22#1062330411yescharacteristic
553C22#1062330811yescharacteristic
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—81no—
559C4—81no—
560C4—222no—
561C4—441no—
562C4—441no—
563C4—442no—
564C4—442no—
565C4—881no—
566C4—881no—
567C4D11×#11711yescharacteristic
568C4#1062310311yescharacteristic
569C4#1062322411yescharacteristic
570C4#1062323911yescharacteristic
571C2—442no—
572C2#1307148211yescharacteristic
573C2#1307741111yescharacteristic
574C2#1307749411yescharacteristic
575C2#1308115411yescharacteristic
576C2#1308115811yescharacteristic
577C2#1308116411yescharacteristic
578C2#1308116811yescharacteristic
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#22620
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. #13069353C2semidirect
5. #13069351C2semidirect
6. #13069203C2semidirect
7. #13069202C2semidirect
8. #13069200C2semidirect
12. #13068514C2semidirect
13. #13068512C2semidirect
15. C11×#1920C2semidirect
43. #10622473C4semidirect
198. #1920D11semidirect
478. C11#22620semidirect

Maximal subgroups

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

subgroupindex
C2×#106224732
#130715082
#130715052
#130693532
#130693512
#130692032
#130692022
#130692002
#130687102
#130687092
#130686402
#130685142
#130685122
#130683912
C11×#19202
#2262011