Finite Group Databasebeta

← #14765932

Subgroups — #14765932

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic
2C4×#66923C211yesmaximal, characteristic, complemented
3#13071080C211yesmaximal, characteristic
4#13069571C211yesmaximal, characteristic, complemented
5#13069386C211yesmaximal, characteristic, complemented
6#13069359C211yesmaximal, characteristic, complemented
7#13069354C211yesmaximal, characteristic, complemented
8#13069313C211yesmaximal, characteristic
9#13069313C211yesmaximal, characteristic
10#13069244C211yesmaximal, characteristic
11#13069237C211yesmaximal, characteristic
12#13069195C211yesmaximal, characteristic, complemented
13#13069188C211yesmaximal, characteristic, complemented
14#13068627C211yesmaximal, characteristic
15C11×#1767C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66925—21no—
18C2×#66923C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C43×C11C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32#10622553—21no—
33#10622553—21no—
34#10622552C2211yescharacteristic
35#10622552C2211yescharacteristic
36C4×(C2×D11)⋊C4—21no—
37#10622549C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622546—21no—
42#10622546—21no—
43C4×Dic11⋊C4—21no—
44C4×Dic11⋊C4—21no—
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622460C418yescomplemented
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11D411yescharacteristic
69C2×C42×C11D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C4×D44—22no—
95C4×D44C2×C414yes—
96#66925—44no—
97#66923—22no—
98#66923C2×C414yes—
99C11×C4⋊C8—22no—
100C11×C4⋊C8C2×C414yes—
101C11×#97—41no—
102C11×#97—41no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112#66885—41no—
113#66885—41no—
114#66885C2×C414yes—
115#66885C2×C414yes—
116#66882—41no—
117#66882C2×C414yes—
118#66881—41no—
119#66881C2×C414yes—
120#22120—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44C22×C412yes—
142C2×C4×D11—24no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C42×C11—22no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—41no—
163C42×C11—41no—
164C42×C11—41no—
165C42×C11C22×C412yes—
166C42×C11#4112yes—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C412yes—
184C4⋊Dic11C22×C412yes—
185C4⋊Dic11C22×C412yes—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C2×#478—111no—
196C4×#125—111no—
197#2293—111no—
198#1989—111no—
199#1949—111no—
200#1944—111no—
201#1943—111no—
202#1936—111no—
203#1936—111no—
204#1926—111no—
205#1925—111no—
206#1919—111no—
207#1918—111no—
208#1804—111no—
209#1767D1111yescharacteristic, complemented
210C23×C11C22×D411yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
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×C11C4×D412yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—41no—
246C2×Dic11—41no—
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×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263D44—22no—
264D44—22no—
265D44—41no—
266D44—41no—
267C4×D11—48no—
268C8×C11—22no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C2×#125—111no—
273C2×C4×D4—111no—
274C2×#117—221no—
275#478—118no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#97C2×D1111yescharacteristic
287C2×#97C2×D1111yescharacteristic
288#390—111no—
289#390—111no—
290#389—111no—
291#389—111no—
292#389—111no—
293#389—111no—
294#388—221no—
295#388—221no—
296#387—221no—
297#387—221no—
298#382—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—221no—
303C4×C4⋊C4—221no—
304C4×C22⋊C4—221no—
305C43C2×D1111yescharacteristic
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#336C2×D1111yescharacteristic
315#336C2×D1111yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#53611yescharacteristic
318C22×C11#53711yescharacteristic
319C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C11#57511yescharacteristic
321C22×C11#57511yescharacteristic
322C22×C11#57511yescharacteristic
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11#51911yescharacteristic
337C4×C11#52011yescharacteristic
338C4×C11#54111yescharacteristic
339C4×C11#54211yescharacteristic
340Dic11—42no—
341Dic11—42no—
342Dic11—42no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C22×D4—111no—
348C23×C4—221no—
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#125—114no—
354#125—222no—
355C4×D4—114no—
356C4×D4—222no—
357#117—444no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—221no—
377C2×C42—221no—
378C2×C42—221no—
379C2×C42D4411yescharacteristic
380C2×C42D4411yescharacteristic
381C2×C42D4411yescharacteristic
382C2×C42D4411yescharacteristic
383C2×C42C22×D1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386#107—114no—
387#107—441no—
388#106—114no—
389#106—441no—
390C4⋊C8—22no—
391C4⋊C8C4×D1114yes—
392#102—114no—
393#102—114no—
394#102—441no—
395#102—441no—
396#97—41no—
397#97—41no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407C2×C11#232311yescharacteristic
408C2×C11#294311yescharacteristic
409C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
410C2×C11#323411yescharacteristic
411C2×C11#324011yescharacteristic
412C2×C11#325111yescharacteristic
413C2×C11#325611yescharacteristic
414D11—82no—
415C24—221no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—224no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4411yescharacteristic
434C22×C4C2×D4411yescharacteristic
435C22×C4C2×D4411yescharacteristic
436C22×C4C2×D4411yescharacteristic
437C22×C4C2×D4411yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×C4×D1112yes—
450C2×C8C2×C4×D1112yes—
451C4⋊C4—112no—
452C4⋊C4—112no—
453C4⋊C4—112no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C22⋊C4—224no—
472C22⋊C4—442no—
473C22⋊C4—442no—
474C22⋊C4—442no—
475C22⋊C4—442no—
476C42—22no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—442no—
485C42—442no—
486C42—442no—
487C42C2×C4×D1112yes—
488C42#433912yes—
489C11#2212011yescharacteristic, complemented, Sylow
490C23—222no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23C22×D4411yescharacteristic
498D4—222no—
499D4—222no—
500D4—441no—
501D4—441no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—448no—
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×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4C4×D4412yes—
540C2×C4C4×D4412yes—
541C2×C4#6696112yes—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4#6703711yescharacteristic
545C2×C4#6704011yescharacteristic
546C2×C4#6704311yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—22no—
549C8—22no—
550C8—41no—
551C8—41no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22C2×C4×D4411yescharacteristic
560C22#1062304111yescharacteristic
561C22#1062305711yescharacteristic
562C22C2×#6696111yescharacteristic
563C22#1062327911yescharacteristic
564C22#1062327911yescharacteristic
565C22#1062327911yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—442no—
573C4—442no—
574C4—442no—
575C4—881no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4#1062307711yescharacteristic
580C4#1062309211yescharacteristic
581C4#1062310311yescharacteristic
582C4#1062311411yescharacteristic
583C2—882no—
584C2#1307129911yescharacteristic
585C2#1307741811yescharacteristic
586C2C4×#6696111yescharacteristic
587C2#1307980811yescharacteristic
588C2#1307985811yescharacteristic
589C2#1307997911yescharacteristic
590C2#1308001711yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1767C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1767D11
hypocenterC11#22120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
2. C4×#66923C2semidirect
4. #13069571C2semidirect
5. #13069386C2semidirect
6. #13069359C2semidirect
7. #13069354C2semidirect
12. #13069195C2semidirect
13. #13069188C2semidirect
15. C11×#1767C2semidirect
49. #10622460C4semidirect
209. #1767D11semidirect
489. C11#22120semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
C4×#669232
#130710802
#130695712
#130693862
#130693592
#130693542
#130693132
#130692442
#130692372
#130691952
#130691882
#130686272
C11×#17672
#2212011