Finite Group Databasebeta

← #14765930

Subgroups — #14765930

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×#10622622C211yesmaximal, characteristic
2C4×#66923C211yesmaximal, characteristic, complemented
3#13069573C211yesmaximal, characteristic, complemented
4#13069384C211yesmaximal, characteristic, complemented
5#13069356C211yesmaximal, characteristic, complemented
6#13069351C211yesmaximal, characteristic, complemented
7#13069316C211yesmaximal, characteristic
8#13069316C211yesmaximal, characteristic
9#13069240C211yesmaximal, characteristic
10#13069233C211yesmaximal, characteristic
11#13069191C211yesmaximal, characteristic, complemented
12#13069184C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic
14#13068469C211yesmaximal, characteristic, complemented
15C11×#2293C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117—21no—
18C2×#66923C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#390C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#388—21no—
24C11×#388—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C22⋊C4—21no—
27C43×C11C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622622C418yescomplemented
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622549C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622546—21no—
41#10622546—21no—
42C4×Dic11⋊C4—21no—
43C4×Dic11⋊C4—21no—
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C4×D4×C11—22no—
63C4×D4×C11C2×C414yes—
64C11×#117—44no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C42×C11D411yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C42×C11D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66923—22no—
98#66923C2×C414yes—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102#66896—41no—
103#66896—41no—
104#66896C2×C414yes—
105#66896C2×C414yes—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112#66872—41no—
113#66872C2×C414yes—
114#66871—41no—
115#66871C2×C414yes—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)C2×C414yes—
118#66867—41no—
119#66867—41no—
120#22120—111nomaximal, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11C22×C412yes—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4C22×C412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C42×C11—22no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—41no—
164C42×C11—41no—
165C42×C11—41no—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11#4112yes—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C22×C412yes—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181C4×Dic11—42no—
182C4×Dic11—42no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8C22×C412yes—
194C2×C11⋊C8C22×C412yes—
195C2×#478—111no—
196C4×#125—111no—
197#2293D1111yescharacteristic
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#1767—111no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11C22×D411yescharacteristic
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—41no—
221D4×C11—41no—
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—22no—
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—21no—
238C2×C4×C11—48no—
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×C11C4×D412yes—
248C2×C4×C11C4×D412yes—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C11⋊C8—22no—
269C11⋊C8—22no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C2×#125—111no—
273C2×C4×D4C2×D1111yescharacteristic
274C2×#117—21no—
275#478—118no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×#97—111no—
287C2×#97—111no—
288#390C2×D1111yescharacteristic
289#390C2×D1111yescharacteristic
290#389—111no—
291#389—111no—
292#389C2×D1111yescharacteristic
293#389C2×D1111yescharacteristic
294#388—21no—
295#388—21no—
296#387—221no—
297#387—221no—
298#382—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—221no—
302C4×C4⋊C4—221no—
303C4×C4⋊C4C2×D1111yescharacteristic
304C4×C22⋊C4—21no—
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#336—111no—
315#336—111no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11C2×C4×D411yescharacteristic
324C22×C11#53611yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C11#57511yescharacteristic
328C22×C11#57511yescharacteristic
329C22×C11#57511yescharacteristic
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#51911yescharacteristic
340C4×C11#52011yescharacteristic
341C4×C11#54111yescharacteristic
342C4×C11#54211yescharacteristic
343Dic11—42no—
344Dic11—42no—
345Dic11—81no—
346Dic11—81no—
347C22×D4C22×D1111yescharacteristic
348C23×C4—21no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353#125—114no—
354#125—222no—
355C4×D4—22no—
356C4×D4C4×D1114yes—
357#117—44no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
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×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42—221no—
378C2×C42—221no—
379C2×C42C22⋊D1111yescharacteristic
380C2×C42C22⋊D1111yescharacteristic
381C2×C42C22⋊D1111yescharacteristic
382C2×C42C22⋊D1111yescharacteristic
383C2×C42C22×D1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386#107—114no—
387#107—441no—
388#106—114no—
389#106—441no—
390C4⋊C8—114no—
391C4⋊C8—222no—
392#102—114no—
393#102—114no—
394#102—441no—
395#102—441no—
396#97—441no—
397#97—441no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407C2×C11—82no—
408C2×C11#232311yescharacteristic
409C2×C11#294311yescharacteristic
410C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
411C2×C11#323411yescharacteristic
412C2×C11#324011yescharacteristic
413C2×C11#325111yescharacteristic
414C2×C11#325611yescharacteristic
415C24—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×C4×D1112yes—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—224no—
461C4⋊C4—224no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4C2×C4×D1112yes—
471C22⋊C4—24no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C42—22no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—42no—
485C42—442no—
486C42—442no—
487C42C2×C4×D1112yes—
488C42#433912yes—
489C11#2212011yescharacteristic, complemented, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C22×C22⋊D1111yescharacteristic
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
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—21no—
518C2×C4—48no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—222no—
528C2×C4—222no—
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×C22⋊D1112yes—
540C2×C4C4×C22⋊D1112yes—
541C2×C4#6698512yes—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4C2×#433911yescharacteristic
544C2×C4#6704211yescharacteristic
545C2×C4#6704311yescharacteristic
546C2×C4#6704311yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—222no—
549C8—222no—
550C8—441no—
551C8—441no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×C4×C22⋊D1111yescharacteristic
560C22C2×#6698511yescharacteristic
561C22#1062335311yescharacteristic
562C22#1062335311yescharacteristic
563C22#1062335311yescharacteristic
564C22#1062335611yescharacteristic
565C22#1062336411yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—442no—
576C4—442no—
577C4—881no—
578C4—881no—
579C4#1062304711yescharacteristic
580C4#1062304911yescharacteristic
581C4#1062305411yescharacteristic
582C4#1062306511yescharacteristic
583C2—82no—
584C2#1307129811yescharacteristic
585C2#1307741411yescharacteristic
586C2C4×#6698511yescharacteristic
587C2#1307980211yescharacteristic
588C2#1307985211yescharacteristic
589C2#1307997211yescharacteristic
590C2#1308001211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2293C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2293D11
hypocenterC11#22120
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #2293

Complements

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

NH ≅ G/Ntype
2. C4×#66923C2semidirect
3. #13069573C2semidirect
4. #13069384C2semidirect
5. #13069356C2semidirect
6. #13069351C2semidirect
11. #13069191C2semidirect
12. #13069184C2semidirect
14. #13068469C2semidirect
32. #10622622C4semidirect
489. C11#22120semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
C4×#669232
#130695732
#130693842
#130693562
#130693512
#130693162
#130692402
#130692332
#130691912
#130691842
#130686262
#130684692
C11×#22932
#2212011