Finite Group Databasebeta

← #14775732

Subgroups — #14775732

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622483C211yesmaximal, characteristic
2#13071669C211yesmaximal, characteristic, complemented
3#13071525C211yesmaximal, characteristic
4#13069587C211yesmaximal, characteristic, complemented
5#13069385C211yesmaximal, characteristic, complemented
6#13069358C211yesmaximal, characteristic, complemented
7#13069198C211yesmaximal, characteristic, complemented
8#13069196C211yesmaximal, characteristic, complemented
9#13068874C211yesmaximal, characteristic
10#13068862C211yesmaximal, characteristic
11#13068490C211yesmaximal, characteristic, complemented
12#13068440C211yesmaximal, characteristic
13#13068440C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1941C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66941C2211yescharacteristic
19C2×#66940—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622602—21no—
32#10622600—21no—
33#10622598C2211yescharacteristic
34#10622591—21no—
35#10622590C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622483C418yescomplemented
46#10622281—21no—
47D11×#95—21no—
48#10622265—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92#66946—22no—
93#66946—22no—
94#66946—41no—
95#66946C2×C414yes—
96#66941—22no—
97#66941C2×C414yescomplemented
98#66940—44no—
99C4×D44—22no—
100C4×D44—41no—
101C11×#106—41no—
102C11×#106C2×C414yescomplemented
103C4×C8×C11—41no—
104C11×#95—21no—
105C11×#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66885C2×C414yes—
116#66885Q814yescomplemented
117#66879—22no—
118#66879—41no—
119Dic11⋊C8C2×C414yescomplemented
120#66873—22no—
121#66873C2×C414yes—
122#66872C2×C414yescomplemented
123#66871—41no—
124#22975—111nomaximal, Sylow
125C23×D11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C22×C412yes—
144C2×D44C2×Q812yes—
145C2×D44#4112yes—
146C2×C4×D11—24no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—81no—
152C2×C4×D11—81no—
153C2×C4×D11—81no—
154C2×C4×D11—81no—
155C2×Dic22—24no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C2×Q812yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4C22×C412yes—
174C42×C11—21no—
175C42×C11—21no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—81no—
184C4⋊Dic11C22×C412yes—
185C4⋊Dic11C2×Q812yes—
186Dic11⋊C4—24no—
187Dic11⋊C4—22no—
188Dic11⋊C4—41no—
189Dic11⋊C4—42no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11C22×C412yes—
196C4×Dic11#4112yes—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×#476—111no—
204#2365—111no—
205#2349—111no—
206#1993—111no—
207#1949—111no—
208#1944—111no—
209#1941D1111yescharacteristic, complemented
210#1920—111no—
211#1919—111no—
212#1864—111no—
213#1862—111no—
214#1771—111no—
215#1762—111no—
216#1762—111no—
217C4×#102—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11AGL(1,ℤ/8)12yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×Q811yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11C4×D412yes—
270C2×Dic11C4×D412yes—
271D44—22no—
272D44—22no—
273D44—22no—
274D44C4×Q814yescomplemented
275C4×D11—84no—
276C4×D11—84no—
277C4×D11—84no—
278Dic22—48no—
279C8×C11—22no—
280C8×C11—22no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C2×C4⋊Q8—111no—
284C2×C4×Q8—221no—
285C2×C4×D4—111no—
286C2×C4×D4—111no—
287C2×C4×D4—111no—
288#476—118no—
289C2×#107—111no—
290C2×#106—111no—
291C2×#106C2×D1111yescharacteristic
292C2×#106C2×D1111yescharacteristic
293C2×C4⋊C8—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#97—111no—
299C2×#97—111no—
300C2×C4×C8C2×D1111yescharacteristic
301#391—221no—
302#389—111no—
303#389—111no—
304#389C2×D1111yescharacteristic
305#389C2×D1111yescharacteristic
306#387—221no—
307#387—221no—
308#385—221no—
309#385—221no—
310#382—111no—
311#380—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C2×#95—221no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340C2×D1111yescharacteristic
324#340C2×D1111yescharacteristic
325#336—111no—
326#336—111no—
327C22×C11C2×C4×D411yescharacteristic
328C22×C11#54611yescharacteristic
329C22×C11D4×Q811yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11#57511yescharacteristic
332C22×C11#57711yescharacteristic
333C22×C11#57711yescharacteristic
334C2×D11—24no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—42no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11C2×C4×Q811yescharacteristic
348C4×C11#52011yescharacteristic
349C4×C11#55211yescharacteristic
350C4×C11#55411yescharacteristic
351Dic11—22no—
352Dic11—22no—
353Dic11—42no—
354Dic11—42no—
355Dic11—41no—
356Dic11—41no—
357Dic11—81no—
358C22×Q8—221no—
359C22×D4—111no—
360C23×C4—221no—
361C23×C4—221no—
362C23×C4—221no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4⋊Q8—114no—
368C4⋊Q8—222no—
369C4×Q8—444no—
370C4×D4—114no—
371C4×D4—222no—
372C4×D4—222no—
373C4×D4—222no—
374C4×D4—441no—
375C4×D4—441no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399#107—441no—
400#106—41no—
401#106—114no—
402#106C4×D1114yescomplemented
403C4⋊C8—114no—
404#102—114no—
405#102—114no—
406#102—114no—
407#102—222no—
408#97—222no—
409#97—441no—
410C4×C8—41no—
411#95—21no—
412#95—21no—
413#95—111no—
414#95—111no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422C2×C11#236011yescharacteristic
423C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C11#294911yescharacteristic
425C2×C11#330611yescharacteristic
426C2×C11#331111yescharacteristic
427C2×C11#338411yescharacteristic
428C2×C11#338811yescharacteristic
429D11—44no—
430C24—221no—
431C2×Q8—224no—
432C2×Q8—442no—
433C2×Q8—442no—
434C2×D4—112no—
435C2×D4—112no—
436C2×D4—112no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—221no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—224no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—881no—
457C22×C4—881no—
458C22×C4—881no—
459C22×C4—881no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8C2×C4×D1112yes—
474C2×C8Q8×D1112yes—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—112no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—222no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—441no—
492C4⋊C4—442no—
493C4⋊C4—881no—
494C4⋊C4C2×C4×D1112yes—
495C4⋊C4C2×C4×D1112yes—
496C22⋊C4—224no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C42—21no—
500C42—21no—
501C42—112no—
502C42—112no—
503C42—221no—
504C42—221no—
505C42—442no—
506C42—442no—
507C42—442no—
508C11#2297511yescharacteristic, complemented, Sylow
509C23—222no—
510C23—222no—
511C23—222no—
512C23—441no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23C2×D4×D1111yescharacteristic
517Q8—448no—
518D4—114no—
519D4—222no—
520D4—222no—
521D4—222no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—222no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—222no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—884no—
561C2×C4—884no—
562C2×C4—884no—
563C2×C4#6696712yes—
564C2×C4C22×C4×D1111yescharacteristic
565C2×C4#6703711yescharacteristic
566C2×C4C2×Q8×D1111yescharacteristic
567C2×C4#6704011yescharacteristic
568C2×C4#41×D1111yescharacteristic
569C2×C4#41×D1111yescharacteristic
570C8—22no—
571C8—22no—
572C8—222no—
573C8—441no—
574C22—224no—
575C22—442no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22C4×D4×D1111yescharacteristic
582C22#1062314111yescharacteristic
583C22#1062325811yescharacteristic
584C22C2×#6696711yescharacteristic
585C22#1062329311yescharacteristic
586C22#1062329911yescharacteristic
587C22#1062330111yescharacteristic
588C4—22no—
589C4—41no—
590C4—42no—
591C4—42no—
592C4—81no—
593C4—81no—
594C4—222no—
595C4—222no—
596C4—441no—
597C4—441no—
598C4—442no—
599C4—442no—
600C4—881no—
601C4#1062303511yescharacteristic
602C4C4×Q8×D1111yescharacteristic
603C4#1062316711yescharacteristic
604C4#1062322411yescharacteristic
605C2—444no—
606C2#1307161811yescharacteristic
607C2C4×#6696711yescharacteristic
608C2#1307747011yescharacteristic
609C2#1308058311yescharacteristic
610C2#1308065811yescharacteristic
611C2#1308152011yescharacteristic
612C2#1308156711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1941C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1941D11
hypocenterC11#22975
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
2. #13071669C2semidirect
4. #13069587C2semidirect
5. #13069385C2semidirect
6. #13069358C2semidirect
7. #13069198C2semidirect
8. #13069196C2semidirect
11. #13068490C2semidirect
15. C11×#1941C2semidirect
45. #10622483C4semidirect
97. #66941C2×C4semidirect
102. C11×#106C2×C4semidirect
116. #66885Q8semidirect
119. Dic11⋊C8C2×C4semidirect
122. #66872C2×C4semidirect
209. #1941D11semidirect
274. D44C4×Q8semidirect
402. #106C4×D11semidirect
508. C11#22975semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
#130716692
#130715252
#130695872
#130693852
#130693582
#130691982
#130691962
#130688742
#130688622
#130684902
#130684402
C4×#668852
C11×#19412
#2297511