Finite Group Databasebeta

← #14756896

Subgroups — #14756896

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622323C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic
3#13070979C211yesmaximal, characteristic, complemented
4#13069244C211yesmaximal, characteristic
5#13069237C211yesmaximal, characteristic
6#13069209C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13068970C211yesmaximal, characteristic
9#13068970C211yesmaximal, characteristic
10#13068887C211yesmaximal, characteristic, complemented
11#13068873C211yesmaximal, characteristic, complemented
12#13068513C211yesmaximal, characteristic, complemented
13C4×#66880C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic
15C11×#1746C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#376C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33#10622552C2211yescharacteristic
34#10622552C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622323C418yescomplemented
42#10622282—21no—
43#10622282—21no—
44#10622280—21no—
45#10622277—21no—
46#10622262—21no—
47#10622262—21no—
48#10622262—21no—
49#10622261—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
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)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
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×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×#4314—22no—
94C2×#4314—22no—
95C2×#4314C2×C414yes—
96C4×D44—22no—
97C4×D44C2×C414yes—
98C4×Dic22—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C4×Dic22C2×C414yes—
104C11×#97C2×C414yes—
105C4×C8×C11—22no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66885—22no—
117#66885—22no—
118#66885C2×C414yes—
119#66882—22no—
120#66882C2×C414yes—
121#66881—22no—
122#66880—22no—
123#66880—22no—
124#66880C2×C414yes—
125#21128—111nomaximal, Sylow
126C23×D11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44C22×C412yes—
147C2×C4×D11—24no—
148C2×C4×D11—81no—
149C2×C4×D11—81no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22C22×C412yes—
154C2×Dic22#4112yes—
155C2×Dic22#4112yes—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C22×C412yes—
167C2×C8×C11C22×C412yes—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C22×C412yes—
173C42×C11#4112yes—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178(C2×D11)⋊C4—81no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C412yes—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11#4112yes—
190C4⋊Dic11#4112yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—24no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11—81no—
203#4314—28no—
204C2×#440—111no—
205#2319—111no—
206#2276—111no—
207#1926—111no—
208#1925—111no—
209#1921—111no—
210#1918—111no—
211#1880—111no—
212#1880—111no—
213#1865—111no—
214#1863—111no—
215#1776—111no—
216C4×#103—111no—
217C4×#102—111no—
218#1746D1111yescharacteristic, complemented
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
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×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11C4×D412yes—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
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—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272D44—22no—
273D44—22no—
274D44—41no—
275D44—41no—
276C4×D11—84no—
277Dic22—22no—
278Dic22—22no—
279Dic22—22no—
280Dic22#11714yes—
281C8×C11—22no—
282C8×C11—22no—
283C8×C11—41no—
284C8×C11—41no—
285C22×SD16—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8—111no—
288C2×C4×Q8—111no—
289C2×C4×D4—111no—
290#440—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#97C2×D1111yescharacteristic
301C2×C4×C8C2×D1111yescharacteristic
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#388—221no—
307#388—221no—
308#381—221no—
309#380—221no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—221no—
315C4×C4⋊C4—221no—
316C4×C4⋊C4—221no—
317#376—221no—
318#376C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#336C2×D1111yescharacteristic
326#336C2×D1111yescharacteristic
327#336C2×D1111yescharacteristic
328#336C2×D1111yescharacteristic
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11#57611yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11C2×#11711yescharacteristic
350C4×C11C4×#4111yescharacteristic
351C4×C11#52911yescharacteristic
352C4×C11#52911yescharacteristic
353Dic11—24no—
354Dic11—42no—
355Dic11—42no—
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8—111no—
361C22×D4—111no—
362C23×C4—221no—
363C2×SD16—114no—
364C2×SD16—222no—
365C2×SD16—222no—
366C22×C8C22×D1111yescharacteristic
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4×Q8—114no—
371C4×Q8—222no—
372C4×Q8—222no—
373C4×Q8—222no—
374C4×Q8—222no—
375C4×Q8—222no—
376C4×D4—114no—
377C4×D4—222no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#107—114no—
405#107—222no—
406#106—222no—
407#103—114no—
408#103—222no—
409#103—222no—
410#102—114no—
411#102—222no—
412#102—222no—
413#97C4×D1114yes—
414C4×C8—22no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95D4411yescharacteristic
422#95D4411yescharacteristic
423#95D4411yescharacteristic
424#95D4411yescharacteristic
425C2×C11#229011yescharacteristic
426C2×C11#294611yescharacteristic
427C2×C11#294711yescharacteristic
428C2×C11#311911yescharacteristic
429C2×C11#312111yescharacteristic
430C2×C11#312411yescharacteristic
431C2×C11#312611yescharacteristic
432D11—82no—
433C24—221no—
434C2×Q8—112no—
435C2×Q8—112no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×D4—112no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—881no—
455C22×C4—881no—
456C22×C4C2×D4411yescharacteristic
457C22×C4C2×D4411yescharacteristic
458C22×C4C2×D4411yescharacteristic
459C22×C4C2×D4411yescharacteristic
460C22×C4C2×D4411yescharacteristic
461C22×C4C2×D4411yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—228no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8C2×C4×D1112yes—
475C2×C8C2×C4×D1112yes—
476C4⋊C4—112no—
477C4⋊C4—112no—
478C4⋊C4—112no—
479C4⋊C4—112no—
480C4⋊C4—224no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C22⋊C4—224no—
494C22⋊C4—881no—
495C22⋊C4—881no—
496C22⋊C4—881no—
497C22⋊C4—881no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—224no—
503C42—224no—
504C42—224no—
505C42—881no—
506C42—881no—
507C42—881no—
508C42—881no—
509C42C2×C4×D1112yes—
510C42#433912yes—
511C11#2112811yescharacteristic, complemented, Sylow
512C23—222no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23C22×D4411yescharacteristic
520Q8—114no—
521Q8—222no—
522Q8—222no—
523Q8—222no—
524D4—222no—
525D4—222no—
526D4—441no—
527D4—441no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—884no—
566C2×C4C4×D4412yes—
567C2×C4C4×D4412yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#433911yescharacteristic
570C2×C4#41×D1111yescharacteristic
571C2×C4#41×D1111yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C8—22no—
575C8—22no—
576C8—41no—
577C8—41no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22C2×C4×D4411yescharacteristic
586C22#1062305511yescharacteristic
587C22#1062305511yescharacteristic
588C22#1062328211yescharacteristic
589C22#1062328211yescharacteristic
590C22#1062328311yescharacteristic
591C22#1062328411yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—224no—
599C4—442no—
600C4—442no—
601C4—442no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4D11×#11711yescharacteristic
606C4#1062305311yescharacteristic
607C4#1062305911yescharacteristic
608C4#1062305911yescharacteristic
609C2—882no—
610C2#1307106011yescharacteristic
611C2#1307745011yescharacteristic
612C2#1307746111yescharacteristic
613C2#1307881711yescharacteristic
614C2#1307884711yescharacteristic
615C2#1307888011yescharacteristic
616C2#1307890811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1746C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#21128
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
3. #13070979C2semidirect
6. #13069209C2semidirect
7. #13069188C2semidirect
10. #13068887C2semidirect
11. #13068873C2semidirect
12. #13068513C2semidirect
13. C4×#66880C2semidirect
15. C11×#1746C2semidirect
41. #10622323C4semidirect
218. #1746D11semidirect
511. C11#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#106223232
#130712602
#130709792
#130692442
#130692372
#130692092
#130691882
#130689702
#130688872
#130688732
#130685132
C4×#668802
C4×#668852
C11×#17462
#2112811