Finite Group Databasebeta

← #14760938

Subgroups — #14760938

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622501C211yesmaximal, characteristic
2#13071146C211yesmaximal, characteristic
3C4×#66945C211yesmaximal, characteristic
4#13069258C211yesmaximal, characteristic, complemented
5#13069250C211yesmaximal, characteristic, complemented
6#13069191C211yesmaximal, characteristic, complemented
7#13068927C211yesmaximal, characteristic
8#13068818C211yesmaximal, characteristic
9#13068709C211yesmaximal, characteristic
10#107×Dic11C211yesmaximal, characteristic, complemented
11#13068504C211yesmaximal, characteristic, complemented
12#13068435C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic
15C11×#1918C211yesmaximal, characteristic, complemented
16C2×#66950C2211yescharacteristic
17C2×#66945C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622602—21no—
32#10622600C2211yescharacteristic
33C4⋊C4×Dic11—21no—
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C4×(C2×D11)⋊C4—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C42×Dic11—21no—
44#10622542C2211yescharacteristic
45#10622501C418yescomplemented
46#10622279—21no—
47#10622279—21no—
48#10622267—21no—
49#10622261—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
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×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66950—22no—
95#66950C2×C414yes—
96#66945—22no—
97#66945—22no—
98#66945—22no—
99#66945C2×C414yes—
100#66940—22no—
101#66940—22no—
102C42×D11—22no—
103C42×D11—22no—
104C11×#107C2×C414yescomplemented
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⋊#95—21no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8C2×C414yes—
116#66882—22no—
117#66880—22no—
118#66880C2×C414yescomplemented
119C8×Dic11—22no—
120C8×Dic11—22no—
121#66874—22no—
122#66874C2×C414yescomplemented
123#66872—22no—
124#66872C2×C414yescomplemented
125C4×#485—111nomaximal, Sylow
126C23×D11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—41no—
151C2×C4×D11C22×C412yes—
152C2×C4×D11#4112yes—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22C22×C412yes—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C412yes—
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⋊C4C22×C412yes—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4#4112yes—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—42no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C412yes—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189C4×Dic11—24no—
190C4×Dic11—24no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—42no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11#4112yes—
199C4×Dic11#4112yes—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C412yes—
206C2×#485—111no—
207C4×C22⋊Q8—111no—
208C4×#117—111no—
209#1928—111no—
210#1927—111no—
211#1919—111no—
212#1918D1111yescharacteristic, complemented
213#1873—111no—
214#1854—111no—
215#1825—111no—
216C4×#107—111no—
217C4×#106—111no—
218C4×#103—111no—
219C4×#103—111no—
220C4×C22⋊C8—111no—
221C23×C11C22×D411yescharacteristic
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11C4×D412yes—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
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×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#13512yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
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×Dic11C4×D412yes—
270C2×Dic11#12312yes—
271C2×Dic11#12312yes—
272C2×Dic11#13512yes—
273C2×Dic11#13712yes—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—44no—
279C4×D11—44no—
280Dic22—22no—
281Dic22—22no—
282Dic22—41no—
283Dic22—41no—
284C8×C11—22no—
285C8×C11—41no—
286C11⋊C8—22no—
287C11⋊C8—41no—
288C2×C22⋊Q8—111no—
289C2×C4×Q8—111no—
290C2×#117—111no—
291C2×#117—111no—
292C22×C42—111no—
293#485—118no—
294C2×#107—111no—
295C2×#107C2×D1111yescharacteristic
296C2×#106—111no—
297C2×#106—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×C22⋊C8—111no—
303C2×C22⋊C8—111no—
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306#391—111no—
307#389C2×D1111yescharacteristic
308#387—221no—
309#385—221no—
310#380—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—221no—
316C4×C4⋊C4C2×D1111yescharacteristic
317C4×C22⋊C4—221no—
318C4×C22⋊C4—221no—
319C4×C22⋊C4—221no—
320#376—221no—
321C43—221no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336C2×D1111yescharacteristic
332C22×C11C2×C4×D411yescharacteristic
333C22×C11C2×#12311yescharacteristic
334C22×C11#52511yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11C2×#13511yescharacteristic
337C22×C11C2×#13711yescharacteristic
338C22×C11#57511yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C4×C11—22no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—81no—
352C4×C11C4×#4111yescharacteristic
353C4×C11C4×#4111yescharacteristic
354C4×C11#52911yescharacteristic
355C4×C11#52911yescharacteristic
356Dic11—22no—
357Dic11—22no—
358Dic11—42no—
359Dic11—42no—
360Dic11—42no—
361Dic11—81no—
362Dic11#48514yescomplemented
363C22×Q8—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22⋊Q8—114no—
372C22⋊Q8—222no—
373C4×Q8—222no—
374C4×Q8—222no—
375#117—114no—
376#117—222no—
377#117—222no—
378#117—222no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C42—21no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—222no—
398C2×C42—222no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#107—222no—
408#107C4×D1114yescomplemented
409#106—114no—
410#106—222no—
411#103—114no—
412#103—114no—
413#103—222no—
414#103—222no—
415C22⋊C8—114no—
416C22⋊C8—222no—
417C4×C8—222no—
418C4×C8—222no—
419#95—21no—
420#95—21no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11C4×#12311yescharacteristic
429C2×C11C4×#13511yescharacteristic
430C2×C11C4×#13711yescharacteristic
431C2×C11C2×#48511yescharacteristic
432C2×C11#309111yescharacteristic
433C2×C11#310211yescharacteristic
434C2×C11#310711yescharacteristic
435D11—42no—
436C24—111no—
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—441no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8C2×C4×D1112yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—442no—
495C4⋊C4C2×C4×D1112yes—
496C4⋊C4C2×C4×D1112yes—
497C4⋊C4#434312yes—
498C22⋊C4—224no—
499C22⋊C4—224no—
500C22⋊C4—224no—
501C22⋊C4—442no—
502C42—21no—
503C42—21no—
504C42—42no—
505C42—112no—
506C42—112no—
507C42—222no—
508C42—222no—
509C42—224no—
510C42—224no—
511C42—442no—
512C42—442no—
513C42—442no—
514C42—442no—
515C42—442no—
516C11C4×#48511yescharacteristic, complemented, Sylow
517C23—112no—
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—221no—
524C23C2×D4×D1111yescharacteristic
525Q8—222no—
526Q8—222no—
527Q8—441no—
528Q8—441no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4#6696512yes—
574C2×C4C22×C4×D1111yescharacteristic
575C2×C4C2×#434311yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C8—22no—
581C8—41no—
582C8—222no—
583C8—441no—
584C22—222no—
585C22—222no—
586C22—222no—
587C22—441no—
588C22—441no—
589C22—441no—
590C22—441no—
591C22C4×D4×D1111yescharacteristic
592C22#1062315811yescharacteristic
593C22D11×#12311yescharacteristic
594C22C2×#6696511yescharacteristic
595C22D11×#13511yescharacteristic
596C22D11×#13711yescharacteristic
597C22#1062330811yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—41no—
603C4—81no—
604C4—114no—
605C4—222no—
606C4—222no—
607C4—442no—
608C4—442no—
609C4—442no—
610C4—881no—
611C4#1062305311yescharacteristic
612C4C4×#434311yescharacteristic
613C4#1062322211yescharacteristic
614C4#1062323711yescharacteristic
615C2—442no—
616C2#1307113711yescharacteristic
617C2C4×#6696511yescharacteristic
618C2#1307743211yescharacteristic
619C2D11×#48511yescharacteristic
620C2#1307852411yescharacteristic
621C2#1307864111yescharacteristic
622C2#1307868911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1918C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1918D11
hypocenterC11C4×#485
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #13069258C2semidirect
5. #13069250C2semidirect
6. #13069191C2semidirect
10. #107×Dic11C2semidirect
11. #13068504C2semidirect
12. #13068435C2semidirect
13. #13068435C2semidirect
15. C11×#1918C2semidirect
45. #10622501C4semidirect
104. C11×#107C2×C4semidirect
118. #66880C2×C4semidirect
122. #66874C2×C4semidirect
124. #66872C2×C4semidirect
212. #1918D11semidirect
362. Dic11#485semidirect
408. #107C4×D11semidirect
516. C11C4×#485semidirect

Maximal subgroups

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

subgroupindex
C2×#106225012
#130711462
C4×#669452
#130692582
#130692502
#130691912
#130689272
#130688182
#130687092
#107×Dic112
#130685042
#130684352
#130683732
C11×#19182
C4×#48511