Finite Group Databasebeta

← #14758108

Subgroups — #14758108

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622323C211yesmaximal, characteristic
2#13071090C211yesmaximal, characteristic, complemented
3#13071077C211yesmaximal, characteristic
4#13069495C211yesmaximal, characteristic
5#13069468C211yesmaximal, characteristic
6#13069352C211yesmaximal, characteristic, complemented
7#13069347C211yesmaximal, characteristic, complemented
8#13069311C211yesmaximal, characteristic
9#13069304C211yesmaximal, characteristic, complemented
10#13069297C211yesmaximal, characteristic
11#13069290C211yesmaximal, characteristic, complemented
12#13068449C211yesmaximal, characteristic, complemented
13#13068444C211yesmaximal, characteristic
14#97×Dic11C211yesmaximal, characteristic, complemented
15C11×#1776C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×#66925—21no—
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622601C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622587C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C4×(C2×D11)⋊C4—21no—
45#10622545—21no—
46C4×Dic11⋊C4—21no—
47C42×Dic11C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622323C418yescomplemented
50#10622282—21no—
51#10622282—21no—
52#10622265—21no—
53#10622265—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C2×#4314—22no—
94C2×#4314—22no—
95C2×#4314C2×C414yes—
96C4×D44—22no—
97C4×D44C2×C414yes—
98#66925—44no—
99C4×Dic22—22no—
100C4×Dic22C2×C414yes—
101C11×#107—22no—
102C11×#106—22no—
103C11×#97C2×C414yes—
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⋊#95—21no—
114#66885C2×C414yes—
115#66882C2×C414yes—
116#66880C2×C414yes—
117#66879—22no—
118#66879—22no—
119C8×Dic11—22no—
120C8×Dic11—22no—
121#66874—22no—
122#66874—22no—
123#66873—22no—
124#66873—22no—
125#66867—22no—
126#21288—111nomaximal, Sylow
127C23×D11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44C22×C412yes—
148C2×C4×D11—24no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C412yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C22×C412yes—
161C2×C8×C11#4112yes—
162C2×C8×C11#4112yes—
163C11×C4⋊C4—21no—
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—21no—
171C42×C11—42no—
172C42×C11—42no—
173C42×C11C22×C412yes—
174C42×C11#4112yes—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22×C412yes—
183C4⋊Dic11C22×C412yes—
184Dic11⋊C4—24no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C4×Dic11—24no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—41no—
197C4×Dic11—41no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8#4112yes—
203C2×C11⋊C8#4112yes—
204#4314—28no—
205C2×#440—111no—
206#2295—111no—
207#2293—111no—
208#1973—111no—
209#1968—111no—
210#1943—111no—
211#1942—111no—
212#1936—111no—
213#1935—111no—
214#1934—111no—
215#1933—111no—
216#1776D1111yescharacteristic, complemented
217#1763—111no—
218#1762—111no—
219C4×#97—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
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×C11—41no—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11AGL(1,ℤ/8)12yes—
272C2×Dic11#13712yes—
273D44—22no—
274D44—22no—
275D44—41no—
276D44—41no—
277C4×D11—48no—
278Dic22—22no—
279Dic22—22no—
280Dic22—41no—
281Dic22—41no—
282C8×C11—22no—
283C8×C11#11714yescomplemented
284C11⋊C8—22no—
285C11⋊C8—22no—
286C22×SD16—111no—
287C2×C4×Q8—111no—
288C2×C4×D4—111no—
289C2×#117—221no—
290#440—118no—
291C2×#107—111no—
292C2×#107C2×D1111yescharacteristic
293C2×#106C2×D1111yescharacteristic
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#97—111no—
301C2×#97—111no—
302C2×#97—111no—
303C2×#97C2×D1111yescharacteristic
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306#391—111no—
307#391—111no—
308#390—111no—
309#390—111no—
310#389—111no—
311#389—111no—
312#389—111no—
313#389—111no—
314#388—221no—
315#388—221no—
316#387—221no—
317#387—221no—
318C4×C4⋊C4—221no—
319C4×C4⋊C4C2×D1111yescharacteristic
320C4×C4⋊C4C2×D1111yescharacteristic
321C4×C22⋊C4—221no—
322#376—221no—
323C43—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330C22×C11C2×C4×D411yescharacteristic
331C22×C11#53211yescharacteristic
332C22×C11#53211yescharacteristic
333C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11C2×#11711yescharacteristic
351C4×C11C4×#4111yescharacteristic
352C4×C11#52911yescharacteristic
353C4×C11#52911yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—41no—
357Dic11—41no—
358Dic11—42no—
359Dic11—42no—
360Dic11—42no—
361C22×Q8—111no—
362C22×D4—111no—
363C23×C4—221no—
364C2×SD16—114no—
365C2×SD16—222no—
366C2×SD16—222no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C4×Q8—114no—
372C4×Q8—222no—
373C4×D4—114no—
374C4×D4—222no—
375#117—444no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—22no—
403#107—114no—
404#106—22no—
405#103—114no—
406#103—222no—
407#103—222no—
408#102—114no—
409#102—222no—
410#102—222no—
411#97—222no—
412#97—222no—
413#97—222no—
414#97C4×D1114yes—
415C4×C8—222no—
416C4×C8—222no—
417#95—21no—
418#95—21no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11#229311yescharacteristic
428C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
429C2×C11C4×#13711yescharacteristic
430C2×C11#318011yescharacteristic
431C2×C11#318111yescharacteristic
432C2×C11#318211yescharacteristic
433C2×C11#318311yescharacteristic
434D11—82no—
435C24—221no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×D4—112no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—224no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—228no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—112no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8C2×C4×D1112yes—
475C2×C8C2×C4×D1112yes—
476C2×C8#433912yes—
477C2×C8#433912yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—224no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C22⋊C4—224no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—42no—
501C42—42no—
502C42—222no—
503C42—222no—
504C42—224no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—441no—
510C42—441no—
511C42C2×C4×D1112yes—
512C42#434312yes—
513C11#2128811yescharacteristic, complemented, Sylow
514C23—222no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23C2×D4×D1111yescharacteristic
522Q8—222no—
523Q8—222no—
524Q8—441no—
525Q8—441no—
526D4—222no—
527D4—222no—
528D4—441no—
529D4—441no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
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—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—448no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4#6694612yes—
569C2×C4#6694612yes—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C2×#433911yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×#434311yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C8—22no—
577C8—222no—
578C8—222no—
579C8#6692514yescomplemented
580C22—442no—
581C22—442no—
582C22—442no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—881no—
587C22C2×#6694611yescharacteristic
588C22#1062307911yescharacteristic
589C22#1062307911yescharacteristic
590C22D11×AGL(1,ℤ/8)11yescharacteristic
591C22#1062330411yescharacteristic
592C22D11×#13711yescharacteristic
593C22#1062330811yescharacteristic
594C4—22no—
595C4—22no—
596C4—81no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4—222no—
601C4—222no—
602C4—441no—
603C4—441no—
604C4—442no—
605C4—442no—
606C4—442no—
607C4C2×#6692511yescharacteristic
608C4#1062305311yescharacteristic
609C4#1062311111yescharacteristic
610C4#1062311111yescharacteristic
611C2—882no—
612C2#1307107711yescharacteristic
613C2#1307742311yescharacteristic
614C2#1307743411yescharacteristic
615C2#1307931211yescharacteristic
616C2#1307932311yescharacteristic
617C2#1307933111yescharacteristic
618C2#1307934111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1776C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1776D11
hypocenterC11#21288
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
2. #13071090C2semidirect
6. #13069352C2semidirect
7. #13069347C2semidirect
9. #13069304C2semidirect
11. #13069290C2semidirect
12. #13068449C2semidirect
14. #97×Dic11C2semidirect
15. C11×#1776C2semidirect
49. #10622323C4semidirect
216. #1776D11semidirect
283. C8×C11#117semidirect
513. C11#21288semidirect
579. C8#66925semidirect

Maximal subgroups

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

subgroupindex
C2×#106223232
#130710902
#130710772
#130694952
#130694682
#130693522
#130693472
#130693112
#130693042
#130692972
#130692902
#130684492
#130684442
#97×Dic112
C11×#17762
#2128811