Finite Group Databasebeta

← #14660184

Subgroups — #14660184

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622849C211yesmaximal, characteristic
2#13077135C211yesmaximal, characteristic
3#13077035C211yesmaximal, characteristic, complemented
4#13068348C211yesmaximal, characteristic, complemented
5#13068325C211yesmaximal, characteristic, complemented
6C2×#10622169C211yesmaximal, characteristic, complemented
7C2×C11×#410C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C11×#410—22no—
16C11×#410C414yescomplemented
17C2×C11×#99—22no—
18#10622849—22no—
19#10622849—22no—
20C2×#66901C414yescomplemented
21#10622846—22no—
22#10622845—22no—
23#10622838C412yescomplemented
24#10622828C412yescomplemented
25#10622610—22no—
26#10622610—22no—
27C4×#4318—22no—
28#10622170—22no—
29#10622169—22no—
30#10622165—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41C2×C412yes—
42C2×C11×#41C2×C412yes—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2×C411yescharacteristic
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C11×#117—21no—
49C11×#117—21no—
50C11×#117—21no—
51C11×#117—21no—
52C11×#117—21no—
53C11×#117C2×C412yes—
54C11×#117C2×C412yes—
55C11×#117D412yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64#66979—21no—
65#66979—21no—
66#66979—21no—
67#66979—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71#66979C2×C412yes—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4×Dic11—21no—
75C2×C4×Dic11C2×C412yes—
76C2×#4318—21no—
77C2×#4318—21no—
78C2×#4318—21no—
79C2×#4318—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318C2×C412yes—
84C2×#4318C2×C412yes—
85C2×#4318D412yes—
86C2×#4318D412yes—
87C2×#4318D412yes—
88C22×C11⋊C8—21no—
89C22×C11⋊C8D412yes—
90C11×#99—28no—
91#66901—28no—
92#66899—24no—
93#66896—24no—
94#66867—24no—
95C4×C11⋊C8—24no—
96#10951—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C4212yes—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11C4212yes—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×Dic11—22no—
157C22×Dic11—41no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—41no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4C22⋊C414yes—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—41no—
170C22⋊Dic11—22no—
171C22⋊Dic11—41no—
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174C4⋊Dic11—22no—
175C4⋊Dic11—41no—
176C4⋊Dic11—41no—
177C4⋊Dic11—41no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—41no—
182#4318—22no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318C22⋊C414yes—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8C22⋊C414yes—
196C2×#421—111no—
197#2896—111no—
198C2×#410D1111yescharacteristic
199#2873—111no—
200#1740—111no—
201#1733—111no—
202C2×H(3,ℤ/4)—111no—
203C23×C11—22no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—81no—
207C23×C11—82no—
208C23×C11C2×C22⋊C411yescharacteristic
209C23×C11C4×D411yescharacteristic
210C23×C11C4×D411yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12711yescharacteristic
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—41no—
218Q8×C11—41no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—82no—
237C2×C4×C11—82no—
238C2×C4×C11C2×C4211yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11#11711yescharacteristic
242C2×C4×C11#11711yescharacteristic
243C2×C4×C11#11711yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12411yescharacteristic
263C2×C4×C11#12411yescharacteristic
264C2×C4×C11#12611yescharacteristic
265C2×C4×C11#12611yescharacteristic
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—82no—
269C2×Dic11—82no—
270C11⋊C8—24no—
271C11⋊C8—24no—
272C22×#41C2×D1111yescharacteristic
273C22×M16—111no—
274C22×M16—111no—
275C2×#117—111no—
276C2×#117—111no—
277C2×#117C2×D1111yescharacteristic
278C2×#117C2×D1111yescharacteristic
279#421—222no—
280#421—222no—
281C2×#104—114no—
282#419—112no—
283#418—112no—
284#417—222no—
285#416—222no—
286#410—22no—
287#410Dic1114yescomplemented
288C2×#99—22no—
289#405—222no—
290#405—222no—
291C4×M16—222no—
292#342—222no—
293#339—222no—
294H(3,ℤ/4)—222no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—42no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11C4×C22⋊C411yescharacteristic
307C22×C11#38611yescharacteristic
308C22×C11#38811yescharacteristic
309C22×C11#38811yescharacteristic
310C22×C11#39011yescharacteristic
311C22×C11#39011yescharacteristic
312C22×C11#39011yescharacteristic
313C4×C11—44no—
314C4×C11—42no—
315C4×C11—82no—
316C4×C11C4×C22⋊C411yescharacteristic
317C4×C11C4×C22⋊C411yescharacteristic
318C4×C11#38611yescharacteristic
319C4×C11#38611yescharacteristic
320C4×C11#38811yescharacteristic
321C4×C11#38811yescharacteristic
322C4×C11#38811yescharacteristic
323C4×C11#38811yescharacteristic
324Dic11—82no—
325Dic11—82no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41C4×D1112yes—
337C2×#41C2×Dic1112yes—
338C22×Q8C4×D1111yescharacteristic
339C22×D4—21no—
340C22×D4C4×D1111yescharacteristic
341C23×C4—21no—
342C23×C4C22×D1111yescharacteristic
343C2×M16—112no—
344C2×M16—112no—
345C2×M16—112no—
346C2×M16—112no—
347C2×M16—112no—
348C2×M16—221no—
349C2×M16—221no—
350C2×M16—221no—
351C2×M16—221no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16—221no—
355C22×C8—112no—
356C22×C8—221no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—112no—
363#117—221no—
364#117—221no—
365#117—221no—
366#117—221no—
367#117—221no—
368#117—221no—
369#117—221no—
370#117C2×Dic1112yes—
371#117C2×Dic1112yes—
372#117C22⋊D1112yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4C22⋊D1112yes—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—112no—
384C2×C42—221no—
385#104—228no—
386#103—224no—
387#102—224no—
388#99—28no—
389#97—224no—
390C4×C8—224no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—82no—
399C2×C11#143711yescharacteristic
400C24—21no—
401C24C2×C22⋊D1111yescharacteristic
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8C4×Dic1112yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4C4×Dic1112yes—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—222no—
446C22×C4—441no—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4#433911yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4#434111yescharacteristic
456C22×C4#434111yescharacteristic
457C22×C4#434111yescharacteristic
458C22×C4#434111yescharacteristic
459C22×C4C22×Dic1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461M16—114no—
462M16—222no—
463M16—222no—
464M16—222no—
465M16—222no—
466M16—222no—
467M16—222no—
468M16—222no—
469C2×C8—114no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8—222no—
474C2×C8—222no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—41no—
479C4⋊C4—222no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—41no—
486C22⋊C4—222no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4C22⋊Dic1114yes—
491C42—22no—
492C42—22no—
493C42—22no—
494C42—41no—
495C42—222no—
496C42—222no—
497C42—222no—
498C42—441no—
499C11#1095111yescharacteristic, complemented, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—81no—
504C23—82no—
505C23C4×C22⋊D1111yescharacteristic
506C23C4×C22⋊D1111yescharacteristic
507C23#6698911yescharacteristic
508C23#6699211yescharacteristic
509C23#6699211yescharacteristic
510C23#6699311yescharacteristic
511C23C2×C22⋊Dic1111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—882no—
538C2×C4—882no—
539C2×C4#6693011yescharacteristic
540C2×C4#6693011yescharacteristic
541C2×C4#6693211yescharacteristic
542C2×C4#6693211yescharacteristic
543C2×C4C22⋊C4×D1111yescharacteristic
544C2×C4C22⋊C4×D1111yescharacteristic
545C2×C4(C22⋊D11)⋊C411yescharacteristic
546C2×C4(C22⋊D11)⋊C411yescharacteristic
547C2×C4(C22⋊D11)⋊C411yescharacteristic
548C2×C4(C22⋊D11)⋊C411yescharacteristic
549C2×C4#6693611yescharacteristic
550C2×C4#6693611yescharacteristic
551C2×C4#6693711yescharacteristic
552C2×C4#6693711yescharacteristic
553C2×C4#6693811yescharacteristic
554C2×C4#6693811yescharacteristic
555C2×C4C2×C4×Dic1111yescharacteristic
556C2×C4#6697911yescharacteristic
557C2×C4C4×C22⋊D1111yescharacteristic
558C2×C4C4×C22⋊D1111yescharacteristic
559C2×C4D4×Dic1111yescharacteristic
560C2×C4D4×Dic1111yescharacteristic
561C2×C4D4×Dic1111yescharacteristic
562C2×C4D4×Dic1111yescharacteristic
563C2×C4#6698811yescharacteristic
564C2×C4#6699011yescharacteristic
565C2×C4#6699111yescharacteristic
566C2×C4#6699111yescharacteristic
567C8—224no—
568C8—224no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22#1062255811yescharacteristic
581C22#1062255811yescharacteristic
582C22#1062257011yescharacteristic
583C22#1062257011yescharacteristic
584C22C4×C22⋊Dic1111yescharacteristic
585C22#1062283311yescharacteristic
586C22#1062283411yescharacteristic
587C4—44no—
588C4—42no—
589C4—82no—
590C4—882no—
591C4—882no—
592C4C22⋊C4×Dic1111yescharacteristic
593C4C22⋊C4×Dic1111yescharacteristic
594C4#1062255711yescharacteristic
595C4#1062255711yescharacteristic
596C4#1062256411yescharacteristic
597C4#1062256411yescharacteristic
598C4#1062256911yescharacteristic
599C4#1062256911yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2#1306685311yescharacteristic
subgroupG/H
centerC4#10622569
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#410C2
socleC2×C11#1437
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#410D11
hypocenterC11#10951
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
3. #13077035C2semidirect
4. #13068348C2semidirect
5. #13068325C2semidirect
6. C2×#10622169C2semidirect
16. C11×#410C4semidirect
20. C2×#66901C4semidirect
23. #10622838C4semidirect
24. #10622828C4semidirect
287. #410Dic11semidirect
499. C11#10951semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
#130771352
#130770352
#130683482
#130683252
C2×#106221692
C2×C11×#4102
#1095111