Finite Group Databasebeta

← #14660233

Subgroups — #14660233

Order 2816.

990 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×#10622849C211yesmaximal, characteristic
2#13077034C211yesmaximal, characteristic, complemented
3#13071107C211yesmaximal, characteristic
4#13068348C211yesmaximal, characteristic, complemented
5C2×#10622193C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×C11×#421C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66979C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C11×#421—22no—
16C11×#421C414yescomplemented
17C2×C11×#104—22no—
18#10622849—22no—
19#10622849C414yescomplemented
20C2×#66901—22no—
21#10622843C412yescomplemented
22#10622834C412yescomplemented
23#10622833—22no—
24C4×C22⋊Dic11—22no—
25#10622735—22no—
26M16×Dic11—22no—
27#10622714—22no—
28#10622193—22no—
29#10622170—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
48C23×Dic11—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16C2×C412yes—
53C2×C11×M16D412yes—
54C2×C11×M16D412yes—
55C22×C8×C11—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117C2×C412yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—21no—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11D412yes—
66#66979—21no—
67#66979—21no—
68#66979—21no—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73#66979C2×C412yes—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2×C412yes—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2×C412yes—
83C2×C4×Dic11D412yes—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318C2×C412yes—
88C2×#4318D412yes—
89C2×#4318D412yes—
90C22×C11⋊C8—21no—
91C11×#104—28no—
92#66901—28no—
93C11⋊#95—24no—
94#66879—24no—
95C8×Dic11—24no—
96#10959—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—41no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×Dic11—22no—
156C22×Dic11—44no—
157C22×Dic11—41no—
158C22×Dic11—41no—
159C22×Dic11—41no—
160C22×Dic11C22⋊C414yes—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16C22⋊C414yescomplemented
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—41no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—41no—
172C42×C11—22no—
173C42×C11—41no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176C22⋊Dic11—22no—
177C22⋊Dic11—48no—
178C22⋊Dic11—41no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—41no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—41no—
189C4×Dic11—41no—
190C4×Dic11—41no—
191#4318—22no—
192#4318—22no—
193#4318—22no—
194#4318C22⋊C414yescomplemented
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×#421—111no—
199C2×#421D1111yescharacteristic
200#2873—111no—
201#2297—111no—
202#1740—111no—
203C2×#339—111no—
204C2×#339—111no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—44no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11C2×C22⋊C411yescharacteristic
211C23×C11C4×D411yescharacteristic
212C23×C11C4×D411yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11#12111yescharacteristic
215C23×C11#12411yescharacteristic
216C23×C11#12711yescharacteristic
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—41no—
220Q8×C11—41no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—42no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
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—24no—
267C2×Dic11—24no—
268C2×Dic11—42no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11—42no—
274C2×Dic11—82no—
275C8×C11—24no—
276C11⋊C8—24no—
277C22×#41C2×D1111yescharacteristic
278C22×M16—111no—
279C22×M16C2×D1111yescharacteristic
280C2×#117—111no—
281C2×#117—111no—
282C2×#117C2×D1111yescharacteristic
283C22×C42—111no—
284#421—22no—
285#421—114no—
286#421—222no—
287#421Dic1114yescomplemented
288C2×#104—22no—
289C2×#104—222no—
290#405—222no—
291#405—222no—
292C4×M16—222no—
293#391—112no—
294#390—112no—
295#386—222no—
296C4×C22⋊C4—222no—
297#342—222no—
298#339—222no—
299#339—222no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—44no—
308C22×C11—42no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11C4×C22⋊C411yescharacteristic
312C22×C11#38611yescharacteristic
313C22×C11#38811yescharacteristic
314C22×C11#38811yescharacteristic
315C22×C11#39011yescharacteristic
316C22×C11#39011yescharacteristic
317C22×C11#39011yescharacteristic
318C4×C11—42no—
319C4×C11—82no—
320C4×C11C4×C22⋊C411yescharacteristic
321C4×C11C4×C22⋊C411yescharacteristic
322C4×C11#38611yescharacteristic
323C4×C11#38611yescharacteristic
324C4×C11#38811yescharacteristic
325C4×C11#38811yescharacteristic
326C4×C11#38811yescharacteristic
327C4×C11#38811yescharacteristic
328Dic11—44no—
329Dic11—44no—
330Dic11—82no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41C4×D1112yes—
342C2×#41C2×Dic1112yes—
343C22×Q8C4×D1111yescharacteristic
344C22×D4—21no—
345C22×D4C4×D1111yescharacteristic
346C23×C4—21no—
347C23×C4—221no—
348C23×C4C22×D1111yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—112no—
353C2×M16—112no—
354C2×M16—112no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16C2×Dic1112yes—
359C2×M16C22⋊D1112yes—
360C2×M16C22⋊D1112yes—
361C22×C8—21no—
362C22×C8—221no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—112no—
367#117—221no—
368#117—221no—
369#117—221no—
370#117—221no—
371#117—221no—
372#117—221no—
373#117—221no—
374#117C2×Dic1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—221no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—224no—
382C2×C42—21no—
383C2×C42—112no—
384C2×C42—112no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42—221no—
389C2×C42—221no—
390C2×C42—221no—
391#104—28no—
392#104—228no—
393#97—224no—
394C4×C8—224no—
395#95—224no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—82no—
403C2×C11#143711yescharacteristic
404C2×C11#188412yes—
405C24—21no—
406C24D4×D1111yescharacteristic
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C4×Dic1112yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C4×Dic1112yes—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—114no—
450C22×C4—222no—
451C22×C4—444no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4—441no—
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4#433911yescharacteristic
458C22×C4#433911yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4#434111yescharacteristic
463C22×C4#434111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4#434111yescharacteristic
466C22×C4C22×Dic1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469M16—22no—
470M16—22no—
471M16—22no—
472M16—114no—
473M16—222no—
474M16—222no—
475M16—222no—
476M16C22⋊Dic1114yescomplemented
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—222no—
488C4⋊C4—441no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—448no—
495C22⋊C4—441no—
496C42—22no—
497C42—41no—
498C42—222no—
499C42—222no—
500C42—222no—
501C42—222no—
502C42—222no—
503C42—441no—
504C42—441no—
505C42—441no—
506C11#1095911yescharacteristic, complemented, Sylow
507C23—22no—
508C23—42no—
509C23—44no—
510C23—41no—
511C23—41no—
512C23C22⋊C4×D1111yescharacteristic
513C23(C22⋊D11)⋊C411yescharacteristic
514C23#6693711yescharacteristic
515C23#6693811yescharacteristic
516C23D4×Dic1111yescharacteristic
517C23#6699111yescharacteristic
518C23#6699311yescharacteristic
519Q8—22no—
520Q8—22no—
521Q8—41no—
522Q8—41no—
523D4—22no—
524D4—22no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4—42no—
529D4—41no—
530D4—41no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—442no—
543C2×C4—444no—
544C2×C4—444no—
545C2×C4—442no—
546C2×C4—444no—
547C2×C4—442no—
548C2×C4—882no—
549C2×C4#6693011yescharacteristic
550C2×C4#6693011yescharacteristic
551C2×C4#6693211yescharacteristic
552C2×C4#6693211yescharacteristic
553C2×C4C22⋊C4×D1111yescharacteristic
554C2×C4(C22⋊D11)⋊C411yescharacteristic
555C2×C4(C22⋊D11)⋊C411yescharacteristic
556C2×C4(C22⋊D11)⋊C411yescharacteristic
557C2×C4#6693611yescharacteristic
558C2×C4#6693611yescharacteristic
559C2×C4#6693711yescharacteristic
560C2×C4#6693811yescharacteristic
561C2×C4C2×C4×Dic1111yescharacteristic
562C2×C4#6697911yescharacteristic
563C2×C4C4×C22⋊D1111yescharacteristic
564C2×C4C4×C22⋊D1111yescharacteristic
565C2×C4C4×C22⋊D1111yescharacteristic
566C2×C4C4×C22⋊D1111yescharacteristic
567C2×C4D4×Dic1111yescharacteristic
568C2×C4D4×Dic1111yescharacteristic
569C2×C4D4×Dic1111yescharacteristic
570C2×C4#6698811yescharacteristic
571C2×C4#6698911yescharacteristic
572C2×C4#6699011yescharacteristic
573C2×C4#6699111yescharacteristic
574C2×C4#6699211yescharacteristic
575C2×C4#6699211yescharacteristic
576C2×C4C2×C22⋊Dic1111yescharacteristic
577C8—24no—
578C8—224no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—44no—
587C22—42no—
588C22—82no—
589C22—82no—
590C22C22⋊C4×Dic1111yescharacteristic
591C22#1062255711yescharacteristic
592C22#1062256411yescharacteristic
593C22#1062256911yescharacteristic
594C22#1062257011yescharacteristic
595C22#1062257011yescharacteristic
596C22#1062283411yescharacteristic
597C4—42no—
598C4—82no—
599C4—444no—
600C4—444no—
601C4—882no—
602C4C22⋊C4×Dic1111yescharacteristic
603C4#1062255711yescharacteristic
604C4#1062255811yescharacteristic
605C4#1062255811yescharacteristic
606C4#1062256411yescharacteristic
607C4#1062256911yescharacteristic
608C4C4×C22⋊Dic1111yescharacteristic
609C4#1062283311yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—82no—
617C2#1306685311yescharacteristic
618C2#1306899612yes—
subgroupG/H
centerC2×C4#66990
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#421C2
socleC22×C11#386
prime radicalC22×C11×#41C22
cosocleC23×C4×C11C23
hypercenterC2×#421D11
hypocenterC11#10959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #13077034C2semidirect
4. #13068348C2semidirect
5. C2×#10622193C2semidirect
6. C2×#10622170C2semidirect
16. C11×#421C4semidirect
19. #10622849C4semidirect
21. #10622843C4semidirect
22. #10622834C4semidirect
164. C11×M16C22⋊C4semidirect
194. #4318C22⋊C4semidirect
287. #421Dic11semidirect
476. M16C22⋊Dic11semidirect
506. C11#10959semidirect

Maximal subgroups

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

subgroupindex
C2×#106228492
#130770342
#130711072
#130683482
C2×#106221932
C2×#106221702
C2×C11×#4212
#1095911