Finite Group Databasebeta

← #14660287

Subgroups — #14660287

Order 2816.

1578 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
1C22×#66977C211yesmaximal, characteristic
2C22×#66880C212yesmaximal, complemented
3C2×#10622825C211yesmaximal, characteristic
4C2×#10622189C212yesmaximal, complemented
5C22×C11×C22⋊C8C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C23×Dic22C2211yescharacteristic
8C23×C8×C11C2212yes—
9C22×C22⋊Dic11—21no—
10C22×C22⋊Dic11—21no—
11C22×C4⋊Dic11C2212yes—
12C22×C4⋊Dic11C2211yescharacteristic
13C2×#66977—22no—
14C2×#66977—24no—
15C2×#66977—24no—
16C2×#66977C414yescomplemented
17C22×Dic11⋊C4—21no—
18C2×C11×C22⋊C8—22no—
19C2×C11×C22⋊C8—24no—
20#10622825—24no—
21C2×C11⋊#95—21no—
22C2×#66880—24no—
23C2×#66880—24no—
24C2×#66880—24no—
25#10622189—24no—
26C25×C11D411yescharacteristic
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—22no—
30C23×C4×C11—22no—
31C23×C4×C11—22no—
32C23×C4×C11—22no—
33C23×C4×C11C2×C412yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D412yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11—21no—
39C23×Dic11—22no—
40C22×Dic22—22no—
41C22×Dic22—22no—
42C22×Dic22—22no—
43C22×Dic22—22no—
44C22×Dic22—22no—
45C22×Dic22—21no—
46C22×Dic22C2×C412yes—
47C22×Dic22D414yes—
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11—22no—
53C22×C8×C11—22no—
54C22×C8×C11D414yes—
55C2×C22⋊Dic11—28no—
56C2×C22⋊Dic11—24no—
57C2×C22⋊Dic11—24no—
58C2×C22⋊Dic11—42no—
59C2×C22⋊Dic11—42no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2×C412yes—
68C2×C4⋊Dic11D414yes—
69C2×C4⋊Dic11D414yes—
70#66977—216no—
71#66977—28no—
72#66977—28no—
73C2×Dic11⋊C4—28no—
74C2×Dic11⋊C4—24no—
75C11×C22⋊C8—28no—
76C11⋊#95—24no—
77#66880—216no—
78#10970—111nomaximal, Sylow
79C24×C11—22no—
80C24×C11—21no—
81C24×C11—22no—
82C24×C11—21no—
83C24×C11—22no—
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11C22⋊C412yes—
88C24×C11SD1612yes—
89C24×C11Q1612yes—
90C24×C11C2×D411yescharacteristic
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C22⋊C412yes—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—24no—
123C22×Dic11—24no—
124C22×Dic11—24no—
125C22×Dic11—41no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11—41no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C22×Dic11—41no—
134C22×Dic11—42no—
135C22×Dic11—41no—
136C22×Dic11—42no—
137C2×Dic22—22no—
138C2×Dic22—24no—
139C2×Dic22—24no—
140C2×Dic22—24no—
141C2×Dic22—24no—
142C2×Dic22—24no—
143C2×Dic22—24no—
144C2×Dic22—24no—
145C2×Dic22—41no—
146C2×Dic22—42no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×Dic22—41no—
150C2×Dic22—42no—
151C2×Dic22—42no—
152C2×Dic22C22⋊C414yescomplemented
153C2×C8×C11—24no—
154C2×C8×C11—24no—
155C2×C8×C11—24no—
156C2×C8×C11—42no—
157C2×C8×C11—42no—
158C2×C8×C11—42no—
159C2×C8×C11—42no—
160C22⋊Dic11—216no—
161C22⋊Dic11—48no—
162C4⋊Dic11—22no—
163C4⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—24no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C4⋊Dic11C22⋊C414yescomplemented
169Dic11⋊C4—216no—
170C22×C22⋊Q8—111no—
171C22×#103—112no—
172C22×C22⋊C8D1111yescharacteristic
173C2×#380—111no—
174C2×#340—112no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—24no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11#10314yescomplemented
198C23×C11C2×C22⋊C411yescharacteristic
199C23×C11#12012yes—
200C23×C11#12011yescharacteristic
201C23×C11#12112yes—
202C23×C11#12311yescharacteristic
203C23×C11C2×SD1611yescharacteristic
204C23×C11C2×Q1611yescharacteristic
205C23×C11#13512yes—
206C23×C11AGL(1,ℤ/8)11yescharacteristic
207C23×C11#13711yescharacteristic
208C23×C11#13712yes—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—44no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11—44no—
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C4×D412yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11#12112yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#12312yes—
231C2×C4×C11#12311yescharacteristic
232C2×C4×C11#12412yes—
233C2×C4×C11#12712yes—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—44no—
243C2×Dic11—44no—
244C2×Dic11—44no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—82no—
248C2×Dic11—82no—
249C2×Dic11—82no—
250C2×Dic11—82no—
251Dic22—28no—
252Dic22—44no—
253Dic22—44no—
254Dic22—44no—
255C8×C11—44no—
256C23×Q8—111no—
257C24×C4C2×D1111yescharacteristic
258C23×C8C2×D1112yes—
259C2×C22⋊Q8—114no—
260C2×C22⋊Q8—224no—
261C2×C22⋊Q8—224no—
262C2×C22⋊Q8—222no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—221no—
266C22×C22⋊C4—221no—
267C22×C22⋊C4—221no—
268C2×#103—224no—
269C2×#103—224no—
270C2×#103—224no—
271C2×C22⋊C8—22no—
272C2×C22⋊C8—24no—
273#380—224no—
274C2×#95—221no—
275#340—224no—
276C22×C11—24no—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—42no—
287C22×C11#37911yescharacteristic
288C22×C11#38611yescharacteristic
289C22×C11#38611yescharacteristic
290C22×C11#39212yes—
291C22×C11#39412yes—
292C22×C11C2×#10311yescharacteristic
293C22×C11#41611yescharacteristic
294C22×C11#41711yescharacteristic
295C22×C11#41911yescharacteristic
296C22×C11#44812yes—
297C22×C11#44912yes—
298C22×C11#45011yescharacteristic
299C22×C11#45111yescharacteristic
300C22×C11#45112yes—
301C22×C11#45212yes—
302C22×C11#45212yes—
303C22×C11#46512yes—
304C22×C11#46712yes—
305C22×C11#46812yes—
306C22×C11#47012yes—
307C22×C11#48311yescharacteristic
308C22×C11#48411yescharacteristic
309C22×C11#48512yes—
310C4×C11—42no—
311C4×C11#38612yes—
312C4×C11#39012yes—
313C4×C11#39212yes—
314C4×C11#39412yes—
315Dic11—44no—
316Dic11—44no—
317Dic11—84no—
318C25D4411yescharacteristic
319C22×Q8—112no—
320C22×Q8—114no—
321C22×Q8—222no—
322C22×Q8—221no—
323C22×Q8—222no—
324C22×Q8—222no—
325C22×Q8—222no—
326C22×Q8—222no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—221no—
334C23×C4—221no—
335C23×C4—222no—
336C23×C4C4×D1112yes—
337C23×C4D4411yescharacteristic
338C23×C4C22⋊D1112yes—
339C23×C4C22×D1111yescharacteristic
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8C22⋊D1114yes—
347C22⋊Q8—228no—
348C22⋊Q8—228no—
349C22⋊Q8—2216no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—114no—
352C2×C4⋊C4—114no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C22⋊C4—228no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367#103—2216no—
368C22⋊C8—28no—
369#95—224no—
370C2×C11—44no—
371C2×C11#143811yescharacteristic
372C2×C11#178711yescharacteristic
373C2×C11#178811yescharacteristic
374C2×C11#187211yescharacteristic
375C2×C11#187311yescharacteristic
376C2×C11#189211yescharacteristic
377C2×C11#189411yescharacteristic
378C2×C11#200012yes—
379C2×C11#200112yes—
380C2×C11#203512yes—
381C2×C11#203612yes—
382C24—22no—
383C24—21no—
384C24—21no—
385C24—22no—
386C24—21no—
387C24—22no—
388C24—21no—
389C24—22no—
390C24#431412yes—
391C24Dic4412yes—
392C24(C2×D11)⋊C412yes—
393C24C2×D4411yescharacteristic
394C2×Q8—114no—
395C2×Q8—222no—
396C2×Q8—224no—
397C2×Q8—224no—
398C2×Q8—224no—
399C2×Q8—224no—
400C2×Q8—224no—
401C2×Q8—224no—
402C2×Q8—224no—
403C2×Q8—442no—
404C2×Q8—442no—
405C2×Q8—441no—
406C2×Q8—442no—
407C2×Q8—442no—
408C2×Q8—442no—
409C2×Q8—441no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—224no—
435C22×C4—441no—
436C22×C4—441no—
437C22×C4—442no—
438C22×C4—441no—
439C22×C4—441no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4(C2×D11)⋊C412yes—
448C22×C4C2×C4×D1111yescharacteristic
449C22×C4#433912yes—
450C22×C4D4×D1112yes—
451C22×C4D4×D1112yes—
452C22×C4D4×D1112yes—
453C22×C4#434112yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1111yescharacteristic
456C2×C8—24no—
457C2×C8—24no—
458C2×C8—24no—
459C2×C8—42no—
460C2×C8—42no—
461C2×C8—42no—
462C2×C8—42no—
463C4⋊C4—114no—
464C4⋊C4—2216no—
465C4⋊C4—222no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C22⋊C4—2216no—
472C22⋊C4—448no—
473C11#1097011yescharacteristic, complemented, Sylow
474C23—22no—
475C23—24no—
476C23—24no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—22no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23#6688014yescomplemented
497C23#6693512yes—
498C23#6693511yescharacteristic
499C23#6693911yescharacteristic
500C23C2×#431411yescharacteristic
501C23#6695712yes—
502C23C2×Dic4411yescharacteristic
503C23#6696111yescharacteristic
504C23#6696212yes—
505C23#6696211yescharacteristic
506C23C2×(C2×D11)⋊C411yescharacteristic
507C23#6698312yes—
508Q8—228no—
509Q8—444no—
510Q8—444no—
511Q8—444no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—444no—
528C2×C4—444no—
529C2×C4—444no—
530C2×C4—444no—
531C2×C4—444no—
532C2×C4—444no—
533C2×C4—444no—
534C2×C4—882no—
535C2×C4—882no—
536C2×C4—882no—
537C2×C4—882no—
538C2×C4C22⋊C4×D1111yescharacteristic
539C2×C4C22⋊C4×D1111yescharacteristic
540C2×C4(C22⋊D11)⋊C412yes—
541C2×C4#6693612yes—
542C2×C4#6693712yes—
543C2×C4#6693712yes—
544C2×C4#6693812yes—
545C2×C4C4×C22⋊D1112yes—
546C2×C4#6698211yescharacteristic
547C2×C4#6699012yes—
548C2×C4#6699012yes—
549C2×C4#6699112yes—
550C2×C4#6699212yes—
551C2×C4#6699212yes—
552C2×C4#6699312yes—
553C2×C4#6700611yescharacteristic
554C8—44no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—42no—
559C22—44no—
560C22—44no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—42no—
565C22—44no—
566C22#1062233411yescharacteristic
567C22#1062233511yescharacteristic
568C22#1062233612yes—
569C22#1062234411yescharacteristic
570C22#1062234612yes—
571C22#1062234612yes—
572C22#1062234712yes—
573C22#1062235112yes—
574C22#1062235212yes—
575C22#1062235211yescharacteristic
576C22#1062256811yescharacteristic
577C22#1062257111yescharacteristic
578C22#1062257312yes—
579C22#1062257412yes—
580C22C2×#6688011yescharacteristic
581C22#1062272611yescharacteristic
582C22#1062272712yes—
583C22#1062272912yes—
584C22#1062273311yescharacteristic
585C22#1062274611yescharacteristic
586C22#1062274712yes—
587C22#1062275012yes—
588C22#1062282611yescharacteristic
589C4—42no—
590C4—444no—
591C4—444no—
592C4—884no—
593C4#1062256912yes—
594C4#1062257012yes—
595C4#1062257212yes—
596C4#1062283612yes—
597C2—44no—
598C2#1306685511yescharacteristic
599C2#1306855211yescharacteristic
600C2#1306855711yescharacteristic
601C2#1306892111yescharacteristic
602C2#1306892611yescharacteristic
603C2#1306903911yescharacteristic
604C2#1306904911yescharacteristic
605C2#1306962112yes—
606C2#1306962612yes—
607C2#1306981312yes—
608C2#1306982012yes—
subgroupG/H
centerC24C2×D44
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×C22⋊C8C2
socleC24×C11C2×D4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenterC22×C22⋊C8D11
hypocenterC11#10970
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#66880C2semidirect
4. C2×#10622189C2semidirect
16. C2×#66977C4semidirect
152. C2×Dic22C22⋊C4semidirect
168. C4⋊Dic11C22⋊C4semidirect
197. C23×C11#103semidirect
473. C11#10970semidirect
496. C23#66880semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C22×#668802
C2×#106228252
C2×#106221892
C22×C11×C22⋊C82
#1097011