Finite Group Databasebeta

← #14755295

Subgroups — #14755295

Order 2816.

1702 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×#67004C211yesmaximal, characteristic
2#13081819C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4#13071200C211yesmaximal, characteristic, complemented
5#13068983C218yesmaximal, complemented
6#13068354C211yesmaximal, characteristic, complemented
7#13068326C211yesmaximal, characteristic, complemented
8C2×C11×#421C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13#10623358—22no—
14#10623358C2214yes—
15#41×Dic11—22no—
16#41×Dic11—22no—
17C2×#67004—22no—
18C2×#67004—24no—
19C2×#67004C418yescomplemented
20C2×#67004C2214yes—
21#10623343—21no—
22C22×#4326—21no—
23#10623329—21no—
24#10623329—22no—
25C22×#4324—21no—
26C2×#66979—22no—
27C2×#66979C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C22×#4318C2211yescharacteristic
30C11×#421—24no—
31C2×C11×#104C2214yes—
32#10622733—22no—
33#10622733C2214yescomplemented
34C2×#66880—22no—
35#10622587—22no—
36#10622556—22no—
37#10622542C2214yescomplemented
38#10622192C2214yescomplemented
39#10622161C2214yescomplemented
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D412yes—
46C2×C11×#41D414yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C22×Dic22—21no—
55C22×Dic22—21no—
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×Dic22—21no—
61C22×Dic22—22no—
62C22×Dic22C2×C414yescomplemented
63C22×Dic22C2312yes—
64C2×C11×M16—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16C2312yes—
68C22×C8×C11—21no—
69C11×#117—22no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2312yes—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11D412yes—
77#67004—216no—
78#67004—28no—
79#67004C2×C4116yescomplemented
80Q8×Dic11—24no—
81Q8×Dic11—24no—
82C2×#4326—28no—
83C2×#4326—24no—
84D4×Dic11—28no—
85D4×Dic11—24no—
86D4×Dic11—24no—
87D4×Dic11—28no—
88C2×#4324—28no—
89C2×#4324—24no—
90#66979—24no—
91#66979—24no—
92#66979—21no—
93#66979—21no—
94#66979—21no—
95#66979—21no—
96#66979—21no—
97#66979—21no—
98#66979—24no—
99#66979D412yes—
100#66979C2312yes—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11D412yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4×Dic11—24no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11D412yes—
107C2×#4318—21no—
108C2×#4318—22no—
109C2×#4318C2×C414yescomplemented
110C2×#4318C2312yes—
111C22×C11⋊C8—21no—
112C11×#104—28no—
113C11⋊#95—28no—
114#66880—28no—
115#20944—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11C2×D411yescharacteristic
118C11×#41—24no—
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—24no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41C22⋊C418yes—
126C11×#41C22×C414yes—
127C11×#41C2×D414yes—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11C22⋊C414yes—
131C2×Q8×C11C2×D412yes—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11C22⋊C414yes—
139C2×D4×C11C2×D412yes—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—28no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—41no—
161C22×Dic11—41no—
162C22×Dic11—42no—
163C22×Dic11C2×D414yes—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—22no—
174C2×Dic22—41no—
175C2×Dic22—41no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22—42no—
181C2×Dic22C22×C414yes—
182C11×M16—22no—
183C11×M16—22no—
184C11×M16—42no—
185C2×C8×C11—22no—
186C2×C8×C11—42no—
187C11×C4⋊C4—42no—
188C11×C22⋊C4—42no—
189C42×C11—22no—
190C42×C11—22no—
191C22⋊Dic11—28no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196#4326—216no—
197#4324—216no—
198C4⋊Dic11—28no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11C2×D414yes—
203C4×Dic11—28no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208#4318—24no—
209#4318—22no—
210#4318C22×C414yes—
211C2×C11⋊C8—24no—
212C2×C11⋊C8—22no—
213C22×#137—111no—
214#3428—111no—
215C2×#421D1111yescharacteristic
216C2×#419—111no—
217#2310—111no—
218#1882—118no—
219#1742—111no—
220#1733—111no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—42no—
224C23×C11—82no—
225C23×C11C4×D412yes—
226C23×C11#12011yescharacteristic
227C23×C11#12011yescharacteristic
228C23×C11#12112yes—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—24no—
232Q8×C11C2×C22⋊C414yes—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—28no—
236D4×C11—22no—
237D4×C11—24no—
238D4×C11C2×C22⋊C414yes—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C4×D412yes—
249C2×C4×C11C4×D412yes—
250C2×C4×C11C4×D412yes—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12112yes—
254C2×C4×C11#12112yes—
255C2×C4×C11#12112yes—
256C2×C4×C11#12312yes—
257C2×C4×C11#12312yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—82no—
273C2×Dic11—88no—
274Dic22—24no—
275Dic22—24no—
276Dic22—42no—
277Dic22—42no—
278Dic22—44no—
279Dic22—44no—
280C8×C11—42no—
281C11⋊C8—24no—
282C22×#41C2×D1111yescharacteristic
283C23×Q8—111no—
284C2×#137—114no—
285C2×#137—118no—
286C2×#137—222no—
287C2×#137—224no—
288C22×Q16—221no—
289C22×SD16—221no—
290C22×M16—111no—
291C22×M16C2×D1111yescharacteristic
292#520—114no—
293#520—222no—
294#519—221no—
295#518—222no—
296#518—221no—
297C4×#41—222no—
298C4×#41—222no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—222no—
302C2×#117C2×D1111yescharacteristic
303#421—24no—
304C2×#104C2×D1114yes—
305#419—114no—
306#419—222no—
307C2×#103—222no—
308#391—114no—
309#391—222no—
310#381—222no—
311#343—114no—
312#339—114no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—24no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—84no—
321C22×C11#38612yes—
322C22×C11#38612yes—
323C22×C11C2×C4×D411yescharacteristic
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12111yescharacteristic
326C4×C11—24no—
327C4×C11—82no—
328C4×C11#38612yes—
329C4×C11#38612yes—
330C4×C11C22×C22⋊C411yescharacteristic
331C4×C11C2×C4×D411yescharacteristic
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×#12311yescharacteristic
334Dic11—44no—
335Dic11—44no—
336Dic11—44no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41C4×D1114yes—
342C2×#41D4412yes—
343C2×#41C22⋊D1114yes—
344C2×#41C22×D1112yes—
345C22×Q8—114no—
346C22×Q8—112no—
347C22×Q8—221no—
348C22×Q8—222no—
349C22×Q8—221no—
350C22×Q8—221no—
351C22×Q8—221no—
352C22×Q8—221no—
353C22×Q8—222no—
354C22×Q8—222no—
355C22×Q8D4411yescharacteristic
356C22×D4—21no—
357C22×D4D4411yescharacteristic
358C23×C4—21no—
359C23×C4—221no—
360C23×C4C22×D1111yescharacteristic
361#137—1116no—
362#137—2216no—
363#137—228no—
364C2×Q16—228no—
365C2×Q16—224no—
366C2×SD16—228no—
367C2×SD16—224no—
368C2×M16—21no—
369C2×M16—22no—
370C2×M16—22no—
371C2×M16—114no—
372C2×M16—112no—
373C2×M16—221no—
374C2×M16—222no—
375C2×M16C22×D1112yes—
376C22×C8—21no—
377C22×C8—221no—
378C4×Q8—224no—
379C4×Q8—224no—
380C4×D4—228no—
381C4×D4—228no—
382C4×D4—224no—
383C4×D4—224no—
384#117—22no—
385#117—22no—
386#117—112no—
387#117—112no—
388#117—224no—
389#117—224no—
390#117—224no—
391#117—221no—
392#117—221no—
393#117—221no—
394#117—221no—
395#117—221no—
396#117—221no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—224no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—112no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—221no—
405C2×C42—112no—
406C2×C42—224no—
407C2×C42—221no—
408C2×C42C22×D1112yes—
409#104—28no—
410#103—228no—
411#95—228no—
412C2×C11—21no—
413C2×C11—22no—
414C2×C11—21no—
415C2×C11—22no—
416C2×C11—44no—
417C2×C11C2×#38611yescharacteristic
418C2×C11#302212yes—
419C24—21no—
420C24D4×D1111yescharacteristic
421#41—24no—
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—22no—
427#41—22no—
428#41(C2×D11)⋊C418yes—
429#41C2×C4×D1114yes—
430#41C2×C22⋊D1114yes—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—114no—
434C2×Q8—224no—
435C2×Q8—222no—
436C2×Q8—224no—
437C2×Q8—224no—
438C2×Q8—224no—
439C2×Q8—224no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8—222no—
443C2×Q8—222no—
444C2×Q8—441no—
445C2×Q8—441no—
446C2×Q8—442no—
447C2×Q8—442no—
448C2×Q8—442no—
449C2×Q8—442no—
450C2×Q8—442no—
451C2×Q8(C2×D11)⋊C414yes—
452C2×Q8C2×D4412yes—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—24no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4(C2×D11)⋊C414yes—
460C2×D4C2×D4412yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—114no—
468C22×C4—224no—
469C22×C4—222no—
470C22×C4—228no—
471C22×C4—222no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—442no—
475C22×C4C2×C4×D1112yes—
476C22×C4C2×D4411yescharacteristic
477C22×C4C2×D4411yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4#434112yes—
482C22×C4#434112yes—
483C22×C4C2×C22⋊D1112yes—
484C22×C4C23×D1111yescharacteristic
485Q16—2216no—
486SD16—2216no—
487M16—22no—
488M16—22no—
489M16—42no—
490M16—114no—
491M16—224no—
492M16—222no—
493C2×C8—22no—
494C2×C8—42no—
495C2×C8—224no—
496C2×C8—222no—
497C4⋊C4—42no—
498C4⋊C4—114no—
499C4⋊C4—228no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C22⋊C4—42no—
504C22⋊C4—228no—
505C22⋊C4—222no—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C42—22no—
510C42—22no—
511C42—228no—
512C42—222no—
513C42—222no—
514C42—222no—
515C42—222no—
516C11#2094411yescharacteristic, complemented, Sylow
517C23—22no—
518C23—24no—
519C23—42no—
520C23—82no—
521C23(C22⋊D11)⋊C412yes—
522C23#6693511yescharacteristic
523C23#6693511yescharacteristic
524C23#6699212yes—
525C23C2×D4×D1111yescharacteristic
526Q8—22no—
527Q8—24no—
528Q8—224no—
529Q8—224no—
530Q8—442no—
531Q8—442no—
532Q8—444no—
533Q8—444no—
534Q8C2×(C2×D11)⋊C414yes—
535D4—24no—
536D4—24no—
537D4—28no—
538D4—22no—
539D4—24no—
540D4C2×(C2×D11)⋊C414yes—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—28no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—444no—
556C2×C4—882no—
557C2×C4—888no—
558C2×C4(C22⋊D11)⋊C412yes—
559C2×C4(C22⋊D11)⋊C412yes—
560C2×C4(C22⋊D11)⋊C412yes—
561C2×C4#6693511yescharacteristic
562C2×C4#6693511yescharacteristic
563C2×C4#6693912yes—
564C2×C4#6693912yes—
565C2×C4C2×(C2×D11)⋊C412yes—
566C2×C4C2×(C2×D11)⋊C412yes—
567C2×C4#6699212yes—
568C2×C4#6699212yes—
569C2×C4#6699212yes—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C22×D4411yescharacteristic
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C8—42no—
577C8—224no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—24no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—84no—
586C22#1062257112yes—
587C22#1062257112yes—
588C22C2×(C22⋊D11)⋊C411yescharacteristic
589C22C2×#6693511yescharacteristic
590C22C2×#6699211yescharacteristic
591C4—24no—
592C4—82no—
593C4—444no—
594C4—444no—
595C4—444no—
596C4#1062257112yes—
597C4#1062257112yes—
598C4C2×(C22⋊D11)⋊C411yescharacteristic
599C4C2×#6693911yescharacteristic
600C4C22×(C2×D11)⋊C411yescharacteristic
601C4C2×#6699211yescharacteristic
602C2—21no—
603C2—22no—
604C2—21no—
605C2—22no—
606C2—44no—
607C2C2×#1062257111yescharacteristic
608C2#1307799612yes—
subgroupG/H
centerC22C2×#66935
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#421C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#421D11
hypocenterC11#20944
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
4. #13071200C2semidirect
5. #13068983C2semidirect
6. #13068354C2semidirect
7. #13068326C2semidirect
19. C2×#67004C4semidirect
33. #10622733C22semidirect
37. #10622542C22semidirect
38. #10622192C22semidirect
39. #10622161C22semidirect
62. C22×Dic22C2×C4semidirect
79. #67004C2×C4semidirect
109. C2×#4318C2×C4semidirect
516. C11#20944semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
#130818192
C2×#106227332
#130712002
#130689832
#130683542
#130683262
C2×C11×#4212
#2094411