Finite Group Databasebeta

← #14755362

Subgroups — #14755362

Order 2816.

1694 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623356C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic
4C22×#66888C211yesmaximal, characteristic, complemented
5#13069016C214yesmaximal, complemented
6#13069006C214yesmaximal, complemented
7#13068327C211yesmaximal, characteristic, complemented
8#13068325C211yesmaximal, characteristic, complemented
9C11×#2896C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623356—24no—
15#10623356C418yescomplemented
16C2×#66997C2212yes—
17C2×#66989C2212yes—
18C2×#66988—22no—
19C2×#66979C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977—22no—
22C22×#4318C2211yescharacteristic
23#10623047—22no—
24#10623047—22no—
25#10623047—22no—
26#10623047C2214yes—
27C2×#66940—22no—
28C2×#66930—22no—
29C2×C4×Dic22—22no—
30C11×#419C2212yes—
31C11×#418C2212yes—
32C11×#417—22no—
33C11×#416—22no—
34#10622846—22no—
35#10622845—22no—
36#10622838C2212yes—
37#10622828C2212yes—
38C2×#66888—24no—
39C2×#66888C2214yes—
40#10622193C2214yes—
41#10622170C2214yes—
42C2×C11×#41—22no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41C2×C414yes—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11D412yes—
56C22×Dic22—21no—
57C22×Dic22—21no—
58C22×Dic22—21no—
59C22×Dic22—21no—
60C22×Dic22—22no—
61C22×Dic22—22no—
62C22×Dic22C2×C414yes—
63C22×Dic22D412yes—
64C22×Dic22D414yes—
65C22×Dic22C2312yes—
66C2×C11×M16—21no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16C2312yes—
70C22×C8×C11—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117D412yes—
74C11×#117C2312yes—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—24no—
81#66997—24no—
82#66997C2×C418yescomplemented
83#66989—24no—
84#66989C2×C418yescomplemented
85#66988—216no—
86#66979—21no—
87#66979—21no—
88#66979—22no—
89#66979C2×C414yes—
90#66979D412yes—
91#66979C2312yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11D412yes—
94#66977—216no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2312yes—
100C2×#4318—21no—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318C2312yes—
104C22×C11⋊C8—21no—
105#66940—28no—
106#66940—28no—
107#66930—28no—
108#66930—28no—
109C4×Dic22—28no—
110C4×Dic22—28no—
111C11×#103—24no—
112C11×#102—24no—
113#66899—24no—
114#66896—24no—
115#66888—28no—
116#20954—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C11×#41—24no—
120C11×#41—24no—
121C11×#41—24no—
122C11×#41—24no—
123C11×#41—42no—
124C11×#41—42no—
125C11×#41—42no—
126C11×#41—42no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—42no—
142C2×D4×C11C22×C412yes—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—42no—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—22no—
164C22×Dic11C22⋊C418yes—
165C22×Dic11C2×D414yes—
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—24no—
173C2×Dic22—24no—
174C2×Dic22—24no—
175C2×Dic22—24no—
176C2×Dic22—24no—
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—22no—
180C2×Dic22—22no—
181C2×Dic22C22⋊C418yes—
182C2×Dic22C22×C414yes—
183C2×Dic22C2×D414yes—
184C11×M16—22no—
185C11×M16—22no—
186C11×M16—42no—
187C2×C8×C11—22no—
188C2×C8×C11—42no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4C2×D414yes—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C42×C11—22no—
194C42×C11—22no—
195C22⋊Dic11—216no—
196C22⋊Dic11—24no—
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C4⋊Dic11—24no—
200C4⋊Dic11—22no—
201C4⋊Dic11C2×D414yes—
202Dic11⋊C4—216no—
203Dic11⋊C4—216no—
204C4×Dic11—216no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11C22×C414yes—
209#4318—22no—
210#4318—22no—
211#4318—42no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—42no—
214C2×#536—111no—
215C2×#519—111no—
216#2896—111no—
217#2896D1111yescharacteristic
218C22×#101—111no—
219#1888—114no—
220#1886—114no—
221#1733—111no—
222#1733—111no—
223C23×C11—22no—
224C23×C11—42no—
225C23×C11—44no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11C2×C22⋊C412yes—
229C23×C11#12011yescharacteristic
230C23×C11#12011yescharacteristic
231C23×C11#12312yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—44no—
240D4×C11—44no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—44no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C4×D412yes—
253C2×C4×C11C4×D412yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12112yes—
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12312yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276C2×Dic11C2×C22⋊C418yes—
277Dic22—24no—
278Dic22—24no—
279Dic22—24no—
280Dic22—24no—
281Dic22—28no—
282Dic22—28no—
283C8×C11—42no—
284C11⋊C8—42no—
285C22×#41C2×D1111yescharacteristic
286C23×Q8—111no—
287C22×M16—111no—
288C22×M16C2×D1111yescharacteristic
289#536—118no—
290#536—224no—
291C2×C4⋊Q8—112no—
292C2×#124—112no—
293C2×#123—222no—
294C2×C22⋊Q8—222no—
295#519—114no—
296#519—222no—
297#519—222no—
298#519—222no—
299C2×C4×Q8—222no—
300C2×C4×Q8—222no—
301C2×#117—111no—
302C2×#117—111no—
303C2×#117—222no—
304C2×#117C2×D1111yescharacteristic
305#419—112no—
306#419C2×D1112yes—
307#418—112no—
308#418C2×D1112yes—
309#417—22no—
310#417—222no—
311#416—22no—
312#416—222no—
313C2×#101—114no—
314C2×#101—224no—
315#339—114no—
316#339—114no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11#38612yes—
327C22×C11#38612yes—
328C22×C11C22×C22⋊C411yescharacteristic
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×#12311yescharacteristic
331C4×C11—44no—
332C4×C11—42no—
333C4×C11#38612yes—
334C4×C11#38612yes—
335C4×C11C2×C4×D411yescharacteristic
336C4×C11C2×C4×D411yescharacteristic
337C4×C11C2×#12111yescharacteristic
338C4×C11C2×#12111yescharacteristic
339Dic11—28no—
340Dic11—44no—
341Dic11—44no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—22no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41C4×D1114yes—
350C22×Q8—114no—
351C22×Q8—112no—
352C22×Q8—114no—
353C22×Q8—112no—
354C22×Q8—222no—
355C22×Q8—221no—
356C22×Q8—221no—
357C22×Q8—222no—
358C22×Q8—221no—
359C22×Q8—221no—
360C22×Q8C22×D1111yescharacteristic
361C22×D4—21no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—112no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—21no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—112no—
370C2×M16—221no—
371C2×M16—222no—
372C2×M16—222no—
373C2×M16C22×D1112yes—
374C22×C8—21no—
375C22×C8—221no—
376C4⋊Q8—118no—
377C4⋊Q8—224no—
378#124—118no—
379#124—224no—
380#123—2216no—
381C22⋊Q8—2216no—
382C4×Q8—228no—
383C4×Q8—228no—
384C4×Q8—228no—
385C4×Q8—228no—
386#117—21no—
387#117—21no—
388#117—114no—
389#117—112no—
390#117—112no—
391#117—228no—
392#117—228no—
393#117—221no—
394#117—222no—
395#117—221no—
396#117C22⋊D1112yes—
397#117C22×D1112yes—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—224no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1112yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C42—21no—
408C2×C42—112no—
409C2×C42—224no—
410C2×C42—221no—
411#103—24no—
412#103—224no—
413#102—24no—
414#102—224no—
415#101—228no—
416C2×C11—21no—
417C2×C11—21no—
418C2×C11—22no—
419C2×C11—22no—
420C2×C11—82no—
421C2×C11C2×#38611yescharacteristic
422C2×C11#302012yes—
423C24—21no—
424C24D4×D1111yescharacteristic
425#41—24no—
426#41—24no—
427#41—24no—
428#41—24no—
429#41—42no—
430#41—42no—
431#41—42no—
432#41—42no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—118no—
439C2×Q8—114no—
440C2×Q8—114no—
441C2×Q8—224no—
442C2×Q8—224no—
443C2×Q8—224no—
444C2×Q8—224no—
445C2×Q8—224no—
446C2×Q8—224no—
447C2×Q8—224no—
448C2×Q8—222no—
449C2×Q8—222no—
450C2×Q8—224no—
451C2×Q8—224no—
452C2×Q8—222no—
453C2×Q8—222no—
454C2×Q8—222no—
455C2×Q8—222no—
456C2×Q8C2×C4×D1112yes—
457C2×D4—24no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—42no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×C4×D1112yes—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—118no—
474C22×C4—114no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4C2×C4×D1112yes—
481C22×C4#433912yes—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1112yes—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4#434112yes—
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C23×D1111yescharacteristic
490M16—22no—
491M16—22no—
492M16—42no—
493M16—222no—
494M16—222no—
495M16—442no—
496C2×C8—22no—
497C2×C8—42no—
498C2×C8—222no—
499C2×C8—442no—
500C4⋊C4—22no—
501C4⋊C4—114no—
502C4⋊C4—2216no—
503C4⋊C4—2216no—
504C4⋊C4—224no—
505C4⋊C4—222no—
506C4⋊C4C2×C22⋊D1114yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—2216no—
510C22⋊C4—224no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C42—22no—
514C42—22no—
515C42—114no—
516C42—2216no—
517C42—222no—
518C42—222no—
519C42—222no—
520C11#2095411yescharacteristic, complemented, Sylow
521C23—22no—
522C23—42no—
523C23—44no—
524C23—41no—
525C23—41no—
526C23C22⋊C4×D1112yes—
527C23#6693612yes—
528C23#6699011yescharacteristic
529C23#6699011yescharacteristic
530C23C2×D4×D1111yescharacteristic
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—224no—
536Q8—224no—
537Q8—224no—
538Q8—224no—
539Q8—228no—
540Q8—228no—
541D4—22no—
542D4—22no—
543D4—44no—
544D4—44no—
545D4—41no—
546D4—41no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—118no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—228no—
558C2×C4—228no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4C22⋊C4×D1112yes—
564C2×C4(C22⋊D11)⋊C412yes—
565C2×C4(C22⋊D11)⋊C412yes—
566C2×C4#6693612yes—
567C2×C4#6693712yes—
568C2×C4#6693712yes—
569C2×C4C4×C22⋊D1112yes—
570C2×C4C4×C22⋊D1112yes—
571C2×C4#6699011yescharacteristic
572C2×C4#6699011yescharacteristic
573C2×C4#6699112yes—
574C2×C4#6699112yes—
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×#433911yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×#434111yescharacteristic
580C2×C4C22×C22⋊D1111yescharacteristic
581C8—42no—
582C8—442no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—42no—
587C22—42no—
588C22—44no—
589C22—42no—
590C22—82no—
591C22—82no—
592C22#1062256912yes—
593C22#1062256912yes—
594C22C2×C22⋊C4×D1111yescharacteristic
595C22C2×#6693611yescharacteristic
596C22C2×#6699011yescharacteristic
597C4—42no—
598C4—44no—
599C4—228no—
600C4—444no—
601C4—444no—
602C4#1062256912yes—
603C4#1062256912yes—
604C4C2×(C22⋊D11)⋊C411yescharacteristic
605C4C2×#6693711yescharacteristic
606C4C2×C4×C22⋊D1111yescharacteristic
607C4C2×#6699111yescharacteristic
608C2—21no—
609C2—21no—
610C2—22no—
611C2—22no—
612C2—82no—
613C2C2×#1062256911yescharacteristic
614C2#1307797812yes—
subgroupG/H
centerC22C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2896C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2896D11
hypocenterC11#20954
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
4. C22×#66888C2semidirect
5. #13069016C2semidirect
6. #13069006C2semidirect
7. #13068327C2semidirect
8. #13068325C2semidirect
15. #10623356C4semidirect
82. #66997C2×C4semidirect
84. #66989C2×C4semidirect
520. C11#20954semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106230472
#130771352
C22×#668882
#130690162
#130690062
#130683272
#130683252
C11×#28962
#2095411