Finite Group Databasebeta

← #14769433

Subgroups — #14769433

Order 2816.

1582 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623108C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×#10622416C212yesmaximal, complemented
4#13071516C211yesmaximal, characteristic, complemented
5#13069542C211yesmaximal, characteristic, complemented
6#13069421C211yesmaximal, characteristic, complemented
7#13069053C212yesmaximal, complemented
8#13068932C212yesmaximal, complemented
9#13068555C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4313C2212yes—
15#10623108—24no—
16#10623108C418yescomplemented
17C2×#66948—22no—
18C2×#66948C2212yes—
19C2×#66946—21no—
20C2×C4⋊C4×D11C2212yes—
21C2×#66927—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66885C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33#10622602—22no—
34#10622600C2212yes—
35#10622586—21no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622451—24no—
41#10622416—28no—
42C11×#340C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—24no—
49C2×#4343—42no—
50C2×#4343—42no—
51C2×#4343C2×C418yescomplemented
52C22×D44—22no—
53C22×D44—21no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44D411yescharacteristic
57C22×D44C2312yes—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11C2312yes—
61C22×C8×C11C2312yes—
62C4×Q8×C11—22no—
63C4×Q8×C11C2×C414yescomplemented
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4D412yes—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C2×#4313—24no—
82C2×#4313—24no—
83C2×#4313—42no—
84#66948—24no—
85#66948—216no—
86#66948C2×C418yescomplemented
87#66946—44no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—42no—
90#66927—28no—
91#66927—22no—
92#66927C2×C414yescomplemented
93C4×D44—28no—
94C4×D44C2×C414yes—
95C4×D44D414yes—
96C11×C4⋊C8—22no—
97C11×#103—24no—
98#66899—22no—
99#66899D414yescomplemented
100C11⋊#95—21no—
101C11⋊#95—22no—
102#66885—24no—
103#66885—42no—
104(C2×D11)⋊C8—24no—
105#66873—24no—
106#66873—42no—
107C4×C11⋊C8—22no—
108#22432—111nomaximal, Sylow
109C23×D11—22no—
110C23×D11C2×D412yes—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C22×C412yes—
115C2×Q8×C11C2×D412yes—
116C2×Q8×C11#4112yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11C2×D412yes—
126#4343—216no—
127#4343—48no—
128#4343—48no—
129#4343—48no—
130C2×D44—28no—
131C2×D44—28no—
132C2×D44—24no—
133C2×D44—24no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—44no—
142C2×D44—44no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44—81no—
146C2×D44—81no—
147C2×D44—82no—
148C2×D44—82no—
149C2×D44C22⋊C414yes—
150C2×D44C22×C414yes—
151C2×C4×D11—28no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×C4×D11—44no—
159C2×C4×D11—44no—
160C2×C4×D11—82no—
161C2×C4×D11C22×C414yes—
162C2×C4×D11C2×D414yes—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4C22×C412yes—
173C42×C11—24no—
174C42×C11C22×C412yes—
175C42×C11C2×D412yes—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—44no—
178(C2×D11)⋊C4C22⋊C418yes—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11C22⋊C414yes—
183C4⋊Dic11C2×D412yes—
184Dic11⋊C4—44no—
185C4×Dic11—42no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C2×D412yes—
192#4313—48no—
193C2×#550—111no—
194C2×#436—111no—
195C2×#417—112no—
196D4×C4⋊C4—111no—
197#1982—111no—
198#1957—111no—
199#1895—112no—
200#1874—112no—
201#1803D1111yescharacteristic, complemented
202#1788—112no—
203C4×#103—111no—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11C2×C22⋊C414yes—
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11C4×D414yescomplemented
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11C2×C22⋊C412yes—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11AGL(1,ℤ/8)12yes—
237C2×C4×C11#13712yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11C2×C22⋊C414yes—
253D44—24no—
254D44—24no—
255D44—28no—
256D44—416no—
257D44—42no—
258D44—42no—
259D44—48no—
260D44—84no—
261D44—88no—
262C4×D11—24no—
263C4×D11—24no—
264C4×D11—24no—
265C4×D11—24no—
266C4×D11—416no—
267C4×D11—88no—
268C8×C11—42no—
269C11⋊C8—22no—
270C11⋊C8—41no—
271C22×#41—112no—
272C22×M16—112no—
273#550—118no—
274#550—224no—
275C2×#127—111no—
276C2×#127—221no—
277C2×#121—112no—
278C2×#121—222no—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—111no—
281C2×C4×D4—221no—
282C2×C4×D4—221no—
283C22×C4⋊C4—112no—
284#436—224no—
285C2×C4⋊C8C2×D1111yescharacteristic
286#417—228no—
287C2×#103—111no—
288C2×#103—111no—
289C2×#103C2×D1112yes—
290C2×#102—112no—
291C2×#102—112no—
292C2×#102—112no—
293C2×#102—112no—
294C2×C22⋊C8—112no—
295C2×C4×C8—111no—
296#389—221no—
297#385—222no—
298#384C2×D1111yescharacteristic
299#380—112no—
300C4×C4⋊C4—111no—
301#340—111no—
302#340—111no—
303#340C2×D1112yes—
304C22×C11C22×C22⋊C411yescharacteristic
305C22×C11D4211yescharacteristic
306C22×C11#54611yescharacteristic
307C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C11C2×#13711yescharacteristic
309C22×C11#57611yescharacteristic
310C22×C11#57711yescharacteristic
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—24no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C4×C11—24no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—82no—
329C4×C11#41714yescomplemented
330C4×C11C2×C4×D411yescharacteristic
331C4×C11#51811yescharacteristic
332C4×C11D4211yescharacteristic
333C4×C11#54611yescharacteristic
334Dic11—24no—
335Dic11—42no—
336Dic11—81no—
337C2×#41—118no—
338C2×#41—224no—
339C2×#41—224no—
340C2×#41—224no—
341C2×#41—442no—
342C2×#41—442no—
343C22×Q8C22×D1111yescharacteristic
344C22×D4—111no—
345C22×D4—112no—
346C22×D4—222no—
347C22×D4—222no—
348C22×D4—221no—
349C22×D4—221no—
350C23×C4—112no—
351C23×C4—222no—
352C23×C4—222no—
353C2×M16—224no—
354C2×M16—224no—
355C2×M16—442no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1112yes—
359#127—114no—
360#127—228no—
361#127—222no—
362#121—118no—
363#121—2216no—
364#121—224no—
365C4×Q8—22no—
366C4×Q8C4×D1114yescomplemented
367C4×D4—114no—
368C4×D4—114no—
369C4×D4—228no—
370C4×D4—444no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—442no—
380C2×C4⋊C4C22×D1112yes—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—112no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388C4⋊C8—22no—
389#103—24no—
390#103—114no—
391#103—222no—
392#102—224no—
393#102—224no—
394#102—442no—
395#102—442no—
396C22⋊C8—224no—
397C4×C8—222no—
398#95—222no—
399#95—221no—
400C2×C11D4×C22⋊C411yescharacteristic
401C2×C11C2×#41711yescharacteristic
402C2×C11#289711yescharacteristic
403C2×C11#327411yescharacteristic
404C2×C11#327811yescharacteristic
405C2×C11#333211yescharacteristic
406C2×C11#333311yescharacteristic
407D11—44no—
408D11—84no—
409C24—112no—
410C24—222no—
411#41—2216no—
412#41—448no—
413#41—448no—
414#41—448no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8C2×C4×D1112yes—
419C2×Q8D4×D1112yes—
420C2×Q8#434312yes—
421C2×D4—114no—
422C2×D4—114no—
423C2×D4—228no—
424C2×D4—228no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—444no—
435C2×D4—444no—
436C2×D4—442no—
437C2×D4—442no—
438C2×D4—881no—
439C2×D4—881no—
440C2×D4—882no—
441C2×D4—882no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—112no—
446C22×C4—114no—
447C22×C4—114no—
448C22×C4—228no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—444no—
456C22×C4—444no—
457C22×C4—444no—
458C22×C4—444no—
459C22×C4—882no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463M16—448no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—114no—
480C4⋊C4—112no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—444no—
485C4⋊C4C2×C4×D1112yes—
486C22⋊C4—118no—
487C22⋊C4—228no—
488C22⋊C4—444no—
489C42—24no—
490C42—442no—
491C42C2×C4×D1112yes—
492C42D4×D1112yes—
493C11#2243211yescharacteristic, complemented, Sylow
494C23—114no—
495C23—222no—
496C23—222no—
497C23—222no—
498C23—222no—
499C23—222no—
500C23—222no—
501C23—224no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23C2×D4×D1111yescharacteristic
509Q8—22no—
510Q8—22no—
511Q8—22no—
512Q8#6694614yescomplemented
513D4—224no—
514D4—224no—
515D4—228no—
516D4—4416no—
517D4—442no—
518D4—442no—
519D4—448no—
520D4—884no—
521D4—888no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—114no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—4416no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—888no—
548C2×C4C22⋊C4×D1112yes—
549C2×C4C22⋊C4×D1112yes—
550C2×C4#6696712yes—
551C2×C4#6697112yes—
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×#434311yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704211yescharacteristic
558C8—42no—
559C8—222no—
560C8—441no—
561C22—224no—
562C22—224no—
563C22—224no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22—442no—
568C22—444no—
569C22—444no—
570C22—444no—
571C22—882no—
572C22—882no—
573C22—882no—
574C22—882no—
575C22C2×C22⋊C4×D1111yescharacteristic
576C22#1062314011yescharacteristic
577C22#1062316111yescharacteristic
578C22C2×#6696711yescharacteristic
579C22C2×#6697111yescharacteristic
580C22#1062330511yescharacteristic
581C22#1062330911yescharacteristic
582C4—24no—
583C4—22no—
584C4—42no—
585C4—82no—
586C4—224no—
587C4—442no—
588C4—881no—
589C4#1062241614yescomplemented
590C4C2×#6694611yescharacteristic
591C4#1062305211yescharacteristic
592C4#1062314011yescharacteristic
593C4#1062316111yescharacteristic
594C2—444no—
595C2—884no—
596C2#1307143611yescharacteristic
597C2C2×#1062241611yescharacteristic
598C2#1307714011yescharacteristic
599C2#1308023111yescharacteristic
600C2#1308027711yescharacteristic
601C2#1308094011yescharacteristic
602C2#1308095111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22432
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×#10622416C2semidirect
4. #13071516C2semidirect
5. #13069542C2semidirect
6. #13069421C2semidirect
7. #13069053C2semidirect
8. #13068932C2semidirect
9. #13068555C2semidirect
10. C4×#66899C2semidirect
11. C11×#1803C2semidirect
16. #10623108C4semidirect
51. C2×#4343C2×C4semidirect
63. C4×Q8×C11C2×C4semidirect
86. #66948C2×C4semidirect
92. #66927C2×C4semidirect
99. #66899D4semidirect
201. #1803D11semidirect
222. Q8×C11C4×D4semidirect
329. C4×C11#417semidirect
366. C4×Q8C4×D11semidirect
493. C11#22432semidirect
512. Q8#66946semidirect
589. C4#10622416semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106224512
C2×#106224162
#130715162
#130695422
#130694212
#130690532
#130689322
#130685552
C4×#668992
C11×#18032
#2243211