Finite Group Databasebeta

← #14726682

Subgroups — #14726682

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622649C212yesmaximal, complemented
2#13071972C211yesmaximal, characteristic, complemented
3#13067551C214yesmaximal, complemented
4#13067534C214yesmaximal, complemented
5#13067184C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic, complemented
8C2×C11×H(5,𝔽2)—21no—
9C23×D44C2211yescharacteristic, complemented
10C11×#547—22no—
11C11×#546—24no—
12D42×C11—22no—
13C11×#537C2212yescomplemented
14C11×#534—21no—
15C11×#534C2212yescomplemented
16C11×#532—21no—
17C2×C11×#121—21no—
18C2×C11×#121C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66990—21no—
21C22×#4323—22no—
22C2×#66983—21no—
23#10622825C2211yescharacteristic, complemented
24C2×C22⋊(C11⋊C8)C2212yescomplemented
25#10622649—24no—
26#10622649C2218yescomplemented
27#10622604C2212yescomplemented
28C2×#66873—22no—
29#10622573C2212yescomplemented
30#10622568—21no—
31#10622552—21no—
32#10622175C2218yescomplemented
33#10622166C2212yescomplemented
34#10622163C2212yescomplemented
35C24×D11—21no—
36C11×H(5,𝔽2)—44no—
37C11×H(5,𝔽2)—44no—
38C2×C11×#41—24no—
39C2×C11×#41—22no—
40C22×D4×C11—24no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11D411yescharacteristic
45C22×D4×C11D412yescomplemented
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—22no—
49C22×D44—22no—
50C22×D44—21no—
51C22×D44—22no—
52C22×D44—44no—
53C22×D44C2312yes—
54C11×C4⋊Q8—21no—
55C11×#127—21no—
56C11×#124—22no—
57C11×#123—24no—
58C11×#123—24no—
59C11×C22⋊Q8—24no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121—24no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121D414yescomplemented
68C11×#121C2314yes—
69C11×#120—24no—
70C11×#120—24no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D412yescomplemented
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4C2311yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C22⋊Dic11—21no—
84#66990—44no—
85C2×#4323—28no—
86C2×#4323—48no—
87#66983—44no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—21no—
92C22×C11⋊C8—22no—
93C11⋊#95C2312yes—
94C22⋊(C11⋊C8)—22no—
95C22⋊(C11⋊C8)C2314yes—
96#66873—28no—
97#18194—111nomaximal, Sylow
98C24×C11—22no—
99C24×C11—22no—
100C24×C11C2×D411yescharacteristic
101C24×C11C2×D411yescharacteristic
102C23×D11—22no—
103C23×D11—44no—
104C23×D11—42no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—82no—
108C11×#41—44no—
109C11×#41—416no—
110C11×#41—44no—
111C2×Q8×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—24no—
115C2×D4×C11—22no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—44no—
122C2×D4×C11—416no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—82no—
128C2×D4×C11D814yescomplemented
129C2×D4×C11C2×D414yes—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—44no—
145C2×C22⋊D11—44no—
146C2×C22⋊D11—82no—
147C22×Dic11—22no—
148C2×D44—24no—
149C2×D44—28no—
150C2×D44—24no—
151C2×D44—44no—
152C2×D44—42no—
153C2×D44—44no—
154C2×D44—48no—
155C2×D44—41no—
156C2×D44—41no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C2×D414yes—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—22no—
168C42×C11—21no—
169C42×C11—21no—
170C22⋊Dic11—42no—
171#4323—416no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—82no—
175C4⋊Dic11—42no—
176C2×C11⋊C8—24no—
177C2×C11⋊C8—44no—
178#3496D1111yescharacteristic, complemented
179C2×#447—112no—
180#2408—111no—
181#1598—114no—
182#1595—114no—
183#1519—112no—
184#1459—111no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—24no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—82no—
195C23×C11—82no—
196C23×C11—82no—
197C23×C11—82no—
198C23×C11#12012yes—
199C23×C11C2×D812yes—
200C23×C11C2×D812yescomplemented
201C23×C11AGL(1,ℤ/8)12yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—24no—
204C22×D11—42no—
205C22×D11—48no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—88no—
212C22×D11—88no—
213C22×D11—84no—
214C22×D11—84no—
215Q8×C11—44no—
216D4×C11—28no—
217D4×C11—44no—
218D4×C11—44no—
219D4×C11—48no—
220D4×C11—44no—
221D4×C11—44no—
222D4×C11—48no—
223D4×C11—44no—
224D4×C11—82no—
225D4×C11—82no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—24no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—48no—
236C2×C4×C11—44no—
237C2×C4×C11—44no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—81no—
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
244C2×C4×C11C2×D812yescomplemented
245C2×C4×C11C22×D412yes—
246C22⋊D11—88no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—28no—
251D44—44no—
252D44—44no—
253D44—44no—
254C11⋊C8—44no—
255C2×H(5,𝔽2)—21no—
256C23×D4—111no—
257C22×D8—222no—
258#547—22no—
259#546—24no—
260D42—22no—
261#537C2×D1112yescomplemented
262#534—21no—
263#534C2×D1112yescomplemented
264#532—21no—
265C2×#121—21no—
266C2×#121—221no—
267C2×#121C2×D1112yes—
268C2×#120—221no—
269C2×C4×D4C2×D1111yescharacteristic
270#447—118no—
271#447—224no—
272C2×#102—222no—
273C2×C22⋊C8—112no—
274#394—112no—
275#392—112no—
276#390—221no—
277#380—111no—
278#379—221no—
279#327—118no—
280#324—112no—
281#323—112no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—21no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—44no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—81no—
296C22×C11—164no—
297C22×C11—164no—
298C22×C11#44714yes—
299C22×C11C2×#12011yescharacteristic
300C22×C11C22×D811yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—816no—
308C2×D11—82no—
309C2×D11—82no—
310C4×C11—22no—
311C4×C11—21no—
312C4×C11—22no—
313C4×C11—44no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11B(4,𝔽2)12yes—
317Dic11—82no—
318C25—221no—
319H(5,𝔽2)—44no—
320H(5,𝔽2)—44no—
321C2×#41—24no—
322C2×#41—22no—
323C22×D4—24no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—21no—
327C22×D4—112no—
328C22×D4—222no—
329C22×D4—222no—
330C22×D4—221no—
331C22×D4—222no—
332C22×D4—444no—
333C22×D4C22⋊D1111yescharacteristic
334C22×D4C22⋊D1112yescomplemented
335C23×C4C22⋊D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C2×D8—228no—
338C2×D8—448no—
339C22×C8—222no—
340C4⋊Q8—21no—
341#127—21no—
342#124—22no—
343#123—24no—
344#123—24no—
345C22⋊Q8—24no—
346#121—22no—
347#121—22no—
348#121—24no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—444no—
354#121C22⋊D1114yescomplemented
355#121C22×D1114yes—
356#120—24no—
357#120—24no—
358#120—444no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C22⋊D1112yescomplemented
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4C22⋊D1111yescharacteristic
374C2×C22⋊C4C22×D1111yescharacteristic
375C2×C42C22⋊D1111yescharacteristic
376#102—228no—
377C22⋊C8—114no—
378C22⋊C8—222no—
379#95—112no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—24no—
383C2×C11—42no—
384C2×C11—84no—
385C2×C11C2×#44711yescharacteristic
386C2×C11#302111yescharacteristic
387C2×C11C2×B(4,𝔽2)11yescharacteristic
388D11—84no—
389C24—22no—
390C24—22no—
391C24—222no—
392C24—444no—
393C24—442no—
394C24—442no—
395C24—442no—
396C24—882no—
397C24C2×C22⋊D1111yescharacteristic
398C24C2×C22⋊D1111yescharacteristic
399#41—44no—
400#41—416no—
401#41—44no—
402C2×Q8—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—44no—
413C2×D4—416no—
414C2×D4—44no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—82no—
419C2×D4—228no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—442no—
423C2×D4—444no—
424C2×D4—444no—
425C2×D4—448no—
426C2×D4—444no—
427C2×D4—444no—
428C2×D4—441no—
429C2×D4—441no—
430C2×D4—882no—
431C2×D4#432314yescomplemented
432C2×D4C2×C22⋊D1114yes—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—222no—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1112yes—
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1112yes—
447C22×C4C23×D1111yescharacteristic
448D8—4416no—
449C2×C8—224no—
450C2×C8—444no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—442no—
456C4⋊C4C2×C22⋊D1114yes—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—444no—
464C22⋊C4—442no—
465C22⋊C4—444no—
466C22⋊C4—882no—
467C42—21no—
468C42—21no—
469C11#1819411yescharacteristic, complemented, Sylow
470C23—21no—
471C23—21no—
472C23—24no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—44no—
478C23—44no—
479C23—82no—
480C23—82no—
481C23—82no—
482C23—82no—
483C23—224no—
484C23—442no—
485C23—448no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—884no—
492C23—888no—
493C23—888no—
494C23—884no—
495C23C2×#432312yes—
496C23C2×#432312yescomplemented
497C23#6698512yes—
498C23#6700612yes—
499C23C22×C22⋊D1111yescharacteristic
500Q8—44no—
501D4—28no—
502D4—44no—
503D4—44no—
504D4—48no—
505D4—44no—
506D4—44no—
507D4—48no—
508D4—44no—
509D4—82no—
510D4—82no—
511D4—228no—
512D4—444no—
513D4—444no—
514D4—444no—
515D4—888no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—24no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—48no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4C2×#432312yescomplemented
536C2×C4#6700611yescharacteristic
537C2×C4#6700611yescharacteristic
538C2×C4C22×C22⋊D1112yes—
539C8—444no—
540C22—21no—
541C22—22no—
542C22—21no—
543C22—22no—
544C22—22no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—81no—
554C22—164no—
555C22—164no—
556C22—444no—
557C22—444no—
558C22—444no—
559C22—882no—
560C22—882no—
561C22—8816no—
562C22—882no—
563C22—882no—
564C22#1062283014yes—
565C22C22×#432311yescharacteristic
566C22C2×#6698511yescharacteristic
567C22C2×#6700611yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—44no—
572C4—41no—
573C4—41no—
574C4—882no—
575C4#1062285712yes—
576C2—21no—
577C2—21no—
578C2—24no—
579C2—42no—
580C2—84no—
581C2—884no—
582C2C2×#1062283011yescharacteristic
583C2#1307798811yescharacteristic
584C2C2×#1062285711yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18194
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#10622649C2semidirect
2. #13071972C2semidirect
3. #13067551C2semidirect
4. #13067534C2semidirect
5. #13067184C2semidirect
6. #13066934C2semidirect
7. C11×#3496C2semidirect
9. C23×D44C22semidirect
13. C11×#537C22semidirect
15. C11×#534C22semidirect
23. #10622825C22semidirect
24. C2×C22⋊(C11⋊C8)C22semidirect
26. #10622649C22semidirect
27. #10622604C22semidirect
29. #10622573C22semidirect
32. #10622175C22semidirect
33. #10622166C22semidirect
34. #10622163C22semidirect
45. C22×D4×C11D4semidirect
67. C11×#121D4semidirect
76. C2×C11×C4⋊C4D4semidirect
128. C2×D4×C11D8semidirect
178. #3496D11semidirect
200. C23×C11C2×D8semidirect
244. C2×C4×C11C2×D8semidirect
261. #537C2×D11semidirect
263. #534C2×D11semidirect
334. C22×D4C22⋊D11semidirect
354. #121C22⋊D11semidirect
365. C2×C4⋊C4C22⋊D11semidirect
431. C2×D4#4323semidirect
469. C11#18194semidirect
496. C23C2×#4323semidirect
535. C2×C4C2×#4323semidirect

Maximal subgroups

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

subgroupindex
C2×#106226492
#130719722
#130675512
#130675342
#130671842
#130669342
C11×#34962
#1819411