Finite Group Databasebeta

← #14684143

Subgroups — #14684143

Order 2816.

1506 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622560C211yesmaximal, characteristic
2#13066886C212yesmaximal, complemented
3#13066876C212yesmaximal, complemented
4#13066853C212yesmaximal
5#13066848C212yesmaximal, complemented
6#13066840C212yesmaximal, complemented
7#13066838C212yesmaximal
8#13066838C211yesmaximal, characteristic
9C11×#1439C211yesmaximal, characteristic
10C24×Dic11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622560C418yescomplemented
32C25×C11C2311yescharacteristic
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×Dic11—22no—
38C23×Dic11—24no—
39C23×Dic11—42no—
40C23×Dic11—41no—
41C23×Dic11—41no—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C22×Dic22—41no—
47C22×Dic22—41no—
48C22×Dic22—42no—
49C22×Dic22—42no—
50C22×Dic22C2×C414yescomplemented
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—41no—
53C2×C11×C22⋊C4—24no—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—41no—
56C2×C11×C22⋊C4—41no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C22⋊Dic11—42no—
60C2×C22⋊Dic11—42no—
61C2×C22⋊Dic11—41no—
62C2×C22⋊Dic11—41no—
63C2×C22⋊Dic11C2×C418yes—
64C2×C22⋊Dic11Q814yescomplemented
65C2×C4×Dic11—24no—
66C2×C4×Dic11—42no—
67C2×C4×Dic11—42no—
68C11×#95—42no—
69C11×#95—41no—
70C11⋊#95—24no—
71C11⋊#95—24no—
72C11⋊#95—42no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95C2×C414yescomplemented
80C11⋊#95C2×C418yescomplemented
81#14596—111nomaximal, Sylow
82C24×C11—22no—
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—21no—
88C24×C11—21no—
89C24×C11—21no—
90C24×C11C22×C412yes—
91C24×C11C2×Q812yes—
92C24×C11#4112yes—
93C24×C11C2411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11#4114yes—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—48no—
143C22×Dic11—44no—
144C22×Dic11—44no—
145C22×Dic11—48no—
146C22×Dic11—44no—
147C22×Dic11C22×C414yes—
148C22×Dic11C22×C414yes—
149C22×Dic11C2×Q814yes—
150C22×Dic11#4114yes—
151C2×Dic22—44no—
152C2×Dic22—48no—
153C2×Dic22—44no—
154C2×Dic22—48no—
155C2×Dic22—44no—
156C11×C4⋊C4—44no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—48no—
159C22⋊Dic11—48no—
160C22⋊Dic11—44no—
161C4×Dic11—48no—
162C2×#393—111no—
163#1446—112no—
164#1443—112no—
165#1439D1111yescharacteristic
166#1437—112no—
167#1436—112no—
168#1434—112no—
169C22⋊#95—112no—
170C22⋊#95—111no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—42no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—41no—
193C23×C11C4×Q814yes—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×Q811yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4112yes—
198C23×C11C2×#4112yes—
199C23×C11H(5,𝔽2)12yes—
200C23×C11H(5,𝔽2)11yescharacteristic
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C112−1+411yescharacteristic
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—416no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258Dic22—416no—
259C23×Q8—111no—
260C24×C4—111no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C22⋊C4—112no—
263C22×C22⋊C4—111no—
264C22×C22⋊C4C2×D1112yes—
265C22×C22⋊C4C2×D1111yescharacteristic
266C22×C42—112no—
267#393—118no—
268C2×#95—111no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95C2×D1112yes—
280C2×#95C2×D1111yescharacteristic
281C22×C11—24no—
282C22×C11—28no—
283C22×C11—44no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—44no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—44no—
292C22×C11C2×C4×Q811yescharacteristic
293C22×C11C4×#4112yes—
294C22×C11#51811yescharacteristic
295C22×C11#51812yes—
296C22×C11#52011yescharacteristic
297C22×C11#53812yes—
298C22×C11#53811yescharacteristic
299C22×C11#53812yes—
300C22×C11#53911yescharacteristic
301C22×C11#54212yes—
302C22×C11#54212yes—
303C22×C11#54311yescharacteristic
304C22×C11#54411yescharacteristic
305C22×C11#55112yes—
306C22×C11#55111yescharacteristic
307C22×C11#55112yes—
308C22×C11#55111yescharacteristic
309C22×C11#55412yes—
310C22×C11#55412yes—
311C22×C11#55512yes—
312C22×C11#56011yescharacteristic
313C22×C11#56012yes—
314C22×C11H(3,𝔽4)11yescharacteristic
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—44no—
318C4×C11—82no—
319Dic11—44no—
320Dic11—44no—
321Dic11—44no—
322Dic11—44no—
323C25C22×D1111yescharacteristic
324C22×Q8—114no—
325C22×Q8—442no—
326C22×Q8—441no—
327C22×Q8—441no—
328C22×Q8—442no—
329C23×C4—112no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—224no—
334C23×C4—222no—
335C23×C4—441no—
336C23×C4—442no—
337C23×C4—441no—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C23×C4C22×D1111yescharacteristic
341C23×C4C22×D1112yes—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—41no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—118no—
350C2×C22⋊C4—114no—
351C2×C22⋊C4—441no—
352C2×C22⋊C4—442no—
353C2×C22⋊C4—442no—
354C2×C22⋊C4—441no—
355C2×C22⋊C4C4×D1114yes—
356C2×C42—224no—
357C2×C42—442no—
358C2×C42—442no—
359#95—42no—
360#95—41no—
361#95—114no—
362#95—118no—
363#95—224no—
364#95—224no—
365#95—442no—
366#95—442no—
367#95—442no—
368#95—442no—
369#95—442no—
370#95—442no—
371#95—442no—
372C2×C11—44no—
373C2×C11#232911yescharacteristic
374C2×C11#233712yes—
375C2×C11#236812yes—
376C2×C11#237211yescharacteristic
377C2×C11#237511yescharacteristic
378C2×C11#273611yescharacteristic
379C2×C11#273712yes—
380C2×C11#274211yescharacteristic
381C2×C11#276011yescharacteristic
382C2×C11#276311yescharacteristic
383C2×C11#278412yes—
384C24—22no—
385C24—21no—
386C24—22no—
387C24—21no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—21no—
392C24C2×C4×D1112yes—
393C24#434112yes—
394C24Q8×D1112yes—
395C24C23×D1111yescharacteristic
396C2×Q8—444no—
397C2×Q8—448no—
398C2×Q8—444no—
399C2×Q8—448no—
400C2×Q8—444no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—114no—
423C22×C4—114no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—444no—
451C22×C4—448no—
452C22×C4—448no—
453C22×C4—444no—
454C22×C4—444no—
455C22×C4C2×C4×D1112yes—
456C22×C4C2×C4×D1112yes—
457C22×C4#434114yes—
458C4⋊C4—44no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—448no—
462C22⋊C4—444no—
463C42—448no—
464C11#1459611yescharacteristic, complemented, Sylow
465C23—22no—
466C23—22no—
467C23—24no—
468C23—24no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—41no—
487C23#6694014yes—
488C23C22×C4×D1111yescharacteristic
489C23C2×#434111yescharacteristic
490C23C2×#434112yes—
491C23#6703711yescharacteristic
492C23#6703712yes—
493C23#6703711yescharacteristic
494C23C2×Q8×D1111yescharacteristic
495C23#41×D1112yes—
496C23#6704211yescharacteristic
497C23#6704212yes—
498C23#6704311yescharacteristic
499Q8—4416no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—4416no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—442no—
553C22—28no—
554C22—24no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—44no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22#1062301711yescharacteristic
565C22C2×#6694011yescharacteristic
566C22#1062305411yescharacteristic
567C22C4×#434112yes—
568C22#1062307612yes—
569C22#1062311811yescharacteristic
570C22#1062311812yes—
571C22#1062313311yescharacteristic
572C22#1062314712yes—
573C22#1062314812yes—
574C22#1062314811yescharacteristic
575C22#1062315112yes—
576C22#1062315411yescharacteristic
577C22#1062316511yescharacteristic
578C22#1062316612yes—
579C22#1062316712yes—
580C22#1062318912yes—
581C22#1062319011yescharacteristic
582C22#1062319312yes—
583C22#1062321312yes—
584C22#1062321411yescharacteristic
585C22#1062323512yes—
586C22#1062325111yescharacteristic
587C4—44no—
588C4—42no—
589C4—42no—
590C4—82no—
591C4—444no—
592C4—444no—
593C4—444no—
594C4—444no—
595C2—44no—
596C2#1307134611yescharacteristic
597C2#1307142312yes—
598C2#1307169712yes—
599C2#1307172511yescharacteristic
600C2#1307175311yescharacteristic
601C2#1307566311yescharacteristic
602C2#1307567312yes—
603C2#1307574611yescharacteristic
604C2#1307599511yescharacteristic
605C2#1307603311yescharacteristic
606C2#1307631812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1439D11
hypocenterC11#14596
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #13066886C2semidirect
3. #13066876C2semidirect
5. #13066848C2semidirect
6. #13066840C2semidirect
31. #10622560C4semidirect
50. C22×Dic22C2×C4semidirect
64. C2×C22⋊Dic11Q8semidirect
79. C11⋊#95C2×C4semidirect
80. C11⋊#95C2×C4semidirect
464. C11#14596semidirect

Maximal subgroups

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

subgroupindex
C2×#106225602
#130668862
#130668762
#130668532
#130668482
#130668402
#130668382
C11×#14392
#1459611