Finite Group Databasebeta

← #14685015

Subgroups — #14685015

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×Dic11C211yesmaximal, characteristic
2C2×#10622586C212yesmaximal, complemented
3C2×#10622559C212yesmaximal
4C2×#10622825C211yesmaximal, characteristic
5#13066847C214yesmaximal, complemented
6#13066845C212yesmaximal, complemented
7#13066838C212yesmaximal
8C2×C11×#380C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C24×Dic11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2212yes—
16C22×C4⋊Dic11C2212yes—
17C22×Dic11⋊C4C2214yes—
18C22×C4×Dic11—24no—
19C22×C4×Dic11—28no—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C11×#380—24no—
23C2×C11×#95C2212yes—
24#10622825C418yescomplemented
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2212yes—
29#10622586—28no—
30#10622559—28no—
31C25×C11C2311yescharacteristic
32C23×C4×C11—24no—
33C23×C4×C11—24no—
34C23×C4×C11C2×C414yes—
35C23×C4×C11D414yes—
36C23×C4×C11Q814yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—22no—
42C23×Dic11—22no—
43C23×Dic11—22no—
44C23×Dic11—22no—
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11—24no—
48C23×Dic11—24no—
49C23×Dic11D414yes—
50C23×Dic11Q814yes—
51C23×Dic11C2314yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11C2×C418yes—
64C2×C4⋊Dic11—24no—
65C2×C4⋊Dic11—24no—
66C2×C4⋊Dic11C2×C418yescomplemented
67C2×Dic11⋊C4—28no—
68C2×Dic11⋊C4—28no—
69C2×Dic11⋊C4—28no—
70C2×C4×Dic11—232no—
71C2×C4×Dic11—24no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11D418yes—
77C11×#95—24no—
78C11⋊#95—28no—
79C11⋊#95—28no—
80C11⋊#95—28no—
81C11⋊#95C2×C418yescomplemented
82#14697—111nomaximal, Sylow
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—22no—
86C24×C11—22no—
87C24×C11C22×C412yes—
88C24×C11C2×D412yes—
89C24×C11C2×D412yes—
90C24×C11C2×Q812yes—
91C24×C11C2×Q812yes—
92C24×C11#4112yes—
93C24×C11#4112yes—
94C24×C11C2411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—216no—
98C22×C4×C11—28no—
99C22×C4×C11—216no—
100C22×C4×C11—28no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11C4⋊C4116yescomplemented
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×Q812yes—
118C22×C4×C11C2×Q812yes—
119C22×C4×C11#4114yes—
120C22×Dic11—28no—
121C22×Dic11—28no—
122C22×Dic11—28no—
123C22×Dic11—28no—
124C22×Dic11—216no—
125C22×Dic11—216no—
126C22×Dic11—216no—
127C22×Dic11—216no—
128C22×Dic11—28no—
129C22×Dic11—28no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11C22×C418yes—
145C22×Dic11C2×D414yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×Q814yes—
149C22×Dic11#4114yes—
150C22×Dic11#4114yes—
151C11×C4⋊C4—44no—
152C11×C4⋊C4—44no—
153C11×C22⋊C4—48no—
154C22⋊Dic11—216no—
155C4⋊Dic11—216no—
156Dic11⋊C4—416no—
157C4×Dic11—216no—
158C4×Dic11—216no—
159C23×C42—111no—
160C2×#389—112no—
161C2×#385—112no—
162C2×#380—111no—
163C2×#380D1111yescharacteristic
164#1436—114no—
165C4⋊#95—112no—
166C22⋊#95—112no—
167C23×C11—24no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—24no—
172C23×C11—24no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11C2×C4⋊C414yes—
184C23×C11C4×D414yes—
185C23×C11C4×Q814yes—
186C23×C11#12114yes—
187C23×C11C22⋊Q814yes—
188C23×C11#12514yes—
189C23×C11C4⋊Q814yes—
190C23×C11C23×C411yescharacteristic
191C23×C11C22×D412yes—
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×Q811yescharacteristic
195C23×C11C22×Q811yescharacteristic
196C23×C11C2×#4112yes—
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—232no—
206C2×C4×C11—42no—
207C2×C4×C11—44no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—44no—
215C2×C4×C11—44no—
216C2×C4×C11C2×C4⋊C414yes—
217C2×C4×C11C2×C4⋊C414yes—
218C2×C4×C11C4×D418yes—
219C2×C4×C11#12014yes—
220C2×C4×C11C22⋊Q818yes—
221C2×C4×C11#12314yes—
222C2×Dic11—232no—
223C2×Dic11—232no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—28no—
237C2×Dic11—28no—
238C2×Dic11—28no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11#12118yes—
244C2×Dic11C22⋊Q818yes—
245C24×C4—111no—
246C24×C4—111no—
247C24×C4C2×D1111yescharacteristic
248C22×C4⋊C4—112no—
249C22×C4⋊C4—114no—
250C22×C4⋊C4C2×D1111yescharacteristic
251C22×C4⋊C4C2×D1111yescharacteristic
252C22×C22⋊C4—112no—
253C22×C22⋊C4C2×D1112yes—
254C22×C42—112no—
255C22×C42—112no—
256C22×C42—228no—
257C22×C42—224no—
258#389—228no—
259#385—228no—
260#380—24no—
261#380—118no—
262C2×#95—112no—
263C2×#95—114no—
264C2×#95—114no—
265C2×#95—114no—
266C2×#95C2×D1112yes—
267C22×C11—24no—
268C22×C11—24no—
269C22×C11—28no—
270C22×C11—24no—
271C22×C11—24no—
272C22×C11—28no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—28no—
276C22×C11—28no—
277C22×C11#38918yescomplemented
278C22×C11C22×C4⋊C411yescharacteristic
279C22×C11C2×C4×D412yes—
280C22×C11C2×C4×D411yescharacteristic
281C22×C11C2×C4×Q811yescharacteristic
282C22×C11C4×#4112yes—
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×#12111yescharacteristic
285C22×C11C2×#12112yes—
286C22×C11C2×C22⋊Q812yes—
287C22×C11C2×C22⋊Q811yescharacteristic
288C22×C11C2×C22⋊Q812yes—
289C22×C11C2×#12311yescharacteristic
290C22×C11#52511yescharacteristic
291C22×C11#52511yescharacteristic
292C22×C11#52512yes—
293C22×C11#52512yes—
294C22×C11C2×#12511yescharacteristic
295C22×C11#52912yes—
296C22×C11#52912yes—
297C22×C11C2×C4⋊Q811yescharacteristic
298C22×C11#53212yes—
299C22×C11#53312yes—
300C22×C11#53312yes—
301C4×C11—24no—
302C4×C11—82no—
303C4×C11—82no—
304C4×C11#38518yescomplemented
305Dic11—28no—
306Dic11—28no—
307Dic11—48no—
308C25C22×D1111yescharacteristic
309C23×C4—24no—
310C23×C4—24no—
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—114no—
314C23×C4—114no—
315C23×C4—114no—
316C23×C4—224no—
317C23×C4—224no—
318C23×C4—224no—
319C23×C4—224no—
320C23×C4—222no—
321C23×C4—222no—
322C23×C4—222no—
323C23×C4—222no—
324C23×C4Dic2214yes—
325C23×C4C4×D1114yes—
326C23×C4C22⋊D1114yes—
327C23×C4C22×D1112yes—
328C23×C4C22×D1112yes—
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—118no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—228no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—228no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—224no—
346C2×C22⋊C4—224no—
347C2×C42—118no—
348C2×C42—224no—
349C2×C42—224no—
350C2×C42—2232no—
351C2×C42—224no—
352C2×C42—224no—
353C2×C42—224no—
354#95—24no—
355#95—118no—
356#95—228no—
357#95—228no—
358#95—228no—
359C2×C11—28no—
360C2×C11C2×#38511yescharacteristic
361C2×C11C2×#38911yescharacteristic
362C2×C11#229611yescharacteristic
363C2×C11C4×#12112yes—
364C2×C11C4×C22⋊Q812yes—
365C2×C11#284711yescharacteristic
366C2×C11#284811yescharacteristic
367C2×C11#285112yes—
368C2×C11#285411yescharacteristic
369C2×C11#285511yescharacteristic
370C2×C11#285712yes—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24C2×Dic2212yes—
376C24C2×C4×D1112yes—
377C24D4×D1112yes—
378C24#434112yes—
379C24Q8×D1112yes—
380C24#434312yes—
381C24C2×C22⋊D1112yes—
382C24C23×D1111yescharacteristic
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—216no—
386C22×C4—216no—
387C22×C4—28no—
388C22×C4—28no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—118no—
406C22×C4—2216no—
407C22×C4—2216no—
408C22×C4—228no—
409C22×C4—228no—
410C22×C4—228no—
411C22×C4—228no—
412C22×C4—2216no—
413C22×C4—2216no—
414C22×C4—228no—
415C22×C4—228no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4Dic11⋊C4116yescomplemented
431C22×C4C2×Dic2212yes—
432C22×C4C2×Dic2212yes—
433C22×C4C2×C4×D1112yes—
434C22×C4C2×C4×D1112yes—
435C22×C4D4×D1114yes—
436C22×C4#434114yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1112yes—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—2216no—
442C4⋊C4—4416no—
443C22⋊C4—48no—
444C22⋊C4—2216no—
445C42—2216no—
446C42—2216no—
447C11#1469711yescharacteristic, complemented, Sylow
448C23—24no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23#6694014yes—
465C23#6694114yes—
466C23#6694314yes—
467C23#6694614yes—
468C23C2×Dic11⋊C414yes—
469C23#6699114yes—
470C23#6699914yes—
471C23C22×Dic2211yescharacteristic
472C23C22×C4×D1111yescharacteristic
473C23C2×D4×D1112yes—
474C23C2×D4×D1111yescharacteristic
475C23C2×#434112yes—
476C23C2×#434111yescharacteristic
477C23C2×Q8×D1111yescharacteristic
478C23C2×#434311yescharacteristic
479C23#41×D1112yes—
480C23#41×D1112yes—
481C23C22×C22⋊D1111yescharacteristic
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—232no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—118no—
498C2×C4—118no—
499C2×C4—2232no—
500C2×C4—2232no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—228no—
514C2×C4—228no—
515C2×C4—228no—
516C2×C4—444no—
517C2×C4—444no—
518C2×C4—444no—
519C2×C4—444no—
520C2×C4#6693118yes—
521C2×C4(C22⋊D11)⋊C418yes—
522C2×C4C2×Dic11⋊C414yes—
523C2×C4C2×Dic11⋊C414yes—
524C2×C4#6698814yes—
525C2×C4#6699014yes—
526C22—28no—
527C22—28no—
528C22—24no—
529C22—24no—
530C22—24no—
531C22—28no—
532C22—24no—
533C22—24no—
534C22—28no—
535C22—24no—
536C22#1062258618yescomplemented
537C22C2×#6693112yes—
538C22C2×(C22⋊D11)⋊C412yes—
539C22C2×#6694011yescharacteristic
540C22C2×#6694111yescharacteristic
541C22C2×#6694311yescharacteristic
542C22C2×#6694611yescharacteristic
543C22#1062304812yes—
544C22#1062305312yes—
545C22#1062312712yes—
546C22#1062313112yes—
547C22D11×#12112yes—
548C22#1062313712yes—
549C22#1062315312yes—
550C22#1062315512yes—
551C22D11×C22⋊Q812yes—
552C22#1062315812yes—
553C22C22×Dic11⋊C411yescharacteristic
554C22C2×#6698811yescharacteristic
555C22C2×#6699011yescharacteristic
556C22C2×#6699111yescharacteristic
557C22C2×#6699911yescharacteristic
558C22#1062335911yescharacteristic
559C22#1062335911yescharacteristic
560C4—24no—
561C4—82no—
562C4—82no—
563C4—228no—
564C4—228no—
565C4—448no—
566C4#1062255918yescomplemented
567C2—28no—
568C2C2×#1062255911yescharacteristic
569C2C2×#1062258611yescharacteristic
570C2#1307109811yescharacteristic
571C2#1307112212yes—
572C2#1307114412yes—
573C2#1307689511yescharacteristic
574C2#1307690011yescharacteristic
575C2#1307692412yes—
576C2#1307694211yescharacteristic
577C2#1307695011yescharacteristic
578C2#1307696612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#14697
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622586C2semidirect
5. #13066847C2semidirect
6. #13066845C2semidirect
24. #10622825C4semidirect
66. C2×C4⋊Dic11C2×C4semidirect
81. C11⋊#95C2×C4semidirect
111. C22×C4×C11C4⋊C4semidirect
277. C22×C11#389semidirect
304. C4×C11#385semidirect
430. C22×C4Dic11⋊C4semidirect
447. C11#14697semidirect
536. C22#10622586semidirect
566. C4#10622559semidirect

Maximal subgroups

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

subgroupindex
C23×C4×Dic112
C2×#106225862
C2×#106225592
C2×#106228252
#130668472
#130668452
#130668382
C2×C11×#3802
#1469711