Finite Group Databasebeta

← #14685137

Subgroups — #14685137

Order 2816.

3342 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66993C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622552C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic, complemented
5C2×#10622570C218yesmaximal, complemented
6C2×#10622589C211yesmaximal, characteristic, complemented
7C2×C42×Dic11C211yesmaximal, characteristic, complemented
8C2×C11×#390C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11C2214yes—
11C23×D44C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2214yes—
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2214yes—
16C2×#66993—24no—
17C2×#66993—24no—
18C2×#66993C418yescomplemented
19C22×(C2×D11)⋊C4C2214yes—
20C22×(C2×D11)⋊C4C2214yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2214yes—
23C22×C4×Dic11C2214yes—
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C11×#390—24no—
27#10622834—24no—
28#10622601—24no—
29#10622589—24no—
30#10622570—232no—
31#10622552—24no—
32C42×Dic11—24no—
33C25×C11C2312yes—
34C24×D11C2312yes—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11C2×C414yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C22×C22⋊D11—28no—
46C22×C22⋊D11—28no—
47C22×C22⋊D11—216no—
48C22×C22⋊D11—216no—
49C22×C22⋊D11C2×C4116yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44C2×C414yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C22⋊C4—216no—
64C2×C11×C22⋊C4—28no—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11D414yescomplemented
68C2×C22⋊Dic11—216no—
69C2×C22⋊Dic11—28no—
70#66993—232no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—216no—
73C2×(C2×D11)⋊C4—216no—
74C2×(C2×D11)⋊C4—28no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×Dic11⋊C4—216no—
79C2×Dic11⋊C4—28no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—28no—
83C2×C4×Dic11—28no—
84C2×C4×Dic11C2×C414yes—
85C2×C4×Dic11D414yes—
86C2×C4×Dic11D414yes—
87C2×C4×Dic11D4116yescomplemented
88C2×C4×Dic11D414yescomplemented
89#14713—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—28no—
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—28no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11C22×C414yes—
99C24×C11C2411yescharacteristic
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—28no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—28no—
108C23×D11C22×C414yes—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—44no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—28no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D418yes—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C2×C22⋊D11—232no—
133C2×C22⋊D11—264no—
134C2×C22⋊D11—432no—
135C2×C22⋊D11—416no—
136C2×C22⋊D11—416no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—28no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11C22×C414yes—
145C22×Dic11C2×D418yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×D418yes—
150C22×Dic11#4118yes—
151C2×D44—28no—
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—44no—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44—44no—
158C11×C4⋊C4—44no—
159C11×C22⋊C4—416no—
160C42×C11—28no—
161C22⋊Dic11—416no—
162(C2×D11)⋊C4—416no—
163(C2×D11)⋊C4—416no—
164C4⋊Dic11—44no—
165Dic11⋊C4—416no—
166C4×Dic11—232no—
167C4×Dic11—28no—
168C4×Dic11C22⋊C4116yescomplemented
169C22×#127—111no—
170C2×#390—111no—
171C2×#390—111no—
172C2×#390—111no—
173C2×#390—118no—
174C2×#390D1111yescharacteristic, complemented
175C2×#384—111no—
176C2×C43—111no—
177C23×C11—24no—
178C23×C11—216no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—48no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—42no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—42no—
190C23×C11—48no—
191C23×C11—44no—
192C23×C11—48no—
193C23×C11—44no—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C22×D411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C22×D414yes—
199C23×C11C22×D411yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C11C2×#4111yescharacteristic
202C23×C11C2×#4114yes—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—216no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—48no—
210C22×D11—42no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—42no—
215C22×D11—44no—
216C22×D11—48no—
217C22×D11—44no—
218C22×D11—48no—
219C22×D11—44no—
220D4×C11—416no—
221C2×C4×C11—28no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—28no—
225C2×C4×C11—44no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11—42no—
229C2×C4×C11C2×C22⋊C414yes—
230C2×C4×C11C4×D414yes—
231C2×C4×C11C4×D414yes—
232C2×C4×C11#12114yes—
233C2×C4×C11#12114yes—
234C2×C4×C11#12414yes—
235C2×C4×C11#12714yes—
236C2×C4×C11#12718yescomplemented
237C22⋊D11—464no—
238C2×Dic11—24no—
239C2×Dic11—28no—
240C2×Dic11—28no—
241C2×Dic11—24no—
242C2×Dic11—44no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—44no—
246C2×Dic11C2×C22⋊C418yes—
247C2×Dic11C4×D4116yes—
248C2×Dic11#121116yes—
249C2×Dic11#12418yes—
250C2×Dic11#12718yes—
251C2×Dic11#12718yescomplemented
252D44—416no—
253C23×D4—114no—
254C23×D4—111no—
255C23×D4C2×D1111yescharacteristic
256C2×#127—118no—
257C2×#127—224no—
258C2×#127—224no—
259C22×C4⋊C4—114no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C22⋊C4—114no—
263C22×C22⋊C4—114no—
264C22×C22⋊C4—114no—
265C22×C22⋊C4C2×D1114yes—
266C22×C42—111no—
267C22×C42—114no—
268C22×C42—111no—
269C22×C42C2×D1111yescharacteristic
270#390—24no—
271#390—2232no—
272#390—224no—
273#390—224no—
274#390—224no—
275#384—224no—
276C43—224no—
277C22×C11—48no—
278C22×C11—48no—
279C22×C11—44no—
280C22×C11—48no—
281C22×C11—84no—
282C22×C11—84no—
283C22×C11—84no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11C22×C22⋊C411yescharacteristic
287C22×C11C2×C4×D411yescharacteristic
288C22×C11C2×C4×D411yescharacteristic
289C22×C11C2×C4×D414yes—
290C22×C11C2×#12111yescharacteristic
291C22×C11C2×#12111yescharacteristic
292C22×C11C2×#12114yes—
293C22×C11C2×#12411yescharacteristic
294C22×C11C2×#12412yes—
295C22×C11C2×#12712yes—
296C22×C11C2×#12712yes—
297C22×C11C2×#12712yes—
298C22×C11C2×#12711yescharacteristic
299C22×C11#53214yes—
300C22×C11#53212yes—
301C22×C11#53214yes—
302C22×C11#53212yes—
303C2×D11—48no—
304C2×D11—48no—
305C2×D11—44no—
306C2×D11—48no—
307C2×D11—84no—
308C2×D11—84no—
309C2×D11—84no—
310C2×D11—82no—
311C2×D11—82no—
312C4×C11—28no—
313C4×C11—82no—
314C4×C11#39018yescomplemented
315Dic11—28no—
316Dic11—82no—
317Dic11#390116yescomplemented
318C25—112no—
319C25C22×D1112yes—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—1116no—
327C22×D4—114no—
328C22×D4—228no—
329C22×D4—228no—
330C22×D4—2216no—
331C22×D4—2216no—
332C22×D4—222no—
333C22×D4—222no—
334C22×D4—222no—
335C22×D4—222no—
336C22×D4—222no—
337C22×D4—222no—
338C22×D4C4×D1114yes—
339C23×C4—112no—
340C23×C4—112no—
341C23×C4—112no—
342C23×C4C22×D1112yes—
343C23×C4C22×D1112yes—
344C23×C4C22×D1111yescharacteristic
345#127—2232no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—2216no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C22⋊C4—216no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—2216no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—2216no—
359C2×C22⋊C4—228no—
360C2×C22⋊C4—2216no—
361C2×C22⋊C4—228no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—114no—
365C2×C42—114no—
366C2×C42—114no—
367C2×C42—1116no—
368C2×C42—114no—
369C2×C42—228no—
370C2×C42—228no—
371C2×C42—222no—
372C2×C42—222no—
373C2×C42C22⋊D1114yescomplemented
374C2×C11—84no—
375C2×C11C2×#39012yes—
376C2×C11C2×#39011yescharacteristic
377C2×C11C4×#12712yes—
378C2×C11C4×#12712yes—
379C2×C11#285612yes—
380C2×C11#285612yes—
381C2×C11#285812yes—
382C2×C11#285811yescharacteristic
383C2×C11#286711yescharacteristic
384D11—84no—
385C24—22no—
386C24—28no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—28no—
392C24—22no—
393C24—114no—
394C24—222no—
395C24—222no—
396C24—228no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24—228no—
401C24—222no—
402C24C2×C4×D1114yes—
403C24C23×D1111yescharacteristic
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—2232no—
412C2×D4—2264no—
413C2×D4—228no—
414C2×D4—228no—
415C2×D4—228no—
416C2×D4—4416no—
417C2×D4—4432no—
418C2×D4—4416no—
419C2×D4—444no—
420C2×D4—444no—
421C2×D4—444no—
422C2×D4—444no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—28no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—118no—
434C22×C4—118no—
435C22×C4—114no—
436C22×C4—118no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—228no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4C2×C4×D1112yes—
445C22×C4#433912yes—
446C22×C4D4×D1118yes—
447C22×C4D4×D1112yes—
448C22×C4D4×D1112yes—
449C22×C4D4×D1112yes—
450C22×C4#434112yes—
451C22×C4C2×C22⋊D1114yes—
452C22×C4C2×C22⋊D1112yes—
453C4⋊C4—44no—
454C4⋊C4—4416no—
455C4⋊C4—444no—
456C22⋊C4—416no—
457C22⋊C4—4416no—
458C22⋊C4—4416no—
459C22⋊C4—4416no—
460C42—28no—
461C42—1116no—
462C42—2232no—
463C42—228no—
464C11#1471311yescharacteristic, complemented, Sylow
465C23—24no—
466C23—24no—
467C23—24no—
468C23—216no—
469C23—44no—
470C23—44no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—42no—
476C23—48no—
477C23—44no—
478C23—48no—
479C23—48no—
480C23—44no—
481C23—44no—
482C23—224no—
483C23—224no—
484C23—224no—
485C23—2216no—
486C23—444no—
487C23—444no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—444no—
492C23—442no—
493C23—448no—
494C23—444no—
495C23—448no—
496C23—448no—
497C23—444no—
498C23—444no—
499C23C22×C4×D1111yescharacteristic
500C23C2×#433911yescharacteristic
501C23C2×D4×D1111yescharacteristic
502C23C2×D4×D1111yescharacteristic
503C23C2×D4×D1114yes—
504C23C2×D4×D1111yescharacteristic
505C23C2×#434111yescharacteristic
506C23#41×D1114yes—
507C23C22×C22⋊D1111yescharacteristic
508D4—416no—
509D4—4464no—
510D4—4416no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—28no—
514C2×C4—28no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—118no—
520C2×C4—118no—
521C2×C4—1116no—
522C2×C4—1116no—
523C2×C4—118no—
524C2×C4—118no—
525C2×C4—224no—
526C2×C4—228no—
527C2×C4—228no—
528C2×C4—224no—
529C2×C4—444no—
530C2×C4—444no—
531C2×C4—444no—
532C2×C4—442no—
533C2×C4C22⋊C4×D1114yes—
534C2×C4(C22⋊D11)⋊C414yes—
535C2×C4#6693714yes—
536C2×C4#6693814yes—
537C2×C4C4×C22⋊D1114yes—
538C2×C4#6699214yes—
539C2×C4#6699314yes—
540C2×C4#6699318yescomplemented
541C22—48no—
542C22—48no—
543C22—48no—
544C22—44no—
545C22—82no—
546C22—84no—
547C22—84no—
548C22—84no—
549C22—82no—
550C22—448no—
551C22—448no—
552C22—448no—
553C22—444no—
554C22—882no—
555C22—884no—
556C22—884no—
557C22—884no—
558C22—882no—
559C22C2×C22⋊C4×D1111yescharacteristic
560C22C2×(C22⋊D11)⋊C411yescharacteristic
561C22C2×#6693711yescharacteristic
562C22C2×#6693811yescharacteristic
563C22C4×D4×D1114yes—
564C22#1062307914yes—
565C22#1062312714yes—
566C22D11×#12114yes—
567C22#1062319912yes—
568C22D11×#12412yes—
569C22D11×#12712yes—
570C22D11×#12712yes—
571C22C2×C4×C22⋊D1111yescharacteristic
572C22C2×#6699211yescharacteristic
573C22C2×#6699312yes—
574C22C2×#6699311yescharacteristic
575C22#1062336312yes—
576C4—28no—
577C4—82no—
578C4—1116no—
579C4—228no—
580C4—882no—
581C4#1062257018yescomplemented
582C2—84no—
583C2—884no—
584C2D11×#39012yes—
585C2C2×#1062257011yescharacteristic
586C2C4×#6699312yes—
587C2#1307118012yes—
588C2#1307695912yes—
589C2#1307696012yes—
590C2#1307697012yes—
591C2#1307697111yescharacteristic
592C2#1307701011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC22×#66993C2
hypercenterC2×#390D11
hypocenterC11#14713
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622552C2semidirect
4. C2×#10622601C2semidirect
5. C2×#10622570C2semidirect
6. C2×#10622589C2semidirect
7. C2×C42×Dic11C2semidirect
8. C2×C11×#390C2semidirect
18. C2×#66993C4semidirect
67. C2×C42×C11D4semidirect
87. C2×C4×Dic11D4semidirect
88. C2×C4×Dic11D4semidirect
168. C4×Dic11C22⋊C4semidirect
174. C2×#390D11semidirect
236. C2×C4×C11#127semidirect
251. C2×Dic11#127semidirect
314. C4×C11#390semidirect
317. Dic11#390semidirect
373. C2×C42C22⋊D11semidirect
464. C11#14713semidirect
540. C2×C4#66993semidirect
581. C4#10622570semidirect

Maximal subgroups

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

subgroupindex
C22×#669932
C2×#106228342
C2×#106225522
C2×#106226012
C2×#106225702
C2×#106225892
C2×C42×Dic112
C2×C11×#3902
#1471311