Finite Group Databasebeta

← #14769090

Subgroups — #14769090

Order 2816.

1512 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×#10623008C211yesmaximal, characteristic
2C2×#10622319C212yesmaximal, complemented
3C2×#10622340C212yesmaximal, complemented
4#13069414C212yesmaximal, complemented
5#13068912C212yesmaximal, complemented
6#13068907C212yesmaximal, complemented
7#13068596C211yesmaximal, characteristic, complemented
8#13068527C212yesmaximal, complemented
9C11×#1749C211yesmaximal, characteristic, complemented
10C22×#4339C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×#66983C411yescharacteristic
13C2×#66983C412yes—
14C2×#66983C411yescharacteristic
15C22×#4313C2212yes—
16C22×C8×D11C2212yes—
17#10623008—28no—
18C2×#66928C412yes—
19C2×#66927C411yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C411yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622340—28no—
36#10622319—28no—
37C11×#336C2212yes—
38#10622162C2211yescharacteristic
39#10622162C2211yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11C2×C412yes—
44C22×C22⋊D11C2×C412yes—
45C2×#4339—24no—
46C2×#4339—24no—
47C2×#4339—24no—
48C2×#4339—24no—
49C2×#4339—42no—
50C2×#4339—42no—
51C22×D44C2×C412yes—
52C22×D44C2×C412yes—
53C22×D44C2×C411yescharacteristic
54C22×D44C2×C411yescharacteristic
55C22×C4×D11C2312yes—
56C22×C4×D11C2312yes—
57C22×Dic22C2×C412yes—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C2×C42×C11—24no—
61C2×C42×C11C2×C411yescharacteristic
62C2×C42×C11C2×C411yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65#66983—24no—
66#66983—28no—
67#66983—24no—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×C4⋊Dic11C2×C412yes—
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C22×C11⋊C8C2312yes—
76C22×C11⋊C8C2312yes—
77C2×#4313—24no—
78C2×#4313—24no—
79C2×#4313—42no—
80C2×C8×D11—24no—
81C2×C8×D11—24no—
82C2×C8×D11—42no—
83#66928—28no—
84#66927—24no—
85C4×D44—24no—
86C4×D44—24no—
87C4×D44—24no—
88C4×D44D418yes—
89#66922—24no—
90C11×C22⋊C8—22no—
91C11×C22⋊C8D414yescomplemented
92C11×#97—24no—
93C22⋊(C11⋊C8)—24no—
94(C2×D11)⋊C8—24no—
95(C2×D11)⋊C8—24no—
96(C2×D11)⋊C8—24no—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—42no—
99(C2×D11)⋊C8—42no—
100C4⋊(C11⋊C8)—24no—
101#22403—111nomaximal, Sylow
102C24×C11C22×C411yescharacteristic
103C23×D11C22×C412yes—
104C23×D11C22×C412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—41no—
111C22×C4×C11—41no—
112C22×C4×C11—41no—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C22×C411yescharacteristic
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C411yescharacteristic
118C22×C4×C11C2×D412yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C2×C22⋊D11—24no—
122C2×C22⋊D11—24no—
123C2×C22⋊D11—24no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—42no—
127C22×Dic11C22×C412yes—
128C22×Dic11C22×C412yes—
129#4339—48no—
130#4339—48no—
131#4339—48no—
132#4339—48no—
133C2×D44—24no—
134C2×D44—24no—
135C2×D44—22no—
136C2×D44—24no—
137C2×D44—24no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—42no—
141C2×D44—41no—
142C2×D44—41no—
143C2×D44—42no—
144C2×D44C22⋊C414yes—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11C2×D414yes—
156C2×C4×D11C2×D414yes—
157C2×Dic22—24no—
158C2×Dic22—24no—
159C2×Dic22—42no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11C2×D414yes—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D414yes—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4C22⋊C418yes—
174C4⋊Dic11—24no—
175C4⋊Dic11—22no—
176C4⋊Dic11C22⋊C414yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183#4313—48no—
184C8×D11—48no—
185C2×#532—111no—
186C2×#435—112no—
187C2×#408—112no—
188#1955—112no—
189#1870—112no—
190#1869—112no—
191#1797—111no—
192#1780—112no—
193#1749D1111yescharacteristic, complemented
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—21no—
200C23×C11C4×D412yes—
201C23×C11C23×C411yescharacteristic
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11C2×C22⋊C414yes—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—44no—
230C2×C4×C11—44no—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11C4×D412yes—
234C2×C4×C11#13112yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)12yes—
239C22⋊D11—48no—
240C22⋊D11—48no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11C2×C22⋊C414yes—
247D44—44no—
248D44—48no—
249D44—48no—
250D44—44no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—24no—
255C4×D11—42no—
256C4×D11—42no—
257C4×D11—42no—
258C4×D11—42no—
259Dic22—48no—
260C8×C11—24no—
261C8×C11—42no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C22×#41—112no—
265C22×M16—112no—
266C23×C8—112no—
267#532—228no—
268C2×C4⋊Q8—111no—
269C2×#127—111no—
270C2×#124—112no—
271C2×#121—112no—
272C2×#121—111no—
273C2×#121—111no—
274C2×C4×D4—111no—
275C2×C4×D4—112no—
276C2×C4×D4—111no—
277C22×C42C2×D1111yescharacteristic
278#435—228no—
279C2×C4⋊C8—112no—
280#408—228no—
281C2×C22⋊C8—112no—
282C2×C22⋊C8—112no—
283C2×C22⋊C8—112no—
284C2×C22⋊C8—112no—
285C2×C22⋊C8—112no—
286C2×C22⋊C8—112no—
287C2×C22⋊C8—112no—
288C2×C22⋊C8C2×D1111yescharacteristic
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×#97C2×D1112yes—
291#336—111no—
292#336—111no—
293#336C2×D1112yes—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11C2×C4×D411yescharacteristic
303C22×C11#51811yescharacteristic
304C22×C11C2×#13111yescharacteristic
305C22×C11#56811yescharacteristic
306C22×C11#56811yescharacteristic
307C22×C11#56811yescharacteristic
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—42no—
322C4×C11—22no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—22no—
326C4×C11—41no—
327C4×C11D4212yes—
328C4×C11#54612yes—
329Dic11—24no—
330Dic11—42no—
331C2×#41—224no—
332C2×#41—224no—
333C2×#41—224no—
334C2×#41—224no—
335C2×#41—442no—
336C2×#41—442no—
337C22×Q8—112no—
338C22×D4—112no—
339C22×D4—112no—
340C22×D4—111no—
341C22×D4—112no—
342C22×D4—112no—
343C22×D4—111no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4C4×D1111yescharacteristic
347C23×C4C4×D1111yescharacteristic
348C23×C4C22×D1111yescharacteristic
349C2×M16—224no—
350C2×M16—224no—
351C2×M16—442no—
352C22×C8—112no—
353C22×C8—112no—
354C22×C8—224no—
355C22×C8—224no—
356C22×C8—442no—
357C22×C8C22×D1112yes—
358C22×C8C22×D1112yes—
359C4⋊Q8—224no—
360#127—224no—
361#124—228no—
362#121—228no—
363#121—224no—
364#121—224no—
365C4×D4—118no—
366C4×D4—224no—
367C4×D4—224no—
368C4×D4—224no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—111no—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4—112no—
376C2×C42—24no—
377C2×C42C4×D1111yescharacteristic
378C2×C42C4×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—224no—
382C22⋊C8—22no—
383C22⋊C8—224no—
384C22⋊C8—224no—
385C22⋊C8—224no—
386C22⋊C8—224no—
387C22⋊C8—224no—
388C22⋊C8—442no—
389C22⋊C8—442no—
390C22⋊C8D4414yescomplemented
391#97—24no—
392C2×C11—42no—
393C2×C11D4×C22⋊C411yescharacteristic
394C2×C11#287911yescharacteristic
395C2×C11#288011yescharacteristic
396C2×C11#293211yescharacteristic
397C2×C11#293511yescharacteristic
398C2×C11#298011yescharacteristic
399C2×C11#298111yescharacteristic
400D11—44no—
401D11—82no—
402C24—112no—
403C24—112no—
404C24C2×C4×D1111yescharacteristic
405#41—448no—
406#41—448no—
407#41—448no—
408#41—448no—
409C2×Q8—224no—
410C2×Q8—224no—
411C2×Q8—442no—
412C2×D4—114no—
413C2×D4—224no—
414C2×D4—224no—
415C2×D4—224no—
416C2×D4—224no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—222no—
421C2×D4—224no—
422C2×D4—442no—
423C2×D4—441no—
424C2×D4—441no—
425C2×D4—442no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—442no—
429C2×D4—442no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—114no—
441C22×C4—112no—
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—222no—
451C22×C4—222no—
452C22×C4C2×C4×D1111yescharacteristic
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×D4412yes—
458C22×C4#433912yes—
459C22×C4C23×D1111yescharacteristic
460M16—448no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C2×C8—448no—
473C2×C8C2×D4414yes—
474C4⋊C4—114no—
475C4⋊C4—224no—
476C4⋊C4—222no—
477C22⋊C4—118no—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C42—22no—
482C42—22no—
483C42—22no—
484C42D4×D1114yes—
485C11#2240311yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—114no—
493C23—222no—
494C23—222no—
495C23—222no—
496C23—222no—
497C23—222no—
498C23—222no—
499C23—222no—
500C23—222no—
501C23—222no—
502C23—222no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23C4×D4412yes—
507C23C22×C4×D1111yescharacteristic
508Q8—448no—
509D4—444no—
510D4—448no—
511D4—448no—
512D4—444no—
513D4—448no—
514D4—448no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—44no—
529C2×C4—44no—
530C2×C4—114no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4C4×D4412yes—
545C2×C4C22⋊C4×D1112yes—
546C2×C4C22⋊C4×D1112yes—
547C2×C4#6696012yes—
548C2×C4C22×D4411yescharacteristic
549C2×C4C2×#433911yescharacteristic
550C2×C4C2×D4×D1112yes—
551C2×C4#6704212yes—
552C8—24no—
553C8—42no—
554C8—442no—
555C8—442no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—224no—
564C22—224no—
565C22—224no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—442no—
570C22—442no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22C2×C4×D4411yescharacteristic
578C22C2×C22⋊C4×D1111yescharacteristic
579C22#1062305211yescharacteristic
580C22C2×#6696011yescharacteristic
581C22#1062327611yescharacteristic
582C22#1062327611yescharacteristic
583C22#1062327611yescharacteristic
584C4—22no—
585C4—22no—
586C4—22no—
587C4—22no—
588C4—41no—
589C4—224no—
590C4—442no—
591C4D4×D4412yes—
592C4#1062308112yes—
593C2—42no—
594C2—444no—
595C2—882no—
596C2C22⋊C4×D4411yescharacteristic
597C2#1307705911yescharacteristic
598C2#1307706611yescharacteristic
599C2#1307733511yescharacteristic
600C2#1307736211yescharacteristic
601C2#1307768611yescharacteristic
602C2#1307769411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC2×#10623008C2
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22403
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. C2×#10622319C2semidirect
3. C2×#10622340C2semidirect
4. #13069414C2semidirect
5. #13068912C2semidirect
6. #13068907C2semidirect
7. #13068596C2semidirect
8. #13068527C2semidirect
9. C11×#1749C2semidirect
91. C11×C22⋊C8D4semidirect
193. #1749D11semidirect
390. C22⋊C8D44semidirect
485. C11#22403semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106223192
C2×#106223402
#130694142
#130689122
#130689072
#130685962
#130685272
C11×#17492
#2240311