Finite Group Databasebeta

← #14807446

Subgroups — #14807446

Order 2816.

1216 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622671C211yesmaximal, characteristic, complemented
2C2×#10622701C211yesmaximal, characteristic, complemented
3#13074366C211yesmaximal, characteristic, complemented
4#13069617C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069590C211yesmaximal, characteristic, complemented
7#13069428C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal, complemented
9#13068964C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C2×C11×#542C211yesmaximal, characteristic, complemented
12C11×#542—24no—
13C11×#542—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—21no—
16C2×C11×#124—21no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C22×#4325C2212yes—
26C22×#4323C2212yes—
27C2×#66983C2212yes—
28C2×#66927C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66896C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622701—24no—
33#10622671—24no—
34#10622604—21no—
35#10622604—21no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38#10622573—21no—
39#10622573—21no—
40#10622552C2212yes—
41#10622549C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—22no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8D414yescomplemented
59C11×#126—28no—
60C11×#124—28no—
61C11×#124—22no—
62C11×#124D414yescomplemented
63C11×#123—28no—
64C11×C22⋊Q8—28no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8—22no—
67C11×#121—22no—
68C11×#121—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×#4325—24no—
93C2×#4325—24no—
94C2×#4325—42no—
95C2×#4323—24no—
96C2×#4323—24no—
97C2×#4323—42no—
98#66983—42no—
99#66983—42no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×C4⋊Dic11C2312yes—
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2312yes—
106#66927—22no—
107#66927—22no—
108#66899—42no—
109#66896—42no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—24no—
113#66873—24no—
114#66873—24no—
115#66867—22no—
116C4×C11⋊C8—22no—
117#25614—111nomaximal, Sylow
118C24×C11—21no—
119C24×C11C2×D411yescharacteristic
120C23×D11—22no—
121C2×Q8×C11—24no—
122C2×Q8×C11—21no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—82no—
126C2×Q8×C11C2×D412yes—
127C2×D4×C11—24no—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—82no—
132C2×D4×C11C2×D412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—82no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—44no—
149C2×C22⋊D11—82no—
150C2×C22⋊D11—82no—
151C22×Dic11—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—42no—
159C2×D44—42no—
160C2×D44—82no—
161C2×D44—82no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C42×C11—24no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11C2×D412yes—
182C42×C11C2×D412yes—
183#4325—48no—
184#4323—48no—
185(C2×D11)⋊C4—44no—
186(C2×D11)⋊C4—82no—
187(C2×D11)⋊C4—82no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8#4114yes—
196C2×#542D1111yescharacteristic, complemented
197C2×#496—111no—
198C2×#486—111no—
199#2619—111no—
200#2000—112no—
201#1999—112no—
202#1993—111no—
203#1958—111no—
204#1880—112no—
205#1879—112no—
206#1750—111no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C22×D411yescharacteristic
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225Q8×C11—24no—
226Q8×C11—42no—
227Q8×C11—84no—
228D4×C11—24no—
229D4×C11—42no—
230D4×C11—84no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—84no—
250C2×C4×C11#12012yes—
251C2×C4×C11#12012yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4112yes—
255C2×C4×C11H(5,𝔽2)12yes—
256C22⋊D11—88no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260D44—42no—
261D44—42no—
262D44—42no—
263D44—42no—
264D44—84no—
265D44—84no—
266C11⋊C8—24no—
267C11⋊C8—42no—
268C22×SD16—112no—
269C22×D8—112no—
270#542—24no—
271#542—24no—
272C2×C4⋊Q8C2×D1111yescharacteristic
273C2×#127—111no—
274C2×#126—21no—
275C2×#124—21no—
276C2×#124C2×D1111yescharacteristic
277C2×#123—21no—
278C2×C22⋊Q8—21no—
279C2×C22⋊Q8C2×D1111yescharacteristic
280C2×#121—112no—
281C2×#121C2×D1111yescharacteristic
282C2×C4×Q8C2×D1111yescharacteristic
283C2×C4×D4C2×D1111yescharacteristic
284C2×#117C2×D1111yescharacteristic
285#496—224no—
286#486—224no—
287C2×#103—112no—
288C2×#102—112no—
289C2×#102—112no—
290C2×#102—112no—
291C2×C22⋊C8—112no—
292C2×#97—111no—
293C2×C4×C8—111no—
294#394—221no—
295#394—221no—
296#392—221no—
297#392—221no—
298#390—112no—
299#382—111no—
300#340—112no—
301#340—112no—
302#336—112no—
303C22×C11—42no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11C2×#12011yescharacteristic
314C22×C11#53211yescharacteristic
315C22×C11#53511yescharacteristic
316C22×C11#57612yes—
317C22×C11#57712yes—
318C2×D11—82no—
319C2×D11—82no—
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C4×C11—22no—
326C4×C11—22no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—42no—
332C4×C11—41no—
333C4×C11#54612yes—
334C4×C11#55012yes—
335Dic11—82no—
336C22×Q8—21no—
337C22×Q8C22×D1111yescharacteristic
338C22×D4—21no—
339C22×D4—112no—
340C22×D4—222no—
341C22×D4—221no—
342C22×D4—221no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—21no—
345C23×C4C22×D1111yescharacteristic
346C2×SD16—224no—
347C2×SD16—224no—
348C2×SD16—442no—
349C2×D8—224no—
350C2×D8—224no—
351C2×D8—442no—
352C22×C8—112no—
353C22×C8—112no—
354C4⋊Q8—22no—
355C4⋊Q8C22⋊D1114yescomplemented
356#127—222no—
357#127—222no—
358#126—28no—
359#124—28no—
360#124—22no—
361#124C22⋊D1114yescomplemented
362#123—28no—
363C22⋊Q8—28no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366#121—22no—
367#121—22no—
368#121—442no—
369#121—442no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×D4—22no—
373C4×D4—22no—
374#117—22no—
375#117—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—222no—
392C2×C22⋊C4C22⋊D1111yescharacteristic
393C2×C22⋊C4C22⋊D1111yescharacteristic
394C2×C42—21no—
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397#103—442no—
398#102—224no—
399#102—224no—
400#102—442no—
401C22⋊C8—224no—
402#97—222no—
403C4×C8—222no—
404#95—221no—
405#95—221no—
406C2×C11—81no—
407C2×C11—82no—
408C2×C11#243111yescharacteristic
409C2×C11#300811yescharacteristic
410C2×C11#301011yescharacteristic
411C2×C11#317912yes—
412C2×C11#322412yes—
413D11—162no—
414C24—21no—
415C24—222no—
416C24C2×C22⋊D1111yescharacteristic
417C2×Q8—24no—
418C2×Q8—21no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—82no—
422C2×Q8C2×C22⋊D1112yes—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—82no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—444no—
435C2×D4—442no—
436C2×D4—442no—
437C2×D4—882no—
438C2×D4—882no—
439C2×D4—882no—
440C2×D4—882no—
441C2×D4C2×C22⋊D1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—82no—
451C22×C4—222no—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458SD16—448no—
459D8—448no—
460C2×C8—114no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4C2×C22⋊D1112yes—
476C4⋊C4C2×C22⋊D1112yes—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—444no—
485C22⋊C4—882no—
486C22⋊C4—882no—
487C42—24no—
488C42—21no—
489C42—21no—
490C42C2×C22⋊D1112yes—
491C42C2×C22⋊D1112yes—
492C11#2561411yescharacteristic, complemented, Sylow
493C23—21no—
494C23—21no—
495C23—22no—
496C23—22no—
497C23—21no—
498C23—22no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—42no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23C22×C22⋊D1111yescharacteristic
511Q8—24no—
512Q8—42no—
513Q8—84no—
514D4—24no—
515D4—42no—
516D4—84no—
517D4—442no—
518D4—442no—
519D4—442no—
520D4—442no—
521D4—884no—
522D4—884no—
523D4—888no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—84no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4#6700612yes—
547C2×C4#6700612yes—
548C2×C4#41×D1112yes—
549C2×C4#6704212yes—
550C2×C4C22×C22⋊D1111yescharacteristic
551C2×C4C22×C22⋊D1111yescharacteristic
552C8—224no—
553C8—442no—
554C22—41no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—82no—
563C22—82no—
564C22—882no—
565C22—882no—
566C22—882no—
567C22—882no—
568C22—882no—
569C22—882no—
570C22—882no—
571C22#1062336111yescharacteristic
572C22#1062336311yescharacteristic
573C22#1062336612yes—
574C22#1062336812yes—
575C22C2×#6700611yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—41no—
584C4—882no—
585C4#1062336012yes—
586C4#1062336512yes—
587C2—81no—
588C2—82no—
589C2—1762no—
590C2#1307223111yescharacteristic
591C2#1307788411yescharacteristic
592C2#1307790211yescharacteristic
593C2#1307929312yes—
594C2#1307970412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
hypercenterC2×#542D11
hypocenterC11#25614
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10622671C2semidirect
2. C2×#10622701C2semidirect
3. #13074366C2semidirect
4. #13069617C2semidirect
5. #13069612C2semidirect
6. #13069590C2semidirect
7. #13069428C2semidirect
8. #13068971C2semidirect
9. #13068964C2semidirect
10. #13068382C2semidirect
11. C2×C11×#542C2semidirect
58. C11×C4⋊Q8D4semidirect
62. C11×#124D4semidirect
196. C2×#542D11semidirect
355. C4⋊Q8C22⋊D11semidirect
361. #124C22⋊D11semidirect
492. C11#25614semidirect

Maximal subgroups

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

subgroupindex
C2×#106226712
C2×#106227012
#130743662
#130696172
#130696122
#130695902
#130694282
#130689712
#130689642
#130683822
C2×C11×#5422
#2561411