Finite Group Databasebeta

← #14787677

Subgroups — #14787677

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic, complemented
4#13069803C212yesmaximal, complemented
5#13069611C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069410C211yesmaximal, characteristic, complemented
8#13068935C212yesmaximal, complemented
9#13068812C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66991C2212yes—
16C2×#66991C2212yes—
17C2×#66983—21no—
18C2×#66983—21no—
19C2×#66979—21no—
20#10623094—24no—
21#10623094—24no—
22C2×#66945C2212yes—
23C2×#66938—22no—
24C2×C4×D44C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C4×C11×D8—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825—21no—
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yes—
36#10622621—24no—
37#10622600C2212yes—
38C2×#66872C2212yes—
39#10622574—22no—
40#10622548C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—22no—
51C22×D44D411yescharacteristic
52C22×C4×D11C2312yes—
53C22×Dic22—21no—
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11D414yescomplemented
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70#66991—24no—
71#66991—24no—
72#66991—24no—
73#66991—42no—
74#66983—28no—
75#66983—44no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4D412yes—
79#66979—28no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2312yes—
86C2×C4×Dic11—22no—
87C22×C11⋊C8C2312yes—
88#66945—24no—
89#66945—24no—
90#66938—216no—
91C4×D44—22no—
92C4×D44—22no—
93#66922—22no—
94#66922D414yescomplemented
95C11×#107—22no—
96C11×#102—22no—
97C11×#102—22no—
98C4×C8×C11—22no—
99#66896—24no—
100#66896—42no—
101C11⋊#95—22no—
102(C2×D11)⋊C8—24no—
103(C2×D11)⋊C8—42no—
104#66872—24no—
105C4⋊(C11⋊C8)—22no—
106#24117—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C23×D11C2×D412yes—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11C2×D412yes—
121C2×D4×C11#4112yes—
122C22×C4×C11—21no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—28no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—82no—
137C2×C22⋊D11—82no—
138C2×C22⋊D11—82no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11C2×D412yes—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
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×Dic22—24no—
152C2×Dic22—81no—
153C2×Dic22—81no—
154C11×D8—28no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11#4112yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—42no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169C22⋊Dic11—28no—
170C22⋊Dic11—44no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—44no—
174C4⋊Dic11—24no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11C2×D414yes—
182C4×Dic11—28no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×#555—111no—
187C2×#476—111no—
188C2×C4×D8D1111yescharacteristic, complemented
189#2537—111no—
190#2034—112no—
191#1999—112no—
192#1990—111no—
193#1954—111no—
194#1875—112no—
195#1854—112no—
196#1802—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—48no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—84no—
237C2×C4×C11#12012yes—
238C2×C4×C11#12012yes—
239C2×C4×C11#13512yes—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C22⋊D11—88no—
248C22⋊D11—88no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258D44—44no—
259C4×D11—42no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—42no—
263Dic22—84no—
264C8×C11—22no—
265C8×C11—41no—
266C11⋊C8—42no—
267C22×D8C2×D1111yescharacteristic
268#555—224no—
269#555—224no—
270C2×C4⋊Q8—111no—
271C2×#124—222no—
272C2×#121—112no—
273C2×#121—112no—
274C2×#121—221no—
275C2×#121—221no—
276C2×C4×D4—111no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×C4×D4C2×D1111yescharacteristic
279C2×#117—112no—
280C2×#117—221no—
281#476—224no—
282C4×D8—24no—
283C2×#107C2×D1111yescharacteristic
284C2×#106—112no—
285C2×C4⋊C8—111no—
286C2×#102—112no—
287C2×#102—112no—
288C2×#102C2×D1111yescharacteristic
289C2×#102C2×D1111yescharacteristic
290C2×C22⋊C8—112no—
291C2×C22⋊C8—112no—
292C2×C4×C8C2×D1111yescharacteristic
293#394—222no—
294#384—111no—
295#380—112no—
296#380—221no—
297#340—112no—
298#340—112no—
299#340—112no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C2×#12011yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11#54711yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57711yescharacteristic
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11#44914yes—
332C4×C11#52511yescharacteristic
333C4×C11#53711yescharacteristic
334C4×C11#54811yescharacteristic
335C4×C11#55011yescharacteristic
336Dic11—42no—
337Dic11—44no—
338Dic11—82no—
339C22×Q8—221no—
340C22×D4—111no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4C22×D1111yescharacteristic
344C22×D4C22×D1111yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—112no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—22no—
351C22×C8—112no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C4⋊Q8—114no—
355C4⋊Q8—222no—
356#124—2216no—
357#121—224no—
358#121—228no—
359#121—224no—
360#121—224no—
361#121—442no—
362#121—444no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—222no—
367C4×D4—222no—
368C4×D4C22⋊D1114yescomplemented
369#117—224no—
370#117—228no—
371#117—224no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—112no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C42—222no—
388C2×C42C22×D1111yescharacteristic
389#107—22no—
390#106—224no—
391C4⋊C8—222no—
392#102—22no—
393#102—22no—
394#102—224no—
395#102—442no—
396C22⋊C8—224no—
397C22⋊C8—442no—
398C4×C8—22no—
399#95—222no—
400C2×C11—82no—
401C2×C11—82no—
402C2×C11#240711yescharacteristic
403C2×C11C2×#44911yescharacteristic
404C2×C11#301211yescharacteristic
405C2×C11#330311yescharacteristic
406C2×C11#332511yescharacteristic
407C2×C11#334111yescharacteristic
408C2×C11#335411yescharacteristic
409D11—82no—
410C24—21no—
411C24—21no—
412C24—112no—
413C2×Q8—224no—
414C2×Q8—881no—
415C2×Q8—881no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—228no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—444no—
431C2×D4—444no—
432C2×D4—882no—
433C2×D4—882no—
434C2×D4—882no—
435C2×D4#433912yes—
436C2×D4C2×C22⋊D1112yes—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—112no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4D4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457D8—28no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8#433912yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—114no—
471C4⋊C4—222no—
472C4⋊C4—224no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—442no—
477C4⋊C4—881no—
478C4⋊C4C2×C22⋊D1112yes—
479C22⋊C4—24no—
480C22⋊C4—42no—
481C22⋊C4—228no—
482C22⋊C4—228no—
483C22⋊C4—224no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C42—228no—
487C42D4×D1112yes—
488C42C2×C22⋊D1112yes—
489C11#2411711yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—222no—
510C23—222no—
511C23C2×D4×D1111yescharacteristic
512Q8—884no—
513D4—22no—
514D4—22no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—444no—
522D4—888no—
523D4—888no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—222no—
537C2×C4—222no—
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#6696412yes—
548C2×C4#6696512yes—
549C2×C4#6699012yes—
550C2×C4#6699012yes—
551C2×C4C2×#433911yescharacteristic
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4#6704211yescharacteristic
555C2×C4#6704311yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—22no—
558C8—41no—
559C8—442no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22#1062308111yescharacteristic
582C22#1062308211yescharacteristic
583C22C2×#6696411yescharacteristic
584C22C2×#6696511yescharacteristic
585C22#1062330011yescharacteristic
586C22#1062330111yescharacteristic
587C22C2×#6699011yescharacteristic
588C4—22no—
589C4—42no—
590C4—81no—
591C4—442no—
592C4—444no—
593C4—882no—
594C4#1062277114yes—
595C4#1062308311yescharacteristic
596C4#1062308411yescharacteristic
597C4#1062332211yescharacteristic
598C4#1062336411yescharacteristic
599C2—82no—
600C2—82no—
601C2—882no—
602C2#1307196111yescharacteristic
603C2C2×#1062277111yescharacteristic
604C2#1307791611yescharacteristic
605C2#1308054611yescharacteristic
606C2#1308086011yescharacteristic
607C2#1308104011yescharacteristic
608C2#1308121311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
hypercenterC2×C4×D8D11
hypocenterC11#24117
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. C2×#10622621C2semidirect
3. #13073529C2semidirect
4. #13069803C2semidirect
5. #13069611C2semidirect
6. #13069577C2semidirect
7. #13069410C2semidirect
8. #13068935C2semidirect
9. #13068812C2semidirect
10. #13068616C2semidirect
11. C2×C4×C11×D8C2semidirect
62. C4×D4×C11D4semidirect
94. #66922D4semidirect
188. C2×C4×D8D11semidirect
368. C4×D4C22⋊D11semidirect
489. C11#24117semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106226212
#130735292
#130698032
#130696112
#130695772
#130694102
#130689352
#130688122
#130686162
C2×C4×C11×D82
#2411711