Finite Group Databasebeta

← #14788548

Subgroups — #14788548

Order 2816.

1394 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×#10622688C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic, complemented
3#13073986C211yesmaximal, characteristic, complemented
4#13069847C212yesmaximal, complemented
5#13069704C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13068950C212yesmaximal, complemented
9#13068877C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic
12C22×C11×#41—21no—
13C11×#550—24no—
14C11×#550—24no—
15C2×C11×#127C2212yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4324C2212yes—
24C2×C4×Dic22C2211yescharacteristic
25#10622843—21no—
26C2×#66896C2211yescharacteristic
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622688—24no—
32C4×#4324—24no—
33#10622597—22no—
34#10622586—21no—
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622548C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C2×C11×#41—28no—
46C2×C11×#41—44no—
47C2×C11×#41—44no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—22no—
56C23×C4×C11—21no—
57C22×Dic22C2311yescharacteristic
58C11×#127—24no—
59C11×#127—24no—
60C11×#127—22no—
61C11×#127D414yes—
62C11×#121—28no—
63C11×#121—216no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C4×D4×C11—22no—
69C4×D4×C11D414yes—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D412yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2312yes—
76C2×C42×C11C2311yescharacteristic
77C2×#4324—22no—
78C2×#4324—22no—
79C2×#4324—24no—
80C2×#4324—24no—
81C2×#4324—22no—
82C2×#4324—42no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—22no—
89C2×C4×Dic11—21no—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2311yescharacteristic
93C4×Dic22—22no—
94C4×Dic22—22no—
95#66896—22no—
96#66896—24no—
97#66896—24no—
98#66896—42no—
99#66896—42no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103#66874—22no—
104#66872—22no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#24188—111nomaximal, Sylow
108C24×C11—22no—
109C24×C11—21no—
110C11×#41—432no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11SD1614yescomplemented
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—44no—
129C2×D4×C11—44no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11—81no—
133C2×D4×C11—81no—
134C2×D4×C11—82no—
135C2×D4×C11—82no—
136C2×D4×C11C2×D414yes—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—28no—
139C22×C4×C11—21no—
140C22×C4×C11—24no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22#4112yescomplemented
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—24no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11C2×D412yes—
168C42×C11C2×D412yes—
169#4324—28no—
170#4324—48no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4⋊Dic11—81no—
177Dic11⋊C4—42no—
178Dic11⋊C4—82no—
179C4×Dic11—42no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8#4112yescomplemented
189C2×#550D1111yescharacteristic
190C2×#460—111no—
191C2×C4×SD16—111no—
192#2582—111no—
193#2041—112no—
194#2014—112no—
195#1984—111no—
196#1957—111no—
197#1877—112no—
198#1864—112no—
199#1802—111no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—41no—
210C23×C11—42no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215Q8×C11—28no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—416no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—48no—
226D4×C11—84no—
227D4×C11—88no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—416no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—48no—
240C2×C4×C11#12012yes—
241C2×C4×C11#12012yes—
242C2×C4×C11C2×SD1614yes—
243C2×C4×C11C2×SD1612yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×Dic11—22no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—41no—
260Dic22—22no—
261Dic22—22no—
262Dic22—41no—
263Dic22—41no—
264C11⋊C8—22no—
265C11⋊C8—41no—
266C11⋊C8—42no—
267C22×#41—21no—
268C22×SD16—111no—
269C22×SD16—112no—
270#550—24no—
271#550—24no—
272C2×#127C2×D1112yes—
273C2×#127C2×D1111yescharacteristic
274C2×#121—21no—
275C2×#121—22no—
276C2×C4×Q8—111no—
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4C2×D1112yes—
279C2×C4×D4C2×D1111yescharacteristic
280#460—224no—
281C4×SD16—224no—
282C2×#106—111no—
283C2×C4⋊C8—111no—
284C2×#103—111no—
285C2×#102—112no—
286C2×#102—112no—
287C2×#102—111no—
288C2×#102—112no—
289C2×#102—112no—
290C2×C4×C8—111no—
291#398—222no—
292#391—112no—
293#391—221no—
294#389—112no—
295#389—221no—
296#384—111no—
297#340—112no—
298#336—112no—
299#336—112no—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—81no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—81no—
310C22×C11—82no—
311C22×C11—81no—
312C22×C11—82no—
313C22×C11—81no—
314C22×C11C2×#12011yescharacteristic
315C22×C11#54811yescharacteristic
316C22×C11#55011yescharacteristic
317C22×C11C22×SD1611yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57711yescharacteristic
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11#45014yes—
326C4×C11#52511yescharacteristic
327C4×C11#53711yescharacteristic
328C4×C11#54611yescharacteristic
329C4×C11#54711yescharacteristic
330Dic11—42no—
331Dic11—82no—
332Dic11—81no—
333C2×#41—28no—
334C2×#41—44no—
335C2×#41—44no—
336C22×Q8—111no—
337C22×Q8C22⋊D1111yescharacteristic
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4C22×D1112yes—
343C22×D4C22×D1111yescharacteristic
344C23×C4—22no—
345C23×C4—21no—
346C2×SD16—222no—
347C2×SD16—222no—
348C2×SD16—222no—
349C2×SD16—224no—
350C2×SD16—224no—
351C2×SD16—442no—
352C22×C8—111no—
353C22×C8—112no—
354C22×C8—111no—
355#127—24no—
356#127—24no—
357#127—22no—
358#127C22⋊D1114yes—
359#121—28no—
360#121—216no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—222no—
364C4×Q8—222no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—22no—
368C4×D4C22⋊D1114yes—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4C22⋊D1111yescharacteristic
376C2×C4⋊C4C22⋊D1112yes—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C42—221no—
381C2×C42C22×D1112yes—
382C2×C42C22×D1111yescharacteristic
383#106—222no—
384C4⋊C8—222no—
385#103—222no—
386#102—224no—
387#102—222no—
388#102—224no—
389#102—442no—
390#102—442no—
391C4×C8—222no—
392#95—222no—
393#95—222no—
394#95—222no—
395C2×C11—82no—
396C2×C11—84no—
397C2×C11#240711yescharacteristic
398C2×C11C2×#45011yescharacteristic
399C2×C11#301211yescharacteristic
400C2×C11#336211yescharacteristic
401C2×C11#336811yescharacteristic
402C2×C11#339211yescharacteristic
403C2×C11#339911yescharacteristic
404C24—22no—
405C24—21no—
406#41—432no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—112no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×Q8—221no—
413C2×Q8—221no—
414C2×Q8—221no—
415C2×Q8#432414yescomplemented
416C2×D4—28no—
417C2×D4—28no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—22no—
430C2×D4—44no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—81no—
435C2×D4—81no—
436C2×D4—82no—
437C2×D4—82no—
438C2×D4C2×C22⋊D1114yes—
439C2×D4C2×C22⋊D1112yes—
440C22×C4—28no—
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—44no—
444C22×C4—42no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—221no—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455SD16—228no—
456SD16—448no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—222no—
461C2×C8—221no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—222no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4—882no—
476C4⋊C4—881no—
477C4⋊C4C2×C22⋊D1112yes—
478C22⋊C4—28no—
479C22⋊C4—24no—
480C42—22no—
481C42—22no—
482C42—442no—
483C42C2×C22⋊D1112yes—
484C42C2×C22⋊D1112yes—
485C11#2418811yescharacteristic, complemented, Sylow
486C23—24no—
487C23—22no—
488C23—42no—
489C23—41no—
490C23—42no—
491C23—41no—
492C23—42no—
493C23—41no—
494C23—42no—
495C23—41no—
496C23—42no—
497C23—41no—
498C23—42no—
499C23—41no—
500C23C22×C22⋊D1111yescharacteristic
501Q8—28no—
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506D4—24no—
507D4—22no—
508D4—24no—
509D4—22no—
510D4—416no—
511D4—48no—
512D4—41no—
513D4—42no—
514D4—41no—
515D4—42no—
516D4—84no—
517D4—88no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—416no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—222no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4#6698512yes—
540C2×C4C2×#432414yes—
541C2×C4C2×#432412yes—
542C2×C4#6700612yes—
543C2×C4#6700612yes—
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#6704211yescharacteristic
547C2×C4#6704311yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C8—222no—
551C8—442no—
552C8—441no—
553C22—44no—
554C22—42no—
555C22—44no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—82no—
560C22—81no—
561C22—82no—
562C22—81no—
563C22—82no—
564C22—81no—
565C22—82no—
566C22—81no—
567C22C2×#6698511yescharacteristic
568C22C22×#432411yescharacteristic
569C22#1062336211yescharacteristic
570C22#1062336511yescharacteristic
571C22#1062336611yescharacteristic
572C22#1062336711yescharacteristic
573C22C2×#6700611yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—442no—
579C4—882no—
580C4—881no—
581C4#1062283114yes—
582C4#1062335511yescharacteristic
583C4#1062335911yescharacteristic
584C4#1062336011yescharacteristic
585C4#1062336411yescharacteristic
586C2—84no—
587C2—82no—
588C2#1307195511yescharacteristic
589C2C2×#1062283111yescharacteristic
590C2#1307792011yescharacteristic
591C2#1308128311yescharacteristic
592C2#1308134111yescharacteristic
593C2#1308159711yescharacteristic
594C2#1308165811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11#24188
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10622688C2semidirect
2. C2×C4×#4324C2semidirect
3. #13073986C2semidirect
4. #13069847C2semidirect
5. #13069704C2semidirect
6. #13069553C2semidirect
7. #13069423C2semidirect
8. #13068950C2semidirect
9. #13068877C2semidirect
10. #13068616C2semidirect
113. C2×Q8×C11SD16semidirect
158. C2×Dic22#41semidirect
188. C2×C11⋊C8#41semidirect
415. C2×Q8#4324semidirect
485. C11#24188semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
C2×C4×#43242
#130739862
#130698472
#130697042
#130695532
#130694232
#130689502
#130688772
#130686162
C2×C11×#5502
#2418811