Finite Group Databasebeta

← #14788556

Subgroups — #14788556

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×#10623108C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13069850C212yesmaximal, complemented
5#13069703C212yesmaximal, complemented
6#13069553C211yesmaximal, characteristic, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13068953C212yesmaximal, complemented
9#13068876C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2582C211yesmaximal, characteristic, complemented
12C22×#4343—21no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×#4325C2211yescharacteristic
16C22×#4325C2212yes—
17#10623108—24no—
18#10623108—24no—
19C2×#66948—21no—
20C2×#66948—22no—
21C2×#66927C2212yes—
22C2×#66927C2211yescharacteristic
23C2×C4×D44C2212yes—
24C2×C4×D44C2211yescharacteristic
25C11×#398—22no—
26C11×#391—21no—
27C11×#391C2212yes—
28C11×#389—21no—
29C11×#389C2212yes—
30C11×#384C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622640—24no—
33C4×#4325—24no—
34C2×#66873C2211yescharacteristic
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66872C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C2×#4343—28no—
48C2×#4343—44no—
49C2×#4343—44no—
50C22×D44—22no—
51C22×D44—21no—
52C22×D44—22no—
53C22×D44—21no—
54C22×D44C2312yes—
55C22×D44C2311yescharacteristic
56C22×C4×D11—22no—
57C22×C4×D11—21no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C42×C11—21no—
71C2×C42×C11C2312yes—
72C2×C42×C11C2311yescharacteristic
73C2×#4325—22no—
74C2×#4325—22no—
75C2×#4325—24no—
76C2×#4325—24no—
77C2×#4325—22no—
78C2×#4325—42no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C22×C11⋊C8C2311yescharacteristic
85#66948—28no—
86#66948—216no—
87#66927—24no—
88#66927—24no—
89#66927—22no—
90#66927D414yes—
91C4×D44—24no—
92C4×D44—22no—
93C4×D44—24no—
94C4×D44D414yes—
95C11×#95—22no—
96C11×#95—22no—
97C11×#95—22no—
98#66899—22no—
99#66873—22no—
100#66873—24no—
101#66873—24no—
102#66873—42no—
103#66873—42no—
104#66872—22no—
105C4⋊(C11⋊C8)—22no—
106C4×C11⋊C8—22no—
107#24188—111nomaximal, Sylow
108C23×D11—22no—
109C23×D11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11SD1614yescomplemented
118C2×Q8×C11#4112yescomplemented
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128#4343—432no—
129C2×D44—28no—
130C2×D44—28no—
131C2×D44—24no—
132C2×D44—24no—
133C2×D44—22no—
134C2×D44—21no—
135C2×D44—22no—
136C2×D44—21no—
137C2×D44—22no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—22no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—44no—
144C2×D44—44no—
145C2×D44—42no—
146C2×D44—42no—
147C2×D44—81no—
148C2×D44—81no—
149C2×D44—82no—
150C2×D44—82no—
151C2×D44C2×D414yes—
152C2×D44C2×D412yes—
153C2×C4×D11—28no—
154C2×C4×D11—24no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4—82no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—42no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174#4325—28no—
175#4325—48no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—24no—
178C4⋊Dic11—21no—
179C4⋊Dic11C2×D412yes—
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×#550—111no—
190C2×#460—111no—
191C2×C4×SD16—111no—
192#2582D1111yescharacteristic, complemented
193#2041—112no—
194#2014—112no—
195#1984—111no—
196#1957—111no—
197#1877—112no—
198#1864—112no—
199#1802—111no—
200C23×C11C22×D411yescharacteristic
201C22×D11—24no—
202C22×D11—22no—
203C22×D11—41no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—41no—
207C22×D11—42no—
208C22×D11—41no—
209C22×D11—42no—
210C22×D11—41no—
211C22×D11—42no—
212C22×D11—41no—
213C22×D11—42no—
214C22×D11—41no—
215Q8×C11—28no—
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11#12012yes—
237C2×C4×C11#12012yes—
238C2×C4×C11C2×SD1614yes—
239C2×C4×C11C2×SD1612yes—
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
247C2×Dic11—22no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250D44—22no—
251D44—22no—
252D44—24no—
253D44—24no—
254D44—416no—
255D44—42no—
256D44—42no—
257D44—41no—
258D44—41no—
259D44—48no—
260D44—84no—
261D44—88no—
262C4×D11—416no—
263C4×D11—48no—
264C11⋊C8—22no—
265C11⋊C8—41no—
266C11⋊C8—42no—
267C22×#41—221no—
268C22×SD16—111no—
269C22×SD16—112no—
270#550—224no—
271#550—224no—
272C2×#127—111no—
273C2×#127—112no—
274C2×#121—221no—
275C2×#121—222no—
276C2×C4×Q8C2×D1111yescharacteristic
277C2×C4×Q8C2×D1111yescharacteristic
278C2×C4×D4—111no—
279C2×C4×D4—112no—
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—22no—
292#391—21no—
293#391C2×D1112yes—
294#389—21no—
295#389C2×D1112yes—
296#384C2×D1111yescharacteristic
297#340—112no—
298#336—112no—
299#336—112no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#54811yescharacteristic
302C22×C11#55011yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11#57611yescharacteristic
306C22×C11#57711yescharacteristic
307C2×D11—42no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—42no—
311C2×D11—44no—
312C2×D11—42no—
313C2×D11—81no—
314C2×D11—82no—
315C2×D11—82no—
316C2×D11—81no—
317C2×D11—82no—
318C2×D11—81no—
319C2×D11—82no—
320C2×D11—81no—
321C4×C11—24no—
322C4×C11—22no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—82no—
326C4×C11—81no—
327C4×C11#45014yes—
328C4×C11#52511yescharacteristic
329C4×C11#53711yescharacteristic
330C4×C11#54611yescharacteristic
331C4×C11#54711yescharacteristic
332Dic11—42no—
333C2×#41—228no—
334C2×#41—444no—
335C2×#41—444no—
336C22×Q8C22⋊D1111yescharacteristic
337C22×Q8C22×D1111yescharacteristic
338C22×D4—111no—
339C22×D4—112no—
340C22×D4—222no—
341C22×D4—221no—
342C22×D4—222no—
343C22×D4—221no—
344C23×C4—222no—
345C23×C4—221no—
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—114no—
356#127—224no—
357#127—224no—
358#127—222no—
359#121—228no—
360#121—2216no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—114no—
366C4×D4—224no—
367C4×D4—224no—
368C4×D4—222no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4C22⋊D1111yescharacteristic
375C2×C4⋊C4C22⋊D1112yes—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—222no—
379C2×C22⋊C4—221no—
380C2×C42—21no—
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—22no—
393#95—22no—
394#95—22no—
395C2×C11#240711yescharacteristic
396C2×C11C2×#45011yescharacteristic
397C2×C11#301211yescharacteristic
398C2×C11#336211yescharacteristic
399C2×C11#336811yescharacteristic
400C2×C11#339211yescharacteristic
401C2×C11#339911yescharacteristic
402D11—82no—
403D11—84no—
404C24—222no—
405C24—221no—
406#41—4432no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8#432514yescomplemented
415C2×Q8#434312yescomplemented
416C2×D4—112no—
417C2×D4—114no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—224no—
421C2×D4—224no—
422C2×D4—222no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—222no—
426C2×D4—221no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—222no—
432C2×D4—444no—
433C2×D4—444no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4—881no—
437C2×D4—881no—
438C2×D4—882no—
439C2×D4—882no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—228no—
444C22×C4—221no—
445C22×C4—224no—
446C22×C4—444no—
447C22×C4—444no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455SD16—228no—
456SD16—448no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—222no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—82no—
476C4⋊C4—112no—
477C4⋊C4—221no—
478C22⋊C4—228no—
479C22⋊C4—224no—
480C42—22no—
481C42—22no—
482C42—42no—
483C42D4×D1112yes—
484C42D4×D1112yes—
485C11#2418811yescharacteristic, complemented, Sylow
486C23—224no—
487C23—222no—
488C23—442no—
489C23—441no—
490C23—441no—
491C23—442no—
492C23—442no—
493C23—441no—
494C23—442no—
495C23—441no—
496C23—442no—
497C23—441no—
498C23—442no—
499C23—441no—
500C23C22×C22⋊D1111yescharacteristic
501Q8—28no—
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—222no—
507D4—222no—
508D4—224no—
509D4—224no—
510D4—4416no—
511D4—442no—
512D4—442no—
513D4—441no—
514D4—441no—
515D4—448no—
516D4—884no—
517D4—888no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—222no—
535C2×C4—4416no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—448no—
539C2×C4#6699012yes—
540C2×C4#6699012yes—
541C2×C4C2×#432514yes—
542C2×C4C2×#432512yes—
543C2×C4#6700212yes—
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×D4×D1111yescharacteristic
546C2×C4C2×#434311yescharacteristic
547C2×C4#6704011yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704211yescharacteristic
550C8—222no—
551C8—441no—
552C8—442no—
553C22—444no—
554C22—442no—
555C22—442no—
556C22—444no—
557C22—444no—
558C22—442no—
559C22—882no—
560C22—881no—
561C22—882no—
562C22—881no—
563C22—882no—
564C22—881no—
565C22—882no—
566C22—881no—
567C22C2×#6699011yescharacteristic
568C22C22×#432511yescharacteristic
569C22#1062334811yescharacteristic
570C22C2×#6700211yescharacteristic
571C22#1062336511yescharacteristic
572C22#1062336611yescharacteristic
573C22#1062336811yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—81no—
580C4—442no—
581C4#1062265914yes—
582C4#1062315811yescharacteristic
583C4#1062316011yescharacteristic
584C4#1062316111yescharacteristic
585C4#1062316211yescharacteristic
586C2—884no—
587C2—882no—
588C2#1307196311yescharacteristic
589C2C2×#1062265911yescharacteristic
590C2#1307791711yescharacteristic
591C2#1308128711yescharacteristic
592C2#1308134511yescharacteristic
593C2#1308159311yescharacteristic
594C2#1308165411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2582C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
hypercenter#2582D11
hypocenterC11#24188
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2582

Complements

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

NH ≅ G/Ntype
2. C2×#10622640C2semidirect
3. C2×C4×#4325C2semidirect
4. #13069850C2semidirect
5. #13069703C2semidirect
6. #13069553C2semidirect
7. #13069421C2semidirect
8. #13068953C2semidirect
9. #13068876C2semidirect
10. #13068613C2semidirect
11. C11×#2582C2semidirect
117. C2×Q8×C11SD16semidirect
118. C2×Q8×C11#41semidirect
188. C2×C11⋊C8#41semidirect
192. #2582D11semidirect
414. C2×Q8#4325semidirect
415. C2×Q8#4343semidirect
485. C11#24188semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×#106226402
C2×C4×#43252
#130698502
#130697032
#130695532
#130694212
#130689532
#130688762
#130686132
C11×#25822
#2418811