Finite Group Databasebeta

← #14757438

Subgroups — #14757438

Order 2816.

1726 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623199C211yesmaximal, characteristic
2C2×#10622416C212yesmaximal, complemented
3C2×#10622384C212yesmaximal, complemented
4C2×#10622320C211yesmaximal, characteristic, complemented
5D11×#384C211yesmaximal, characteristic, complemented
6#13069433C211yesmaximal, characteristic, complemented
7#13069432C211yesmaximal, characteristic, complemented
8#13069430C211yesmaximal, characteristic, complemented
9#13069420C212yesmaximal, complemented
10#13069416C212yesmaximal, complemented
11C11×#1959C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C22×#4341C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×#66997C2211yescharacteristic
16C2×#66993C2211yescharacteristic
17C22×#4313C2212yes—
18#10623199—24no—
19#10623199C418yescomplemented
20C2×C4⋊C4×D11—22no—
21C2×C4⋊C4×D11C2212yes—
22C2×#66937—22no—
23C2×(C22⋊D11)⋊C4—22no—
24C2×#66928C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#102C2212yes—
28C2×C11×#97C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×#66885C2212yes—
33C2×#66880C2212yes—
34C2×C8×Dic11C2212yes—
35#10622589—22no—
36#10622589C2212yes—
37C2×#66874C2212yes—
38C2×#66873C2212yes—
39#10622548C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41#10622416—28no—
42#10622384—28no—
43#10622320—24no—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C22×C22⋊D11—22no—
48C23×Dic11—21no—
49C2×#4343—22no—
50C2×#4343—24no—
51C2×#4343—24no—
52C2×#4343C2×C414yes—
53C2×#4341—24no—
54C2×#4341—22no—
55C2×#4341—24no—
56C2×#4341C2×C414yes—
57C22×D44—21no—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—22no—
61C22×C4×D11D412yes—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2312yes—
65C11×#124—22no—
66C11×#124C2×C414yescomplemented
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—22no—
70C2×C42×C11C2311yescharacteristic
71#66997—22no—
72#66997C2×C414yescomplemented
73#66993—22no—
74#66993C2×C414yescomplemented
75C2×(C2×D11)⋊C4—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11C2312yes—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11D412yes—
82C2×C4×Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C2×#4313—24no—
85C2×#4313—24no—
86C2×#4313D418yescomplemented
87C4⋊C4×D11—24no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—48no—
90#66937—216no—
91(C22⋊D11)⋊C4—216no—
92#66928—22no—
93#66928C2×C414yescomplemented
94C42×D11C2×C414yes—
95C42×D11D414yes—
96C11×#103—24no—
97C11×#102—24no—
98C11×#97—22no—
99#66899—24no—
100#66896—24no—
101#66885—24no—
102#66880—24no—
103C8×Dic11—24no—
104#66874—24no—
105#66873—24no—
106#66867—22no—
107#21200—111nomaximal, Sylow
108C24×C11—21no—
109C23×D11—21no—
110C23×D11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11C22×C412yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—28no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—44no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—42no—
128C2×C22⋊D11—42no—
129C22×Dic11—24no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D412yes—
136#4343—216no—
137#4343—48no—
138#4341—216no—
139#4341—48no—
140C2×D44—24no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—42no—
145C2×D44—42no—
146C2×D44C22×C412yes—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—48no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—44no—
154C2×C4×D11C22⋊C418yes—
155C2×C4×D11C22×C412yes—
156C2×C4×D11C2×D412yes—
157C2×C4×D11C2×D414yes—
158C2×C4×D11#4114yes—
159C2×Dic22—22no—
160C2×Dic22—21no—
161C2×Dic22—22no—
162C2×Dic22C22×C412yes—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11C2×D414yes—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—44no—
169C11×C22⋊C4—28no—
170C42×C11C22×C412yes—
171C42×C11C2×D412yes—
172(C2×D11)⋊C4—28no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—44no—
176Dic11⋊C4—28no—
177Dic11⋊C4—44no—
178Dic11⋊C4—48no—
179C4×Dic11C22⋊C418yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8C2×D414yes—
185#4313—216no—
186C2×#532—111no—
187C2×#417—112no—
188C2×#417—112no—
189C2×C4×M16—111no—
190C2×#384—111no—
191#1959—111no—
192#1959—111no—
193#1959—111no—
194#1959D1111yescharacteristic, complemented
195#1957—112no—
196#1956—112no—
197C23×C11—22no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11C2×C22⋊C412yes—
211C22×D11#12412yes—
212C22×D11#12712yes—
213Q8×C11—24no—
214Q8×C11—42no—
215D4×C11—24no—
216D4×C11—42no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11C2×C22⋊C414yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4112yes—
229C22⋊D11—48no—
230C22⋊D11—416no—
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—48no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11C2×C22⋊C414yes—
239C2×Dic11#12412yes—
240C2×Dic11#12712yes—
241C2×Dic11AGL(1,ℤ/8)14yes—
242C2×Dic11#13714yes—
243D44—24no—
244D44—48no—
245D44—42no—
246C4×D11—216no—
247C4×D11—48no—
248C4×D11—88no—
249C4×D11C4×D418yes—
250C4×D11#12118yes—
251Dic22—24no—
252Dic22—42no—
253C8×C11—24no—
254C11⋊C8—24no—
255C22×#41—111no—
256C22×#41—111no—
257C22×M16—112no—
258#532—118no—
259#532—224no—
260C2×C4⋊Q8—111no—
261C2×#127—111no—
262C2×#124—111no—
263C2×#124C2×D1111yescharacteristic
264C2×#121—222no—
265C2×C4×D4—222no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—222no—
268C22×C42—111no—
269#417—228no—
270#417—228no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—112no—
274C2×#103C2×D1112yes—
275C2×#102—112no—
276C2×#102—112no—
277C2×#102—112no—
278C2×#102C2×D1112yes—
279C4×M16—224no—
280C2×#97—111no—
281C2×#97C2×D1111yescharacteristic
282C2×C4×C8—112no—
283#384—112no—
284#384—111no—
285#384—222no—
286#384C2×D1111yescharacteristic
287C22×C11—44no—
288C22×C11—42no—
289C22×C11—82no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×C22⋊C411yescharacteristic
293C22×C11C2×#12411yescharacteristic
294C22×C11C2×#12711yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)12yes—
296C22×C11C2×#13712yes—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—22no—
300C2×D11—22no—
301C2×D11—44no—
302C2×D11—42no—
303C2×D11—82no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11#39014yes—
307C4×C11—24no—
308C4×C11—42no—
309C4×C11—82no—
310C4×C11C2×C4×D412yes—
311C4×C11C2×#12112yes—
312Dic11—42no—
313Dic11—82no—
314Dic11#39014yes—
315Dic11#41718yescomplemented
316C2×#41—114no—
317C2×#41—114no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—224no—
321C2×#41—224no—
322C2×#41—224no—
323C2×#41—224no—
324C22×Q8—111no—
325C22×Q8C22×D1111yescharacteristic
326C22×D4—111no—
327C22×D4—221no—
328C22×D4—222no—
329C22×D4—221no—
330C22×D4C22×D1111yescharacteristic
331C23×C4—111no—
332C23×C4—112no—
333C23×C4—221no—
334C23×C4—222no—
335C23×C4—221no—
336C2×M16—118no—
337C2×M16—224no—
338C2×M16—224no—
339C22×C8—112no—
340C22×C8C22×D1112yes—
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343#127—114no—
344#127—222no—
345#124—22no—
346#124—114no—
347#124—222no—
348#124C4×D1114yescomplemented
349#121—2216no—
350C4×D4—2216no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—448no—
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—222no—
363C2×C42—112no—
364C2×C42—111no—
365C2×C42—114no—
366C2×C42—114no—
367C2×C42C22×D1111yescharacteristic
368#103—24no—
369#103—224no—
370#103—224no—
371#103—224no—
372#102—24no—
373#102—224no—
374#102—224no—
375#102—224no—
376#97—22no—
377#97—222no—
378C4×C8—224no—
379C2×C11—82no—
380C2×C11C2×#39011yescharacteristic
381C2×C11C2×#41712yes—
382C2×C11#314112yes—
383C2×C11#315111yescharacteristic
384C2×C11#315211yescharacteristic
385D11—24no—
386D11—82no—
387C24—21no—
388C24—111no—
389C24—221no—
390#41—2216no—
391#41—2216no—
392#41—448no—
393#41—448no—
394C2×Q8—21no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—112no—
398C2×Q8—221no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8C2×C4×D1112yes—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—112no—
406C2×D4—224no—
407C2×D4—228no—
408C2×D4—224no—
409C2×D4—222no—
410C2×D4—221no—
411C2×D4—222no—
412C2×D4—442no—
413C2×D4—442no—
414C2×D4—444no—
415C2×D4—444no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4C2×C4×D1112yes—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—112no—
422C22×C4—111no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—118no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4—444no—
437C22×C4—448no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4D4×D1112yes—
441C22×C4C23×D1111yescharacteristic
442M16—2216no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—114no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8D4×D1114yes—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—44no—
452C4⋊C4—228no—
453C4⋊C4—222no—
454C4⋊C4—222no—
455C4⋊C4—444no—
456C4⋊C4—444no—
457C4⋊C4—448no—
458C22⋊C4—28no—
459C22⋊C4—228no—
460C42—118no—
461C42—112no—
462C42—112no—
463C42C2×C4×D1112yes—
464C42D4×D1112yes—
465C11#2120011yescharacteristic, complemented, Sylow
466C23—22no—
467C23—41no—
468C23—42no—
469C23—42no—
470C23—41no—
471C23—112no—
472C23—112no—
473C23—112no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—441no—
478C23—442no—
479C23—442no—
480C23—441no—
481C23C2×D4×D1111yescharacteristic
482Q8—24no—
483Q8—42no—
484Q8—224no—
485Q8—442no—
486D4—24no—
487D4—42no—
488D4—224no—
489D4—448no—
490D4—4416no—
491D4—448no—
492D4—442no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—112no—
501C2×C4—114no—
502C2×C4—112no—
503C2×C4—114no—
504C2×C4—114no—
505C2×C4—112no—
506C2×C4—118no—
507C2×C4—118no—
508C2×C4—2216no—
509C2×C4—222no—
510C2×C4—448no—
511C2×C4—448no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—444no—
516C2×C4—888no—
517C2×C4C22⋊C4×D1114yes—
518C2×C4C22×C4×D1111yescharacteristic
519C2×C4C2×D4×D1112yes—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#41×D1112yes—
522C8—24no—
523C8—224no—
524C22—44no—
525C22—42no—
526C22—81no—
527C22—81no—
528C22—82no—
529C22—114no—
530C22—222no—
531C22—222no—
532C22—224no—
533C22—224no—
534C22—444no—
535C22—442no—
536C22—881no—
537C22—881no—
538C22—882no—
539C22C2×C22⋊C4×D1111yescharacteristic
540C22D11×#12411yescharacteristic
541C22D11×#12711yescharacteristic
542C22D11×AGL(1,ℤ/8)12yes—
543C22D11×#13712yes—
544C4—24no—
545C4—42no—
546C4—82no—
547C4—118no—
548C4—114no—
549C4—442no—
550C4—882no—
551C4C4×D4×D1112yes—
552C4D11×#12112yes—
553C2—82no—
554C2—224no—
555C2—882no—
556C2D11×#39011yescharacteristic
557C2D11×#41712yes—
558C2#1307900812yes—
559C2#1307906511yescharacteristic
560C2#1307907211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1959C2
socleC23×C11C22×D4
prime radicalC2×#10623199C2
cosocleC22×C4×C11C24
hypercenter#1959D11
hypocenterC11#21200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#10622416C2semidirect
3. C2×#10622384C2semidirect
4. C2×#10622320C2semidirect
5. D11×#384C2semidirect
6. #13069433C2semidirect
7. #13069432C2semidirect
8. #13069430C2semidirect
9. #13069420C2semidirect
10. #13069416C2semidirect
11. C11×#1959C2semidirect
19. #10623199C4semidirect
66. C11×#124C2×C4semidirect
72. #66997C2×C4semidirect
74. #66993C2×C4semidirect
86. C2×#4313D4semidirect
93. #66928C2×C4semidirect
194. #1959D11semidirect
315. Dic11#417semidirect
348. #124C4×D11semidirect
465. C11#21200semidirect

Maximal subgroups

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

subgroupindex
C2×#106231992
C2×#106224162
C2×#106223842
C2×#106223202
D11×#3842
#130694332
#130694322
#130694302
#130694202
#130694162
C11×#19592
#2120011