Finite Group Databasebeta

← #14804242

Subgroups — #14804242

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic, complemented
2C2×#10622640C212yesmaximal, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13073558C211yesmaximal, characteristic
5#13069931C212yesmaximal, complemented
6#13069703C212yesmaximal, complemented
7#13069543C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068971C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2365C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C22×#4325C2212yes—
15C22×#4325C2212yes—
16C22×#4325C2212yes—
17C2×#66948—21no—
18C2×#66948—21no—
19C2×#66927C2211yescharacteristic
20C2×#66927C2212yes—
21C2×C4×D44C2211yescharacteristic
22C11×#391C2212yes—
23C11×#389—21no—
24C11×#387—22no—
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2212yes—
29#10622698—24no—
30#10622696—24no—
31#10622640—28no—
32C2×#66873C2212yes—
33C2×#66873C2211yescharacteristic
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36#10622552C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2212yes—
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622284—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×Q8×C11C2312yes—
45C22×D44—21no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—21no—
49C22×D44C2312yes—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yescomplemented
54C4×Q8×C11—24no—
55C4×Q8×C11—42no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11—22no—
65C2×C42×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67C2×#4325—24no—
68C2×#4325—24no—
69C2×#4325—24no—
70C2×#4325—24no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4325—42no—
74C2×#4325—42no—
75C2×#4325—42no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11C2311yescharacteristic
80C22×C11⋊C8C2312yes—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83#66948—44no—
84#66948—44no—
85#66927—24no—
86#66927—22no—
87#66927—22no—
88#66927—42no—
89C4×D44—22no—
90C4×D44—22no—
91C11×#95—22no—
92C11×#95—21no—
93C11×#95—22no—
94C11×#95D412yes—
95#66899—24no—
96#66873—24no—
97#66873—22no—
98#66873—42no—
99#66873D414yescomplemented
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)—24no—
102C4×C11⋊C8—22no—
103#25366—111nomaximal, Sylow
104C23×D11—21no—
105C23×D11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D414yes—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C2×D44—21no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—44no—
133C2×D44—44no—
134C2×D44—44no—
135C2×D44—42no—
136C2×D44—42no—
137C2×D44—44no—
138C2×D44—42no—
139C2×D44—42no—
140C2×D44—82no—
141C2×D44—81no—
142C2×D44—81no—
143C2×D44—82no—
144C2×D44C2×D412yes—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4SD1614yescomplemented
156C11×C4⋊C4C2×D412yes—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—44no—
160C42×C11—42no—
161C42×C11C2×D412yes—
162C42×C11#4112yes—
163#4325—48no—
164#4325—48no—
165#4325—48no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—44no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8C2×D412yes—
179C2×C11⋊C8#4112yes—
180C2×#492—111no—
181C2×#460—112no—
182C2×#461—111no—
183#2541—111no—
184#2365D1111yescharacteristic, complemented
185#2055—112no—
186#2014—112no—
187#1982—111no—
188#1939—111no—
189#1880—112no—
190C4×#102—111no—
191C23×C11C22×D411yescharacteristic
192C22×D11—22no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206Q8×C11—24no—
207Q8×C11—24no—
208Q8×C11—42no—
209Q8×C11—42no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11C2×SD1614yes—
229C2×C4×C11C2×SD1612yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240D44—22no—
241D44—22no—
242D44—42no—
243D44—41no—
244D44—42no—
245D44—42no—
246D44—41no—
247D44—42no—
248D44—88no—
249D44—84no—
250D44—88no—
251D44—84no—
252C4×D11—84no—
253C11⋊C8—22no—
254C11⋊C8—22no—
255C11⋊C8—42no—
256C22×SD16—112no—
257C22×SD16—112no—
258C22×SD16—112no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#127—111no—
261C2×#127—112no—
262C2×#121—221no—
263C2×#121—221no—
264C2×C4×Q8C2×D1112yes—
265C2×C4×D4—111no—
266#492—224no—
267#461—224no—
268#460—228no—
269C2×C4⋊C8—112no—
270C2×C4⋊C8—111no—
271C2×#103—112no—
272C2×#102—111no—
273C2×#102—112no—
274C2×#102—111no—
275C2×#102—112no—
276C2×C4×C8—111no—
277#392—222no—
278#391C2×D1112yes—
279#390—112no—
280#389—21no—
281#387—22no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4C2×D1111yescharacteristic
284C4×C4⋊C4C2×D1111yescharacteristic
285#340—111no—
286#340—111no—
287#336—112no—
288C22×C11C2×#12111yescharacteristic
289C22×C11D4211yescharacteristic
290C22×C11#55011yescharacteristic
291C22×C11C22×SD1611yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11#57711yescharacteristic
294C22×C11#57711yescharacteristic
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—24no—
310C4×C11—22no—
311C4×C11—44no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—81no—
315C4×C11#46014yescomplemented
316C4×C11#53211yescharacteristic
317C4×C11#54011yescharacteristic
318C4×C11D4211yescharacteristic
319C4×C11#54611yescharacteristic
320Dic11—81no—
321C22×Q8C22×D1112yes—
322C22×D4—111no—
323C22×D4—112no—
324C22×D4—221no—
325C22×D4—222no—
326C22×D4—222no—
327C22×D4—221no—
328C23×C4—221no—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—224no—
332C2×SD16—224no—
333C2×SD16—224no—
334C2×SD16—224no—
335C2×SD16—442no—
336C2×SD16—442no—
337C2×SD16—442no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—112no—
341C4⋊Q8—22no—
342C4⋊Q8D4414yescomplemented
343#127—224no—
344#127—222no—
345#127—222no—
346#127—442no—
347#121—444no—
348#121—444no—
349C4×Q8—24no—
350C4×Q8—42no—
351C4×D4—222no—
352C4×D4—222no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C4⋊C4C22⋊D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—221no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C42—22no—
365C2×C42—21no—
366C2×C42C22×D1112yes—
367C2×C42C22×D1111yescharacteristic
368C4⋊C8—224no—
369C4⋊C8—222no—
370#103—224no—
371#102—114no—
372#102—222no—
373#102—224no—
374#102—442no—
375C4×C8—222no—
376#95—22no—
377#95—21no—
378#95—22no—
379#95C22⋊D1112yes—
380C2×C11#242811yescharacteristic
381C2×C11C2×#46011yescharacteristic
382C2×C11#304311yescharacteristic
383C2×C11#327211yescharacteristic
384C2×C11D4×SD1611yescharacteristic
385C2×C11#339211yescharacteristic
386C2×C11#339711yescharacteristic
387D11—82no—
388D11—162no—
389C24—221no—
390C24—222no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8C2×D4414yes—
397C2×D4—112no—
398C2×D4—221no—
399C2×D4—222no—
400C2×D4—221no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—221no—
404C2×D4—222no—
405C2×D4—221no—
406C2×D4—222no—
407C2×D4—221no—
408C2×D4—222no—
409C2×D4—444no—
410C2×D4—444no—
411C2×D4—444no—
412C2×D4—442no—
413C2×D4—442no—
414C2×D4—444no—
415C2×D4—442no—
416C2×D4—442no—
417C2×D4—882no—
418C2×D4—881no—
419C2×D4—881no—
420C2×D4—882no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—221no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434SD16—448no—
435SD16—448no—
436C2×C8—112no—
437C2×C8—112no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—44no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4#432514yescomplemented
455C4⋊C4D4×D1112yes—
456C22⋊C4—444no—
457C22⋊C4—442no—
458C22⋊C4—444no—
459C42—22no—
460C42—22no—
461C42—44no—
462C42—42no—
463C42C2×D4412yes—
464C42#433912yes—
465C11#2536611yescharacteristic, complemented, Sylow
466C23—222no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23—442no—
480C23C22×C22⋊D1111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485D4—222no—
486D4—222no—
487D4—442no—
488D4—442no—
489D4—441no—
490D4—442no—
491D4—441no—
492D4—442no—
493D4—888no—
494D4—884no—
495D4—888no—
496D4—884no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—884no—
517C2×C4#6698312yes—
518C2×C4#6698312yes—
519C2×C4C2×#432514yes—
520C2×C4C2×#432512yes—
521C2×C4#6700212yes—
522C2×C4C22×D4411yescharacteristic
523C2×C4C2×#433911yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#41×D1111yescharacteristic
527C2×C4#6704211yescharacteristic
528C8—222no—
529C8—222no—
530C8—442no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22—882no—
539C22—882no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22C2×#6698311yescharacteristic
546C22D4×C22⋊D1111yescharacteristic
547C22C22×#432511yescharacteristic
548C22C2×#6700211yescharacteristic
549C22#1062336511yescharacteristic
550C22#1062336811yescharacteristic
551C22#1062336811yescharacteristic
552C4—22no—
553C4—24no—
554C4—44no—
555C4—42no—
556C4—42no—
557C4—81no—
558C4—881no—
559C4#1062264014yescomplemented
560C4#1062307911yescharacteristic
561C4D4×D4411yescharacteristic
562C4#1062308511yescharacteristic
563C4#1062309311yescharacteristic
564C2—882no—
565C2—1762no—
566C2#1307219811yescharacteristic
567C2C2×#1062264011yescharacteristic
568C2#1307813711yescharacteristic
569C2#1308021611yescharacteristic
570C2D4×#432511yescharacteristic
571C2#1308159311yescharacteristic
572C2#1308163611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socleC23×C11C22×D4
prime radical#13073558C2
hypercenter#2365D11
hypocenterC11#25366
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
1. C2×#10622698C2semidirect
2. C2×#10622640C2semidirect
3. C2×#10622696C2semidirect
5. #13069931C2semidirect
6. #13069703C2semidirect
7. #13069543C2semidirect
8. #13069335C2semidirect
9. #13068971C2semidirect
10. C4×#66873C2semidirect
11. C11×#2365C2semidirect
53. C11×C4⋊Q8D4semidirect
99. #66873D4semidirect
155. C11×C4⋊C4SD16semidirect
184. #2365D11semidirect
315. C4×C11#460semidirect
342. C4⋊Q8D44semidirect
454. C4⋊C4#4325semidirect
465. C11#25366semidirect
559. C4#10622640semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226402
C2×#106226962
#130735582
#130699312
#130697032
#130695432
#130693352
#130689712
C4×#668732
C11×#23652
#2536611