Finite Group Databasebeta

← #14810790

Subgroups — #14810790

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622680C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13073615C211yesmaximal, characteristic, complemented
4#13069759C212yesmaximal, complemented
5#13069749C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068964C212yesmaximal, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C2×C11×#554C211yesmaximal, characteristic, complemented
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#125C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4—21no—
25C2×#67000—21no—
26C22×#4323C2212yes—
27C2×#66927C2211yescharacteristic
28C2×#66896C2212yes—
29#10622680—24no—
30#10622628—24no—
31#10622604—21no—
32#10622604—21no—
33#10622601—21no—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37#10622552C2212yes—
38#10622552C2212yes—
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C22×D44—21no—
54C22×D44—21no—
55C22×D44C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#125D414yes—
62C11×C22⋊Q8—28no—
63C11×C22⋊Q8—28no—
64C11×C22⋊Q8—28no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11D414yes—
73C2×C11×C4⋊C4—28no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#67000—44no—
92C2×#4323—24no—
93C2×#4323—24no—
94C2×#4323—24no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×C4⋊Dic11C2312yes—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2312yes—
102C22×C11⋊C8C2312yes—
103#66927—22no—
104#66927—22no—
105#66896—24no—
106C11⋊#95—21no—
107#66873—24no—
108#66873—24no—
109#66873—24no—
110C4⋊(C11⋊C8)—22no—
111#66867—22no—
112#25946—111nomaximal, Sylow
113C24×C11—21no—
114C23×D11—22no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—41no—
119C2×Q8×C11—82no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11C2×D412yes—
123C2×D4×C11#4114yes—
124C22×C4×C11—24no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—82no—
133C22×C4×C11—82no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—22no—
142C2×D44—22no—
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44—82no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C2×D412yes—
175C42×C11C2×D412yes—
176#4323—48no—
177(C2×D11)⋊C4—44no—
178(C2×D11)⋊C4—44no—
179(C2×D11)⋊C4—82no—
180(C2×D11)⋊C4—82no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4×Dic11—42no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×#554D1111yescharacteristic, complemented
191C2×#490—111no—
192C2×#459—111no—
193#2548—111no—
194#2025—112no—
195#2023—112no—
196#1989—111no—
197#1985—111no—
198#1879—112no—
199#1879—112no—
200#1762—111no—
201C23×C11—22no—
202C23×C11—24no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—42no—
206C23×C11C22×D411yescharacteristic
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214Q8×C11—44no—
215Q8×C11—84no—
216D4×C11—22no—
217D4×C11—24no—
218D4×C11#12414yescomplemented
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
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—48no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—84no—
240C2×C4×C11—84no—
241C2×C4×C11#12012yes—
242C2×C4×C11#12012yes—
243C2×C4×C11AGL(1,ℤ/8)12yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4112yes—
247C2×C4×C112−1+412yes—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251D44—42no—
252D44—42no—
253D44—42no—
254D44—42no—
255D44—84no—
256D44—84no—
257C11⋊C8—42no—
258C11⋊C8—42no—
259C22×D8—112no—
260#554—24no—
261#554—24no—
262C2×C4⋊Q8C2×D1111yescharacteristic
263C2×#127—111no—
264C2×#125C2×D1111yescharacteristic
265C2×#125C2×D1111yescharacteristic
266C2×#124—221no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8—21no—
270C2×C4×Q8C2×D1111yescharacteristic
271C2×C4×D4C2×D1111yescharacteristic
272C2×C4×D4C2×D1111yescharacteristic
273C2×C4×D4C2×D1111yescharacteristic
274C22×C4⋊C4—21no—
275#490—224no—
276#459—224no—
277C2×C4⋊C8—111no—
278C2×#102—112no—
279C2×#102—112no—
280C2×#102—112no—
281C2×#102—112no—
282C2×#97—111no—
283#394—221no—
284#394—221no—
285#390—112no—
286#390—112no—
287#390—221no—
288C4×C4⋊C4—111no—
289#340—112no—
290#340—112no—
291#340—112no—
292#336—112no—
293#336—112no—
294C22×C11—24no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11C2×#12011yescharacteristic
300C22×C11#54812yes—
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11#57511yescharacteristic
303C22×C11#57612yes—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C2×D11—82no—
310C2×D11—82no—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—41no—
317C4×C11—41no—
318C4×C11—42no—
319C4×C11—42no—
320C4×C11C2×#12411yescharacteristic
321C4×C11#53611yescharacteristic
322C4×C11#54812yes—
323Dic11—82no—
324C22×Q8—21no—
325C22×Q8C22⋊D1111yescharacteristic
326C22×D4—112no—
327C22×D4—221no—
328C22×D4—221no—
329C22×D4C22×D1111yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4—21no—
333C2×D8—224no—
334C2×D8—224no—
335C2×D8—224no—
336C22×C8—112no—
337C22×C8—112no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340#127—222no—
341#127—222no—
342#125—22no—
343#125—22no—
344#125—22no—
345#125C22⋊D1114yes—
346#124—444no—
347C22⋊Q8—28no—
348C22⋊Q8—28no—
349C22⋊Q8—28no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4C22⋊D1114yes—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4C22⋊D1111yescharacteristic
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C42—221no—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—222no—
383#102—224no—
384#102—224no—
385#102—224no—
386#102—224no—
387#97—222no—
388#95—221no—
389C2×C11—44no—
390C2×C11#243611yescharacteristic
391C2×C11#300611yescharacteristic
392C2×C11#300811yescharacteristic
393C2×C11#336612yes—
394C2×C11#337012yes—
395D11—162no—
396C24—21no—
397C24—222no—
398C2×Q8—24no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—41no—
402C2×Q8—82no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—222no—
406C2×D4—222no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—442no—
412C2×D4—442no—
413C2×D4—442no—
414C2×D4—442no—
415C2×D4—882no—
416C2×D4#434314yes—
417C2×D4C2×C22⋊D1112yes—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—82no—
427C22×C4—82no—
428C22×C4—222no—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436D8—448no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—222no—
455C4⋊C4—222no—
456C4⋊C4C2×C22⋊D1112yes—
457C4⋊C4C2×C22⋊D1112yes—
458C4⋊C4C2×C22⋊D1112yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—444no—
463C22⋊C4—444no—
464C22⋊C4—882no—
465C22⋊C4—882no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—442no—
471C42C2×C22⋊D1112yes—
472C42C2×C22⋊D1112yes—
473C11#2594611yescharacteristic, complemented, Sylow
474C23—24no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—42no—
479C23—442no—
480C23—442no—
481C23—442no—
482C23—442no—
483C23—442no—
484C23—442no—
485C23—442no—
486C23C22×C22⋊D1111yescharacteristic
487Q8—44no—
488Q8—84no—
489D4—22no—
490D4—24no—
491D4—442no—
492D4—442no—
493D4—442no—
494D4—442no—
495D4—884no—
496D4—884no—
497D4#6700014yescomplemented
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—48no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4#6700212yes—
524C2×C4#6700612yes—
525C2×C4#6700612yes—
526C2×C4C2×#434312yes—
527C2×C4#6704012yes—
528C2×C4C22×C22⋊D1111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—442no—
531C8—442no—
532C22—24no—
533C22—44no—
534C22—42no—
535C22—42no—
536C22—44no—
537C22—882no—
538C22—882no—
539C22—882no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22#1062334812yes—
545C22C2×#6700211yescharacteristic
546C22#1062335311yescharacteristic
547C22#1062336612yes—
548C22C2×#6700611yescharacteristic
549C4—22no—
550C4—22no—
551C4—22no—
552C4—41no—
553C4—42no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—882no—
559C4C2×#6700011yescharacteristic
560C4#1062334711yescharacteristic
561C4#1062334812yes—
562C2—44no—
563C2—1762no—
564C2#1307227011yescharacteristic
565C2#1307786811yescharacteristic
566C2#1307788411yescharacteristic
567C2#1308132312yes—
568C2#1308136912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenterC2×#554D11
hypocenterC11#25946
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622680C2semidirect
3. #13073615C2semidirect
4. #13069759C2semidirect
5. #13069749C2semidirect
6. #13069574C2semidirect
7. #13069557C2semidirect
8. #13068964C2semidirect
9. #13068964C2semidirect
10. #13068441C2semidirect
11. C2×C11×#554C2semidirect
190. C2×#554D11semidirect
218. D4×C11#124semidirect
473. C11#25946semidirect
497. D4#67000semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
C2×#106226282
#130736152
#130697592
#130697492
#130695742
#130695572
#130689642
#130684412
C2×C11×#5542
#2594611