Finite Group Databasebeta

← #14660449

Subgroups — #14660449

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66901C212yesmaximal, complemented
2C2×#10622845C212yesmaximal, complemented
3C2×#10622168C211yesmaximal, characteristic, complemented
4#13066845C211yesmaximal, characteristic, complemented
5C2×C11×#537C211yesmaximal, characteristic
6C22×C11×#41C2212yes—
7C11×#537—24no—
8C11×#537—22no—
9C11×#537C414yescomplemented
10C2×C11×C22⋊Q8—22no—
11C2×C11×#121—22no—
12C2×C11×#121—22no—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4×Dic11C2211yescharacteristic
16C22×#4318C2212yes—
17C2×#66901—24no—
18C2×#66901—24no—
19C2×#66901—24no—
20#10622845—24no—
21#10622845—24no—
22C2×#66899—22no—
23C2×#66896—22no—
24C2×C11⋊#95—22no—
25#10622168—22no—
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41—22no—
33C2×C11×#41—22no—
34C2×C11×#41—22no—
35C2×C11×#41—22no—
36C2×C11×#41C2×C414yes—
37C2×C11×#41D414yes—
38C22×Q8×C11D412yes—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11D412yes—
42C23×C4×C11—22no—
43C23×C4×C11D412yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C23×Dic11—21no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8—28no—
49C11×#121—28no—
50C11×#121—28no—
51C11×#121—28no—
52C11×#121—28no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C412yes—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C22⋊C4—24no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D412yescomplemented
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11D412yescomplemented
67C2×#4318—22no—
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318—22no—
71C2×#4318—22no—
72C2×#4318D414yescomplemented
73C22×C11⋊C8—22no—
74#66901—216no—
75#66899—28no—
76#66896—28no—
77C11⋊#95—44no—
78#11002—111nomaximal, Sylow
79C24×C11—22no—
80C24×C11C2×D411yescharacteristic
81C11×#41—24no—
82C11×#41—24no—
83C11×#41—24no—
84C11×#41—24no—
85C11×#41—24no—
86C11×#41—24no—
87C11×#41—24no—
88C11×#41—24no—
89C11×#41—42no—
90C11×#41—42no—
91C11×#41—42no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11C22⋊C414yes—
103C2×D4×C11—24no—
104C2×D4×C11—24no—
105C2×D4×C11—28no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—82no—
116C2×D4×C11—82no—
117C2×D4×C11C22⋊C414yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11C22⋊C414yes—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4112yes—
138C22×C4×C11#4111yescharacteristic
139C22×C4×C11#4111yescharacteristic
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—41no—
145C22×Dic11—41no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—41no—
149C22×Dic11—41no—
150C22×Dic11—41no—
151C22×Dic11—41no—
152C11×C4⋊C4—28no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C22⋊C4—216no—
156C4⋊Dic11—24no—
157C4⋊Dic11—42no—
158C4×Dic11—24no—
159C4×Dic11—42no—
160#4318—24no—
161#4318—24no—
162#4318—42no—
163#4318—42no—
164C2×C11⋊C8—24no—
165C2×C11⋊C8—42no—
166C2×C11⋊C8—42no—
167C2×#537D1111yescharacteristic
168C22×#104—112no—
169C2×#417—112no—
170C2×#343—111no—
171C4⋊#95—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—24no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11C2×C22⋊C411yescharacteristic
184C23×C11#12011yescharacteristic
185C23×C11#12011yescharacteristic
186C23×C11#12111yescharacteristic
187C23×C11#12111yescharacteristic
188C23×C11#12411yescharacteristic
189C23×C11#12711yescharacteristic
190Q8×C11—24no—
191Q8×C11—24no—
192Q8×C11—42no—
193Q8×C11—42no—
194D4×C11—24no—
195D4×C11—24no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—44no—
199D4×C11—44no—
200D4×C11—42no—
201D4×C11—42no—
202D4×C11—88no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11—44no—
212C2×C4×C11—44no—
213C2×C4×C11—44no—
214C2×C4×C11—82no—
215C2×C4×C11C2×C22⋊C412yes—
216C2×C4×C11C4×D412yes—
217C2×C4×C11C4×D411yescharacteristic
218C2×C4×C11C4×D411yescharacteristic
219C2×C4×C11#12012yes—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11#12112yes—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#12112yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12312yes—
228C2×C4×C11#12312yes—
229C2×C4×C11#12411yescharacteristic
230C2×C4×C11#12711yescharacteristic
231C2×Dic11—24no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—44no—
239C2×Dic11—42no—
240C2×Dic11—82no—
241C2×Dic11—81no—
242C2×Dic11—81no—
243C11⋊C8—44no—
244C22×#41C2×D1112yes—
245C22×M16—112no—
246#537—24no—
247#537—22no—
248#537Dic1114yescomplemented
249C2×C22⋊Q8—22no—
250C2×#121—22no—
251C2×#121—22no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C42—111no—
255C2×#104—224no—
256C2×#104—224no—
257C2×#104—224no—
258#417—224no—
259#417—224no—
260C2×#103—222no—
261C2×#102—222no—
262C2×#95—222no—
263#343—222no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—82no—
283C22×C11#37911yescharacteristic
284C22×C11#39011yescharacteristic
285C22×C11#39011yescharacteristic
286C22×C11#39211yescharacteristic
287C22×C11#39211yescharacteristic
288C22×C11#39411yescharacteristic
289C22×C11#39411yescharacteristic
290C22×C11#45311yescharacteristic
291C22×C11#45411yescharacteristic
292C22×C11#45511yescharacteristic
293C22×C11#45611yescharacteristic
294C4×C11—44no—
295C4×C11—44no—
296C4×C11#38612yes—
297C4×C11#38612yes—
298C4×C11#39212yes—
299C4×C11#39412yes—
300Dic11—44no—
301Dic11—82no—
302C2×#41—22no—
303C2×#41—22no—
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41C2×Dic1114yes—
313C2×#41C22⋊D1114yes—
314C22×Q8C22⋊D1112yes—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4C22⋊D1112yes—
318C23×C4—22no—
319C23×C4—221no—
320C23×C4—221no—
321C23×C4C22⋊D1112yes—
322C23×C4C22×D1111yescharacteristic
323C2×M16—114no—
324C2×M16—222no—
325C2×M16—222no—
326C2×M16—222no—
327C2×M16—222no—
328C2×M16—222no—
329C22×C8—222no—
330C22⋊Q8—28no—
331C22⋊Q8—28no—
332#121—28no—
333#121—28no—
334#121—28no—
335#121—28no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C2×Dic1112yes—
344C2×C4⋊C4C22⋊D1112yes—
345C2×C22⋊C4—24no—
346C2×C42—112no—
347C2×C42—222no—
348C2×C42—222no—
349C2×C42—221no—
350#104—2216no—
351#103—228no—
352#102—228no—
353#95—444no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11—84no—
359C2×C11#143811yescharacteristic
360C2×C11#179211yescharacteristic
361C2×C11#179311yescharacteristic
362C2×C11#200611yescharacteristic
363C2×C11#200711yescharacteristic
364C2×C11#203911yescharacteristic
365C2×C11#204011yescharacteristic
366C24—22no—
367C24C2×C22⋊D1111yescharacteristic
368#41—24no—
369#41—24no—
370#41—24no—
371#41—24no—
372#41—24no—
373#41—24no—
374#41—24no—
375#41—24no—
376#41—42no—
377#41—42no—
378#41—42no—
379#41—42no—
380#41—42no—
381#41—42no—
382#41—42no—
383#41—42no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8C22⋊Dic1114yes—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—28no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—82no—
403C2×D4—82no—
404C2×D4C22⋊Dic1114yes—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—441no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—441no—
427C22×C4—441no—
428C22×C4C22⋊Dic1114yes—
429C22×C4D4×D1112yes—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4#434111yescharacteristic
433C22×C4#434111yescharacteristic
434C22×C4#434112yes—
435C22×C4C22×Dic1111yescharacteristic
436C22×C4C2×C22⋊D1112yes—
437C22×C4C2×C22⋊D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439M16—224no—
440M16—224no—
441M16—442no—
442M16—442no—
443C2×C8—224no—
444C2×C8—442no—
445C2×C8—442no—
446C4⋊C4—28no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—224no—
450C4⋊C4—442no—
451C22⋊C4—216no—
452C42—224no—
453C42—442no—
454C11#1100211yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23#6698911yescharacteristic
467C23#6699111yescharacteristic
468C23#6699111yescharacteristic
469C23#6699311yescharacteristic
470C23C2×C22⋊Dic1111yescharacteristic
471C23#6700611yescharacteristic
472C23#6700611yescharacteristic
473Q8—24no—
474Q8—24no—
475Q8—42no—
476Q8—42no—
477D4—24no—
478D4—24no—
479D4—44no—
480D4—44no—
481D4—44no—
482D4—44no—
483D4—42no—
484D4—42no—
485D4—88no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—82no—
498C2×C4—224no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—444no—
506C2×C4—442no—
507C2×C4—882no—
508C2×C4—881no—
509C2×C4—881no—
510C2×C4D4×Dic1111yescharacteristic
511C2×C4D4×Dic1111yescharacteristic
512C2×C4D4×Dic1112yes—
513C2×C4#6698812yes—
514C2×C4#6698812yes—
515C2×C4#6698911yescharacteristic
516C2×C4#6699012yes—
517C2×C4#6699012yes—
518C2×C4#6699112yes—
519C2×C4#6699212yes—
520C2×C4#6699212yes—
521C2×C4#6699212yes—
522C2×C4#6699212yes—
523C2×C4#6699311yescharacteristic
524C2×C4C2×C22⋊Dic1112yes—
525C2×C4#6700612yes—
526C8—444no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—82no—
546C22#1062283411yescharacteristic
547C22#1062283411yescharacteristic
548C22#1062283511yescharacteristic
549C22#1062283511yescharacteristic
550C22#1062283611yescharacteristic
551C22#1062283611yescharacteristic
552C22#1062285411yescharacteristic
553C22#1062285511yescharacteristic
554C22#1062285811yescharacteristic
555C22#1062285911yescharacteristic
556C22#1062286011yescharacteristic
557C4—44no—
558C4—44no—
559C4—444no—
560C4—882no—
561C4#1062283312yes—
562C4#1062283312yes—
563C4#1062283512yes—
564C4#1062283612yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—84no—
570C2#1306685711yescharacteristic
571C2#1306857011yescharacteristic
572C2#1306857511yescharacteristic
573C2#1306965811yescharacteristic
574C2#1306966311yescharacteristic
575C2#1306983711yescharacteristic
576C2#1306984211yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#537C2
socleC23×C11#120
cosocleC23×C4×C11C23
hypercenterC2×#537D11
hypocenterC11#11002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#66901C2semidirect
2. C2×#10622845C2semidirect
3. C2×#10622168C2semidirect
4. #13066845C2semidirect
9. C11×#537C4semidirect
62. C2×C4⋊Dic11D4semidirect
66. C2×C4×Dic11D4semidirect
72. C2×#4318D4semidirect
248. #537Dic11semidirect
454. C11#11002semidirect

Maximal subgroups

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

subgroupindex
C22×#669012
C2×#106228452
C2×#106221682
#130668452
C2×C11×#5372
#1100211