Finite Group Databasebeta

← #14787686

Subgroups — #14787686

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3C2×C4×#4314C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic
5#13069813C212yesmaximal, complemented
6#13069621C212yesmaximal, complemented
7#13069577C211yesmaximal, characteristic, complemented
8#13068931C212yesmaximal, complemented
9#13068811C212yesmaximal, complemented
10#13068622C211yesmaximal, characteristic, complemented
11C11×#1954C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66991—21no—
14C2×D4×Dic11—21no—
15C2×#66983C2212yes—
16C22×C4⋊Dic11C2212yes—
17C2×#66977C2212yes—
18C22×#4314C2211yescharacteristic
19#10623074—24no—
20#10623074—24no—
21C2×#66943—21no—
22C2×#66931—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C11×C22⋊C8C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30#10622825C2212yes—
31C2×#66885C2212yes—
32C2×#66885C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2212yes—
35C2×#66880C2211yescharacteristic
36C2×#66880C2212yes—
37#10622600—21no—
38#10622574—22no—
39#10622548C2211yescharacteristic
40#10622455—24no—
41C4×#4314—24no—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C23×Dic11—22no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63#66991—44no—
64D4×Dic11—28no—
65#66983—24no—
66#66983—42no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79#66977—24no—
80#66977—24no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C2×#4314—22no—
85C2×#4314—22no—
86C2×#4314—22no—
87#66943—28no—
88#66931—216no—
89C4×D44—22no—
90C4×D44—22no—
91#66922—22no—
92#66922D414yescomplemented
93C4×Dic22—22no—
94C4×Dic22D414yescomplemented
95C11×C4⋊C8—22no—
96C11×C22⋊C8—24no—
97C11×C22⋊C8—42no—
98C4×C8×C11—22no—
99C11⋊#95—22no—
100#66885—22no—
101#66885—24no—
102#66881—22no—
103#66881—24no—
104#66880—22no—
105#66880—42no—
106#24118—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C23×D11—21no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11SD1614yescomplemented
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—82no—
125C22×Dic11—28no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—82no—
132C22×Dic11—82no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44#4112yes—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×Dic22—24no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—81no—
149C2×Dic22—81no—
150C2×Dic22C2×D412yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11#4112yes—
160C11×C4⋊C4—22no—
161C11×C22⋊C4—24no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—28no—
165C22⋊Dic11—44no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—28no—
169C4⋊Dic11—24no—
170C4⋊Dic11—21no—
171C4⋊Dic11—22no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—42no—
177C4⋊Dic11—81no—
178C4⋊Dic11C2×D412yes—
179C4⋊Dic11C2×D414yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—24no—
182C4×Dic11—24no—
183#4314—28no—
184C2×#554—111no—
185C2×#476—111no—
186C2×C4×SD16—111no—
187#2537—111no—
188#2035—112no—
189#2000—112no—
190#1990—111no—
191#1954D1111yescharacteristic, complemented
192#1874—112no—
193#1853—112no—
194#1803—111no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11C2×SD1614yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210D4×C11—28no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C2×SD1612yes—
223C2×C4×C11#13712yes—
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C22⋊D11—88no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—42no—
246C2×Dic11—88no—
247D44—22no—
248D44—22no—
249D44—41no—
250D44—41no—
251C4×D11—84no—
252Dic22—22no—
253Dic22—22no—
254Dic22—41no—
255Dic22—41no—
256Dic22—84no—
257C8×C11—22no—
258C8×C11—41no—
259C8×C11—42no—
260C22×SD16—111no—
261#554—224no—
262#554—224no—
263C2×C4⋊Q8—111no—
264C2×#125—221no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—222no—
267C2×#121—112no—
268C2×#121—221no—
269C2×C4×Q8—111no—
270C2×C4×D4—111no—
271C2×C4×D4—221no—
272C2×C4×D4C2×D1111yescharacteristic
273C22×C4⋊C4—112no—
274#476—224no—
275C4×SD16—224no—
276C2×#106—111no—
277C2×#106—112no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—111no—
280C2×#103—112no—
281C2×#102—111no—
282C2×#102—112no—
283C2×C22⋊C8C2×D1112yes—
284C2×C22⋊C8C2×D1112yes—
285C2×C4×C8C2×D1111yescharacteristic
286#394—222no—
287#384—111no—
288#380—112no—
289#380—221no—
290#340—112no—
291#340—112no—
292#340—112no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#54611yescharacteristic
302C22×C11#54711yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C2×#13711yescharacteristic
305C22×C11#57611yescharacteristic
306C22×C11#57711yescharacteristic
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11#44814yes—
317C4×C11#52511yescharacteristic
318C4×C11#53711yescharacteristic
319C4×C11#54811yescharacteristic
320C4×C11#55011yescharacteristic
321Dic11—42no—
322Dic11—44no—
323Dic11—42no—
324Dic11—81no—
325Dic11—82no—
326C22×Q8—111no—
327C22×Q8—221no—
328C22×D4—111no—
329C22×D4—222no—
330C22×D4D4411yescharacteristic
331C23×C4—222no—
332C23×C4—221no—
333C23×C4C22×D1112yes—
334C2×SD16—222no—
335C2×SD16—222no—
336C2×SD16—222no—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1112yes—
339C22×C8C22×D1111yescharacteristic
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342#125—228no—
343C22⋊Q8—2216no—
344C22⋊Q8—224no—
345C22⋊Q8—224no—
346#121—224no—
347#121—442no—
348#121—444no—
349C4×Q8—114no—
350C4×Q8—222no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—228no—
354C4×D4—222no—
355C4×D4—222no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4D4411yescharacteristic
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4D4412yes—
374C2×C42—221no—
375C2×C42C22×D1111yescharacteristic
376#106—222no—
377#106—224no—
378C4⋊C8—22no—
379#103—222no—
380#103—442no—
381#102—222no—
382#102—224no—
383C22⋊C8—24no—
384C22⋊C8—42no—
385C4×C8—22no—
386#95—222no—
387C2×C11—44no—
388C2×C11#240711yescharacteristic
389C2×C11C2×#44811yescharacteristic
390C2×C11#301211yescharacteristic
391C2×C11#329511yescharacteristic
392C2×C11#333111yescharacteristic
393C2×C11#333511yescharacteristic
394C2×C11#335711yescharacteristic
395D11—82no—
396C24—221no—
397C24C2×D4412yes—
398C2×Q8—112no—
399C2×Q8—224no—
400C2×Q8—221no—
401C2×Q8—221no—
402C2×Q8—221no—
403C2×Q8—221no—
404C2×Q8—221no—
405C2×Q8—881no—
406C2×Q8—881no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—112no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4—882no—
418C2×D4#431414yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4—228no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4—882no—
435C22×C4—882no—
436C22×C4C2×D4412yes—
437C22×C4C2×D4411yescharacteristic
438C22×C4C2×D4411yescharacteristic
439C22×C4C23×D1111yescharacteristic
440SD16—228no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—21no—
447C2×C8—22no—
448C2×C8—21no—
449C2×C8#434112yes—
450C4⋊C4—22no—
451C4⋊C4—112no—
452C4⋊C4—114no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—224no—
456C4⋊C4—224no—
457C4⋊C4—221no—
458C4⋊C4—222no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—442no—
464C4⋊C4—881no—
465C22⋊C4—24no—
466C22⋊C4—228no—
467C22⋊C4—444no—
468C22⋊C4—444no—
469C22⋊C4—442no—
470C42—224no—
471C42D4×D1112yes—
472C42D4×D1112yes—
473C11#2411811yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—222no—
481C23—441no—
482C23—441no—
483C23—441no—
484C23—441no—
485C23—441no—
486C23—441no—
487C23C2×#431414yes—
488C23C22×D4411yescharacteristic
489Q8—222no—
490Q8—222no—
491Q8—441no—
492Q8—441no—
493Q8—884no—
494D4—28no—
495D4—222no—
496D4—222no—
497D4—441no—
498D4—441no—
499D4—888no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—442no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—888no—
525C2×C4—884no—
526C2×C4#6693512yes—
527C2×C4#6693512yes—
528C2×C4C2×#431412yes—
529C2×C4#6696212yes—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×#434111yescharacteristic
533C2×C4#6703711yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—22no—
537C8—42no—
538C8—41no—
539C22—24no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22C2×#6693511yescharacteristic
554C22#1062308511yescharacteristic
555C22#1062308611yescharacteristic
556C22C22×#431411yescharacteristic
557C22C2×#6696211yescharacteristic
558C22#1062328211yescharacteristic
559C22#1062328311yescharacteristic
560C4—22no—
561C4—42no—
562C4—442no—
563C4—442no—
564C4—444no—
565C4—881no—
566C4—882no—
567C4#1062235114yes—
568C4#1062313711yescharacteristic
569C4#1062313911yescharacteristic
570C4#1062320811yescharacteristic
571C4#1062324911yescharacteristic
572C2—44no—
573C2—882no—
574C2#1307195911yescharacteristic
575C2C2×#1062235111yescharacteristic
576C2#1307792311yescharacteristic
577C2#1308044111yescharacteristic
578C2#1308093311yescharacteristic
579C2#1308097411yescharacteristic
580C2#1308124311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1954C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenter#1954D11
hypocenterC11#24118
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. C2×#10622455C2semidirect
3. C2×C4×#4314C2semidirect
5. #13069813C2semidirect
6. #13069621C2semidirect
7. #13069577C2semidirect
8. #13068931C2semidirect
9. #13068811C2semidirect
10. #13068622C2semidirect
11. C11×#1954C2semidirect
92. #66922D4semidirect
94. C4×Dic22D4semidirect
111. C2×D4×C11SD16semidirect
191. #1954D11semidirect
418. C2×D4#4314semidirect
473. C11#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106224552
C2×C4×#43142
#130735292
#130698132
#130696212
#130695772
#130689312
#130688112
#130686222
C11×#19542
#2411811