Finite Group Databasebeta

← #14803618

Subgroups — #14803618

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2#13073569C211yesmaximal, characteristic, complemented
3#13071681C211yesmaximal, characteristic, complemented
4#13070022C212yesmaximal, complemented
5#13069924C212yesmaximal, complemented
6#13069567C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068966C212yesmaximal, complemented
9#13068614C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×D4×Dic11—21no—
16C2×D4×Dic11C2212yes—
17C2×#66977—21no—
18C2×#66977—21no—
19C2×#66922C2211yescharacteristic
20C11×#459—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2212yes—
23#10622834—21no—
24#10622834C2212yes—
25#10622834C2212yes—
26#10622833—22no—
27C2×#66896C2212yes—
28C2×#66896C2211yescharacteristic
29C2×#66896C2212yes—
30C2×#66896C2211yescharacteristic
31C2×Dic11⋊C8C2212yes—
32#10622683—24no—
33#10622589C2212yes—
34#10622562—22no—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×Dic11—22no—
49C22×Dic22—21no—
50C2×C11×D8—24no—
51C2×C11×D8—24no—
52C2×C11×D8—42no—
53C22×C8×C11C2312yes—
54C11×#127—22no—
55C11×#127D414yes—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66D4×Dic11—24no—
67D4×Dic11—42no—
68D4×Dic11—44no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75#66977—44no—
76#66977—44no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83#66922—22no—
84#66922—22no—
85C11×C4⋊C8—22no—
86C11×#102—24no—
87#66896—24no—
88#66896—24no—
89#66896—22no—
90#66896—22no—
91C11⋊#95—21no—
92C11⋊#95D412yes—
93Dic11⋊C8—42no—
94C4×C11⋊C8—22no—
95#25318—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11—22no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—81no—
113C2×D4×C11—81no—
114C2×D4×C11C2×D414yes—
115C2×D4×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—44no—
127C22×Dic11—44no—
128C22×Dic11—82no—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22—42no—
134C11×D8—48no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C22⋊C4—42no—
141C42×C11C2×D412yes—
142C42×C11#4112yes—
143C22⋊Dic11—44no—
144C22⋊Dic11—44no—
145C22⋊Dic11—44no—
146C22⋊Dic11—44no—
147C22⋊Dic11—82no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—42no—
155C4⋊Dic11D814yescomplemented
156C4⋊Dic11#4112yes—
157Dic11⋊C4—44no—
158Dic11⋊C4—44no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C4×Dic11—42no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×#486—111no—
169C2×#459D1111yescharacteristic
170#2542—111no—
171#2366—111no—
172#2071—112no—
173#2054—112no—
174#1988—111no—
175#1939—111no—
176#1879—112no—
177#1802—112no—
178C4×#102—111no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—41no—
182C23×C11—42no—
183C23×C11—41no—
184C23×C11—42no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—42no—
189C23×C11—42no—
190C23×C11—42no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11C22×D411yescharacteristic
194D4×C11—22no—
195D4×C11—22no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—42no—
199D4×C11—41no—
200D4×C11—42no—
201D4×C11—41no—
202D4×C11—48no—
203D4×C11—84no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11C2×D812yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—88no—
235C2×Dic11C2×D814yes—
236Dic22—84no—
237C8×C11—42no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C22×D8C2×D1112yes—
241C2×C4⋊Q8—111no—
242C2×#127C2×D1111yescharacteristic
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C4×D4—112no—
246C2×C4×D4—221no—
247C2×C4×D4C2×D1111yescharacteristic
248#486—224no—
249#459—24no—
250C2×C4⋊C8—112no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×#102—111no—
253C2×#102—112no—
254C2×#102—112no—
255C2×#102—111no—
256C2×#102C2×D1112yes—
257C2×C4×C8—111no—
258#399—222no—
259#390—112no—
260#390—112no—
261#390—221no—
262#386—222no—
263#384—112no—
264C4×C4⋊C4—111no—
265C4×C4⋊C4—111no—
266#340—112no—
267#340—112no—
268#340—111no—
269#340—111no—
270#336—112no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—82no—
278C22×C11—81no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—82no—
284C22×C11—81no—
285C22×C11C2×#12111yescharacteristic
286C22×C11#54611yescharacteristic
287C22×C11#54811yescharacteristic
288C22×C11C22×D811yescharacteristic
289C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C11#57711yescharacteristic
291C22×C11#57711yescharacteristic
292C4×C11—22no—
293C4×C11—81no—
294C4×C11#45914yes—
295C4×C11#52911yescharacteristic
296C4×C11#54211yescharacteristic
297C4×C11#54611yescharacteristic
298C4×C11#54711yescharacteristic
299Dic11—24no—
300Dic11—42no—
301Dic11—42no—
302Dic11—81no—
303Dic11—82no—
304C22×Q8—221no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4C22×D1111yescharacteristic
308C22×D4C22×D1112yes—
309C23×C4—21no—
310C23×C4—222no—
311C2×D8—24no—
312C2×D8—24no—
313C2×D8—42no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8C22×D1112yes—
317C4⋊Q8—222no—
318C4⋊Q8—222no—
319#127—22no—
320#127C22⋊D1114yes—
321C22⋊Q8—444no—
322C22⋊Q8—444no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—224no—
326C4×D4—442no—
327C4×D4—444no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—21no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—112no—
344C2×C42—221no—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—22no—
347C4⋊C8—442no—
348#102—24no—
349#102—222no—
350#102—222no—
351#102—224no—
352#102—224no—
353C4×C8—222no—
354#95—112no—
355#95—221no—
356C2×C11—82no—
357C2×C11—84no—
358C2×C11#242711yescharacteristic
359C2×C11C2×#45911yescharacteristic
360C2×C11#304211yescharacteristic
361C2×C11#329411yescharacteristic
362C2×C11#333211yescharacteristic
363C2×C11#335811yescharacteristic
364C2×C11#337311yescharacteristic
365C24—21no—
366C24—22no—
367C2×Q8—442no—
368C2×Q8—442no—
369C2×Q8—442no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—81no—
385C2×D4—81no—
386C2×D4#434112yes—
387C2×D4C2×C22⋊D1114yes—
388C22×C4—21no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—222no—
397C22×C4—444no—
398C22×C4—444no—
399C22×C4—882no—
400C22×C4D4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403D8—48no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—221no—
408C2×C8—221no—
409C2×C8—221no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—221no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—114no—
416C4⋊C4—112no—
417C4⋊C4—222no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—222no—
421C4⋊C4—221no—
422C4⋊C4—222no—
423C4⋊C4—444no—
424C4⋊C4—444no—
425C4⋊C4—442no—
426C22⋊C4—42no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C22⋊C4—444no—
430C22⋊C4—444no—
431C22⋊C4—882no—
432C42—222no—
433C42—222no—
434C42—442no—
435C42#434112yes—
436C42C2×C22⋊D1112yes—
437C11#2531811yescharacteristic, complemented, Sylow
438C23—24no—
439C23—22no—
440C23—41no—
441C23—42no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—42no—
450C23—42no—
451C23—41no—
452C23C2×D4×D1111yescharacteristic
453Q8—884no—
454D4—22no—
455D4—24no—
456D4—24no—
457D4—22no—
458D4—48no—
459D4—41no—
460D4—42no—
461D4—41no—
462D4—42no—
463D4—84no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—84no—
470C2×C4—114no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—441no—
485C2×C4—888no—
486C2×C4D8×D1112yes—
487C2×C4#6696412yes—
488C2×C4#6699212yes—
489C2×C4#6699212yes—
490C2×C4C2×#434111yescharacteristic
491C2×C4C2×#434111yescharacteristic
492C2×C4#6703711yescharacteristic
493C2×C4#41×D1111yescharacteristic
494C2×C4#6704311yescharacteristic
495C2×C4C22×C22⋊D1111yescharacteristic
496C8—42no—
497C8—441no—
498C8—441no—
499C22—44no—
500C22—42no—
501C22—44no—
502C22—42no—
503C22—44no—
504C22—42no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—82no—
512C22—82no—
513C22#1062312911yescharacteristic
514C22#1062314311yescharacteristic
515C22C2×D8×D1111yescharacteristic
516C22C2×#6696411yescharacteristic
517C22#1062330611yescharacteristic
518C22#1062330611yescharacteristic
519C22C2×#6699211yescharacteristic
520C4—22no—
521C4—81no—
522C4—224no—
523C4—442no—
524C4—442no—
525C4—882no—
526C4—881no—
527C4#1062276314yes—
528C4#1062313111yescharacteristic
529C4#1062313411yescharacteristic
530C4#1062333711yescharacteristic
531C4#1062335511yescharacteristic
532C2—84no—
533C2—82no—
534C2#1307219511yescharacteristic
535C2C2×#1062276311yescharacteristic
536C2#1307813011yescharacteristic
537C2#1308043211yescharacteristic
538C2#1308094611yescharacteristic
539C2#1308124611yescharacteristic
540C2#1308141211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11#25318
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
2. #13073569C2semidirect
3. #13071681C2semidirect
4. #13070022C2semidirect
5. #13069924C2semidirect
6. #13069567C2semidirect
7. #13069332C2semidirect
8. #13068966C2semidirect
9. #13068614C2semidirect
10. C4×#66896C2semidirect
155. C4⋊Dic11D8semidirect
437. C11#25318semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
#130735692
#130716812
#130700222
#130699242
#130695672
#130693322
#130689662
#130686142
C4×#668962
C2×C11×#4592
#2531811