Finite Group Databasebeta

← #14803617

Subgroups — #14803617

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×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622456C211yesmaximal, characteristic
3#13073570C211yesmaximal, characteristic, complemented
4#13071680C211yesmaximal, characteristic, complemented
5#13070023C212yesmaximal, complemented
6#13069928C212yesmaximal, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068965C212yesmaximal, complemented
9#13068615C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#1988C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999—21no—
14C2×#66999—21no—
15C22×D88C2212yes—
16C2×#66946C2212yes—
17C2×#66927C2211yescharacteristic
18C2×C4×D44—21no—
19C2×C4×D44C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2212yes—
23C2×Dic11⋊C8C2212yes—
24#10622701—24no—
25#10622605—22no—
26#10622601C2212yes—
27#10622601C2212yes—
28#10622589C2212yes—
29C2×#66873C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66873C2212yes—
32C2×#66873C2211yescharacteristic
33#10622552—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622456—24no—
37#10622278—22no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11—22no—
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2311yescharacteristic
59#66999—44no—
60#66999—44no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C2×D88—24no—
76C2×D88—24no—
77C2×D88—42no—
78#66946—24no—
79#66946—42no—
80#66927—22no—
81#66927D414yes—
82C4×D44—22no—
83C4×D44—22no—
84C4×D44—44no—
85C11×C4⋊C8—22no—
86C11×#95—21no—
87C11⋊#95D412yes—
88#66885—24no—
89Dic11⋊C8—42no—
90#66873—24no—
91#66873—24no—
92#66873—22no—
93#66873—22no—
94C4×C11⋊C8—22no—
95#25318—111nomaximal, Sylow
96C23×D11—21no—
97C23×D11—22no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11C2×D412yes—
109C22×Dic11C2×D412yes—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—81no—
125C2×D44—81no—
126C2×D44C2×D414yes—
127C2×D44#4112yes—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—82no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4#4112yes—
144C42×C11—42no—
145C42×C11C2×D412yes—
146C42×C11#4112yes—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—42no—
152(C2×D11)⋊C4—82no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11D814yescomplemented
157Dic11⋊C4—44no—
158Dic11⋊C4—44no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167D88—48no—
168C2×#486—111no—
169C2×#459—111no—
170#2542—111no—
171#2366—111no—
172#2071—112no—
173#2054—112no—
174#1988D1111yescharacteristic, complemented
175#1939—111no—
176#1879—112no—
177#1802—112no—
178C4×#102—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—24no—
181C22×D11—22no—
182C22×D11—41no—
183C22×D11—42no—
184C22×D11—41no—
185C22×D11—42no—
186C22×D11—41no—
187C22×D11—42no—
188C22×D11—41no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—41no—
193C22×D11—41no—
194Q8×C11—84no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11C2×D812yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11C2×D814yes—
225D44—22no—
226D44—22no—
227D44—24no—
228D44—24no—
229D44—42no—
230D44—42no—
231D44—41no—
232D44—41no—
233D44—48no—
234D44—84no—
235C4×D11—88no—
236C4×D11—84no—
237C8×C11—42no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C22×D8—112no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×#127—111no—
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C4×D4—112no—
246C2×C4×D4—111no—
247C2×C4×D4—221no—
248#486—224no—
249#459—224no—
250C2×C4⋊C8—112no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×#102—112no—
253C2×#102—111no—
254C2×#102—112no—
255C2×#102—112no—
256C2×#102—111no—
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⋊C4C2×D1111yescharacteristic
266#340—111no—
267#340—111no—
268#340C2×D1112yes—
269#340C2×D1112yes—
270#336—112no—
271C22×C11C2×#12111yescharacteristic
272C22×C11#54611yescharacteristic
273C22×C11#54811yescharacteristic
274C22×C11C22×D811yescharacteristic
275C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C11#57711yescharacteristic
277C22×C11#57711yescharacteristic
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—44no—
281C2×D11—42no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—82no—
285C2×D11—81no—
286C2×D11—82no—
287C2×D11—82no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—82no—
291C2×D11—81no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—81no—
295C4×C11—82no—
296C4×C11#45914yes—
297C4×C11#52911yescharacteristic
298C4×C11#54211yescharacteristic
299C4×C11#54611yescharacteristic
300C4×C11#54711yescharacteristic
301Dic11—24no—
302Dic11—42no—
303Dic11—81no—
304C22×Q8—21no—
305C22×D4—112no—
306C22×D4—111no—
307C22×D4—221no—
308C22×D4—221no—
309C23×C4—222no—
310C23×C4—221no—
311C2×D8—224no—
312C2×D8—224no—
313C2×D8—442no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8C22×D1112yes—
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319#127—114no—
320#127—222no—
321C22⋊Q8—444no—
322C22⋊Q8—444no—
323C4×D4—224no—
324C4×D4—222no—
325C4×D4—222no—
326C4×D4—444no—
327C4×D4—442no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4C22×D1112yes—
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—222no—
343C2×C42—21no—
344C2×C42—112no—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—22no—
347C4⋊C8—442no—
348#102—222no—
349#102—224no—
350#102—224no—
351#102—224no—
352#102—222no—
353C4×C8—222no—
354#95—21no—
355#95—112no—
356C2×C11#242711yescharacteristic
357C2×C11C2×#45911yescharacteristic
358C2×C11#304211yescharacteristic
359C2×C11#329411yescharacteristic
360C2×C11#333211yescharacteristic
361C2×C11#335811yescharacteristic
362C2×C11#337311yescharacteristic
363D11—82no—
364D11—84no—
365C24—221no—
366C24—222no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×D4—114no—
371C2×D4—112no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—221no—
375C2×D4—222no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—222no—
379C2×D4—222no—
380C2×D4—221no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—221no—
384C2×D4—442no—
385C2×D4—442no—
386C2×D4—881no—
387C2×D4—881no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—112no—
392C22×C4—112no—
393C22×C4—221no—
394C22×C4—444no—
395C22×C4—444no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—882no—
400C22×C4D4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403D8—448no—
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—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—42no—
419C4⋊C4—114no—
420C4⋊C4—222no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—444no—
424C4⋊C4—444no—
425C4⋊C4#434312yes—
426C22⋊C4—444no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C22⋊C4—444no—
430C22⋊C4—442no—
431C22⋊C4—882no—
432C42—42no—
433C42—222no—
434C42—222no—
435C42#433912yes—
436C42D4×D1112yes—
437C11#2531811yescharacteristic, complemented, Sylow
438C23—224no—
439C23—222no—
440C23—441no—
441C23—441no—
442C23—442no—
443C23—441no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—441no—
448C23—441no—
449C23—442no—
450C23—441no—
451C23—442no—
452C23C2×D4×D1111yescharacteristic
453Q8—84no—
454D4—224no—
455D4—222no—
456D4—222no—
457D4—224no—
458D4—441no—
459D4—442no—
460D4—441no—
461D4—442no—
462D4—448no—
463D4—884no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—114no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—888no—
485C2×C4—884no—
486C2×C4#6693712yes—
487C2×C4#6693712yes—
488C2×C4D8×D1112yes—
489C2×C4#6696712yes—
490C2×C4C2×#433911yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×#434311yescharacteristic
493C2×C4#6704011yescharacteristic
494C2×C4#41×D1111yescharacteristic
495C2×C4#6704211yescharacteristic
496C8—42no—
497C8—441no—
498C8—441no—
499C22—444no—
500C22—442no—
501C22—444no—
502C22—442no—
503C22—444no—
504C22—442no—
505C22—881no—
506C22—882no—
507C22—882no—
508C22—881no—
509C22—881no—
510C22—882no—
511C22—881no—
512C22—882no—
513C22C2×#6693711yescharacteristic
514C22#1062316111yescharacteristic
515C22#1062316411yescharacteristic
516C22C2×D8×D1111yescharacteristic
517C22C2×#6696711yescharacteristic
518C22#1062330911yescharacteristic
519C22#1062330911yescharacteristic
520C4—22no—
521C4—42no—
522C4—82no—
523C4—81no—
524C4—224no—
525C4—442no—
526C4—881no—
527C4#1062239914yes—
528C4#1062311111yescharacteristic
529C4#1062311311yescharacteristic
530C4#1062320711yescharacteristic
531C4#1062325711yescharacteristic
532C2—884no—
533C2—882no—
534C2#1307219411yescharacteristic
535C2C2×#1062239911yescharacteristic
536C2#1307812711yescharacteristic
537C2#1308042611yescharacteristic
538C2#1308094011yescharacteristic
539C2#1308125011yescharacteristic
540C2#1308140711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC2×#10622456C2
hypercenter#1988D11
hypocenterC11#25318
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. #13073570C2semidirect
4. #13071680C2semidirect
5. #13070023C2semidirect
6. #13069928C2semidirect
7. #13069332C2semidirect
8. #13068965C2semidirect
9. #13068615C2semidirect
10. C4×#66873C2semidirect
11. C11×#1988C2semidirect
156. C4⋊Dic11D8semidirect
174. #1988D11semidirect
437. C11#25318semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106224562
#130735702
#130716802
#130700232
#130699282
#130693322
#130689652
#130686152
C4×#668732
C11×#19882
#2531811