Finite Group Databasebeta

← #14677240

Subgroups — #14677240

Order 2816.

2054 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic
2C2×#10622843C211yesmaximal, characteristic
3C2×#10622843C211yesmaximal, characteristic
4C2×#10622843C211yesmaximal, characteristic
5#13066869C214yesmaximal
6#13066848C214yesmaximal
7#13066846C211yesmaximal, characteristic
8C4×C11⋊#95C211yesmaximal, characteristic
9C22×C11×C4⋊Q8C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C2×C11×C4⋊Q8—24no—
13C2×C11×C4⋊Q8—24no—
14C2×C11×C4⋊Q8C418yescomplemented
15C22×C11×C4⋊C4C2214yes—
16C22×C42×C11C2211yescharacteristic
17C2×Q8×Dic11—24no—
18C2×Q8×Dic11—24no—
19C2×Q8×Dic11—24no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26#10622843—24no—
27#10622843—24no—
28#10622843—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2214yes—
33C2×C11⋊#95C2214yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C22×Q8×C11—22no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11C2×C414yes—
47C22×Q8×C11C2×C414yes—
48C22×Q8×C11D414yes—
49C22×Q8×C11D414yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C11×C4⋊Q8—232no—
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4C2×C4116yes—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11C2×C414yes—
66Q8×Dic11—232no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—24no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11D414yes—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11D414yes—
85C11⋊#95—28no—
86C11⋊#95—24no—
87C11⋊#95—28no—
88C11⋊#95—28no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95Q818yescomplemented
92#14024—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C2×Q8×C11—28no—
95C2×Q8×C11—28no—
96C2×Q8×C11—28no—
97C2×Q8×C11—28no—
98C2×Q8×C11—28no—
99C2×Q8×C11—28no—
100C2×Q8×C11—28no—
101C2×Q8×C11—28no—
102C2×Q8×C11—28no—
103C2×Q8×C11—44no—
104C2×Q8×C11—44no—
105C2×Q8×C11—44no—
106C2×Q8×C11—44no—
107C2×Q8×C11C22⋊C4116yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
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×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C414yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×Q814yes—
133C22×C4×C11#4114yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11C2×D414yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×Q814yes—
162C22×Dic11C2×Q814yes—
163C11×C4⋊C4—232no—
164C42×C11—28no—
165C4⋊Dic11—216no—
166C4⋊Dic11—28no—
167C4⋊Dic11—44no—
168C4×Dic11—216no—
169C4×Dic11—28no—
170C4×Dic11—44no—
171C22×C4⋊Q8D1111yescharacteristic
172C22×C4×Q8—111no—
173C2×#391—111no—
174C2×#391—111no—
175C2×#391—111no—
176#1441—114no—
177#1436—114no—
178C4⋊#95—111no—
179C4×#95—111no—
180C23×C11C23×C411yescharacteristic
181C23×C11C22×D411yescharacteristic
182C23×C11C22×D411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C22×Q812yes—
186C23×C11C2×#4111yescharacteristic
187C23×C11C2×#4111yescharacteristic
188C23×C11C2×#4112yes—
189C23×C112−1+412yes—
190C23×C112−1+412yes—
191Q8×C11—232no—
192Q8×C11—416no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11C2×C22⋊C418yes—
213C2×C4×C11C2×C22⋊C414yes—
214C2×C4×C11C4×D414yes—
215C2×C4×C11C4×D414yes—
216C2×C4×C11C4×Q818yescomplemented
217C2×C4×C11#12014yes—
218C2×C4×C11#12114yes—
219C2×C4×C11#12114yes—
220C2×C4×C11#12314yes—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—28no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11C4⋊Q814yescomplemented
248C23×Q8C2×D1111yescharacteristic
249C23×Q8C2×D1111yescharacteristic
250C2×C4⋊Q8—24no—
251C2×C4⋊Q8—24no—
252C2×C4⋊Q8Dic1118yescomplemented
253C2×C4×Q8—224no—
254C2×C4×Q8—224no—
255C2×C4×Q8—224no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4C2×D1114yes—
260C22×C42—111no—
261C22×C42—112no—
262C22×C42—111no—
263C22×C42C2×D1111yescharacteristic
264#391—224no—
265#391—224no—
266#391—224no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—114no—
270C2×#95—112no—
271C2×#95—114no—
272C2×#95—114no—
273C2×#95—112no—
274C22×C11C22×C22⋊C411yescharacteristic
275C22×C11C2×C4×D411yescharacteristic
276C22×C11C2×C4×D411yescharacteristic
277C22×C11C2×C4×Q812yes—
278C22×C11#51912yes—
279C22×C11C2×#12011yescharacteristic
280C22×C11C2×#12111yescharacteristic
281C22×C11C2×#12111yescharacteristic
282C22×C11C2×#12311yescharacteristic
283C22×C11C2×C4⋊Q811yescharacteristic
284C22×C11#53211yescharacteristic
285C22×C11#53312yes—
286C22×C11#53611yescharacteristic
287C22×C11#53611yescharacteristic
288C22×C11#54112yes—
289C22×C11#54712yes—
290C22×C11#54812yes—
291C22×C11#54812yes—
292C22×C11D4×Q812yes—
293C22×C11D4×Q812yes—
294C22×C11D4×Q812yes—
295C22×C11#55612yes—
296C22×C11#55712yes—
297C4×C11—28no—
298C4×C11—28no—
299C4×C11—44no—
300C4×C11#38618yes—
301Dic11—24no—
302Dic11—44no—
303Dic11—42no—
304Dic11—44no—
305Dic11—82no—
306C22×Q8—22no—
307C22×Q8—22no—
308C22×Q8—22no—
309C22×Q8—22no—
310C22×Q8—22no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8C2×Dic1114yes—
317C22×Q8C2×Dic1114yes—
318C22×Q8C22⋊D1114yes—
319C22×Q8C22⋊D1114yes—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—112no—
323C23×C4—112no—
324C23×C4—112no—
325C23×C4C22×D1112yes—
326C23×C4C22×D1112yes—
327C23×C4C22×D1112yes—
328C23×C4C22×D1111yescharacteristic
329C4⋊Q8—232no—
330C4×Q8—2232no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—224no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4C2×Dic11116yes—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—114no—
346C2×C42—224no—
347C2×C42—224no—
348C2×C42—222no—
349C2×C42—224no—
350C2×C42—222no—
351C2×C42—222no—
352C2×C42—222no—
353C2×C42—222no—
354C2×C42C2×Dic1114yes—
355#95—118no—
356#95—224no—
357#95—224no—
358#95—228no—
359#95—224no—
360#95—228no—
361#95—228no—
362C2×C11C2×#38611yescharacteristic
363C2×C11C4×C4⋊Q811yescharacteristic
364C2×C11#232711yescharacteristic
365C2×C11Q8×C22⋊C412yes—
366C2×C11#236512yes—
367C2×C11#242912yes—
368C2×C11#243211yescharacteristic
369C2×C11#243411yescharacteristic
370C2×C11#244612yes—
371C2×C11#254511yescharacteristic
372C2×C11#254611yescharacteristic
373C24C23×D1111yescharacteristic
374C2×Q8—28no—
375C2×Q8—28no—
376C2×Q8—28no—
377C2×Q8—28no—
378C2×Q8—28no—
379C2×Q8—28no—
380C2×Q8—28no—
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—44no—
384C2×Q8—44no—
385C2×Q8—44no—
386C2×Q8—44no—
387C2×Q8C22⋊Dic11116yes—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—112no—
403C22×C4—114no—
404C22×C4—112no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—221no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4D4×D1112yes—
430C22×C4D4×D1112yes—
431C22×C4#434112yes—
432C22×C4#434112yes—
433C22×C4Q8×D1114yes—
434C22×C4#434314yes—
435C22×C4C22×Dic1114yes—
436C22×C4C22×Dic1114yes—
437C22×C4C22×Dic1114yes—
438C22×C4C22×Dic1112yes—
439C22×C4C2×C22⋊D1114yes—
440C22×C4C2×C22⋊D1114yes—
441C22×C4C2×C22⋊D1112yes—
442C22×C4C2×C22⋊D1112yes—
443C4⋊C4—232no—
444C4⋊C4—2216no—
445C4⋊C4—228no—
446C4⋊C4—444no—
447C42—28no—
448C42—2216no—
449C42—228no—
450C42—444no—
451C11#1402411yescharacteristic, complemented, Sylow
452C23C2×D4×D1111yescharacteristic
453C23C2×D4×D1111yescharacteristic
454C23C2×#434111yescharacteristic
455C23C2×#434111yescharacteristic
456C23C2×Q8×D1112yes—
457C23C2×#434312yes—
458C23#6704012yes—
459C23#6704012yes—
460C23C23×Dic1111yescharacteristic
461C23C22×C22⋊D1111yescharacteristic
462C23C22×C22⋊D1111yescharacteristic
463Q8—232no—
464Q8—416no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—114no—
485C2×C4—222no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—228no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—442no—
498C2×C4—442no—
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—442no—
508C2×C4—444no—
509C2×C4—442no—
510C2×C4—444no—
511C2×C4D4×Dic1114yes—
512C2×C4D4×Dic1114yes—
513C2×C4#6698814yes—
514C2×C4#6699014yes—
515C2×C4#6699214yes—
516C2×C4#6699214yes—
517C2×C4Q8×Dic1118yescomplemented
518C2×C4C2×C22⋊Dic1118yes—
519C2×C4C2×C22⋊Dic1114yes—
520C22#1062325212yes—
521C22D11×C4⋊Q811yescharacteristic
522C22#1062325511yescharacteristic
523C22#1062325511yescharacteristic
524C22#1062325611yescharacteristic
525C22#1062325712yes—
526C22#1062325812yes—
527C22#1062325912yes—
528C22#1062326212yes—
529C22#1062326312yes—
530C22C2×D4×Dic1111yescharacteristic
531C22C2×D4×Dic1111yescharacteristic
532C22C2×#6698811yescharacteristic
533C22C2×#6699011yescharacteristic
534C22C2×#6699211yescharacteristic
535C22C2×#6699211yescharacteristic
536C22C2×Q8×Dic1112yes—
537C22#1062334312yes—
538C22Q8×C22⋊D1112yes—
539C22Q8×C22⋊D1112yes—
540C22#1062334812yes—
541C22#1062334812yes—
542C22C22×C22⋊Dic1111yescharacteristic
543C4—28no—
544C4—28no—
545C4—44no—
546C4—224no—
547C4—444no—
548C4—442no—
549C4—444no—
550C4—882no—
551C4#1062283318yes—
552C2C2×#1062283311yescharacteristic
553C2C4⋊Q8×Dic1111yescharacteristic
554C2#1307133611yescharacteristic
555C2Q8×C22⋊Dic1112yes—
556C2#1307167612yes—
557C2#1307221812yes—
558C2#1307224111yescharacteristic
559C2#1307225711yescharacteristic
560C2#1307238812yes—
561C2#1307359311yescharacteristic
562C2#1307360211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×C4⋊Q8C2
socle, prime radical, cosocleC24×C11C24
hypercenterC22×C4⋊Q8D11
hypocenterC11#14024
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
14. C2×C11×C4⋊Q8C4semidirect
91. C11⋊#95Q8semidirect
216. C2×C4×C11C4×Q8semidirect
247. C2×Dic11C4⋊Q8semidirect
252. C2×C4⋊Q8Dic11semidirect
451. C11#14024semidirect
517. C2×C4Q8×Dic11semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106228432
#130668692
#130668482
#130668462
C4×C11⋊#952
C22×C11×C4⋊Q82
#1402411