Finite Group Databasebeta

← #14676002

Subgroups — #14676002

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2C2×#10622824C211yesmaximal, characteristic
3C2×#10622556C211yesmaximal, characteristic
4C2×#10622556C211yesmaximal, characteristic
5C2×#10622555C211yesmaximal, characteristic
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic
7#13066882C214yesmaximal, complemented
8Dic11⋊#95C214yesmaximal, complemented
9C2×C11×#381C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4—24no—
18C22×Dic11⋊C4—24no—
19C22×Dic11⋊C4C418yescomplemented
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C11×#381—24no—
25C2×C11×#95C2214yes—
26#10622824—24no—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32#10622556—24no—
33#10622556—24no—
34#10622555—24no—
35C22⋊C4×Dic11—24no—
36C25×C11C2311yescharacteristic
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—22no—
42C23×C4×C11—22no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2312yes—
46C23×C4×C11C2312yes—
47C23×Dic11—28no—
48C23×Dic11—22no—
49C23×Dic11—22no—
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—22no—
53C23×Dic11—22no—
54C23×Dic11C2×C414yes—
55C23×Dic11C2×C414yes—
56C23×Dic11D414yes—
57C23×Dic11D414yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4D414yes—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11D414yes—
75C2×Dic11⋊C4—232no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4C2×C418yes—
83C2×Dic11⋊C4C2×C418yes—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—28no—
86C11×#95—28no—
87C11⋊#95—28no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—28no—
91C11⋊#95—28no—
92#13904—111nomaximal, Sylow
93C24×C11—24no—
94C24×C11—24no—
95C24×C11C22×C412yes—
96C24×C11C2×D412yes—
97C24×C11C2×D412yes—
98C24×C11C2×D412yes—
99C24×C11C2×D412yes—
100C24×C11#4112yes—
101C24×C11#4112yes—
102C24×C11C2411yescharacteristic
103C22×C4×C11—28no—
104C22×C4×C11—28no—
105C22×C4×C11—28no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—44no—
124C22×C4×C11—44no—
125C22×C4×C11C22×C414yes—
126C22×C4×C11C2×D414yes—
127C22×Dic11—216no—
128C22×Dic11—216no—
129C22×Dic11—216no—
130C22×Dic11—28no—
131C22×Dic11—28no—
132C22×Dic11—28no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—44no—
150C22×Dic11—44no—
151C22×Dic11—44no—
152C22×Dic11—44no—
153C22×Dic11C22⋊C4116yes—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C412yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C2×D414yes—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×D412yes—
162C22×Dic11#4118yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—44no—
165C22⋊Dic11—28no—
166C22⋊Dic11—44no—
167Dic11⋊C4—216no—
168Dic11⋊C4—216no—
169Dic11⋊C4—48no—
170C4×Dic11—48no—
171C23×C4⋊C4—111no—
172C2×#381—111no—
173C2×#381—111no—
174C2×#381—111no—
175C2×#381D1111yescharacteristic
176C2×#380—111no—
177C2×C4×C22⋊C4—111no—
178#1445—114no—
179C4⋊#95—114no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—28no—
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11C2×C22⋊C414yes—
191C23×C11C4×D414yes—
192C23×C11C4×D414yes—
193C23×C11#12114yes—
194C23×C11#12114yes—
195C23×C11#12414yes—
196C23×C11#12714yes—
197C23×C11C23×C411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C22×D411yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C23×C11C2×#4111yescharacteristic
204C23×C11C2×#4114yes—
205C23×C112−1+414yes—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—28no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—44no—
218C2×C4×C11—416no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—232no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—28no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240C2×Dic11—416no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—44no—
246C2×Dic11C2×C22⋊C414yes—
247C2×Dic11C2×C22⋊C414yes—
248C2×Dic11#11718yes—
249C2×Dic11#12318yes—
250C2×Dic11#12318yes—
251C24×C4—111no—
252C24×C4—111no—
253C24×C4C2×D1111yescharacteristic
254C22×C4⋊C4—112no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—118no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—224no—
259C22×C4⋊C4—224no—
260C22×C22⋊C4—111no—
261C22×C22⋊C4—111no—
262C22×C22⋊C4C2×D1111yescharacteristic
263C22×C22⋊C4C2×D1111yescharacteristic
264C22×C42—112no—
265#381—24no—
266#381—224no—
267#381—224no—
268#381—224no—
269#380—224no—
270C4×C22⋊C4—224no—
271C2×#95—114no—
272C2×#95—114no—
273C2×#95—114no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95C2×D1114yes—
277C22×C11—24no—
278C22×C11—28no—
279C22×C11—28no—
280C22×C11—28no—
281C22×C11—28no—
282C22×C11—28no—
283C22×C11—28no—
284C22×C11—24no—
285C22×C11#39018yes—
286C22×C11C22×C22⋊C411yescharacteristic
287C22×C11C2×#11712yes—
288C22×C11C2×C4×D411yescharacteristic
289C22×C11C2×C4×D411yescharacteristic
290C22×C11#51912yes—
291C22×C11C2×#12111yescharacteristic
292C22×C11C2×#12111yescharacteristic
293C22×C11C2×#12312yes—
294C22×C11C2×#12312yes—
295C22×C11C2×#12411yescharacteristic
296C22×C11C2×#12711yescharacteristic
297C22×C11#53612yes—
298C22×C11#53612yes—
299C22×C11#54714yes—
300C22×C11#54714yes—
301C22×C11#55214yes—
302C22×C11#55214yes—
303C4×C11—44no—
304C4×C11—44no—
305C4×C11—82no—
306Dic11—24no—
307Dic11—44no—
308Dic11—44no—
309Dic11—82no—
310Dic11#38118yescomplemented
311C25C22×D1111yescharacteristic
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—111no—
319C23×C4—114no—
320C23×C4—114no—
321C23×C4—114no—
322C23×C4—111no—
323C23×C4—114no—
324C23×C4—112no—
325C23×C4—112no—
326C23×C4—112no—
327C23×C4—228no—
328C23×C4—222no—
329C23×C4—222no—
330C23×C4—222no—
331C23×C4—222no—
332C23×C4—222no—
333C23×C4—222no—
334C23×C4C4×D1114yes—
335C23×C4C22×D1112yes—
336C23×C4C22×D1112yes—
337C23×C4C22×D1112yes—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—118no—
340C2×C4⋊C4—2232no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—224no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—228no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—114no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4C22⋊D1114yes—
359C2×C42—224no—
360C2×C42—228no—
361#95—28no—
362#95—224no—
363#95—224no—
364#95—228no—
365#95—228no—
366#95—228no—
367C2×C11—28no—
368C2×C11C2×#38111yescharacteristic
369C2×C11C2×#39011yescharacteristic
370C2×C11#231011yescharacteristic
371C2×C11#234412yes—
372C2×C11#234412yes—
373C2×C11#248612yes—
374C2×C11#248612yes—
375C2×C11#250112yes—
376C2×C11#250312yes—
377C24—24no—
378C24—24no—
379C24C2×C4×D1112yes—
380C24#433912yes—
381C24D4×D1112yes—
382C24D4×D1112yes—
383C24D4×D1112yes—
384C24#434112yes—
385C24C2×C22⋊D1112yes—
386C24C23×D1111yescharacteristic
387C22×C4—28no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—44no—
406C22×C4—44no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—118no—
413C22×C4—1116no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—2216no—
420C22×C4—2216no—
421C22×C4—2216no—
422C22×C4—224no—
423C22×C4—228no—
424C22×C4—228no—
425C22×C4—228no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—444no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4—444no—
445C22×C4C2×C4×D1114yes—
446C22×C4C2×C22⋊D1114yes—
447C4⋊C4—2216no—
448C4⋊C4—2216no—
449C4⋊C4—448no—
450C22⋊C4—28no—
451C22⋊C4—44no—
452C22⋊C4—228no—
453C22⋊C4—444no—
454C42—448no—
455C11#1390411yescharacteristic, complemented, Sylow
456C23—24no—
457C23—24no—
458C23—28no—
459C23—28no—
460C23—24no—
461C23—24no—
462C23—28no—
463C23—24no—
464C23—24no—
465C23—28no—
466C23C22⋊C4×D1114yes—
467C23(C22⋊D11)⋊C414yes—
468C23#6693714yes—
469C23#6693814yes—
470C23C4×C22⋊D1114yes—
471C23#6699214yes—
472C23#6699314yes—
473C23C22×C4×D1111yescharacteristic
474C23C2×#433911yescharacteristic
475C23C2×D4×D1111yescharacteristic
476C23C2×D4×D1111yescharacteristic
477C23C2×D4×D1111yescharacteristic
478C23C2×#434111yescharacteristic
479C23#41×D1114yes—
480C23#6704314yes—
481C23C22×C22⋊D1111yescharacteristic
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—28no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—416no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—114no—
501C2×C4—118no—
502C2×C4—118no—
503C2×C4—118no—
504C2×C4—114no—
505C2×C4—2232no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—228no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—444no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—4416no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—444no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—444no—
527C22—28no—
528C22—28no—
529C22—24no—
530C22—28no—
531C22—28no—
532C22—24no—
533C22—28no—
534C22—28no—
535C22#1062257018yes—
536C22C2×C22⋊C4×D1111yescharacteristic
537C22C2×(C22⋊D11)⋊C411yescharacteristic
538C22C2×#6693711yescharacteristic
539C22C2×#6693811yescharacteristic
540C22#1062304712yes—
541C22D11×#11712yes—
542C22#1062306214yes—
543C22#1062317912yes—
544C22#1062317912yes—
545C22#1062318114yes—
546C22D11×#12312yes—
547C22D11×#12312yes—
548C22#1062318614yes—
549C22C2×C4×C22⋊D1111yescharacteristic
550C22C2×#6699211yescharacteristic
551C22C2×#6699311yescharacteristic
552C22#1062335514yes—
553C4—44no—
554C4—44no—
555C4—82no—
556C4—118no—
557C4—224no—
558C4—444no—
559C4—444no—
560C4—882no—
561C2—28no—
562C2D11×#38111yescharacteristic
563C2C2×#1062257011yescharacteristic
564C2#1307120111yescharacteristic
565C2#1307148012yes—
566C2#1307148612yes—
567C2#1307292112yes—
568C2#1307292312yes—
569C2#1307308512yes—
570C2#1307309912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#381C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#381D11
hypocenterC11#13904
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
7. #13066882C2semidirect
8. Dic11⋊#95C2semidirect
19. C22×Dic11⋊C4C4semidirect
310. Dic11#381semidirect
455. C11#13904semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106228242
C2×#106225562
C2×#106225552
C2×C22⋊C4×Dic112
#130668822
Dic11⋊#952
C2×C11×#3812
#1390411