Finite Group Databasebeta

← #14660239

Subgroups — #14660239

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66870C212yesmaximal
2C2×#10622826C211yesmaximal, characteristic
3C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
4C2×#10622165C212yesmaximal, complemented
5C11×C22⋊#95C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C22⋊Dic11C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C22×(C2×D11)⋊C4C412yescomplemented
12C22×C4×Dic11—21no—
13C2×C11×#95—22no—
14#10622826—21no—
15#10622826—21no—
16#10622826—22no—
17C4×C22⋊Dic11—24no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C412yescomplemented
20C2×#66870—24no—
21C2×#66870—24no—
22C2×#66870C418yescomplemented
23#10622165—24no—
24C25×C11C2311yescharacteristic
25C24×D11C2×C411yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—44no—
30C23×C4×C11C2×C412yes—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D412yes—
34C22×C22⋊D11—22no—
35C22×C22⋊D11—22no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C22×C22⋊D11—22no—
39C22×C22⋊D11—22no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11C2×C414yes—
42C23×Dic11—22no—
43C23×Dic11C2×C411yescharacteristic
44C23×Dic11C2×C412yes—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4C2×C414yes—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11C2×C414yes—
59C2×C22⋊Dic11D414yes—
60C2×C22⋊Dic11D414yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—44no—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—44no—
66C11×#95—44no—
67C11⋊#95—24no—
68C11⋊#95—22no—
69C11⋊#95—22no—
70#66870—216no—
71#10960—111nomaximal, Sylow
72C24×C11—42no—
73C24×C11—42no—
74C24×C11C22×C411yescharacteristic
75C24×C11C22×C412yes—
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C24×C11C2×D412yes—
79C24×C11C2×D412yes—
80C24×C11#4112yes—
81C24×C11#4112yes—
82C24×C11#4112yes—
83C23×D11—21no—
84C23×D11—21no—
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—42no—
88C23×D11—42no—
89C23×D11C4212yescomplemented
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—21no—
95C22×C4×C11—24no—
96C22×C4×C11—21no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—24no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11—48no—
104C22×C4×C11—48no—
105C22×C4×C11—44no—
106C22×C4×C11—44no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11C22⋊C412yes—
110C22×C4×C11C22⋊C412yes—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—24no—
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—24no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—42no—
123C2×C22⋊D11—42no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—41no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—44no—
137C22×Dic11—44no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11C4212yescomplemented
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—42no—
144C11×C22⋊C4—42no—
145C22⋊Dic11—24no—
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—42no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11C22⋊C418yescomplemented
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—44no—
154C4×Dic11—48no—
155C22×#99—112no—
156C2×#386—111no—
157C2×C4×C22⋊C4—111no—
158C2×#342—112no—
159C22⋊#95D1111yescharacteristic, complemented
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—42no—
170C23×C11—44no—
171C23×C11—44no—
172C23×C11—42no—
173C23×C11—44no—
174C23×C11C2×C4211yescharacteristic
175C23×C11C2×C22⋊C412yes—
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11#11711yescharacteristic
178C23×C11#11712yes—
179C23×C11C4×D412yes—
180C23×C11C4×D412yes—
181C23×C11C4×D412yes—
182C23×C11C4×D412yes—
183C23×C11C4×D412yes—
184C23×C11C4×D412yes—
185C23×C11#12011yescharacteristic
186C23×C11#12112yes—
187C23×C11#12112yes—
188C23×C11#12112yes—
189C23×C11#12311yescharacteristic
190C23×C11#12312yes—
191C23×C11#12412yes—
192C23×C11#12411yescharacteristic
193C23×C11#12612yes—
194C23×C11#12711yescharacteristic
195C22×D11—22no—
196C22×D11—24no—
197C22×D11—44no—
198C22×D11—41no—
199C22×D11—42no—
200C22×D11—41no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—44no—
204C22×D11—82no—
205C22×D11—82no—
206C22×D11—84no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—48no—
215C2×C4×C11—48no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—48no—
219C2×C4×C11—44no—
220C2×C4×C11—82no—
221C2×C4×C11—82no—
222C2×C4×C11—84no—
223C2×C4×C11#9914yescomplemented
224C22⋊D11—44no—
225C22⋊D11—44no—
226C22⋊D11—44no—
227C22⋊D11—44no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—28no—
231C2×Dic11—44no—
232C2×Dic11—44no—
233C2×Dic11—48no—
234C2×Dic11—48no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—84no—
242C23×D4—111no—
243C24×C4C2×D1111yescharacteristic
244C22×C22⋊C4—112no—
245C22×C22⋊C4—111no—
246C22×C22⋊C4—112no—
247C22×C22⋊C4C2×D1112yes—
248C22×C42—221no—
249C2×#99—118no—
250C2×#99—224no—
251C2×#99—224no—
252#386—221no—
253#386—221no—
254#386—222no—
255C4×C22⋊C4—224no—
256C2×#95—22no—
257C2×#95—112no—
258C2×#95—221no—
259#342—224no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—22no—
269C22×C11—24no—
270C22×C11—24no—
271C22×C11—22no—
272C22×C11—24no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—24no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11C4×C22⋊C412yes—
285C22×C11C4×C22⋊C411yescharacteristic
286C22×C11#38612yes—
287C22×C11#38611yescharacteristic
288C22×C11#38812yes—
289C22×C11#38812yes—
290C22×C11#38812yes—
291C22×C11#39012yes—
292C22×C11#39011yescharacteristic
293C22×C11C2×#9912yes—
294C22×C11#41012yes—
295C2×D11—42no—
296C2×D11—44no—
297C2×D11—84no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—82no—
301C2×D11—84no—
302C4×C11—24no—
303C4×C11—42no—
304C4×C11—84no—
305Dic11—48no—
306Dic11—42no—
307Dic11—82no—
308C25—111no—
309C25C22×D1111yescharacteristic
310C22×D4—114no—
311C22×D4—221no—
312C22×D4—222no—
313C22×D4—222no—
314C22×D4—222no—
315C22×D4—222no—
316C22×D4—222no—
317C22×D4—221no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—44no—
322C23×C4—111no—
323C23×C4—112no—
324C23×C4—222no—
325C23×C4C4×D1112yes—
326C23×C4D4411yescharacteristic
327C23×C4D4411yescharacteristic
328C23×C4C22⋊D1112yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—114no—
335C2×C22⋊C4—114no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—221no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—221no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4C4×D1114yes—
348C2×C42—224no—
349C2×C42—444no—
350#99—2216no—
351#95—44no—
352#95—224no—
353#95—222no—
354#95—222no—
355C2×C11—22no—
356C2×C11—22no—
357C2×C11—22no—
358C2×C11—22no—
359C2×C11—22no—
360C2×C11—22no—
361C2×C11#143711yescharacteristic
362C2×C11C4×#9912yes—
363C2×C11#189811yescharacteristic
364C2×C11#189911yescharacteristic
365C2×C11#196412yes—
366D11—82no—
367C24—42no—
368C24—42no—
369C24—112no—
370C24—221no—
371C24—221no—
372C24—222no—
373C24—222no—
374C24—442no—
375C24—442no—
376C24C2×C4×D1111yescharacteristic
377C24C2×C4×D1112yes—
378C24C2×D4411yescharacteristic
379C24#433912yes—
380C24D4×D1112yes—
381C24D4×D1112yes—
382C24#434112yes—
383C24#434312yes—
384C24C2×C22⋊D1111yescharacteristic
385C2×D4—224no—
386C2×D4—224no—
387C2×D4—224no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—224no—
391C2×D4—441no—
392C2×D4—442no—
393C2×D4—442no—
394C2×D4—441no—
395C2×D4—442no—
396C2×D4—442no—
397C2×D4—442no—
398C2×D4—442no—
399C2×D4—441no—
400C2×D4—441no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—48no—
415C22×C4—48no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—112no—
421C22×C4—221no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—444no—
431C22×C4—444no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4(C2×D11)⋊C412yes—
435C22×C4(C2×D11)⋊C412yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—118no—
441C22⋊C4—224no—
442C22⋊C4—224no—
443C22⋊C4—224no—
444C22⋊C4—444no—
445C22⋊C4—442no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4—444no—
449C42—448no—
450C11#1096011yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—44no—
460C23—44no—
461C23—42no—
462C23—44no—
463C23—42no—
464C23—44no—
465C23—222no—
466C23—224no—
467C23—444no—
468C23—444no—
469C23—442no—
470C23—442no—
471C23—441no—
472C23—441no—
473C23—442no—
474C23—882no—
475C23—882no—
476C23—884no—
477C23C42×D1111yescharacteristic
478C23#6692511yescharacteristic
479C23C4×D4412yes—
480C23C22⋊C4×D1112yes—
481C23(C22⋊D11)⋊C412yes—
482C23(C22⋊D11)⋊C412yes—
483C23#6693511yescharacteristic
484C23#6693712yes—
485C23#6693812yes—
486C23#6693911yescharacteristic
487C23#6694512yes—
488C23#6694612yes—
489C23#6694612yes—
490C23#6694712yes—
491C23#6694812yes—
492C23#6695112yes—
493C23C2×(C2×D11)⋊C411yescharacteristic
494C23C4×C22⋊D1112yes—
495C23#6699212yes—
496C23#6699311yescharacteristic
497C23#6700011yescharacteristic
498D4—444no—
499D4—444no—
500D4—444no—
501D4—444no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—48no—
510C2×C4—48no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—84no—
518C2×C4—228no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—444no—
522C2×C4—444no—
523C2×C4—448no—
524C2×C4—448no—
525C2×C4—442no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—884no—
532C2×C4#6687014yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—21no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—442no—
558C22—444no—
559C22—884no—
560C22—884no—
561C22—881no—
562C22—881no—
563C22—882no—
564C22#1062227812yes—
565C22#1062227912yes—
566C22#1062228212yes—
567C22#1062228312yes—
568C22C4×(C2×D11)⋊C411yescharacteristic
569C22C2×#6687012yes—
570C22#1062257012yes—
571C22#1062257111yescharacteristic
572C22#1062260111yescharacteristic
573C22#1062260312yes—
574C22#1062261912yes—
575C4—24no—
576C4—42no—
577C4—84no—
578C4—448no—
579C4—442no—
580C4—882no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—882no—
588C2#1306685211yescharacteristic
589C2C4×#6687012yes—
590C2#1306906711yescharacteristic
591C2#1306907211yescharacteristic
592C2#1306945112yes—
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C2×C42
FrattiniC25C22×D11
FittingC11×C22⋊#95C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenterC22⋊#95D11
hypocenterC11#10960
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic11C2semidirect
4. C2×#10622165C2semidirect
5. C11×C22⋊#95C2semidirect
11. C22×(C2×D11)⋊C4C4semidirect
19. C2×C11⋊#95C4semidirect
22. C2×#66870C4semidirect
89. C23×D11C42semidirect
140. C22×Dic11C42semidirect
151. C22⋊Dic11C22⋊C4semidirect
159. C22⋊#95D11semidirect
223. C2×C4×C11#99semidirect
450. C11#10960semidirect
532. C2×C4#66870semidirect

Maximal subgroups

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

subgroupindex
C22×#668702
C2×#106228262
C2×C4×C22⋊Dic112
C2×#106221652
C11×C22⋊#952
#1096011