Finite Group Databasebeta

← #14660241

Subgroups — #14660241

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×#66898C212yesmaximal
2C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
3C2×#10622164C212yesmaximal, complemented
4#13066839C211yesmaximal, characteristic, complemented
5C2×C11×#386C211yesmaximal, characteristic
6C23×D4×C11C2211yescharacteristic
7C24×C4×C11C2211yescharacteristic
8C22×C11×C22⋊C4C412yescomplemented
9C22×C11×C22⋊C4C2211yescharacteristic
10C22×C22⋊Dic11C2212yes—
11C22×C22⋊Dic11C2212yes—
12C22×C4×Dic11—21no—
13C11×#386—21no—
14C11×#386—22no—
15C11×#386—21no—
16C2×C11×#95C412yescomplemented
17C2×#66898—24no—
18C2×#66898—24no—
19C2×#66898C418yescomplemented
20C4×C22⋊Dic11—24no—
21C2×C11⋊#95—21no—
22C2×C11⋊#95—22no—
23#10622164—24no—
24C25×C11C2×C411yescharacteristic
25C25×C11C2311yescharacteristic
26C22×D4×C11—22no—
27C22×D4×C11—22no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C22×D4×C11C2×C414yes—
34C23×C4×C11—22no—
35C23×C4×C11—22no—
36C23×C4×C11—44no—
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C412yes—
39C23×C4×C11C2×C412yes—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D412yes—
42C23×C4×C11D411yescharacteristic
43C23×Dic11—22no—
44C23×Dic11—22no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—44no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11C2×C414yes—
61C2×C22⋊Dic11C2×C414yes—
62C2×C22⋊Dic11D414yes—
63C2×C22⋊Dic11D414yes—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—44no—
66C11×#95—22no—
67C11×#95—22no—
68#66898—216no—
69C11⋊#95—24no—
70C11⋊#95—44no—
71#10960—111nomaximal, Sylow
72C24×C11—21no—
73C24×C11—21no—
74C24×C11—22no—
75C24×C11—22no—
76C24×C11—42no—
77C24×C11—42no—
78C24×C11—42no—
79C24×C11—42no—
80C24×C11C4212yescomplemented
81C24×C11C22×C411yescharacteristic
82C24×C11C22×C412yes—
83C24×C11C2×D411yescharacteristic
84C24×C11C2×D411yescharacteristic
85C24×C11C2×D412yes—
86C24×C11C2×D412yes—
87C24×C11#4112yes—
88C24×C11#4112yes—
89C24×C11#4112yes—
90C2×D4×C11—24no—
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—42no—
102C2×D4×C11—42no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—41no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—24no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—48no—
125C22×C4×C11—48no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C4212yescomplemented
129C22×C4×C11C22⋊C412yes—
130C22×C4×C11C22⋊C412yes—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—44no—
136C22×Dic11—44no—
137C22×Dic11—44no—
138C22×Dic11—44no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C11×C22⋊C4—44no—
142C11×C22⋊C4—42no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—44no—
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—24no—
149C22⋊Dic11—24no—
150C22⋊Dic11—24no—
151C22⋊Dic11—42no—
152C22⋊Dic11—42no—
153C22⋊Dic11C22⋊C418yescomplemented
154C4×Dic11—48no—
155C22×#99—112no—
156C2×#386D1111yescharacteristic
157C2×C4×C22⋊C4—111no—
158C2×#342—112no—
159C22⋊#95—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—24no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—44no—
171C23×C11—42no—
172C23×C11—44no—
173C23×C11—44no—
174C23×C11—42no—
175C23×C11—44no—
176C23×C11—44no—
177C23×C11—44no—
178C23×C11—41no—
179C23×C11—42no—
180C23×C11—41no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11—84no—
186C23×C11C2×C4211yescharacteristic
187C23×C11C2×C22⋊C412yes—
188C23×C11C2×C22⋊C411yescharacteristic
189C23×C11#11712yes—
190C23×C11#11711yescharacteristic
191C23×C11C4×D412yes—
192C23×C11C4×D412yes—
193C23×C11C4×D412yes—
194C23×C11C4×D412yes—
195C23×C11C4×D412yes—
196C23×C11C4×D412yes—
197C23×C11#12011yescharacteristic
198C23×C11#12112yes—
199C23×C11#12112yes—
200C23×C11#12112yes—
201C23×C11#12312yes—
202C23×C11#12311yescharacteristic
203C23×C11#12412yes—
204C23×C11#12411yescharacteristic
205C23×C11#12612yes—
206C23×C11#12711yescharacteristic
207D4×C11—44no—
208D4×C11—44no—
209D4×C11—44no—
210D4×C11—44no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—48no—
221C2×C4×C11—48no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—84no—
231C2×C4×C11#9914yescomplemented
232C2×Dic11—28no—
233C2×Dic11—44no—
234C2×Dic11—44no—
235C2×Dic11—48no—
236C2×Dic11—48no—
237C2×Dic11—48no—
238C2×Dic11—44no—
239C2×Dic11—82no—
240C2×Dic11—82no—
241C2×Dic11—84no—
242C23×D4C2×D1111yescharacteristic
243C24×C4C2×D1111yescharacteristic
244C22×C22⋊C4—112no—
245C22×C22⋊C4—112no—
246C22×C22⋊C4Dic1112yescomplemented
247C22×C22⋊C4C2×D1111yescharacteristic
248C22×C42—221no—
249C2×#99—118no—
250C2×#99—224no—
251C2×#99—224no—
252#386—21no—
253#386—22no—
254#386—21no—
255C4×C22⋊C4—224no—
256C2×#95—221no—
257C2×#95—222no—
258C2×#95Dic1112yescomplemented
259#342—224no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—21no—
268C22×C11—24no—
269C22×C11—24no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—24no—
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×C11—42no—
285C22×C11—44no—
286C22×C11—84no—
287C22×C11—84no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11—82no—
291C22×C11C4×C22⋊C412yes—
292C22×C11C4×C22⋊C411yescharacteristic
293C22×C11#38612yes—
294C22×C11#38611yescharacteristic
295C22×C11#38812yes—
296C22×C11#38812yes—
297C22×C11#38812yes—
298C22×C11#39012yes—
299C22×C11#39011yescharacteristic
300C22×C11C2×#9912yes—
301C22×C11#41012yes—
302C4×C11—24no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—82no—
306Dic11—48no—
307Dic11—84no—
308C25C2×Dic1111yescharacteristic
309C25C22×D1111yescharacteristic
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C4×D1114yes—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—44no—
321C23×C4—222no—
322C23×C4—222no—
323C23×C4C2×Dic1111yescharacteristic
324C23×C4C2×Dic1112yes—
325C23×C4C2×Dic1112yes—
326C23×C4C22⋊D1111yescharacteristic
327C23×C4C22⋊D1112yes—
328C23×C4C22⋊D1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—114no—
337C2×C22⋊C4—114no—
338C2×C22⋊C4—114no—
339C2×C22⋊C4—114no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—222no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C22⋊C4—222no—
347C2×C22⋊C4—222no—
348C2×C42—224no—
349C2×C42—444no—
350#99—2216no—
351#95—22no—
352#95—22no—
353#95—224no—
354#95—444no—
355C2×C11—22no—
356C2×C11—22no—
357C2×C11—22no—
358C2×C11—22no—
359C2×C11—22no—
360C2×C11—22no—
361C2×C11—82no—
362C2×C11#143711yescharacteristic
363C2×C11C4×#9912yes—
364C2×C11#189811yescharacteristic
365C2×C11#189911yescharacteristic
366C2×C11#196412yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—42no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24C4×Dic1112yescomplemented
376C24C2×C4×D1112yes—
377C24#433912yes—
378C24D4×D1112yes—
379C24D4×D1112yes—
380C24#434112yes—
381C24#434112yes—
382C24C22×Dic1111yescharacteristic
383C24C2×C22⋊D1111yescharacteristic
384C24C2×C22⋊D1111yescharacteristic
385C2×D4—24no—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—41no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—444no—
428C22×C4—444no—
429C22×C4—444no—
430C22×C4—444no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4C4×Dic1112yescomplemented
434C22×C4C22⋊Dic1112yes—
435C22×C4C22⋊Dic1112yes—
436C22⋊C4—44no—
437C22⋊C4—41no—
438C22⋊C4—42no—
439C22⋊C4—41no—
440C22⋊C4—44no—
441C22⋊C4—118no—
442C22⋊C4—224no—
443C22⋊C4—224no—
444C22⋊C4—224no—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C22⋊C4—442no—
448C22⋊C4—442no—
449C42—448no—
450C11#1096011yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—44no—
463C23—42no—
464C23—44no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23#6693012yes—
478C23#6693212yes—
479C23C22⋊C4×D1112yes—
480C23(C22⋊D11)⋊C412yes—
481C23(C22⋊D11)⋊C412yes—
482C23#6693612yes—
483C23#6693712yes—
484C23#6693812yes—
485C23C2×C4×Dic1111yescharacteristic
486C23#6697911yescharacteristic
487C23C4×C22⋊D1112yes—
488C23C4×C22⋊D1112yes—
489C23D4×Dic1112yes—
490C23D4×Dic1112yes—
491C23#6698811yescharacteristic
492C23#6698911yescharacteristic
493C23#6699011yescharacteristic
494C23#6699112yes—
495C23#6699212yes—
496C23#6699311yescharacteristic
497C23C2×C22⋊Dic1111yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—48no—
512C2×C4—48no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—84no—
522C2×C4—228no—
523C2×C4—444no—
524C2×C4—444no—
525C2×C4—448no—
526C2×C4—448no—
527C2×C4—448no—
528C2×C4—444no—
529C2×C4—882no—
530C2×C4—882no—
531C2×C4—884no—
532C2×C4#6689814yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—24no—
546C22—24no—
547C22—22no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—44no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C22⋊C4×Dic1112yes—
565C22#1062255712yes—
566C22#1062255812yes—
567C22#1062256412yes—
568C22#1062256912yes—
569C22#1062257012yes—
570C22C4×C22⋊Dic1111yescharacteristic
571C22C2×#6689812yes—
572C22#1062283311yescharacteristic
573C22#1062283411yescharacteristic
574C22#1062285312yes—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—82no—
579C4—448no—
580C4—884no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2#1306685311yescharacteristic
589C2C4×#6689812yes—
590C2#1306907011yescharacteristic
591C2#1306907511yescharacteristic
592C2#1306945312yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC23×C11C2×C42
FrattiniC25C22×D11
FittingC2×C11×#386C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenterC2×#386D11
hypocenterC11#10960
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic11C2semidirect
3. C2×#10622164C2semidirect
4. #13066839C2semidirect
8. C22×C11×C22⋊C4C4semidirect
16. C2×C11×#95C4semidirect
19. C2×#66898C4semidirect
80. C24×C11C42semidirect
128. C22×C4×C11C42semidirect
153. C22⋊Dic11C22⋊C4semidirect
231. C2×C4×C11#99semidirect
246. C22×C22⋊C4Dic11semidirect
258. C2×#95Dic11semidirect
375. C24C4×Dic11semidirect
433. C22×C4C4×Dic11semidirect
450. C11#10960semidirect
532. C2×C4#66898semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
C2×C4×C22⋊Dic112
C2×#106221642
#130668392
C2×C11×#3862
#1096011