Finite Group Databasebeta

← #14788841

Subgroups — #14788841

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C2×#10622795C212yesmaximal, complemented
3C2×#10622663C211yesmaximal, characteristic
4C22⋊Q8×Dic11C211yesmaximal, characteristic
5#13069861C212yesmaximal, complemented
6#13069714C212yesmaximal, complemented
7#13069537C212yesmaximal, complemented
8#13068594C211yesmaximal, characteristic
9#13068552C211yesmaximal, characteristic
10#13068551C211yesmaximal, characteristic
11C2×C11×#451C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×Q16C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×#66997—28no—
18C2×#66997—21no—
19C2×#66997—21no—
20C2×#66997C2212yes—
21C2×#66997C2212yes—
22C22×#4326C2212yes—
23C22×Dic11⋊C4—21no—
24C22×Dic11⋊C4—21no—
25C22×C4×Dic11C2211yescharacteristic
26C11×#451—24no—
27C2×C11×#103C2212yes—
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622795—28no—
35C2×#66880C2212yes—
36C2×#66880C2212yes—
37C2×Dic11⋊C8C2212yes—
38#10622663—24no—
39#10622598C2211yescharacteristic
40#10622594—21no—
41C4⋊C4×Dic11—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C2×#66874C2212yes—
44#10622563—21no—
45C22⋊C4×Dic11—21no—
46#10622188C2212yes—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2312yes—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11D411yescharacteristic
58C23×Dic11D411yescharacteristic
59C22×Dic22—21no—
60C22×Dic22—24no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—42no—
64C22×Dic22C2312yes—
65C2×C11×Q16—24no—
66C2×C11×Q16—24no—
67C2×C11×Q16—42no—
68C22×C8×C11C2312yes—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8D414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75Q8×Dic11—24no—
76#66997—28no—
77#66997—28no—
78#66997—24no—
79#66997—24no—
80#66997—24no—
81#66997D418yes—
82C2×#4326—24no—
83C2×#4326—24no—
84C2×#4326—42no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103C11×#103—24no—
104C11×C22⋊C8—22no—
105#66899—24no—
106#66899—42no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—22no—
113#66880—24no—
114#66880—42no—
115Dic11⋊C8—24no—
116#66874—24no—
117#24212—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C2×Q8×C11—24no—
120C2×Q8×C11—22no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—48no—
129C2×Q8×C11—48no—
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C2×Q8×C11C2×D414yes—
133C2×Q8×C11C2×D412yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11Q1614yescomplemented
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—48no—
169C2×Dic22—48no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22C2×D414yes—
173C11×Q16—48no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—24no—
181C22⋊Dic11—42no—
182#4326—48no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—42no—
195C4×Dic11—42no—
196C4×Dic11C2×D414yes—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C22×C4⋊Q8—111no—
201C2×#462—112no—
202C2×#451—111no—
203C2×#451D1111yescharacteristic
204C4×C22⋊Q8—111no—
205#2043—112no—
206#2016—112no—
207#1981—112no—
208#1797—111no—
209#1787—111no—
210#1787—111no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11#12112yes—
216C23×C11C2×Q1612yes—
217C23×C11#13712yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—24no—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—48no—
223Q8×C11—42no—
224Q8×C11—42no—
225Q8×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—48no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11#12112yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11H(5,𝔽2)12yes—
245C2×Dic11—28no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—28no—
253C2×Dic11—24no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11#12012yes—
264C2×Dic11#12012yes—
265C2×Dic11C2×Q1612yes—
266C2×Dic11C2×Q1612yes—
267C2×Dic11#13712yes—
268C2×Dic11#13712yes—
269Dic22—24no—
270Dic22—24no—
271Dic22—48no—
272Dic22—42no—
273Dic22—42no—
274C8×C11—42no—
275C11⋊C8—42no—
276C23×Q8—111no—
277C23×Q8C2×D1111yescharacteristic
278C22×Q16—112no—
279C22×Q16C2×D1112yes—
280C2×C4⋊Q8—112no—
281C2×C4⋊Q8—112no—
282C2×C4⋊Q8—221no—
283C2×C4⋊Q8—221no—
284C2×C4⋊Q8—228no—
285C2×C22⋊Q8C2×D1111yescharacteristic
286C2×C4×Q8—111no—
287C22×C4⋊C4—221no—
288C22×C4⋊C4—221no—
289C22×C42—111no—
290#462—228no—
291#451—24no—
292#451—224no—
293C2×C4⋊C8—112no—
294C2×#103—112no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103C2×D1112yes—
300C2×C22⋊C8—111no—
301C2×C22⋊C8C2×D1111yescharacteristic
302#391—111no—
303#389—111no—
304#387—221no—
305#385—221no—
306#380—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—221no—
309C4×C22⋊C4—221no—
310#336—112no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11#46214yescomplemented
318C22×C11C2×#12011yescharacteristic
319C22×C11C2×#12111yescharacteristic
320C22×C11#53511yescharacteristic
321C22×C11C22×Q1611yescharacteristic
322C22×C11C2×#13711yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11C2×#13711yescharacteristic
325C4×C11—22no—
326C4×C11—44no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11D4212yes—
330C4×C11#54612yes—
331Dic11—22no—
332Dic11—22no—
333Dic11—22no—
334Dic11—44no—
335Dic11—81no—
336Dic11—81no—
337Dic11#45114yescomplemented
338C22×Q8—24no—
339C22×Q8—21no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—42no—
343C22×Q8—112no—
344C22×Q8—224no—
345C22×Q8—221no—
346C22×Q8—222no—
347C22×Q8—222no—
348C22×Q8—442no—
349C22×Q8C22×D1112yes—
350C22×Q8C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356C2×Q16—24no—
357C2×Q16—24no—
358C2×Q16—42no—
359C2×Q16—224no—
360C2×Q16—224no—
361C2×Q16—442no—
362C22×C8—112no—
363C22×C8C22×D1112yes—
364C4⋊Q8—118no—
365C4⋊Q8—224no—
366C4⋊Q8—224no—
367C4⋊Q8—228no—
368C4⋊Q8—228no—
369C4⋊Q8—224no—
370C22⋊Q8—22no—
371C22⋊Q8C22⋊D1114yes—
372C4×Q8—224no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4—228no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—221no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—224no—
392C2×C42—221no—
393C2×C42—221no—
394C4⋊C8—224no—
395#103—24no—
396#103—224no—
397#103—224no—
398#103—224no—
399#103—442no—
400#103—442no—
401C22⋊C8—22no—
402C22⋊C8—222no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11—24no—
409C2×C11#240811yescharacteristic
410C2×C11C2×#45111yescharacteristic
411C2×C11#300411yescharacteristic
412C2×C11C2×#46211yescharacteristic
413C2×C11#303911yescharacteristic
414C2×C11#320911yescharacteristic
415C2×C11#321811yescharacteristic
416C24D4×D1111yescharacteristic
417C2×Q8—24no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—48no—
427C2×Q8—48no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—114no—
431C2×Q8—224no—
432C2×Q8—222no—
433C2×Q8—222no—
434C2×Q8—222no—
435C2×Q8—222no—
436C2×Q8—222no—
437C2×Q8—448no—
438C2×Q8—448no—
439C2×Q8—442no—
440C2×Q8—442no—
441C2×Q8D4×D1114yes—
442C2×Q8C2×C22⋊D1112yes—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—111no—
452C22×C4—114no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4D4×D1111yescharacteristic
468C22×C4#434112yes—
469C22×C4C2×C22⋊D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—48no—
472Q16—448no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—228no—
482C4⋊C4—228no—
483C4⋊C4—228no—
484C4⋊C4—228no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4C2×C22⋊D1112yes—
490C22⋊C4—24no—
491C22⋊C4—442no—
492C42—114no—
493C42—222no—
494C42—222no—
495C42—222no—
496C42—442no—
497C42—442no—
498C11#2421211yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—21no—
502C23—21no—
503C23Q16×D1112yes—
504C23#6697112yes—
505C23#6699212yes—
506C23C2×D4×D1111yescharacteristic
507Q8—24no—
508Q8—24no—
509Q8—24no—
510Q8—48no—
511Q8—42no—
512Q8—42no—
513Q8—42no—
514Q8—224no—
515Q8—224no—
516Q8—448no—
517Q8—442no—
518Q8—442no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—48no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—228no—
540C2×C4—228no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—224no—
548C2×C4—448no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4#6699212yes—
558C2×C4C2×D4×D1112yes—
559C2×C4C2×#434111yescharacteristic
560C2×C4#6703712yes—
561C2×C4C22×C22⋊D1111yescharacteristic
562C8—42no—
563C8—442no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22#1062279514yescomplemented
571C22D11×#12011yescharacteristic
572C22#1062312311yescharacteristic
573C22C2×Q16×D1111yescharacteristic
574C22C2×#6697111yescharacteristic
575C22D11×#13711yescharacteristic
576C22D11×#13711yescharacteristic
577C22C2×#6699211yescharacteristic
578C4—22no—
579C4—42no—
580C4—44no—
581C4—42no—
582C4—114no—
583C4—222no—
584C4—222no—
585C4—222no—
586C4—444no—
587C4—881no—
588C4—881no—
589C4#1062312212yes—
590C4D4×C22⋊D1112yes—
591C2—24no—
592C2#1307196911yescharacteristic
593C2D11×#45111yescharacteristic
594C2#1307785111yescharacteristic
595C2C2×#1062279511yescharacteristic
596C2#1307810111yescharacteristic
597C2#1307956211yescharacteristic
598C2#1307964611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#451D11
hypocenterC11#24212
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#10622795C2semidirect
5. #13069861C2semidirect
6. #13069714C2semidirect
7. #13069537C2semidirect
157. C22×Dic11Q16semidirect
317. C22×C11#462semidirect
337. Dic11#451semidirect
498. C11#24212semidirect
570. C22#10622795semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106227952
C2×#106226632
C22⋊Q8×Dic112
#130698612
#130697142
#130695372
#130685942
#130685522
#130685512
C2×C11×#4512
#2421211