Finite Group Databasebeta

← #14668745

Subgroups — #14668745

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C211yesmaximal, characteristic
2#13071198C211yesmaximal, characteristic
3#13066740C214yesmaximal, complemented
4C22×C11×#99C211yesmaximal, characteristic
5C23×D4×C11C2211yescharacteristic
6C22×C11×C22⋊C4—21no—
7C22×C22⋊Dic11—21no—
8C2×#66979C411yescharacteristic, complemented
9C2×#66979C411yescharacteristic, complemented
10C2×C11×#99—21no—
11C2×C11×#99—22no—
12C2×C11×#99C414yescomplemented
13C2×C11×#99C2212yes—
14#10622860—21no—
15#10622860—21no—
16#10622834—21no—
17#10622834—21no—
18#10622834C412yescomplemented
19#10622834C2212yes—
20C2×#66898—21no—
21C2×#66898—22no—
22C2×#66898C414yescomplemented
23C2×#66898C2212yes—
24C25×C11D411yescharacteristic
25C25×C11D411yescharacteristic
26C22×D4×C11—41no—
27C22×D4×C11—41no—
28C22×D4×C11—42no—
29C22×D4×C11C2×C412yes—
30C22×D4×C11C2×C411yescharacteristic
31C22×D4×C11C2×C412yes—
32C22×D4×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×D4×C11D412yes—
35C22×D4×C11Q812yes—
36C22×D4×C11C2311yescharacteristic
37C23×C4×C11—41no—
38C23×C4×C11C2×C411yescharacteristic
39C23×Dic11—41no—
40C2×C11×C22⋊C4—24no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4—42no—
44C2×C22⋊Dic11—24no—
45C2×C22⋊Dic11—22no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—22no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—22no—
52C2×C22⋊Dic11—41no—
53C2×C22⋊Dic11—42no—
54#66979—42no—
55#66979—41no—
56#66979—41no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C412yescomplemented
59C2×C4×Dic11—21no—
60C2×C4×Dic11C2×C412yescomplemented
61C11×#99—24no—
62C11×#99—22no—
63C11×#99C2×C414yescomplemented
64#66898—24no—
65#66898—22no—
66#66898C2×C414yescomplemented
67#12582—111nomaximal, Sylow
68C24×C11—21no—
69C24×C11—21no—
70C24×C11—22no—
71C24×C11—21no—
72C24×C11—22no—
73C24×C11—21no—
74C24×C11—82no—
75C24×C11—82no—
76C24×C11C22⋊C411yescharacteristic
77C24×C11C22⋊C411yescharacteristic
78C24×C11C22⋊C412yes—
79C24×C11C22⋊C412yes—
80C24×C11C22⋊C411yescharacteristic
81C24×C11C4⋊C412yes—
82C24×C11C4⋊C412yes—
83C24×C11C2×D411yescharacteristic
84C24×C11C2×D411yescharacteristic
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—42no—
92C2×D4×C11—42no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11C4212yes—
102C2×D4×C11C22⋊C412yes—
103C2×D4×C11C22⋊C412yes—
104C2×D4×C11C4⋊C412yes—
105C2×D4×C11C4⋊C412yes—
106C2×D4×C11C4⋊C412yes—
107C2×D4×C11C22×C411yescharacteristic
108C2×D4×C11C22×C411yescharacteristic
109C2×D4×C11C2×D411yescharacteristic
110C2×D4×C11C2×Q811yescharacteristic
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—44no—
115C22×C4×C11—42no—
116C22×C4×C11—84no—
117C22×C4×C11C4212yes—
118C22×C4×C11C22⋊C411yescharacteristic
119C22×C4×C11C4⋊C412yes—
120C22×C4×C11C22×C411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—44no—
124C22×Dic11—42no—
125C22×Dic11—84no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—44no—
128C11×C22⋊C4—42no—
129C22⋊Dic11—24no—
130C22⋊Dic11—44no—
131C22⋊Dic11—42no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134C22⋊Dic11—42no—
135C22⋊Dic11—82no—
136C22⋊Dic11—82no—
137C22⋊Dic11—82no—
138C22⋊Dic11—82no—
139C4⋊Dic11—42no—
140C4⋊Dic11—42no—
141C4×Dic11—42no—
142C4×Dic11—42no—
143C22×#99—111no—
144C22×#99D1111yescharacteristic
145#2309—111no—
146#1393—114no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—42no—
164C23×C11—44no—
165C23×C11—44no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11—82no—
171C23×C11—82no—
172C23×C11—82no—
173C23×C11—82no—
174C23×C11—82no—
175C23×C11—82no—
176C23×C11—84no—
177C23×C11—84no—
178C23×C11#9512yes—
179C23×C11#9512yes—
180C23×C11#9512yes—
181C23×C11#9911yescharacteristic
182C23×C11#9911yescharacteristic
183C23×C11#9912yes—
184C23×C11C2×C22⋊C411yescharacteristic
185C23×C11C2×C22⋊C411yescharacteristic
186C23×C11C2×C22⋊C411yescharacteristic
187C23×C11C2×C4⋊C411yescharacteristic
188C23×C11C2×C4⋊C411yescharacteristic
189D4×C11—42no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—44no—
208C2×C4×C11—88no—
209C2×C4×C11—84no—
210C2×C4×C11#9512yes—
211C2×C4×C11C2×C4211yescharacteristic
212C2×C4×C11C2×C4⋊C411yescharacteristic
213C2×Dic11—44no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—88no—
221C2×Dic11—84no—
222C23×D4C2×D1111yescharacteristic
223C2×#117—111no—
224C2×#117—111no—
225C22×C22⋊C4—21no—
226C22×C22⋊C4—221no—
227C2×#99—21no—
228C2×#99—22no—
229C2×#99—112no—
230C2×#99—114no—
231C2×#99—221no—
232C2×#99—222no—
233C2×#99Dic1114yescomplemented
234C2×#99C2×D1112yes—
235#390—112no—
236#390—112no—
237#390—221no—
238#390—221no—
239#379—221no—
240#379—221no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—21no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—44no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—42no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11#34212yes—
275C22×C11#34212yes—
276C22×C11C2×#9511yescharacteristic
277C22×C11C2×#9911yescharacteristic
278C22×C11C2×#9911yescharacteristic
279C4×C11—22no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—84no—
283Dic11—82no—
284Dic11—84no—
285Dic11—82no—
286C25D4411yescharacteristic
287C25C22⋊D1111yescharacteristic
288C22×D4—41no—
289C22×D4—41no—
290C22×D4—42no—
291C22×D4Dic2212yes—
292C22×D4C4×D1112yes—
293C22×D4C4×D1111yescharacteristic
294C22×D4D4411yescharacteristic
295C22×D4C2×Dic1112yes—
296C22×D4C22⋊D1112yes—
297C22×D4C22⋊D1111yescharacteristic
298C22×D4C22×D1111yescharacteristic
299C23×C4—41no—
300C23×C4—441no—
301C23×C4C4×D1111yescharacteristic
302#117—442no—
303#117—441no—
304#117—441no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—41no—
311C2×C22⋊C4—224no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—442no—
320C2×C22⋊C4—441no—
321C2×C42—112no—
322C2×C42—221no—
323#99—24no—
324#99—22no—
325#99—114no—
326#99—224no—
327#99—222no—
328#99C2×Dic1114yescomplemented
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—22no—
332C2×C11—22no—
333C2×C11—41no—
334C2×C11—41no—
335C2×C11—42no—
336C2×C11—42no—
337C2×C11—41no—
338C2×C11—41no—
339C2×C11C2×#34211yescharacteristic
340C2×C11#212712yes—
341C24—21no—
342C24—21no—
343C24—21no—
344C24—22no—
345C24—21no—
346C24—22no—
347C24—82no—
348C24—82no—
349C24Dic11⋊C412yes—
350C24C4⋊Dic1112yes—
351C24(C2×D11)⋊C411yescharacteristic
352C24(C2×D11)⋊C411yescharacteristic
353C24(C2×D11)⋊C412yes—
354C24(C2×D11)⋊C411yescharacteristic
355C24C22⋊Dic1112yes—
356C24C2×D4411yescharacteristic
357C24C2×C22⋊D1111yescharacteristic
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4C4×Dic1112yes—
375C2×D4Dic11⋊C412yes—
376C2×D4Dic11⋊C412yes—
377C2×D4C4⋊Dic1112yes—
378C2×D4(C2×D11)⋊C412yes—
379C2×D4C22⋊Dic1112yes—
380C2×D4C2×Dic2211yescharacteristic
381C2×D4C2×C4×D1111yescharacteristic
382C2×D4C22×Dic1111yescharacteristic
383C2×D4C2×C22⋊D1111yescharacteristic
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—42no—
388C22×C4—44no—
389C22×C4—84no—
390C22×C4—222no—
391C22×C4—222no—
392C22×C4—442no—
393C22×C4—444no—
394C22×C4—884no—
395C22×C4C4×Dic1112yes—
396C22×C4Dic11⋊C412yes—
397C22×C4(C2×D11)⋊C411yescharacteristic
398C22×C4C2×C4×D1111yescharacteristic
399C4⋊C4—442no—
400C4⋊C4—442no—
401C22⋊C4—24no—
402C22⋊C4—42no—
403C22⋊C4—44no—
404C22⋊C4—224no—
405C22⋊C4—442no—
406C22⋊C4—444no—
407C22⋊C4—442no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—882no—
411C22⋊C4—882no—
412C22⋊C4—882no—
413C22⋊C4—882no—
414C42—442no—
415C42—442no—
416C11#1258211yescharacteristic, complemented, Sylow
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—42no—
434C23—44no—
435C23—44no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—82no—
441C23—82no—
442C23—82no—
443C23—82no—
444C23—82no—
445C23—82no—
446C23—84no—
447C23—84no—
448C23#6687011yescharacteristic
449C23#6687011yescharacteristic
450C23#6687012yes—
451C23C11⋊#9512yes—
452C23C11⋊#9512yes—
453C23C11⋊#9512yes—
454C23C2×Dic11⋊C411yescharacteristic
455C23C2×C4⋊Dic1111yescharacteristic
456C23C2×(C2×D11)⋊C411yescharacteristic
457C23C2×(C2×D11)⋊C411yescharacteristic
458C23C2×C22⋊Dic1111yescharacteristic
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464D4—42no—
465D4—41no—
466D4—41no—
467D4—41no—
468D4—41no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—44no—
478C2×C4—88no—
479C2×C4—84no—
480C2×C4—444no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—888no—
488C2×C4—884no—
489C2×C4C11⋊#9512yes—
490C2×C4C2×C4×Dic1111yescharacteristic
491C2×C4C2×Dic11⋊C411yescharacteristic
492C22—22no—
493C22—22no—
494C22—22no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—22no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—44no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—82no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22#1062216512yes—
526C22#1062216512yes—
527C22C2×#6687011yescharacteristic
528C22C2×#6687011yescharacteristic
529C22C2×C11⋊#9511yescharacteristic
530C4—22no—
531C4—21no—
532C4—21no—
533C4—84no—
534C4—882no—
535C4—884no—
536C4—882no—
537C2—21no—
538C2—21no—
539C2—22no—
540C2—22no—
541C2—41no—
542C2—41no—
543C2—42no—
544C2—42no—
545C2—41no—
546C2—41no—
547C2C2×#1062216511yescharacteristic
548C2#1307028312yes—
subgroupG/H
centerC22C2×#66870
commutatorC2×C4×C11C2×C42
FrattiniC22×D4C22×D11
FittingC22×C11×#99C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenterC22×#99D11
hypocenterC11#12582
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. #13066740C2semidirect
8. C2×#66979C4semidirect
9. C2×#66979C4semidirect
12. C2×C11×#99C4semidirect
18. #10622834C4semidirect
22. C2×#66898C4semidirect
58. C2×C4⋊Dic11C2×C4semidirect
60. C2×C4×Dic11C2×C4semidirect
63. C11×#99C2×C4semidirect
66. #66898C2×C4semidirect
233. C2×#99Dic11semidirect
328. #99C2×Dic11semidirect
416. C11#12582semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130711982
#130667402
C22×C11×#992
#1258211