Finite Group Databasebeta

← #14790443

Subgroups — #14790443

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076950C212yesmaximal, complemented
2C4×#66988C211yesmaximal, characteristic
3#13069968C212yesmaximal, complemented
4#13069782C212yesmaximal, complemented
5#13069602C212yesmaximal, complemented
6#13069029C212yesmaximal
7#13068897C212yesmaximal
8#13068604C211yesmaximal, characteristic
9C11×#3501C211yesmaximal, characteristic
10C11×#554—22no—
11C11×#554—24no—
12D4×Q8×C11—22no—
13C11×#544—21no—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C11×#518C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66988C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23#10622843—22no—
24#10622833C2211yescharacteristic
25C2×#66898C2212yes—
26#10622825C2212yes—
27C4×C22⋊Dic11—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29#10622591—21no—
30#10622591—24no—
31#10622586—22no—
32#10622559C2211yescharacteristic
33#10622559C2214yes—
34#10622557—21no—
35#10622556C2211yescharacteristic
36#10622556C2214yes—
37C4×Dic11⋊C4—21no—
38#10622164C2214yes—
39#10622164C2214yes—
40#10622164C2212yes—
41C22×Q8×C11—21no—
42C22×Q8×C11D412yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—24no—
51C11×#125—22no—
52C11×#125—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—24no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—24no—
70C4×D4×C11—24no—
71C11×#117—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D414yes—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4C2314yes—
81C2×C42×C11D411yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2311yescharacteristic
86C2×C22⋊Dic11C2311yescharacteristic
87#66988—22no—
88#66988Q814yescomplemented
89C2×C4⋊Dic11—22no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98#66898—24no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—24no—
107C11⋊#95—22no—
108#24351—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C24×C11C2411yescharacteristic
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—44no—
116C2×Q8×C11—82no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C2×Q812yes—
120C2×D4×C11#4112yes—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—24no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—42no—
146C22×Dic11C2×Q812yescomplemented
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—24no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C42×C11—24no—
164C42×C11—21no—
165C42×C11—21no—
166C22⋊Dic11—24no—
167C22⋊Dic11—21no—
168C22⋊Dic11—24no—
169C22⋊Dic11—22no—
170C22⋊Dic11—24no—
171C22⋊Dic11—42no—
172C22⋊Dic11C2×Q812yescomplemented
173C4⋊Dic11—44no—
174Dic11⋊C4—24no—
175Dic11⋊C4—48no—
176Dic11⋊C4—42no—
177C4×Dic11—42no—
178C4×Dic11—41no—
179C4×Dic11—42no—
180C4×Dic11—41no—
181#3501D1111yescharacteristic
182#2855—112no—
183C4×#123—111no—
184#2062—112no—
185#2030—112no—
186#1996—112no—
187#1890—112no—
188#1867—112no—
189#1799—111no—
190C23×C11—21no—
191C23×C11—21no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11C22⋊Q812yes—
197C23×C11C22×D411yescharacteristic
198C23×C11C22×D412yes—
199C23×C11C22×Q811yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C112−1+412yes—
202Q8×C11—44no—
203Q8×C11—82no—
204Q8×C11—82no—
205Q8×C11—82no—
206D4×C11—24no—
207D4×C11—24no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—21no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—44no—
223C2×C4×C11—81no—
224C2×C4×C11—82no—
225C2×C4×C11—82no—
226C2×C4×C11#12011yescharacteristic
227C2×C4×C11#12012yes—
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11C22⋊Q812yes—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—44no—
245C2×Dic11—44no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—44no—
249#554—24no—
250#554—22no—
251D4×Q8—22no—
252#544—21no—
253#543—21no—
254#543C2×D1112yes—
255#533—21no—
256C2×#123—111no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C2×D1112yes—
259#518C2×D1112yes—
260C2×C4×D4C2×D1111yescharacteristic
261C22×C42—111no—
262C2×#99—112no—
263#391—222no—
264#389—222no—
265#388—221no—
266#387—224no—
267#387—221no—
268#386—111no—
269#385—111no—
270#385—114no—
271#381—114no—
272#381—111no—
273#380—112no—
274C4×C4⋊C4—221no—
275C4×C22⋊C4—111no—
276C4×C22⋊C4—221no—
277#342—112no—
278#342—114no—
279#342—114no—
280C22×C11—22no—
281C22×C11—21no—
282C22×C11—22no—
283C22×C11—21no—
284C22×C11—22no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—81no—
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×C22⋊Q811yescharacteristic
294C22×C11#53611yescharacteristic
295C22×C11#54812yes—
296C22×C11D4×Q812yes—
297C4×C11—22no—
298C4×C11—21no—
299C4×C11—22no—
300C4×C11—41no—
301C4×C11—44no—
302C4×C11—44no—
303C4×C11—41no—
304C4×C11#45812yes—
305Dic11—42no—
306Dic11—42no—
307Dic11—42no—
308Dic11—84no—
309Dic11—81no—
310C22×Q8—21no—
311C22×Q8C22⋊D1112yes—
312C22×D4C22×D1111yescharacteristic
313C23×C4—111no—
314C23×C4—111no—
315C23×C4C22⋊D1111yescharacteristic
316C23×C4C22×D1111yescharacteristic
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—24no—
320#125—22no—
321#125—24no—
322#123—114no—
323#123—222no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—24no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—24no—
341C4×D4—24no—
342#117—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4C22⋊D1111yescharacteristic
350C2×C4⋊C4C22⋊D1114yes—
351C2×C4⋊C4C22⋊D1112yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—111no—
354C2×C22⋊C4—111no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—221no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4C22⋊D1111yescharacteristic
359C2×C22⋊C4C22×D1111yescharacteristic
360C2×C22⋊C4C22×D1114yes—
361C2×C42—221no—
362C2×C42—221no—
363C2×C42—222no—
364C2×C42—221no—
365C2×C42—222no—
366C2×C42C22⋊D1111yescharacteristic
367#99—224no—
368#95—221no—
369#95—221no—
370#95—221no—
371#95—221no—
372#95—221no—
373#95—222no—
374#95—224no—
375#95—224no—
376#95—224no—
377C2×C11—21no—
378C2×C11—22no—
379C2×C11—21no—
380C2×C11—22no—
381C2×C11—42no—
382C2×C11#240911yescharacteristic
383C2×C11C2×#45811yescharacteristic
384C2×C11#302511yescharacteristic
385C24C2×C22⋊D1111yescharacteristic
386C24C23×D1111yescharacteristic
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—44no—
392C2×Q8—82no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4Q8×D1112yes—
396C2×D4#434312yes—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—112no—
404C22×C4—221no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—221no—
411C22×C4—221no—
412C22×C4—224no—
413C22×C4—442no—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1114yes—
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1114yes—
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1112yes—
423C4⋊C4—22no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—24no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—224no—
435C4⋊C4—444no—
436C4⋊C4—442no—
437C4⋊C4—448no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—112no—
444C22⋊C4—224no—
445C22⋊C4—221no—
446C22⋊C4—224no—
447C22⋊C4—222no—
448C22⋊C4—224no—
449C22⋊C4—442no—
450C42—24no—
451C42—21no—
452C42—21no—
453C42—442no—
454C42—441no—
455C42—442no—
456C42—441no—
457C11#2435111yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23#6699912yes—
465C23C2×Q8×D1111yescharacteristic
466C23C2×#434311yescharacteristic
467C23#6704012yes—
468C23C22×C22⋊D1111yescharacteristic
469C23C22×C22⋊D1112yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—24no—
475D4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—44no—
491C2×C4—81no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—222no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—442no—
502C2×C4—441no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—444no—
510C2×C4—444no—
511C2×C4—441no—
512C2×C4—444no—
513C2×C4#6699912yes—
514C2×C4#6700611yescharacteristic
515C2×C4#6700612yes—
516C2×C4#6700611yescharacteristic
517C22—22no—
518C22—21no—
519C22—22no—
520C22—21no—
521C22—22no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—81no—
529C22C2×#6699911yescharacteristic
530C22Q8×C22⋊D1112yes—
531C22#1062334711yescharacteristic
532C22#1062334812yes—
533C22C2×#6700611yescharacteristic
534C4—22no—
535C4—21no—
536C4—22no—
537C4—41no—
538C4—44no—
539C4—44no—
540C4—41no—
541C4—442no—
542C4—442no—
543C4—442no—
544C4—884no—
545C4—881no—
546C4#1062285612yes—
547C2—21no—
548C2—22no—
549C2—21no—
550C2—22no—
551C2—42no—
552C2#1307197511yescharacteristic
553C2C2×#1062285611yescharacteristic
554C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenter#3501D11
hypocenterC11#24351
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13076950C2semidirect
3. #13069968C2semidirect
4. #13069782C2semidirect
5. #13069602C2semidirect
88. #66988Q8semidirect
146. C22×Dic11C2×Q8semidirect
172. C22⋊Dic11C2×Q8semidirect
457. C11#24351semidirect

Maximal subgroups

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

subgroupindex
#130769502
C4×#669882
#130699682
#130697822
#130696022
#130690292
#130688972
#130686042
C11×#35012
#2435111