Finite Group Databasebeta

← #14790449

Subgroups — #14790449

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#13082419C211yesmaximal, characteristic
2#13076955C212yesmaximal, complemented
3#13069969C212yesmaximal, complemented
4#13069783C212yesmaximal, complemented
5#13069601C212yesmaximal, complemented
6#13069030C212yesmaximal
7#13068896C212yesmaximal
8#13068604C211yesmaximal, characteristic
9C4×C11×#123C211yesmaximal, characteristic
10C2×C11×#123C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13#10623329C2212yes—
14C2×#66977—21no—
15C2×#66977C2212yes—
16#10623074—22no—
17#10623070—24no—
18D4×Dic22—22no—
19#10623031—21no—
20#10623014—21no—
21#10623014C2212yes—
22#10623001—21no—
23C11×#388—21no—
24C11×#387—21no—
25C11×#386C2211yescharacteristic
26C11×#385C2211yescharacteristic
27C11×#381C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66898C2212yes—
32#10622825C2212yes—
33#10622824C2214yes—
34#10622823C2214yes—
35#10622546—24no—
36#10622542—22no—
37#10622541—22no—
38#10622165C2214yes—
39#10622165C2214yes—
40#10622164C2212yes—
41C22×D4×C11C2311yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×Dic22—21no—
47C22×Dic22D412yes—
48C11×#123—22no—
49C11×#123Q814yescomplemented
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4D411yescharacteristic
58C2×C11×C22⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4C2311yescharacteristic
60C2×C11×C22⋊C4C2311yescharacteristic
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11D411yescharacteristic
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11C2314yes—
69C2×C22⋊Dic11C2314yes—
70D4×Dic11—24no—
71D4×Dic11—24no—
72#66979—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11D412yes—
76#66977—22no—
77#66977—22no—
78#66977—22no—
79#66977—22no—
80#66977—22no—
81#66977—22no—
82#66977—22no—
83#66977—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—24no—
86C2×Dic11⋊C4D414yes—
87#66943—24no—
88#66941—24no—
89#66931—24no—
90#66931—24no—
91#66931—24no—
92#66931—24no—
93#66923—22no—
94#66922—21no—
95#66922—21no—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103#66898—24no—
104C11⋊#95—22no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108#24351—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C24×C11C2411yescharacteristic
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11C2×Q812yes—
114C2×D4×C11#4112yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×Q812yescomplemented
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11C2×D414yes—
140C22×Dic11C2×D414yes—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—44no—
146C2×Dic22—82no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—42no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4C2×Q812yescomplemented
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—42no—
160C42×C11—41no—
161C42×C11—42no—
162C42×C11—41no—
163C22⋊Dic11—24no—
164C22⋊Dic11—24no—
165C22⋊Dic11—24no—
166C22⋊Dic11—24no—
167C22⋊Dic11—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—44no—
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178Dic11⋊C4—24no—
179Dic11⋊C4—48no—
180C4×Dic11—24no—
181#3501—111no—
182#2855—112no—
183C4×#123D1111yescharacteristic
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×D412yes—
198C23×C11C22×D411yescharacteristic
199C23×C11C22×Q811yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C112−1+412yes—
202D4×C11—24no—
203D4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—81no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12012yes—
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11C22⋊Q812yes—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—44no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11—82no—
244C2×Dic11—82no—
245Dic22—44no—
246Dic22—82no—
247Dic22—82no—
248Dic22—82no—
249#554—224no—
250#554—222no—
251D4×Q8—222no—
252#544—221no—
253#543—112no—
254#543—221no—
255#533—221no—
256C2×#123C2×D1111yescharacteristic
257C2×C22⋊Q8—112no—
258C2×C22⋊Q8—221no—
259#518—112no—
260C2×C4×D4C2×D1111yescharacteristic
261C22×C42C2×D1111yescharacteristic
262C2×#99—112no—
263#391—222no—
264#389—222no—
265#388—21no—
266#387—21no—
267#387—224no—
268#386C2×D1111yescharacteristic
269#385—114no—
270#385C2×D1111yescharacteristic
271#381—114no—
272#381C2×D1111yescharacteristic
273#380—112no—
274C4×C4⋊C4—21no—
275C4×C22⋊C4—21no—
276C4×C22⋊C4C2×D1111yescharacteristic
277#342—112no—
278#342—114no—
279#342—114no—
280C22×C11—21no—
281C22×C11—22no—
282C22×C11—21no—
283C22×C11—22no—
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—42no—
301C4×C11—42no—
302C4×C11—41no—
303C4×C11—42no—
304C4×C11—41no—
305C4×C11—81no—
306C4×C11#45812yes—
307Dic11—44no—
308Dic11—44no—
309Dic11—84no—
310C22×Q8—112no—
311C22×Q8—221no—
312C22×D4C22×D1111yescharacteristic
313C23×C4C22⋊D1111yescharacteristic
314C23×C4C22×D1111yescharacteristic
315C23×C4C22×D1111yescharacteristic
316C23×C4C22×D1111yescharacteristic
317C4⋊Q8—221no—
318C4⋊Q8—221no—
319C4⋊Q8—224no—
320#125—222no—
321#125—224no—
322#123—22no—
323#123Dic2214yescomplemented
324C22⋊Q8—224no—
325C22⋊Q8—224no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328C22⋊Q8—222no—
329C22⋊Q8—222no—
330C22⋊Q8—222no—
331C22⋊Q8—222no—
332C22⋊Q8—222no—
333C22⋊Q8—222no—
334C22⋊Q8—222no—
335C22⋊Q8—222no—
336C4×Q8—222no—
337C4×Q8—222no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—224no—
341C4×D4—224no—
342#117—222no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—114no—
355C2×C22⋊C4—114no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4C22⋊D1111yescharacteristic
358C2×C22⋊C4C22×D1111yescharacteristic
359C2×C22⋊C4C22×D1111yescharacteristic
360C2×C22⋊C4C22×D1111yescharacteristic
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42C22⋊D1111yescharacteristic
367#99—224no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—224no—
374#95—224no—
375#95—224no—
376#95—222no—
377C2×C11—22no—
378C2×C11—21no—
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—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—444no—
392C2×Q8—882no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4C2×Dic2212yes—
396C2×D4#433912yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—114no—
411C22×C4—114no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—224no—
415C22×C4C2×Dic2212yescomplemented
416C22×C4D4×D1112yes—
417C22×C4D4×D1112yes—
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1111yescharacteristic
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—42no—
426C4⋊C4—222no—
427C4⋊C4—224no—
428C4⋊C4—222no—
429C4⋊C4—222no—
430C4⋊C4—224no—
431C4⋊C4—222no—
432C4⋊C4—224no—
433C4⋊C4—222no—
434C4⋊C4—222no—
435C4⋊C4—224no—
436C4⋊C4—448no—
437C4⋊C4—444no—
438C22⋊C4—24no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—42no—
444C22⋊C4—224no—
445C22⋊C4—224no—
446C22⋊C4—224no—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4C2×Dic2212yescomplemented
450C42—21no—
451C42—21no—
452C42—42no—
453C42—41no—
454C42—42no—
455C42—41no—
456C42—224no—
457C11#2435111yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23#6697712yes—
465C23C22×Dic2211yescharacteristic
466C23C2×#433911yescharacteristic
467C23C2×D4×D1112yes—
468C23#6704312yes—
469C23C22×C22⋊D1111yescharacteristic
470Q8—444no—
471Q8—882no—
472Q8—882no—
473Q8—882no—
474D4—24no—
475D4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—81no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—444no—
510C2×C4—444no—
511C2×C4—882no—
512C2×C4—882no—
513C2×C4#6697712yes—
514C2×C4#6699011yescharacteristic
515C2×C4#6699012yes—
516C2×C4#6699011yescharacteristic
517C22—21no—
518C22—22no—
519C22—21no—
520C22—22no—
521C22—22no—
522C22—41no—
523C22—41no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—81no—
529C22D4×Dic2212yes—
530C22#1062308312yes—
531C22C2×#6697711yescharacteristic
532C22C2×#6699011yescharacteristic
533C22#1062335611yescharacteristic
534C4—22no—
535C4—21no—
536C4—22no—
537C4—42no—
538C4—42no—
539C4—41no—
540C4—42no—
541C4—41no—
542C4—81no—
543C4—444no—
544C4—444no—
545C4—884no—
546C4#1062266612yes—
547C2—21no—
548C2—21no—
549C2—22no—
550C2—22no—
551C2—42no—
552C2#1307198111yescharacteristic
553C2C2×#1062266611yescharacteristic
554C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC4×C11×#123C2
socleC22×C11C2×#120
prime radicalC22×D4×C11C23
hypercenterC4×#123D11
hypocenterC11#24351
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. #13076955C2semidirect
3. #13069969C2semidirect
4. #13069783C2semidirect
5. #13069601C2semidirect
49. C11×#123Q8semidirect
135. C22×C4×C11C2×Q8semidirect
156. C11×C22⋊C4C2×Q8semidirect
323. #123Dic22semidirect
415. C22×C4C2×Dic22semidirect
449. C22⋊C4C2×Dic22semidirect
457. C11#24351semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130769552
#130699692
#130697832
#130696012
#130690302
#130688962
#130686042
C4×C11×#1232
#2435111