Finite Group Databasebeta

← #14810801

Subgroups — #14810801

Order 2816.

1490 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
1#13072268C212yesmaximal, complemented
2#13071972C211yesmaximal, characteristic
3#13069779C214yesmaximal, complemented
4#13069602C212yesmaximal, complemented
5#13069024C214yesmaximal, complemented
6C4×#66898C211yesmaximal, characteristic, complemented
7C11×#3501C211yesmaximal, characteristic, complemented
8C23×D44C2211yescharacteristic
9C11×#554—22no—
10C11×#554—24no—
11D4×Q8×C11—22no—
12C11×#544—21no—
13C11×#543—21no—
14C11×#543C2212yes—
15C11×#533—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2212yes—
18C11×#518C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×#67000—22no—
21C2×#66990C2212yes—
22C2×#66983—21no—
23C2×#66898C2212yes—
24#10622825C2211yescharacteristic
25C4×C22⋊Dic11C2212yes—
26#10622604—21no—
27#10622604—24no—
28#10622601—22no—
29#10622573—21no—
30#10622568C2212yes—
31#10622568C2218yes—
32#10622552—21no—
33#10622164C2218yes—
34#10622164C2212yes—
35C24×D11C2312yes—
36C22×Q8×C11—21no—
37C22×Q8×C11D412yescomplemented
38C22×D4×C11C2311yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—22no—
42C22×D44—21no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—22no—
46C22×D44—44no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—24no—
50C11×#125—22no—
51C11×#125—24no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—24no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C11×#117—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D412yescomplemented
75C2×C11×C4⋊C4D414yescomplemented
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4C2314yes—
80C2×C42×C11D411yescharacteristic
81C2×C22⋊Dic11C2312yes—
82C2×C22⋊Dic11C2314yes—
83#67000—48no—
84#66990—28no—
85#66983—44no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—28no—
91C2×C4⋊Dic11—21no—
92C2×C4×Dic11—22no—
93#66898—24no—
94C11⋊#95—22no—
95C11⋊#95—21no—
96#25947—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C24×C11C2411yescharacteristic
99C23×D11—24no—
100C23×D11—22no—
101C23×D11—24no—
102C23×D11—24no—
103C23×D11—44no—
104C23×D11—82no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—44no—
110C2×Q8×C11—82no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11#4114yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C2×C22⋊D11—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—82no—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C2×D44—24no—
135C2×D44—28no—
136C2×D44—44no—
137C2×D44—42no—
138C2×D44—48no—
139C2×D44—44no—
140C2×D44—41no—
141C2×D44—42no—
142C2×D44—41no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—24no—
158C11×C22⋊C4—22no—
159C42×C11—24no—
160C42×C11—21no—
161C42×C11—21no—
162C22⋊Dic11—24no—
163C22⋊Dic11—24no—
164C22⋊Dic11—24no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—416no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—88no—
169(C2×D11)⋊C4—82no—
170C4⋊Dic11—42no—
171C4×Dic11—44no—
172#3501D1111yescharacteristic, complemented
173#2435—112no—
174#2408—111no—
175#2029—114no—
176#1996—112no—
177#1889—114no—
178C4×#99—111no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11#12412yescomplemented
186C23×C11C22×D411yescharacteristic
187C23×C11C22×D412yes—
188C23×C11C2×#4112yes—
189C23×C112−1+412yes—
190C22×D11—28no—
191C22×D11—24no—
192C22×D11—48no—
193C22×D11—42no—
194C22×D11—44no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—48no—
201C22×D11—88no—
202C22×D11—88no—
203Q8×C11—44no—
204Q8×C11—82no—
205Q8×C11—82no—
206Q8×C11—82no—
207D4×C11—28no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
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—41no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11—41no—
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×C11#12412yescomplemented
230C22⋊D11—88no—
231C2×Dic11—44no—
232C2×Dic11—42no—
233C2×Dic11—44no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—44no—
237D44—44no—
238D44—48no—
239D44—44no—
240C23×D4—111no—
241#554—22no—
242#554—24no—
243D4×Q8—22no—
244#544—21no—
245#543—21no—
246#543C2×D1112yes—
247#533—21no—
248C2×#124—222no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8C2×D1112yes—
251C2×#121—221no—
252C2×#120—112no—
253#518C2×D1112yes—
254C2×C4×D4C2×D1111yescharacteristic
255C2×#99—112no—
256#394—221no—
257#394—224no—
258#392—221no—
259#390—222no—
260#390—221no—
261#380—111no—
262#379—118no—
263#379—112no—
264C4×C22⋊C4—112no—
265#342—118no—
266#342—112no—
267C22×C11—22no—
268C22×C11—21no—
269C22×C11—22no—
270C22×C11—21no—
271C22×C11—22no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—81no—
278C22×C11C2×#12011yescharacteristic
279C22×C11C2×#12411yescharacteristic
280C22×C11#53611yescharacteristic
281C22×C11#54814yes—
282C2×D11—416no—
283C2×D11—44no—
284C2×D11—44no—
285C2×D11—44no—
286C2×D11—82no—
287C2×D11—88no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—82no—
291C4×C11—22no—
292C4×C11—21no—
293C4×C11—22no—
294C4×C11—41no—
295C4×C11—44no—
296C4×C11—44no—
297C4×C11—41no—
298C4×C11B(4,𝔽2)12yes—
299Dic11—84no—
300Dic11—82no—
301C25—112no—
302C22×Q8—21no—
303C22×Q8C22⋊D1112yescomplemented
304C22×D4—222no—
305C22×D4—221no—
306C22×D4—222no—
307C22×D4—221no—
308C22×D4—222no—
309C22×D4—444no—
310C22×D4C22×D1111yescharacteristic
311C23×C4C22⋊D1111yescharacteristic
312C23×C4C22×D1111yescharacteristic
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—24no—
316#125—22no—
317#125—24no—
318#124—448no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331#121—444no—
332#120—228no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—24no—
338C4×D4—24no—
339#117—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22⋊D1111yescharacteristic
344C2×C4⋊C4C22⋊D1112yescomplemented
345C2×C4⋊C4C22⋊D1114yescomplemented
346C2×C22⋊C4—22no—
347C2×C22⋊C4—112no—
348C2×C22⋊C4—114no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—222no—
351C2×C22⋊C4—228no—
352C2×C22⋊C4—222no—
353C2×C22⋊C4—228no—
354C2×C22⋊C4C22⋊D1111yescharacteristic
355C2×C22⋊C4C22×D1111yescharacteristic
356C2×C22⋊C4C22×D1114yes—
357C2×C42—222no—
358C2×C42C22⋊D1111yescharacteristic
359#99—224no—
360#95—222no—
361#95—221no—
362C2×C11—21no—
363C2×C11—24no—
364C2×C11—21no—
365C2×C11—42no—
366C2×C11#243611yescharacteristic
367C2×C11C2×B(4,𝔽2)11yescharacteristic
368C2×C11#302711yescharacteristic
369D11—84no—
370C24—224no—
371C24—222no—
372C24—224no—
373C24—224no—
374C24—444no—
375C24—882no—
376C24C2×C22⋊D1111yescharacteristic
377C24C23×D1111yescharacteristic
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—44no—
383C2×Q8—82no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—224no—
387C2×D4—228no—
388C2×D4—444no—
389C2×D4—442no—
390C2×D4—448no—
391C2×D4—444no—
392C2×D4—444no—
393C2×D4—444no—
394C2×D4—441no—
395C2×D4—442no—
396C2×D4—441no—
397C2×D4—882no—
398C2×D4#434314yes—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—224no—
406C22×C4—222no—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1114yes—
413C22×C4C2×C22⋊D1114yes—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1112yes—
416C4⋊C4—22no—
417C4⋊C4—24no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—442no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—24no—
432C22⋊C4—22no—
433C22⋊C4—224no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C22⋊C4—444no—
437C22⋊C4—4416no—
438C22⋊C4—444no—
439C22⋊C4—888no—
440C22⋊C4—882no—
441C42—24no—
442C42—21no—
443C42—21no—
444C42—444no—
445C11#2594711yescharacteristic, complemented, Sylow
446C23—21no—
447C23—21no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—228no—
453C23—224no—
454C23—448no—
455C23—442no—
456C23—444no—
457C23—442no—
458C23—442no—
459C23—442no—
460C23—442no—
461C23—448no—
462C23—442no—
463C23—888no—
464C23—888no—
465C23#6700012yescomplemented
466C23C2×#434312yes—
467C23#6704012yes—
468C23C22×C22⋊D1111yescharacteristic
469C23C22×C22⋊D1112yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—28no—
475D4—444no—
476D4—448no—
477D4—444no—
478D4—888no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—21no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—82no—
496C2×C4—82no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4—444no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—444no—
503C2×C4#6700012yescomplemented
504C2×C4#6700611yescharacteristic
505C2×C4#6700612yes—
506C2×C4#6700611yescharacteristic
507C22—22no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—22no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—41no—
517C22—81no—
518C22—444no—
519C22—4416no—
520C22—444no—
521C22—444no—
522C22—882no—
523C22—888no—
524C22—882no—
525C22—882no—
526C22—882no—
527C22C2×#6700011yescharacteristic
528C22#1062334711yescharacteristic
529C22#1062334814yes—
530C22C2×#6700611yescharacteristic
531C4—22no—
532C4—21no—
533C4—22no—
534C4—44no—
535C4—41no—
536C4—41no—
537C4—44no—
538C4—882no—
539C4—884no—
540C4#1062285712yes—
541C2—21no—
542C2—24no—
543C2—21no—
544C2—42no—
545C2—884no—
546C2#1307227011yescharacteristic
547C2C2×#1062285711yescharacteristic
548C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3501C2
socleC22×C11C2×#120
prime radical#13071972C2
hypercenter#3501D11
hypocenterC11#25947
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. #13072268C2semidirect
3. #13069779C2semidirect
4. #13069602C2semidirect
5. #13069024C2semidirect
6. C4×#66898C2semidirect
7. C11×#3501C2semidirect
37. C22×Q8×C11D4semidirect
74. C2×C11×C4⋊C4D4semidirect
75. C2×C11×C4⋊C4D4semidirect
172. #3501D11semidirect
185. C23×C11#124semidirect
229. C2×C4×C11#124semidirect
303. C22×Q8C22⋊D11semidirect
344. C2×C4⋊C4C22⋊D11semidirect
345. C2×C4⋊C4C22⋊D11semidirect
445. C11#25947semidirect
465. C23#67000semidirect
503. C2×C4#67000semidirect

Maximal subgroups

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

subgroupindex
#130722682
#130719722
#130697792
#130696022
#130690242
C4×#668982
C11×#35012
#2594711