Finite Group Databasebeta

← #14809056

Subgroups — #14809056

Order 2816.

1618 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622856C214yesmaximal, complemented
2#13073088C212yesmaximal, complemented
3#13072924C211yesmaximal, characteristic, complemented
4#13069745C214yesmaximal, complemented
5#13069453C212yesmaximal, complemented
6C4×#66898C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)C2212yes—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537—21no—
13C11×#534—21no—
14C11×#534C2212yes—
15C11×#532—21no—
16C2×C11×#121—21no—
17C2×C11×#121C2212yes—
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66988C2212yes—
20C2×#66988C2218yescomplemented
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22#10622856—216no—
23#10622834—22no—
24C2×#66898C2212yes—
25C2×#66898C2218yescomplemented
26#10622825—21no—
27#10622825C2211yescharacteristic, complemented
28C4×C22⋊Dic11C2212yescomplemented
29#10622596—21no—
30#10622589—22no—
31#10622566—21no—
32#10622562—24no—
33#10622556C2212yescomplemented
34#10622541—21no—
35#10622164C2212yescomplemented
36C11×H(5,𝔽2)—28no—
37C11×H(5,𝔽2)—44no—
38C2×C11×#41—22no—
39C2×C11×#41—24no—
40C22×D4×C11—22no—
41C22×D4×C11—24no—
42C22×D4×C11—21no—
43C22×D4×C11D412yes—
44C22×D4×C11C2314yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11D411yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C11×C4⋊Q8—21no—
50C11×#127—21no—
51C11×#124—22no—
52C11×#123—24no—
53C11×#123—24no—
54C11×C22⋊Q8—24no—
55C11×#121—22no—
56C11×#121—22no—
57C11×#121—24no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#121—22no—
64C11×#120—24no—
65C11×#120—24no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D412yes—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D414yes—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4C2311yescharacteristic
77C2×C42×C11D411yescharacteristic
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—28no—
80C2×C22⋊Dic11C2312yes—
81C2×C22⋊Dic11C2314yes—
82#66988—28no—
83#66988—216no—
84#66988—48no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—28no—
92C2×C4×Dic11—22no—
93#66898—216no—
94#66898D418yescomplemented
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—21no—
99#25772—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11C2×D414yes—
102C24×C11C2×D411yescharacteristic
103C24×C11C2411yescharacteristic
104C11×#41—416no—
105C11×#41—44no—
106C11×#41—44no—
107C2×Q8×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—28no—
113C2×D4×C11—24no—
114C2×D4×C11—24no—
115C2×D4×C11—28no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—44no—
121C2×D4×C11—416no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—82no—
125C2×D4×C11C2×D414yes—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11C2×D414yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—24no—
157C42×C11—21no—
158C42×C11—21no—
159C22⋊Dic11—24no—
160C22⋊Dic11—24no—
161C22⋊Dic11—416no—
162C22⋊Dic11—44no—
163C22⋊Dic11C2×D418yescomplemented
164C4⋊Dic11—42no—
165C4⋊Dic11—41no—
166C4⋊Dic11—42no—
167C4⋊Dic11—41no—
168Dic11⋊C4—416no—
169Dic11⋊C4—44no—
170C4×Dic11—44no—
171#3496D1111yescharacteristic
172C2×#458—114no—
173#2501—112no—
174#2486—111no—
175#2022—114no—
176#1964—112no—
177C4×#99—111no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—24no—
181C23×C11—28no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—44no—
187C23×C11—44no—
188C23×C11—44no—
189C23×C11—82no—
190C23×C11—82no—
191C23×C11#12712yes—
192C23×C11C22×D412yes—
193C23×C11C22×D411yescharacteristic
194C23×C11C22×D412yes—
195C23×C11H(5,𝔽2)12yes—
196Q8×C11—44no—
197D4×C11—28no—
198D4×C11—44no—
199D4×C11—48no—
200D4×C11—44no—
201D4×C11—44no—
202D4×C11—48no—
203D4×C11—44no—
204D4×C11—82no—
205D4×C11—82no—
206D4×C11—82no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—28no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—48no—
218C2×C4×C11—44no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—81no—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12012yes—
225C2×C4×C11#12011yescharacteristic
226C2×C4×C11#12712yes—
227C2×Dic11—28no—
228C2×Dic11—44no—
229C2×Dic11—44no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—48no—
237C2×H(5,𝔽2)C2×D1112yes—
238#547—22no—
239#546—24no—
240D42—22no—
241#537—21no—
242#534—21no—
243#534C2×D1112yes—
244#532—21no—
245C2×#123—112no—
246C2×#123—118no—
247C2×#121—21no—
248C2×#121C2×D1112yes—
249C2×C4×D4C2×D1111yescharacteristic
250C22×C4⋊C4—111no—
251#458—2216no—
252C2×#99—112no—
253C2×#99—118no—
254#399—224no—
255#398—221no—
256#397—221no—
257#390—222no—
258#389—221no—
259#384—222no—
260#381—112no—
261#380—111no—
262#380—221no—
263C4×C22⋊C4—112no—
264#342—112no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—21no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—44no—
278C22×C11—81no—
279C22×C11—88no—
280C22×C11—164no—
281C22×C11C2×#12011yescharacteristic
282C22×C11C2×#12711yescharacteristic
283C22×C11#53511yescharacteristic
284C22×C11D4214yes—
285C4×C11—22no—
286C4×C11—21no—
287C4×C11—22no—
288C4×C11—44no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11#45812yescomplemented
292Dic11—48no—
293Dic11—82no—
294Dic11—82no—
295H(5,𝔽2)—28no—
296H(5,𝔽2)—44no—
297C2×#41—22no—
298C2×#41—24no—
299C22×D4—22no—
300C22×D4—24no—
301C22×D4—21no—
302C22×D4C22⋊D1112yes—
303C22×D4C22×D1114yes—
304C22×D4C22×D1111yescharacteristic
305C23×C4—112no—
306C23×C4C22⋊D1111yescharacteristic
307C23×C4C22×D1111yescharacteristic
308C4⋊Q8—21no—
309#127—21no—
310#124—22no—
311#123—24no—
312#123—24no—
313#123—2216no—
314#123—228no—
315#123—448no—
316C22⋊Q8—24no—
317#121—22no—
318#121—22no—
319#121—24no—
320#121—22no—
321#121—22no—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—22no—
326#120—24no—
327#120—24no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—228no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4C22⋊D1111yescharacteristic
341C2×C4⋊C4C22⋊D1112yes—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—114no—
344C2×C22⋊C4—112no—
345C2×C22⋊C4—222no—
346C2×C22⋊C4—228no—
347C2×C22⋊C4C22⋊D1111yescharacteristic
348C2×C22⋊C4C22⋊D1114yes—
349C2×C22⋊C4C22×D1111yescharacteristic
350C2×C42—222no—
351C2×C42C22⋊D1111yescharacteristic
352#99—118no—
353#99—2216no—
354#95—222no—
355#95—221no—
356#95—222no—
357#95—222no—
358C2×C11—24no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—42no—
362C2×C11—84no—
363C2×C11#243311yescharacteristic
364C2×C11C2×#45811yescharacteristic
365C2×C11#302811yescharacteristic
366C24—22no—
367C24C2×C22⋊D1114yes—
368C24C2×C22⋊D1111yescharacteristic
369C24C23×D1111yescharacteristic
370#41—416no—
371#41—44no—
372#41—44no—
373C2×Q8—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—28no—
379C2×D4—28no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—44no—
387C2×D4—416no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—82no—
391C2×D4D4×D1114yes—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—224no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—224no—
404C22×C4C2×C22⋊D1114yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1112yes—
411C22×C4C2×C22⋊D1111yescharacteristic
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—4416no—
418C4⋊C4—442no—
419C4⋊C4—444no—
420C4⋊C4—441no—
421C4⋊C4—442no—
422C4⋊C4—441no—
423C22⋊C4—24no—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—24no—
429C22⋊C4—118no—
430C22⋊C4—224no—
431C22⋊C4—224no—
432C22⋊C4—4416no—
433C22⋊C4—444no—
434C42—21no—
435C42—21no—
436C42—444no—
437C11#2577211yescharacteristic, complemented, Sylow
438C23—21no—
439C23—21no—
440C23—24no—
441C23—28no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—82no—
450C23—82no—
451C23#6699312yes—
452C23C2×D4×D1112yes—
453C23#6703712yes—
454C23C22×C22⋊D1112yes—
455C23C22×C22⋊D1111yescharacteristic
456Q8—44no—
457D4—28no—
458D4—44no—
459D4—48no—
460D4—48no—
461D4—44no—
462D4—44no—
463D4—44no—
464D4—82no—
465D4—82no—
466D4—82no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—28no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—24no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—48no—
478C2×C4—44no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—81no—
483C2×C4—228no—
484C2×C4—444no—
485C2×C4—444no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—448no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4#6699312yes—
494C2×C4#6700611yescharacteristic
495C2×C4#6700612yes—
496C2×C4#6700611yescharacteristic
497C22—21no—
498C22—22no—
499C22—21no—
500C22—22no—
501C22—22no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—41no—
506C22—41no—
507C22—44no—
508C22—44no—
509C22—44no—
510C22—81no—
511C22—88no—
512C22—164no—
513C22D4×C22⋊D1114yes—
514C22C2×#6699311yescharacteristic
515C22#1062333611yescharacteristic
516C22C2×#6700611yescharacteristic
517C4—22no—
518C4—21no—
519C4—22no—
520C4—41no—
521C4—44no—
522C4—41no—
523C4—448no—
524C4—882no—
525C4—882no—
526C4#1062285612yescomplemented
527C2—24no—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—84no—
532C2#1307224911yescharacteristic
533C2C2×#1062285611yescharacteristic
534C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#25772
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#10622856C2semidirect
2. #13073088C2semidirect
3. #13072924C2semidirect
4. #13069745C2semidirect
5. #13069453C2semidirect
6. C4×#66898C2semidirect
20. C2×#66988C22semidirect
21. C22×C4⋊Dic11C22semidirect
25. C2×#66898C22semidirect
27. #10622825C22semidirect
28. C4×C22⋊Dic11C22semidirect
33. #10622556C22semidirect
35. #10622164C22semidirect
94. #66898D4semidirect
163. C22⋊Dic11C2×D4semidirect
291. C4×C11#458semidirect
437. C11#25772semidirect
526. C4#10622856semidirect

Maximal subgroups

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

subgroupindex
C2×#106228562
#130730882
#130729242
#130697452
#130694532
C4×#668982
C11×#34962
#2577211