Finite Group Databasebeta

← #14810362

Subgroups — #14810362

Order 2816.

1406 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073109C212yesmaximal, complemented
2#13072933C211yesmaximal, characteristic, complemented
3#13069864C214yesmaximal, complemented
4#13069453C212yesmaximal, complemented
5#13068564C214yesmaximal, 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
19C22×C4⋊Dic11C2211yescharacteristic, complemented
20#10622834—22no—
21#10622833C2212yes—
22#10622833C2218yescomplemented
23C2×#66898C2212yes—
24C2×#66898C2218yescomplemented
25#10622825—21no—
26#10622825C2211yescharacteristic, complemented
27C4×C22⋊Dic11C2212yescomplemented
28#10622599—21no—
29#10622590—22no—
30#10622566—24no—
31#10622562—21no—
32#10622559C2212yescomplemented
33#10622541—21no—
34#10622164C2212yescomplemented
35C11×H(5,𝔽2)—28no—
36C11×H(5,𝔽2)—44no—
37C2×C11×#41—22no—
38C2×C11×#41—24no—
39C22×D4×C11—22no—
40C22×D4×C11—24no—
41C22×D4×C11—21no—
42C22×D4×C11D412yes—
43C22×D4×C11C2314yes—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C11×C4⋊Q8—21no—
49C11×#127—21no—
50C11×#124—22no—
51C11×#123—24no—
52C11×#123—24no—
53C11×C22⋊Q8—24no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—24no—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121—22no—
63C11×#120—24no—
64C11×#120—24no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D412yes—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D414yes—
75C2×C11×C22⋊C4C2311yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11C2312yes—
80C2×C22⋊Dic11C2314yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—22no—
88#66898—24no—
89#66898—48no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—21no—
93C11⋊#95—22no—
94C11⋊#95—28no—
95#25900—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11C2×D414yes—
98C24×C11C2×D411yescharacteristic
99C24×C11C2411yescharacteristic
100C11×#41—416no—
101C11×#41—44no—
102C11×#41—44no—
103C2×Q8×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—24no—
109C2×D4×C11—24no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—44no—
117C2×D4×C11—416no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—82no—
121C2×D4×C11#4114yes—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—82no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—24no—
152C42×C11—21no—
153C42×C11—21no—
154C22⋊Dic11—24no—
155C22⋊Dic11—24no—
156C22⋊Dic11—24no—
157C22⋊Dic11—82no—
158C22⋊Dic11—88no—
159C4⋊Dic11—42no—
160C4⋊Dic11—41no—
161C4⋊Dic11—42no—
162C4⋊Dic11—41no—
163Dic11⋊C4—82no—
164C4×Dic11—44no—
165#3496D1111yescharacteristic
166#2504—112no—
167#2487—111no—
168#2044—114no—
169#1964—112no—
170#1790—114no—
171C4×#99—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—24no—
175C23×C11—28no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—44no—
181C23×C11—44no—
182C23×C11—44no—
183C23×C11—82no—
184C23×C11—82no—
185C23×C11#12412yes—
186C23×C11C22×D411yescharacteristic
187C23×C11C22×D412yes—
188C23×C11C2×#4112yes—
189C23×C11H(5,𝔽2)12yes—
190Q8×C11—44no—
191D4×C11—28no—
192D4×C11—44no—
193D4×C11—48no—
194D4×C11—44no—
195D4×C11—44no—
196D4×C11—48no—
197D4×C11—44no—
198D4×C11—82no—
199D4×C11—82no—
200D4×C11—82no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—24no—
208C2×C4×C11—28no—
209C2×C4×C11—42no—
210C2×C4×C11—41no—
211C2×C4×C11—48no—
212C2×C4×C11—44no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—81no—
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11#12012yes—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12412yes—
221C2×Dic11—44no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—44no—
226C2×Dic11—42no—
227C2×Dic11—48no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—44no—
231C2×H(5,𝔽2)C2×D1112yes—
232#547—22no—
233#546—24no—
234D42—22no—
235#537—21no—
236#534—21no—
237#534C2×D1112yes—
238#532—21no—
239C2×#121—21no—
240C2×#121C2×D1112yes—
241C2×C4×D4C2×D1111yescharacteristic
242C22×C4⋊C4—111no—
243C2×#99—112no—
244C2×#99—118no—
245#400—221no—
246#399—221no—
247#397—224no—
248#390—222no—
249#389—221no—
250#386—112no—
251#386—118no—
252#385—112no—
253#382—222no—
254#380—111no—
255#380—221no—
256C4×C22⋊C4—112no—
257#342—112no—
258C22×C11—21no—
259C22×C11—22no—
260C22×C11—21no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—41no—
267C22×C11—41no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—81no—
272C22×C11—88no—
273C22×C11—164no—
274C22×C11C2×#12011yescharacteristic
275C22×C11C2×#12411yescharacteristic
276C22×C11#53511yescharacteristic
277C22×C11#54614yes—
278C4×C11—22no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—44no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11#45812yes—
285Dic11—82no—
286Dic11—84no—
287Dic11—82no—
288H(5,𝔽2)—28no—
289H(5,𝔽2)—44no—
290C2×#41—22no—
291C2×#41—24no—
292C22×D4—22no—
293C22×D4—24no—
294C22×D4—21no—
295C22×D4C22⋊D1112yes—
296C22×D4C22×D1114yes—
297C22×D4C22×D1111yescharacteristic
298C23×C4—112no—
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22×D1111yescharacteristic
301C4⋊Q8—21no—
302#127—21no—
303#124—22no—
304#123—24no—
305#123—24no—
306C22⋊Q8—24no—
307#121—22no—
308#121—22no—
309#121—24no—
310#121—22no—
311#121—22no—
312#121—22no—
313#121—22no—
314#121—22no—
315#121—22no—
316#120—24no—
317#120—24no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22⋊D1112yes—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—112no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—228no—
336C2×C22⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4C22⋊D1114yes—
338C2×C22⋊C4C22×D1111yescharacteristic
339C2×C42—222no—
340C2×C42C22⋊D1111yescharacteristic
341#99—224no—
342#99—448no—
343#95—222no—
344#95—221no—
345#95—222no—
346#95—228no—
347#95—222no—
348C2×C11—21no—
349C2×C11—24no—
350C2×C11—21no—
351C2×C11—42no—
352C2×C11—84no—
353C2×C11#243511yescharacteristic
354C2×C11C2×#45811yescharacteristic
355C2×C11#302711yescharacteristic
356C24—22no—
357C24C2×C22⋊D1114yes—
358C24C2×C22⋊D1111yescharacteristic
359C24C23×D1111yescharacteristic
360#41—416no—
361#41—44no—
362#41—44no—
363C2×Q8—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—24no—
367C2×D4—22no—
368C2×D4—28no—
369C2×D4—28no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—44no—
377C2×D4—416no—
378C2×D4—44no—
379C2×D4—44no—
380C2×D4—82no—
381C2×D4#434114yes—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—224no—
389C22×C4—222no—
390C22×C4—224no—
391C22×C4—222no—
392C22×C4—882no—
393C22×C4C2×C22⋊D1114yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1112yes—
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1112yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—442no—
407C4⋊C4—441no—
408C4⋊C4—442no—
409C4⋊C4—441no—
410C4⋊C4—882no—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—22no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—24no—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C22⋊C4—224no—
420C22⋊C4—888no—
421C22⋊C4—882no—
422C42—21no—
423C42—21no—
424C42—444no—
425C11#2590011yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—24no—
429C23—28no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—44no—
435C23—44no—
436C23—44no—
437C23—82no—
438C23—82no—
439C23#6698912yes—
440C23C2×#434112yes—
441C23#6703712yes—
442C23C22×C22⋊D1111yescharacteristic
443C23C22×C22⋊D1112yes—
444Q8—44no—
445D4—28no—
446D4—44no—
447D4—48no—
448D4—44no—
449D4—44no—
450D4—48no—
451D4—44no—
452D4—82no—
453D4—82no—
454D4—82no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—28no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—48no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—444no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—448no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—444no—
480C2×C4—442no—
481C2×C4#6698912yes—
482C2×C4#6700611yescharacteristic
483C2×C4#6700612yes—
484C2×C4#6700611yescharacteristic
485C22—21no—
486C22—22no—
487C22—21no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—41no—
494C22—41no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22—81no—
499C22—88no—
500C22—164no—
501C22C2×#6698911yescharacteristic
502C22#1062333611yescharacteristic
503C22#1062333714yes—
504C22C2×#6700611yescharacteristic
505C4—22no—
506C4—21no—
507C4—22no—
508C4—41no—
509C4—44no—
510C4—41no—
511C4—882no—
512C4—884no—
513C4—882no—
514C4#1062285612yes—
515C2—21no—
516C2—24no—
517C2—21no—
518C2—42no—
519C2—84no—
520C2#1307226311yescharacteristic
521C2C2×#1062285611yescharacteristic
522C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#25900
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. #13073109C2semidirect
2. #13072933C2semidirect
3. #13069864C2semidirect
4. #13069453C2semidirect
5. #13068564C2semidirect
6. C4×#66898C2semidirect
19. C22×C4⋊Dic11C22semidirect
22. #10622833C22semidirect
24. C2×#66898C22semidirect
26. #10622825C22semidirect
27. C4×C22⋊Dic11C22semidirect
32. #10622559C22semidirect
34. #10622164C22semidirect
425. C11#25900semidirect

Maximal subgroups

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

subgroupindex
#130731092
#130729332
#130698642
#130694532
#130685642
C4×#668982
C11×#34962
#2590011