Finite Group Databasebeta

← #14727614

Subgroups — #14727614

Order 2816.

1408 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079373C212yesmaximal, complemented
2#13074421C211yesmaximal, characteristic, complemented
3#13067636C214yesmaximal, complemented
4#13067568C214yesmaximal, complemented
5#13067184C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic, complemented
7C2×C11×#534C211yesmaximal, characteristic
8C23×D4×C11—21no—
9C11×#534—24no—
10C11×#534—22no—
11C11×#534C2214yes—
12C2×C11×#123—22no—
13C2×C11×#121—21no—
14C2×C11×#121C2212yes—
15C2×C11×#120—22no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#66977C2211yescharacteristic, complemented
18#10622860—21no—
19#10622831—22no—
20#10622825C2211yescharacteristic, complemented
21#10622823—21no—
22C2×C22⋊(C11⋊C8)C2212yescomplemented
23#10622654—24no—
24#10622653C2214yescomplemented
25#10622647C2214yescomplemented
26#10622584—22no—
27#10622562C2212yescomplemented
28#10622561—22no—
29#10622560C2212yescomplemented
30#10622175C2218yescomplemented
31#10622163C2214yescomplemented
32C25×C11—21no—
33C25×C11D411yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11—24no—
38C22×D4×C11—21no—
39C22×D4×C11—44no—
40C22×D4×C11—44no—
41C22×D4×C11D412yes—
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×Dic22C2311yescharacteristic, complemented
46C11×#123—28no—
47C11×#123—28no—
48C11×#121—24no—
49C11×#121—24no—
50C11×#121—22no—
51C11×#121—22no—
52C11×#121D414yes—
53C11×#121C2314yes—
54C11×#120—28no—
55C11×#120—28no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C11×C22⋊C4C2312yes—
64C2×C22⋊Dic11—21no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×#4324—24no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2311yescharacteristic, complemented
71#66977—22no—
72#66977—22no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—22no—
75C22×C11⋊C8—22no—
76#66896—24no—
77C11⋊#95—22no—
78C11⋊#95C2312yescomplemented
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)C2314yescomplemented
81#66874—24no—
82#66872—24no—
83#18285—111nomaximal, Sylow
84C24×C11—21no—
85C24×C11—21no—
86C24×C11—22no—
87C24×C11—24no—
88C24×C11—22no—
89C24×C11—44no—
90C24×C11—81no—
91C24×C11—81no—
92C24×C11—82no—
93C24×C11—82no—
94C24×C11SD1614yescomplemented
95C24×C11C2×D412yes—
96C24×C11C2×D411yescharacteristic
97C2×D4×C11—28no—
98C2×D4×C11—24no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—48no—
103C2×D4×C11—416no—
104C2×D4×C11—48no—
105C2×D4×C11—48no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11—82no—
109C2×D4×C11—82no—
110C2×D4×C11C2×D414yes—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—44no—
116C22×C4×C11—81no—
117C22×C4×C11—81no—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—21no—
126C2×Dic22—22no—
127C2×Dic22—81no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4C2×D414yes—
131C11×C22⋊C4—28no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C22⋊Dic11—41no—
137C22⋊Dic11—41no—
138C22⋊Dic11—42no—
139C22⋊Dic11—82no—
140C22⋊Dic11—82no—
141#4324—84no—
142C4⋊Dic11—22no—
143C4⋊Dic11—81no—
144Dic11⋊C4—42no—
145Dic11⋊C4—82no—
146C2×C11⋊C8—24no—
147C2×C11⋊C8—82no—
148C2×#534D1111yescharacteristic
149#3187—112no—
150#2626—111no—
151#1613—114no—
152#1601—114no—
153#1519—112no—
154C2×#323—111no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—24no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—48no—
167C23×C11—44no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11—84no—
173C23×C11—84no—
174C23×C11—84no—
175C23×C11—84no—
176C23×C11—816no—
177C23×C11#12011yescharacteristic
178C23×C11#12011yescharacteristic
179C23×C11C2×SD1614yes—
180C23×C11C2×SD1612yes—
181C23×C11AGL(1,ℤ/8)12yes—
182C23×C11C22×D411yescharacteristic
183D4×C11—44no—
184D4×C11—416no—
185D4×C11—44no—
186D4×C11—44no—
187D4×C11—48no—
188D4×C11—82no—
189D4×C11—84no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—48no—
197C2×C4×C11—42no—
198C2×C4×C11—44no—
199C2×C4×C11—42no—
200C2×C4×C11—81no—
201C2×C4×C11#12012yes—
202C2×C4×C11C22×D412yes—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210Dic22—44no—
211C11⋊C8—44no—
212C23×D4—21no—
213#534—24no—
214#534—22no—
215#534C2×D1114yes—
216C2×#123—22no—
217C2×C22⋊Q8—111no—
218C2×#121—21no—
219C2×#121C2×D1112yes—
220C2×#120—22no—
221C22×C22⋊C4C2×D1111yescharacteristic
222#483—222no—
223#481—114no—
224#465—224no—
225#450—222no—
226#448—114no—
227C2×C22⋊C8—112no—
228#399—112no—
229#396—222no—
230#393—112no—
231#385—221no—
232#380—111no—
233#379—221no—
234#327—118no—
235#323—114no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—24no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11—44no—
246C22×C11—48no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—44no—
250C22×C11—44no—
251C22×C11—44no—
252C22×C11—82no—
253C22×C11—84no—
254C22×C11—88no—
255C22×C11—816no—
256C22×C11#45012yes—
257C22×C11#45012yes—
258C22×C11C2×#12011yescharacteristic
259C22×C11C22×SD1611yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—44no—
264C4×C11—42no—
265Dic11—82no—
266Dic11—81no—
267Dic11—81no—
268C25—21no—
269C25C22⋊D1111yescharacteristic
270C22×Q8—111no—
271C22×D4—22no—
272C22×D4—24no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4—21no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C22⋊D1112yes—
279C23×C4—21no—
280C23×C4C22⋊D1111yescharacteristic
281C23×C4C22×D1111yescharacteristic
282C2×SD16—224no—
283C22×C8—222no—
284#123—28no—
285#123—28no—
286C22⋊Q8—222no—
287C22⋊Q8—222no—
288#121—24no—
289#121—24no—
290#121—22no—
291#121—22no—
292#121C22⋊D1114yes—
293#121C22×D1114yes—
294#120—28no—
295#120—28no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—222no—
301C2×C4⋊C4C22⋊D1112yes—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4C22⋊D1112yes—
311C2×C22⋊C4C22×D1112yes—
312#106—224no—
313#103—224no—
314#102—224no—
315C22⋊C8—114no—
316C22⋊C8—222no—
317#95—112no—
318#95—222no—
319C2×C11—21no—
320C2×C11—22no—
321C2×C11—21no—
322C2×C11—22no—
323C2×C11—44no—
324C2×C11—84no—
325C2×C11C2×#45011yescharacteristic
326C2×C11#301911yescharacteristic
327C2×C11#302611yescharacteristic
328C24—21no—
329C24—22no—
330C24—21no—
331C24—24no—
332C24—22no—
333C24—44no—
334C24—81no—
335C24—81no—
336C24—82no—
337C24—82no—
338C24#432414yescomplemented
339C24C2×C22⋊D1112yes—
340C24C2×C22⋊D1111yescharacteristic
341C2×Q8—222no—
342C2×Q8—881no—
343C2×D4—28no—
344C2×D4—24no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—48no—
349C2×D4—416no—
350C2×D4—48no—
351C2×D4—44no—
352C2×D4—48no—
353C2×D4—44no—
354C2×D4—82no—
355C2×D4—82no—
356C2×D4C2×C22⋊D1114yes—
357C22×C4—24no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—44no—
362C22×C4—81no—
363C22×C4—81no—
364C22×C4—222no—
365C22×C4—221no—
366C22×C4—221no—
367C22×C4C2×C22⋊D1112yes—
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1112yes—
370C22×C4C2×C22⋊D1112yes—
371C22×C4C23×D1111yescharacteristic
372SD16—884no—
373C2×C8—224no—
374C2×C8—882no—
375C4⋊C4—24no—
376C4⋊C4—22no—
377C4⋊C4—222no—
378C4⋊C4—442no—
379C4⋊C4—882no—
380C4⋊C4—881no—
381C4⋊C4C2×C22⋊D1114yes—
382C22⋊C4—28no—
383C22⋊C4—24no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—442no—
388C22⋊C4—441no—
389C22⋊C4—441no—
390C22⋊C4—882no—
391C22⋊C4—882no—
392C11#1828511yescharacteristic, complemented, Sylow
393C23—24no—
394C23—22no—
395C23—22no—
396C23—24no—
397C23—24no—
398C23—41no—
399C23—41no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—48no—
405C23—44no—
406C23—44no—
407C23—44no—
408C23—81no—
409C23—81no—
410C23—84no—
411C23—84no—
412C23—84no—
413C23—84no—
414C23—816no—
415C23#6698512yes—
416C23C2×#432414yes—
417C23C2×#432412yes—
418C23#6700611yescharacteristic
419C23#6700611yescharacteristic
420C23C22×C22⋊D1111yescharacteristic
421Q8—444no—
422D4—44no—
423D4—416no—
424D4—44no—
425D4—44no—
426D4—48no—
427D4—82no—
428D4—84no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—48no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4#6700612yes—
448C2×C4C22×C22⋊D1112yes—
449C8—444no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—24no—
457C22—42no—
458C22—42no—
459C22—44no—
460C22—48no—
461C22—42no—
462C22—42no—
463C22—44no—
464C22—44no—
465C22—44no—
466C22—82no—
467C22—84no—
468C22—88no—
469C22—816no—
470C22#1062283112yes—
471C22#1062283112yes—
472C22C2×#6698511yescharacteristic
473C22C22×#432411yescharacteristic
474C22C2×#6700611yescharacteristic
475C4—22no—
476C4—22no—
477C4—44no—
478C4—42no—
479C4—882no—
480C4—881no—
481C4—881no—
482C2—21no—
483C2—22no—
484C2—21no—
485C2—22no—
486C2—44no—
487C2—84no—
488C2C2×#1062283111yescharacteristic
489C2#1307797311yescharacteristic
490C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#534C2
socleC22×C11C2×#120
hypercenterC2×#534D11
hypocenterC11#18285
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. #13079373C2semidirect
2. #13074421C2semidirect
3. #13067636C2semidirect
4. #13067568C2semidirect
5. #13067184C2semidirect
6. C2×#10622163C2semidirect
17. C2×#66977C22semidirect
20. #10622825C22semidirect
22. C2×C22⋊(C11⋊C8)C22semidirect
24. #10622653C22semidirect
25. #10622647C22semidirect
27. #10622562C22semidirect
29. #10622560C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
45. C22×Dic22C23semidirect
70. C2×C4⋊Dic11C23semidirect
78. C11⋊#95C23semidirect
80. C22⋊(C11⋊C8)C23semidirect
94. C24×C11SD16semidirect
338. C24#4324semidirect
392. C11#18285semidirect

Maximal subgroups

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

subgroupindex
#130793732
#130744212
#130676362
#130675682
#130671842
C2×#106221632
C2×C11×#5342
#1828511