Finite Group Databasebeta

← #14727621

Subgroups — #14727621

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079369C212yesmaximal, complemented
2#13074350C211yesmaximal, characteristic
3#13067607C214yesmaximal, complemented
4#13067539C214yesmaximal, complemented
5#13067188C212yesmaximal, complemented
6C2×#10622163C211yesmaximal, characteristic, complemented
7C2×C11×#543C211yesmaximal, characteristic, complemented
8C11×#543—24no—
9C11×#543—22no—
10C11×#543C2214yes—
11C2×C11×C22⋊Q8—22no—
12C2×C11×C22⋊Q8—21no—
13C2×C11×C22⋊Q8—22no—
14C2×C11×C22⋊Q8C2212yes—
15C22×C11×C22⋊C4—21no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#67006—21no—
18C2×#66983C2211yescharacteristic
19#10622840—22no—
20#10622826—21no—
21#10622825C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622661—24no—
24#10622659C2214yescomplemented
25#10622656C2214yescomplemented
26#10622581—22no—
27#10622574—22no—
28#10622573C2212yes—
29#10622566C2212yes—
30#10622176C2218yescomplemented
31#10622163C2214yes—
32C25×C11D411yescharacteristic
33C22×Q8×C11—21no—
34C22×Q8×C11D412yescomplemented
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C22×C22⋊D11—22no—
41C22×D44C2311yescharacteristic
42C11×C22⋊Q8—28no—
43C11×C22⋊Q8—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—28no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—28no—
50C11×C22⋊Q8D414yescomplemented
51C11×C22⋊Q8C2314yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D412yescomplemented
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C11×C22⋊C4C2312yes—
64#67006—44no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—21no—
67C2×#4325—24no—
68#66983—22no—
69#66983—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2311yescharacteristic
74C22×C11⋊C8—22no—
75#66899—24no—
76C11⋊#95—22no—
77C11⋊#95C2312yes—
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yes—
80#66873—24no—
81#66872—24no—
82#18286—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—22no—
86C24×C11—81no—
87C24×C11—81no—
88C24×C11SD1614yescomplemented
89C24×C11C2×D412yes—
90C24×C11C2×D411yescharacteristic
91C23×D11—21no—
92C2×Q8×C11—24no—
93C2×Q8×C11—22no—
94C2×Q8×C11—82no—
95C2×Q8×C11—82no—
96C2×Q8×C11C2×D414yes—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—21no—
103C22×C4×C11—81no—
104C22×C4×C11—81no—
105C22×C4×C11—82no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—44no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—82no—
118C2×C22⋊D11—82no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C2×D44—22no—
122C2×D44—81no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4C2×D414yes—
129C11×C22⋊C4—28no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C11×C22⋊C4—24no—
134C22⋊Dic11—44no—
135C22⋊Dic11—42no—
136#4325—84no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—82no—
139C4⋊Dic11—22no—
140C4⋊Dic11—81no—
141C2×C11⋊C8—24no—
142C2×C11⋊C8—82no—
143C2×#543D1111yescharacteristic, complemented
144#3187—112no—
145#2617—111no—
146#1608—114no—
147#1596—114no—
148#1520—112no—
149C2×#323—111no—
150C23×C11—22no—
151C23×C11—24no—
152C23×C11—22no—
153C23×C11—24no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—42no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—81no—
161C23×C11—81no—
162C23×C11—84no—
163C23×C11—84no—
164C23×C11#12011yescharacteristic
165C23×C11#12011yescharacteristic
166C23×C11C2×SD1614yes—
167C23×C11C2×SD1612yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—44no—
176Q8×C11—82no—
177Q8×C11—84no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—44no—
187C2×C4×C11—44no—
188C2×C4×C11—42no—
189C2×C4×C11—81no—
190C2×C4×C11—84no—
191C2×C4×C11—84no—
192C2×C4×C11#12012yes—
193C2×C4×C11C22×D412yes—
194C22⋊D11—88no—
195C22⋊D11—82no—
196C22⋊D11—82no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203D44—44no—
204C11⋊C8—44no—
205#543—24no—
206#543—22no—
207#543C2×D1114yes—
208C2×C22⋊Q8—22no—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—22no—
211C2×C22⋊Q8C2×D1112yes—
212C2×#121—111no—
213C2×#120—221no—
214C22×C22⋊C4—21no—
215C22×C22⋊C4C2×D1111yescharacteristic
216#483—114no—
217#481—222no—
218#465—224no—
219#450—114no—
220#448—222no—
221C2×C22⋊C8—112no—
222#397—112no—
223#394—222no—
224#392—112no—
225#386—221no—
226#380—111no—
227#328—118no—
228#323—114no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—24no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—44no—
239C22×C11—48no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—84no—
244C22×C11#44812yes—
245C22×C11#44812yes—
246C22×C11C2×#12011yescharacteristic
247C22×C11C22×SD1611yescharacteristic
248C22×C11C2×#13711yescharacteristic
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—81no—
252C2×D11—81no—
253C2×D11—81no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—44no—
258C4×C11—44no—
259Dic11—82no—
260Dic11—81no—
261C25C22⋊D1111yescharacteristic
262C22×Q8—21no—
263C22×Q8C22⋊D1112yescomplemented
264C22×D4—111no—
265C22×D4—221no—
266C22×D4—222no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4C22⋊D1111yescharacteristic
270C23×C4C22×D1111yescharacteristic
271C2×SD16—224no—
272C22×C8—222no—
273C22⋊Q8—28no—
274C22⋊Q8—28no—
275C22⋊Q8—24no—
276C22⋊Q8—28no—
277C22⋊Q8—24no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8—28no—
281C22⋊Q8C22⋊D1114yescomplemented
282C22⋊Q8C22×D1114yes—
283#121—222no—
284#121—222no—
285#120—444no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4C22⋊D1112yescomplemented
292C2×C22⋊C4—22no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—22no—
298C2×C22⋊C4—221no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—222no—
302C2×C22⋊C4C22⋊D1112yes—
303C2×C22⋊C4C22×D1112yes—
304#106—224no—
305#103—224no—
306#102—224no—
307C22⋊C8—114no—
308C22⋊C8—222no—
309#95—112no—
310#95—222no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—22no—
314C2×C11—22no—
315C2×C11—44no—
316C2×C11C2×#44811yescharacteristic
317C2×C11#301911yescharacteristic
318C2×C11#302611yescharacteristic
319D11—161no—
320C24—21no—
321C24—22no—
322C24—21no—
323C24—81no—
324C24—81no—
325C24—221no—
326C24#432514yescomplemented
327C24C2×C22⋊D1112yes—
328C24C2×C22⋊D1111yescharacteristic
329C2×Q8—24no—
330C2×Q8—22no—
331C2×Q8—82no—
332C2×Q8—82no—
333C2×Q8C2×C22⋊D1114yes—
334C2×D4—222no—
335C2×D4—444no—
336C2×D4—442no—
337C2×D4—442no—
338C2×D4—441no—
339C2×D4—441no—
340C2×D4—881no—
341C2×D4—882no—
342C2×D4—882no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—81no—
350C22×C4—81no—
351C22×C4—82no—
352C22×C4—82no—
353C22×C4—222no—
354C22×C4—221no—
355C22×C4C2×C22⋊D1112yes—
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1112yes—
358C22×C4C2×C22⋊D1112yes—
359C22×C4C23×D1111yescharacteristic
360SD16—884no—
361C2×C8—224no—
362C2×C8—882no—
363C4⋊C4—24no—
364C4⋊C4—28no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—24no—
368C4⋊C4—222no—
369C4⋊C4—881no—
370C4⋊C4C2×C22⋊D1114yes—
371C22⋊C4—28no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—24no—
375C22⋊C4—24no—
376C22⋊C4—444no—
377C22⋊C4—442no—
378C22⋊C4—442no—
379C22⋊C4—882no—
380C11#1828611yescharacteristic, complemented, Sylow
381C23—24no—
382C23—22no—
383C23—22no—
384C23—24no—
385C23—41no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—81no—
392C23—81no—
393C23—84no—
394C23—84no—
395C23—442no—
396C23—442no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23C2×#432514yes—
401C23C2×#432512yes—
402C23#6699512yes—
403C23#6700611yescharacteristic
404C23#6700611yescharacteristic
405C23C22×C22⋊D1111yescharacteristic
406Q8—44no—
407Q8—82no—
408Q8—84no—
409D4—444no—
410D4—888no—
411D4—882no—
412D4—882no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—81no—
425C2×C4—84no—
426C2×C4—84no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4#6700612yes—
434C2×C4C22×C22⋊D1112yes—
435C8—444no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—44no—
446C22—48no—
447C22—42no—
448C22—42no—
449C22—82no—
450C22—84no—
451C22—882no—
452C22—882no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22#1062284012yes—
457C22#1062284012yes—
458C22C22×#432511yescharacteristic
459C22C2×#6699511yescharacteristic
460C22C2×#6700611yescharacteristic
461C4—22no—
462C4—22no—
463C4—42no—
464C4—44no—
465C4—44no—
466C4—882no—
467C4—881no—
468C2—21no—
469C2—22no—
470C2—21no—
471C2—22no—
472C2—44no—
473C2—1761no—
474C2C2×#1062284011yescharacteristic
475C2#1307797311yescharacteristic
476C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#543C2
socleC22×C11C2×#120
prime radical#13074350C2
hypercenterC2×#543D11
hypocenterC11#18286
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #13079369C2semidirect
3. #13067607C2semidirect
4. #13067539C2semidirect
5. #13067188C2semidirect
6. C2×#10622163C2semidirect
7. C2×C11×#543C2semidirect
24. #10622659C22semidirect
25. #10622656C22semidirect
30. #10622176C22semidirect
34. C22×Q8×C11D4semidirect
50. C11×C22⋊Q8D4semidirect
55. C2×C11×C4⋊C4D4semidirect
88. C24×C11SD16semidirect
143. C2×#543D11semidirect
263. C22×Q8C22⋊D11semidirect
281. C22⋊Q8C22⋊D11semidirect
291. C2×C4⋊C4C22⋊D11semidirect
326. C24#4325semidirect
380. C11#18286semidirect

Maximal subgroups

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

subgroupindex
#130793692
#130743502
#130676072
#130675392
#130671882
C2×#106221632
C2×C11×#5432
#1828611