Finite Group Databasebeta

← #14649542

Subgroups — #14649542

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076904C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic
3#13068525C211yesmaximal, characteristic
4C2×#10622105C211yesmaximal, characteristic, complemented
5C2×#10622090C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×(C2×D11)⋊C4—21no—
10C2×#66977C2211yescharacteristic
11C2×#66950C412yescomplemented
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×(C2×D11)⋊C8—22no—
19#10622600C412yescomplemented
20#10622568—21no—
21#10622563—21no—
22#10622281—22no—
23#10622277—22no—
24#10622277—22no—
25#10622105—22no—
26#10622090—22no—
27C24×D11D411yescharacteristic
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11D411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11—21no—
34C22×C4×D11—21no—
35C22×C4×D11—21no—
36C22×C4×D11—44no—
37C22×C4×D11C2×C412yes—
38C22×C4×D11D412yes—
39C22×Dic22C2×C411yescharacteristic
40C22×C8×C11—21no—
41C2×C11×C4⋊C4C2×C412yes—
42C2×C11×C22⋊C4—21no—
43C2×C22⋊Dic11—21no—
44C2×(C2×D11)⋊C4—24no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—44no—
48C2×C4⋊Dic11—22no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50#66977—21no—
51#66977—21no—
52#66977—21no—
53#66977—21no—
54C2×Dic11⋊C4—21no—
55C22×C11⋊C8—21no—
56#66950—44no—
57C11×C22⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95D412yes—
62C11⋊#95—24no—
63C11⋊#95—21no—
64C11⋊#95—22no—
65C11⋊#95D412yes—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68(C2×D11)⋊C8—44no—
69#9154—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C23×D11—21no—
73C23×D11—24no—
74C23×D11—21no—
75C23×D11—21no—
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—42no—
79C23×D11C22⋊C412yes—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—42no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—22no—
97C22×Dic11—21no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11C22⋊C412yes—
104C2×C4×D11—24no—
105C2×C4×D11—24no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—44no—
113C2×C4×D11—44no—
114C2×C4×D11—44no—
115C2×C4×D11—44no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—42no—
119C2×C8×C11—42no—
120C2×C8×C11—41no—
121C11×C4⋊C4—42no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C22⋊Dic11—41no—
125C22⋊Dic11—41no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—48no—
128(C2×D11)⋊C4—44no—
129C4⋊Dic11—21no—
130C4⋊Dic11—21no—
131C4⋊Dic11—44no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134C2×C11⋊C8—42no—
135C2×C11⋊C8—41no—
136#2848—111no—
137C2×#381—111no—
138#1779—111no—
139C2×#328—111no—
140C2×#328—111no—
141#1294—111no—
142#1294D1111yescharacteristic, complemented
143C23×C11—22no—
144C23×C11—22no—
145C23×C11C2×C22⋊C411yescharacteristic
146C23×C11#12011yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11#13511yescharacteristic
149C23×C11#13511yescharacteristic
150C23×C11#13711yescharacteristic
151C23×C11#13711yescharacteristic
152C22×D11—24no—
153C22×D11—24no—
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—22no—
160C22×D11—44no—
161C22×D11—44no—
162C22×D11—44no—
163C22×D11—44no—
164C22×D11—42no—
165C22×D11—42no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11#9914yes—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—82no—
184C2×C4×C11—82no—
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—82no—
202C2×Dic11—82no—
203C4×D11—44no—
204C4×D11—44no—
205C4×D11—44no—
206C4×D11—44no—
207Dic22—81no—
208Dic22—81no—
209C8×C11—81no—
210C11⋊C8—81no—
211C24×C4—111no—
212C2×C22⋊Q8—111no—
213C2×C22⋊Q8—112no—
214C22×C22⋊C4—221no—
215C2×C22⋊C8—111no—
216C2×C22⋊C8—222no—
217C2×C22⋊C8C2×D1111yescharacteristic
218#385—222no—
219#385—221no—
220#381—222no—
221#381—222no—
222#380—112no—
223#380C2×D1111yescharacteristic
224#379—221no—
225C2×#95—111no—
226C2×#95—221no—
227C2×#95C2×D1111yescharacteristic
228#328—222no—
229#328—222no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11#38611yescharacteristic
239C22×C11C2×#9912yes—
240C22×C11#41611yescharacteristic
241C22×C11#41911yescharacteristic
242C22×C11#42112yes—
243C22×C11#45211yescharacteristic
244C22×C11#45211yescharacteristic
245C22×C11#48511yescharacteristic
246C22×C11#48511yescharacteristic
247C2×D11—24no—
248C2×D11—24no—
249C2×D11—24no—
250C2×D11—44no—
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—42no—
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—42no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—82no—
263C4×C11—82no—
264Dic11—42no—
265Dic11—82no—
266Dic11—81no—
267Dic11—81no—
268C25—111no—
269C22×Q8—111no—
270C23×C4—21no—
271C23×C4—111no—
272C23×C4—112no—
273C23×C4—112no—
274C23×C4—221no—
275C23×C4—221no—
276C23×C4—221no—
277C23×C4—221no—
278C23×C4—221no—
279C23×C4—444no—
280C23×C4C22×D1111yescharacteristic
281C22×C8—21no—
282C22×C8—221no—
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287C22⋊Q8—444no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4C4×D1112yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C22⋊C4—224no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4—444no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—221no—
301C22⋊C8—221no—
302C22⋊C8—444no—
303#95—21no—
304#95—21no—
305#95—112no—
306#95—222no—
307#95—224no—
308#95—221no—
309#95D4412yes—
310C2×C11—21no—
311C2×C11—21no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11#151112yes—
315C2×C11#151612yes—
316C2×C11#187311yescharacteristic
317C2×C11#189711yescharacteristic
318C2×C11#189811yescharacteristic
319D11—44no—
320C24—112no—
321C24—224no—
322C24—221no—
323C24—221no—
324C24—221no—
325C24—221no—
326C24—221no—
327C24—221no—
328C24—442no—
329C24D4×D1111yescharacteristic
330C2×Q8—221no—
331C2×Q8—221no—
332C2×Q8—442no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—112no—
341C22×C4—224no—
342C22×C4—224no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4—442no—
353C22×C4—442no—
354C22×C4—444no—
355C22×C4—444no—
356C22×C4—444no—
357C22×C4—444no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—442no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4C2×C4×D1111yescharacteristic
364C22×C4C2×D4411yescharacteristic
365C22×C4#433911yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4D4×D1111yescharacteristic
368C22×C4#434311yescharacteristic
369C2×C8—42no—
370C2×C8—41no—
371C2×C8—442no—
372C2×C8—441no—
373C4⋊C4—42no—
374C4⋊C4—221no—
375C4⋊C4—221no—
376C4⋊C4—444no—
377C4⋊C4—441no—
378C4⋊C4—441no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—444no—
382C22⋊C4—448no—
383C22⋊C4—444no—
384C22⋊C4—441no—
385C22⋊C4—441no—
386C11#915411yescharacteristic, complemented, Sylow
387C23—22no—
388C23—22no—
389C23—114no—
390C23—224no—
391C23—224no—
392C23—222no—
393C23—222no—
394C23—222no—
395C23—222no—
396C23—222no—
397C23—222no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23—444no—
402C23—442no—
403C23—442no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23C22⋊C4×D1111yescharacteristic
409C23#6693511yescharacteristic
410C23#6694711yescharacteristic
411C23#6696511yescharacteristic
412C23#6696811yescharacteristic
413C23#6696911yescharacteristic
414C23#6697111yescharacteristic
415Q8—881no—
416Q8—881no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—444no—
435C2×C4—444no—
436C2×C4—444no—
437C2×C4—444no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—882no—
448C2×C4—882no—
449C2×C4C4×D4411yescharacteristic
450C2×C4#6693711yescharacteristic
451C2×C4#6694611yescharacteristic
452C2×C4#6694811yescharacteristic
453C8—81no—
454C8—881no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—224no—
464C22—224no—
465C22—224no—
466C22—444no—
467C22—444no—
468C22—444no—
469C22—444no—
470C22—442no—
471C22—442no—
472C22—442no—
473C22—442no—
474C22#1062227811yescharacteristic
475C22D11×#9912yes—
476C22#1062238511yescharacteristic
477C22#1062239611yescharacteristic
478C22#1062241511yescharacteristic
479C22#1062242311yescharacteristic
480C22#1062243412yes—
481C22#1062248011yescharacteristic
482C22#1062250111yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—82no—
488C4—82no—
489C4—442no—
490C4—882no—
491C4—881no—
492C4—881no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—444no—
498C2#1306714712yes—
499C2#1306716912yes—
500C2#1306892711yescharacteristic
501C2#1306906311yescharacteristic
502C2#1306906811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9154
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. C2×#10622105C2semidirect
5. C2×#10622090C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
11. C2×#66950C4semidirect
19. #10622600C4semidirect
142. #1294D11semidirect
386. C11#9154semidirect

Maximal subgroups

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

subgroupindex
#130769042
C2×#106222772
#130685252
C2×#106221052
C2×#106220902
#130664942
C11×#12942
#915411