Finite Group Databasebeta

← #14803656

Subgroups — #14803656

Order 2816.

946 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13071680C211yesmaximal, characteristic
4#13070020C212yesmaximal, complemented
5#13069931C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068953C212yesmaximal, complemented
9#13068613C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2567C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C22×#4325C2212yes—
15C2×#66946—21no—
16C2×#66927C2211yescharacteristic
17C2×C4×D44C2212yes—
18C11×#395—22no—
19C11×#391C2212yes—
20C11×#389—21no—
21C11×#389—21no—
22C11×#384C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26#10622701—24no—
27#10622640—24no—
28#10622601—21no—
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32#10622552C2212yes—
33C4×C4⋊Dic11C2211yescharacteristic
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622278—22no—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C42×C11—21no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—24no—
65C2×#4325—24no—
66C2×#4325—42no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4×Dic11—21no—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76#66946—44no—
77#66927—22no—
78#66927D414yes—
79C4×D44—24no—
80C4×D44—42no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95D412yes—
84#66899—22no—
85#66899—22no—
86C11⋊#95—21no—
87#66873—24no—
88#66873—24no—
89#66873—24no—
90C4⋊(C11⋊C8)—22no—
91C4⋊(C11⋊C8)—42no—
92C4×C11⋊C8—22no—
93#25322—111nomaximal, Sylow
94C23×D11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—42no—
101C2×Q8×C11—81no—
102C2×Q8×C11—81no—
103C2×Q8×C11#4112yes—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—21no—
114C2×D44—24no—
115C2×D44—24no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—81no—
124C2×D44—81no—
125C2×D44C2×D414yes—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—82no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—42no—
136C11×C4⋊C4—82no—
137C11×C4⋊C4—82no—
138C11×C4⋊C4SD1614yescomplemented
139C42×C11—22no—
140C42×C11—22no—
141C42×C11—42no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144#4325—48no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—82no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11#4112yes—
152C4×Dic11—42no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×#486—111no—
163C2×#460—111no—
164#2567D1111yescharacteristic, complemented
165#2366—111no—
166#2071—112no—
167#2055—112no—
168#1987—111no—
169#1939—111no—
170#1877—112no—
171#1802—112no—
172C4×#103—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—24no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—84no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11C2×SD1614yes—
205C2×C4×C11C2×SD1612yes—
206C2×C4×C11#13712yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×C4×C112−1+411yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219D44—24no—
220D44—24no—
221D44—42no—
222D44—42no—
223D44—48no—
224D44—84no—
225C4×D11—88no—
226C11⋊C8—41no—
227C11⋊C8—42no—
228C11⋊C8—41no—
229C22×SD16—112no—
230C2×C4⋊Q8C2×D1111yescharacteristic
231C2×#127—111no—
232C2×C4×Q8C2×D1111yescharacteristic
233C2×C4×D4—112no—
234C2×C4×D4—221no—
235#486—224no—
236#460—224no—
237C2×C4⋊C8—111no—
238C2×C4⋊C8—112no—
239C2×#103—111no—
240C2×#103—111no—
241C2×#102—112no—
242C2×#102—112no—
243C2×#102—112no—
244C2×C4×C8—111no—
245#395—22no—
246#391C2×D1112yes—
247#390—112no—
248#390—221no—
249#389—21no—
250#389—21no—
251#386—222no—
252#384C2×D1112yes—
253C4×C4⋊C4—111no—
254C4×C4⋊C4C2×D1111yescharacteristic
255#340—112no—
256#340—111no—
257#340—112no—
258#340—111no—
259#336—112no—
260C22×C11C2×#12111yescharacteristic
261C22×C11#54611yescharacteristic
262C22×C11#54811yescharacteristic
263C22×C11C22×SD1611yescharacteristic
264C22×C11C2×#13711yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57611yescharacteristic
267C2×D11—44no—
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—82no—
273C2×D11—82no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—81no—
279C4×C11—82no—
280C4×C11#46114yes—
281C4×C11#52911yescharacteristic
282C4×C11#54211yescharacteristic
283C4×C11#54611yescharacteristic
284C4×C11#54711yescharacteristic
285Dic11—42no—
286Dic11—81no—
287C22×Q8—21no—
288C22×Q8C22×D1111yescharacteristic
289C22×D4—112no—
290C22×D4—221no—
291C22×D4—221no—
292C23×C4—222no—
293C2×SD16—224no—
294C2×SD16—224no—
295C2×SD16—442no—
296C22×C8—112no—
297C22×C8—111no—
298C22×C8—111no—
299C4⋊Q8—22no—
300C4⋊Q8—22no—
301#127—114no—
302#127—222no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×D4—224no—
306C4×D4—442no—
307C4×D4—444no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C4⋊C4C22×D1112yes—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—21no—
322C2×C42—221no—
323C2×C42C22×D1112yes—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—222no—
326C4⋊C8—442no—
327#103—222no—
328#103—222no—
329#102—224no—
330#102—224no—
331#102—224no—
332C4×C8—222no—
333#95—22no—
334#95—22no—
335#95—221no—
336#95C22⋊D1112yes—
337C2×C11#242711yescharacteristic
338C2×C11C2×#46111yescharacteristic
339C2×C11#304111yescharacteristic
340C2×C11#329511yescharacteristic
341C2×C11#333311yescharacteristic
342C2×C11#336211yescharacteristic
343C2×C11#337511yescharacteristic
344D11—84no—
345C24—222no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—42no—
352C2×Q8—81no—
353C2×Q8—81no—
354C2×Q8#434312yes—
355C2×D4—114no—
356C2×D4—224no—
357C2×D4—224no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—442no—
364C2×D4—442no—
365C2×D4—881no—
366C2×D4—881no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—444no—
373C22×C4—444no—
374C22×C4—882no—
375C22×C4C2×C22⋊D1112yes—
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1112yes—
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C23×D1111yescharacteristic
380SD16—448no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—222no—
384C2×C8—221no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—222no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—82no—
398C4⋊C4—82no—
399C4⋊C4—112no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4#432514yescomplemented
404C22⋊C4—444no—
405C22⋊C4—444no—
406C22⋊C4—882no—
407C42—22no—
408C42—22no—
409C42—42no—
410C42—442no—
411C42D4×D1112yes—
412C42#434112yes—
413C11#2532211yescharacteristic, complemented, Sylow
414C23—224no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—442no—
420C23—442no—
421C23C22×C22⋊D1111yescharacteristic
422Q8—22no—
423Q8—22no—
424Q8—41no—
425Q8—41no—
426Q8—84no—
427D4—224no—
428D4—224no—
429D4—442no—
430D4—442no—
431D4—448no—
432D4—884no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—222no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—888no—
456C2×C4#6699112yes—
457C2×C4#6699112yes—
458C2×C4C2×#432514yes—
459C2×C4C2×#432512yes—
460C2×C4#6699512yes—
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C2×#434311yescharacteristic
464C2×C4#6704011yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C2×C4#6704211yescharacteristic
467C8—442no—
468C8—441no—
469C8—441no—
470C22—444no—
471C22—444no—
472C22—444no—
473C22—882no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22C2×#6699111yescharacteristic
478C22C22×#432511yescharacteristic
479C22C2×#6699511yescharacteristic
480C22#1062334811yescharacteristic
481C22#1062336011yescharacteristic
482C22#1062336611yescharacteristic
483C22#1062336611yescharacteristic
484C4—22no—
485C4—24no—
486C4—42no—
487C4—42no—
488C4—82no—
489C4—81no—
490C4—442no—
491C4—881no—
492C4#1062269614yes—
493C4#1062315511yescharacteristic
494C4#1062316111yescharacteristic
495C4#1062316211yescharacteristic
496C4#1062317411yescharacteristic
497C2—884no—
498C2#1307218911yescharacteristic
499C2C2×#1062269611yescharacteristic
500C2#1307811511yescharacteristic
501C2#1308043411yescharacteristic
502C2#1308094811yescharacteristic
503C2#1308128711yescharacteristic
504C2#1308143011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2567C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2567D11
hypocenterC11#25322
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2567

Complements

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

NH ≅ G/Ntype
4. #13070020C2semidirect
5. #13069931C2semidirect
6. #13069565C2semidirect
7. #13069335C2semidirect
8. #13068953C2semidirect
9. #13068613C2semidirect
10. C4×#66899C2semidirect
11. C11×#2567C2semidirect
138. C11×C4⋊C4SD16semidirect
164. #2567D11semidirect
403. C4⋊C4#4325semidirect
413. C11#25322semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226402
#130716802
#130700202
#130699312
#130695652
#130693352
#130689532
#130686132
C4×#668992
C11×#25672
#2532211