Finite Group Databasebeta

← #14803660

Subgroups — #14803660

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×#10622307C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13073821C211yesmaximal, characteristic, complemented
4#13071680C211yesmaximal, characteristic
5#13070023C212yesmaximal, complemented
6#13069930C212yesmaximal, complemented
7#13069564C211yesmaximal, characteristic, complemented
8#13069334C211yesmaximal, characteristic, complemented
9#13068947C212yesmaximal, complemented
10#13068615C212yesmaximal, complemented
11C4×C11×#103C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4325C2212yes—
14C2×#66946C2212yes—
15C2×#66927C2211yescharacteristic
16C2×C4×D44—21no—
17C2×#66922C2211yescharacteristic
18C2×C11×#103C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622843C2212yes—
23C2×#66885C2212yes—
24C2×#66885C2212yes—
25C2×Dic11⋊C8C2212yes—
26#10622640—24no—
27#10622601C2212yes—
28#10622592—22no—
29#10622589C2212yes—
30C2×#66873C2212yes—
31#10622552—21no—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622541—21no—
34#10622541—21no—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622307—24no—
37#10622278—22no—
38C11×#340C2211yescharacteristic
39C11×#340C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4325—24no—
61C2×#4325—24no—
62C2×#4325—42no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11C2312yes—
73C22×C11⋊C8C2312yes—
74#66946—24no—
75#66946—42no—
76#66927—22no—
77#66927D414yes—
78C4×D44—44no—
79#66922—22no—
80#66922—22no—
81C11×#103—22no—
82C11×#103—22no—
83C4×C8×C11—22no—
84C11×#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95D412yes—
88#66885—24no—
89#66885—24no—
90Dic11⋊C8—42no—
91#66873—24no—
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#4112yes—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—22no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×D44—24no—
112C2×D44—24no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—81no—
121C2×D44—81no—
122C2×D44C2×D414yes—
123C2×C4×D11—44no—
124C2×C4×D11—44no—
125C2×C4×D11—82no—
126C2×Dic22—42no—
127C2×Dic22—81no—
128C2×Dic22—81no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4#4112yes—
142C42×C11—42no—
143C42×C11—42no—
144C42×C11C2×D412yes—
145C42×C11#4112yes—
146#4325—48no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—42no—
154C4⋊Dic11SD1614yescomplemented
155Dic11⋊C4—82no—
156Dic11⋊C4—82no—
157C4×Dic11—22no—
158C4×Dic11—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×#486—111no—
163C2×#460—111no—
164#2567—111no—
165#2366—111no—
166#2071—112no—
167#2055—112no—
168#1987—111no—
169#1939—111no—
170#1877—112no—
171#1802—112no—
172C4×#103D1111yescharacteristic, complemented
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—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11C2×SD1614yes—
218D44—24no—
219D44—24no—
220D44—42no—
221D44—42no—
222D44—48no—
223D44—84no—
224C4×D11—88no—
225Dic22—84no—
226C8×C11—41no—
227C8×C11—41no—
228C11⋊C8—42no—
229C22×SD16—112no—
230C2×C4⋊Q8—111no—
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×#103C2×D1111yescharacteristic
240C2×#103C2×D1111yescharacteristic
241C2×#102—112no—
242C2×#102—112no—
243C2×#102—112no—
244C2×C4×C8C2×D1111yescharacteristic
245#395—222no—
246#391—112no—
247#390—112no—
248#390—221no—
249#389—221no—
250#389—221no—
251#386—222no—
252#384—112no—
253C4×C4⋊C4—111no—
254C4×C4⋊C4C2×D1111yescharacteristic
255#340—112no—
256#340—112no—
257#340C2×D1111yescharacteristic
258#340C2×D1111yescharacteristic
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—22no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11#46114yes—
280C4×C11#52911yescharacteristic
281C4×C11#54211yescharacteristic
282C4×C11#54611yescharacteristic
283C4×C11#54711yescharacteristic
284Dic11—24no—
285Dic11—42no—
286Dic11—82no—
287C22×Q8—221no—
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×C8C22×D1111yescharacteristic
298C22×C8C22×D1111yescharacteristic
299C4⋊Q8—222no—
300C4⋊Q8—222no—
301#127—114no—
302#127—222no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×D4—224no—
306C4×D4—444no—
307C4×D4—442no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C4⋊C4C22×D1111yescharacteristic
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—112no—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—222no—
326C4⋊C8—442no—
327#103—22no—
328#103—22no—
329#102—224no—
330#102—224no—
331#102—224no—
332C4×C8—22no—
333#95—21no—
334#95—112no—
335#95—222no—
336#95—222no—
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—442no—
352C2×Q8—881no—
353C2×Q8—881no—
354C2×Q8#433912yes—
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—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—222no—
374C22×C4—444no—
375C22×C4—444no—
376C22×C4—882no—
377C22×C4D4×D1111yescharacteristic
378C22×C4D4×D1111yescharacteristic
379C22×C4C23×D1111yescharacteristic
380SD16—448no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—222no—
388C2×C8—222no—
389C2×C8—222no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—42no—
396C4⋊C4—114no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—442no—
401C4⋊C4—882no—
402C4⋊C4—882no—
403C4⋊C4#433912yes—
404C22⋊C4—444no—
405C22⋊C4—444no—
406C22⋊C4—882no—
407C42—42no—
408C42—42no—
409C42—222no—
410C42—222no—
411C42#433912yes—
412C42D4×D1112yes—
413C11#2532211yescharacteristic, complemented, Sylow
414C23—224no—
415C23—442no—
416C23—442no—
417C23—442no—
418C23—442no—
419C23—442no—
420C23—442no—
421C23C2×D4×D1111yescharacteristic
422Q8—22no—
423Q8—22no—
424Q8—41no—
425Q8—41no—
426Q8—884no—
427D4—224no—
428D4—224no—
429D4—442no—
430D4—442no—
431D4—448no—
432D4—884no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—114no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—888no—
457C2×C4#6693712yes—
458C2×C4#6693712yes—
459C2×C4SD16×D1112yes—
460C2×C4#6697112yes—
461C2×C4C2×#433911yescharacteristic
462C2×C4C2×#433911yescharacteristic
463C2×C4C2×#433911yescharacteristic
464C2×C4C2×D4×D1111yescharacteristic
465C2×C4#6704211yescharacteristic
466C2×C4#6704311yescharacteristic
467C8—41no—
468C8—41no—
469C8—442no—
470C22—444no—
471C22—444no—
472C22—444no—
473C22—882no—
474C22—882no—
475C22—882no—
476C22—882no—
477C22C2×#6693711yescharacteristic
478C22#1062308111yescharacteristic
479C22#1062308311yescharacteristic
480C22C2×SD16×D1111yescharacteristic
481C22C2×#6697111yescharacteristic
482C22#1062330011yescharacteristic
483C22#1062330011yescharacteristic
484C4—22no—
485C4—42no—
486C4—42no—
487C4—81no—
488C4—81no—
489C4—224no—
490C4—442no—
491C4—882no—
492C4#1062243114yes—
493C4#1062301011yescharacteristic
494C4#1062306511yescharacteristic
495C4#1062308111yescharacteristic
496C4#1062308211yescharacteristic
497C2—884no—
498C2#1307219311yescharacteristic
499C2C2×#1062243111yescharacteristic
500C2#1307812211yescharacteristic
501C2#1308044211yescharacteristic
502C2#1308095611yescharacteristic
503C2#1308128511yescharacteristic
504C2#1308142811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC4×#103D11
hypocenterC11#25322
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
3. #13073821C2semidirect
5. #13070023C2semidirect
6. #13069930C2semidirect
7. #13069564C2semidirect
8. #13069334C2semidirect
9. #13068947C2semidirect
10. #13068615C2semidirect
11. C4×C11×#103C2semidirect
154. C4⋊Dic11SD16semidirect
172. C4×#103D11semidirect
413. C11#25322semidirect

Maximal subgroups

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

subgroupindex
C2×#106223072
C2×#106226402
#130738212
#130716802
#130700232
#130699302
#130695642
#130693342
#130689472
#130686152
C4×C11×#1032
#2532211