Finite Group Databasebeta

← #14804266

Subgroups — #14804266

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622698C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3C2×#10622696C212yesmaximal, complemented
4#13071680C211yesmaximal, characteristic
5#13069931C212yesmaximal, complemented
6#13069699C212yesmaximal, complemented
7#13069540C211yesmaximal, characteristic, complemented
8#13069335C211yesmaximal, characteristic, complemented
9#13068953C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2546C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2212yes—
14C2×C4×Q8×C11C2211yescharacteristic
15C22×#4325C2212yes—
16C22×#4325C2212yes—
17C22×#4325C2212yes—
18C2×#66946—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44C2212yes—
21C11×#398—22no—
22C11×#391C2212yes—
23C11×#389—21no—
24C11×#389—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2211yescharacteristic
28C2×#66899C2212yes—
29C2×#66899C2211yescharacteristic
30#10622698—24no—
31#10622696—28no—
32#10622640—24no—
33#10622601—21no—
34C2×#66873C2212yes—
35#10622552C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622278—22no—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43#10622162C2212yes—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C22×C4×D11—22no—
50C11×C4⋊Q8—24no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—42no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11—21no—
65C2×C42×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67C2×#4325—24no—
68C2×#4325—24no—
69C2×#4325—24no—
70C2×#4325—24no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4325—42no—
74C2×#4325—42no—
75C2×#4325—42no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4×Dic11—21no—
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66946—44no—
86#66927—22no—
87#66927D414yes—
88C4×D44—24no—
89C4×D44—42no—
90C11×#95—22no—
91C11×#95—22no—
92C11×#95D412yes—
93#66899—24no—
94#66899—22no—
95#66899—42no—
96#66899D414yescomplemented
97C11⋊#95—21no—
98#66873—24no—
99C4⋊(C11⋊C8)—22no—
100C4⋊(C11⋊C8)—24no—
101C4×C11⋊C8—22no—
102#25368—111nomaximal, Sylow
103C23×D11—22no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C2×D412yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—21no—
125C22×Dic11—21no—
126C2×D44—24no—
127C2×D44—24no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—42no—
134C2×D44—42no—
135C2×D44—81no—
136C2×D44—81no—
137C2×D44C2×D414yes—
138C2×C4×D11—44no—
139C2×C4×D11—44no—
140C2×C4×D11—82no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4SD1614yescomplemented
150C42×C11—22no—
151C42×C11—22no—
152C42×C11—42no—
153C42×C11C2×D412yes—
154C42×C11#4112yes—
155#4325—48no—
156#4325—48no—
157#4325—48no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—82no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D412yes—
165C4×Dic11—42no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C2×D412yes—
174C2×C11⋊C8#4112yes—
175C2×#492—111no—
176C2×#460—111no—
177C2×#461—112no—
178#2546D1111yescharacteristic, complemented
179#2366—111no—
180#2055—112no—
181#2013—112no—
182#1981—111no—
183#1939—111no—
184#1877—112no—
185C4×#103—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—24no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11—42no—
194Q8×C11—22no—
195Q8×C11—22no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—42no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11#12112yes—
219C2×C4×C11#12112yes—
220C2×C4×C11C2×SD1614yes—
221C2×C4×C11C2×SD1612yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235D44—24no—
236D44—24no—
237D44—42no—
238D44—42no—
239D44—48no—
240D44—84no—
241C4×D11—88no—
242C11⋊C8—22no—
243C11⋊C8—22no—
244C11⋊C8—42no—
245C22×SD16—112no—
246C22×SD16—112no—
247C22×SD16—112no—
248C2×C4⋊Q8C2×D1111yescharacteristic
249C2×C4⋊Q8C2×D1112yes—
250C2×#127—111no—
251C2×C4×Q8C2×D1111yescharacteristic
252C2×C4×D4—112no—
253C2×C4×D4—221no—
254#492—224no—
255#461—228no—
256#460—224no—
257C2×C4⋊C8—112no—
258C2×C4⋊C8—111no—
259C2×#103—111no—
260C2×#103—112no—
261C2×#103—111no—
262C2×#103—112no—
263C2×#102—112no—
264C2×C4×C8—111no—
265#398—22no—
266#391C2×D1112yes—
267#390—112no—
268#390—221no—
269#389—21no—
270#389—21no—
271#386—222no—
272C4×C4⋊C4—111no—
273C4×C4⋊C4C2×D1111yescharacteristic
274#340—111no—
275#340—111no—
276#336—112no—
277C22×C11C2×#12111yescharacteristic
278C22×C11D4211yescharacteristic
279C22×C11#55011yescharacteristic
280C22×C11C22×SD1611yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11#57711yescharacteristic
283C22×C11#57711yescharacteristic
284C2×D11—44no—
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—82no—
288C2×D11—82no—
289C2×D11—82no—
290C2×D11—82no—
291C4×C11—24no—
292C4×C11—22no—
293C4×C11—42no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11—81no—
297C4×C11#46114yescomplemented
298C4×C11#53211yescharacteristic
299C4×C11#54011yescharacteristic
300C4×C11D4211yescharacteristic
301C4×C11#54611yescharacteristic
302Dic11—42no—
303Dic11—81no—
304C22×Q8C22×D1112yes—
305C22×Q8C22×D1111yescharacteristic
306C22×D4—112no—
307C22×D4—221no—
308C22×D4—221no—
309C23×C4—222no—
310C2×SD16—224no—
311C2×SD16—224no—
312C2×SD16—224no—
313C2×SD16—224no—
314C2×SD16—224no—
315C2×SD16—224no—
316C2×SD16—442no—
317C2×SD16—442no—
318C2×SD16—442no—
319C22×C8—111no—
320C22×C8—111no—
321C22×C8—112no—
322C4⋊Q8—24no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—42no—
326#127—114no—
327#127—222no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×D4—224no—
331C4×D4—442no—
332C4×D4—444no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4C22⋊D1111yescharacteristic
341C2×C4⋊C4C22⋊D1111yescharacteristic
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—222no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C42—21no—
347C2×C42—221no—
348C2×C42C22×D1112yes—
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—224no—
351C4⋊C8—222no—
352#103—114no—
353#103—224no—
354#103—222no—
355#103—442no—
356#102—224no—
357C4×C8—222no—
358#95—22no—
359#95—22no—
360#95—221no—
361#95C22⋊D1112yes—
362C2×C11#242811yescharacteristic
363C2×C11C2×#46111yescharacteristic
364C2×C11#304211yescharacteristic
365C2×C11#327811yescharacteristic
366C2×C11D4×SD1611yescharacteristic
367C2×C11#339211yescharacteristic
368C2×C11#340011yescharacteristic
369D11—84no—
370C24—222no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8D4×D1112yes—
383C2×D4—114no—
384C2×D4—224no—
385C2×D4—224no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—442no—
393C2×D4—881no—
394C2×D4—881no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—882no—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1111yescharacteristic
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C23×D1111yescharacteristic
408SD16—448no—
409SD16—448no—
410SD16—448no—
411C2×C8—112no—
412C2×C8—112no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—222no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—44no—
424C4⋊C4—44no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4—112no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4#432514yescomplemented
433C22⋊C4—444no—
434C22⋊C4—444no—
435C22⋊C4—882no—
436C42—22no—
437C42—22no—
438C42—42no—
439C42—442no—
440C42D4×D1112yes—
441C42#434112yes—
442C11#2536811yescharacteristic, complemented, Sylow
443C23—224no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23C22×C22⋊D1111yescharacteristic
451Q8—22no—
452Q8—22no—
453Q8—41no—
454Q8—41no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459D4—224no—
460D4—224no—
461D4—442no—
462D4—442no—
463D4—448no—
464D4—884no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—222no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—888no—
488C2×C4#6699112yes—
489C2×C4#6699112yes—
490C2×C4C2×#432514yes—
491C2×C4C2×#432512yes—
492C2×C4#6699512yes—
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4C2×#434111yescharacteristic
496C2×C4#6703711yescharacteristic
497C2×C4#41×D1111yescharacteristic
498C2×C4#6704211yescharacteristic
499C8—222no—
500C8—222no—
501C8—442no—
502C22—444no—
503C22—444no—
504C22—444no—
505C22—882no—
506C22—882no—
507C22—882no—
508C22—882no—
509C22C2×#6699111yescharacteristic
510C22D4×C22⋊D1111yescharacteristic
511C22C22×#432511yescharacteristic
512C22C2×#6699511yescharacteristic
513C22#1062336511yescharacteristic
514C22#1062336811yescharacteristic
515C22#1062336811yescharacteristic
516C4—22no—
517C4—24no—
518C4—42no—
519C4—42no—
520C4—82no—
521C4—81no—
522C4—442no—
523C4—881no—
524C4#1062269614yescomplemented
525C4#1062312711yescharacteristic
526C4#1062314011yescharacteristic
527C4#1062314311yescharacteristic
528C4#1062315011yescharacteristic
529C2—884no—
530C2#1307220011yescharacteristic
531C2C2×#1062269611yescharacteristic
532C2#1307812411yescharacteristic
533C2#1308027811yescharacteristic
534C2D4×#432511yescharacteristic
535C2#1308159311yescharacteristic
536C2#1308166511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2546C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2546D11
hypocenterC11#25368
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2546

Complements

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

NH ≅ G/Ntype
3. C2×#10622696C2semidirect
5. #13069931C2semidirect
6. #13069699C2semidirect
7. #13069540C2semidirect
8. #13069335C2semidirect
9. #13068953C2semidirect
10. C4×#66899C2semidirect
11. C11×#2546C2semidirect
96. #66899D4semidirect
149. C11×C4⋊C4SD16semidirect
178. #2546D11semidirect
297. C4×C11#461semidirect
432. C4⋊C4#4325semidirect
442. C11#25368semidirect
524. C4#10622696semidirect

Maximal subgroups

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

subgroupindex
C2×#106226982
C2×#106226402
C2×#106226962
#130716802
#130699312
#130696992
#130695402
#130693352
#130689532
C4×#668992
C11×#25462
#2536811