Finite Group Databasebeta

← #14804268

Subgroups — #14804268

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×#10622306C211yesmaximal, characteristic
2C2×#10622461C211yesmaximal, characteristic
3C2×#10622454C212yesmaximal, complemented
4#13073604C211yesmaximal, characteristic, complemented
5#13071680C211yesmaximal, characteristic
6#13069934C212yesmaximal, complemented
7#13069701C212yesmaximal, complemented
8#13069538C211yesmaximal, characteristic, complemented
9#13068949C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C22×#4314C2212yes—
14C22×#4314C2212yes—
15C2×#66946—21no—
16C2×#66927C2211yescharacteristic
17C2×C4×D44C2212yes—
18C2×#66922C2211yescharacteristic
19C2×#66922C2212yes—
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C4⋊C8C2212yes—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2212yes—
26C2×#66880C2212yes—
27C2×#66880C2211yescharacteristic
28C2×#66880C2212yes—
29C2×#66880C2211yescharacteristic
30#10622601—21no—
31#10622598—21no—
32#10622598—21no—
33#10622552C2212yes—
34C4×C4⋊Dic11C2211yescharacteristic
35#10622542C2212yes—
36#10622461—24no—
37#10622454—28no—
38#10622306—24no—
39#10622278—22no—
40#10622274—22no—
41C11×#336C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×D44—21no—
45C22×D44—21no—
46C22×D44C2312yes—
47C22×C4×D11—22no—
48C22×Dic22C2312yes—
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C42×C11C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—21no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×#4314—24no—
71C2×#4314—24no—
72C2×#4314—24no—
73C2×#4314—24no—
74C2×#4314—24no—
75C2×#4314—24no—
76C2×#4314—42no—
77C2×#4314—42no—
78C2×#4314—42no—
79#66946—44no—
80#66927—22no—
81#66927D414yes—
82C4×D44—24no—
83C4×D44—42no—
84#66922—24no—
85#66922—22no—
86#66922—22no—
87#66922—42no—
88C4×Dic22—22no—
89C4×Dic22—22no—
90C11×C4⋊C8—24no—
91C11×C4⋊C8—22no—
92C4×C8×C11—22no—
93C11×#95D412yes—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—21no—
97#66885—24no—
98#66880—22no—
99#66880—24no—
100#66880—42no—
101#66880D414yescomplemented
102#25368—111nomaximal, Sylow
103C23×D11—22no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
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—
129C2×Dic22—21no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—22no—
135C2×Dic22—22no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22C2×D412yes—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11C2×D412yes—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—22no—
151C11×C4⋊C4SD1614yescomplemented
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D412yes—
155C42×C11#4112yes—
156(C2×D11)⋊C4—44no—
157(C2×D11)⋊C4—44no—
158(C2×D11)⋊C4—82no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—44no—
165C4⋊Dic11—44no—
166C4⋊Dic11—42no—
167C4⋊Dic11—42no—
168C4⋊Dic11C2×D412yes—
169Dic11⋊C4—42no—
170C4×Dic11—42no—
171C4×Dic11—42no—
172#4314—48no—
173#4314—48no—
174#4314—48no—
175C2×#492—111no—
176C2×#460—111no—
177C2×#461—112no—
178#2546—111no—
179#2366—111no—
180#2055—112no—
181#2013—112no—
182#1981—111no—
183#1939D1111yescharacteristic, complemented
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—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11#12112yes—
202C2×C4×C11#12112yes—
203C2×C4×C11C2×SD1614yes—
204C2×C4×C11C2×SD1612yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227D44—24no—
228D44—24no—
229D44—42no—
230D44—42no—
231D44—48no—
232D44—84no—
233C4×D11—88no—
234Dic22—22no—
235Dic22—22no—
236Dic22—41no—
237Dic22—41no—
238Dic22—42no—
239Dic22—42no—
240Dic22—42no—
241Dic22—42no—
242C8×C11—22no—
243C8×C11—22no—
244C8×C11—42no—
245C22×SD16—112no—
246C22×SD16—112no—
247C22×SD16—112no—
248C2×C4⋊Q8—111no—
249C2×C4⋊Q8—112no—
250C2×#127—111no—
251C2×C4×Q8—111no—
252C2×C4×D4—112no—
253C2×C4×D4—221no—
254#492—224no—
255#461—228no—
256#460—224no—
257C2×C4⋊C8C2×D1112yes—
258C2×C4⋊C8C2×D1111yescharacteristic
259C2×#103—111no—
260C2×#103—112no—
261C2×#103—111no—
262C2×#103—112no—
263C2×#102—112no—
264C2×C4×C8C2×D1111yescharacteristic
265#398—222no—
266#391—112no—
267#390—112no—
268#390—221no—
269#389—221no—
270#389—221no—
271#386—222no—
272C4×C4⋊C4—111no—
273C4×C4⋊C4C2×D1111yescharacteristic
274#340—111no—
275#340—111no—
276#336C2×D1112yes—
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#46114yescomplemented
295C4×C11#53211yescharacteristic
296C4×C11#54011yescharacteristic
297C4×C11D4211yescharacteristic
298C4×C11#54611yescharacteristic
299Dic11—42no—
300Dic11—42no—
301Dic11—81no—
302Dic11—82no—
303Dic11—81no—
304C22×Q8—111no—
305C22×Q8—112no—
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×C8C22×D1112yes—
320C22×C8C22×D1111yescharacteristic
321C22×C8C22×D1111yescharacteristic
322C4⋊Q8—224no—
323C4⋊Q8—222no—
324C4⋊Q8—222no—
325C4⋊Q8—442no—
326#127—114no—
327#127—222no—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×D4—224no—
331C4×D4—442no—
332C4×D4—444no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—111no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4D4411yescharacteristic
342C2×C4⋊C4D4411yescharacteristic
343C2×C22⋊C4—222no—
344C2×C22⋊C4—222no—
345C2×C22⋊C4—222no—
346C2×C42—221no—
347C2×C42—221no—
348C2×C42C22×D1112yes—
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—24no—
351C4⋊C8—22no—
352#103—114no—
353#103—224no—
354#103—222no—
355#103—442no—
356#102—224no—
357C4×C8—22no—
358#95—221no—
359#95—222no—
360#95—222no—
361#95D4412yes—
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—112no—
372C2×Q8—221no—
373C2×Q8—221no—
374C2×Q8—222no—
375C2×Q8—222no—
376C2×Q8—221no—
377C2×Q8—221no—
378C2×Q8—222no—
379C2×Q8—222no—
380C2×Q8—221no—
381C2×Q8—222no—
382C2×Q8—222no—
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—221no—
396C22×C4—221no—
397C22×C4—221no—
398C22×C4—222no—
399C22×C4—221no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—882no—
403C22×C4C2×D4412yes—
404C22×C4C2×D4411yescharacteristic
405C22×C4C2×D4412yes—
406C22×C4C2×D4411yescharacteristic
407C22×C4C23×D1111yescharacteristic
408SD16—448no—
409SD16—448no—
410SD16—448no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8D4×D1112yes—
419C2×C8#434312yes—
420C4⋊C4—22no—
421C4⋊C4—112no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—444no—
428C4⋊C4—444no—
429C4⋊C4—442no—
430C4⋊C4—442no—
431C4⋊C4—442no—
432C4⋊C4#431414yescomplemented
433C22⋊C4—444no—
434C22⋊C4—444no—
435C22⋊C4—882no—
436C42—22no—
437C42—22no—
438C42—442no—
439C42—442no—
440C42D4×D1112yes—
441C42#434312yes—
442C11#2536811yescharacteristic, complemented, Sylow
443C23—224no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23—442no—
449C23—442no—
450C23C22×D4411yescharacteristic
451Q8—222no—
452Q8—222no—
453Q8—441no—
454Q8—441no—
455Q8—442no—
456Q8—442no—
457Q8—442no—
458Q8—442no—
459D4—224no—
460D4—224no—
461D4—442no—
462D4—448no—
463D4—442no—
464D4—884no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—441no—
486C2×C4—442no—
487C2×C4—888no—
488C2×C4#6694812yes—
489C2×C4#6694812yes—
490C2×C4C2×#431414yes—
491C2×C4C2×#431412yes—
492C2×C4#6696212yes—
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×D4×D1111yescharacteristic
495C2×C4C2×#434311yescharacteristic
496C2×C4C2×#434311yescharacteristic
497C2×C4#6704211yescharacteristic
498C2×C4#6704211yescharacteristic
499C8—22no—
500C8—22no—
501C8—42no—
502C22—444no—
503C22—444no—
504C22—444no—
505C22—882no—
506C22—882no—
507C22—882no—
508C22—882no—
509C22C2×#6694811yescharacteristic
510C22D4×D4411yescharacteristic
511C22#1062310811yescharacteristic
512C22C22×#431411yescharacteristic
513C22C2×#6696211yescharacteristic
514C22#1062328211yescharacteristic
515C22#1062328211yescharacteristic
516C4—22no—
517C4—24no—
518C4—42no—
519C4—442no—
520C4—442no—
521C4—882no—
522C4—881no—
523C4—881no—
524C4#1062245414yescomplemented
525C4#1062314011yescharacteristic
526C4#1062316111yescharacteristic
527C4#1062322911yescharacteristic
528C4#1062325611yescharacteristic
529C2—884no—
530C2#1307220211yescharacteristic
531C2C2×#1062245411yescharacteristic
532C2#1307812911yescharacteristic
533C2#1308028411yescharacteristic
534C2D4×#431411yescharacteristic
535C2#1308159811yescharacteristic
536C2#1308167111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1939D11
hypocenterC11#25368
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
3. C2×#10622454C2semidirect
4. #13073604C2semidirect
6. #13069934C2semidirect
7. #13069701C2semidirect
8. #13069538C2semidirect
9. #13068949C2semidirect
10. C4×#66880C2semidirect
11. C11×#1939C2semidirect
101. #66880D4semidirect
151. C11×C4⋊C4SD16semidirect
183. #1939D11semidirect
294. C4×C11#461semidirect
432. C4⋊C4#4314semidirect
442. C11#25368semidirect
524. C4#10622454semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
C2×#106224612
C2×#106224542
#130736042
#130716802
#130699342
#130697012
#130695382
#130689492
C4×#668802
C11×#19392
#2536811