Finite Group Databasebeta

← #14803643

Subgroups — #14803643

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic, complemented
4#13070029C212yesmaximal, complemented
5#13069926C212yesmaximal, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068626C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2366C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2212yes—
15C22×#4323C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×#66922C2211yescharacteristic
18C11×#390—21no—
19C11×#390C2212yes—
20C11×#386—22no—
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622685—24no—
27#10622683—24no—
28#10622600—21no—
29#10622600—21no—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32#10622552C2212yes—
33#10622549C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622286—22no—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622162C2212yes—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22—21no—
50C11×#127—22no—
51C11×#127D414yes—
52C4×D4×C11—24no—
53C4×D4×C11—42no—
54C4×D4×C11—44no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11—21no—
63C2×C42×C11C2312yes—
64C2×C42×C11C2311yescharacteristic
65C2×#4323—24no—
66C2×#4323—24no—
67C2×#4323—42no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C4×D44—22no—
78C4×D44—22no—
79#66922—22no—
80#66922—22no—
81C11×#95—21no—
82C11×#95D412yes—
83#66896—24no—
84#66896—24no—
85#66896—24no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66873—22no—
89#66873—22no—
90C4⋊(C11⋊C8)—22no—
91C4⋊(C11⋊C8)—42no—
92C4×C11⋊C8—22no—
93#25321—111nomaximal, Sylow
94C24×C11—22no—
95C23×D11—21no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—81no—
106C2×D4×C11—81no—
107C2×D4×C11C2×D414yes—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—44no—
111C22×C4×C11—44no—
112C22×C4×C11—82no—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—22no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44#4112yes—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×Dic22—42no—
130C2×Dic22—81no—
131C2×Dic22—81no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4#4112yes—
138C11×C22⋊C4—44no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—82no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—42no—
144C42×C11C2×D412yes—
145C42×C11#4112yes—
146#4323—48no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—82no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—42no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—21no—
164C2×#486—111no—
165C2×#459—111no—
166#2563—111no—
167#2366D1111yescharacteristic, complemented
168#2073—112no—
169#2054—112no—
170#1987—111no—
171#1939—111no—
172#1879—112no—
173#1804—112no—
174C4×#102—111no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190D4×C11—24no—
191D4×C11—24no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—48no—
195D4×C11—84no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—88no—
211C2×C4×C11#12112yes—
212C2×C4×C11#12112yes—
213C2×C4×C11#13512yes—
214C2×C4×C11AGL(1,ℤ/8)12yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227D44—22no—
228D44—22no—
229D44—41no—
230D44—41no—
231C4×D11—84no—
232Dic22—84no—
233C11⋊C8—41no—
234C11⋊C8—42no—
235C11⋊C8—41no—
236C22×D8—112no—
237C2×C4⋊Q8—111no—
238C2×#127C2×D1111yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—111no—
241C2×C4×D4C2×D1112yes—
242#486—224no—
243#459—224no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—112no—
246C2×#102—112no—
247C2×#102—112no—
248C2×#102—112no—
249C2×#102—111no—
250C2×#102—111no—
251C2×C4×C8—111no—
252#393—222no—
253#390—21no—
254#390—112no—
255#390C2×D1112yes—
256#386—22no—
257#382—112no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4C2×D1111yescharacteristic
261C4×C4⋊C4C2×D1111yescharacteristic
262#340—112no—
263#340—111no—
264#340—112no—
265#340—111no—
266#336—112no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54611yescharacteristic
276C22×C11#54811yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57611yescharacteristic
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—81no—
293C4×C11#46314yes—
294C4×C11#52911yescharacteristic
295C4×C11#54211yescharacteristic
296C4×C11#54611yescharacteristic
297C4×C11#54711yescharacteristic
298Dic11—81no—
299Dic11—82no—
300C22×Q8—221no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—111no—
304C22×D4C22×D1112yes—
305C23×C4—22no—
306C23×C4—221no—
307C2×D8—224no—
308C2×D8—224no—
309C2×D8—442no—
310C22×C8—112no—
311C22×C8—111no—
312C22×C8—111no—
313C4⋊Q8—222no—
314C4⋊Q8—222no—
315#127—22no—
316#127D4414yes—
317C4×D4—24no—
318C4×D4—42no—
319C4×D4—44no—
320C4×D4—222no—
321C4×D4—222no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C42—21no—
336C2×C42C22×D1112yes—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—222no—
339C4⋊C8—442no—
340#102—222no—
341#102—224no—
342#102—224no—
343#102—224no—
344#102—222no—
345C4×C8—222no—
346#95—21no—
347#95—222no—
348#95—222no—
349#95C22⋊D1112yes—
350C2×C11—84no—
351C2×C11#242711yescharacteristic
352C2×C11C2×#46311yescharacteristic
353C2×C11#304111yescharacteristic
354C2×C11#330511yescharacteristic
355C2×C11#332511yescharacteristic
356C2×C11#336111yescharacteristic
357C2×C11#336611yescharacteristic
358D11—82no—
359C24—22no—
360C24—221no—
361C2×Q8—442no—
362C2×Q8—881no—
363C2×Q8—881no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—81no—
374C2×D4—81no—
375C2×D4—112no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C2×D4C2×D4414yes—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—44no—
385C22×C4—44no—
386C22×C4—82no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4—442no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4C2×C22⋊D1112yes—
393C22×C4C2×C22⋊D1112yes—
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397D8—448no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—222no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—222no—
404C2×C8—221no—
405C2×C8—222no—
406C2×C8—221no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—222no—
416C4⋊C4—442no—
417C4⋊C4#434112yes—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C22⋊C4—82no—
421C22⋊C4—442no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C42—22no—
425C42—22no—
426C42—42no—
427C42C2×D4412yes—
428C42#433912yes—
429C11#2532111yescharacteristic, complemented, Sylow
430C23—24no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—222no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23C22×C22⋊D1111yescharacteristic
445Q8—884no—
446D4—24no—
447D4—24no—
448D4—42no—
449D4—42no—
450D4—48no—
451D4—84no—
452D4—222no—
453D4—222no—
454D4—441no—
455D4—441no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—88no—
471C2×C4—441no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4—884no—
478C2×C4#6698312yes—
479C2×C4#6698312yes—
480C2×C4#6698512yes—
481C2×C4#6700312yes—
482C2×C4C22×D4411yescharacteristic
483C2×C4C2×#433911yescharacteristic
484C2×C4C2×#434111yescharacteristic
485C2×C4#6703711yescharacteristic
486C2×C4#41×D1111yescharacteristic
487C2×C4#6704311yescharacteristic
488C8—442no—
489C8—441no—
490C8—441no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22C2×#6698311yescharacteristic
506C22C2×#6698511yescharacteristic
507C22#1062333711yescharacteristic
508C22C2×#6700311yescharacteristic
509C22#1062336211yescharacteristic
510C22#1062336611yescharacteristic
511C22#1062336611yescharacteristic
512C4—22no—
513C4—42no—
514C4—42no—
515C4—42no—
516C4—81no—
517C4—881no—
518C4—882no—
519C4#1062262914yes—
520C4#1062308511yescharacteristic
521C4#1062308611yescharacteristic
522C4#1062308811yescharacteristic
523C4#1062309211yescharacteristic
524C2—84no—
525C2—882no—
526C2#1307218711yescharacteristic
527C2C2×#1062262911yescharacteristic
528C2#1307811911yescharacteristic
529C2#1308056611yescharacteristic
530C2#1308085811yescharacteristic
531C2#1308127211yescharacteristic
532C2#1308131911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenter#2366D11
hypocenterC11#25321
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
3. #13073785C2semidirect
4. #13070029C2semidirect
5. #13069926C2semidirect
6. #13069564C2semidirect
7. #13069335C2semidirect
8. #13068964C2semidirect
9. #13068626C2semidirect
10. C4×#66873C2semidirect
11. C11×#2366C2semidirect
167. #2366D11semidirect
429. C11#25321semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
C2×#106226852
#130737852
#130700292
#130699262
#130695642
#130693352
#130689642
#130686262
C4×#668732
C11×#23662
#2532111