Finite Group Databasebeta

← #14803645

Subgroups — #14803645

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×#10622701C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13071680C211yesmaximal, characteristic, complemented
4#13070030C212yesmaximal, complemented
5#13069926C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13069335C211yesmaximal, characteristic, complemented
8#13068967C212yesmaximal, complemented
9#13068623C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C11×#2563C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4323C2212yes—
15C2×#66946—21no—
16C2×#66927C2211yescharacteristic
17C2×C4×D44C2212yes—
18C11×#393—22no—
19C11×#390C2212yes—
20C11×#382C2212yes—
21C11×#380—21no—
22C11×#380—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622701—24no—
27#10622628—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×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44C2312yes—
49C22×C4×D11—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C42×C11C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4323—24no—
65C2×#4323—24no—
66C2×#4323—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#66896—22no—
85#66896—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#25321—111nomaximal, Sylow
94C24×C11—21no—
95C23×D11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11—81no—
98C2×Q8×C11—81no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11#4112yes—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C2×D44—24no—
118C2×D44—24no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—42no—
125C2×D44—42no—
126C2×D44—81no—
127C2×D44—81no—
128C2×D44C2×D414yes—
129C2×C4×D11—44no—
130C2×C4×D11—44no—
131C2×C4×D11—82no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—42no—
139C11×C22⋊C4—42no—
140C11×C22⋊C4—82no—
141C11×C22⋊C4—82no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11C2×D412yes—
145C42×C11#4112yes—
146#4323—48no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11#4112yes—
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#2563D1111yescharacteristic, complemented
167#2366—111no—
168#2073—112no—
169#2054—112no—
170#1987—111no—
171#1939—111no—
172#1879—112no—
173#1804—112no—
174C4×#102—111no—
175C23×C11—22no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11C22×D411yescharacteristic
183C22×D11—24no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190Q8×C11—84no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11#13512yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11H(5,𝔽2)11yescharacteristic
219C2×C4×C112−1+411yescharacteristic
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226D44—24no—
227D44—24no—
228D44—42no—
229D44—42no—
230D44—48no—
231D44—84no—
232C4×D11—88no—
233C11⋊C8—41no—
234C11⋊C8—42no—
235C11⋊C8—41no—
236C22×D8—112no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×#127—111no—
239C2×C4×D4—112no—
240C2×C4×D4—221no—
241C2×C4×D4C2×D1111yescharacteristic
242#486—224no—
243#459—224no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—112no—
246C2×#102—111no—
247C2×#102—111no—
248C2×#102—112no—
249C2×#102—112no—
250C2×#102—112no—
251C2×C4×C8—111no—
252#393—22no—
253#390—112no—
254#390—221no—
255#390C2×D1112yes—
256#386—222no—
257#382C2×D1112yes—
258#380—21no—
259#380—21no—
260C4×C4⋊C4—111no—
261C4×C4⋊C4C2×D1111yescharacteristic
262#340—112no—
263#340—111no—
264#340—112no—
265#340—111no—
266#336—112no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
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—44no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—82no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—82no—
288C4×C11—22no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—81no—
292C4×C11—82no—
293C4×C11#46314yes—
294C4×C11#52911yescharacteristic
295C4×C11#54211yescharacteristic
296C4×C11#54611yescharacteristic
297C4×C11#54711yescharacteristic
298Dic11—42no—
299Dic11—81no—
300C22×Q8—21no—
301C22×D4—112no—
302C22×D4—221no—
303C22×D4—221no—
304C22×D4C22×D1111yescharacteristic
305C23×C4—21no—
306C23×C4—222no—
307C2×D8—224no—
308C2×D8—224no—
309C2×D8—442no—
310C22×C8—112no—
311C22×C8—111no—
312C22×C8—111no—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315#127—114no—
316#127—222no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—224no—
320C4×D4—442no—
321C4×D4—444no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C42—221no—
336C2×C42C22×D1112yes—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—222no—
339C4⋊C8—442no—
340#102—224no—
341#102—224no—
342#102—224no—
343#102—222no—
344#102—222no—
345C4×C8—222no—
346#95—22no—
347#95—22no—
348#95—221no—
349#95C22⋊D1112yes—
350C2×C11—82no—
351C2×C11#242711yescharacteristic
352C2×C11C2×#46311yescharacteristic
353C2×C11#304111yescharacteristic
354C2×C11#330511yescharacteristic
355C2×C11#332511yescharacteristic
356C2×C11#336111yescharacteristic
357C2×C11#336611yescharacteristic
358D11—84no—
359C24—21no—
360C24—222no—
361C2×Q8—42no—
362C2×Q8—81no—
363C2×Q8—81no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—114no—
370C2×D4—224no—
371C2×D4—224no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—442no—
378C2×D4—442no—
379C2×D4—881no—
380C2×D4—881no—
381C2×D4#434312yes—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—444no—
390C22×C4—444no—
391C22×C4—882no—
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—222no—
403C2×C8—221no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8—222no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—42no—
414C4⋊C4—112no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C22⋊C4—42no—
419C22⋊C4—82no—
420C22⋊C4—82no—
421C22⋊C4—444no—
422C22⋊C4—444no—
423C22⋊C4—882no—
424C42—22no—
425C42—22no—
426C42—442no—
427C42D4×D1112yes—
428C42#434112yes—
429C11#2532111yescharacteristic, complemented, Sylow
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—224no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—442no—
442C23—442no—
443C23—442no—
444C23C22×C22⋊D1111yescharacteristic
445Q8—84no—
446D4—22no—
447D4—22no—
448D4—41no—
449D4—41no—
450D4—224no—
451D4—224no—
452D4—442no—
453D4—442no—
454D4—448no—
455D4—884no—
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—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4—222no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—888no—
478C2×C4#6699112yes—
479C2×C4#6699112yes—
480C2×C4#6700212yes—
481C2×C4#6700312yes—
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×#434111yescharacteristic
484C2×C4C2×#434311yescharacteristic
485C2×C4#6704011yescharacteristic
486C2×C4#41×D1111yescharacteristic
487C2×C4#6704211yescharacteristic
488C8—442no—
489C8—441no—
490C8—441no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—444no—
499C22—444no—
500C22—444no—
501C22—882no—
502C22—882no—
503C22—882no—
504C22—882no—
505C22C2×#6699111yescharacteristic
506C22#1062334811yescharacteristic
507C22C2×#6700211yescharacteristic
508C22C2×#6700311yescharacteristic
509C22#1062336011yescharacteristic
510C22#1062336611yescharacteristic
511C22#1062336611yescharacteristic
512C4—22no—
513C4—42no—
514C4—42no—
515C4—81no—
516C4—82no—
517C4—442no—
518C4—881no—
519C4#1062267014yes—
520C4#1062315511yescharacteristic
521C4#1062316111yescharacteristic
522C4#1062316211yescharacteristic
523C4#1062317411yescharacteristic
524C2—82no—
525C2—884no—
526C2#1307218911yescharacteristic
527C2C2×#1062267011yescharacteristic
528C2#1307811511yescharacteristic
529C2#1308056011yescharacteristic
530C2#1308085211yescharacteristic
531C2#1308127611yescharacteristic
532C2#1308132311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2563C2
socleC23×C11C22×D4
prime radicalC2×#10622628C2
hypercenter#2563D11
hypocenterC11#25321
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#10622701C2semidirect
3. #13071680C2semidirect
4. #13070030C2semidirect
5. #13069926C2semidirect
6. #13069565C2semidirect
7. #13069335C2semidirect
8. #13068967C2semidirect
9. #13068623C2semidirect
10. C4×#66896C2semidirect
11. C11×#2563C2semidirect
166. #2563D11semidirect
429. C11#25321semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226282
#130716802
#130700302
#130699262
#130695652
#130693352
#130689672
#130686232
C4×#668962
C11×#25632
#2532111