Finite Group Databasebeta

← #14787744

Subgroups — #14787744

Order 2816.

1090 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3C2×C4×#4326C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13069811C212yesmaximal, complemented
6#13069625C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069409C211yesmaximal, characteristic
9#13068927C212yesmaximal, complemented
10#13068816C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×#4326C2211yescharacteristic
15#10623115—24no—
16#10623115—24no—
17C2×#66951—22no—
18C2×#66950C2212yes—
19C2×#66945C2212yes—
20C2×#66928—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2212yes—
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66881C2212yes—
32C2×#66880C2212yes—
33C4×#4326—24no—
34#10622607—22no—
35#10622601—21no—
36#10622600C2212yes—
37#10622598—21no—
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622464—24no—
42C11×#340C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D44D411yescharacteristic
47C22×C4×D11C2312yes—
48C22×Dic22—21no—
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2312yes—
51C4×Q8×C11—22no—
52C4×Q8×C11D414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60#66999—24no—
61#66999—24no—
62C2×#4326—22no—
63C2×#4326—22no—
64C2×#4326—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4D412yes—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81#66951—216no—
82#66950—24no—
83#66950—42no—
84#66945—24no—
85#66945—24no—
86#66928—28no—
87C4×D44—22no—
88C4×D44—22no—
89#66922—22no—
90#66922D414yes—
91C4×Dic22—28no—
92C4×Dic22—22no—
93C4×Dic22—22no—
94C11×C4⋊C8—22no—
95C11×#103—42no—
96#66899—22no—
97C11⋊#95—22no—
98(C2×D11)⋊C8—24no—
99(C2×D11)⋊C8—42no—
100#66881—24no—
101#66880—24no—
102#66874—22no—
103#66871—22no—
104C4×C11⋊C8—22no—
105#24123—111nomaximal, Sylow
106C23×D11C2×D412yes—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11C2×D412yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11C2×D412yes—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—22no—
132C2×Dic22—24no—
133C2×Dic22—21no—
134C2×Dic22—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—42no—
139C2×Dic22—42no—
140C2×Dic22#4112yes—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—81no—
150C11×C4⋊C4C2×D412yes—
151C42×C11—24no—
152C42×C11C2×D412yes—
153C42×C11C2×D412yes—
154#4326—28no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—82no—
160C4⋊Dic11—22no—
161C4⋊Dic11—24no—
162C4⋊Dic11—22no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—44no—
166C4⋊Dic11C2×D414yes—
167Dic11⋊C4—28no—
168Dic11⋊C4—42no—
169C4×Dic11—28no—
170C4×Dic11—42no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8#4112yes—
177C2×#556—111no—
178C2×#475—111no—
179C2×C4×Q16—111no—
180#2538—111no—
181#2035—112no—
182#2001—112no—
183#1990—111no—
184#1954—111no—
185#1873—112no—
186#1854—112no—
187#1803D1111yescharacteristic, complemented
188C23×C11C22×D411yescharacteristic
189C22×D11—22no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196Q8×C11—22no—
197Q8×C11—22no—
198Q8×C11—41no—
199Q8×C11—41no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11#13512yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C2×C4×C112−1+411yescharacteristic
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233D44—44no—
234C4×D11—42no—
235C4×D11—42no—
236C4×D11—42no—
237C4×D11—42no—
238Dic22—22no—
239Dic22—22no—
240Dic22—41no—
241Dic22—41no—
242Dic22—48no—
243C8×C11—42no—
244C11⋊C8—22no—
245C11⋊C8—41no—
246C22×Q16—111no—
247#556—224no—
248#556—224no—
249C2×C4⋊Q8—111no—
250C2×#126—222no—
251C2×#124—221no—
252C2×C22⋊Q8—112no—
253C2×C22⋊Q8—112no—
254C2×C4×Q8—111no—
255C2×C4×Q8—221no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×D4—111no—
258C2×#117—112no—
259#475—224no—
260C4×Q16—224no—
261C2×#107—111no—
262C2×#106—112no—
263C2×C4⋊C8C2×D1111yescharacteristic
264C2×#103—111no—
265C2×#103—112no—
266C2×#103—111no—
267C2×#103C2×D1112yes—
268C2×C22⋊C8—112no—
269C2×C22⋊C8—112no—
270C2×C4×C8—111no—
271#396—222no—
272#390—221no—
273#389—221no—
274#384C2×D1111yescharacteristic
275#380—112no—
276#340—112no—
277#340—112no—
278#340C2×D1112yes—
279C22×C11C2×#12011yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11#54711yescharacteristic
282C22×C11C2×#13511yescharacteristic
283C22×C11C2×#13711yescharacteristic
284C22×C11#57711yescharacteristic
285C22×C11#57811yescharacteristic
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—42no—
293C4×C11—22no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—82no—
297C4×C11#45214yes—
298C4×C11#52511yescharacteristic
299C4×C11#53711yescharacteristic
300C4×C11#54811yescharacteristic
301C4×C11#55011yescharacteristic
302Dic11—42no—
303Dic11—42no—
304Dic11—44no—
305Dic11—81no—
306C22×Q8—111no—
307C22×Q8—221no—
308C22×Q8C22×D1111yescharacteristic
309C22×D4—111no—
310C23×C4—112no—
311C2×Q16—222no—
312C2×Q16—222no—
313C2×Q16—222no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8C22×D1112yes—
317C4⋊Q8—114no—
318C4⋊Q8—222no—
319#126—2216no—
320#124—228no—
321C22⋊Q8—224no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324C22⋊Q8—442no—
325C4×Q8—22no—
326C4×Q8—228no—
327C4×Q8—222no—
328C4×Q8—222no—
329C4×Q8D4414yes—
330C4×D4—222no—
331C4×D4—222no—
332#117—224no—
333#117—224no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—111no—
339C2×C4⋊C4—111no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22×D1112yes—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C22⋊C4—112no—
347C2×C22⋊C4—222no—
348C2×C22⋊C4—222no—
349C2×C22⋊C4—222no—
350C2×C22⋊C4—222no—
351C2×C42—21no—
352C2×C42—222no—
353C2×C42—221no—
354C2×C42C22×D1111yescharacteristic
355#107—222no—
356#106—224no—
357C4⋊C8—22no—
358#103—42no—
359#103—224no—
360#103—222no—
361#103—222no—
362C22⋊C8—224no—
363C22⋊C8—442no—
364C4×C8—222no—
365#95—222no—
366C2×C11#240711yescharacteristic
367C2×C11C2×#45211yescharacteristic
368C2×C11#301311yescharacteristic
369C2×C11#330411yescharacteristic
370C2×C11#332811yescharacteristic
371C2×C11#334211yescharacteristic
372C2×C11#335611yescharacteristic
373D11—82no—
374C24—112no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—112no—
381C2×Q8—224no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8—442no—
388C2×Q8—442no—
389C2×Q8C2×D4412yes—
390C2×D4—222no—
391C2×D4—222no—
392C2×D4—222no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—112no—
397C22×C4—222no—
398C22×C4—221no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4D4×D1111yescharacteristic
407C22×C4D4×D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—228no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—112no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8—221no—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—42no—
424C4⋊C4—81no—
425C4⋊C4—114no—
426C4⋊C4—228no—
427C4⋊C4—222no—
428C4⋊C4—224no—
429C4⋊C4—222no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4—444no—
433C4⋊C4—442no—
434C4⋊C4C2×D4412yes—
435C22⋊C4—228no—
436C22⋊C4—228no—
437C22⋊C4—224no—
438C22⋊C4—444no—
439C22⋊C4—882no—
440C42—24no—
441C42—228no—
442C42—442no—
443C42C2×D4412yes—
444C42D4×D1112yes—
445C11#2412311yescharacteristic, complemented, Sylow
446C23—222no—
447C23—222no—
448C23—222no—
449C23—222no—
450C23—222no—
451C23—222no—
452C23—222no—
453C23C2×D4×D1111yescharacteristic
454Q8—22no—
455Q8—22no—
456Q8—41no—
457Q8—41no—
458Q8—222no—
459Q8—222no—
460Q8—441no—
461Q8—441no—
462Q8—448no—
463D4—444no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—222no—
476C2×C4—224no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—441no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—441no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4#6693512yes—
492C2×C4#6693512yes—
493C2×C4#6696912yes—
494C2×C4#6697112yes—
495C2×C4C22×D4411yescharacteristic
496C2×C4C2×D4×D1111yescharacteristic
497C2×C4#6703711yescharacteristic
498C2×C4#6704011yescharacteristic
499C2×C4#41×D1111yescharacteristic
500C2×C4#41×D1111yescharacteristic
501C8—42no—
502C8—222no—
503C8—441no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—442no—
511C22C2×#6693511yescharacteristic
512C22#1062314311yescharacteristic
513C22#1062316211yescharacteristic
514C22C2×#6696911yescharacteristic
515C22C2×#6697111yescharacteristic
516C22#1062330611yescharacteristic
517C22#1062331011yescharacteristic
518C4—22no—
519C4—42no—
520C4—42no—
521C4—82no—
522C4—444no—
523C4—442no—
524C4—442no—
525C4—881no—
526C4#1062242314yes—
527C4#1062304111yescharacteristic
528C4#1062305511yescharacteristic
529C4#1062313011yescharacteristic
530C4#1062316411yescharacteristic
531C2—882no—
532C2#1307196211yescharacteristic
533C2C2×#1062242311yescharacteristic
534C2#1307793311yescharacteristic
535C2#1308055811yescharacteristic
536C2#1308090211yescharacteristic
537C2#1308104511yescharacteristic
538C2#1308123411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1803D11
hypocenterC11#24123
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×C4×#4326C2semidirect
5. #13069811C2semidirect
6. #13069625C2semidirect
7. #13069576C2semidirect
9. #13068927C2semidirect
10. #13068816C2semidirect
11. C11×#1803C2semidirect
187. #1803D11semidirect
445. C11#24123semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106224642
C2×C4×#43262
#130735392
#130698112
#130696252
#130695762
#130694092
#130689272
#130688162
C11×#18032
#2412311