Finite Group Databasebeta

← #14788674

Subgroups — #14788674

Order 2816.

1180 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3#13073974C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal, complemented
5#13069693C212yesmaximal, complemented
6#13069557C211yesmaximal, characteristic, complemented
7#13069441C211yesmaximal, characteristic, complemented
8#13068964C212yesmaximal, complemented
9#13068863C212yesmaximal, complemented
10#13068631C211yesmaximal, characteristic, complemented
11C2×C11×#559C211yesmaximal, characteristic, complemented
12C11×#559—24no—
13C11×#559—24no—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124—21no—
16C2×C11×#124C2212yes—
17C2×C11×#123—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2212yes—
22C22×#4325C2211yescharacteristic
23C22×#4323C2212yes—
24C2×C4×D44C2211yescharacteristic
25#10622844—21no—
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66896C2212yes—
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31#10622685—24no—
32#10622639—24no—
33#10622605—21no—
34#10622602—22no—
35C2×#66873C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622552C2212yes—
38#10622549C2211yescharacteristic
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C23×C4×C11—22no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C11×#127—22no—
54C11×#127D414yes—
55C11×#124—28no—
56C11×#124—24no—
57C11×#124—24no—
58C11×#123—216no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C4×D4×C11—28no—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C2×C42×C11C2311yescharacteristic
76C2×#4325—22no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4323—24no—
80C2×#4323—24no—
81C2×#4323—42no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—22no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×D44—22no—
92C4×D44—22no—
93#66899—22no—
94#66899—42no—
95#66896—24no—
96#66896—24no—
97#66896—42no—
98C11⋊#95—22no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101#66873—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#24198—111nomaximal, Sylow
106C24×C11—22no—
107C23×D11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—42no—
115C2×Q8×C11C2×D412yes—
116C2×D4×C11—24no—
117C2×D4×C11—24no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—44no—
124C2×D4×C11—82no—
125C2×D4×C11C2×D414yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—28no—
129C22×C4×C11—82no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—22no—
137C22×Dic11—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44#4112yes—
144C2×C4×D11—42no—
145C2×C4×D11—82no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C2×D412yes—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C42×C11—24no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159#4325—28no—
160#4323—48no—
161(C2×D11)⋊C4—44no—
162(C2×D11)⋊C4—42no—
163(C2×D11)⋊C4—82no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168Dic11⋊C4—82no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8#4112yes—
178C2×#559D1111yescharacteristic, complemented
179C2×#459—111no—
180C2×#440—111no—
181#2580—111no—
182#2042—112no—
183#2012—112no—
184#1985—111no—
185#1961—111no—
186#1879—112no—
187#1862—112no—
188#1805—111no—
189C23×C11—24no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11C22×D411yescharacteristic
197C22×D11—22no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—42no—
201C22×D11—42no—
202Q8×C11—22no—
203Q8×C11—22no—
204Q8×C11—44no—
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—24no—
208D4×C11—24no—
209D4×C11—48no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—84no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—88no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240D44—22no—
241D44—22no—
242D44—41no—
243D44—41no—
244C4×D11—84no—
245C11⋊C8—22no—
246C11⋊C8—41no—
247C11⋊C8—42no—
248C22×SD16—111no—
249C22×D8—112no—
250#559—24no—
251#559—24no—
252C2×#127C2×D1111yescharacteristic
253C2×#124—21no—
254C2×#124C2×D1112yes—
255C2×#123—22no—
256C2×C4×Q8C2×D1111yescharacteristic
257C2×C4×Q8C2×D1111yescharacteristic
258C2×C4×D4—21no—
259C2×C4×D4—111no—
260C2×C4×D4C2×D1112yes—
261#459—224no—
262#440—224no—
263C2×#107—111no—
264C2×C4⋊C8—111no—
265C2×#103—111no—
266C2×#103—112no—
267C2×#102—112no—
268C2×#102—112no—
269C2×#102—111no—
270C2×#102—112no—
271C2×#97—111no—
272#399—221no—
273#393—221no—
274#390—112no—
275#389—112no—
276#385—222no—
277#382—111no—
278#340—112no—
279#336—112no—
280#336—112no—
281C22×C11—44no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—82no—
285C22×C11—82no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54811yescharacteristic
290C22×C11#55011yescharacteristic
291C22×C11#57512yes—
292C22×C11#57612yes—
293C2×D11—44no—
294C2×D11—42no—
295C2×D11—82no—
296C2×D11—81no—
297C2×D11—81no—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—42no—
304C4×C11#52511yescharacteristic
305C4×C11#53711yescharacteristic
306C4×C11#54611yescharacteristic
307C4×C11#54711yescharacteristic
308Dic11—82no—
309Dic11—81no—
310C22×Q8C22⋊D1111yescharacteristic
311C22×Q8C22×D1111yescharacteristic
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—111no—
315C22×D4C22×D1112yes—
316C23×C4—22no—
317C23×C4—221no—
318C2×SD16—222no—
319C2×SD16—222no—
320C2×SD16—222no—
321C2×D8—224no—
322C2×D8—224no—
323C2×D8—442no—
324C22×C8—111no—
325C22×C8—112no—
326C22×C8—111no—
327#127—22no—
328#127C22⋊D1114yes—
329#124—28no—
330#124—24no—
331#124—24no—
332#123—216no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8C22⋊D1114yes—
337C4×D4—28no—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—222no—
341C4×D4—222no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4C22⋊D1111yescharacteristic
347C2×C4⋊C4C22⋊D1112yes—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—21no—
356C2×C42C22×D1112yes—
357C2×C42C22×D1111yescharacteristic
358#107—222no—
359C4⋊C8—222no—
360#103—222no—
361#103—442no—
362#102—224no—
363#102—224no—
364#102—222no—
365#102—442no—
366#97—222no—
367#95—221no—
368#95—221no—
369#95—222no—
370C2×C11—84no—
371C2×C11#240711yescharacteristic
372C2×C11#300511yescharacteristic
373C2×C11#300811yescharacteristic
374C2×C11#337012yes—
375C2×C11#340312yes—
376D11—82no—
377C24—22no—
378C24—221no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—42no—
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—44no—
395C2×D4—82no—
396C2×D4—112no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—221no—
400C2×D4—221no—
401C2×D4—221no—
402C2×D4C2×C22⋊D1114yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—28no—
406C22×C4—82no—
407C22×C4—82no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4—442no—
411C22×C4—882no—
412C22×C4C2×C22⋊D1112yes—
413C22×C4C2×C22⋊D1112yes—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417SD16—228no—
418D8—448no—
419C2×C8—112no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—222no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—222no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—24no—
431C4⋊C4—21no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—882no—
437C4⋊C4C2×C22⋊D1112yes—
438C22⋊C4—28no—
439C22⋊C4—28no—
440C22⋊C4—28no—
441C22⋊C4—444no—
442C22⋊C4—442no—
443C22⋊C4—882no—
444C42—24no—
445C42—22no—
446C42—22no—
447C42C2×C22⋊D1112yes—
448C42C2×C22⋊D1112yes—
449C11#2419811yescharacteristic, complemented, Sylow
450C23—24no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—222no—
458C23—442no—
459C23—441no—
460C23—442no—
461C23—441no—
462C23C22×C22⋊D1111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—44no—
466Q8—41no—
467Q8—41no—
468D4—24no—
469D4—24no—
470D4—48no—
471D4—42no—
472D4—42no—
473D4—84no—
474D4—222no—
475D4—222no—
476D4—441no—
477D4—441no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—88no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—441no—
497C2×C4—884no—
498C2×C4#6700612yes—
499C2×C4#6700612yes—
500C2×C4#41×D1111yescharacteristic
501C2×C4#41×D1111yescharacteristic
502C2×C4#6704211yescharacteristic
503C2×C4#6704311yescharacteristic
504C2×C4C22×C22⋊D1111yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C8—222no—
507C8—442no—
508C8—441no—
509C22—44no—
510C22—44no—
511C22—44no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—444no—
517C22—442no—
518C22—881no—
519C22—882no—
520C22—881no—
521C22#1062335312yes—
522C22#1062336211yescharacteristic
523C22#1062336511yescharacteristic
524C22#1062336612yes—
525C22C2×#6700611yescharacteristic
526C4—22no—
527C4—22no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—882no—
533C4—881no—
534C4#1062335511yescharacteristic
535C4#1062335911yescharacteristic
536C4#1062336011yescharacteristic
537C4#1062336411yescharacteristic
538C2—84no—
539C2—882no—
540C2#1307195511yescharacteristic
541C2#1307785811yescharacteristic
542C2#1307788411yescharacteristic
543C2#1308136312yes—
544C2#1308170012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenterC2×#559D11
hypocenterC11#24198
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
3. #13073974C2semidirect
4. #13069852C2semidirect
5. #13069693C2semidirect
6. #13069557C2semidirect
7. #13069441C2semidirect
8. #13068964C2semidirect
9. #13068863C2semidirect
10. #13068631C2semidirect
11. C2×C11×#559C2semidirect
178. C2×#559D11semidirect
449. C11#24198semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×#106226392
#130739742
#130698522
#130696932
#130695572
#130694412
#130689642
#130688632
#130686312
C2×C11×#5592
#2419811