Finite Group Databasebeta

← #14788559

Subgroups — #14788559

Order 2816.

1082 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×#10622703C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic
3#13073986C211yesmaximal, characteristic, complemented
4#13069852C212yesmaximal
5#13069710C212yesmaximal
6#13069553C211yesmaximal, characteristic, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13068957C212yesmaximal, complemented
9#13068884C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic
11C2×C11×#556C211yesmaximal, characteristic
12C11×#556—24no—
13C11×#556—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124C2212yes—
17C2×C11×C22⋊Q8—21no—
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C22×#4326C2212yes—
23C22×#4324C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25#10622843—21no—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66896C2211yescharacteristic
30C2×#66896C2212yes—
31#10622703—24no—
32C4×#4324—24no—
33#10622597—22no—
34#10622586—21no—
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622548C2211yescharacteristic
38#10622542C2212yes—
39#10622541C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2212yes—
44#10622162C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C22×Dic22C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8D414yes—
52C11×#126—216no—
53C11×#124—24no—
54C11×#124—24no—
55C11×C22⋊Q8—28no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—22no—
59C4×Q8×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11D414yes—
62C11×#117—28no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D412yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—22no—
72C2×C42×C11—22no—
73C2×C42×C11C2312yes—
74C2×C42×C11C2311yescharacteristic
75C2×#4326—24no—
76C2×#4326—24no—
77C2×#4326—42no—
78C2×#4324—22no—
79C2×#4324—22no—
80C2×#4324—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C4×Dic22—22no—
92C4×Dic22—22no—
93#66899—24no—
94#66899—24no—
95#66899—42no—
96#66896—22no—
97#66896—42no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101#66874—22no—
102#66872—22no—
103C4⋊(C11⋊C8)—22no—
104C4×C11⋊C8—22no—
105#24189—111nomaximal, Sylow
106C24×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C2×D414yes—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22#4112yes—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—28no—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—24no—
151C42×C11—28no—
152C42×C11—22no—
153C42×C11—22no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156#4326—48no—
157#4324—28no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—42no—
163C4⋊Dic11—81no—
164Dic11⋊C4—42no—
165Dic11⋊C4—82no—
166C4×Dic11—42no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8#4112yes—
176C2×#556D1111yescharacteristic
177C2×#462—111no—
178C2×C4×SD16—111no—
179#2582—111no—
180#2042—112no—
181#2015—112no—
182#1984—111no—
183#1956—111no—
184#1878—112no—
185#1865—112no—
186#1802—111no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195Q8×C11—24no—
196Q8×C11—24no—
197Q8×C11—42no—
198Q8×C11—42no—
199Q8×C11—44no—
200D4×C11—22no—
201D4×C11—22no—
202D4×C11—41no—
203D4×C11—41no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—48no—
219C2×C4×C11#12012yes—
220C2×C4×C11#12012yes—
221C2×C4×C11#13512yes—
222C2×C4×C11#13712yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C112−1+411yescharacteristic
229C2×Dic11—22no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—41no—
236C2×Dic11—42no—
237C2×Dic11—41no—
238Dic22—22no—
239Dic22—22no—
240Dic22—41no—
241Dic22—41no—
242C11⋊C8—22no—
243C11⋊C8—41no—
244C11⋊C8—42no—
245C22×Q16—112no—
246C22×SD16—111no—
247#556—24no—
248#556—24no—
249C2×C4⋊Q8C2×D1111yescharacteristic
250C2×#126—22no—
251C2×#124C2×D1112yes—
252C2×C22⋊Q8—21no—
253C2×C4×Q8—111no—
254C2×C4×Q8C2×D1112yes—
255C2×C4×Q8C2×D1111yescharacteristic
256C2×C4×D4C2×D1111yescharacteristic
257C2×#117—21no—
258#462—224no—
259C4×SD16—224no—
260C2×#106—111no—
261C2×C4⋊C8—111no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—111no—
265C2×#103—112no—
266C2×#102—111no—
267C2×#102—112no—
268C2×C4×C8—111no—
269#398—222no—
270#391—112no—
271#391—221no—
272#389—112no—
273#389—221no—
274#384—111no—
275#340—112no—
276#336—112no—
277#336—112no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—81no—
285C22×C11C2×#12011yescharacteristic
286C22×C11#54811yescharacteristic
287C22×C11#55011yescharacteristic
288C22×C11C2×#13511yescharacteristic
289C22×C11C2×#13711yescharacteristic
290C22×C11#57711yescharacteristic
291C22×C11#57811yescharacteristic
292C4×C11—22no—
293C4×C11—44no—
294C4×C11—42no—
295C4×C11—42no—
296C4×C11—42no—
297C4×C11#45214yes—
298C4×C11#52511yescharacteristic
299C4×C11#53711yescharacteristic
300C4×C11#54611yescharacteristic
301C4×C11#54711yescharacteristic
302Dic11—42no—
303Dic11—82no—
304Dic11—81no—
305C22×Q8—111no—
306C22×Q8C22⋊D1111yescharacteristic
307C22×Q8C22×D1112yes—
308C22×D4C22×D1111yescharacteristic
309C23×C4—21no—
310C2×Q16—224no—
311C2×Q16—224no—
312C2×Q16—442no—
313C2×SD16—222no—
314C2×SD16—222no—
315C2×SD16—222no—
316C22×C8—111no—
317C22×C8—112no—
318C22×C8—111no—
319C4⋊Q8—22no—
320C4⋊Q8C22⋊D1114yes—
321#126—216no—
322#124—24no—
323#124—24no—
324C22⋊Q8—28no—
325C4×Q8—24no—
326C4×Q8—24no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—222no—
330C4×Q8—222no—
331C4×D4—22no—
332C4×D4C22⋊D1114yes—
333#117—28no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—222no—
343C2×C4⋊C4C22⋊D1111yescharacteristic
344C2×C4⋊C4C22⋊D1112yes—
345C2×C4⋊C4C22×D1111yescharacteristic
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C42—22no—
350C2×C42—221no—
351C2×C42C22×D1112yes—
352C2×C42C22×D1111yescharacteristic
353#106—222no—
354C4⋊C8—222no—
355#103—224no—
356#103—224no—
357#103—222no—
358#103—442no—
359#102—222no—
360#102—442no—
361C4×C8—222no—
362#95—222no—
363#95—222no—
364#95—222no—
365C2×C11—82no—
366C2×C11#240711yescharacteristic
367C2×C11C2×#45211yescharacteristic
368C2×C11#301311yescharacteristic
369C2×C11#336411yescharacteristic
370C2×C11#336911yescharacteristic
371C2×C11#339411yescharacteristic
372C2×C11#339811yescharacteristic
373C24—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—112no—
383C2×Q8—221no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—221no—
387C2×Q8—221no—
388C2×Q8C2×C22⋊D1114yes—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C2×C22⋊D1112yes—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4C2×C22⋊D1112yes—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C23×D1111yescharacteristic
408Q16—448no—
409SD16—228no—
410C2×C8—112no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8—222no—
419C4⋊C4—28no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—21no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—442no—
430C4⋊C4—442no—
431C4⋊C4—882no—
432C4⋊C4—881no—
433C4⋊C4C2×C22⋊D1112yes—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—24no—
437C42—28no—
438C42—22no—
439C42—22no—
440C42—442no—
441C42C2×C22⋊D1112yes—
442C42C2×C22⋊D1112yes—
443C11#2418911yescharacteristic, complemented, Sylow
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C22×C22⋊D1111yescharacteristic
452Q8—24no—
453Q8—24no—
454Q8—42no—
455Q8—44no—
456Q8—42no—
457Q8—222no—
458Q8—222no—
459Q8—441no—
460Q8—441no—
461D4—22no—
462D4—22no—
463D4—41no—
464D4—41no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—48no—
480C2×C4—222no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—441no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4#6700312yes—
490C2×C4#6700412yes—
491C2×C4#6700612yes—
492C2×C4#6700612yes—
493C2×C4#41×D1111yescharacteristic
494C2×C4#41×D1111yescharacteristic
495C2×C4#6704211yescharacteristic
496C2×C4#6704311yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C2×C4C22×C22⋊D1111yescharacteristic
499C8—222no—
500C8—442no—
501C8—441no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22C2×#6700311yescharacteristic
510C22C2×#6700411yescharacteristic
511C22#1062336211yescharacteristic
512C22#1062336511yescharacteristic
513C22#1062336811yescharacteristic
514C22#1062336911yescharacteristic
515C22C2×#6700611yescharacteristic
516C4—22no—
517C4—42no—
518C4—42no—
519C4—44no—
520C4—42no—
521C4—442no—
522C4—882no—
523C4—881no—
524C4#1062285214yes—
525C4#1062335511yescharacteristic
526C4#1062335911yescharacteristic
527C4#1062336011yescharacteristic
528C4#1062336411yescharacteristic
529C2—82no—
530C2#1307195511yescharacteristic
531C2C2×#1062285211yescharacteristic
532C2#1307793111yescharacteristic
533C2#1308129711yescharacteristic
534C2#1308135211yescharacteristic
535C2#1308161211yescharacteristic
536C2#1308164711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#556D11
hypocenterC11#24189
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10622703C2semidirect
3. #13073986C2semidirect
6. #13069553C2semidirect
7. #13069419C2semidirect
8. #13068957C2semidirect
9. #13068884C2semidirect
443. C11#24189semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×C4×#43242
#130739862
#130698522
#130697102
#130695532
#130694192
#130689572
#130688842
#130686162
C2×C11×#5562
#2418911