Finite Group Databasebeta

← #14810742

Subgroups — #14810742

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic, complemented
2C2×#10622668C211yesmaximal, characteristic
3#13074105C211yesmaximal, characteristic
4#13069765C212yesmaximal, complemented
5#13069760C212yesmaximal
6#13069563C211yesmaximal, characteristic, complemented
7#13069555C211yesmaximal, characteristic, complemented
8#13068973C212yesmaximal
9#13068959C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#464C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×Q8×Dic11C2212yes—
17#10623101—24no—
18#10623101—24no—
19C2×#66943—22no—
20C2×#66943C2212yes—
21C2×#66922—21no—
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C11×#464—24no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29#10622843C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32#10622834C2212yes—
33C2×#66896C2212yes—
34#10622668—24no—
35#10622566—21no—
36#10622560—21no—
37#10622558—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C22×Dic22—21no—
49C22×Dic22D411yescharacteristic
50C2×C11×Q16—22no—
51C2×C11×Q16—24no—
52C2×C11×SD16—22no—
53C2×C11×SD16—24no—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×#124—22no—
57C11×#124—22no—
58C4×Q8×C11—22no—
59C4×Q8×C11D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68Q8×Dic11—24no—
69Q8×Dic11—24no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2312yes—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4D412yes—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2312yes—
82#66943—216no—
83#66943—24no—
84#66943—24no—
85#66922—28no—
86#66922—22no—
87#66922D414yes—
88C4×Dic22—28no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×C4⋊C8—22no—
92C11×#103—22no—
93C11×#102—22no—
94#66899—24no—
95#66899—24no—
96#66896—24no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100#66867—22no—
101#25941—111nomaximal, Sylow
102C24×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C2×D412yes—
110C2×Q8×C11#4114yes—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C2×Dic22—22no—
126C2×Dic22—24no—
127C2×Dic22—42no—
128C2×Dic22—44no—
129C11×Q16—44no—
130C11×SD16—44no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4C2×D412yes—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—42no—
140C42×C11—24no—
141C42×C11C2×D412yes—
142C42×C11C2×D412yes—
143C22⋊Dic11—44no—
144C22⋊Dic11—82no—
145C4⋊Dic11—28no—
146C4⋊Dic11—28no—
147C4⋊Dic11—22no—
148C4⋊Dic11—24no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11C2×D414yes—
153Dic11⋊C4—28no—
154Dic11⋊C4—24no—
155C4×Dic11—28no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—81no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×#557—111no—
163C2×#489—111no—
164C2×#464D1111yescharacteristic
165#2592—111no—
166#2026—112no—
167#2025—112no—
168#1987—111no—
169#1985—111no—
170#1880—112no—
171#1878—112no—
172#1763—111no—
173C23×C11—41no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11C22×D411yescharacteristic
179Q8×C11—22no—
180Q8×C11—24no—
181Q8×C11—41no—
182Q8×C11—41no—
183Q8×C11—42no—
184Q8×C11#12414yes—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—42no—
188C2×C4×C11—22no—
189C2×C4×C11—24no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11#12012yes—
199C2×C4×C11#12012yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4112yes—
203C2×C4×C112−1+412yes—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—44no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215Dic22—44no—
216Dic22—48no—
217C8×C11—41no—
218C8×C11—41no—
219C11⋊C8—42no—
220C22×Q16C2×D1111yescharacteristic
221C22×SD16C2×D1111yescharacteristic
222#557—224no—
223#557—224no—
224C2×C4⋊Q8—111no—
225C2×C4⋊Q8—221no—
226C2×#125—112no—
227C2×#125—222no—
228C2×#124C2×D1111yescharacteristic
229C2×C4×Q8—111no—
230C2×C4×Q8—112no—
231C2×C4×Q8—221no—
232C2×C4×Q8C2×D1111yescharacteristic
233#489—224no—
234#464—24no—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×#103—112no—
237C2×#103—112no—
238C2×#103C2×D1111yescharacteristic
239C2×#102—112no—
240C2×#102C2×D1111yescharacteristic
241C2×#97—111no—
242#397—221no—
243#393—221no—
244#391—112no—
245#390—112no—
246#388—222no—
247C4×C4⋊C4—111no—
248#340—112no—
249#340—112no—
250#340—112no—
251#336—112no—
252#336—112no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11C2×#12011yescharacteristic
259C22×C11#54812yes—
260C22×C11#57512yes—
261C22×C11#57711yescharacteristic
262C22×C11#57811yescharacteristic
263C4×C11—24no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—81no—
268C4×C11C2×#12411yescharacteristic
269C4×C11#53611yescharacteristic
270C4×C11#54812yes—
271Dic11—42no—
272Dic11—44no—
273Dic11—42no—
274Dic11—82no—
275C22×Q8—111no—
276C22×Q8—221no—
277C22×Q8C22×D1111yescharacteristic
278C22×Q8C22×D1111yescharacteristic
279C22×D4C22×D1111yescharacteristic
280C2×Q16—24no—
281C2×Q16—22no—
282C2×SD16—24no—
283C2×SD16—22no—
284C22×C8—112no—
285C22×C8C22×D1111yescharacteristic
286C22×C8C22×D1111yescharacteristic
287C4⋊Q8—114no—
288C4⋊Q8—228no—
289C4⋊Q8—222no—
290#125—224no—
291#125—2216no—
292#125—224no—
293#124—22no—
294#124—22no—
295C4×Q8—22no—
296C4×Q8—228no—
297C4×Q8—224no—
298C4×Q8—224no—
299C4×Q8—222no—
300C4×Q8—222no—
301C4×Q8C22⋊D1114yes—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—112no—
318C2×C42—222no—
319C2×C42—221no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—22no—
322#103—22no—
323#103—224no—
324#103—224no—
325#102—22no—
326#102—224no—
327#97—222no—
328#95—222no—
329#95—222no—
330#95—221no—
331C2×C11—161no—
332C2×C11#243611yescharacteristic
333C2×C11#300511yescharacteristic
334C2×C11#301311yescharacteristic
335C2×C11#337112yes—
336C2×C11#337712yes—
337C24—21no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—21no—
344C2×Q8—224no—
345C2×Q8—222no—
346C2×Q8—442no—
347C2×Q8—444no—
348C2×Q8#434114yes—
349C2×Q8C2×C22⋊D1112yes—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4D4×D1111yescharacteristic
362C22×C4D4×D1111yescharacteristic
363C22×C4C23×D1111yescharacteristic
364Q16—44no—
365SD16—44no—
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—222no—
371C2×C8—222no—
372C2×C8—222no—
373C4⋊C4—24no—
374C4⋊C4—21no—
375C4⋊C4—114no—
376C4⋊C4—228no—
377C4⋊C4—228no—
378C4⋊C4—228no—
379C4⋊C4—222no—
380C4⋊C4—224no—
381C4⋊C4—224no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4C2×C22⋊D1112yes—
386C22⋊C4—42no—
387C22⋊C4—42no—
388C22⋊C4—444no—
389C22⋊C4—882no—
390C42—24no—
391C42—228no—
392C42—222no—
393C42—222no—
394C42—881no—
395C42D4×D1112yes—
396C42C2×C22⋊D1112yes—
397C11#2594111yescharacteristic, complemented, Sylow
398C23—41no—
399C23—41no—
400C23—42no—
401C23—41no—
402C23—42no—
403C23C2×D4×D1111yescharacteristic
404Q8—22no—
405Q8—24no—
406Q8—41no—
407Q8—41no—
408Q8—42no—
409Q8—444no—
410Q8—448no—
411Q8#6698914yes—
412D4—41no—
413D4—41no—
414D4—42no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—224no—
431C2×C4—222no—
432C2×C4—444no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4#6699012yes—
437C2×C4#6699012yes—
438C2×C4C2×D4×D1111yescharacteristic
439C2×C4C2×#434112yes—
440C2×C4#6704312yes—
441C2×C4C22×C22⋊D1111yescharacteristic
442C8—41no—
443C8—41no—
444C8—442no—
445C22—82no—
446C22—81no—
447C22—82no—
448C22—81no—
449C22—81no—
450C22#1062312912yes—
451C22#1062330111yescharacteristic
452C22#1062330211yescharacteristic
453C22#1062330812yes—
454C22C2×#6699011yescharacteristic
455C4—22no—
456C4—24no—
457C4—22no—
458C4—42no—
459C4—81no—
460C4—442no—
461C4—444no—
462C4—442no—
463C4—882no—
464C4#1062312912yes—
465C4C2×#6698911yescharacteristic
466C4#1062335611yescharacteristic
467C2—161no—
468C2#1307227511yescharacteristic
469C2#1307785711yescharacteristic
470C2#1307792711yescharacteristic
471C2#1308138112yes—
472C2#1308145512yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#464D11
hypocenterC11#25941
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
4. #13069765C2semidirect
6. #13069563C2semidirect
7. #13069555C2semidirect
9. #13068959C2semidirect
10. #13068446C2semidirect
397. C11#25941semidirect

Maximal subgroups

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

subgroupindex
C2×#106231012
C2×#106226682
#130741052
#130697652
#130697602
#130695632
#130695552
#130689732
#130689592
#130684462
C2×C11×#4642
#2594111