Finite Group Databasebeta

← #14803303

Subgroups — #14803303

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2#13073986C211yesmaximal, characteristic, complemented
3#13073619C211yesmaximal, characteristic
4#13069988C212yesmaximal, complemented
5#13069929C212yesmaximal, complemented
6#13069472C212yesmaximal, complemented
7#13069423C211yesmaximal, characteristic
8#13069380C211yesmaximal, characteristic, complemented
9#13069296C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#460C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66989—21no—
16C2×C4×Dic22C2211yescharacteristic
17C11×#460—24no—
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#102C2212yes—
20#10622843C2212yes—
21C2×#66899C2211yescharacteristic
22C2×#66899C2211yescharacteristic
23#10622835—22no—
24#10622834—21no—
25#10622834C2212yes—
26#10622834C2212yes—
27C2×#66896C2212yes—
28C2×#66896C2212yes—
29C2×#66881C2212yes—
30C2×Dic11⋊C8C2212yes—
31C2×C8×Dic11C2212yes—
32#10622597—22no—
33#10622586C2212yes—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36#10622542—21no—
37#10622541—21no—
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622443—24no—
40#10622189C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C22×Dic22D411yescharacteristic
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—42no—
51C22×C8×C11C2312yes—
52C11×#127—22no—
53C11×#127—22no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64#66989—44no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4D412yes—
73C2×C4×Dic11—21no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×C4⋊C8D414yes—
80C11×#102—24no—
81#66899—22no—
82#66899—22no—
83#66896—24no—
84#66896—42no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66881—42no—
90Dic11⋊C8—24no—
91C8×Dic11—24no—
92C4×C11⋊C8—22no—
93#25295—111nomaximal, Sylow
94C24×C11—22no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11#4112yes—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—81no—
112C2×D4×C11—81no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11C2×D412yes—
122C22×Dic11C2×D412yes—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22SD1614yescomplemented
126C11×SD16—48no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11C2×D414yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—42no—
133C42×C11—42no—
134C42×C11C2×D412yes—
135C42×C11#4112yes—
136C22⋊Dic11—44no—
137C22⋊Dic11—44no—
138C22⋊Dic11—82no—
139C22⋊Dic11—82no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—42no—
148C4⋊Dic11—81no—
149Dic11⋊C4—24no—
150Dic11⋊C4—82no—
151C4×Dic11—22no—
152C4×Dic11—22no—
153C4×Dic11—42no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8#4112yes—
160C2×#460D1111yescharacteristic
161C2×C8×Q8—111no—
162#2582—111no—
163#2548—111no—
164#2065—112no—
165#2055—112no—
166#1968—112no—
167#1957—111no—
168#1948—111no—
169#1934—112no—
170C4×#103—111no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11C22×D411yescharacteristic
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—41no—
182Q8×C11—41no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—84no—
188D4×C11—84no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11C2×SD1614yes—
222Dic22—28no—
223C8×C11—24no—
224C11⋊C8—22no—
225C11⋊C8—41no—
226C22×SD16C2×D1112yes—
227C2×#127C2×D1111yescharacteristic
228C2×#124—221no—
229C2×C4×Q8—111no—
230C2×C4×Q8C2×D1111yescharacteristic
231#460—24no—
232C8×Q8—224no—
233C2×#106—112no—
234C2×C4⋊C8—112no—
235C2×C4⋊C8C2×D1111yescharacteristic
236C2×#103—111no—
237C2×#103—111no—
238C2×#102—112no—
239C2×#102—112no—
240C2×#102C2×D1112yes—
241C2×C4×C8—112no—
242C2×C4×C8—111no—
243#398—222no—
244#394—222no—
245#391—112no—
246#391—221no—
247#390—112no—
248#390—112no—
249#390—221no—
250#389—112no—
251#389—221no—
252#384—111no—
253C4×C4⋊C4—111no—
254#340—112no—
255#340—111no—
256#340—111no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11—82no—
264C22×C11C2×#12111yescharacteristic
265C22×C11#54811yescharacteristic
266C22×C11#55011yescharacteristic
267C22×C11C22×SD1611yescharacteristic
268C22×C11C2×#13511yescharacteristic
269C22×C11#57611yescharacteristic
270C22×C11#57711yescharacteristic
271C4×C11—22no—
272C4×C11—42no—
273C4×C11—81no—
274C4×C11#46514yes—
275C4×C11#52911yescharacteristic
276C4×C11#54211yescharacteristic
277C4×C11#54611yescharacteristic
278C4×C11#54811yescharacteristic
279Dic11—24no—
280Dic11—42no—
281Dic11—81no—
282Dic11—81no—
283Dic11—82no—
284C22×Q8—111no—
285C22×Q8C22×D1111yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C22×D1112yes—
289C2×SD16—24no—
290C2×SD16—24no—
291C2×SD16—42no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8C22×D1112yes—
295#127—22no—
296#127—22no—
297#124—444no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—222no—
301C4×Q8—222no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—112no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C42—21no—
317C2×C42—112no—
318C2×C42—221no—
319C2×C42C22×D1111yescharacteristic
320#106—442no—
321C4⋊C8—224no—
322C4⋊C8C22⋊D1114yes—
323#103—222no—
324#103—222no—
325#102—24no—
326#102—224no—
327#102—442no—
328C4×C8—224no—
329C4×C8—222no—
330#95—222no—
331#95—222no—
332#95—222no—
333#95—221no—
334C2×C11—162no—
335C2×C11#242611yescharacteristic
336C2×C11C2×#46511yescharacteristic
337C2×C11#306211yescharacteristic
338C2×C11#336211yescharacteristic
339C2×C11#336511yescharacteristic
340C2×C11#339211yescharacteristic
341C2×C11#339611yescharacteristic
342C24—22no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—114no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×Q8#434112yes—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—81no—
363C2×D4—81no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—112no—
367C22×C4—112no—
368C22×C4—222no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—48no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—112no—
378C2×C8—221no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8C2×C22⋊D1114yes—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—42no—
387C4⋊C4—224no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—442no—
396C4⋊C4—881no—
397C4⋊C4—882no—
398C22⋊C4—444no—
399C22⋊C4—444no—
400C22⋊C4—882no—
401C22⋊C4—882no—
402C42—42no—
403C42—222no—
404C42—222no—
405C42—442no—
406C42#434112yes—
407C42C2×C22⋊D1112yes—
408C11#2529511yescharacteristic, complemented, Sylow
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—42no—
416C23C2×D4×D1111yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—41no—
420Q8—41no—
421Q8—228no—
422D4—42no—
423D4—42no—
424D4—42no—
425D4—42no—
426D4—84no—
427D4—84no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—114no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—442no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4SD16×D1112yes—
452C2×C4#6696912yes—
453C2×C4#6699112yes—
454C2×C4#6699112yes—
455C2×C4C2×#434111yescharacteristic
456C2×C4C2×#434111yescharacteristic
457C2×C4#6703711yescharacteristic
458C2×C4#41×D1111yescharacteristic
459C2×C4#6704311yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C8—24no—
462C8—222no—
463C8—441no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—82no—
471C22#1062312911yescharacteristic
472C22#1062313011yescharacteristic
473C22C2×SD16×D1111yescharacteristic
474C22C2×#6696911yescharacteristic
475C22#1062330511yescharacteristic
476C22#1062330611yescharacteristic
477C22C2×#6699111yescharacteristic
478C4—22no—
479C4—42no—
480C4—81no—
481C4—224no—
482C4—442no—
483C4—882no—
484C4—881no—
485C4—881no—
486C4#1062278414yes—
487C4#1062313111yescharacteristic
488C4#1062313411yescharacteristic
489C4#1062333711yescharacteristic
490C4#1062336211yescharacteristic
491C2—162no—
492C2#1307217811yescharacteristic
493C2C2×#1062278411yescharacteristic
494C2#1307829011yescharacteristic
495C2#1308128211yescharacteristic
496C2#1308131611yescharacteristic
497C2#1308159611yescharacteristic
498C2#1308162711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#460C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC2×#460D11
hypocenterC11#25295
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
2. #13073986C2semidirect
4. #13069988C2semidirect
5. #13069929C2semidirect
6. #13069472C2semidirect
8. #13069380C2semidirect
9. #13069296C2semidirect
10. C4×#66899C2semidirect
125. C2×Dic22SD16semidirect
408. C11#25295semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130739862
#130736192
#130699882
#130699292
#130694722
#130694232
#130693802
#130692962
C4×#668992
C2×C11×#4602
#2529511