Finite Group Databasebeta

← #14757235

Subgroups — #14757235

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622473C212yesmaximal
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4C4×#66945C211yesmaximal, characteristic
5#13069385C212yesmaximal, complemented
6#13069383C212yesmaximal, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069374C211yesmaximal, characteristic, complemented
9#13069372C211yesmaximal, characteristic, complemented
10#13068331C212yesmaximal
11C11×#1948C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×#66945C2212yes—
14C2×#66945C2211yescharacteristic
15C2×#66945C2211yescharacteristic
16C2×C42×D11C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66881C2212yes—
22C2×Dic11⋊C8C2212yes—
23#10622600—21no—
24#10622600—21no—
25#10622590C2212yes—
26C4⋊C4×Dic11—21no—
27C4⋊C4×Dic11—21no—
28C4⋊C4×Dic11C2211yescharacteristic
29C4⋊C4×Dic11C2211yescharacteristic
30C2×#66871C2212yes—
31C2×#66871C2212yes—
32C4×(C2×D11)⋊C4—21no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C42×Dic11—21no—
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622473—28no—
38D11×C4⋊C8C418yescomplemented
39#10622279—21no—
40#10622261—21no—
41C11×#340C2212yes—
42#10622189C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×C4×D11D411yescharacteristic
46C22×C4×D11D411yescharacteristic
47C22×C4×D11C2311yescharacteristic
48C22×C8×C11C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C2×C8×D11—24no—
75C2×C8×D11—24no—
76C2×C8×D11C2×C418yes—
77#66945—22no—
78#66945—22no—
79#66945—24no—
80#66945—24no—
81#66945D414yes—
82#66945Q814yes—
83C42×D11C2×C414yes—
84C42×D11Q814yes—
85C11×#106—24no—
86C11×C4⋊C8C2×C414yes—
87C11×#95—21no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93#66881—24no—
94Dic11⋊C8C2×C418yes—
95#66871—24no—
96#66871—24no—
97C4⋊(C11⋊C8)C2×C414yes—
98#21169—111nomaximal, Sylow
99C23×D11C2×D411yescharacteristic
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—41no—
115C2×C4×D11—41no—
116C2×C4×D11C4⋊C414yes—
117C2×C4×D11C4⋊C414yes—
118C2×C4×D11C22×C412yes—
119C2×C4×D11C2×D412yes—
120C2×C4×D11C2×Q812yes—
121C2×C4×D11C2×Q812yes—
122C2×C4×D11#4112yes—
123C2×C4×D11#4112yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11C22×C414yes—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4C2×D412yes—
134C11×C4⋊C4C2×Q812yes—
135C42×C11—42no—
136C42×C11C22×C412yes—
137C42×C11C2×Q812yes—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—24no—
140(C2×D11)⋊C4—44no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—42no—
146C4⋊Dic11—42no—
147C4⋊Dic11C2×D412yes—
148C4⋊Dic11C2×Q812yes—
149C4×Dic11—24no—
150C4×Dic11—24no—
151C4×Dic11—42no—
152C4×Dic11—42no—
153C4×Dic11—44no—
154C4×Dic11—42no—
155C4×Dic11C4⋊C414yes—
156C4×Dic11C4⋊C414yes—
157C4×Dic11C22×C412yes—
158C4×Dic11C2×Q812yes—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8C22×C414yes—
162C8×D11—216no—
163C2×#427—112no—
164C22×C4⋊C8—111no—
165#2285—111no—
166C4×#117—111no—
167#1949—112no—
168#1949—112no—
169#1948—111no—
170#1948D1111yescharacteristic, complemented
171#1947—111no—
172#1947—111no—
173#1735—112no—
174C23×C11C22×D411yescharacteristic
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—21no—
178C22×D11—21no—
179C22×D11C2×C4⋊C412yes—
180C22×D11#12112yes—
181C22×D11C22⋊Q812yes—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11C2×C4⋊C412yes—
194C2×C4×C11C2×C4⋊C412yes—
195C2×C4×C11#13512yes—
196C2×C4×C11#13512yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×Q811yescharacteristic
200C2×C4×C11C22×Q811yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11C2×C4⋊C412yes—
217C2×Dic11C2×C4⋊C412yes—
218C2×Dic11C2×C4⋊C412yes—
219C2×Dic11#12112yes—
220C2×Dic11C22⋊Q812yes—
221C4×D11—28no—
222C4×D11—44no—
223C4×D11C4×D414yes—
224C4×D11C4×Q814yes—
225C4×D11#12514yes—
226C4×D11C4⋊Q814yes—
227C8×C11—24no—
228C11⋊C8—24no—
229C23×C8—112no—
230C2×#117—111no—
231C2×#117—111no—
232C2×#117—112no—
233C22×C42—111no—
234#427—228no—
235C2×#107—112no—
236C2×#107—112no—
237C2×#106—112no—
238C2×#106C2×D1112yes—
239C2×C4⋊C8—112no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8—118no—
242C2×C4⋊C8C2×D1111yescharacteristic
243#384—111no—
244#384C2×D1111yescharacteristic
245#382—112no—
246#380—221no—
247#380—221no—
248C4×C4⋊C4—111no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—111no—
251C4×C4⋊C4—221no—
252C4×C4⋊C4—221no—
253C4×C4⋊C4C2×D1111yescharacteristic
254C4×C22⋊C4—221no—
255C4×C22⋊C4—221no—
256#376—221no—
257C43—221no—
258#340—112no—
259#340—112no—
260#340—112no—
261#340C2×D1112yes—
262C22×C11C22×C4⋊C411yescharacteristic
263C22×C11C2×#12111yescharacteristic
264C22×C11C2×C22⋊Q811yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11C2×#13511yescharacteristic
267C22×C11#57511yescharacteristic
268C22×C11#57511yescharacteristic
269C2×D11—22no—
270C2×D11—22no—
271C2×D11—22no—
272C2×D11—22no—
273C2×D11—22no—
274C2×D11—22no—
275C2×D11#38914yes—
276C4×C11—22no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—82no—
280C4×C11#42714yescomplemented
281C4×C11C2×C4×D411yescharacteristic
282C4×C11C2×C4×Q811yescharacteristic
283C4×C11C2×#12511yescharacteristic
284C4×C11C2×C4⋊Q811yescharacteristic
285Dic11—22no—
286Dic11—22no—
287Dic11—42no—
288Dic11—42no—
289Dic11—82no—
290Dic11#38914yes—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—111no—
294C22×C8—112no—
295C22×C8—118no—
296C22×C8—224no—
297C22×C8—224no—
298C22×C8C22×D1112yes—
299#117—114no—
300#117—114no—
301#117—222no—
302#117—222no—
303#117—224no—
304#117—224no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22×D1112yes—
313C2×C4⋊C4C22×D1111yescharacteristic
314C2×C4⋊C4C22×D1111yescharacteristic
315C2×C22⋊C4—221no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—222no—
318C2×C42—21no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42—111no—
322C2×C42—114no—
323C2×C42—114no—
324C2×C42—221no—
325C2×C42—221no—
326C2×C42—222no—
327C2×C42—221no—
328C2×C42—221no—
329C2×C42—221no—
330C2×C42C22×D1111yescharacteristic
331#107—224no—
332#107—224no—
333#106—24no—
334#106—224no—
335C4⋊C8—118no—
336C4⋊C8—114no—
337C4⋊C8C4×D1114yes—
338#95—21no—
339#95—221no—
340#95—221no—
341#95—222no—
342#95—222no—
343#95—221no—
344C2×C11C2×#38911yescharacteristic
345C2×C11C2×#42711yescharacteristic
346C2×C11#291111yescharacteristic
347C2×C11#303511yescharacteristic
348C2×C11#303511yescharacteristic
349C2×C11#307611yescharacteristic
350C2×C11#307611yescharacteristic
351D11—24no—
352C24—111no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—111no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—111no—
364C22×C4—111no—
365C22×C4—114no—
366C22×C4—114no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—222no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4D4×D1111yescharacteristic
375C22×C4D4×D1111yescharacteristic
376C22×C4C23×D1111yescharacteristic
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—114no—
380C2×C8—2216no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8C2×C4×D1114yes—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—112no—
391C4⋊C4—112no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—222no—
396C4⋊C4—442no—
397C4⋊C4—442no—
398C4⋊C4D4×D1112yes—
399C4⋊C4Q8×D1112yes—
400C22⋊C4—224no—
401C22⋊C4—224no—
402C22⋊C4—444no—
403C42—42no—
404C42—114no—
405C42—114no—
406C42—112no—
407C42—112no—
408C42—224no—
409C42—224no—
410C42—444no—
411C42—442no—
412C42—442no—
413C42—442no—
414C42C2×C4×D1112yes—
415C42Q8×D1112yes—
416C11#2116911yescharacteristic, complemented, Sylow
417C23—112no—
418C23—112no—
419C23—112no—
420C23—221no—
421C23—221no—
422C23—221no—
423C23—221no—
424C23C2×D4×D1111yescharacteristic
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—112no—
437C2×C4—112no—
438C2×C4—112no—
439C2×C4—114no—
440C2×C4—114no—
441C2×C4—114no—
442C2×C4—114no—
443C2×C4—112no—
444C2×C4—112no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—228no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—444no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4C4⋊C4×D1112yes—
461C2×C4C4⋊C4×D1112yes—
462C2×C4#6696912yes—
463C2×C4#6696912yes—
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4C2×D4×D1111yescharacteristic
466C2×C4C2×Q8×D1111yescharacteristic
467C2×C4C2×Q8×D1111yescharacteristic
468C2×C4#41×D1111yescharacteristic
469C2×C4#41×D1111yescharacteristic
470C8—24no—
471C8—224no—
472C22—114no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—222no—
478C22—222no—
479C22C2×C4⋊C4×D1111yescharacteristic
480C22D11×#12111yescharacteristic
481C22D11×C22⋊Q811yescharacteristic
482C22C2×#6696911yescharacteristic
483C22C2×#6696911yescharacteristic
484C22#1062330411yescharacteristic
485C22#1062330811yescharacteristic
486C4—22no—
487C4—42no—
488C4—42no—
489C4—82no—
490C4—114no—
491C4—222no—
492C4—222no—
493C4—442no—
494C4—442no—
495C4—882no—
496C4#1062247314yescomplemented
497C4C4×D4×D1111yescharacteristic
498C4C4×Q8×D1111yescharacteristic
499C4D11×#12511yescharacteristic
500C4D11×C4⋊Q811yescharacteristic
501C2—224no—
502C2D11×#38911yescharacteristic
503C2C2×#1062247311yescharacteristic
504C2#1307720311yescharacteristic
505C2#1307806611yescharacteristic
506C2#1307807211yescharacteristic
507C2#1307839911yescharacteristic
508C2#1307840511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1948D11
hypocenterC11#21169
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
5. #13069385C2semidirect
6. #13069383C2semidirect
7. #13069380C2semidirect
8. #13069374C2semidirect
9. #13069372C2semidirect
11. C11×#1948C2semidirect
38. D11×C4⋊C8C4semidirect
170. #1948D11semidirect
280. C4×C11#427semidirect
416. C11#21169semidirect
496. C4#10622473semidirect

Maximal subgroups

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

subgroupindex
C2×#106224732
C2×D11×C4⋊C82
#130710212
C4×#669452
#130693852
#130693832
#130693802
#130693742
#130693722
#130683312
C11×#19482
#2116911