Finite Group Databasebeta

← #14810401

Subgroups — #14810401

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#10622373C212yesmaximal, complemented
3#13076959C211yesmaximal, characteristic
4#13069761C212yesmaximal, complemented
5#13069760C212yesmaximal, complemented
6#13069575C212yesmaximal, complemented
7#13068939C211yesmaximal, characteristic, complemented
8#13068938C211yesmaximal, characteristic, complemented
9#13068936C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1875C211yesmaximal, characteristic, complemented
12C2×C11×#121C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66993C2211yescharacteristic
15C2×#66992—22no—
16C2×#66983C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19#10623048—28no—
20C2×#66943C2212yes—
21C2×#66941C2212yes—
22C2×#66931—22no—
23C2×C4×Dic22—22no—
24C2×C11×#102C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2212yes—
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66885C2212yes—
30C2×C8×Dic11C2212yes—
31#10622601C2211yescharacteristic
32#10622589C2211yescharacteristic
33C2×#66873C2212yes—
34#10622570—22no—
35#10622373—28no—
36C11×#340C2212yes—
37#10622189C2212yes—
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41C22×D4×C11—21no—
42C22×D4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C22×C22⋊D11—22no—
46C23×Dic11D412yes—
47C22×D44C2311yescharacteristic
48C22×Dic22—22no—
49C22×C8×C11C2312yes—
50C11×#121—22no—
51C11×#121—22no—
52C11×#117—24no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—22no—
60#66993—24no—
61#66992—48no—
62#66983—22no—
63#66983—22no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66#66979—24no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11D412yes—
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79#66943—24no—
80#66943—24no—
81#66941—24no—
82#66941D418yescomplemented
83#66931—216no—
84C4×Dic22—216no—
85C11×#102—24no—
86C11×C22⋊C8—22no—
87#66896—24no—
88C22⋊(C11⋊C8)—22no—
89#66885—24no—
90C8×Dic11—24no—
91#66873—24no—
92#25905—111nomaximal, Sylow
93C24×C11—21no—
94C24×C11C2×D411yescharacteristic
95C23×D11—21no—
96C2×D4×C11—22no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—22no—
100C2×D4×C11—44no—
101C2×D4×C11—42no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—44no—
111C2×C22⋊D11—44no—
112C2×C22⋊D11—44no—
113C2×C22⋊D11—44no—
114C2×C22⋊D11—42no—
115C22×Dic11—24no—
116C22×Dic11—24no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—21no—
120C22×Dic11C2×D412yes—
121C22×Dic11C2×D412yes—
122C2×D44—22no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—22no—
126C2×Dic22—28no—
127C2×Dic22—44no—
128C2×Dic22—44no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C2×D414yes—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—42no—
138C42×C11—24no—
139C22⋊Dic11—24no—
140C22⋊Dic11—44no—
141(C2×D11)⋊C4—44no—
142(C2×D11)⋊C4—42no—
143C4⋊Dic11—28no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11C2×D414yes—
148Dic11⋊C4—28no—
149Dic11⋊C4—28no—
150Dic11⋊C4—44no—
151C4×Dic11—24no—
152C4×Dic11—24no—
153C4×Dic11—22no—
154C4×Dic11C2×D414yes—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×#533—111no—
159C2×#486—112no—
160#2856—111no—
161#2025—112no—
162#2025—112no—
163#1990—112no—
164#1875—111no—
165#1875—111no—
166#1875—111no—
167#1875D1111yescharacteristic, complemented
168C4×C22⋊C8—111no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11#12412yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—41no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—42no—
184C22×D11—42no—
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—84no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11#12412yes—
198C2×C4×C11C22×D412yes—
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C112−1+412yes—
202C22⋊D11—84no—
203C22⋊D11—88no—
204C2×Dic11—22no—
205C2×Dic11—24no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—48no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11#12014yes—
214C2×Dic11#13514yes—
215C2×Dic11AGL(1,ℤ/8)14yes—
216D44—42no—
217D44—42no—
218Dic22—416no—
219C8×C11—42no—
220C11⋊C8—42no—
221#533—228no—
222C2×C4⋊Q8—112no—
223C2×#127—111no—
224C2×#125—112no—
225C2×C22⋊Q8—222no—
226C2×#121—111no—
227C2×#121—222no—
228C2×#121C2×D1111yescharacteristic
229C2×C4×Q8—222no—
230C2×#117—111no—
231C2×#117C2×D1111yescharacteristic
232C22×C42—111no—
233#486—228no—
234C2×#102—112no—
235C2×#102—112no—
236C2×#102—112no—
237C2×#102C2×D1112yes—
238C2×C22⋊C8—111no—
239C2×C22⋊C8C2×D1111yescharacteristic
240C2×C4×C8—112no—
241#390—111no—
242#390—111no—
243#390—222no—
244#384—111no—
245#340—112no—
246#340—112no—
247#340—112no—
248#340C2×D1112yes—
249#336—112no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11C2×#12011yescharacteristic
261C22×C11C2×#12411yescharacteristic
262C22×C11#53611yescharacteristic
263C22×C11C2×#13512yes—
264C22×C11C2×AGL(1,ℤ/8)12yes—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—82no—
269C2×D11—82no—
270C4×C11—22no—
271C4×C11—44no—
272C4×C11—81no—
273C4×C11#54812yes—
274C4×C11#54812yes—
275Dic11—44no—
276Dic11—42no—
277Dic11—81no—
278Dic11#44918yes—
279C22×Q8—222no—
280C22×D4—21no—
281C22×D4—111no—
282C22×D4—222no—
283C22×D4—221no—
284C22×D4C22×D1111yescharacteristic
285C23×C4—112no—
286C23×C4C22×D1111yescharacteristic
287C22×C8—112no—
288C22×C8C22×D1112yes—
289C4⋊Q8—118no—
290C4⋊Q8—224no—
291#127—224no—
292#125—224no—
293#125—224no—
294C22⋊Q8—2216no—
295#121—22no—
296#121—22no—
297#121—222no—
298#121—222no—
299#121—448no—
300C4×Q8—2216no—
301#117—24no—
302#117—224no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C4⋊C4C22×D1112yes—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—222no—
316C2×C22⋊C4—221no—
317C2×C42—21no—
318C2×C42—111no—
319C2×C42—112no—
320C2×C42—111no—
321C2×C42—224no—
322C2×C42—221no—
323#102—24no—
324#102—224no—
325#102—224no—
326#102—224no—
327C22⋊C8—22no—
328C22⋊C8—222no—
329C4×C8—224no—
330C2×C11—42no—
331C2×C11—161no—
332C2×C11#243611yescharacteristic
333C2×C11C2×#44912yes—
334C2×C11#313111yescharacteristic
335C2×C11#313811yescharacteristic
336C2×C11#322812yes—
337D11—161no—
338C24—21no—
339C24—221no—
340C24D4×D1111yescharacteristic
341C2×Q8—228no—
342C2×Q8—444no—
343C2×Q8—444no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—22no—
348C2×D4—44no—
349C2×D4—42no—
350C2×D4—221no—
351C2×D4—222no—
352C2×D4—221no—
353C2×D4—222no—
354C2×D4—444no—
355C2×D4—444no—
356C2×D4—444no—
357C2×D4—444no—
358C2×D4—442no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—224no—
366C22×C4—224no—
367C22×C4—224no—
368C22×C4—222no—
369C22×C4—221no—
370C22×C4#433912yes—
371C22×C4D4×D1111yescharacteristic
372C22×C4#434112yes—
373C22×C4C23×D1111yescharacteristic
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—114no—
384C4⋊C4—228no—
385C4⋊C4—228no—
386C4⋊C4—228no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—444no—
391C4⋊C4D4×D1114yes—
392C22⋊C4—24no—
393C22⋊C4—42no—
394C22⋊C4—224no—
395C22⋊C4—444no—
396C22⋊C4—444no—
397C22⋊C4—442no—
398C42—24no—
399C42—114no—
400C42—224no—
401C42—224no—
402C42—222no—
403C11#2590511yescharacteristic, complemented, Sylow
404C23—22no—
405C23—22no—
406C23—21no—
407C23—21no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—41no—
412C23—41no—
413C23—441no—
414C23—442no—
415C23—442no—
416C23—441no—
417C23—441no—
418C23#6693812yes—
419C23C2×D4×D1111yescharacteristic
420Q8—4416no—
421D4—42no—
422D4—42no—
423D4—84no—
424D4—442no—
425D4—442no—
426D4—888no—
427D4—884no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—114no—
438C2×C4—114no—
439C2×C4—114no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—224no—
444C2×C4—448no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4#6693812yes—
450C2×C4C2×#433911yescharacteristic
451C2×C4C2×D4×D1112yes—
452C2×C4C2×#434111yescharacteristic
453C2×C4#6704312yes—
454C8—42no—
455C8—442no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—42no—
460C22—42no—
461C22—82no—
462C22—81no—
463C22—81no—
464C22—82no—
465C22—81no—
466C22—882no—
467C22—881no—
468C22—881no—
469C22—882no—
470C22—881no—
471C22C2×#6693811yescharacteristic
472C22D11×#12011yescharacteristic
473C22#1062317911yescharacteristic
474C22D11×#13512yes—
475C22D11×AGL(1,ℤ/8)12yes—
476C4—22no—
477C4—44no—
478C4—81no—
479C4—118no—
480C4—442no—
481C4—444no—
482C4—881no—
483C4#1062308312yes—
484C4#1062312912yes—
485C2—42no—
486C2—161no—
487C2—1761no—
488C2#1307227211yescharacteristic
489C2D11×#44912yes—
490C2#1307893611yescharacteristic
491C2#1307898811yescharacteristic
492C2#1307975012yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radical#13076959C2
hypercenter#1875D11
hypocenterC11#25905
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
2. C2×#10622373C2semidirect
4. #13069761C2semidirect
5. #13069760C2semidirect
6. #13069575C2semidirect
7. #13068939C2semidirect
8. #13068938C2semidirect
9. #13068936C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C11×#1875C2semidirect
82. #66941D4semidirect
167. #1875D11semidirect
403. C11#25905semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106223732
#130769592
#130697612
#130697602
#130695752
#130689392
#130689382
#130689362
C22⋊C8×Dic112
C11×#18752
#2590511