Finite Group Databasebeta

← #14759013

Subgroups — #14759013

Order 2816.

1186 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×#10622320C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069575C212yesmaximal, complemented
5#13069416C212yesmaximal, complemented
6#13069048C212yesmaximal
7#13069046C212yesmaximal
8#13068449C211yesmaximal, characteristic, complemented
9#13068447C211yesmaximal, characteristic, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C11×#1763C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2211yescharacteristic
14C2×#66997C2211yescharacteristic
15C22×#4313C2212yes—
16#10623109—24no—
17#10623109C418yescomplemented
18C2×#66950C2211yescharacteristic
19C2×#66949—21no—
20C2×#66942—21no—
21C2×#66941C2211yescharacteristic
22C2×#66925—21no—
23C2×#66925—21no—
24C2×C42×D11C2211yescharacteristic
25C2×C4×Dic22—21no—
26C2×C4×Dic22C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#97C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66880C2212yes—
32C2×C8×Dic11C2212yes—
33#10622600C2212yes—
34#10622589C2212yes—
35C2×#66874C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4—21no—
38C2×#66867C2211yescharacteristic
39#10622320—24no—
40#10622280—21no—
41#10622263—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C4×Q8×C11—22no—
54C4×Q8×C11C2×C414yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61#66999—22no—
62#66999C2×C414yes—
63#66997—22no—
64#66997C2×C414yes—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C2×#4313—24no—
85C2×#4313—24no—
86C2×#4313—24no—
87#66950—22no—
88#66950C2×C414yes—
89#66949—28no—
90#66942—28no—
91#66941—22no—
92#66941C2×C414yes—
93#66925—28no—
94#66925—44no—
95C42×D11C2×C414yes—
96C42×D11D414yes—
97C4×Dic22—22no—
98C4×Dic22—28no—
99C4×Dic22C2×C414yes—
100C11×#103—24no—
101C11×#97—22no—
102C11×#95—21no—
103#66899—24no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106#66880—24no—
107C8×Dic11—24no—
108#66874—24no—
109#66867—22no—
110#21409—111nomaximal, Sylow
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C412yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—24no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11C22⋊C414yes—
134C2×C4×D11C22⋊C414yes—
135C2×C4×D11C22×C412yes—
136C2×C4×D11C2×D412yes—
137C2×Dic22—24no—
138C2×Dic22—21no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—42no—
142C2×Dic22—42no—
143C2×Dic22C22×C412yes—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11#4114yes—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C22×C412yes—
152C42×C11—24no—
153C42×C11—42no—
154C42×C11C22×C412yes—
155C42×C11C2×D412yes—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—44no—
159C4⋊Dic11—24no—
160C4⋊Dic11—21no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11C22×C412yes—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168Dic11⋊C4—24no—
169Dic11⋊C4—44no—
170Dic11⋊C4—44no—
171C4×Dic11—24no—
172C4×Dic11—42no—
173C4×Dic11C22⋊C414yes—
174C4×Dic11C22⋊C414yes—
175C4×Dic11C22×C412yes—
176C4×Dic11C2×D412yes—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8#4114yes—
180#4313—216no—
181C2×#533—111no—
182C2×C4×M16—111no—
183#2285—111no—
184#1990—112no—
185#1956—112no—
186#1894—112no—
187#1894—112no—
188#1763—111no—
189#1763—111no—
190#1763—111no—
191#1763D1111yescharacteristic, complemented
192C23×C11C22×D411yescharacteristic
193C22×D11—22no—
194C22×D11—21no—
195C22×D11—22no—
196C22×D11—21no—
197C22×D11C2×C22⋊C412yes—
198Q8×C11—22no—
199Q8×C11—22no—
200Q8×C11—42no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4112yes—
217C2×C4×C11C2×#4112yes—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11C2×C22⋊C412yes—
228C2×Dic11C2×C22⋊C412yes—
229C2×Dic11C2×C22⋊C412yes—
230C2×Dic11AGL(1,ℤ/8)12yes—
231C2×Dic11#13712yes—
232C2×Dic11#13714yes—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—24no—
236C4×D11—28no—
237C4×D11—28no—
238Dic22—22no—
239Dic22—22no—
240Dic22—42no—
241Dic22—48no—
242C8×C11—24no—
243C11⋊C8—24no—
244C22×M16—112no—
245#533—118no—
246#533—224no—
247C2×C4⋊Q8—111no—
248C2×C4⋊Q8—111no—
249C2×#125—221no—
250C2×C22⋊Q8—111no—
251C2×C22⋊Q8—111no—
252C2×C22⋊Q8—221no—
253C2×C4×Q8—111no—
254C2×C4×Q8—221no—
255C2×C4×Q8C2×D1111yescharacteristic
256C2×#117—221no—
257C2×#117—221no—
258C22×C42—111no—
259C2×#103—112no—
260C2×#103—112no—
261C2×#103—112no—
262C2×#103C2×D1112yes—
263C4×M16—224no—
264C2×#97—111no—
265C2×#97C2×D1111yescharacteristic
266C2×C4×C8—112no—
267#384—112no—
268#382—221no—
269#380—112no—
270#380—221no—
271C4×C4⋊C4—111no—
272C4×C4⋊C4—221no—
273C4×C4⋊C4C2×D1111yescharacteristic
274#340—112no—
275#340—112no—
276#340—112no—
277#340C2×D1112yes—
278C22×C11C22×C22⋊C411yescharacteristic
279C22×C11#53212yes—
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×#13712yes—
282C22×C11C2×#13711yescharacteristic
283C2×D11—22no—
284C2×D11—22no—
285C2×D11—22no—
286C2×D11—42no—
287C2×D11—42no—
288C4×C11—22no—
289C4×C11—22no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11—82no—
293C4×C11C4×#4111yescharacteristic
294C4×C11C4×#4111yescharacteristic
295C4×C11#52512yes—
296Dic11—22no—
297Dic11—42no—
298Dic11—42no—
299Dic11—82no—
300Dic11#41714yes—
301Dic11#41914yes—
302C22×Q8—111no—
303C22×Q8—221no—
304C22×Q8C22×D1111yescharacteristic
305C23×C4—111no—
306C23×C4—111no—
307C23×C4—111no—
308C2×M16—224no—
309C2×M16—224no—
310C2×M16—224no—
311C22×C8—112no—
312C22×C8C22×D1112yes—
313C4⋊Q8—114no—
314C4⋊Q8—114no—
315C4⋊Q8—222no—
316C4⋊Q8—222no—
317#125—228no—
318C22⋊Q8—114no—
319C22⋊Q8—114no—
320C22⋊Q8—222no—
321C22⋊Q8—228no—
322C22⋊Q8—222no—
323C4×Q8—22no—
324C4×Q8—114no—
325C4×Q8—228no—
326C4×Q8—222no—
327C4×Q8C4×D1114yes—
328#117—228no—
329#117—444no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4C22×D1112yes—
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—221no—
344C2×C22⋊C4—221no—
345C2×C22⋊C4—222no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—111no—
351C2×C42—114no—
352C2×C42—114no—
353C2×C42—221no—
354C2×C42—221no—
355C2×C42C22×D1111yescharacteristic
356#103—24no—
357#103—224no—
358#103—224no—
359#103—224no—
360#97—22no—
361#97—222no—
362C4×C8—224no—
363#95—21no—
364#95—222no—
365#95—221no—
366C2×C11#229711yescharacteristic
367C2×C11C2×#41911yescharacteristic
368C2×C11C2×#41711yescharacteristic
369C2×C11#318212yes—
370C2×C11#318512yes—
371D11—42no—
372C24—111no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—112no—
377C2×Q8—224no—
378C2×Q8—221no—
379C2×Q8—222no—
380C2×Q8—222no—
381C2×Q8—442no—
382C2×Q8—442no—
383C2×Q8C2×C4×D1112yes—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—111no—
388C22×C4—111no—
389C22×C4—111no—
390C22×C4—114no—
391C22×C4—114no—
392C22×C4—112no—
393C22×C4—112no—
394C22×C4—222no—
395C22×C4—224no—
396C22×C4—222no—
397C22×C4—222no—
398C22×C4—222no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—222no—
402C22×C4D4×D1111yescharacteristic
403C22×C4D4×D1111yescharacteristic
404C22×C4C23×D1111yescharacteristic
405M16—2216no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—114no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8#433914yes—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—112no—
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—224no—
420C4⋊C4—224no—
421C4⋊C4—224no—
422C4⋊C4—224no—
423C4⋊C4—221no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—444no—
427C4⋊C4—444no—
428C4⋊C4C2×C4×D1112yes—
429C22⋊C4—224no—
430C22⋊C4—224no—
431C22⋊C4—444no—
432C42—24no—
433C42—42no—
434C42—114no—
435C42—114no—
436C42—112no—
437C42—112no—
438C42—224no—
439C42—442no—
440C42C2×C4×D1112yes—
441C42D4×D1112yes—
442C11#2140911yescharacteristic, complemented, Sylow
443C23—112no—
444C23—221no—
445C23—222no—
446C23—221no—
447C23—222no—
448C23C2×D4×D1111yescharacteristic
449Q8—22no—
450Q8—22no—
451Q8—42no—
452Q8—222no—
453Q8—222no—
454Q8—448no—
455Q8—442no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—114no—
471C2×C4—112no—
472C2×C4—112no—
473C2×C4—228no—
474C2×C4—228no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—222no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4C22⋊C4×D1112yes—
488C2×C4C22⋊C4×D1112yes—
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×#433912yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4#41×D1112yes—
493C8—24no—
494C8—224no—
495C22—222no—
496C22—222no—
497C22—222no—
498C22—442no—
499C22—442no—
500C22C2×C22⋊C4×D1111yescharacteristic
501C22#1062307912yes—
502C22D11×AGL(1,ℤ/8)11yescharacteristic
503C22D11×#13712yes—
504C22D11×#13711yescharacteristic
505C4—22no—
506C4—22no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—114no—
511C4—114no—
512C4—222no—
513C4—442no—
514C4—442no—
515C4—882no—
516C4C4×#433911yescharacteristic
517C4#1062305311yescharacteristic
518C4#1062307812yes—
519C2—442no—
520C2#1307110211yescharacteristic
521C2D11×#41911yescharacteristic
522C2D11×#41711yescharacteristic
523C2#1307933112yes—
524C2#1307935812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#21409
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069416C2semidirect
8. #13068449C2semidirect
9. #13068447C2semidirect
10. #13068446C2semidirect
11. C11×#1763C2semidirect
17. #10623109C4semidirect
191. #1763D11semidirect
442. C11#21409semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106223202
#130710202
#130695752
#130694162
#130690482
#130690462
#130684492
#130684472
#130684462
C11×#17632
#2140911