Finite Group Databasebeta

← #14758999

Subgroups — #14758999

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×D11×#97C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13069587C212yesmaximal, complemented
5#13069434C212yesmaximal, complemented
6#13069038C212yesmaximal
7#13069036C212yesmaximal
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×C8×D11C2212yes—
16#10623109—24no—
17#10623109C418yescomplemented
18C2×#66950C2211yescharacteristic
19C2×#66949—21no—
20C2×#66942—21no—
21C2×#66941C2211yescharacteristic
22C2×#66925—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#97C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66880C2212yes—
31C2×#66879C2212yes—
32#10622600C2212yes—
33#10622590C2212yes—
34C2×#66874C2212yes—
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622545—21no—
38C2×#66867C2211yescharacteristic
39D11×#97—24no—
40#10622277—21no—
41#10622264—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×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C2×C8×D11—24no—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85#66950—22no—
86#66950C2×C414yes—
87#66949—28no—
88#66942—28no—
89#66941—22no—
90#66941C2×C414yes—
91#66925—28no—
92C42×D11C2×C414yes—
93C42×D11D414yes—
94C4×Dic22—22no—
95C4×Dic22—28no—
96C4×Dic22C2×C414yes—
97C11×#103—24no—
98C11×#97—22no—
99C11×#95—21no—
100#66899—24no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105#66880—24no—
106#66879—24no—
107#66874—24no—
108#66867—22no—
109#21407—111nomaximal, Sylow
110C23×D11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C2×C4×D11—24no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—41no—
131C2×C4×D11—41no—
132C2×C4×D11C22⋊C414yes—
133C2×C4×D11C22⋊C414yes—
134C2×C4×D11C22×C412yes—
135C2×C4×D11C2×D412yes—
136C2×Dic22—24no—
137C2×Dic22—21no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—42no—
141C2×Dic22—42no—
142C2×Dic22C22×C412yes—
143C2×C8×C11—22no—
144C2×C8×C11—22no—
145C2×C8×C11#4114yes—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4C22×C412yes—
151C42×C11—24no—
152C42×C11—42no—
153C42×C11C22×C412yes—
154C42×C11C2×D412yes—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157(C2×D11)⋊C4—44no—
158C4⋊Dic11—24no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11C22×C412yes—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167Dic11⋊C4—24no—
168C4×Dic11—24no—
169C4×Dic11—42no—
170C4×Dic11C22⋊C414yes—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22×C412yes—
173C4×Dic11C2×D412yes—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8#4114yes—
177C8×D11—216no—
178C2×#533—111no—
179C22×#97—111no—
180#2283—111no—
181#1993—112no—
182#1960—112no—
183#1892—112no—
184#1892—112no—
185#1763—111no—
186#1763—111no—
187#1763—111no—
188#1763D1111yescharacteristic, complemented
189C23×C11C22×D411yescharacteristic
190C22×D11—22no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11C2×C22⋊C412yes—
194C22×D11#13714yes—
195Q8×C11—22no—
196Q8×C11—22no—
197Q8×C11—42no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4112yes—
214C2×C4×C11C2×#4112yes—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—21no—
218C2×Dic11—21no—
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—
230C4×D11—28no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—24no—
234C4×D11—44no—
235Dic22—22no—
236Dic22—22no—
237Dic22—48no—
238Dic22—42no—
239C8×C11—24no—
240C11⋊C8—24no—
241C23×C8—112no—
242#533—118no—
243#533—224no—
244C2×C4⋊Q8—111no—
245C2×C4⋊Q8—111no—
246C2×#125—221no—
247C2×C22⋊Q8—111no—
248C2×C22⋊Q8—111no—
249C2×C22⋊Q8—221no—
250C2×C4×Q8—111no—
251C2×C4×Q8—221no—
252C2×C4×Q8C2×D1111yescharacteristic
253C2×#117—221no—
254C22×C42—111no—
255C2×#103—112no—
256C2×#103—112no—
257C2×#103—112no—
258C2×#103C2×D1112yes—
259C2×#97—112no—
260C2×#97—111no—
261C2×#97—224no—
262C2×#97C2×D1111yescharacteristic
263#383—221no—
264#382—112no—
265#381—221no—
266#380—112no—
267C4×C4⋊C4—111no—
268C4×C4⋊C4C2×D1111yescharacteristic
269C4×C22⋊C4—221no—
270#376—221no—
271#340—112no—
272#340—112no—
273#340—112no—
274#340C2×D1112yes—
275C22×C11C22×C22⋊C411yescharacteristic
276C22×C11#53212yes—
277C22×C11C2×#13712yes—
278C22×C11#57511yescharacteristic
279C22×C11#57511yescharacteristic
280C2×D11—22no—
281C2×D11—24no—
282C2×D11—24no—
283C2×D11—22no—
284C2×D11#41914yes—
285C4×C11—22no—
286C4×C11—22no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11C4×#4111yescharacteristic
291C4×C11C4×#4111yescharacteristic
292C4×C11#52512yes—
293Dic11—22no—
294Dic11—22no—
295Dic11—22no—
296Dic11—42no—
297Dic11—42no—
298Dic11—82no—
299C22×Q8—111no—
300C22×Q8—221no—
301C22×Q8C22×D1111yescharacteristic
302C23×C4—111no—
303C23×C4—111no—
304C23×C4—111no—
305C22×C8—112no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8—224no—
309C22×C8C22×D1112yes—
310C4⋊Q8—114no—
311C4⋊Q8—114no—
312C4⋊Q8—222no—
313C4⋊Q8—222no—
314#125—228no—
315C22⋊Q8—114no—
316C22⋊Q8—114no—
317C22⋊Q8—222no—
318C22⋊Q8—228no—
319C22⋊Q8—222no—
320C4×Q8—22no—
321C4×Q8—114no—
322C4×Q8—228no—
323C4×Q8—222no—
324C4×Q8C4×D1114yes—
325#117—228no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—221no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1111yescharacteristic
337C2×C22⋊C4—221no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—222no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—111no—
343C2×C42—111no—
344C2×C42—111no—
345C2×C42—114no—
346C2×C42—114no—
347C2×C42—221no—
348C2×C42—221no—
349C2×C42C22×D1111yescharacteristic
350#103—24no—
351#103—224no—
352#103—224no—
353#103—224no—
354#97—22no—
355#97—224no—
356#97—222no—
357#95—21no—
358#95—222no—
359#95—222no—
360#95—222no—
361#95—221no—
362C2×C11#229711yescharacteristic
363C2×C11C2×#41911yescharacteristic
364C2×C11#289611yescharacteristic
365C2×C11#318112yes—
366C2×C11#318112yes—
367D11—24no—
368C24—111no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—112no—
373C2×Q8—224no—
374C2×Q8—221no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×Q8—442no—
378C2×Q8—442no—
379C2×Q8C2×C4×D1112yes—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—111no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—114no—
387C22×C4—112no—
388C22×C4—112no—
389C22×C4—114no—
390C22×C4—224no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—222no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4D4×D1111yescharacteristic
399C22×C4D4×D1111yescharacteristic
400C22×C4C23×D1111yescharacteristic
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—114no—
404C2×C8—2216no—
405C2×C8—222no—
406C2×C8—222no—
407C2×C8#433914yes—
408C4⋊C4—24no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—112no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4—224no—
417C4⋊C4—224no—
418C4⋊C4—224no—
419C4⋊C4—221no—
420C4⋊C4—222no—
421C4⋊C4—222no—
422C4⋊C4C2×C4×D1112yes—
423C22⋊C4—224no—
424C22⋊C4—224no—
425C22⋊C4—444no—
426C42—24no—
427C42—42no—
428C42—114no—
429C42—114no—
430C42—112no—
431C42—112no—
432C42—224no—
433C42—442no—
434C42C2×C4×D1112yes—
435C42D4×D1112yes—
436C11#2140711yescharacteristic, complemented, Sylow
437C23—112no—
438C23—114no—
439C23—221no—
440C23—221no—
441C23—222no—
442C23C2×D4×D1111yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—42no—
446Q8—222no—
447Q8—222no—
448Q8—448no—
449Q8—442no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—112no—
464C2×C4—228no—
465C2×C4—221no—
466C2×C4—222no—
467C2×C4—221no—
468C2×C4—222no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—444no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4C22⋊C4×D1112yes—
482C2×C4C22⋊C4×D1112yes—
483C2×C4C22×C4×D1111yescharacteristic
484C2×C4C2×#433912yes—
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4#41×D1112yes—
487C8—24no—
488C8—224no—
489C22—114no—
490C22—224no—
491C22—224no—
492C22—222no—
493C22—222no—
494C22C2×C22⋊C4×D1111yescharacteristic
495C22#1062307912yes—
496C22#1062330411yescharacteristic
497C22D11×#13712yes—
498C22#1062330811yescharacteristic
499C4—22no—
500C4—22no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—222no—
505C4—222no—
506C4—222no—
507C4—442no—
508C4—442no—
509C4—882no—
510C4C4×#433911yescharacteristic
511C4#1062305311yescharacteristic
512C4#1062307812yes—
513C2—224no—
514C2#1307110211yescharacteristic
515C2D11×#41911yescharacteristic
516C2#1307713211yescharacteristic
517C2#1307932112yes—
518C2#1307932312yes—
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#21407
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. #13069587C2semidirect
5. #13069434C2semidirect
8. #13068449C2semidirect
9. #13068447C2semidirect
10. #13068446C2semidirect
11. C11×#1763C2semidirect
17. #10623109C4semidirect
188. #1763D11semidirect
436. C11#21407semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×D11×#972
#130710122
#130695872
#130694342
#130690382
#130690362
#130684492
#130684472
#130684462
C11×#17632
#2140711