Finite Group Databasebeta

← #14760299

Subgroups — #14760299

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622728C211yesmaximal, characteristic
2C2×#10622485C211yesmaximal, characteristic, complemented
3C2×#10622714C211yesmaximal, characteristic, complemented
4#13071305C212yesmaximal, complemented
5#13069480C211yesmaximal, characteristic, complemented
6#13069347C211yesmaximal, characteristic, complemented
7#13069311C212yesmaximal, complemented
8#13069052C212yesmaximal, complemented
9#107×Dic11C211yesmaximal, characteristic, complemented
10#13068440C212yesmaximal, complemented
11C11×#1808C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13C2×#66983C2212yes—
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×D88C2211yescharacteristic
17C2×#66946C2212yes—
18C2×C11×#107C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C11×#380C2212yes—
21#10622728C418yescomplemented
22C2×#66885C2212yes—
23C2×#66882C2211yescharacteristic
24#10622714—24no—
25C2×#66879C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C2×#66873C2212yes—
34#10622570—22no—
35#10622569—22no—
36#10622485—24no—
37#10622283—22no—
38#10622281—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—22no—
44C22×D44C2312yes—
45C22×C4×D11—22no—
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11C2×C414yescomplemented
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C22⋊C4—22no—
54C2×C22⋊Dic11D411yescharacteristic
55C2×C22⋊Dic11D411yescharacteristic
56#66983—24no—
57#66983C2×C418yescomplemented
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62#66979—22no—
63#66979—22no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11D411yescharacteristic
66C2×C4⋊Dic11C2312yes—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C2×D88—22no—
77C2×D88—22no—
78C2×D88C2×C414yes—
79#66946—24no—
80#66946—24no—
81C11×#107—22no—
82C11×#107—22no—
83C11×#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885C2×C418yescomplemented
87#66882C2×C414yescomplemented
88#66879—22no—
89#66879—22no—
90C8×Dic11—22no—
91C8×Dic11D414yescomplemented
92#66873—24no—
93#66873—24no—
94#21524—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C23×D11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C22×C412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4112yes—
106C22×C4×C11C2411yescharacteristic
107C2×C22⋊D11—28no—
108C2×C22⋊D11—82no—
109C2×C22⋊D11—82no—
110C22×Dic11—22no—
111C22×Dic11C2×D411yescharacteristic
112C22×Dic11C2×D411yescharacteristic
113C22×Dic11C2×D411yescharacteristic
114C22×Dic11C2×D411yescharacteristic
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44C22×C414yes—
121C2×C4×D11—44no—
122C2×C4×D11—82no—
123C2×C4×D11—82no—
124C2×C8×C11—28no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C22⋊C4—82no—
136C22⋊Dic11—22no—
137C22⋊Dic11—22no—
138(C2×D11)⋊C4—28no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—82no—
141(C2×D11)⋊C4—82no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22×C414yes—
146Dic11⋊C4—82no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—82no—
150C4×Dic11C2×D412yes—
151C4×Dic11#4112yes—
152#4318—28no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8C2×D412yes—
158C2×C11⋊C8#4112yes—
159D88—28no—
160C2×#466—111no—
161C2×C4×D8—111no—
162C2×#405—111no—
163#2324—112no—
164#1970—111no—
165#1942—111no—
166#1936—112no—
167#1895—112no—
168#1808D1111yescharacteristic, complemented
169C4×#107—111no—
170#1762—112no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11C4×D412yes—
178C23×C11C22×D411yescharacteristic
179C22×D11—24no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C4×D412yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C22⋊D11—88no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—24no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11#12112yes—
220C2×Dic11#12112yes—
221D44—24no—
222D44—24no—
223D44—42no—
224D44—42no—
225C4×D11—88no—
226C8×C11—22no—
227C8×C11C4×D414yes—
228C11⋊C8—22no—
229C11⋊C8—22no—
230C22×D8—111no—
231C22×M16—111no—
232C23×C8C2×D1111yescharacteristic
233C2×#121—112no—
234C2×C4×D4—112no—
235C2×#117—111no—
236#466—118no—
237C4×D8—224no—
238C2×#107—111no—
239C2×#107C2×D1111yescharacteristic
240C2×#107C2×D1111yescharacteristic
241C2×#102—112no—
242C2×#102—112no—
243C2×#102—112no—
244#405—224no—
245C2×#97—111no—
246C2×#97—111no—
247C2×C4×C8—111no—
248C2×C4×C8—111no—
249#390—112no—
250#390—222no—
251#389—112no—
252#388—222no—
253#386—222no—
254#385—222no—
255#380C2×D1112yes—
256C4×C4⋊C4—112no—
257#340—112no—
258#340—112no—
259#340C2×D1112yes—
260C22×C11—22no—
261C22×C11—22no—
262C22×C11—22no—
263C22×C11—41no—
264C22×C11—41no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11C2×#12111yescharacteristic
269C22×C11#53211yescharacteristic
270C22×C11#57611yescharacteristic
271C22×C11#57611yescharacteristic
272C22×C11#57611yescharacteristic
273C22×C11#57811yescharacteristic
274C2×D11—44no—
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—82no—
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—82no—
281C4×C11—22no—
282C4×C11—82no—
283C4×C11—82no—
284C4×C11C2×C4×D411yescharacteristic
285C4×C11C4×#4111yescharacteristic
286C4×C11#52511yescharacteristic
287C4×C11#52911yescharacteristic
288Dic11—22no—
289Dic11—22no—
290Dic11—44no—
291Dic11—41no—
292Dic11—41no—
293C22×D4—112no—
294C22×D4—222no—
295C23×C4—222no—
296C23×C4C22×D1111yescharacteristic
297C2×D8—114no—
298C2×D8—222no—
299C2×D8—222no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16—222no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—111no—
306C22×C8—111no—
307C22×C8C4×D1114yescomplemented
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#121—118no—
311#121—224no—
312C4×D4—224no—
313C4×D4—224no—
314#117—222no—
315#117—222no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4C22×D1112yes—
321C2×C4⋊C4C22×D1112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—111no—
324C2×C22⋊C4—111no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—111no—
330C2×C42—111no—
331C2×C42—222no—
332#107—22no—
333#107—22no—
334#107—114no—
335#102—118no—
336#102—224no—
337#102—224no—
338#97—222no—
339#97—222no—
340C4×C8—114no—
341C4×C8—222no—
342#95—22no—
343#95—222no—
344#95—222no—
345C2×C11—42no—
346C2×C11C4×#12111yescharacteristic
347C2×C11#294811yescharacteristic
348C2×C11#295111yescharacteristic
349C2×C11#305811yescharacteristic
350C2×C11#306111yescharacteristic
351C2×C11#317511yescharacteristic
352C2×C11#317611yescharacteristic
353D11—84no—
354C24—222no—
355C24D4×D1111yescharacteristic
356C2×D4—114no—
357C2×D4—228no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—882no—
364C2×D4—882no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—222no—
376C22×C4—444no—
377C22×C4—882no—
378C22×C4—882no—
379C22×C4C2×C4×D1112yes—
380C22×C4D4×D1111yescharacteristic
381C22×C4#434312yes—
382C22×C4C23×D1111yescharacteristic
383D8—228no—
384M16—228no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—28no—
388C2×C8—112no—
389C2×C8—112no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—221no—
394C2×C8C2×C4×D1112yes—
395C2×C8C2×C4×D1112yes—
396C2×C8D4×D1112yes—
397C2×C8#434112yes—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—114no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—882no—
407C22⋊C4—82no—
408C22⋊C4—222no—
409C22⋊C4—222no—
410C22⋊C4—228no—
411C22⋊C4—444no—
412C22⋊C4—882no—
413C22⋊C4—882no—
414C42—112no—
415C42—112no—
416C42—221no—
417C42—221no—
418C42—882no—
419C11#2152411yescharacteristic, complemented, Sylow
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—224no—
427C23—442no—
428C23—442no—
429C23—442no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23#6694612yes—
434C23C2×D4×D1111yescharacteristic
435D4—224no—
436D4—224no—
437D4—442no—
438D4—442no—
439D4—888no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—112no—
453C2×C4—112no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—224no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—888no—
468C2×C4#6694612yes—
469C2×C4C22×C4×D1111yescharacteristic
470C2×C4C2×D4×D1111yescharacteristic
471C2×C4C2×#434111yescharacteristic
472C2×C4C2×#434311yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C8—22no—
476C8—222no—
477C8—222no—
478C8(C22⋊D11)⋊C414yes—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—444no—
487C22—444no—
488C22—444no—
489C22—882no—
490C22—882no—
491C22—882no—
492C22—882no—
493C22C2×#6694611yescharacteristic
494C22#1062312711yescharacteristic
495C22D11×#12111yescharacteristic
496C22#1062328811yescharacteristic
497C22#1062329711yescharacteristic
498C22#1062330011yescharacteristic
499C22#1062330011yescharacteristic
500C4—22no—
501C4—82no—
502C4—82no—
503C4—222no—
504C4—222no—
505C4—441no—
506C4—444no—
507C4—441no—
508C4C2×(C22⋊D11)⋊C411yescharacteristic
509C4#1062305311yescharacteristic
510C4#1062315511yescharacteristic
511C4#1062315811yescharacteristic
512C2—42no—
513C2—884no—
514C2#1307112211yescharacteristic
515C2#1307746711yescharacteristic
516C2#1307749011yescharacteristic
517C2#1307825911yescharacteristic
518C2#1307828711yescharacteristic
519C2#1307925611yescharacteristic
520C2#1307925911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1808C2
socleC23×C11C22×D4
prime radicalC2×#10622728C2
cosocleC22×C4×C11C24
hypercenter#1808D11
hypocenterC11#21524
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#10622485C2semidirect
3. C2×#10622714C2semidirect
4. #13071305C2semidirect
5. #13069480C2semidirect
6. #13069347C2semidirect
7. #13069311C2semidirect
8. #13069052C2semidirect
9. #107×Dic11C2semidirect
10. #13068440C2semidirect
11. C11×#1808C2semidirect
21. #10622728C4semidirect
48. C22×C8×C11C2×C4semidirect
57. #66983C2×C4semidirect
86. #66885C2×C4semidirect
87. #66882C2×C4semidirect
91. C8×Dic11D4semidirect
168. #1808D11semidirect
307. C22×C8C4×D11semidirect
419. C11#21524semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
C2×#106224852
C2×#106227142
#130713052
#130694802
#130693472
#130693112
#130690522
#107×Dic112
#130684402
C11×#18082
#2152411