Finite Group Databasebeta

← #14769501

Subgroups — #14769501

Order 2816.

1494 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66972C211yesmaximal, characteristic
2C2×#10622324C211yesmaximal, characteristic, complemented
3C2×#10622482C211yesmaximal, characteristic, complemented
4#13071445C212yesmaximal, complemented
5#13069488C211yesmaximal, characteristic, complemented
6#13068953C212yesmaximal, complemented
7#13068947C212yesmaximal, complemented
8#13068638C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10#13068393C211yesmaximal, characteristic, complemented
11C11×#1971C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C22×#4325C2212yes—
15C2×#66972—24no—
16C2×#66972—24no—
17C2×#66972C418yescomplemented
18C22×D88C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66946C2212yes—
21C2×C4×D44C2212yes—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#97C2211yescharacteristic
25C11×#391C2212yes—
26#10622843C2212yes—
27C2×#66899C2212yes—
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622600C2212yes—
33C2×#66873C2212yes—
34C4×(C2×D11)⋊C4C2211yescharacteristic
35#10622482—24no—
36#10622324—24no—
37#10622278—22no—
38#10622278—22no—
39#10622277—22no—
40D11×#95—22no—
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C2×#4343—24no—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—42no—
49C2×#4343—42no—
50C2×#4343C2×C418yescomplemented
51C22×D44—22no—
52C22×D44C2312yes—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11C2311yescharacteristic
57C2×C11×Q16—22no—
58C2×C11×Q16—22no—
59C2×C11×Q16C2×C414yescomplemented
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—24no—
65C2×#4325—24no—
66C2×#4325C2×C418yescomplemented
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4D412yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75#66972—232no—
76C2×D88C2×C414yes—
77C2×D88D414yes—
78C2×D88D414yes—
79C2×C8×D11—22no—
80C2×C8×D11—22no—
81C2×C8×D11C2×C414yescomplemented
82#66946—24no—
83#66946—42no—
84C4×D44—24no—
85C4×D44—42no—
86C11×#106—22no—
87C11×#103—42no—
88C11×#97—22no—
89C11×#95—22no—
90C11×#95—22no—
91#66899—42no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95D412yes—
96#66885—24no—
97(C2×D11)⋊C8—22no—
98#66881—22no—
99#66879—22no—
100#66873—24no—
101#22438—111nomaximal, Sylow
102C23×D11—22no—
103C23×D11C2×D411yescharacteristic
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11C22×C414yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—22no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D411yescharacteristic
117#4343—216no—
118#4343—48no—
119#4343—48no—
120#4343—48no—
121C2×D44—28no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44—22no—
125C2×D44—44no—
126C2×D44—44no—
127C2×D44C22×C414yes—
128C2×D44C2×D414yes—
129C2×D44C2×D414yes—
130C2×C4×D11—28no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—44no—
136C2×C4×D11—44no—
137C2×C4×D11—44no—
138C2×C4×D11—44no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—82no—
142C2×C4×D11—82no—
143C2×C4×D11C22×C412yes—
144C2×C4×D11#4112yes—
145C11×Q16—28no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C22×C412yes—
150C2×C8×C11C2×D412yes—
151C2×C8×C11C2×D412yes—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C42×C11—21no—
155C42×C11—21no—
156#4325—216no—
157(C2×D11)⋊C4—42no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—44no—
160(C2×D11)⋊C4—82no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8C22×C412yes—
171D88C22⋊C4116yescomplemented
172C8×D11—28no—
173C22×#135—111no—
174C2×#442—111no—
175C2×#442—111no—
176#2339—112no—
177#1971—111no—
178#1971D1111yescharacteristic, complemented
179#1877—112no—
180#1877—112no—
181#1807—111no—
182#1788—112no—
183#1752—111no—
184C23×C11C22×D411yescharacteristic
185C22×D11—24no—
186C22×D11—24no—
187C22×D11—24no—
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—42no—
196C22×D11C4×D412yes—
197Q8×C11—24no—
198Q8×C11—24no—
199Q8×C11—42no—
200Q8×C11—42no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11C23×C411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C11H(5,𝔽2)11yescharacteristic
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11C4×D412yes—
225D44—24no—
226D44—24no—
227D44—24no—
228D44—416no—
229D44C2×C22⋊C418yes—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—416no—
235C4×D11—88no—
236C4×D11—88no—
237C8×C11—41no—
238C8×C11C2×C22⋊C414yes—
239C11⋊C8—22no—
240C11⋊C8—41no—
241C22×#41—112no—
242C2×#135—118no—
243C2×#135—224no—
244C2×#135—224no—
245C22×Q16C2×D1111yescharacteristic
246C22×SD16—112no—
247C22×D8—111no—
248C23×C8—111no—
249C2×C4×D4—112no—
250C2×C4×D4—112no—
251#442—224no—
252#442—224no—
253C2×#106—111no—
254C2×#106C2×D1111yescharacteristic
255C2×#103—112no—
256C2×#103C2×D1112yes—
257C2×#102—112no—
258C2×#102—112no—
259C2×C22⋊C8—111no—
260C2×#97—111no—
261C2×#97C2×D1111yescharacteristic
262#391—112no—
263#391C2×D1112yes—
264#386—222no—
265#386—222no—
266#381—222no—
267#380—112no—
268C4×C22⋊C4—111no—
269C2×#95—222no—
270#340—112no—
271#336—111no—
272#336—111no—
273C22×C11C2×C4×D411yescharacteristic
274C22×C11D4211yescharacteristic
275C22×C11D4211yescharacteristic
276C22×C11#57512yes—
277C22×C11#57712yes—
278C2×D11—28no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—42no—
285C2×D11—42no—
286C2×D11—44no—
287C2×D11—44no—
288C2×D11—44no—
289C2×D11—44no—
290C4×C11—44no—
291C4×C11—42no—
292C4×C11—82no—
293C4×C11C22×C22⋊C411yescharacteristic
294C4×C11#51811yescharacteristic
295C4×C11#54611yescharacteristic
296C4×C11#54611yescharacteristic
297Dic11—22no—
298Dic11—42no—
299Dic11—82no—
300C2×#41—118no—
301C2×#41—224no—
302C2×#41—224no—
303C2×#41—224no—
304C2×#41—442no—
305C2×#41—442no—
306C22×Q8C22×D1112yes—
307C22×D4—112no—
308C22×D4—222no—
309C23×C4—111no—
310C23×C4—222no—
311C23×C4—222no—
312C23×C4—222no—
313#135—2232no—
314C2×Q16—22no—
315C2×Q16—22no—
316C2×Q16C4×D1114yescomplemented
317C2×SD16—118no—
318C2×SD16—224no—
319C2×SD16—224no—
320C2×D8—114no—
321C2×D8—114no—
322C2×D8—114no—
323C22×C8—111no—
324C22×C8—114no—
325C22×C8—111no—
326C22×C8—222no—
327C22×C8—222no—
328C22×C8C22×D1111yescharacteristic
329C22×C8C22×D1111yescharacteristic
330C4×D4—224no—
331C4×D4—224no—
332C4×D4—442no—
333C4×D4—442no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C42—111no—
341C2×C42C22×D1111yescharacteristic
342#106—22no—
343#106—222no—
344#103—42no—
345#103—442no—
346#102—224no—
347#102—224no—
348C22⋊C8—222no—
349#97—22no—
350#97—222no—
351#95—22no—
352#95—22no—
353#95—112no—
354#95—222no—
355#95—222no—
356#95—222no—
357C2×C11D4×C22⋊C411yescharacteristic
358C2×C11#294311yescharacteristic
359C2×C11#295211yescharacteristic
360C2×C11#326712yes—
361C2×C11#326712yes—
362D11—42no—
363D11—48no—
364C24—111no—
365C24—222no—
366#41—2216no—
367#41—448no—
368#41—448no—
369#41—448no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8C2×C4×D1114yes—
376C2×D4—114no—
377C2×D4—114no—
378C2×D4—114no—
379C2×D4—228no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—222no—
383C2×D4—444no—
384C2×D4—444no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—111no—
388C22×C4—112no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—228no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—221no—
395C22×C4—221no—
396C22×C4—222no—
397C22×C4—444no—
398C22×C4—444no—
399C22×C4—444no—
400C22×C4—444no—
401C22×C4—444no—
402C22×C4—444no—
403C22×C4—882no—
404C22×C4—882no—
405C22×C4D4×D1112yes—
406C22×C4C23×D1111yescharacteristic
407Q16—28no—
408SD16—2216no—
409D8—1116no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—112no—
414C2×C8—221no—
415C2×C8—221no—
416C2×C8—228no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—221no—
420C2×C8C2×C4×D1112yes—
421C2×C8D4×D1112yes—
422C2×C8D4×D1112yes—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C22⋊C4—442no—
428C22⋊C4—444no—
429C22⋊C4—444no—
430C22⋊C4—882no—
431C42—21no—
432C42—21no—
433C42—221no—
434C42—221no—
435C11#2243811yescharacteristic, complemented, Sylow
436C23—112no—
437C23—224no—
438C23—221no—
439C23—222no—
440C23—222no—
441C23—224no—
442C23—224no—
443C23—221no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23—442no—
448C23C2×D4×D1111yescharacteristic
449Q8—24no—
450Q8—24no—
451Q8—42no—
452Q8—42no—
453D4—118no—
454D4—224no—
455D4—224no—
456D4—224no—
457D4—4416no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—112no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—4416no—
478C2×C4—442no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—888no—
482C2×C4—888no—
483C2×C4C22×C4×D1111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C2×C4#6703711yescharacteristic
487C2×C4#41×D1111yescharacteristic
488C2×C4#6704211yescharacteristic
489C8—41no—
490C8—222no—
491C8—441no—
492C8C22⋊C4×D1114yes—
493C22—222no—
494C22—228no—
495C22—222no—
496C22—222no—
497C22—444no—
498C22—442no—
499C22—444no—
500C22—444no—
501C22—442no—
502C22—444no—
503C22—444no—
504C22—444no—
505C22C4×D4×D1111yescharacteristic
506C22#1062314011yescharacteristic
507C22#1062324811yescharacteristic
508C22#1062330812yes—
509C22#1062330912yes—
510C4—44no—
511C4—42no—
512C4—82no—
513C4—222no—
514C4—442no—
515C4—882no—
516C4C2×C22⋊C4×D1111yescharacteristic
517C4#1062307611yescharacteristic
518C4#1062314311yescharacteristic
519C4#1062320711yescharacteristic
520C2—442no—
521C2—448no—
522C2#1307143711yescharacteristic
523C2#1307741511yescharacteristic
524C2#1307749611yescharacteristic
525C2#1308014012yes—
526C2#1308014812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1971C2
socleC23×C11C22×D4
prime radicalC22×#66972C2
cosocleC22×C4×C11C24
hypercenter#1971D11
hypocenterC11#22438
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
2. C2×#10622324C2semidirect
3. C2×#10622482C2semidirect
4. #13071445C2semidirect
5. #13069488C2semidirect
6. #13068953C2semidirect
7. #13068947C2semidirect
8. #13068638C2semidirect
9. #13068555C2semidirect
10. #13068393C2semidirect
11. C11×#1971C2semidirect
17. C2×#66972C4semidirect
50. C2×#4343C2×C4semidirect
59. C2×C11×Q16C2×C4semidirect
66. C2×#4325C2×C4semidirect
81. C2×C8×D11C2×C4semidirect
171. D88C22⋊C4semidirect
178. #1971D11semidirect
316. C2×Q16C4×D11semidirect
435. C11#22438semidirect

Maximal subgroups

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

subgroupindex
C22×#669722
C2×#106223242
C2×#106224822
#130714452
#130694882
#130689532
#130689472
#130686382
#130685552
#130683932
C11×#19712
#2243811