Finite Group Databasebeta

← #14760724

Subgroups — #14760724

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077519C212yesmaximal, complemented
2C2×#10622810C211yesmaximal, characteristic, complemented
3#13077042C211yesmaximal, characteristic, complemented
4#13069515C211yesmaximal, characteristic, complemented
5#13069407C211yesmaximal, characteristic, complemented
6#13069287C212yesmaximal, complemented
7#13069119C212yesmaximal, complemented
8#13068670C211yesmaximal, characteristic, complemented
9#13068503C211yesmaximal, characteristic, complemented
10#13068419C212yesmaximal, complemented
11C11×#3067C211yesmaximal, characteristic
12C11×#575C2212yes—
13C2×C11×#135C2211yescharacteristic
14C2×C11×#131C2211yescharacteristic
15#41×Dic11C2211yescharacteristic
16C2×#67001C2212yes—
17C2×#67001C2211yescharacteristic
18C11×#473C412yescomplemented
19C11×#472C412yescomplemented
20C11×#471C414yescomplemented
21C2×C11×#108C2211yescharacteristic
22C11×#413C2212yes—
23#10622853C2212yes—
24#10622849C2212yes—
25#10622849C2212yes—
26C2×#66901C2212yes—
27#10622810—24no—
28#10622810—21no—
29#10622810—21no—
30#10622810—21no—
31#10622810—21no—
32#10622809—24no—
33#10622738C2212yes—
34#10622735—21no—
35#10622735C2212yes—
36#10622735C2211yescharacteristic
37M16×Dic11—21no—
38M16×Dic11C2211yescharacteristic
39C2×#66883C2211yescharacteristic
40#10622719C2211yescharacteristic
41#10622714—21no—
42#10622714C2211yescharacteristic
43C2×#66879—21no—
44C2×#66879C2211yescharacteristic
45#10622197C2212yes—
46#10622197C2212yes—
47#10622193C2212yes—
48C2×C11×#41C2312yes—
49C2×C11×#41C2311yescharacteristic
50C11×#137—22no—
51C11×#137C2×C414yes—
52C11×AGL(1,ℤ/8)—22no—
53C11×AGL(1,ℤ/8)C2×C414yes—
54C11×#135—24no—
55C11×#135—21no—
56C11×#135—21no—
57C11×#135—21no—
58C11×#135—21no—
59C2×C11×Q16C2×C411yescharacteristic, complemented
60C2×C11×SD16C2×C412yescomplemented
61C2×C11×D8C2×C411yescharacteristic, complemented
62C11×#131—21no—
63C11×#131—21no—
64C11×#131C2×C412yes—
65C11×#131C2×C412yes—
66C2×C11×M16—21no—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2312yes—
69C22×C8×C11—21no—
70C22×C8×C11C2311yescharacteristic
71#67001—22no—
72#67001—22no—
73#67001—22no—
74#67001—22no—
75#67001—22no—
76#67001D414yes—
77Q8×Dic11—21no—
78D4×Dic11—21no—
79D4×Dic11—22no—
80#66979—21no—
81#66979C2312yes—
82#66979C2311yescharacteristic
83C2×C4×Dic11—21no—
84C2×C4×Dic11C2311yescharacteristic
85C2×#4318—21no—
86C2×#4318—22no—
87C2×#4318C2312yes—
88C2×#4318C2311yescharacteristic
89C22×C11⋊C8—21no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8C2311yescharacteristic
92C11×#108C2×C412yescomplemented
93C11×#108C2×C412yescomplemented
94C11×#101C2×C414yescomplemented
95C11×#100C2×C414yescomplemented
96#66901—24no—
97#66901—22no—
98#66901—22no—
99#66901—24no—
100#66898—24no—
101#66883—21no—
102#66883—21no—
103#66883—24no—
104#66882—21no—
105#66881—21no—
106#66879—21no—
107#66879—21no—
108#66879—21no—
109#66879—22no—
110#66879D411yescharacteristic
111#66879D411yescharacteristic
112#66879D411yescharacteristic
113#66879D411yescharacteristic
114C8×Dic11—21no—
115C8×Dic11—21no—
116C8×Dic11—21no—
117C8×Dic11—22no—
118#21559—111nomaximal, Sylow
119C11×#41—21no—
120C11×#41—21no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41C22×C412yes—
126C11×#41C2×D412yes—
127C2×Q8×C11C22×C412yes—
128C2×Q8×C11#4111yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11C22×C412yes—
132C2×D4×C11#4111yescharacteristic
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—22no—
137C22×Dic11—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—24no—
141C11×SD16—22no—
142C11×SD16—22no—
143C11×SD16—24no—
144C11×SD16—24no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8—24no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—21no—
151C11×M16—22no—
152C11×M16C22×C412yes—
153C11×M16C22×C414yes—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—22no—
158C2×C8×C11C22×C411yescharacteristic
159C2×C8×C11C22×C411yescharacteristic
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11#4111yescharacteristic
163C2×C8×C11#4111yescharacteristic
164C22⋊Dic11—22no—
165C22⋊Dic11—22no—
166C22⋊Dic11#4112yes—
167C4⋊Dic11—22no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11—21no—
172C4×Dic11—22no—
173C4×Dic11—21no—
174C4×Dic11C2×D411yescharacteristic
175C4×Dic11C2×D411yescharacteristic
176#4318—24no—
177#4318—22no—
178#4318—22no—
179#4318—21no—
180#4318—42no—
181#4318—42no—
182#4318C2×D412yes—
183C2×C11⋊C8—24no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—42no—
187C2×C11⋊C8—42no—
188C2×C11⋊C8C2×D412yes—
189C2×C11⋊C8C2×D411yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191C2×C11⋊C8#4112yes—
192#3067D1111yescharacteristic
193#2955—112no—
194C2×#444—111no—
195#2875—111no—
196#1976—111no—
197#1953—111no—
198#1932—112no—
199#1906—112no—
200#1814—111no—
201#1773—111no—
202#1757—112no—
203C23×C11—21no—
204C23×C11—22no—
205C23×C11C2×#4111yescharacteristic
206Q8×C11—21no—
207Q8×C11—22no—
208Q8×C11—22no—
209Q8×C11C4×D412yes—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—21no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11C4×D412yes—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×Dic11—21no—
231C2×Dic11—22no—
232C2×Dic11—21no—
233C2×Dic11—42no—
234C2×Dic11—81no—
235C2×Dic11—82no—
236C8×C11—22no—
237C8×C11—24no—
238C8×C11C4×D411yescharacteristic
239C8×C11C4×D411yescharacteristic
240C8×C11C4×D411yescharacteristic
241C8×C11C4×D411yescharacteristic
242C11⋊C8—22no—
243C11⋊C8—42no—
244C11⋊C8#12112yes—
245C11⋊C8#12112yes—
246#575C2×D1112yes—
247C2×#135C2×D1111yescharacteristic
248C2×#131—111no—
249C2×#131—112no—
250C2×#131C2×D1111yescharacteristic
251C4×#41—111no—
252#473Dic1112yescomplemented
253#472Dic1112yescomplemented
254#471Dic1114yescomplemented
255#444—221no—
256#444—221no—
257#444—221no—
258#444—221no—
259#444—224no—
260#443—224no—
261#430—112no—
262C2×#108—111no—
263C2×#108C2×D1111yescharacteristic
264#427—111no—
265#421—112no—
266#421—112no—
267C2×#104—112no—
268#413C2×D1112yes—
269#410—112no—
270#405—111no—
271#405—112no—
272#405—111no—
273#405—221no—
274#405—221no—
275C4×M16—111no—
276C4×M16—221no—
277C2×#97—111no—
278C2×#97—221no—
279#344—112no—
280#344—112no—
281#339—112no—
282C22×C11—22no—
283C22×C11—41no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—82no—
287C22×C11C4×#4111yescharacteristic
288C22×C11#52511yescharacteristic
289C22×C11#53211yescharacteristic
290C4×C11—22no—
291C4×C11—42no—
292C4×C11C2×C4×D411yescharacteristic
293C4×C11C2×C4×D411yescharacteristic
294C4×C11C2×#12111yescharacteristic
295C4×C11#52911yescharacteristic
296Dic11—42no—
297Dic11—41no—
298Dic11—41no—
299Dic11—82no—
300C2×#41C22×D1111yescharacteristic
301C2×#41C22×D1112yes—
302#137—22no—
303#137C2×Dic1114yes—
304AGL(1,ℤ/8)—22no—
305AGL(1,ℤ/8)C2×Dic1114yes—
306#135—24no—
307#135—21no—
308#135—21no—
309#135—21no—
310#135—21no—
311C2×Q16C2×Dic1111yescharacteristic, complemented
312C2×SD16C2×Dic1112yescomplemented
313C2×D8C2×Dic1111yescharacteristic, complemented
314#131—21no—
315#131—21no—
316#131—114no—
317#131—222no—
318#131—222no—
319#131—222no—
320#131—222no—
321#131—222no—
322#131C2×Dic1112yes—
323#131C2×Dic1112yes—
324C2×M16—21no—
325C2×M16—111no—
326C2×M16—112no—
327C2×M16—221no—
328C2×M16—222no—
329C2×M16C22×D1111yescharacteristic
330C2×M16C22×D1112yes—
331C22×C8—21no—
332C22×C8—111no—
333C22×C8—221no—
334C22×C8—222no—
335C22×C8C22×D1111yescharacteristic
336C4×Q8—221no—
337C4×D4—222no—
338C4×D4—221no—
339#117—111no—
340#117—112no—
341#117—221no—
342C2×C42—111no—
343C2×C42—221no—
344#108—224no—
345#108—221no—
346#108—221no—
347#108C2×Dic1112yescomplemented
348#108C2×Dic1112yescomplemented
349#107—221no—
350#106—221no—
351#104—222no—
352#104—222no—
353#104—224no—
354#104—224no—
355#101C2×Dic1114yescomplemented
356#100C2×Dic1114yescomplemented
357#99—224no—
358#97—111no—
359#97—111no—
360#97—111no—
361#97—111no—
362#97—221no—
363#97—221no—
364#97—222no—
365#97—221no—
366C4×C8—221no—
367C4×C8—221no—
368C4×C8—222no—
369C4×C8—221no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—42no—
374C2×C11—82no—
375C2×C11C4×#12111yescharacteristic
376#41—21no—
377#41—21no—
378#41—22no—
379#41—22no—
380#41—22no—
381#41—22no—
382#41D4×D1112yes—
383#41C22×Dic1112yes—
384C2×Q8#434111yescharacteristic
385C2×Q8C22×Dic1112yes—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4#434111yescharacteristic
389C2×D4C22×Dic1112yes—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4C23×D1111yescharacteristic
395Q16—24no—
396Q16—21no—
397Q16—21no—
398SD16—24no—
399SD16—24no—
400SD16—22no—
401SD16—22no—
402D8—24no—
403D8—21no—
404D8—21no—
405M16—21no—
406M16—22no—
407M16—22no—
408M16—22no—
409M16—112no—
410M16—224no—
411M16—221no—
412M16—222no—
413M16—222no—
414M16—442no—
415M16—442no—
416M16C22×Dic1112yes—
417M16C22×Dic1114yes—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—111no—
423C2×C8—112no—
424C2×C8—111no—
425C2×C8—112no—
426C2×C8—224no—
427C2×C8—221no—
428C2×C8—222no—
429C2×C8—442no—
430C2×C8—442no—
431C2×C8D4×D1111yescharacteristic
432C2×C8D4×D1111yescharacteristic
433C2×C8#434111yescharacteristic
434C2×C8#434111yescharacteristic
435C2×C8C22×Dic1111yescharacteristic
436C2×C8C22×Dic1111yescharacteristic
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—222no—
440C22⋊C4—112no—
441C22⋊C4—222no—
442C22⋊C4—222no—
443C42—111no—
444C42—111no—
445C42—222no—
446C42—221no—
447C42—221no—
448C42—222no—
449C11#2155911yescharacteristic, complemented, Sylow
450C23—21no—
451C23—22no—
452C23#41×D1111yescharacteristic
453Q8—21no—
454Q8—22no—
455Q8—22no—
456Q8D4×Dic1112yes—
457D4—22no—
458D4—22no—
459D4—22no—
460D4—22no—
461D4—21no—
462D4—42no—
463D4—42no—
464D4D4×Dic1112yes—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—222no—
474C2×C4—442no—
475C2×C4—881no—
476C2×C4—882no—
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×#434111yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4C23×Dic1111yescharacteristic
483C8—22no—
484C8—24no—
485C8—112no—
486C8—112no—
487C8—222no—
488C8—442no—
489C8D4×Dic1111yescharacteristic
490C8D4×Dic1111yescharacteristic
491C8D4×Dic1111yescharacteristic
492C8D4×Dic1111yescharacteristic
493C22—22no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—82no—
498C22#1062312711yescharacteristic
499C22#1062313711yescharacteristic
500C22#41×Dic1111yescharacteristic
501C4—22no—
502C4—42no—
503C4—441no—
504C4—441no—
505C4—442no—
506C4—882no—
507C4#1062313111yescharacteristic
508C4D11×#12111yescharacteristic
509C4C2×D4×Dic1111yescharacteristic
510C4C2×D4×Dic1111yescharacteristic
511C2—21no—
512C2—21no—
513C2—21no—
514C2—42no—
515C2—82no—
516C2#121×Dic1111yescharacteristic
subgroupG/H
centerC4D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3067C2
socleC2×C11C4×#121
cosocleC22×C4×C11C24
hypercenter#3067D11
hypocenterC11#21559
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. #13077519C2semidirect
2. C2×#10622810C2semidirect
3. #13077042C2semidirect
4. #13069515C2semidirect
5. #13069407C2semidirect
6. #13069287C2semidirect
7. #13069119C2semidirect
8. #13068670C2semidirect
9. #13068503C2semidirect
10. #13068419C2semidirect
18. C11×#473C4semidirect
19. C11×#472C4semidirect
20. C11×#471C4semidirect
59. C2×C11×Q16C2×C4semidirect
60. C2×C11×SD16C2×C4semidirect
61. C2×C11×D8C2×C4semidirect
92. C11×#108C2×C4semidirect
93. C11×#108C2×C4semidirect
94. C11×#101C2×C4semidirect
95. C11×#100C2×C4semidirect
252. #473Dic11semidirect
253. #472Dic11semidirect
254. #471Dic11semidirect
311. C2×Q16C2×Dic11semidirect
312. C2×SD16C2×Dic11semidirect
313. C2×D8C2×Dic11semidirect
347. #108C2×Dic11semidirect
348. #108C2×Dic11semidirect
355. #101C2×Dic11semidirect
356. #100C2×Dic11semidirect
449. C11#21559semidirect

Maximal subgroups

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

subgroupindex
#130775192
C2×#106228102
#130770422
#130695152
#130694072
#130692872
#130691192
#130686702
#130685032
#130684192
C11×#30672
#2155911