Finite Group Databasebeta

← #14760715

Subgroups — #14760715

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078332C211yesmaximal, characteristic
2#13077515C212yesmaximal, complemented
3C2×#10622809C211yesmaximal, characteristic, complemented
4#13077038C211yesmaximal, characteristic, complemented
5#13069406C211yesmaximal, characteristic, complemented
6#13069288C212yesmaximal, complemented
7#13069114C212yesmaximal, complemented
8#13068667C211yesmaximal, characteristic, complemented
9#13068497C211yesmaximal, characteristic, complemented
10#13068418C212yesmaximal, complemented
11C11×#1976C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623353C2212yes—
14C2×#67001C2212yes—
15C2×#66960C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17#10623053C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C11×#421C2212yes—
20C11×#410C2212yes—
21C11×#405C2211yescharacteristic
22#10622850C2212yes—
23C2×#66901C2212yes—
24#10622809—21no—
25#10622809—21no—
26#10622809—21no—
27#10622809—21no—
28#10622805C412yescomplemented
29#10622790C414yescomplemented
30#10622773C412yescomplemented
31#10622737C2212yes—
32M16×Dic11C2211yescharacteristic
33C2×#66883C2211yescharacteristic
34C2×#66883C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622618C2212yes—
37#10622610C2212yes—
38#10622610C2211yescharacteristic
39#10622437—24no—
40#10622436—24no—
41#10622321—21no—
42#10622320—21no—
43#10622302—21no—
44C4×C8×D11—21no—
45#10622171C2212yes—
46#10622171C2212yes—
47#10622170C2212yes—
48C2×C11×#41C2312yes—
49C2×#4339C2311yescharacteristic
50C11×#135—21no—
51C11×#135—21no—
52C11×#135—21no—
53C11×#135—21no—
54C2×C11×Q16C2×C411yescharacteristic, complemented
55C2×C11×SD16C2×C412yescomplemented
56C2×C11×D8C2×C411yescharacteristic, complemented
57C2×C11×M16C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×#117C2312yes—
60C11×#117C2311yescharacteristic
61#67004—22no—
62#67003—24no—
63#67002—22no—
64#67001—22no—
65#67001—22no—
66#67001—22no—
67#67001—22no—
68#66995C2×C414yes—
69#66985C2×C414yes—
70C2×C4×Dic11C2311yescharacteristic
71C2×#4318—22no—
72C2×#4318C2312yes—
73C2×#4318C2312yes—
74C2×#4318C2311yescharacteristic
75C22×C11⋊C8—22no—
76C22×C11⋊C8C2311yescharacteristic
77#66960—21no—
78#66960—21no—
79#66960D412yes—
80#66960D412yes—
81#66954—21no—
82#66954—21no—
83#66954C2×C412yes—
84#66954C2×C412yes—
85C2×#4313—21no—
86C2×#4313—21no—
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66946—21no—
90#66940—21no—
91(C22⋊D11)⋊C4—22no—
92#66925—21no—
93C42×D11—21no—
94C11×#107—21no—
95C11×#106—21no—
96C11×#104—24no—
97C11×#99—24no—
98C11×#97—21no—
99C4×C8×C11—21no—
100#66901—22no—
101#66901—22no—
102#66900C2×C414yescomplemented
103#66897C2×C414yescomplemented
104#66886—24no—
105#66883—21no—
106#66883—21no—
107#66883C2×C412yescomplemented
108#66883C2×C412yescomplemented
109#66879—21no—
110C8×Dic11—21no—
111C8×Dic11D411yescharacteristic
112C8×Dic11D411yescharacteristic
113C8×Dic11D411yescharacteristic
114C8×Dic11D411yescharacteristic
115#66869—24no—
116#66867—21no—
117#66867—22no—
118C4×C11⋊C8—21no—
119C4×C11⋊C8—22no—
120#21558—111nomaximal, Sylow
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C2×Q8×C11C22×C412yes—
126C2×D4×C11—22no—
127C2×D4×C11C22×C412yes—
128C22×C4×C11—22no—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—21no—
131C22×Dic11—21no—
132#4339—21no—
133#4339—21no—
134#4339C22×C412yes—
135#4339C2×D412yes—
136C2×D44#4111yescharacteristic
137C2×C4×D11—22no—
138C2×C4×D11—21no—
139C2×Dic22#4111yescharacteristic
140C11×Q16—21no—
141C11×Q16—21no—
142C11×SD16—22no—
143C11×SD16—22no—
144C11×D8—21no—
145C11×D8—21no—
146C11×M16—21no—
147C11×M16C2×D412yes—
148C2×C8×C11—21no—
149C2×C8×C11C22×C411yescharacteristic
150C2×C8×C11C22×C411yescharacteristic
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11#4111yescharacteristic
154C2×C8×C11#4111yescharacteristic
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4#4112yes—
159C42×C11—21no—
160C42×C11—22no—
161#4326—24no—
162#4325—24no—
163#4324—24no—
164#4323—24no—
165(C2×D11)⋊C4—22no—
166Dic11⋊C4—22no—
167C4×Dic11—22no—
168C4×Dic11—21no—
169C4×Dic11C2×D411yescharacteristic
170C4×Dic11C2×D411yescharacteristic
171#4318—22no—
172#4318—22no—
173#4318—21no—
174#4318—22no—
175#4318—42no—
176#4318—42no—
177#4318C22×C414yes—
178#4318C22×C412yes—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—42no—
183C2×C11⋊C8—42no—
184C2×C11⋊C8C2×D411yescharacteristic
185C2×C11⋊C8C2×D411yescharacteristic
186C2×C11⋊C8C2×D411yescharacteristic
187C2×C11⋊C8C2×D411yescharacteristic
188C2×C11⋊C8#4111yescharacteristic
189C2×C11⋊C8#4111yescharacteristic
190#4313—22no—
191#4313—22no—
192#4313—22no—
193#4313—22no—
194C8×D11—22no—
195C8×D11—22no—
196C8×D11—22no—
197C8×D11—22no—
198#3067—111no—
199#2955—112no—
200C2×#443—111no—
201C4×#131—111no—
202#1976D1111yescharacteristic, complemented
203#1953—111no—
204#1932—112no—
205#1906—112no—
206#1814—111no—
207#1772—111no—
208#1757—112no—
209C23×C11—22no—
210C23×C11C2×#4111yescharacteristic
211C22×D11—21no—
212Q8×C11—22no—
213Q8×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—42no—
217D4×C11—42no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C22⋊D11—22no—
230C22⋊D11—22no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—42no—
235D44—21no—
236D44C4×D412yes—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—44no—
240Dic22—21no—
241Dic22C4×D412yes—
242C8×C11—22no—
243C8×C11C4×D411yescharacteristic
244C8×C11C4×D411yescharacteristic
245C8×C11C4×D411yescharacteristic
246C8×C11C4×D411yescharacteristic
247C11⋊C8—22no—
248C11⋊C8—24no—
249C11⋊C8—42no—
250C11⋊C8#12111yescharacteristic
251C11⋊C8#12111yescharacteristic
252C11⋊C8#12111yescharacteristic
253C11⋊C8#12111yescharacteristic
254#575—112no—
255C2×#135C2×D1111yescharacteristic
256C2×#131—112no—
257C2×#131—111no—
258C2×#131—111no—
259C4×#41—111no—
260#473—112no—
261#472—112no—
262#471—114no—
263#444—224no—
264#443—221no—
265#443—221no—
266#443—221no—
267#443—221no—
268#443—224no—
269#430—112no—
270C2×#108—111no—
271C2×#108—111no—
272#427C2×D1111yescharacteristic
273#421—112no—
274#421C2×D1112yes—
275C2×#104—112no—
276#413—112no—
277#410C2×D1112yes—
278#405—111no—
279#405—112no—
280#405—221no—
281#405—221no—
282#405C2×D1111yescharacteristic
283C4×M16—111no—
284C4×M16—221no—
285C2×C4×C8—111no—
286C2×C4×C8—221no—
287#344—112no—
288#344—112no—
289#339—112no—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11—82no—
293C22×C11C4×#4111yescharacteristic
294C22×C11#52511yescharacteristic
295C22×C11#53211yescharacteristic
296C2×D11—22no—
297C2×D11—42no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—82no—
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×C4×D411yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11#52911yescharacteristic
305Dic11—22no—
306Dic11—22no—
307Dic11—41no—
308C2×#41—111no—
309C2×#41C22×D1112yes—
310#137—114no—
311#137—222no—
312AGL(1,ℤ/8)—114no—
313AGL(1,ℤ/8)—222no—
314#135—21no—
315#135—21no—
316#135—21no—
317#135—21no—
318#135—224no—
319C2×Q16C4×D1111yescharacteristic, complemented
320C2×SD16C4×D1112yescomplemented
321C2×D8C4×D1111yescharacteristic, complemented
322#131—112no—
323#131—112no—
324#131—112no—
325#131—112no—
326#131—221no—
327#131—221no—
328#131—222no—
329#131—222no—
330#131—222no—
331#131—222no—
332#131—221no—
333#131—221no—
334C2×M16—111no—
335C2×M16—112no—
336C2×M16—112no—
337C2×M16—221no—
338C2×M16—222no—
339C2×M16—221no—
340C2×M16C22×D1111yescharacteristic
341C22×C8—111no—
342C22×C8—221no—
343C22×C8—222no—
344C22×C8—221no—
345C22×C8C22×D1111yescharacteristic
346C4×Q8—221no—
347C4×D4—221no—
348C4×D4—222no—
349#117—221no—
350#117C22×D1112yes—
351#117C22×D1111yescharacteristic
352C2×C42—111no—
353C2×C42—221no—
354#108—112no—
355#108—112no—
356#108—224no—
357#108—221no—
358#108—221no—
359#107—21no—
360#106—21no—
361#104—24no—
362#104—224no—
363#104—222no—
364#104—222no—
365#101—114no—
366#100—114no—
367#99—24no—
368#97—21no—
369#97—221no—
370#97—222no—
371#97—221no—
372C4×C8—21no—
373C4×C8—111no—
374C4×C8—111no—
375C4×C8—111no—
376C4×C8—111no—
377C4×C8—221no—
378C4×C8—222no—
379C4×C8—221no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—82no—
384C2×C11C4×#12111yescharacteristic
385D11—42no—
386#41—22no—
387#41—22no—
388#41—22no—
389#41—22no—
390#41—112no—
391#41—112no—
392#41—221no—
393#41—221no—
394C2×Q8—111no—
395C2×Q8C2×C4×D1112yes—
396C2×D4—22no—
397C2×D4—111no—
398C2×D4—221no—
399C2×D4C2×C4×D1112yes—
400C22×C4—22no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4C23×D1111yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—224no—
408SD16—22no—
409SD16—22no—
410SD16—224no—
411SD16—224no—
412D8—21no—
413D8—21no—
414D8—224no—
415M16—21no—
416M16—112no—
417M16—114no—
418M16—222no—
419M16—222no—
420M16—221no—
421M16—222no—
422M16—222no—
423M16—222no—
424M16—222no—
425M16—222no—
426M16—442no—
427M16—442no—
428M16D4×D1112yes—
429C2×C8—21no—
430C2×C8—111no—
431C2×C8—111no—
432C2×C8—111no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—221no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—442no—
444C2×C8—442no—
445C2×C8C2×C4×D1111yescharacteristic
446C2×C8C2×C4×D1111yescharacteristic
447C2×C8D4×D1111yescharacteristic
448C2×C8D4×D1111yescharacteristic
449C2×C8#434111yescharacteristic
450C2×C8#434111yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—222no—
454C22⋊C4—22no—
455C22⋊C4—222no—
456C22⋊C4#434112yes—
457C42—21no—
458C42—22no—
459C42—111no—
460C42—111no—
461C42—222no—
462C42—221no—
463C11#2155811yescharacteristic, complemented, Sylow
464C23—22no—
465C23—221no—
466C23C2×#434111yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—112no—
470Q8—221no—
471D4—22no—
472D4—22no—
473D4—42no—
474D4—42no—
475D4—112no—
476D4—222no—
477D4—222no—
478D4—221no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—221no—
489C2×C4—444no—
490C2×C4—442no—
491C2×C4C22×C4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×#434111yescharacteristic
495C2×C4#41×D1111yescharacteristic
496C2×C4#41×D1111yescharacteristic
497C8—22no—
498C8—111no—
499C8—111no—
500C8—111no—
501C8—111no—
502C8—222no—
503C8—224no—
504C8—442no—
505C8(C22⋊D11)⋊C411yescharacteristic
506C8(C22⋊D11)⋊C411yescharacteristic
507C8(C22⋊D11)⋊C411yescharacteristic
508C8(C22⋊D11)⋊C411yescharacteristic
509C22—41no—
510C22—42no—
511C22—82no—
512C22—222no—
513C22—442no—
514C22C4×#434111yescharacteristic
515C22#1062313711yescharacteristic
516C22#1062324711yescharacteristic
517C4—42no—
518C4—42no—
519C4—82no—
520C4—222no—
521C4—222no—
522C4—441no—
523C4C2×(C22⋊D11)⋊C411yescharacteristic
524C4C4×D4×D1111yescharacteristic
525C4D11×#12111yescharacteristic
526C4#1062321111yescharacteristic
527C2—21no—
528C2—21no—
529C2—21no—
530C2—82no—
531C2—442no—
532C2#1307113211yescharacteristic
subgroupG/H
centerC4D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1976C2
socleC2×C11C4×#121
prime radical#13078332C2
cosocleC22×C4×C11C24
hypercenter#1976D11
hypocenterC11#21558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1976

Complements

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

NH ≅ G/Ntype
2. #13077515C2semidirect
3. C2×#10622809C2semidirect
4. #13077038C2semidirect
5. #13069406C2semidirect
6. #13069288C2semidirect
7. #13069114C2semidirect
8. #13068667C2semidirect
9. #13068497C2semidirect
10. #13068418C2semidirect
11. C11×#1976C2semidirect
28. #10622805C4semidirect
29. #10622790C4semidirect
30. #10622773C4semidirect
54. C2×C11×Q16C2×C4semidirect
55. C2×C11×SD16C2×C4semidirect
56. C2×C11×D8C2×C4semidirect
102. #66900C2×C4semidirect
103. #66897C2×C4semidirect
107. #66883C2×C4semidirect
108. #66883C2×C4semidirect
202. #1976D11semidirect
319. C2×Q16C4×D11semidirect
320. C2×SD16C4×D11semidirect
321. C2×D8C4×D11semidirect
463. C11#21558semidirect

Maximal subgroups

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

subgroupindex
#130783322
#130775152
C2×#106228092
#130770382
#130694062
#130692882
#130691142
#130686672
#130684972
#130684182
C11×#19762
#2155811