Finite Group Databasebeta

← #14760705

Subgroups — #14760705

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#13078336C211yesmaximal, characteristic
2#13077515C212yesmaximal, complemented
3C2×#10622508C211yesmaximal, characteristic, complemented
4#131×Dic11C211yesmaximal, characteristic, complemented
5#13069512C211yesmaximal, characteristic, complemented
6#13069404C211yesmaximal, characteristic, complemented
7#13069283C212yesmaximal, complemented
8#13069115C212yesmaximal, complemented
9#13068497C211yesmaximal, characteristic, complemented
10#13068415C212yesmaximal, complemented
11C11×#1814C211yesmaximal, characteristic, complemented
12C2×C11×#131C2211yescharacteristic
13#41×Dic11C2211yescharacteristic
14#10623353C2212yes—
15C2×#67001C2211yescharacteristic
16C2×#66960C2212yes—
17C2×#66957C2211yescharacteristic
18C2×C11×#108C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C11×#421C2212yes—
21#10622756C412yescomplemented
22#10622755C412yescomplemented
23#10622754C414yescomplemented
24C2×#66889C2212yes—
25#10622745C2212yes—
26#10622737C2212yes—
27#10622735—21no—
28#10622735C2211yescharacteristic
29M16×Dic11—21no—
30M16×Dic11C2211yescharacteristic
31C2×#66883C2211yescharacteristic
32#10622714—21no—
33#10622714C2211yescharacteristic
34C2×C8×Dic11—21no—
35C2×C8×Dic11C2211yescharacteristic
36#10622619C2212yes—
37#10622618C2212yes—
38#10622610C2212yes—
39#10622508—21no—
40#10622508—21no—
41#10622508—21no—
42#10622508—21no—
43#10622437—24no—
44#10622436—24no—
45C11×#344C2212yes—
46#10622194C2212yes—
47#10622170C2212yes—
48C2×C11×#41C2311yescharacteristic
49C2×#4339C2312yes—
50C11×#131—21no—
51C11×#131—21no—
52C11×#131C2×C412yes—
53C11×#131C2×C412yes—
54C2×C11×M16—21no—
55C2×C11×M16C2312yes—
56C2×C11×M16C2311yescharacteristic
57C22×C8×C11—21no—
58C22×C8×C11C2311yescharacteristic
59C11×#117C2312yes—
60#67004C2×C414yes—
61#67003—24no—
62#67002C2×C414yes—
63#67001—21no—
64#67001—21no—
65#67001D412yes—
66#67001D412yes—
67Q8×Dic11—21no—
68#66995—22no—
69D4×Dic11—21no—
70D4×Dic11—22no—
71#66985—22no—
72#66979—21no—
73#66979C2311yescharacteristic
74C2×C4×Dic11—21no—
75C2×C4×Dic11C2311yescharacteristic
76C2×#4318—21no—
77C2×#4318C2312yes—
78C2×#4318C2311yescharacteristic
79C22×C11⋊C8—21no—
80C22×C11⋊C8C2311yescharacteristic
81#66960—22no—
82#66960—22no—
83#66960—22no—
84#66960—22no—
85C2×Dic44C2×C411yescharacteristic, complemented
86#66957—21no—
87#66957—21no—
88#66957—21no—
89#66957—21no—
90C2×D88C2×C411yescharacteristic, complemented
91C2×#4314C2×C412yescomplemented
92C2×#4313—22no—
93C2×C8×D11—22no—
94C11×#108—21no—
95C11×#108—21no—
96C11×#107—21no—
97C11×#106—21no—
98C11×#104—24no—
99#66889—22no—
100#66889—22no—
101#66888C2×C414yescomplemented
102#66887C2×C414yescomplemented
103#66886—24no—
104#66883C2×C412yescomplemented
105#66883C2×C412yescomplemented
106#66879—21no—
107#66879—21no—
108#66879—21no—
109C8×Dic11—21no—
110C8×Dic11—21no—
111C8×Dic11—21no—
112C8×Dic11D411yescharacteristic
113C8×Dic11D411yescharacteristic
114C8×Dic11D411yescharacteristic
115C8×Dic11D411yescharacteristic
116#66870—24no—
117#66869—24no—
118#66867—22no—
119C4×C11⋊C8—22no—
120#21558—111nomaximal, Sylow
121C11×#41—21no—
122C11×#41—21no—
123C11×#41C22×C412yes—
124C11×#41C2×D412yes—
125C2×Q8×C11#4111yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11#4111yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—22no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133#4339—22no—
134#4339—22no—
135#4339—22no—
136#4339—22no—
137C2×D44C22×C412yes—
138C2×C4×D11—22no—
139C2×Dic22C22×C412yes—
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—22no—
143C11×M16—22no—
144C11×M16—21no—
145C11×M16C22×C412yes—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11C22×C411yescharacteristic
151C2×C8×C11C22×C411yescharacteristic
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11#4111yescharacteristic
155C2×C8×C11#4111yescharacteristic
156C11×C4⋊C4—22no—
157C11×C22⋊C4—22no—
158C42×C11—22no—
159C22⋊Dic11—22no—
160C22⋊Dic11#4112yes—
161#4326—24no—
162#4325—24no—
163#4324—24no—
164#4323—24no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4×Dic11—22no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C4×Dic11C2×D411yescharacteristic
171C4×Dic11C2×D411yescharacteristic
172#4318—22no—
173#4318—22no—
174#4318—22no—
175#4318—21no—
176#4318C22×C414yes—
177#4318C2×D412yes—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8C2×D411yescharacteristic
183C2×C11⋊C8C2×D411yescharacteristic
184C2×C11⋊C8C2×D411yescharacteristic
185C2×C11⋊C8C2×D411yescharacteristic
186C2×C11⋊C8#4111yescharacteristic
187C2×C11⋊C8#4111yescharacteristic
188Dic44—21no—
189Dic44—21no—
190D88—21no—
191D88—21no—
192#4314—22no—
193#4314—22no—
194#4313—42no—
195#4313—42no—
196C8×D11—42no—
197C8×D11—42no—
198#3067—111no—
199#2955—112no—
200C2×#443—111no—
201C4×#131—111no—
202#1976—111no—
203#1953—111no—
204#1932—112no—
205#1906—112no—
206#1814D1111yescharacteristic, complemented
207#1772—111no—
208#1757—112no—
209C23×C11—21no—
210C23×C11C2×#4111yescharacteristic
211C22×D11—22no—
212Q8×C11—21no—
213Q8×C11C4×D412yes—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—21no—
217D4×C11C4×D412yes—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C22⋊D11—42no—
229C22⋊D11—42no—
230C2×Dic11—21no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—21no—
234C2×Dic11—42no—
235C2×Dic11—44no—
236D44—22no—
237D44—22no—
238C4×D11—42no—
239C4×D11—42no—
240Dic22—22no—
241Dic22—22no—
242C8×C11—22no—
243C8×C11—42no—
244C8×C11C4×D411yescharacteristic
245C8×C11C4×D411yescharacteristic
246C8×C11C4×D411yescharacteristic
247C8×C11C4×D411yescharacteristic
248C11⋊C8—24no—
249C11⋊C8—22no—
250C11⋊C8#12111yescharacteristic
251C11⋊C8#12111yescharacteristic
252C11⋊C8#12111yescharacteristic
253C11⋊C8#12111yescharacteristic
254#575—112no—
255C2×#135—111no—
256C2×#131—111no—
257C2×#131—112no—
258C2×#131C2×D1111yescharacteristic
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×#108C2×D1111yescharacteristic
272#427C2×D1111yescharacteristic
273#421—112no—
274#421C2×D1112yes—
275C2×#104—112no—
276#413—112no—
277#410—112no—
278#405—111no—
279#405—111no—
280#405—112no—
281#405—221no—
282#405—221no—
283C4×M16—111no—
284C4×M16—221no—
285C2×C4×C8—111no—
286C2×C4×C8—221no—
287#344—112no—
288#344C2×D1112yes—
289#339—112no—
290C22×C11—22no—
291C22×C11—41no—
292C22×C11—42no—
293C22×C11C4×#4111yescharacteristic
294C22×C11#52511yescharacteristic
295C22×C11#53211yescharacteristic
296C2×D11—42no—
297C2×D11—82no—
298C4×C11—22no—
299C4×C11—82no—
300C4×C11C2×C4×D411yescharacteristic
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×#12111yescharacteristic
303C4×C11#52911yescharacteristic
304Dic11—22no—
305Dic11—42no—
306Dic11—41no—
307Dic11—42no—
308C2×#41—112no—
309C2×#41C22×D1111yescharacteristic
310#137—114no—
311#137—222no—
312AGL(1,ℤ/8)—114no—
313AGL(1,ℤ/8)—222no—
314#135—224no—
315#135—221no—
316#135—221no—
317#135—221no—
318#135—221no—
319C2×Q16—111no—
320C2×SD16—112no—
321C2×D8—111no—
322#131—21no—
323#131—21no—
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#131C4×D1112yes—
333#131C4×D1112yes—
334C2×M16—21no—
335C2×M16—111no—
336C2×M16—112no—
337C2×M16—222no—
338C2×M16—221no—
339C2×M16C22×D1112yes—
340C2×M16C22×D1111yescharacteristic
341C22×C8—21no—
342C22×C8—111no—
343C22×C8—222no—
344C22×C8—221no—
345C22×C8C22×D1111yescharacteristic
346C4×Q8—221no—
347C4×D4—222no—
348C4×D4—221no—
349#117—111no—
350#117—221no—
351#117C22×D1112yes—
352C2×C42—111no—
353C2×C42—221no—
354#108—21no—
355#108—21no—
356#108—112no—
357#108—112no—
358#108—224no—
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—224no—
368#97—222no—
369#97—221no—
370#97—221no—
371#97—221no—
372C4×C8—111no—
373C4×C8—111no—
374C4×C8—111no—
375C4×C8—111no—
376C4×C8—222no—
377C4×C8—221no—
378C4×C8—221no—
379C4×C8—221no—
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—42no—
384C2×C11C4×#12111yescharacteristic
385D11—82no—
386#41—21no—
387#41—21no—
388#41—222no—
389#41—222no—
390#41—222no—
391#41—222no—
392#41C2×C4×D1112yes—
393#41D4×D1112yes—
394C2×Q8—112no—
395C2×Q8#434311yescharacteristic
396C2×D4—21no—
397C2×D4—112no—
398C2×D4—222no—
399C2×D4#434311yescharacteristic
400C22×C4—21no—
401C22×C4—222no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4C23×D1111yescharacteristic
405Q16—224no—
406Q16—221no—
407Q16—221no—
408SD16—224no—
409SD16—224no—
410SD16—222no—
411SD16—222no—
412D8—224no—
413D8—221no—
414D8—221no—
415M16—21no—
416M16—22no—
417M16—22no—
418M16—22no—
419M16—22no—
420M16—114no—
421M16—112no—
422M16—222no—
423M16—222no—
424M16—222no—
425M16—221no—
426M16—442no—
427M16—442no—
428M16C2×C4×D1112yes—
429C2×C8—21no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—111no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—111no—
437C2×C8—111no—
438C2×C8—111no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—221no—
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—22no—
452C4⋊C4—222no—
453C4⋊C4—221no—
454C22⋊C4—22no—
455C22⋊C4—112no—
456C22⋊C4—222no—
457C42—22no—
458C42—111no—
459C42—111no—
460C42—222no—
461C42—221no—
462C42—221no—
463C11#2155811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—222no—
466C23#41×D1111yescharacteristic
467Q8—21no—
468Q8—222no—
469Q8—222no—
470Q8#6694612yes—
471D4—22no—
472D4—22no—
473D4—21no—
474D4—222no—
475D4—222no—
476D4—442no—
477D4—442no—
478D4#6694612yes—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—221no—
484C2×C4—222no—
485C2×C4—221no—
486C2×C4—222no—
487C2×C4—442no—
488C2×C4—444no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4C22×C4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×#434111yescharacteristic
495C2×C4C2×#434311yescharacteristic
496C2×C4#41×D1111yescharacteristic
497C8—22no—
498C8—42no—
499C8—111no—
500C8—111no—
501C8—111no—
502C8—111no—
503C8—224no—
504C8—222no—
505C8(C22⋊D11)⋊C411yescharacteristic
506C8(C22⋊D11)⋊C411yescharacteristic
507C8(C22⋊D11)⋊C411yescharacteristic
508C8(C22⋊D11)⋊C411yescharacteristic
509C22—22no—
510C22—41no—
511C22—42no—
512C22—442no—
513C22—882no—
514C22#1062305311yescharacteristic
515C22#1062312711yescharacteristic
516C22#1062315811yescharacteristic
517C4—22no—
518C4—82no—
519C4—222no—
520C4—441no—
521C4—442no—
522C4—442no—
523C4C2×(C22⋊D11)⋊C411yescharacteristic
524C4C2×#6694611yescharacteristic
525C4D11×#12111yescharacteristic
526C4#1062315511yescharacteristic
527C2—21no—
528C2—21no—
529C2—21no—
530C2—42no—
531C2—882no—
532C2#1307112211yescharacteristic
subgroupG/H
centerC4D11×#121
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1814C2
socleC2×C11C4×#121
prime radical#13078336C2
cosocleC22×C4×C11C24
hypercenter#1814D11
hypocenterC11#21558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1814

Complements

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

NH ≅ G/Ntype
2. #13077515C2semidirect
3. C2×#10622508C2semidirect
4. #131×Dic11C2semidirect
5. #13069512C2semidirect
6. #13069404C2semidirect
7. #13069283C2semidirect
8. #13069115C2semidirect
9. #13068497C2semidirect
10. #13068415C2semidirect
11. C11×#1814C2semidirect
21. #10622756C4semidirect
22. #10622755C4semidirect
23. #10622754C4semidirect
85. C2×Dic44C2×C4semidirect
90. C2×D88C2×C4semidirect
91. C2×#4314C2×C4semidirect
101. #66888C2×C4semidirect
102. #66887C2×C4semidirect
104. #66883C2×C4semidirect
105. #66883C2×C4semidirect
206. #1814D11semidirect
463. C11#21558semidirect

Maximal subgroups

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

subgroupindex
#130783362
#130775152
C2×#106225082
#131×Dic112
#130695122
#130694042
#130692832
#130691152
#130684972
#130684152
C11×#18142
#2155811