Finite Group Databasebeta

← #14760717

Subgroups — #14760717

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#13078332C211yesmaximal, characteristic
2#13077517C212yesmaximal, complemented
3#13077041C211yesmaximal, characteristic, complemented
4#13069515C211yesmaximal, characteristic, complemented
5#13069404C211yesmaximal, characteristic, complemented
6#13069282C212yesmaximal, complemented
7#13069120C212yesmaximal, complemented
8#13068671C211yesmaximal, characteristic, complemented
9#13068500C211yesmaximal, characteristic, complemented
10#13068416C212yesmaximal, complemented
11C2×C11×#444C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C2×C11×#131C2212yes—
14#10623353C2212yes—
15C2×#66954C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#444—21no—
19C11×#444—21no—
20C11×#444—21no—
21C11×#444—21no—
22C2×C11×#108C2211yescharacteristic
23C2×C11×#104C2212yes—
24C2×C11×#97C2211yescharacteristic
25#10622853C2212yes—
26#10622850C2212yes—
27#10622849C2212yes—
28#10622805C412yescomplemented
29#10622790C414yescomplemented
30#10622773C412yescomplemented
31#10622758—24no—
32#10622757—24no—
33#10622752C2212yes—
34#10622737C2212yes—
35C2×#66883C2211yescharacteristic
36#10622719C2211yescharacteristic
37#10622714C2212yes—
38#10622714C2211yescharacteristic
39#10622714C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622321—21no—
42#10622321—21no—
43#10622320—21no—
44D11×#97—21no—
45#10622194C2212yes—
46#10622194C2212yes—
47#10622161C2212yes—
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
57C11×#131—22no—
58C11×#131—22no—
59C11×#131—22no—
60C11×#131—22no—
61C2×C11×M16—22no—
62C2×C11×M16C2312yes—
63C22×C8×C11—22no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#67004—22no—
68#67003—24no—
69#67002—22no—
70#66995C2×C414yes—
71#66985C2×C414yes—
72C4×C22⋊D11—22no—
73#66979C2312yes—
74#66979C2311yescharacteristic
75C2×#4318C2312yes—
76C2×#4318C2311yescharacteristic
77C2×#4318C2311yescharacteristic
78#66954—21no—
79#66954—21no—
80#66954—22no—
81#66954C2×C412yes—
82#66954C2×C412yes—
83#66954D414yes—
84C2×#4313—21no—
85C2×#4313—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C4×D44—21no—
89#66925—21no—
90C42×D11—21no—
91C4×Dic22—21no—
92C11×#108—21no—
93C11×#108—21no—
94C11×#104—22no—
95C11×#104—22no—
96C11×#97D411yescharacteristic
97C11×#97D411yescharacteristic
98C11×#97D411yescharacteristic
99C11×#97D411yescharacteristic
100#66901—24no—
101#66900C2×C414yescomplemented
102#66898—24no—
103#66897C2×C414yescomplemented
104#66889—24no—
105#66886—24no—
106#66883C2×C412yescomplemented
107#66883C2×C412yescomplemented
108#66882—21no—
109#66881—21no—
110#66879—22no—
111#66879—21no—
112#66879—21no—
113C8×Dic11—22no—
114C8×Dic11—21no—
115C8×Dic11—21no—
116#66867—21no—
117C4×C11⋊C8—21no—
118#21559—111nomaximal, Sylow
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C2×Q8×C11C22×C412yes—
124C2×D4×C11—22no—
125C2×D4×C11C22×C412yes—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—21no—
130#4339—21no—
131#4339—21no—
132#4339C22×C412yes—
133#4339C2×D412yes—
134C2×D44#4111yescharacteristic
135C2×C4×D11—22no—
136C2×C4×D11—21no—
137C2×Dic22#4111yescharacteristic
138C11×Q16—21no—
139C11×Q16—21no—
140C11×SD16—22no—
141C11×SD16—22no—
142C11×D8—21no—
143C11×D8—21no—
144C11×M16—22no—
145C11×M16—22no—
146C11×M16—42no—
147C11×M16—42no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C2×C8×C11—42no—
151C2×C8×C11C22×C411yescharacteristic
152C2×C8×C11C22×C411yescharacteristic
153C2×C8×C11C2×D412yes—
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11#4111yescharacteristic
159C2×C8×C11#4111yescharacteristic
160C2×C8×C11#4112yes—
161C42×C11—21no—
162C42×C11C2×D411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C22⋊Dic11—22no—
165C22⋊Dic11#4112yes—
166#4326—24no—
167#4325—24no—
168#4324—24no—
169#4323—24no—
170(C2×D11)⋊C4—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—22no—
173Dic11⋊C4—22no—
174C4×Dic11—22no—
175C4×Dic11—21no—
176C4×Dic11—22no—
177#4318—21no—
178#4318—21no—
179#4318—22no—
180#4318C22×C414yes—
181#4318C22×C412yes—
182#4318C2×D412yes—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186#4313—22no—
187#4313—22no—
188#4313—24no—
189C8×D11—22no—
190C8×D11—22no—
191C8×D11—24no—
192#3067—111no—
193#2955—112no—
194C2×#444D1111yescharacteristic, complemented
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—22no—
204C23×C11C2×#4111yescharacteristic
205C22×D11—21no—
206Q8×C11—22no—
207Q8×C11—22no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—42no—
211D4×C11—42no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—81no—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C22⋊D11—22no—
225C22⋊D11—22no—
226C2×Dic11—21no—
227C2×Dic11—22no—
228C2×Dic11—42no—
229D44—21no—
230D44C4×D412yes—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—82no—
234Dic22—21no—
235Dic22C4×D412yes—
236C8×C11—42no—
237C8×C11C4×D411yescharacteristic
238C8×C11C4×D411yescharacteristic
239C8×C11C4×D411yescharacteristic
240C8×C11C4×D411yescharacteristic
241C8×C11#12112yes—
242C8×C11#12112yes—
243C11⋊C8—22no—
244C11⋊C8—24no—
245C11⋊C8—22no—
246#575—112no—
247C2×#135C2×D1111yescharacteristic
248C2×#131—111no—
249C2×#131—111no—
250C2×#131C2×D1112yes—
251C4×#41—111no—
252#473—112no—
253#472—112no—
254#471—114no—
255#444—21no—
256#444—21no—
257#444—21no—
258#444—21no—
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×#104C2×D1112yes—
268#413—112no—
269#410—112no—
270#405—111no—
271#405—111no—
272#405—112no—
273#405—221no—
274#405—221no—
275C4×M16—111no—
276C4×M16—221no—
277C2×#97—221no—
278C2×#97C2×D1111yescharacteristic
279#344—112no—
280#344—112no—
281#339—112no—
282C22×C11—41no—
283C22×C11—42no—
284C22×C11—82no—
285C22×C11C4×#4111yescharacteristic
286C22×C11#52511yescharacteristic
287C22×C11#53211yescharacteristic
288C2×D11—22no—
289C2×D11—42no—
290C4×C11—41no—
291C4×C11—41no—
292C4×C11—42no—
293C4×C11C2×C4×D411yescharacteristic
294C4×C11C2×C4×D411yescharacteristic
295C4×C11C2×#12111yescharacteristic
296C4×C11#52911yescharacteristic
297Dic11—22no—
298Dic11—42no—
299Dic11—82no—
300C2×#41—111no—
301C2×#41C22×D1112yes—
302#137—114no—
303#137—222no—
304AGL(1,ℤ/8)—114no—
305AGL(1,ℤ/8)—222no—
306#135—21no—
307#135—21no—
308#135—21no—
309#135—21no—
310#135—224no—
311C2×Q16C4×D1111yescharacteristic, complemented
312C2×SD16C4×D1112yescomplemented
313C2×D8C4×D1111yescharacteristic, complemented
314#131—22no—
315#131—22no—
316#131—22no—
317#131—22no—
318#131—112no—
319#131—112no—
320#131—114no—
321#131—221no—
322#131—221no—
323#131—222no—
324C2×M16—22no—
325C2×M16—111no—
326C2×M16—111no—
327C2×M16—112no—
328C2×M16—221no—
329C2×M16—221no—
330C2×M16C22×D1112yes—
331C22×C8—22no—
332C22×C8—221no—
333C22×C8—221no—
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4×Q8—221no—
337C4×D4—221no—
338C4×D4—222no—
339#117—111no—
340#117—112no—
341#117—221no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#108—21no—
345#108—21no—
346#108—112no—
347#108—112no—
348#108—224no—
349#107—221no—
350#106—221no—
351#104—22no—
352#104—22no—
353#104—224no—
354#104—224no—
355#101—114no—
356#100—114no—
357#99—224no—
358#97—222no—
359#97—221no—
360#97—221no—
361#97—221no—
362#97C22⋊D1111yescharacteristic
363#97C22⋊D1111yescharacteristic
364#97C22⋊D1111yescharacteristic
365#97C22⋊D1111yescharacteristic
366C4×C8—222no—
367C4×C8—221no—
368C4×C8—221no—
369C4×C8—221no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—82no—
374C2×C11C4×#12111yescharacteristic
375D11—42no—
376#41—22no—
377#41—22no—
378#41—22no—
379#41—22no—
380#41—112no—
381#41—112no—
382#41—221no—
383#41—221no—
384C2×Q8—111no—
385C2×Q8C2×C4×D1112yes—
386C2×D4—22no—
387C2×D4—111no—
388C2×D4—221no—
389C2×D4C2×C4×D1112yes—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—222no—
393C22×C4—221no—
394C22×C4C23×D1111yescharacteristic
395Q16—21no—
396Q16—21no—
397Q16—224no—
398SD16—22no—
399SD16—22no—
400SD16—224no—
401SD16—224no—
402D8—21no—
403D8—21no—
404D8—224no—
405M16—22no—
406M16—22no—
407M16—42no—
408M16—42no—
409M16—112no—
410M16—114no—
411M16—112no—
412M16—221no—
413M16—221no—
414M16—222no—
415M16—222no—
416M16—222no—
417M16—224no—
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—42no—
421C2×C8—222no—
422C2×C8—221no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—224no—
427C2×C8C2×C4×D1111yescharacteristic
428C2×C8C2×C4×D1111yescharacteristic
429C2×C8#433911yescharacteristic
430C2×C8#433911yescharacteristic
431C2×C8D4×D1112yes—
432C2×C8#434112yes—
433C2×C8C2×C22⋊D1111yescharacteristic
434C2×C8C2×C22⋊D1111yescharacteristic
435C2×C8C2×C22⋊D1111yescharacteristic
436C2×C8C2×C22⋊D1111yescharacteristic
437C4⋊C4—222no—
438C4⋊C4—221no—
439C4⋊C4—222no—
440C22⋊C4—112no—
441C22⋊C4—222no—
442C22⋊C4—222no—
443C42—21no—
444C42—222no—
445C42—221no—
446C42—222no—
447C42C2×C22⋊D1111yescharacteristic
448C42C2×C22⋊D1111yescharacteristic
449C11#2155911yescharacteristic, complemented, Sylow
450C23—22no—
451C23—221no—
452C23#41×D1111yescharacteristic
453Q8—22no—
454Q8—22no—
455Q8—112no—
456Q8—221no—
457D4—22no—
458D4—22no—
459D4—42no—
460D4—42no—
461D4—112no—
462D4—222no—
463D4—222no—
464D4—221no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—81no—
471C2×C4—221no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—442no—
476C2×C4—882no—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×D4×D1111yescharacteristic
480C2×C4C2×#434111yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4C22×C22⋊D1111yescharacteristic
483C8—42no—
484C8—222no—
485C8—224no—
486C8—222no—
487C8C4×C22⋊D1111yescharacteristic
488C8C4×C22⋊D1111yescharacteristic
489C8C4×C22⋊D1111yescharacteristic
490C8C4×C22⋊D1111yescharacteristic
491C8#6699112yes—
492C8#6699112yes—
493C22—41no—
494C22—42no—
495C22—82no—
496C22—222no—
497C22—442no—
498C22C4×#434111yescharacteristic
499C22#1062307911yescharacteristic
500C22#1062335911yescharacteristic
501C4—41no—
502C4—41no—
503C4—42no—
504C4—222no—
505C4—442no—
506C4—882no—
507C4C4×D4×D1111yescharacteristic
508C4#1062308811yescharacteristic
509C4C2×C4×C22⋊D1111yescharacteristic
510C4C2×#6699111yescharacteristic
511C2—21no—
512C2—21no—
513C2—21no—
514C2—82no—
515C2—442no—
516C2C4×#6699111yescharacteristic
subgroupG/H
centerC4C2×#66991
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#444C2
socleC2×C11C4×#121
prime radical#13078332C2
cosocleC22×C4×C11C24
hypercenterC2×#444D11
hypocenterC11#21559
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. #13077517C2semidirect
3. #13077041C2semidirect
4. #13069515C2semidirect
5. #13069404C2semidirect
6. #13069282C2semidirect
7. #13069120C2semidirect
8. #13068671C2semidirect
9. #13068500C2semidirect
10. #13068416C2semidirect
11. C2×C11×#444C2semidirect
28. #10622805C4semidirect
29. #10622790C4semidirect
30. #10622773C4semidirect
54. C2×C11×Q16C2×C4semidirect
55. C2×C11×SD16C2×C4semidirect
56. C2×C11×D8C2×C4semidirect
101. #66900C2×C4semidirect
103. #66897C2×C4semidirect
106. #66883C2×C4semidirect
107. #66883C2×C4semidirect
194. C2×#444D11semidirect
311. C2×Q16C4×D11semidirect
312. C2×SD16C4×D11semidirect
313. C2×D8C4×D11semidirect
449. C11#21559semidirect

Maximal subgroups

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

subgroupindex
#130783322
#130775172
#130770412
#130695152
#130694042
#130692822
#130691202
#130686712
#130685002
#130684162
C2×C11×#4442
#2155911