Finite Group Databasebeta

← #14772055

Subgroups — #14772055

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622430C212yesmaximal
2C2×C4×#4325C211yesmaximal, characteristic
3Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13071516C211yesmaximal, characteristic
5#13069358C212yesmaximal, complemented
6#13068868C212yesmaximal, complemented
7#13068864C212yesmaximal
8#13068775C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10#13068486C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C22×#4325C2211yescharacteristic
15C2×#66946C2212yes—
16C2×C4⋊C4×D11—21no—
17C2×C4×D44C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2212yes—
20C11×#384C2211yescharacteristic
21C2×#66899C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66879C2212yes—
24C4×#4325C418yescomplemented
25#10622602—22no—
26#10622600—21no—
27#10622598—22no—
28#10622598C2212yes—
29#10622586C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66872C2211yescharacteristic
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34#10622548—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622430—28no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C4×D11—22no—
47C22×C8×C11C2312yes—
48C4×Q8×C11—22no—
49C4×Q8×C11C2×C414yescomplemented
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57Q8×Dic11—24no—
58Q8×Dic11—42no—
59C2×#4325C2×C414yes—
60C2×#4325D414yes—
61C2×#4325Q814yes—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2312yes—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77#66946—24no—
78#66946—42no—
79C4⋊C4×D11—44no—
80C4×D44—22no—
81C4×D44C2×C414yes—
82C11×C4⋊C8—22no—
83C11×#103—24no—
84#66899C2×C414yescomplemented
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95D412yes—
88#66885—24no—
89#66879—24no—
90#66873C2×C414yes—
91#66872C2×C414yescomplemented
92#66871—24no—
93#66871—42no—
94C4×C11⋊C8C2×C414yescomplemented
95#22671—111nomaximal, Sylow
96C23×D11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11C22×C412yes—
101C2×Q8×C11C2×D412yes—
102C2×Q8×C11C2×Q812yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—22no—
111C22×Dic11C2×D412yes—
112C22×Dic11C2×D412yes—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44C22×C412yes—
117C2×D44C2×D412yes—
118C2×D44C2×Q812yes—
119C2×C4×D11—24no—
120C2×C4×D11—44no—
121C2×C4×D11—44no—
122C2×C4×D11—42no—
123C2×C4×D11—42no—
124C2×C4×D11—82no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—81no—
134C11×C4⋊C4C22×C412yes—
135C42×C11—24no—
136C42×C11C22×C412yes—
137C42×C11#4112yes—
138#4325C4⋊C4116yescomplemented
139(C2×D11)⋊C4—24no—
140(C2×D11)⋊C4—44no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—44no—
147C4⋊Dic11—42no—
148C4⋊Dic11—81no—
149C4⋊Dic11—82no—
150C4⋊Dic11C22×C412yes—
151Dic11⋊C4—44no—
152C4×Dic11—22no—
153C4×Dic11—22no—
154C4×Dic11—44no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8C22×C412yes—
158C2×C11⋊C8C22×C412yes—
159C2×C11⋊C8C2×D412yes—
160C2×C11⋊C8C2×Q812yes—
161C2×#440—112no—
162C2×C4×SD16—111no—
163Q8×C4⋊C4—111no—
164D4×C4⋊C4—111no—
165#1944—112no—
166#1863—112no—
167#1862—112no—
168#1845—111no—
169#1803D1111yescharacteristic, complemented
170#1802—111no—
171#1770—111no—
172C23×C11C22×D411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11C2×C4⋊C414yescomplemented
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11C4×D412yes—
196C2×C4×C11C4×D412yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11#13712yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217D44—22no—
218D44—22no—
219D44—22no—
220D44C2×C4⋊C414yes—
221C4×D11—48no—
222C4×D11—88no—
223C8×C11—42no—
224C11⋊C8—22no—
225C11⋊C8C2×C4⋊C414yescomplemented
226C22×SD16—111no—
227C2×C4×Q8—112no—
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—112no—
230C2×C4×D4—111no—
231C22×C4⋊C4—221no—
232#440—228no—
233C4×SD16—118no—
234C2×#107—112no—
235C2×#107—112no—
236C2×#106—111no—
237C2×C4⋊C8C2×D1111yescharacteristic
238C2×#103—111no—
239C2×#103C2×D1112yes—
240C2×#102—111no—
241C2×#102—112no—
242C2×#97—112no—
243C2×C4×C8—111no—
244#389—112no—
245#389—112no—
246#389—222no—
247#385—222no—
248#384—111no—
249#384—221no—
250#384C2×D1111yescharacteristic
251#380—221no—
252C4×C4⋊C4—111no—
253C4×C4⋊C4—221no—
254#340—112no—
255#340C2×D1112yes—
256#336—112no—
257C22×C11C2×C4×D411yescharacteristic
258C22×C11D4211yescharacteristic
259C22×C11D4×Q811yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11C2×#13711yescharacteristic
262C22×C11#57611yescharacteristic
263C22×C11#57811yescharacteristic
264C2×D11—24no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11#44014yescomplemented
276C4×C11C22×C4⋊C411yescharacteristic
277C4×C11#52011yescharacteristic
278C4×C11#54711yescharacteristic
279C4×C11#55411yescharacteristic
280Dic11—42no—
281Dic11—42no—
282Dic11—42no—
283Dic11—82no—
284C22×Q8C22×D1111yescharacteristic
285C22×D4—111no—
286C23×C4—222no—
287C23×C4—221no—
288C2×SD16—114no—
289C2×SD16—114no—
290C2×SD16—114no—
291C22×C8—111no—
292C22×C8—111no—
293C22×C8C22×D1112yes—
294C4×Q8—22no—
295C4×Q8—224no—
296C4×Q8—442no—
297C4×Q8C4×D1114yescomplemented
298C4×D4—114no—
299C4×D4—224no—
300C4×D4—222no—
301C4×D4—442no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—444no—
315C2×C4⋊C4C22×D1112yes—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—221no—
318C2×C22⋊C4—222no—
319C2×C42—21no—
320C2×C42—112no—
321C2×C42—222no—
322C2×C42C22×D1111yescharacteristic
323#107—224no—
324#107—442no—
325#106—114no—
326C4⋊C8—22no—
327#103—24no—
328#103—114no—
329#102—114no—
330#102—224no—
331#97—224no—
332C4×C8—114no—
333#95—112no—
334#95—222no—
335#95—222no—
336C2×C11D4×C4⋊C411yescharacteristic
337C2×C11C2×#44011yescharacteristic
338C2×C11#295111yescharacteristic
339C2×C11#327411yescharacteristic
340C2×C11#327611yescharacteristic
341C2×C11#338511yescharacteristic
342C2×C11#338611yescharacteristic
343D11—44no—
344C24—221no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8C2×C4×D1112yes—
349C2×Q8D4×D1112yes—
350C2×Q8Q8×D1112yes—
351C2×D4—112no—
352C2×D4—112no—
353C2×D4—112no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—112no—
361C22×C4—112no—
362C22×C4—221no—
363C22×C4—224no—
364C22×C4—222no—
365C22×C4—444no—
366C22×C4—444no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4—882no—
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4C23×D1111yescharacteristic
373SD16—1116no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—112no—
378C2×C8—112no—
379C2×C8—112no—
380C2×C8—112no—
381C2×C8—221no—
382C2×C8—221no—
383C4⋊C4—24no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—42no—
388C4⋊C4—81no—
389C4⋊C4—112no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—221no—
393C4⋊C4—222no—
394C4⋊C4—222no—
395C4⋊C4—444no—
396C4⋊C4—444no—
397C4⋊C4—442no—
398C4⋊C4—881no—
399C4⋊C4—882no—
400C4⋊C4C2×C4×D1112yes—
401C22⋊C4—224no—
402C22⋊C4—444no—
403C42—24no—
404C42—222no—
405C42—222no—
406C42—444no—
407C42C2×C4×D1112yes—
408C42#434112yes—
409C11#2267111yescharacteristic, complemented, Sylow
410C23—222no—
411C23—222no—
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23C2×D4×D1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—22no—
421Q8C4⋊C4×D1114yescomplemented
422D4—114no—
423D4—222no—
424D4—222no—
425D4—222no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—222no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—448no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—888no—
451C2×C4(C22⋊D11)⋊C412yes—
452C2×C4(C22⋊D11)⋊C412yes—
453C2×C4#6696712yes—
454C2×C4#6697112yes—
455C2×C4C22×C4×D1111yescharacteristic
456C2×C4C2×D4×D1111yescharacteristic
457C2×C4C2×#434111yescharacteristic
458C2×C4C2×Q8×D1111yescharacteristic
459C2×C4#6704211yescharacteristic
460C2×C4#6704311yescharacteristic
461C8—42no—
462C8—114no—
463C8—222no—
464C22—224no—
465C22—442no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22C2×(C22⋊D11)⋊C411yescharacteristic
472C22#1062314011yescharacteristic
473C22#1062316311yescharacteristic
474C22C2×#6696711yescharacteristic
475C22C2×#6697111yescharacteristic
476C22#1062330511yescharacteristic
477C22#1062331011yescharacteristic
478C4—24no—
479C4—22no—
480C4—42no—
481C4—82no—
482C4—442no—
483C4—442no—
484C4—442no—
485C4—882no—
486C4#1062243014yescomplemented
487C4C2×C4⋊C4×D1111yescharacteristic
488C4#1062305411yescharacteristic
489C4#1062314211yescharacteristic
490C4#1062316611yescharacteristic
491C2—444no—
492C2#1307151211yescharacteristic
493C2C2×#1062243011yescharacteristic
494C2#1307748711yescharacteristic
495C2#1308023111yescharacteristic
496C2#1308025711yescharacteristic
497C2#1308152511yescharacteristic
498C2#1308153611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22671
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
3. Q8×C4⋊Dic11C2semidirect
5. #13069358C2semidirect
6. #13068868C2semidirect
8. #13068775C2semidirect
10. #13068486C2semidirect
11. C11×#1803C2semidirect
24. C4×#4325C4semidirect
49. C4×Q8×C11C2×C4semidirect
84. #66899C2×C4semidirect
91. #66872C2×C4semidirect
94. C4×C11⋊C8C2×C4semidirect
138. #4325C4⋊C4semidirect
169. #1803D11semidirect
183. Q8×C11C2×C4⋊C4semidirect
225. C11⋊C8C2×C4⋊C4semidirect
275. C4×C11#440semidirect
297. C4×Q8C4×D11semidirect
409. C11#22671semidirect
421. Q8C4⋊C4×D11semidirect
486. C4#10622430semidirect

Maximal subgroups

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

subgroupindex
C2×#106224302
C2×C4×#43252
Q8×C4⋊Dic112
#130715162
#130693582
#130688682
#130688642
#130687752
#130686172
#130684862
C11×#18032
#2267111