Finite Group Databasebeta

← #14770400

Subgroups — #14770400

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069585C212yesmaximal, complemented
4#13069577C211yesmaximal, characteristic, complemented
5#13069571C212yesmaximal, complemented
6#13069563C211yesmaximal, characteristic, complemented
7#13068617C212yesmaximal
8#13068617C211yesmaximal, characteristic
9#13068442C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14C2×Q8×Dic11—21no—
15#10623110—24no—
16#10623110C418yescomplemented
17C2×#66949—22no—
18C2×C4⋊C4×D11—21no—
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2212yes—
21C2×#66923C2212yes—
22C2×#66922C2211yescharacteristic
23C11×#446—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2212yes—
30C2×#66885C2211yescharacteristic
31#10622598—21no—
32#10622598—22no—
33#10622548C2211yescharacteristic
34#10622548C2212yes—
35C4×C4⋊Dic11C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622189C2211yescharacteristic
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2212yes—
44C22×Q8×C11D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C4×Q8×C11C2×C414yes—
53C4×Q8×C11D414yes—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2312yes—
58#66999—28no—
59Q8×Dic11—44no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—21no—
76#66949—216no—
77C4⋊C4×D11—28no—
78C4×D44—24no—
79C4×D44—22no—
80C4×D44C2×C418yes—
81C4×D44C2×C414yes—
82#66923—24no—
83#66923C2×C418yes—
84#66922—22no—
85#66922C2×C414yes—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—24no—
88C11×#97—24no—
89C4×C8×C11—22no—
90C11⋊#95—22no—
91C11⋊#95—21no—
92#66885—22no—
93#66885—24no—
94#66885Q814yescomplemented
95#22522—111nomaximal, Sylow
96C23×D11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22⋊C414yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44C22×C412yes—
114C2×D44C2×Q812yes—
115C2×D44#4112yes—
116C2×C4×D11—24no—
117C2×C4×D11—28no—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—82no—
121C2×C4×D11—82no—
122C2×Dic22—24no—
123C2×Dic22—81no—
124C2×Dic22—81no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11C2×Q812yes—
134C11×C4⋊C4C22⋊C414yes—
135C11×C4⋊C4C22⋊C418yes—
136C42×C11C22×C412yes—
137C42×C11C22×C414yes—
138C42×C11C2×D412yes—
139C42×C11C2×D414yes—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—28no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—44no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153C4⋊Dic11—82no—
154C4⋊Dic11C22×C414yes—
155C4⋊Dic11C22×C412yes—
156C4⋊Dic11C2×Q812yes—
157Dic11⋊C4—28no—
158Dic11⋊C4—28no—
159C4×Dic11—44no—
160C4×Dic11—42no—
161C2×#554—111no—
162C2×#446D1111yescharacteristic, complemented
163Q8×C4⋊C4—111no—
164#1992—112no—
165#1990—111no—
166#1989—112no—
167#1987—111no—
168#1802—111no—
169#1802—112no—
170#1762—112no—
171C4×#102—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—28no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11C2×C22⋊C414yes—
188C2×C4×C11C2×C22⋊C414yes—
189C2×C4×C11C2×C22⋊C412yes—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C112−1+411yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214D44—22no—
215D44—22no—
216D44—22no—
217D44C4×Q814yescomplemented
218C4×D11—48no—
219C4×D11—88no—
220Dic22—84no—
221C8×C11—22no—
222C8×C11—41no—
223C8×C11—42no—
224#554—118no—
225#554—224no—
226C2×C4⋊Q8—111no—
227C2×#125—112no—
228C2×C22⋊Q8—221no—
229C2×C22⋊Q8—222no—
230C2×C4×Q8—221no—
231C2×C4×Q8C2×D1111yescharacteristic
232C2×C4×D4—111no—
233C2×C4×D4—112no—
234C22×C4⋊C4—221no—
235#446—24no—
236C2×C4⋊C8C2×D1111yescharacteristic
237C2×C4⋊C8C2×D1112yes—
238C2×#102—111no—
239C2×#102—111no—
240C2×#102—112no—
241C2×#97C2×D1112yes—
242C2×C4×C8C2×D1111yescharacteristic
243#389—221no—
244#389—222no—
245#384—111no—
246#384—112no—
247C4×C4⋊C4—111no—
248C4×C4⋊C4—112no—
249#340—112no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—111no—
254#340—112no—
255#340—111no—
256C22×C11C22×C22⋊C411yescharacteristic
257C22×C11#54811yescharacteristic
258C22×C11D4×Q811yescharacteristic
259C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C11C2×#13711yescharacteristic
261C22×C11#57611yescharacteristic
262C22×C11#57711yescharacteristic
263C2×D11—24no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C4×C11—24no—
271C4×C11—22no—
272C4×C11—24no—
273C4×C11#41714yes—
274C4×C11C2×C4×Q811yescharacteristic
275C4×C11#51911yescharacteristic
276C4×C11#54811yescharacteristic
277C4×C11D4×Q811yescharacteristic
278Dic11—42no—
279Dic11—42no—
280Dic11—44no—
281Dic11—82no—
282Dic11—81no—
283C22×Q8—221no—
284C22×Q8D4411yescharacteristic
285C22×D4—111no—
286C23×C4—221no—
287C23×C4—222no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1112yes—
290C22×C8C22×D1111yescharacteristic
291C4⋊Q8—114no—
292C4⋊Q8—222no—
293#125—118no—
294#125—224no—
295C22⋊Q8—228no—
296C22⋊Q8—2216no—
297C4×Q8—444no—
298C4×Q8C4×D1114yes—
299C4×Q8C22⋊D1114yes—
300C4×D4—118no—
301C4×D4—114no—
302C4×D4—222no—
303C4×D4—224no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—112no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—228no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4D4411yescharacteristic
318C2×C4⋊C4D4412yes—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—222no—
321C2×C42—222no—
322C2×C42—221no—
323C2×C42C22×D1112yes—
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—22no—
326C4⋊C8—24no—
327#102—114no—
328#102—222no—
329#102—224no—
330#97—24no—
331C4×C8—22no—
332#95—221no—
333#95—222no—
334C2×C11Q8×C22⋊C411yescharacteristic
335C2×C11C2×#41711yescharacteristic
336C2×C11#289711yescharacteristic
337C2×C11#336611yescharacteristic
338C2×C11#337211yescharacteristic
339C2×C11#338411yescharacteristic
340C2×C11#338511yescharacteristic
341D11—44no—
342C24—221no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—224no—
346C2×Q8—881no—
347C2×Q8—881no—
348C2×Q8(C2×D11)⋊C414yes—
349C2×D4—112no—
350C2×D4—112no—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—224no—
359C22×C4—228no—
360C22×C4—222no—
361C22×C4—221no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4—882no—
365C22×C4—882no—
366C22×C4C2×D4411yescharacteristic
367C22×C4C2×D4412yes—
368C22×C4C2×D4412yes—
369C22×C4C2×D4411yescharacteristic
370C22×C4C23×D1111yescharacteristic
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8Q8×D1112yes—
380C4⋊C4—112no—
381C4⋊C4—114no—
382C4⋊C4—112no—
383C4⋊C4—228no—
384C4⋊C4—224no—
385C4⋊C4—228no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—221no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C4⋊C4—444no—
394C4⋊C4—442no—
395C4⋊C4—882no—
396C4⋊C4—881no—
397C4⋊C4(C2×D11)⋊C414yes—
398C4⋊C4(C2×D11)⋊C418yes—
399C22⋊C4—224no—
400C22⋊C4—228no—
401C42—444no—
402C42—442no—
403C42C2×C4×D1114yes—
404C42C2×C4×D1112yes—
405C42C2×C22⋊D1112yes—
406C42C2×C22⋊D1114yes—
407C11#2252211yescharacteristic, complemented, Sylow
408C23—222no—
409C23—222no—
410C23—222no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23C22×D4411yescharacteristic
416Q8—28no—
417Q8—884no—
418D4—114no—
419D4—222no—
420D4—222no—
421D4—222no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—222no—
429C2×C4—224no—
430C2×C4—222no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—448no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—888no—
445C2×C4#6696112yes—
446C2×C4#6696212yes—
447C2×C4C2×(C2×D11)⋊C414yes—
448C2×C4C2×(C2×D11)⋊C412yes—
449C2×C4C2×(C2×D11)⋊C414yes—
450C2×C4C2×(C2×D11)⋊C412yes—
451C2×C4C22×C4×D1111yescharacteristic
452C2×C4C2×Q8×D1111yescharacteristic
453C2×C4#6704011yescharacteristic
454C2×C4#41×D1111yescharacteristic
455C2×C4#6704311yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—22no—
458C8—41no—
459C8—42no—
460C22—224no—
461C22—442no—
462C22—442no—
463C22—442no—
464C22—442no—
465C22—442no—
466C22—442no—
467C22Q8×D4411yescharacteristic
468C22#1062310711yescharacteristic
469C22C2×#6696111yescharacteristic
470C22C2×#6696211yescharacteristic
471C22#1062328211yescharacteristic
472C22#1062328311yescharacteristic
473C22C22×(C2×D11)⋊C411yescharacteristic
474C4—24no—
475C4—24no—
476C4—22no—
477C4—442no—
478C4—444no—
479C4—442no—
480C4—882no—
481C4—881no—
482C4#1062274614yes—
483C4C4×Q8×D1111yescharacteristic
484C4#1062310311yescharacteristic
485C4Q8×C22⋊D1111yescharacteristic
486C4#1062336211yescharacteristic
487C2—444no—
488C2Q8×(C2×D11)⋊C411yescharacteristic
489C2C2×#1062274611yescharacteristic
490C2#1307714311yescharacteristic
491C2#1308132511yescharacteristic
492C2#1308139911yescharacteristic
493C2#1308151711yescharacteristic
494C2#1308152811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22522
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. Q8×C4⋊Dic11C2semidirect
3. #13069585C2semidirect
4. #13069577C2semidirect
5. #13069571C2semidirect
6. #13069563C2semidirect
11. C2×C11×#446C2semidirect
16. #10623110C4semidirect
94. #66885Q8semidirect
162. C2×#446D11semidirect
217. D44C4×Q8semidirect
407. C11#22522semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
Q8×C4⋊Dic112
#130695852
#130695772
#130695712
#130695632
#130686172
#130684422
C4×#668852
C2×C11×#4462
#2252211