Finite Group Databasebeta

← #14770622

Subgroups — #14770622

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069546C212yesmaximal, complemented
4#13069542C211yesmaximal, characteristic
5#13069432C212yesmaximal, complemented
6#13069422C211yesmaximal, characteristic
7#13068622C211yesmaximal, characteristic, complemented
8#13068617C212yesmaximal, complemented
9#13068442C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000—21no—
14C2×Q8×Dic11—21no—
15#10623116—24no—
16#10623116C418yescomplemented
17C2×#66947—22no—
18C2×#66946—21no—
19C2×#66928C2212yes—
20C2×#66927C2211yescharacteristic
21C2×C4×D44C2212yes—
22C2×C4×Dic22C2211yescharacteristic
23C11×#446—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#97C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66885C2212yes—
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×#66885C2212yes—
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2212yes—
35#10622598—21no—
36#10622598—22no—
37#10622548C2212yes—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2211yescharacteristic
44C22×Q8×C11D411yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44C2312yes—
48C22×C4×D11—22no—
49C22×Dic22C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C4×Q8×C11C2×C414yes—
54C4×Q8×C11D414yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C42×C11C2312yes—
59#67000—28no—
60Q8×Dic11—44no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2312yes—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×Dic11⋊C4—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—21no—
76#66947—216no—
77#66946—28no—
78#66928—24no—
79#66928C2×C418yes—
80#66927—22no—
81#66927C2×C414yes—
82C4×D44—24no—
83C4×D44C2×C418yes—
84C4×Dic22—22no—
85C4×Dic22C2×C414yes—
86C11×C4⋊C8—22no—
87C11×C4⋊C8—24no—
88C11×#97—24no—
89C4×C8×C11—22no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92#66885—24no—
93#66885—24no—
94#66885—42no—
95#66885—42no—
96#66880—22no—
97#66880—22no—
98#66880—42no—
99#22546—111nomaximal, Sylow
100C23×D11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C22⋊C414yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C2×D44—24no—
115C2×D44—24no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—22no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—81no—
124C2×D44—81no—
125C2×D44C22×C414yes—
126C2×C4×D11—28no—
127C2×C4×D11—82no—
128C2×C4×D11—82no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22C22×C412yes—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11#4112yes—
144C11×C4⋊C4C22⋊C414yes—
145C11×C4⋊C4C22⋊C418yes—
146C42×C11C22×C412yes—
147C42×C11C22×C414yes—
148C42×C11C2×D412yes—
149C42×C11C2×D414yes—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—28no—
152(C2×D11)⋊C4—28no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—22no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—44no—
160C4⋊Dic11—42no—
161C4⋊Dic11—82no—
162C4⋊Dic11—81no—
163C4⋊Dic11C22×C412yes—
164C4⋊Dic11#4112yes—
165Dic11⋊C4—24no—
166C4×Dic11—24no—
167C4×Dic11—44no—
168C4×Dic11—42no—
169C2×#559—111no—
170C2×#446D1111yescharacteristic, complemented
171Q8×C4⋊C4—111no—
172#1983—112no—
173#1982—111no—
174#1959—112no—
175#1957—111no—
176#1803—111no—
177#1802—112no—
178#1762—112no—
179C4×#103—111no—
180C23×C11C22×D411yescharacteristic
181C22×D11—24no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188Q8×C11—28no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×C22⋊C414yes—
197C2×C4×C11C2×C22⋊C414yes—
198C2×C4×C11C2×C22⋊C412yes—
199C2×C4×C11AGL(1,ℤ/8)12yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C23×C411yescharacteristic
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222D44—24no—
223D44—24no—
224D44—42no—
225D44—42no—
226D44—48no—
227D44—84no—
228C4×D11—88no—
229Dic22—22no—
230Dic22—22no—
231Dic22—41no—
232Dic22—41no—
233C8×C11—22no—
234C8×C11—41no—
235C8×C11—42no—
236#559—118no—
237#559—224no—
238C2×#127—111no—
239C2×#124—112no—
240C2×#124—221no—
241C2×#123—222no—
242C2×C4×Q8—111no—
243C2×C4×Q8—221no—
244C2×C4×Q8C2×D1111yescharacteristic
245C2×C4×D4—112no—
246C2×C4×D4—221no—
247#446—24no—
248C2×C4⋊C8C2×D1112yes—
249C2×C4⋊C8C2×D1111yescharacteristic
250C2×#103—111no—
251C2×#103—111no—
252C2×#103—112no—
253C2×#102—112no—
254C2×#102—112no—
255C2×#102—112no—
256C2×#102—112no—
257C2×#97C2×D1112yes—
258C2×C4×C8C2×D1111yescharacteristic
259#389—221no—
260#389—222no—
261#384—112no—
262#384—111no—
263C4×C4⋊C4—111no—
264C4×C4⋊C4—112no—
265#340—111no—
266#340—112no—
267#340—111no—
268C22×C11C22×C22⋊C411yescharacteristic
269C22×C11#54811yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11#57611yescharacteristic
274C22×C11#57711yescharacteristic
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—82no—
279C2×D11—82no—
280C2×D11—82no—
281C2×D11—82no—
282C4×C11—24no—
283C4×C11—24no—
284C4×C11—22no—
285C4×C11#41714yes—
286C4×C11C4×#4111yescharacteristic
287C4×C11#52011yescharacteristic
288C4×C11#54811yescharacteristic
289C4×C11#55011yescharacteristic
290Dic11—42no—
291Dic11—42no—
292Dic11—42no—
293Dic11—81no—
294Dic11—82no—
295C22×Q8—111no—
296C22×Q8D4411yescharacteristic
297C22×D4—112no—
298C22×D4—221no—
299C22×D4—221no—
300C23×C4—222no—
301C22×C8C22×D1111yescharacteristic
302C22×C8C22×D1112yes—
303C22×C8C22×D1111yescharacteristic
304#127—114no—
305#127—222no—
306#124—118no—
307#124—228no—
308#124—224no—
309#123—2216no—
310C4×Q8—114no—
311C4×Q8—222no—
312C4×Q8—444no—
313C4×Q8C4×D1114yes—
314C4×Q8C22⋊D1114yes—
315C4×D4—118no—
316C4×D4—228no—
317C4×D4—224no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—222no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4D4411yescharacteristic
328C2×C4⋊C4D4412yes—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C42—221no—
333C2×C42—222no—
334C2×C42—221no—
335C2×C42C22×D1112yes—
336C2×C42C22×D1111yescharacteristic
337C4⋊C8—22no—
338C4⋊C8—24no—
339#103—222no—
340#103—222no—
341#103—442no—
342#102—224no—
343#102—224no—
344#102—442no—
345#102—442no—
346#97—24no—
347C4×C8—22no—
348#95—222no—
349#95—221no—
350C2×C11#234111yescharacteristic
351C2×C11C2×#41711yescharacteristic
352C2×C11#289711yescharacteristic
353C2×C11#337311yescharacteristic
354C2×C11#337511yescharacteristic
355C2×C11#339911yescharacteristic
356C2×C11#340011yescharacteristic
357D11—84no—
358C24—222no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—112no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×Q8(C2×D11)⋊C414yes—
368C2×D4—114no—
369C2×D4—224no—
370C2×D4—224no—
371C2×D4—222no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—442no—
377C2×D4—442no—
378C2×D4—881no—
379C2×D4—881no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—228no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—882no—
387C22×C4—882no—
388C22×C4C2×D4412yes—
389C22×C4C2×D4411yescharacteristic
390C22×C4C2×D4412yes—
391C22×C4C2×D4411yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—22no—
401C2×C8#434312yes—
402C4⋊C4—112no—
403C4⋊C4—112no—
404C4⋊C4—224no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—222no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—444no—
412C4⋊C4—442no—
413C4⋊C4—882no—
414C4⋊C4—881no—
415C4⋊C4(C2×D11)⋊C414yes—
416C4⋊C4(C2×D11)⋊C418yes—
417C22⋊C4—228no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C42—224no—
421C42—444no—
422C42—442no—
423C42C2×C4×D1114yes—
424C42C2×C4×D1112yes—
425C42C2×C22⋊D1112yes—
426C42C2×C22⋊D1114yes—
427C11#2254611yescharacteristic, complemented, Sylow
428C23—224no—
429C23—442no—
430C23—442no—
431C23—442no—
432C23—442no—
433C23—442no—
434C23—442no—
435C23C22×D4411yescharacteristic
436Q8—28no—
437Q8—222no—
438Q8—222no—
439Q8—441no—
440Q8—441no—
441D4—224no—
442D4—224no—
443D4—448no—
444D4—442no—
445D4—442no—
446D4—884no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—888no—
469C2×C4#6696112yes—
470C2×C4#6696212yes—
471C2×C4C2×(C2×D11)⋊C414yes—
472C2×C4C2×(C2×D11)⋊C414yes—
473C2×C4C2×(C2×D11)⋊C412yes—
474C2×C4C2×(C2×D11)⋊C412yes—
475C2×C4C22×C4×D1111yescharacteristic
476C2×C4C2×#434311yescharacteristic
477C2×C4#6704011yescharacteristic
478C2×C4#41×D1111yescharacteristic
479C2×C4#6704211yescharacteristic
480C2×C4C22×C22⋊D1111yescharacteristic
481C8—22no—
482C8—42no—
483C8—41no—
484C22—444no—
485C22—444no—
486C22—444no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—882no—
491C22#1062310711yescharacteristic
492C22#1062310811yescharacteristic
493C22C2×#6696111yescharacteristic
494C22C2×#6696211yescharacteristic
495C22#1062328211yescharacteristic
496C22#1062328311yescharacteristic
497C22C22×(C2×D11)⋊C411yescharacteristic
498C4—24no—
499C4—24no—
500C4—22no—
501C4—442no—
502C4—442no—
503C4—442no—
504C4—882no—
505C4—881no—
506C4#1062274614yes—
507C4C4×#434311yescharacteristic
508C4#1062310511yescharacteristic
509C4#1062334811yescharacteristic
510C4#1062336511yescharacteristic
511C2—884no—
512C2#1307145411yescharacteristic
513C2C2×#1062274611yescharacteristic
514C2#1307714311yescharacteristic
515C2#1308141011yescharacteristic
516C2#1308143211yescharacteristic
517C2#1308166011yescharacteristic
518C2#1308167111yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
cosocleC22×C4×C11C24
hypercenterC2×#446D11
hypocenterC11#22546
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. #13069546C2semidirect
5. #13069432C2semidirect
7. #13068622C2semidirect
8. #13068617C2semidirect
9. #13068442C2semidirect
10. C4×#66880C2semidirect
11. C2×C11×#446C2semidirect
16. #10623116C4semidirect
170. C2×#446D11semidirect
427. C11#22546semidirect

Maximal subgroups

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

subgroupindex
C2×#106231162
Q8×C4⋊Dic112
#130695462
#130695422
#130694322
#130694222
#130686222
#130686172
#130684422
C4×#668802
C2×C11×#4462
#2254611