Finite Group Databasebeta

← #14756327

Subgroups — #14756327

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic, complemented
2#13077136C211yesmaximal, characteristic
3C2×#10622579C211yesmaximal, characteristic
4C2×#10622745C211yesmaximal, characteristic
5#13077034C211yesmaximal, characteristic, complemented
6#13069276C214yesmaximal, complemented
7#13069269C214yesmaximal, complemented
8#13068342C211yesmaximal, characteristic, complemented
9C2×C11×#343C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×#66888C2212yes—
18#10622746—21no—
19#10622746—21no—
20#10622745C418yescomplemented
21#10622744C2212yes—
22C2×#66887C2212yes—
23#10622735C2214yes—
24#10622733C2212yes—
25M16×Dic11—22no—
26#10622726—22no—
27#10622714—22no—
28C2×#66874C2212yes—
29#10622579—22no—
30#10622579—22no—
31C2×#66873C2212yes—
32#10622577—22no—
33#10622577C2214yes—
34C2×#66872—21no—
35C2×#66871—21no—
36C11×#343C2214yes—
37#10622196C2214yes—
38C23×C4×C11—21no—
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11—21no—
41C2×#4339—22no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339C2×C414yes—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22C2311yescharacteristic
52C2×C11×M16—21no—
53C2×C11×M16—22no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16C2×C414yes—
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2312yes—
68C2×C22⋊Dic11—21no—
69#66979—21no—
70#66979—21no—
71#66979D412yes—
72#66979C2312yes—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4×Dic11—21no—
76C2×#4318—21no—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318—22no—
80C2×#4318C2×C414yes—
81C2×#4318D412yes—
82C2×#4318D412yes—
83C2×#4318C2312yes—
84C22×C11⋊C8—21no—
85C22×C11⋊C8C2312yes—
86#66888C2×C418yescomplemented
87#66887C2×C418yescomplemented
88#66885—22no—
89#66885—22no—
90#66880—22no—
91#66880—22no—
92#66879—24no—
93C8×Dic11—24no—
94#66874—24no—
95#66873—24no—
96#66872—24no—
97#66871—24no—
98#21076—111nomaximal, Sylow
99C24×C11#4111yescharacteristic
100C23×D11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—82no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—24no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—42no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122#4339—24no—
123#4339—24no—
124#4339—24no—
125#4339—24no—
126#4339—42no—
127#4339—42no—
128#4339—42no—
129#4339—42no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44C22×C412yes—
136C2×C4×D11—24no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—42no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22C22×C412yes—
146C11×M16—24no—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—42no—
151C11×M16C22×C414yes—
152C2×C8×C11—24no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—42no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C22⋊Dic11—22no—
161C22⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D412yes—
165C4⋊Dic11C2×D412yes—
166C4×Dic11—22no—
167C4×Dic11—22no—
168#4318—24no—
169#4318—24no—
170#4318—24no—
171#4318—22no—
172#4318C22×C414yes—
173C2×C11⋊C8—24no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8C2×D414yes—
178C2×#428—111no—
179#2896—111no—
180C2×#417—111no—
181C2×#413—111no—
182#2873—111no—
183#1931—114no—
184#1930—114no—
185C2×#343D1111yescharacteristic, complemented
186#1738—111no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11#11712yes—
190C23×C11#12111yescharacteristic
191C23×C11#12111yescharacteristic
192C23×C11#12612yes—
193C23×C11C2×#4111yescharacteristic
194C22×D11—22no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—81no—
198C22×D11—81no—
199C2×C4×C11—42no—
200C2×C4×C11—82no—
201C2×C4×C11—82no—
202C2×C4×C11—82no—
203C2×C4×C11#11712yes—
204C2×C4×C11C4×D412yes—
205C2×C4×C11C4×D412yes—
206C2×C4×C11C4×D412yes—
207C2×C4×C11C4×D412yes—
208C2×C4×C11#12111yescharacteristic
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12312yes—
211C2×C4×C11#12312yes—
212C2×C4×C11#12412yes—
213C2×C4×C11#12412yes—
214C2×C4×C11#12612yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C22⋊D11—44no—
222C22⋊D11—44no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—81no—
229C2×Dic11—81no—
230D44—22no—
231D44—22no—
232D44—41no—
233D44—41no—
234C4×D11—44no—
235C4×D11—44no—
236Dic22—22no—
237Dic22—22no—
238Dic22—41no—
239Dic22—41no—
240C8×C11—24no—
241C8×C11—42no—
242C11⋊C8—24no—
243C11⋊C8—24no—
244C22×#41—111no—
245C22×M16—111no—
246C22×M16—111no—
247C22×M16C2×D1111yescharacteristic
248C22×M16C2×D1111yescharacteristic
249C2×#117—111no—
250C22×C4⋊C4C2×D1111yescharacteristic
251#428—114no—
252#428—222no—
253C2×#107—221no—
254C2×#106—221no—
255#419—112no—
256#418—112no—
257#417—222no—
258#417—222no—
259#417—221no—
260#417—221no—
261#416—222no—
262C2×#103—112no—
263C2×#102—112no—
264#413—118no—
265C2×#101—112no—
266C2×#100—112no—
267#405—114no—
268#405—222no—
269C4×M16—222no—
270#343C2×D1114yes—
271#341—114no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11#38812yes—
281C22×C11#38812yes—
282C22×C11C2×#11711yescharacteristic
283C22×C11C2×#12111yescharacteristic
284C22×C11C2×#12611yescharacteristic
285C2×D11—42no—
286C2×D11—82no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—82no—
290C4×C11—82no—
291C4×C11#38812yes—
292C4×C11#38812yes—
293C4×C11C2×C4×D411yescharacteristic
294C4×C11C2×C4×D411yescharacteristic
295C4×C11C2×#12311yescharacteristic
296C4×C11C2×#12411yescharacteristic
297Dic11—42no—
298Dic11—42no—
299Dic11—42no—
300C2×#41—114no—
301C2×#41—222no—
302C2×#41—221no—
303C2×#41—221no—
304C2×#41—221no—
305C2×#41—221no—
306C2×#41—222no—
307C2×#41—222no—
308C22×Q8—111no—
309C22×D4—111no—
310C22×D4—221no—
311C23×C4—21no—
312C23×C4—221no—
313C23×C4C22×D1111yescharacteristic
314C2×M16—21no—
315C2×M16—22no—
316C2×M16—21no—
317C2×M16—22no—
318C2×M16—22no—
319C2×M16—112no—
320C2×M16—112no—
321C2×M16—114no—
322C2×M16—112no—
323C2×M16—222no—
324C2×M16—221no—
325C2×M16—222no—
326C2×M16—222no—
327C2×M16C4×D1114yes—
328C2×M16C22×D1112yes—
329C2×M16C22×D1112yes—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—112no—
333C22×C8—221no—
334#117—112no—
335#117—112no—
336#117—221no—
337#117—221no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4C22×D1112yes—
346C2×C22⋊C4—221no—
347C2×C42—221no—
348#107—224no—
349#106—224no—
350#103—224no—
351#103—222no—
352#103—222no—
353#102—224no—
354#102—222no—
355#102—222no—
356#101—118no—
357#100—118no—
358#97—224no—
359C4×C8—224no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—22no—
363C2×C11—22no—
364C2×C11C2×#38811yescharacteristic
365C2×C11#306811yescharacteristic
366C2×C11#306911yescharacteristic
367D11—82no—
368C24—221no—
369C24#433911yescharacteristic
370#41—224no—
371#41—224no—
372#41—224no—
373#41—224no—
374#41—442no—
375#41—442no—
376#41—442no—
377#41—442no—
378C2×Q8—112no—
379C2×Q8—221no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×Q8—221no—
383C2×Q8—221no—
384C2×D4—112no—
385C2×D4—224no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—442no—
394C22×C4—22no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—82no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—221no—
401C22×C4—224no—
402C22×C4—441no—
403C22×C4—441no—
404C22×C4—442no—
405C22×C4C2×C4×D1112yes—
406C22×C4#433911yescharacteristic
407C22×C4#433912yes—
408C22×C4D4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4#434112yes—
413C22×C4#434312yes—
414C22×C4C23×D1111yescharacteristic
415M16—24no—
416M16—22no—
417M16—22no—
418M16—22no—
419M16—42no—
420M16—114no—
421M16—224no—
422M16—224no—
423M16—224no—
424M16—222no—
425M16C2×C4×D1114yes—
426C2×C8—24no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—42no—
430C2×C8—114no—
431C2×C8—224no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—112no—
440C4⋊C4—112no—
441C4⋊C4—221no—
442C4⋊C4—221no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C42—222no—
446C42—222no—
447C11#2107611yescharacteristic, complemented, Sylow
448C23—41no—
449C23—41no—
450C23—222no—
451C23—441no—
452C23—441no—
453C23—881no—
454C23—881no—
455C23#6692512yes—
456C23#6693711yescharacteristic
457C23#6693711yescharacteristic
458C23#6695112yes—
459C23C2×#433911yescharacteristic
460Q8—222no—
461Q8—222no—
462Q8—441no—
463Q8—441no—
464D4—222no—
465D4—222no—
466D4—444no—
467D4—444no—
468D4—441no—
469D4—441no—
470C2×C4—42no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—444no—
480C2×C4—444no—
481C2×C4—881no—
482C2×C4—881no—
483C2×C4#6692512yes—
484C2×C4(C22⋊D11)⋊C412yes—
485C2×C4(C22⋊D11)⋊C412yes—
486C2×C4#6693711yescharacteristic
487C2×C4#6693711yescharacteristic
488C2×C4#6693812yes—
489C2×C4#6693812yes—
490C2×C4#6694612yes—
491C2×C4#6694612yes—
492C2×C4#6694712yes—
493C2×C4#6694712yes—
494C2×C4#6695112yes—
495C2×C4C22×C4×D1111yescharacteristic
496C2×C4C2×#433911yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4C2×#434111yescharacteristic
500C2×C4C2×#434311yescharacteristic
501C8—24no—
502C8—42no—
503C8—224no—
504C8—224no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—442no—
514C22—882no—
515C22—882no—
516C22—881no—
517C22—881no—
518C22#1062228212yes—
519C22#1062228212yes—
520C22C2×#6692511yescharacteristic
521C22C2×#6693711yescharacteristic
522C22C2×#6695111yescharacteristic
523C4—82no—
524C4—442no—
525C4—442no—
526C4—442no—
527C4#1062228212yes—
528C4#1062228212yes—
529C4C2×(C22⋊D11)⋊C411yescharacteristic
530C4C2×#6693811yescharacteristic
531C4C2×#6694611yescharacteristic
532C4C2×#6694711yescharacteristic
533C2—21no—
534C2—21no—
535C2—22no—
536C2—22no—
537C2—882no—
538C2C2×#1062228211yescharacteristic
539C2#1307834311yescharacteristic
540C2#1307835211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#343C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#343D11
hypocenterC11#21076
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
1. C2×#10622577C2semidirect
5. #13077034C2semidirect
6. #13069276C2semidirect
7. #13069269C2semidirect
8. #13068342C2semidirect
9. C2×C11×#343C2semidirect
20. #10622745C4semidirect
86. #66888C2×C4semidirect
87. #66887C2×C4semidirect
185. C2×#343D11semidirect
447. C11#21076semidirect

Maximal subgroups

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

subgroupindex
C2×#106225772
#130771362
C2×#106225792
C2×#106227452
#130770342
#130692762
#130692692
#130683422
C2×C11×#3432
#2107611