Finite Group Databasebeta

← #14755181

Subgroups — #14755181

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10623047C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic, complemented
5#13068974C214yesmaximal, complemented
6#13068960C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C11×#2311C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C2×#67004—24no—
15C2×#67004—24no—
16C2×#67004C418yescomplemented
17C22×#4326C2212yes—
18C22×#4324C2212yes—
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22#10623047—24no—
23#10623047—24no—
24C2×#66940—22no—
25C2×#66930—22no—
26C2×C4×Dic22C2214yes—
27C11×#391C2212yes—
28C11×#390C2212yes—
29C11×#386—22no—
30C11×#380—22no—
31#10622846—24no—
32C2×#66899C2212yes—
33C2×#66896C2212yes—
34C2×#66874—24no—
35C2×#66874C2214yes—
36#10622167C2214yes—
37#10622162C2214yes—
38C2×C11×#41—22no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41C2×C414yes—
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C22×Dic22—21no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22C2×C414yes—
56C22×Dic22D414yes—
57C22×Dic22D414yes—
58C22×Dic22C2312yes—
59C11×#117—22no—
60C11×#117—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11C2312yes—
69C2×C22⋊Dic11—21no—
70#67004—232no—
71C2×#4326—24no—
72C2×#4326—24no—
73C2×#4326C2×C418yescomplemented
74C2×#4324—24no—
75C2×#4324—24no—
76C2×#4324C2×C418yescomplemented
77#66979—22no—
78#66979D414yes—
79C2×C4⋊Dic11C2312yes—
80C2×Dic11⋊C4—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—21no—
83C2×#4318—22no—
84C2×#4318—22no—
85C2×#4318C2×C414yes—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8C2312yes—
90C22×C11⋊C8C2312yes—
91#66940—216no—
92#66930—216no—
93C4×Dic22—28no—
94C4×Dic22—28no—
95C11×#95—24no—
96#66899—24no—
97#66896—24no—
98#66874—28no—
99#20930—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D411yescharacteristic
102C11×#41—28no—
103C11×#41—28no—
104C11×#41—44no—
105C11×#41—44no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11C22×C412yes—
112C2×D4×C11—24no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11C22×C412yes—
121C22×C4×C11—21no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—82no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C2×Dic22—28no—
143C2×Dic22—24no—
144C2×Dic22—24no—
145C2×Dic22—28no—
146C2×Dic22—24no—
147C2×Dic22—28no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22C22⋊C4116yescomplemented
152C2×Dic22C22×C414yes—
153C2×Dic22C2×D414yes—
154C2×Dic22C2×D414yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—42no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—84no—
161C42×C11—22no—
162C42×C11—22no—
163C22⋊Dic11—24no—
164#4326—216no—
165#4324—216no—
166C4⋊Dic11—22no—
167C4⋊Dic11C2×D414yes—
168Dic11⋊C4—216no—
169C4×Dic11—216no—
170C4×Dic11—24no—
171#4318—28no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—44no—
178C2×C11⋊C8C22×C414yes—
179C22×#137—111no—
180C2×#519—111no—
181C2×#416—111no—
182C22×#103—111no—
183#2311D1111yescharacteristic
184#1880—114no—
185#1878—114no—
186#1736—111no—
187#1729—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11C4×D412yes—
196C23×C11#12012yes—
197C23×C11#12112yes—
198C23×C11C22×D411yescharacteristic
199Q8×C11—22no—
200Q8×C11—22no—
201Q8×C11—41no—
202Q8×C11—41no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—48no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—48no—
215C2×C4×C11—42no—
216C2×C4×C11—44no—
217C2×C4×C11—84no—
218C2×C4×C11C2×C22⋊C414yes—
219C2×C4×C11C4×D414yes—
220C2×C4×C11C4×D412yes—
221C2×C4×C11#12012yes—
222C2×C4×C11#12114yes—
223C2×C4×C11#12112yes—
224C2×C4×C11#12314yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—216no—
235C2×Dic11—24no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238Dic22—24no—
239Dic22—24no—
240Dic22—24no—
241Dic22—216no—
242Dic22C2×C22⋊C418yes—
243C11⋊C8—24no—
244C11⋊C8—42no—
245C22×#41C2×D1111yescharacteristic
246C23×Q8—111no—
247C2×#137—118no—
248C2×#137—224no—
249C2×#137—224no—
250C22×Q16—112no—
251C22×SD16—112no—
252C22×M16—111no—
253C23×C8—111no—
254#519—224no—
255#519—224no—
256C2×C4×Q8—114no—
257C2×C4×Q8—222no—
258C2×#117—111no—
259C2×#117—222no—
260C2×#117C2×D1111yescharacteristic
261C22×C4⋊C4C2×D1111yescharacteristic
262#416—224no—
263C2×#103—112no—
264C2×#103—114no—
265C2×#103—224no—
266C2×#102—112no—
267#391C2×D1112yes—
268#390C2×D1112yes—
269#386—22no—
270#380—22no—
271#340—114no—
272#336—114no—
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—22no—
276C22×C11—22no—
277C22×C11—44no—
278C22×C11—42no—
279C22×C11—82no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11#38614yes—
283C22×C11C2×C4×D411yescharacteristic
284C22×C11C2×#12011yescharacteristic
285C22×C11C2×#12111yescharacteristic
286C22×C11#57712yes—
287C22×C11#57812yes—
288C4×C11—44no—
289C4×C11—42no—
290C4×C11—82no—
291C4×C11#38614yes—
292C4×C11C22×C22⋊C411yescharacteristic
293C4×C11C2×C4×D411yescharacteristic
294C4×C11C2×#12111yescharacteristic
295C4×C11C2×#12311yescharacteristic
296Dic11—28no—
297Dic11—44no—
298C2×#41—22no—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41C4×D1114yes—
304C22×Q8—114no—
305C22×Q8—114no—
306C22×Q8—114no—
307C22×Q8—112no—
308C22×Q8—222no—
309C22×Q8—222no—
310C22×Q8—222no—
311C22×Q8—221no—
312C22×Q8C22×D1111yescharacteristic
313C22×D4—21no—
314C22×D4C22×D1111yescharacteristic
315C23×C4—21no—
316C23×C4—21no—
317C23×C4—221no—
318C23×C4C22×D1111yescharacteristic
319#137—2232no—
320C2×Q16—118no—
321C2×Q16—224no—
322C2×Q16—224no—
323C2×SD16—118no—
324C2×SD16—224no—
325C2×SD16—224no—
326C2×M16—114no—
327C2×M16—222no—
328C2×M16—222no—
329C22×C8—112no—
330C22×C8—112no—
331C22×C8—222no—
332C22×C8—222no—
333C22×C8—222no—
334C4×Q8—228no—
335C4×Q8—228no—
336C4×Q8—2216no—
337#117—22no—
338#117—22no—
339#117—114no—
340#117—2216no—
341#117—222no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4C22⋊D1112yes—
348C2×C4⋊C4C22×D1112yes—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4C22⋊D1112yes—
352C2×C42—221no—
353C2×C42—224no—
354C2×C42C22×D1112yes—
355#103—228no—
356#103—224no—
357#102—224no—
358#95—24no—
359C2×C11—24no—
360C2×C11—82no—
361C2×C11C2×#38611yescharacteristic
362C2×C11#294712yes—
363C2×C11#301312yes—
364C2×C11#304311yescharacteristic
365C2×C11#304411yescharacteristic
366C24—21no—
367C24C2×C22⋊D1111yescharacteristic
368#41—28no—
369#41—28no—
370#41—44no—
371#41—44no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—1116no—
378C2×Q8—114no—
379C2×Q8—114no—
380C2×Q8—114no—
381C2×Q8—228no—
382C2×Q8—228no—
383C2×Q8—228no—
384C2×Q8—224no—
385C2×Q8—224no—
386C2×Q8—224no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8C2×C4×D1112yes—
391C2×D4—24no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4C2×C4×D1112yes—
400C22×C4—21no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4C2×C4×D1112yes—
413C22×C4#433912yes—
414C22×C4D4×D1112yes—
415C22×C4D4×D1112yes—
416C22×C4D4×D1112yes—
417C22×C4#434112yes—
418C22×C4C2×C22⋊D1114yes—
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421Q16—2216no—
422SD16—2216no—
423M16—228no—
424C2×C8—114no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8—222no—
429C2×C8—222no—
430C2×C8—444no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—42no—
435C4⋊C4—114no—
436C4⋊C4—2216no—
437C4⋊C4—222no—
438C22⋊C4—24no—
439C22⋊C4—84no—
440C22⋊C4—224no—
441C42—22no—
442C42—22no—
443C42—2216no—
444C42—224no—
445C11#2093011yescharacteristic, complemented, Sylow
446C23—22no—
447C23—22no—
448C23—22no—
449C23—41no—
450C23—41no—
451C23—42no—
452C23—42no—
453C23C4×C22⋊D1112yes—
454C23#6699012yes—
455C23#6699112yes—
456C23C22×C22⋊D1111yescharacteristic
457Q8—22no—
458Q8—22no—
459Q8—41no—
460Q8—41no—
461Q8—118no—
462Q8—224no—
463Q8—224no—
464Q8—224no—
465Q8—2216no—
466D4—22no—
467D4—22no—
468D4—48no—
469D4—41no—
470D4—41no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—48no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—84no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—2216no—
485C2×C4—224no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4C22⋊C4×D1114yes—
489C2×C4(C22⋊D11)⋊C414yes—
490C2×C4#6693614yes—
491C2×C4#6693714yes—
492C2×C4C4×C22⋊D1112yes—
493C2×C4#6699012yes—
494C2×C4#6699112yes—
495C2×C4C22×C4×D1111yescharacteristic
496C2×C4C2×#433911yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C2×C4C2×D4×D1111yescharacteristic
500C2×C4C2×#434111yescharacteristic
501C8—224no—
502C8—442no—
503C22—22no—
504C22—22no—
505C22—24no—
506C22—24no—
507C22—42no—
508C22—44no—
509C22—81no—
510C22—81no—
511C22—82no—
512C22#1062256914yes—
513C22C2×C4×C22⋊D1111yescharacteristic
514C22C2×#6699011yescharacteristic
515C22C2×#6699111yescharacteristic
516C22#1062336712yes—
517C22#1062336912yes—
518C4—44no—
519C4—42no—
520C4—82no—
521C4—228no—
522C4—444no—
523C4#1062256914yes—
524C4C2×C22⋊C4×D1111yescharacteristic
525C4C2×(C22⋊D11)⋊C411yescharacteristic
526C4C2×#6693611yescharacteristic
527C4C2×#6693711yescharacteristic
528C2—24no—
529C2—82no—
530C2C2×#1062256911yescharacteristic
531C2#1307745512yes—
532C2#1307792812yes—
533C2#1307813311yescharacteristic
534C2#1307814211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2311C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2311D11
hypocenterC11#20930
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#10623047C2semidirect
4. C22×#66874C2semidirect
5. #13068974C2semidirect
6. #13068960C2semidirect
7. #13068335C2semidirect
8. #13068313C2semidirect
16. C2×#67004C4semidirect
73. C2×#4326C2×C4semidirect
76. C2×#4324C2×C4semidirect
151. C2×Dic22C22⋊C4semidirect
445. C11#20930semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106230472
C2×#106228462
C22×#668742
#130689742
#130689602
#130683352
#130683132
C11×#23112
#2093011