Finite Group Databasebeta

← #14725488

Subgroups — #14725488

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077746C211yesmaximal, characteristic, complemented
2#13077742C211yesmaximal, characteristic, complemented
3C4×#66957C211yesmaximal, characteristic
4#13067517C212yesmaximal, complemented
5#13067465C212yesmaximal, complemented
6#13067444C212yesmaximal, complemented
7#13067427C212yesmaximal, complemented
8#13067053C211yesmaximal, characteristic, complemented
9#13067053C211yesmaximal, characteristic, complemented
10#13066905C211yesmaximal, characteristic, complemented
11C11×#1567C211yesmaximal, characteristic, complemented
12C2×#66957C411yescharacteristic
13C4×#4339C2211yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C11×#423C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18#10622741—22no—
19#10622740—22no—
20#10622726C411yescharacteristic
21#10622726C411yescharacteristic
22#10622719C411yescharacteristic
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622451C2212yes—
26#10622450—21no—
27#10622448—21no—
28#10622447C2212yes—
29#10622446—21no—
30D11×C4⋊C8—21no—
31#10622444C2212yes—
32#10622443C2212yes—
33C4×Dic44C411yescharacteristic
34C4×Dic44C2211yescharacteristic
35C4×D88C411yescharacteristic
36C4×D88C2211yescharacteristic
37C4×#4314C411yescharacteristic
38C4×#4314C411yescharacteristic
39C4×#4314C2211yescharacteristic
40C4×#4314C2211yescharacteristic
41C11×#335C2212yes—
42C11×#335C2212yes—
43#10622122C2212yes—
44#10622122C2212yes—
45#10622121C2212yes—
46#10622121C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C2×#4339C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C22×C8×C11C2×C411yescharacteristic
54C22×C8×C11C2×C411yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C4×C22⋊D11—21no—
57C4×C22⋊D11—21no—
58C4×C22⋊D11—21no—
59C4×C22⋊D11—21no—
60#66979C2×C411yescharacteristic
61#66979C2×C411yescharacteristic
62C2×#4318—21no—
63C2×Dic44C2×C411yescharacteristic
64#66957—24no—
65C2×D88C2×C411yescharacteristic
66C2×#4314C2×C411yescharacteristic
67C2×#4314C2×C411yescharacteristic
68C2×#4313—22no—
69C2×C8×D11—22no—
70C4×D44C2×C411yescharacteristic
71C4×D44C2×C411yescharacteristic
72C4×D44C2311yescharacteristic
73C4×D44C2311yescharacteristic
74#66925—21no—
75#66925—21no—
76C42×D11—21no—
77C42×D11—21no—
78C4×Dic22C2×C411yescharacteristic
79C4×Dic22C2×C411yescharacteristic
80C4×Dic22C2311yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×C4⋊C8—21no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8C2312yes—
85C11×C4⋊C8C2312yes—
86C4×C8×C11C2×C411yescharacteristic
87C4×C8×C11C2×C411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C22⋊(C11⋊C8)D412yes—
91#66885C2×C411yescharacteristic
92#66885C2×C411yescharacteristic
93#66885C2×C411yescharacteristic
94#66885C2×C411yescharacteristic
95(C2×D11)⋊C8—22no—
96(C2×D11)⋊C8—22no—
97#66882C2×C411yescharacteristic
98#66882C2×C411yescharacteristic
99#66881C2×C411yescharacteristic
100#66881C2×C411yescharacteristic
101#66880C2×C411yescharacteristic
102#66880C2×C411yescharacteristic
103#66880C2×C411yescharacteristic
104#66880C2×C411yescharacteristic
105#66879—22no—
106Dic11⋊C8—22no—
107Dic11⋊C8—22no—
108C8×Dic11—22no—
109C4⋊(C11⋊C8)D411yescharacteristic
110C4⋊(C11⋊C8)D411yescharacteristic
111#66867—21no—
112C4×C11⋊C8C2312yes—
113C4×C11⋊C8C2312yes—
114#18061—111nomaximal, Sylow
115C22×C4×C11C22×C411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—21no—
119C2×C22⋊D11—21no—
120#4339—22no—
121#4339—22no—
122#4339—41no—
123#4339—41no—
124C2×D44C22×C411yescharacteristic
125C2×D44C22×C411yescharacteristic
126C2×C4×D11—21no—
127C2×C4×D11—21no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×Dic22C22×C411yescharacteristic
133C2×Dic22C22×C411yescharacteristic
134C11×M16—81no—
135C11×M16—81no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—41no—
140C2×C8×C11C22×C411yescharacteristic
141C2×C8×C11C22×C411yescharacteristic
142C2×C8×C11C22×C411yescharacteristic
143C2×C8×C11C22×C411yescharacteristic
144C42×C11C22×C411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148C22⋊Dic11—21no—
149C22⋊Dic11—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152(C2×D11)⋊C4—21no—
153(C2×D11)⋊C4—21no—
154C4⋊Dic11C22×C411yescharacteristic
155C4⋊Dic11C22×C411yescharacteristic
156C4⋊Dic11C22×C411yescharacteristic
157C4⋊Dic11C22×C411yescharacteristic
158Dic11⋊C4—21no—
159Dic11⋊C4—21no—
160Dic11⋊C4—21no—
161Dic11⋊C4—21no—
162C4×Dic11—21no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168#4318—42no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8C2×D412yes—
171C2×C11⋊C8C2×D412yes—
172Dic44—22no—
173D88—22no—
174#4314—22no—
175#4314M1614yescomplemented
176#4313—82no—
177C8×D11—82no—
178#2991—111no—
179#2990—111no—
180C4×#135—111no—
181#1592—112no—
182#1584—112no—
183#1581—112no—
184SD16⋊C8—112no—
185#1567D1111yescharacteristic, complemented
186#1489—111no—
187#1489—111no—
188#1451—111no—
189C23×C11C4×D411yescharacteristic
190C22×D11—21no—
191C22×D11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—22no—
197C2×C4×C11C4×D411yescharacteristic
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C22⋊D11—42no—
204C22⋊D11—42no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211D44—21no—
212D44—21no—
213D44—21no—
214D44C2×M1612yes—
215C4×D11—42no—
216C4×D11—42no—
217C4×D11—41no—
218C4×D11—41no—
219C4×D11—41no—
220C4×D11—41no—
221C4×D11—42no—
222C4×D11—42no—
223Dic22—21no—
224Dic22—21no—
225Dic22—21no—
226Dic22C2×M1612yes—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11—42no—
231C8×C11—42no—
232C8×C11C2×M1612yes—
233C11⋊C8—22no—
234C11⋊C8—22no—
235C11⋊C8—42no—
236C2×#135—111no—
237C4×#41—111no—
238C4×#41—111no—
239#446—112no—
240C8×Q8—112no—
241C4×Q16—111no—
242C4×Q16—111no—
243C4×SD16—111no—
244C4×SD16—111no—
245C4×SD16—111no—
246C4×SD16—111no—
247C4×D8—111no—
248C4×D8—111no—
249#436—112no—
250#436—222no—
251#435—222no—
252C8×D4—112no—
253#432—221no—
254#431—111no—
255#431—221no—
256#427—111no—
257#423—221no—
258#423C2×D1111yescharacteristic
259#423C2×D1111yescharacteristic
260C2×C4⋊C8—221no—
261#416—111no—
262#416—111no—
263C4×M16—111no—
264C2×C4×C8C2×D1111yescharacteristic
265#335C2×D1112yes—
266#335C2×D1112yes—
267Q8⋊C8—112no—
268Q8⋊C8—112no—
269D4⋊C8—112no—
270D4⋊C8—112no—
271#322—112no—
272#322—112no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11C2×C4×D411yescharacteristic
277C2×D11—22no—
278C2×D11—41no—
279C2×D11—41no—
280C2×D11—41no—
281C2×D11—41no—
282C2×D11—41no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11#44412yes—
287C4×C11C22×M1611yescharacteristic
288C4×C11#56811yescharacteristic
289C4×C11#57611yescharacteristic
290C4×C11#57811yescharacteristic
291Dic11—22no—
292Dic11—41no—
293Dic11—41no—
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297C2×#41—111no—
298C2×#41—111no—
299#135—224no—
300C2×Q16—111no—
301C2×SD16—111no—
302C2×SD16—111no—
303C2×D8—111no—
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—222no—
307C2×M16—221no—
308C22×C8—222no—
309C22×C8C4×D1111yescharacteristic
310C22×C8C4×D1111yescharacteristic
311C4×Q8—111no—
312C4×Q8—111no—
313C4×Q8—111no—
314C4×Q8—111no—
315C4×D4—111no—
316C4×D4—111no—
317C4×D4—111no—
318C4×D4—111no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4—221no—
323#117—111no—
324#117—111no—
325#117—221no—
326#117—221no—
327C2×C42—221no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330#107—111no—
331#107—111no—
332#106—111no—
333#106—111no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—111no—
337C4⋊C8—111no—
338C4⋊C8—222no—
339C4⋊C8—222no—
340C4⋊C8C22×D1112yes—
341C4⋊C8C22×D1112yes—
342#103—111no—
343#103—111no—
344#103—111no—
345#103—111no—
346#102—111no—
347#102—111no—
348#102—111no—
349#102—111no—
350C22⋊C8—112no—
351C22⋊C8—222no—
352C22⋊C8—222no—
353#97—222no—
354#97—221no—
355C4×C8—112no—
356C4×C8—112no—
357C4×C8—222no—
358C4×C8C4×D1111yescharacteristic
359C4×C8C4×D1111yescharacteristic
360C4×C8C22×D1111yescharacteristic
361C4×C8C22×D1111yescharacteristic
362C2×C11—41no—
363C2×C11D4×M1611yescharacteristic
364C2×C11#295111yescharacteristic
365C2×C11C2×#44411yescharacteristic
366D11—42no—
367D11—81no—
368#41—222no—
369#41—222no—
370#41—441no—
371#41—441no—
372C2×Q8—111no—
373C2×Q8—111no—
374C2×D4—111no—
375C2×D4—111no—
376C2×D4—221no—
377C2×D4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4C2×C4×D1111yescharacteristic
385C22×C4D4×D1111yescharacteristic
386C22×C4#434311yescharacteristic
387Q16—222no—
388SD16—114no—
389SD16—222no—
390D8—222no—
391M16—81no—
392M16—81no—
393M16—442no—
394M16—882no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—41no—
399C2×C8—112no—
400C2×C8—112no—
401C2×C8—222no—
402C2×C8—882no—
403C2×C8C2×C4×D1111yescharacteristic
404C2×C8C2×C4×D1111yescharacteristic
405C2×C8C2×C4×D1111yescharacteristic
406C2×C8C2×C4×D1111yescharacteristic
407C4⋊C4—111no—
408C4⋊C4—111no—
409C4⋊C4—111no—
410C4⋊C4—111no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C22⋊C4—221no—
416C22⋊C4—221no—
417C22⋊C4—221no—
418C22⋊C4—221no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C42—221no—
422C42—221no—
423C42—221no—
424C42—221no—
425C42—221no—
426C42—221no—
427C42C2×C4×D1111yescharacteristic
428C42D4×D1111yescharacteristic
429C42#434311yescharacteristic
430C42C23×D1111yescharacteristic
431C11#1806111yescharacteristic, complemented, Sylow
432C23—221no—
433C23—221no—
434C23#6694611yescharacteristic
435Q8—112no—
436Q8—221no—
437Q8—221no—
438Q8—221no—
439D4—112no—
440D4—221no—
441D4—221no—
442D4—221no—
443D4—442no—
444D4—442no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—221no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4#6694611yescharacteristic
465C2×C4#6694611yescharacteristic
466C2×C4#6694611yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C2×#434311yescharacteristic
470C8—21no—
471C8—21no—
472C8—21no—
473C8—42no—
474C8—42no—
475C8—222no—
476C8—222no—
477C8—442no—
478C8M16×D1112yes—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—222no—
483C22—441no—
484C22—441no—
485C22—441no—
486C22—441no—
487C22—441no—
488C22C2×#6694611yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—222no—
493C4—441no—
494C4—441no—
495C4—441no—
496C4—441no—
497C4—441no—
498C4#1062250712yes—
499C4C2×M16×D1111yescharacteristic
500C4#1062327611yescharacteristic
501C4#1062328811yescharacteristic
502C4#1062329711yescharacteristic
503C2—41no—
504C2—442no—
505C2—881no—
506C2#1307735111yescharacteristic
507C2#1307749011yescharacteristic
508C2C2×#1062250711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1567C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C4
cosocleC42×C11C24
hypercenter#1567D11
hypocenterC11#18061
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1567

Complements

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

NH ≅ G/Ntype
1. #13077746C2semidirect
2. #13077742C2semidirect
4. #13067517C2semidirect
5. #13067465C2semidirect
6. #13067444C2semidirect
7. #13067427C2semidirect
8. #13067053C2semidirect
9. #13067053C2semidirect
10. #13066905C2semidirect
11. C11×#1567C2semidirect
175. #4314M16semidirect
185. #1567D11semidirect
431. C11#18061semidirect

Maximal subgroups

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

subgroupindex
#130777462
#130777422
C4×#669572
#130675172
#130674652
#130674442
#130674272
#130670532
#130669052
C11×#15672
#1806111