Finite Group Databasebeta

← #14725521

Subgroups — #14725521

Order 2816.

652 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#13077737C211yesmaximal, characteristic, complemented
2C4×#67003C211yesmaximal, characteristic
3#13067523C212yesmaximal, complemented
4#13067452C212yesmaximal, complemented
5#13067450C212yesmaximal, complemented
6#13067438C212yesmaximal, complemented
7#13067371C211yesmaximal, characteristic, complemented
8#13067055C211yesmaximal, characteristic, complemented
9#13067053C211yesmaximal, characteristic, complemented
10#13066906C211yesmaximal, characteristic, complemented
11C11×#2990C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13C2×#67003C411yescharacteristic
14C4×#4339C2211yescharacteristic
15C11×#446C2212yes—
16C11×#435—22no—
17C8×D4×C11C2212yes—
18C11×#432—21no—
19C11×#431C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C2×C11×C4⋊C8—21no—
22#10622846C411yescharacteristic
23C4×#4326C411yescharacteristic
24C4×#4326C2211yescharacteristic
25C4×#4325C411yescharacteristic
26C4×#4325C2211yescharacteristic
27C4×#4324C411yescharacteristic
28C4×#4324C2211yescharacteristic
29C4×#4323C411yescharacteristic
30C4×#4323C2211yescharacteristic
31#10622615C411yescharacteristic
32#10622611C411yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622448—21no—
37D11×C4⋊C8—21no—
38#10622341—22no—
39C8×D44C2212yes—
40#10622292C2212yes—
41Q8⋊(C11⋊C8)C2212yes—
42D4⋊(C11⋊C8)C2212yes—
43#10622122C2212yes—
44#10622121C2212yes—
45#10622118C2212yes—
46#10622118C2212yes—
47#10622093C2212yes—
48#10622092C2212yes—
49C2×C11×#41C2×C411yescharacteristic
50C2×#4339C2×C411yescharacteristic
51C2×C11×M16—21no—
52C22×C8×C11—22no—
53C4×Q8×C11C2×C411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×D4×C11—21no—
56C4×D4×C11—21no—
57C4×D4×C11C2×C411yescharacteristic
58C4×D4×C11C2311yescharacteristic
59C11×#117—21no—
60C11×#117C2×C411yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#67003—24no—
64C2×#4326C2×C411yescharacteristic
65C2×#4325C2×C411yescharacteristic
66C2×#4324C2×C411yescharacteristic
67C2×#4323C2×C411yescharacteristic
68C4×C22⋊D11—21no—
69C4×C22⋊D11—21no—
70#66979C2×C411yescharacteristic
71C2×#4318—21no—
72C2×#4318—21no—
73C22×C11⋊C8C2×C411yescharacteristic
74C22×C11⋊C8C2×C411yescharacteristic
75C2×C8×D11—22no—
76C4×D44C2×C411yescharacteristic
77C4×D44C2311yescharacteristic
78#66925—21no—
79C42×D11—21no—
80C4×Dic22C2×C411yescharacteristic
81C4×Dic22C2311yescharacteristic
82C11×C4⋊C8—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8D411yescharacteristic
85C11×C4⋊C8D411yescharacteristic
86C11×C4⋊C8C2312yes—
87C11×C22⋊C8—22no—
88C11×C22⋊C8D412yes—
89C11×#97—22no—
90C4×C8×C11C2312yes—
91#66899C2×C411yescharacteristic
92#66899C2×C411yescharacteristic
93#66896C2×C411yescharacteristic
94#66896C2×C411yescharacteristic
95(C2×D11)⋊C8—22no—
96#66879—22no—
97Dic11⋊C8—22no—
98#66874C2×C411yescharacteristic
99#66874C2×C411yescharacteristic
100#66873C2×C411yescharacteristic
101#66873C2×C411yescharacteristic
102#66872C2×C411yescharacteristic
103#66872C2×C411yescharacteristic
104#66871C2×C411yescharacteristic
105#66871C2×C411yescharacteristic
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108#66867—21no—
109C4×C11⋊C8C2×C411yescharacteristic
110C4×C11⋊C8C2×C411yescharacteristic
111C4×C11⋊C8C2312yes—
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114#18065—111nomaximal, Sylow
115C11×#41—22no—
116C11×#41—41no—
117C2×Q8×C11C22×C411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11C22×C411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—21no—
127#4339—22no—
128#4339—41no—
129C2×D44C22×C411yescharacteristic
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×Dic22C22×C411yescharacteristic
134C11×M16—81no—
135C2×C8×C11—22no—
136C2×C8×C11—82no—
137C2×C8×C11C2×D412yes—
138C2×C8×C11C2×D412yes—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C22×C411yescharacteristic
142C11×C4⋊C4C22×C411yescharacteristic
143C11×C22⋊C4—21no—
144C11×C22⋊C4—21no—
145C11×C22⋊C4—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C22×C411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11#4111yescharacteristic
152C42×C11C2411yescharacteristic
153C22⋊Dic11—21no—
154#4326—22no—
155#4325—22no—
156#4324—22no—
157#4323M1614yescomplemented
158(C2×D11)⋊C4—21no—
159(C2×D11)⋊C4—21no—
160C4⋊Dic11C22×C411yescharacteristic
161C4⋊Dic11C22×C411yescharacteristic
162Dic11⋊C4—21no—
163Dic11⋊C4—21no—
164C4×Dic11—21no—
165C4×Dic11—21no—
166C4×Dic11—21no—
167#4318—42no—
168#4318—81no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—41no—
173C2×C11⋊C8C22×C411yescharacteristic
174C2×C11⋊C8C22×C411yescharacteristic
175C2×C11⋊C8C22×C411yescharacteristic
176C2×C11⋊C8C22×C411yescharacteristic
177C8×D11—82no—
178#2990—111no—
179#2990D1111yescharacteristic, complemented
180C4×#135—111no—
181#1593—112no—
182#1582—112no—
183#1582—112no—
184#1580—112no—
185#1566—111no—
186#1489—111no—
187#1489—111no—
188#1451—111no—
189C23×C11—21no—
190C23×C11C4×D411yescharacteristic
191C22×D11—21no—
192Q8×C11—21no—
193Q8×C11—21no—
194D4×C11—21no—
195D4×C11—42no—
196D4×C11C2×M1612yes—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C4×D411yescharacteristic
211C2×C4×C11C4×D411yescharacteristic
212C2×C4×C11C23×C411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C22⋊D11—42no—
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—21no—
219D44—21no—
220D44C2×M1612yes—
221C4×D11—42no—
222C4×D11—41no—
223C4×D11—41no—
224C4×D11—42no—
225Dic22—21no—
226Dic22—21no—
227C8×C11—22no—
228C8×C11—22no—
229C8×C11—42no—
230C11⋊C8—21no—
231C11⋊C8—21no—
232C11⋊C8—21no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C11⋊C8C2×M1612yes—
236C2×#135—111no—
237C4×#41—111no—
238C4×#41C2×D1111yescharacteristic
239#446—112no—
240#446C2×D1112yes—
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#435—22no—
250#435—222no—
251C8×D4—112no—
252C8×D4C2×D1112yes—
253#432—21no—
254#432—221no—
255#431C2×D1111yescharacteristic
256#427—111no—
257#423—111no—
258#423C2×D1111yescharacteristic
259C2×C4⋊C8—21no—
260C2×C4⋊C8—221no—
261#416—111no—
262#416—111no—
263C4×M16—111no—
264C2×C4×C8—111no—
265#334—112no—
266#334—112no—
267Q8⋊C8—112no—
268Q8⋊C8—112no—
269D4⋊C8—112no—
270D4⋊C8—112no—
271#322—112no—
272#322—112no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11C2×C4×D411yescharacteristic
280C2×D11—22no—
281C2×D11—41no—
282C2×D11—41no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11#44412yes—
290C4×C11C22×M1611yescharacteristic
291C4×C11#56811yescharacteristic
292C4×C11#57711yescharacteristic
293C4×C11#57711yescharacteristic
294Dic11—41no—
295Dic11—41no—
296Dic11—41no—
297C2×#41—111no—
298C2×#41C4×D1111yescharacteristic
299#135—224no—
300C2×Q16—111no—
301C2×SD16—111no—
302C2×SD16—111no—
303C2×D8—111no—
304C2×M16—21no—
305C2×M16—221no—
306C2×M16—221no—
307C22×C8—22no—
308C22×C8—111no—
309C22×C8—111no—
310C22×C8—222no—
311C4×Q8—111no—
312C4×Q8—111no—
313C4×Q8C4×D1111yescharacteristic
314C4×Q8C22×D1111yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—111no—
318C4×D4—111no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4C4×D1111yescharacteristic
322C4×D4C22×D1111yescharacteristic
323#117—21no—
324#117—111no—
325#117—221no—
326#117C4×D1111yescharacteristic
327C2×C42—21no—
328C2×C42—221no—
329C2×C42C22×D1111yescharacteristic
330#107—111no—
331#107—111no—
332#106—111no—
333#106—111no—
334C4⋊C8—22no—
335C4⋊C8—21no—
336C4⋊C8—112no—
337C4⋊C8—222no—
338C4⋊C8—221no—
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22⋊D1111yescharacteristic
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—22no—
351C22⋊C8—222no—
352C22⋊C8C22⋊D1112yes—
353#97—22no—
354#97—222no—
355#97—221no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8—111no—
359C4×C8—111no—
360C4×C8—112no—
361C4×C8C22×D1112yes—
362C2×C11—41no—
363C2×C11—42no—
364C2×C11D4×M1611yescharacteristic
365C2×C11#295211yescharacteristic
366C2×C11C2×#44411yescharacteristic
367D11—42no—
368#41—22no—
369#41—41no—
370#41—222no—
371#41—441no—
372C2×Q8—111no—
373C2×Q8C2×C4×D1111yescharacteristic
374C2×D4—21no—
375C2×D4—111no—
376C2×D4—221no—
377C2×D4C2×C4×D1111yescharacteristic
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4C2×C4×D1111yescharacteristic
385C22×C4#433911yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387Q16—222no—
388SD16—222no—
389SD16—222no—
390D8—114no—
391M16—81no—
392M16—442no—
393M16—881no—
394C2×C8—22no—
395C2×C8—82no—
396C2×C8—111no—
397C2×C8—111no—
398C2×C8—111no—
399C2×C8—111no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—222no—
403C2×C8—441no—
404C2×C8—882no—
405C2×C8C2×C22⋊D1112yes—
406C2×C8C2×C22⋊D1112yes—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—111no—
410C4⋊C4—111no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4C2×C4×D1111yescharacteristic
414C4⋊C4C2×C4×D1111yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—21no—
417C22⋊C4—21no—
418C22⋊C4—221no—
419C22⋊C4—221no—
420C22⋊C4—221no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—221no—
425C42—221no—
426C42—221no—
427C42C2×C4×D1111yescharacteristic
428C42#433911yescharacteristic
429C42C2×C22⋊D1111yescharacteristic
430C42C23×D1111yescharacteristic
431C11#1806511yescharacteristic, complemented, Sylow
432C23—21no—
433C23—221no—
434C23C4×C22⋊D1111yescharacteristic
435Q8—21no—
436Q8—21no—
437Q8—221no—
438Q8—221no—
439D4—21no—
440D4—42no—
441D4—112no—
442D4—221no—
443D4—442no—
444D4M16×D1112yes—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—221no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4C4×C22⋊D1111yescharacteristic
465C2×C4C4×C22⋊D1111yescharacteristic
466C2×C4C4×C22⋊D1111yescharacteristic
467C2×C4C22×C4×D1111yescharacteristic
468C2×C4C2×#433911yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C8—22no—
471C8—22no—
472C8—42no—
473C8—112no—
474C8—221no—
475C8—221no—
476C8—221no—
477C8—442no—
478C8—442no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—222no—
486C22—441no—
487C22—441no—
488C22C2×C4×C22⋊D1111yescharacteristic
489C4—21no—
490C4—21no—
491C4—21no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—441no—
496C4—441no—
497C4—441no—
498C4#1062275812yes—
499C4C2×M16×D1111yescharacteristic
500C4#1062327611yescharacteristic
501C4#1062336711yescharacteristic
502C4#1062336811yescharacteristic
503C2—41no—
504C2—42no—
505C2—442no—
506C2M16×C22⋊D1111yescharacteristic
507C2#1307749711yescharacteristic
508C2C2×#1062275811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2990C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C4
cosocleC42×C11C24
hypercenter#2990D11
hypocenterC11#18065
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2990

Complements

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

NH ≅ G/Ntype
1. #13077737C2semidirect
3. #13067523C2semidirect
4. #13067452C2semidirect
5. #13067450C2semidirect
6. #13067438C2semidirect
7. #13067371C2semidirect
8. #13067055C2semidirect
9. #13067053C2semidirect
10. #13066906C2semidirect
11. C11×#2990C2semidirect
157. #4323M16semidirect
179. #2990D11semidirect
431. C11#18065semidirect

Maximal subgroups

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

subgroupindex
#130777372
C4×#670032
#130675232
#130674522
#130674502
#130674382
#130673712
#130670552
#130670532
#130669062
C11×#29902
#1806511