Finite Group Databasebeta

← #14756754

Subgroups — #14756754

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D88C211yesmaximal, characteristic
2#13071077C211yesmaximal, characteristic, complemented
3C4×#66946C211yesmaximal, characteristic, complemented
4#13069242C212yesmaximal, complemented
5#13069207C212yesmaximal, complemented
6#13068965C212yesmaximal
7#13068874C212yesmaximal, complemented
8C4×#66873C211yesmaximal, characteristic, complemented
9C4×#66873C211yesmaximal, characteristic, complemented
10#13068361C211yesmaximal, characteristic, complemented
11C4×C11×#106C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13C2×#66946C2212yes—
14C2×C4×D44C2211yescharacteristic
15C2×C4×D44C2211yescharacteristic
16C2×#66925—21no—
17C2×C42×D11—21no—
18C2×C11×#106C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25#10622601C2212yes—
26C4⋊C4×Dic11C2212yes—
27#10622586C2212yes—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30C4×(C2×D11)⋊C4—21no—
31C4×(C2×D11)⋊C4—21no—
32C42×Dic11C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34C4×D88C418yescomplemented
35#10622282—22no—
36#10622279—22no—
37C11×#340C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D44C2311yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—21no—
46C22×C4×D11—22no—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11C2311yescharacteristic
60C2×C4⋊Dic11C2311yescharacteristic
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D412yes—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8C2312yes—
68C2×D88—24no—
69C2×D88C2×C414yes—
70#66946—24no—
71#66946—24no—
72C4×D44—22no—
73C4×D44—22no—
74C4×D44C2×C414yes—
75C4×D44C2×C414yescomplemented
76#66925—44no—
77C42×D11—44no—
78C11×#106—24no—
79C4×C8×C11C2×C414yescomplemented
80C11×#95—21no—
81C11×#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84#66885C2×C414yes—
85#66885C2×C414yescomplemented
86#66882C2×C414yescomplemented
87#66873—24no—
88#66873—24no—
89C4×C11⋊C8—22no—
90#21118—111nomaximal, Sylow
91C23×D11—21no—
92C23×D11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2411yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11C2×D412yes—
101C22×Dic11C2×D412yes—
102C2×D44—21no—
103C2×D44—22no—
104C2×D44—21no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44C22×C412yes—
108C2×D44C22×C412yes—
109C2×D44#4114yes—
110C2×C4×D11—28no—
111C2×C4×D11—24no—
112C2×C4×D11—24no—
113C2×C4×D11—44no—
114C2×C4×D11—44no—
115C2×C4×D11—42no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C22×C412yes—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4#4114yes—
127C42×C11—42no—
128C42×C11—42no—
129C42×C11C22×C412yes—
130C42×C11#4112yes—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—24no—
133(C2×D11)⋊C4—24no—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—44no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C22×C412yes—
140Dic11⋊C4—44no—
141C4×Dic11—24no—
142C4×Dic11—22no—
143C4×Dic11—22no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—44no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150D88—28no—
151C2×C4×D8—111no—
152#2293—111no—
153C42×D4—111no—
154#1926—112no—
155#1921—112no—
156#1879—112no—
157#1864—112no—
158C4×#106D1111yescharacteristic, complemented
159C4×#102—111no—
160C4×#102—111no—
161#1744—111no—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—24no—
165C22×D11—22no—
166C22×D11—42no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—41no—
172C22×D11—41no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C4×D412yes—
181C2×C4×C11C4×D412yes—
182C2×C4×C11AGL(1,ℤ/8)12yes—
183C2×C4×C11AGL(1,ℤ/8)12yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C2×#4112yes—
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4112yes—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11#13514yes—
200D44—22no—
201D44—22no—
202D44—22no—
203D44—24no—
204D44—42no—
205D44#11714yescomplemented
206C4×D11—416no—
207C4×D11—48no—
208C4×D11—48no—
209C8×C11—22no—
210C8×C11—22no—
211C11⋊C8—42no—
212C22×D8—111no—
213C2×C4×D4—112no—
214C2×C4×D4—111no—
215C2×C4×D4—111no—
216C2×#117—221no—
217C22×C42—221no—
218C4×D8—118no—
219C2×#107—111no—
220C2×#106C2×D1112yes—
221C2×#102—111no—
222C2×#102—111no—
223C2×#102—112no—
224C2×#102—112no—
225C2×C4×C8—111no—
226C2×C4×C8C2×D1111yescharacteristic
227#390—112no—
228#389—112no—
229#388—222no—
230C4×C4⋊C4—112no—
231C4×C4⋊C4C2×D1111yescharacteristic
232C4×C4⋊C4C2×D1111yescharacteristic
233C4×C22⋊C4—222no—
234C4×C22⋊C4—221no—
235C4×C22⋊C4—221no—
236C43—111no—
237#340—112no—
238#340—112no—
239#340C2×D1112yes—
240#336—112no—
241#336—112no—
242C22×C11C2×C4×D411yescharacteristic
243C22×C11#52512yes—
244C22×C11C2×#13512yes—
245C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
247C2×D11—24no—
248C2×D11—44no—
249C2×D11—44no—
250C2×D11—42no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—82no—
256C2×D11—82no—
257C4×C11—22no—
258C4×C11—44no—
259C4×C11—82no—
260C4×C11#44214yes—
261C4×C11C2×#11711yescharacteristic
262C4×C11C4×#4111yescharacteristic
263C4×C11#52912yes—
264Dic11—24no—
265Dic11—42no—
266Dic11—42no—
267Dic11—42no—
268C22×D4—111no—
269C22×D4—111no—
270C23×C4—222no—
271C23×C4—221no—
272C23×C4—221no—
273C2×D8—114no—
274C2×D8—224no—
275C22×C8—112no—
276C22×C8C22×D1111yescharacteristic
277C22×C8C22×D1111yescharacteristic
278C4×D4—114no—
279C4×D4—114no—
280C4×D4—224no—
281C4×D4—224no—
282C4×D4—222no—
283C4×D4—222no—
284#117—444no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4C22×D1112yes—
289C2×C4⋊C4C22×D1112yes—
290C2×C22⋊C4—222no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—222no—
294C2×C22⋊C4—222no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—112no—
298C2×C42—111no—
299C2×C42—111no—
300C2×C42—112no—
301C2×C42—222no—
302C2×C42—444no—
303C2×C42C22×D1111yescharacteristic
304#107—114no—
305#106—24no—
306#102—114no—
307#102—114no—
308#102—224no—
309#102—224no—
310C4×C8—222no—
311C4×C8C4×D1114yescomplemented
312#95—21no—
313#95—21no—
314#95—222no—
315#95—222no—
316C2×C11#229011yescharacteristic
317C2×C11C4×#13511yescharacteristic
318C2×C11C2×#44211yescharacteristic
319C2×C11#310512yes—
320C2×C11#310612yes—
321D11—44no—
322D11—82no—
323C24—221no—
324C24—221no—
325C2×D4—112no—
326C2×D4—112no—
327C2×D4—114no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—221no—
331C2×D4—221no—
332C2×D4—222no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4—228no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—224no—
341C22×C4—224no—
342C22×C4—444no—
343C22×C4—444no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351D8—228no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8C2×C4×D1112yes—
358C2×C8C2×C4×D1112yes—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—112no—
363C4⋊C4—112no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—444no—
367C4⋊C4#433914yes—
368C22⋊C4—228no—
369C22⋊C4—224no—
370C22⋊C4—224no—
371C22⋊C4—444no—
372C22⋊C4—444no—
373C42—42no—
374C42—42no—
375C42—224no—
376C42—222no—
377C42—222no—
378C42—222no—
379C42—222no—
380C42—444no—
381C42C2×C4×D1112yes—
382C42#434312yes—
383C11#2111811yescharacteristic, complemented, Sylow
384C23—222no—
385C23—224no—
386C23—222no—
387C23—441no—
388C23—441no—
389C23—442no—
390C23—441no—
391C23—441no—
392C23—442no—
393C23—442no—
394C23C2×D4×D1111yescharacteristic
395D4—114no—
396D4—222no—
397D4—222no—
398D4—222no—
399D4—224no—
400D4—442no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—114no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—4416no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—448no—
422C2×C4—448no—
423C2×C4#6694612yes—
424C2×C4#6694612yes—
425C2×C4#6696712yes—
426C2×C4#6696712yes—
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C2×#433912yes—
429C2×C4C2×#434311yescharacteristic
430C2×C4#41×D1112yes—
431C8—22no—
432C8—22no—
433C8—442no—
434C22—224no—
435C22—442no—
436C22—444no—
437C22—444no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—442no—
442C22—882no—
443C22—882no—
444C22C2×#6694611yescharacteristic
445C22#1062307812yes—
446C22C2×#6696711yescharacteristic
447C22C2×#6696711yescharacteristic
448C22D11×#13512yes—
449C4—22no—
450C4—44no—
451C4—82no—
452C4—224no—
453C4—442no—
454C4—442no—
455C4—442no—
456C4#1062248214yes—
457C4C4×#433911yescharacteristic
458C4D11×#11711yescharacteristic
459C4#1062311112yes—
460C2—444no—
461C2—882no—
462C2#1307105711yescharacteristic
463C2#1307738711yescharacteristic
464C2C2×#1062248211yescharacteristic
465C2#1307866712yes—
466C2#1307867412yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#106C2
socleC23×C11C22×D4
prime radicalC22×D88C22
cosocleC22×C4×C11C24
hypercenterC4×#106D11
hypocenterC11#21118
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
2. #13071077C2semidirect
3. C4×#66946C2semidirect
4. #13069242C2semidirect
5. #13069207C2semidirect
7. #13068874C2semidirect
8. C4×#66873C2semidirect
9. C4×#66873C2semidirect
10. #13068361C2semidirect
11. C4×C11×#106C2semidirect
34. C4×D88C4semidirect
75. C4×D44C2×C4semidirect
79. C4×C8×C11C2×C4semidirect
85. #66885C2×C4semidirect
86. #66882C2×C4semidirect
158. C4×#106D11semidirect
205. D44#117semidirect
311. C4×C8C4×D11semidirect
383. C11#21118semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D882
#130710772
C4×#669462
#130692422
#130692072
#130689652
#130688742
C4×#668732
#130683612
C4×C11×#1062
#2111811