Finite Group Databasebeta

← #14771884

Subgroups — #14771884

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D44C211yesmaximal, characteristic
2C2×#10622473C211yesmaximal, characteristic, complemented
3C2×D11×#106C211yesmaximal, characteristic, complemented
4#13071548C212yesmaximal
5#13069384C212yesmaximal, complemented
6#13068818C212yesmaximal, complemented
7#13068805C212yesmaximal, complemented
8#13068780C211yesmaximal, characteristic, complemented
9#13068638C211yesmaximal, characteristic, complemented
10#13068638C211yesmaximal, characteristic, complemented
11C4×C11×#106C211yesmaximal, characteristic, complemented
12C22×C8×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14C2×#66945C2212yes—
15C2×C4⋊C4×D11C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C11×#106C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
20C4×C11×C4⋊C4C2212yes—
21C2×(C2×D11)⋊C8C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×#66882C2212yes—
24C2×#66881C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26#10622600C2212yes—
27#10622600C2212yes—
28C2×#66872C2212yes—
29C2×#66871C2212yes—
30#10622553—22no—
31C4×(C2×D11)⋊C4—22no—
32#10622549C2212yes—
33C2×C4⋊(C11⋊C8)C2211yescharacteristic
34#10622473—24no—
35D11×#106—24no—
36C8×D44C418yescomplemented
37#10622278—22no—
38#10622266—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D44D411yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11C2311yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11—22no—
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4D411yescharacteristic
56C2×(C2×D11)⋊C4D411yescharacteristic
57C2×C4⋊Dic11D411yescharacteristic
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×C4×Dic11—22no—
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C2×C8×D11—22no—
65C2×C8×D11—22no—
66C2×C8×D11—22no—
67C2×C8×D11—22no—
68C2×C8×D11C2×C414yes—
69C2×C8×D11C2×C414yescomplemented
70#66945—24no—
71#66945—42no—
72C4⋊C4×D11—24no—
73C4⋊C4×D11—42no—
74C4×D44C2×C414yes—
75C4×D44Q814yes—
76C11×#106—22no—
77C11×#106D414yescomplemented
78C4×C8×C11C2×C414yescomplemented
79C11×#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84(C2×D11)⋊C8C2×C414yes—
85(C2×D11)⋊C8C2×C414yescomplemented
86#66882—42no—
87#66881—22no—
88#66881—22no—
89#66872—24no—
90#66871—24no—
91C4⋊(C11⋊C8)C2×C414yescomplemented
92#22654—111nomaximal, Sylow
93C23×D11C2×D411yescharacteristic
94C23×D11C2×D411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C2×D44—24no—
105C2×D44C4⋊C414yes—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—44no—
115C2×C4×D11—44no—
116C2×C4×D11—82no—
117C2×C4×D11C22×C412yes—
118C2×C4×D11C22×C412yes—
119C2×C4×D11C2×Q812yes—
120C2×C4×D11C2×Q812yes—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C22×C412yes—
125C2×C8×C11C2×D412yes—
126C2×C8×C11#4112yes—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4C2×D414yes—
131C42×C11—82no—
132C42×C11C22×C412yes—
133C42×C11C2×Q812yes—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—82no—
137(C2×D11)⋊C4C4⋊C414yes—
138(C2×D11)⋊C4C4⋊C414yes—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11C4⋊C414yes—
144Dic11⋊C4—44no—
145C4×Dic11—44no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C22×C412yes—
151C2×C11⋊C8C22×C412yes—
152C8×D11—28no—
153C8×D11—28no—
154C2×C8×D4—111no—
155C2×#427—111no—
156C22×#106—111no—
157#2352—112no—
158#1949—112no—
159#1854—112no—
160#1852—112no—
161#1846—111no—
162#1807—111no—
163#1807—111no—
164C4×#106D1111yescharacteristic, complemented
165C23×C11C22×D411yescharacteristic
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—22no—
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11C2×C4⋊C412yes—
174C22×D11C2×C4⋊C412yes—
175C22×D11#13514yes—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11C2×C4⋊C412yes—
185C2×C4×C11C2×C4⋊C412yes—
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×Q811yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11H(5,𝔽2)11yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11C2×C4⋊C412yes—
203C2×Dic11C2×C4⋊C412yes—
204D44—28no—
205C4×D11—22no—
206C4×D11—22no—
207C4×D11—22no—
208C4×D11—22no—
209C4×D11—22no—
210C4×D11—22no—
211C4×D11—22no—
212C4×D11—22no—
213C4×D11—88no—
214C8×C11—22no—
215C8×C11C4×D414yes—
216C11⋊C8—22no—
217C11⋊C8—22no—
218C23×C8—111no—
219C23×C8—111no—
220C2×C4×D4—111no—
221C2×#117—112no—
222C22×C4⋊C4—112no—
223C8×D4—118no—
224#427—224no—
225C2×#107—112no—
226C2×#107—112no—
227C2×#106—111no—
228C2×#106—111no—
229C2×#106—112no—
230C2×#106—224no—
231C2×#106C2×D1111yescharacteristic
232C2×#106C2×D1111yescharacteristic
233C2×C4⋊C8—111no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8—111no—
236C2×C4×C8C2×D1111yescharacteristic
237#388—222no—
238#387—222no—
239#386—222no—
240#382—112no—
241#380—112no—
242#380—112no—
243C4×C4⋊C4C2×D1112yes—
244C4×C22⋊C4—222no—
245#340—112no—
246#340—112no—
247#340C2×D1112yes—
248C22×C11C22×C4⋊C411yescharacteristic
249C22×C11D4211yescharacteristic
250C22×C11#54711yescharacteristic
251C22×C11C2×#13512yes—
252C22×C11#57712yes—
253C2×D11—24no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—24no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—22no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11#42714yescomplemented
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—44no—
266C4×C11—82no—
267C4×C11C2×C4×D411yescharacteristic
268C4×C11#52011yescharacteristic
269C4×C11D4×Q811yescharacteristic
270C4×C11#55411yescharacteristic
271Dic11—22no—
272Dic11—22no—
273Dic11—82no—
274Dic11—82no—
275C22×D4—111no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—222no—
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—114no—
282C22×C8—114no—
283C22×C8—222no—
284C22×C8—222no—
285C22×C8—222no—
286C22×C8—222no—
287C22×C8C22×D1111yescharacteristic
288C22×C8C22×D1111yescharacteristic
289C4×D4—114no—
290C4×D4—114no—
291#117—224no—
292#117—442no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4—224no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—442no—
299C2×C4⋊C4C22×D1112yes—
300C2×C4⋊C4C22×D1112yes—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—222no—
304C2×C22⋊C4—222no—
305C2×C22⋊C4—222no—
306C2×C42—22no—
307C2×C42—222no—
308C2×C42C22×D1111yescharacteristic
309#107—224no—
310#107—442no—
311#106—22no—
312#106—222no—
313#106—222no—
314#106—224no—
315#106D4414yescomplemented
316C4⋊C8—114no—
317C22⋊C8—114no—
318C22⋊C8—114no—
319C4×C8C4×D1114yescomplemented
320#95—22no—
321#95—222no—
322#95—222no—
323#95—222no—
324#95—222no—
325C2×C11D4×C4⋊C411yescharacteristic
326C2×C11C2×#42711yescharacteristic
327C2×C11#291211yescharacteristic
328C2×C11#328212yes—
329C2×C11#333712yes—
330D11—24no—
331D11—42no—
332C24—111no—
333C24—111no—
334C2×D4—114no—
335C2×D4—224no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—111no—
339C22×C4—111no—
340C22×C4—112no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—444no—
355C22×C4—444no—
356C22×C4—882no—
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4C23×D1111yescharacteristic
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—112no—
363C2×C8—112no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8—221no—
368C2×C8—228no—
369C2×C8—228no—
370C2×C8C2×C4×D1112yes—
371C2×C8C2×C4×D1112yes—
372C2×C8C2×D4412yes—
373C2×C8#433912yes—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—114no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—444no—
383C4⋊C4C2×D4414yes—
384C22⋊C4—114no—
385C22⋊C4—114no—
386C22⋊C4—444no—
387C22⋊C4—444no—
388C22⋊C4—882no—
389C42—82no—
390C42—444no—
391C42C2×C4×D1112yes—
392C42Q8×D1112yes—
393C11#2265411yescharacteristic, complemented, Sylow
394C23—112no—
395C23—114no—
396C23—112no—
397C23—222no—
398C23—221no—
399C23—221no—
400C23—222no—
401C23—222no—
402C23—221no—
403C23—221no—
404C23C2×D4×D1111yescharacteristic
405D4—228no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—112no—
415C2×C4—112no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—222no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—888no—
435C2×C4C4⋊C4×D1112yes—
436C2×C4C4⋊C4×D1112yes—
437C2×C4C22×C4×D1111yescharacteristic
438C2×C4C22×D4411yescharacteristic
439C2×C4C2×#433911yescharacteristic
440C2×C4C2×Q8×D1111yescharacteristic
441C2×C4#6704211yescharacteristic
442C2×C4#6704311yescharacteristic
443C8—22no—
444C8—222no—
445C8—222no—
446C8C4×D4414yes—
447C22—114no—
448C22—224no—
449C22—222no—
450C22—224no—
451C22—222no—
452C22—222no—
453C22—222no—
454C22—222no—
455C22—442no—
456C22—442no—
457C22C2×C4⋊C4×D1111yescharacteristic
458C22D4×D4411yescharacteristic
459C22#1062308211yescharacteristic
460C22#1062329312yes—
461C22D11×#13512yes—
462C4—22no—
463C4—22no—
464C4—44no—
465C4—82no—
466C4—222no—
467C4—222no—
468C4—882no—
469C4—882no—
470C4C2×C4×D4411yescharacteristic
471C4#1062305411yescharacteristic
472C4Q8×D4411yescharacteristic
473C4#1062311011yescharacteristic
474C2—224no—
475C2—442no—
476C2C4⋊C4×D4411yescharacteristic
477C2D11×#42711yescharacteristic
478C2#1307720711yescharacteristic
479C2#1308032512yes—
480C2#1308100012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#106C2
socleC23×C11C22×D4
prime radicalC22×D44D4
cosocleC22×C4×C11C24
hypercenterC4×#106D11
hypocenterC11#22654
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
2. C2×#10622473C2semidirect
3. C2×D11×#106C2semidirect
5. #13069384C2semidirect
6. #13068818C2semidirect
7. #13068805C2semidirect
8. #13068780C2semidirect
9. #13068638C2semidirect
10. #13068638C2semidirect
11. C4×C11×#106C2semidirect
36. C8×D44C4semidirect
69. C2×C8×D11C2×C4semidirect
77. C11×#106D4semidirect
78. C4×C8×C11C2×C4semidirect
85. (C2×D11)⋊C8C2×C4semidirect
91. C4⋊(C11⋊C8)C2×C4semidirect
164. C4×#106D11semidirect
262. C2×D11#427semidirect
315. #106D44semidirect
319. C4×C8C4×D11semidirect
393. C11#22654semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D442
C2×#106224732
C2×D11×#1062
#130715482
#130693842
#130688182
#130688052
#130687802
#130686382
C4×C11×#1062
#2265411