Finite Group Databasebeta

← #14756265

Subgroups — #14756265

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66881C211yesmaximal, characteristic, complemented
2C2×#10622746C211yesmaximal, characteristic
3C2×#10622726C211yesmaximal, characteristic
4#13071204C211yesmaximal, characteristic
5#13070972C211yesmaximal, characteristic, complemented
6#13069251C214yesmaximal, complemented
7#13069244C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17#10622746—24no—
18#10622726C418yescomplemented
19C2×#66885C2212yes—
20C2×#66885C2212yes—
21C2×#66881—24no—
22C2×#66881C2214yes—
23C2×#66880C2212yes—
24C2×#66880C2212yes—
25#10622600—22no—
26C4⋊C4×Dic11—22no—
27#10622571—22no—
28C22⋊C4×Dic11—22no—
29#10622552C2212yes—
30C4×C4⋊Dic11C2214yes—
31#10622542C2212yes—
32C11×#336C2214yes—
33#10622189C2214yes—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C23×Dic11—21no—
37C23×Dic11—21no—
38C2×#4339—22no—
39C2×#4339—22no—
40C2×#4339—22no—
41C2×#4339—22no—
42C2×#4339—22no—
43C2×#4339C2×C414yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22C2311yescharacteristic
47C2×C11×M16—22no—
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C22×C8×C11—22no—
51C22×C8×C11—22no—
52C22×C8×C11C2×C414yes—
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C11×#117—22no—
56C11×#117—22no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11C2312yes—
60C2×C22⋊Dic11—21no—
61C2×(C2×D11)⋊C4—24no—
62#66979—22no—
63#66979C2×C414yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D414yes—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—24no—
75C11⋊#95—24no—
76C11⋊#95—24no—
77#66885—24no—
78#66885C2×C418yescomplemented
79#66881—28no—
80#66880—24no—
81#66880C2×C418yescomplemented
82#21068—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C23×D11—21no—
85C22×C4×C11C22×C412yes—
86C22×C4×C11C2×D414yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11#4112yes—
90C22×C4×C11#4112yes—
91C22×C4×C11#4112yes—
92C22×C4×C11#4112yes—
93C22×C4×C11C2411yescharacteristic
94C2×C22⋊D11—24no—
95C2×C22⋊D11—42no—
96C2×C22⋊D11—42no—
97C22×Dic11—24no—
98C22×Dic11—21no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11—42no—
103C22×Dic11—82no—
104C22×Dic11—82no—
105#4339—28no—
106#4339—28no—
107#4339—44no—
108#4339—44no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44C22×C412yes—
115C2×C4×D11—24no—
116C2×C4×D11—42no—
117C2×C4×D11—42no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22—21no—
122C2×Dic22—21no—
123C2×Dic22C22×C412yes—
124C11×M16—44no—
125C2×C8×C11—28no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11C22×C414yes—
132C11×C4⋊C4—24no—
133C11×C22⋊C4—24no—
134C42×C11—22no—
135C42×C11—22no—
136C22⋊Dic11—24no—
137(C2×D11)⋊C4—84no—
138C4⋊Dic11—24no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11C22×C414yes—
145C4⋊Dic11C2×D414yes—
146C4×Dic11—24no—
147C4×Dic11—84no—
148C22×#106—111no—
149C2×#417—111no—
150C2×#416—111no—
151#2311—111no—
152#2274—111no—
153#1927—114no—
154#1926—114no—
155#1736—111no—
156#1729D1111yescharacteristic, complemented
157C23×C11—22no—
158C23×C11—22no—
159C23×C11C4×D412yes—
160C23×C11#12112yes—
161C23×C11#12312yes—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—42no—
167C22×D11—42no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—24no—
171C2×C4×C11#11714yes—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C4×D414yes—
174C2×C4×C11#12112yes—
175C2×C4×C11#12312yes—
176C2×C4×C11#12414yes—
177C2×C4×C11#12614yes—
178C2×C4×C11C23×C411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C11C2×#4111yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C22⋊D11—48no—
185C2×Dic11—24no—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—44no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—44no—
195C2×Dic11—84no—
196C2×Dic11—84no—
197D44—22no—
198D44—22no—
199D44—41no—
200D44—41no—
201C4×D11—48no—
202Dic22—22no—
203Dic22—22no—
204Dic22—41no—
205Dic22—41no—
206C8×C11—24no—
207C8×C11—42no—
208C22×#41—111no—
209C22×M16C2×D1111yescharacteristic
210C23×C8C2×D1111yescharacteristic
211C2×#117—111no—
212C2×#117C2×D1111yescharacteristic
213C22×C4⋊C4—111no—
214C22×C4⋊C4—111no—
215C2×#106—114no—
216C2×#106—224no—
217#417—224no—
218#416—118no—
219C2×#103—112no—
220C2×#103—112no—
221C2×#102—112no—
222C2×#102—112no—
223#391—112no—
224#390—112no—
225#386—222no—
226#380—222no—
227C4×C4⋊C4—114no—
228C4×C4⋊C4—222no—
229C4×C22⋊C4—222no—
230#340—114no—
231#336C2×D1114yes—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11#38814yes—
237C22×C11C2×C4×D411yescharacteristic
238C22×C11C2×#12111yescharacteristic
239C22×C11C2×#12311yescharacteristic
240C22×C11#57712yes—
241C22×C11#57712yes—
242C2×D11—44no—
243C2×D11—42no—
244C2×D11—82no—
245C2×D11—81no—
246C2×D11—81no—
247C4×C11—44no—
248C4×C11#38814yes—
249C4×C11C2×#11711yescharacteristic
250C4×C11C2×C4×D411yescharacteristic
251C4×C11C2×#12411yescharacteristic
252C4×C11C2×#12611yescharacteristic
253Dic11—44no—
254Dic11—44no—
255Dic11—42no—
256Dic11—82no—
257C2×#41—114no—
258C2×#41—222no—
259C2×#41—222no—
260C2×#41—222no—
261C2×#41—222no—
262C2×#41—222no—
263C22×Q8—111no—
264C22×D4—111no—
265C22×D4—221no—
266C23×C4—221no—
267C23×C4—221no—
268C23×C4—221no—
269C23×C4C22×D1111yescharacteristic
270C2×M16—22no—
271C2×M16—22no—
272C2×M16—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8C4×D1114yes—
276C22×C8C22×D1112yes—
277C22×C8C22×D1112yes—
278#117—22no—
279#117—22no—
280#117—114no—
281#117—222no—
282C2×C4⋊C4—114no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4D4412yes—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—224no—
294C2×C22⋊C4D4412yes—
295C2×C42—221no—
296C2×C42—224no—
297C2×C42C22×D1112yes—
298#106—228no—
299#103—118no—
300#103—224no—
301#102—118no—
302#102—224no—
303#95—224no—
304#95—224no—
305C2×C11—24no—
306C2×C11C2×#38811yescharacteristic
307C2×C11#295212yes—
308C2×C11#304211yescharacteristic
309C2×C11#304311yescharacteristic
310C2×C11#309912yes—
311D11—82no—
312C24—221no—
313C24C2×D4411yescharacteristic
314#41—228no—
315#41—228no—
316#41—444no—
317#41—444no—
318C2×Q8—112no—
319C2×Q8—221no—
320C2×Q8—221no—
321C2×Q8—221no—
322C2×Q8—221no—
323C2×Q8—221no—
324C2×D4—112no—
325C2×D4—224no—
326C2×D4—221no—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—221no—
330C2×D4—221no—
331C2×D4—442no—
332C2×D4—442no—
333C22×C4—221no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—224no—
337C22×C4—224no—
338C22×C4—222no—
339C22×C4—442no—
340C22×C4—442no—
341C22×C4—442no—
342C22×C4—882no—
343C22×C4—882no—
344C22×C4C2×C4×D1112yes—
345C22×C4C2×D4414yes—
346C22×C4C2×D4411yescharacteristic
347C22×C4#433912yes—
348C22×C4D4×D1112yes—
349C22×C4#434112yes—
350C22×C4#434112yes—
351C22×C4#434312yes—
352C22×C4C23×D1111yescharacteristic
353M16—44no—
354C2×C8—28no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8C2×C4×D1114yes—
361C4⋊C4—24no—
362C4⋊C4—114no—
363C4⋊C4—114no—
364C4⋊C4—224no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—442no—
370C22⋊C4—24no—
371C22⋊C4—224no—
372C22⋊C4—884no—
373C42—22no—
374C42—22no—
375C42—224no—
376C42—884no—
377C11#2106811yescharacteristic, complemented, Sylow
378C23—22no—
379C23—22no—
380C23—222no—
381C23—441no—
382C23—442no—
383C23—442no—
384C23—441no—
385C23C4×D4412yes—
386C23#6693912yes—
387C23#6694812yes—
388C23C22×D4411yescharacteristic
389Q8—222no—
390Q8—222no—
391Q8—441no—
392Q8—441no—
393D4—222no—
394D4—222no—
395D4—448no—
396D4—441no—
397D4—441no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—224no—
402C2×C4—222no—
403C2×C4—224no—
404C2×C4—441no—
405C2×C4—442no—
406C2×C4—444no—
407C2×C4—442no—
408C2×C4—441no—
409C2×C4—448no—
410C2×C4—444no—
411C2×C4—442no—
412C2×C4—884no—
413C2×C4—884no—
414C2×C4C4×D4412yes—
415C2×C4(C22⋊D11)⋊C414yes—
416C2×C4#6693814yes—
417C2×C4#6693912yes—
418C2×C4#6694514yes—
419C2×C4#6694812yes—
420C2×C4#6695114yes—
421C2×C4C22×C4×D1111yescharacteristic
422C2×C4C2×#433911yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C2×C4C2×#434111yescharacteristic
425C2×C4C2×#434111yescharacteristic
426C2×C4C2×#434311yescharacteristic
427C8—24no—
428C8—42no—
429C22—24no—
430C22—22no—
431C22—22no—
432C22—24no—
433C22—442no—
434C22—444no—
435C22—882no—
436C22—881no—
437C22—881no—
438C22#1062228314yes—
439C22C2×C4×D4411yescharacteristic
440C22C2×#6693911yescharacteristic
441C22C2×#6694811yescharacteristic
442C22#1062328212yes—
443C22#1062328212yes—
444C4—44no—
445C4—444no—
446C4—442no—
447C4—444no—
448C4—882no—
449C4#1062228314yes—
450C4C2×(C22⋊D11)⋊C411yescharacteristic
451C4C2×#6693811yescharacteristic
452C4C2×#6694511yescharacteristic
453C4C2×#6695111yescharacteristic
454C2—24no—
455C2—882no—
456C2C2×#1062228311yescharacteristic
457C2#1307750112yes—
458C2#1307812911yescharacteristic
459C2#1307813811yescharacteristic
460C2#1307860712yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1729C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1729D11
hypocenterC11#21068
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1729

Complements

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

NH ≅ G/Ntype
1. C22×#66881C2semidirect
5. #13070972C2semidirect
6. #13069251C2semidirect
7. #13069244C2semidirect
8. #13068336C2semidirect
9. C11×#1729C2semidirect
18. #10622726C4semidirect
78. #66885C2×C4semidirect
81. #66880C2×C4semidirect
156. #1729D11semidirect
377. C11#21068semidirect

Maximal subgroups

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

subgroupindex
C22×#668812
C2×#106227462
C2×#106227262
#130712042
#130709722
#130692512
#130692442
#130683362
C11×#17292
#2106811