Finite Group Databasebeta

← #14649546

Subgroups — #14649546

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076898C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic, complemented
3C2×#10622108C212yesmaximal, complemented
4#13066496C212yesmaximal, complemented
5C11×#1779C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C2×#67006—21no—
8C22×C22⋊Dic11—21no—
9C2×#66983C412yescomplemented
10C2×#66983C2211yescharacteristic
11C22×C4⋊Dic11—21no—
12C2×C11×C22⋊C8—22no—
13C2×C11×C22⋊C8C2212yes—
14#10622826—21no—
15#10622826—22no—
16#10622825—24no—
17#10622825C412yescomplemented
18#10622825C2211yescharacteristic
19C2×C11⋊#95C2212yes—
20#10622108—24no—
21C25×C11D411yescharacteristic
22C23×C4×C11—22no—
23C23×C4×C11—22no—
24C23×C4×C11—44no—
25C23×C4×C11C2×C412yes—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D412yes—
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—22no—
30C22×C22⋊D11—21no—
31C23×Dic11—22no—
32C22×D44C2×C411yescharacteristic
33C22×C8×C11—22no—
34#67006—42no—
35#67006—42no—
36C2×C22⋊Dic11—24no—
37C2×C22⋊Dic11—22no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—42no—
40C2×C22⋊Dic11—42no—
41#66983—22no—
42#66983—22no—
43#66983—44no—
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—24no—
47C2×C4⋊Dic11—44no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×C4⋊Dic11C2×C412yes—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—22no—
52C11×C22⋊C8—44no—
53C11⋊#95—22no—
54C11⋊#95—22no—
55C11⋊#95—21no—
56C11⋊#95D414yescomplemented
57#9155—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—21no—
62C24×C11—42no—
63C24×C11—42no—
64C24×C11C22⋊C412yes—
65C24×C11D812yes—
66C24×C11SD1612yes—
67C24×C11C2×D411yescharacteristic
68C23×D11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—24no—
72C22×C4×C11—24no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—48no—
80C22×C4×C11—48no—
81C22×C4×C11C22⋊C412yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×C4×C11#4112yes—
86C2×C22⋊D11—44no—
87C2×C22⋊D11—44no—
88C2×C22⋊D11—44no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C22×Dic11—21no—
96C22×Dic11—22no—
97C22×Dic11—24no—
98C22×Dic11—44no—
99C22×Dic11—44no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C2×D44—22no—
103C2×D44—42no—
104C2×C8×C11—44no—
105C2×C8×C11—42no—
106C22⋊Dic11—48no—
107C22⋊Dic11—44no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—44no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—22no—
113C4⋊Dic11—42no—
114C4⋊Dic11—48no—
115#2847—111no—
116C2×#380—111no—
117#1779D1111yescharacteristic, complemented
118C2×#327—112no—
119#1294—112no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11#10214yes—
141C23×C11C2×C22⋊C411yescharacteristic
142C23×C11#12011yescharacteristic
143C23×C11#12311yescharacteristic
144C23×C11C2×D811yescharacteristic
145C23×C11C2×SD1611yescharacteristic
146C23×C11AGL(1,ℤ/8)11yescharacteristic
147C23×C11#13711yescharacteristic
148C22×D11—41no—
149C22×D11—42no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11—42no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—48no—
162C2×C4×C11—48no—
163C2×C4×C11#9914yes—
164C2×C4×C11C4×D412yes—
165C2×C4×C11#12112yes—
166C22⋊D11—88no—
167C22⋊D11—81no—
168C22⋊D11—81no—
169C22⋊D11—81no—
170C22⋊D11—81no—
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—42no—
179C2×Dic11—44no—
180C2×Dic11—84no—
181C2×Dic11—84no—
182D44—82no—
183C8×C11—82no—
184C24×C4C2×D1111yescharacteristic
185C2×#121—111no—
186C2×#121—112no—
187C2×#120—221no—
188C22×C4⋊C4—221no—
189C22×C22⋊C4—221no—
190C2×C22⋊C8—22no—
191C2×C22⋊C8C2×D1112yes—
192#386—221no—
193#386—222no—
194#380—111no—
195#380—112no—
196#380—224no—
197C2×#95—112no—
198#327—224no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—24no—
208C22×C11—24no—
209C22×C11—24no—
210C22×C11—44no—
211C22×C11—44no—
212C22×C11—44no—
213C22×C11—44no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11#38611yescharacteristic
219C22×C11C2×#9912yes—
220C22×C11C2×#10211yescharacteristic
221C22×C11#41711yescharacteristic
222C22×C11#42112yes—
223C22×C11#44711yescharacteristic
224C22×C11#44811yescharacteristic
225C22×C11#48011yescharacteristic
226C22×C11#48111yescharacteristic
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—82no—
231C2×D11—82no—
232C4×C11—24no—
233C4×C11—22no—
234C4×C11—22no—
235Dic11—84no—
236Dic11—81no—
237Dic11—82no—
238C25D4411yescharacteristic
239C22×D4—111no—
240C22×D4—222no—
241C22×D4—221no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—44no—
245C23×C4—222no—
246C23×C4C4×D1112yes—
247C23×C4D4411yescharacteristic
248C23×C4C22⋊D1112yes—
249C23×C4C22×D1111yescharacteristic
250C22×C8—22no—
251#121—222no—
252#121—222no—
253#121—444no—
254#120—442no—
255#120—442no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—112no—
258C2×C4⋊C4—224no—
259C2×C4⋊C4—444no—
260C2×C22⋊C4—224no—
261C2×C22⋊C4—222no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—222no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—442no—
266C2×C22⋊C4—442no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8—44no—
270#95—114no—
271#95—222no—
272#95—222no—
273#95—221no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—44no—
279C2×C11#151312yes—
280C2×C11#151912yes—
281C2×C11#187411yescharacteristic
282C2×C11#189711yescharacteristic
283C2×C11#189811yescharacteristic
284D11—161no—
285C24—21no—
286C24—21no—
287C24—21no—
288C24—21no—
289C24—42no—
290C24—42no—
291C24—221no—
292C24#431412yes—
293C24D8812yes—
294C24(C2×D11)⋊C412yes—
295C24C2×D4411yescharacteristic
296C2×D4—222no—
297C2×D4—442no—
298C2×D4—444no—
299C2×D4—444no—
300C2×D4—444no—
301C2×D4—441no—
302C2×D4—441no—
303C2×D4—441no—
304C2×D4—441no—
305C2×D4—441no—
306C2×D4—441no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—48no—
318C22×C4—48no—
319C22×C4—224no—
320C22×C4—221no—
321C22×C4—222no—
322C22×C4—444no—
323C22×C4—444no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4(C2×D11)⋊C412yes—
327C22×C4C2×C4×D1111yescharacteristic
328C22×C4D4×D1112yes—
329C22×C4#434112yes—
330C22×C4C2×C22⋊D1111yescharacteristic
331C2×C8—44no—
332C2×C8—42no—
333C4⋊C4—222no—
334C4⋊C4—442no—
335C4⋊C4—448no—
336C22⋊C4—448no—
337C22⋊C4—444no—
338C22⋊C4—441no—
339C22⋊C4—441no—
340C22⋊C4—444no—
341C22⋊C4—442no—
342C11#915511yescharacteristic, complemented, Sylow
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—44no—
356C23—44no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—44no—
362C23—44no—
363C23—441no—
364C23—441no—
365C23—442no—
366C23—442no—
367C23—441no—
368C23#6688514yes—
369C23#6693511yescharacteristic
370C23#6693911yescharacteristic
371C23C2×#431411yescharacteristic
372C23C2×D8811yescharacteristic
373C23#6696111yescharacteristic
374C23#6696211yescharacteristic
375C23C2×(C2×D11)⋊C411yescharacteristic
376D4—882no—
377D4—888no—
378D4—881no—
379D4—881no—
380D4—881no—
381D4—881no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—48no—
391C2×C4—48no—
392C2×C4—444no—
393C2×C4—444no—
394C2×C4—441no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—441no—
400C2×C4—444no—
401C2×C4—884no—
402C2×C4—884no—
403C2×C4#6687014yes—
404C2×C4(C22⋊D11)⋊C412yes—
405C2×C4#6699212yes—
406C8—82no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—24no—
416C22—24no—
417C22—24no—
418C22—44no—
419C22—44no—
420C22—44no—
421C22—44no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22—882no—
430C22—882no—
431C22#1062234511yescharacteristic
432C22#1062234811yescharacteristic
433C22#1062234911yescharacteristic
434C22#1062235111yescharacteristic
435C22C2×#6687012yes—
436C22#1062257111yescharacteristic
437C22C2×#6688511yescharacteristic
438C22#1062274611yescharacteristic
439C22#1062275212yes—
440C4—22no—
441C4—24no—
442C4—22no—
443C4—884no—
444C4—881no—
445C4—882no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—44no—
451C2—1761no—
452C2#1306716012yes—
453C2#1306718512yes—
454C2#1306893111yescharacteristic
455C2#1306906211yescharacteristic
456C2#1306906711yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1779C2
socleC23×C11C2×C22⋊C4
prime radical#13076898C2
cosocleC23×C4×C11C23
hypercenter#1779D11
hypocenterC11#9155
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#10622825C2semidirect
3. C2×#10622108C2semidirect
4. #13066496C2semidirect
5. C11×#1779C2semidirect
9. C2×#66983C4semidirect
17. #10622825C4semidirect
56. C11⋊#95D4semidirect
117. #1779D11semidirect
342. C11#9155semidirect

Maximal subgroups

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

subgroupindex
#130768982
C2×#106228252
C2×#106221082
#130664962
C11×#17792
#915511