Finite Group Databasebeta

← #14652915

Subgroups — #14652915

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076917C211yesmaximal, characteristic
2C2×#10622105C212yesmaximal, complemented
3C2×#10622108C212yesmaximal
4#13066843C211yesmaximal, characteristic, complemented
5C11×#1797C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66977C2211yescharacteristic
9C2×#66928C411yescharacteristic, complemented
10C2×C11×C4⋊C8—21no—
11C2×C11×C22⋊C8C2212yes—
12#10622826—21no—
13#10622826—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17#10622553—21no—
18#10622553—21no—
19#10622552C411yescharacteristic, complemented
20#10622549C411yescharacteristic, complemented
21#10622542C411yescharacteristic, complemented
22C11×#336—21no—
23#10622108—24no—
24#10622105—24no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11—22no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C22×C8×C11—22no—
33C2×C42×C11—42no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39#66983—22no—
40#66983—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48#66977—22no—
49#66977—22no—
50C2×Dic11⋊C4—21no—
51#66928—42no—
52C11×C4⋊C8—42no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—22no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—22no—
60C11⋊#95—42no—
61C11⋊#95—42no—
62C11⋊#95D414yes—
63#9716—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11#4112yes—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—24no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C2×Dic22—22no—
101C2×Dic22—41no—
102C2×Dic22—41no—
103C2×C8×C11—42no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—41no—
109C42×C11—41no—
110C22⋊Dic11—42no—
111(C2×D11)⋊C4—42no—
112(C2×D11)⋊C4—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—22no—
118C4⋊Dic11—22no—
119Dic11⋊C4—41no—
120Dic11⋊C4—41no—
121#2850—111no—
122#1797D1111yescharacteristic, complemented
123C2×#328—112no—
124C2×#327—112no—
125#1434—111no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12112yes—
132C23×C11#13512yes—
133C23×C11AGL(1,ℤ/8)11yescharacteristic
134C23×C11#13711yescharacteristic
135C22×D11—41no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11#9912yes—
163C2×C4×C11C4×D412yes—
164C2×C4×C11#12411yescharacteristic
165C2×C4×C11#12711yescharacteristic
166C22⋊D11—82no—
167C22⋊D11—82no—
168C2×Dic11—44no—
169C2×Dic11—44no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—44no—
180C2×Dic11—82no—
181C2×Dic11—82no—
182C2×Dic11—82no—
183C2×Dic11—82no—
184D44—82no—
185Dic22—82no—
186C8×C11—82no—
187C2×#124—111no—
188C2×C22⋊Q8—111no—
189C2×#121—111no—
190C22×C42C2×D1111yescharacteristic
191C2×C4⋊C8—21no—
192C2×C22⋊C8C2×D1112yes—
193#391—111no—
194#390—111no—
195#388—221no—
196#388—221no—
197#386—221no—
198#386—221no—
199#382—111no—
200C2×#95—112no—
201C2×#95—221no—
202C2×#95—221no—
203#336—21no—
204#328—224no—
205#327—224no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11#39011yescharacteristic
215C22×C11C2×#9911yescharacteristic
216C22×C11#41011yescharacteristic
217C22×C11#41611yescharacteristic
218C22×C11#41711yescharacteristic
219C22×C11#42111yescharacteristic
220C22×C11#42111yescharacteristic
221C22×C11#46312yes—
222C22×C11#46412yes—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—22no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237Dic11—84no—
238Dic11—81no—
239Dic11—81no—
240Dic11—81no—
241C22×Q8—111no—
242C22×D4—111no—
243C22×D4—221no—
244C23×C4—222no—
245C23×C4D4411yescharacteristic
246C23×C4D4411yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C22×C8—22no—
249#124—442no—
250C22⋊Q8—222no—
251C22⋊Q8—222no—
252#121—222no—
253#121—222no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C42—42no—
264C2×C42C4×D1111yescharacteristic
265C2×C42C4×D1111yescharacteristic
266C2×C42C22⋊D1111yescharacteristic
267C2×C42C22⋊D1111yescharacteristic
268C4⋊C8—42no—
269C22⋊C8—22no—
270C22⋊C8—22no—
271#95—114no—
272#95—221no—
273#95—221no—
274#95—221no—
275#95—221no—
276#95—222no—
277#95—442no—
278#95—442no—
279C2×C11—22no—
280C2×C11—22no—
281C2×C11#151211yescharacteristic
282C2×C11#151311yescharacteristic
283C2×C11#151611yescharacteristic
284C2×C11#152111yescharacteristic
285C2×C11#196311yescharacteristic
286C2×C11#196411yescharacteristic
287C2×C11#198311yescharacteristic
288D11—161no—
289C24—221no—
290C24C2×D4411yescharacteristic
291C2×Q8—222no—
292C2×Q8—441no—
293C2×Q8—441no—
294C2×D4—222no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—442no—
298C2×D4—442no—
299C2×D4—441no—
300C2×D4—441no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—224no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4(C2×D11)⋊C411yescharacteristic
321C22×C4(C2×D11)⋊C411yescharacteristic
322C22×C4(C2×D11)⋊C411yescharacteristic
323C22×C4(C2×D11)⋊C411yescharacteristic
324C22×C4C2×C4×D1111yescharacteristic
325C22×C4D4×D1112yes—
326C22×C4#434312yes—
327C22×C4C2×C22⋊D1111yescharacteristic
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—442no—
338C22⋊C4—442no—
339C22⋊C4—442no—
340C22⋊C4—441no—
341C22⋊C4—441no—
342C42—22no—
343C42—22no—
344C42—41no—
345C42—41no—
346C11#971611yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23—441no—
358C23#6694812yes—
359C23#6695712yes—
360C23#6696111yescharacteristic
361C23#6696211yescharacteristic
362C23C2×(C2×D11)⋊C411yescharacteristic
363Q8—882no—
364D4—882no—
365D4—882no—
366D4—882no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—444no—
388C2×C4—444no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—444no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4#6687012yes—
404C2×C4#6694612yes—
405C2×C4#6699311yescharacteristic
406C2×C4#6700011yescharacteristic
407C8—82no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—881no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22—881no—
422C22—881no—
423C22#1062245712yes—
424C22#1062245812yes—
425C22C2×#6687011yescharacteristic
426C22#1062260111yescharacteristic
427C22#1062261911yescharacteristic
428C22#1062272611yescharacteristic
429C22#1062274611yescharacteristic
430C22#1062275211yescharacteristic
431C22#1062275211yescharacteristic
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—884no—
440C4—881no—
441C4—881no—
442C4—881no—
443C2—22no—
444C2—22no—
445C2—1761no—
446C2#1306715511yescharacteristic
447C2#1306716011yescharacteristic
448C2#1306717311yescharacteristic
449C2#1306719411yescharacteristic
450C2#1306944711yescharacteristic
451C2#1306945111yescharacteristic
452C2#1306954611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9716
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#10622105C2semidirect
4. #13066843C2semidirect
5. C11×#1797C2semidirect
9. C2×#66928C4semidirect
19. #10622552C4semidirect
20. #10622549C4semidirect
21. #10622542C4semidirect
122. #1797D11semidirect
346. C11#9716semidirect

Maximal subgroups

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

subgroupindex
#130769172
C2×#106221052
C2×#106221082
#130668432
C11×#17972
#971611