Finite Group Databasebeta

← #14649361

Subgroups — #14649361

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic, complemented
2#13076947C211yesmaximal, characteristic
3C2×#10622089C212yesmaximal
4#13066495C212yesmaximal, complemented
5C11×#1434C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66982—21no—
9C2×C11×#95—21no—
10C2×C11×#95—21no—
11C2×C11×#95C2212yes—
12#10622826—21no—
13#10622825C2211yescharacteristic
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622553—21no—
16#10622553—21no—
17#10622552C411yescharacteristic, complemented
18#10622552C411yescharacteristic, complemented
19#10622541C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21#10622539—24no—
22C2×C4⋊(C11⋊C8)—21no—
23C2×#66867—21no—
24#10622089—24no—
25C23×C4×C11—22no—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C2×C42×C11—22no—
32C2×C42×C11—22no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38#66983—22no—
39#66983—22no—
40#66982—44no—
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
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C22×C11⋊C8—22no—
52C11×#95—24no—
53C11×#95—22no—
54C11×#95—22no—
55C11×#95—42no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)D414yes—
61C4⋊(C11⋊C8)—24no—
62#66867—24no—
63#9118—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—24no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11—42no—
81C22×C4×C11—42no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11#4112yes—
90C2×C22⋊D11—42no—
91C2×C22⋊D11—42no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C2×D44—22no—
98C2×D44—41no—
99C2×D44—41no—
100C42×C11—22no—
101C42×C11—22no—
102C42×C11—21no—
103C42×C11—21no—
104C42×C11—21no—
105C42×C11—21no—
106C22⋊Dic11—42no—
107(C2×D11)⋊C4—42no—
108(C2×D11)⋊C4—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116Dic11⋊C4—42no—
117Dic11⋊C4—42no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—42no—
121C2×#432—111no—
122#2854—111no—
123C2×#327—112no—
124#1434D1111yescharacteristic, complemented
125#1294—112no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11#12112yes—
132C23×C11AGL(1,ℤ/8)11yescharacteristic
133C23×C11AGL(1,ℤ/8)12yes—
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—44no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—82no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11—82no—
169C2×C4×C11#10412yes—
170C2×C4×C11C4×D412yes—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C22⋊D11—82no—
174C22⋊D11—82no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184D44—82no—
185C11⋊C8—44no—
186C2×#123—221no—
187C2×#121—111no—
188C22×C42C2×D1111yescharacteristic
189#432—224no—
190C2×C4⋊C8—221no—
191C2×C22⋊C8—112no—
192C2×#97—221no—
193#390—111no—
194#390—111no—
195#389—111no—
196#389—111no—
197#388—221no—
198#388—221no—
199#386—221no—
200#380—111no—
201C2×#95—21no—
202C2×#95—21no—
203C2×#95C2×D1112yes—
204#327—224no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11#38611yescharacteristic
214C22×C11#41011yescharacteristic
215C22×C11#41011yescharacteristic
216C22×C11#41711yescharacteristic
217C22×C11#41811yescharacteristic
218C22×C11C2×#10411yescharacteristic
219C22×C11#42111yescharacteristic
220C22×C11#46812yes—
221C22×C11#46912yes—
222C2×D11—81no—
223C2×D11—81no—
224C2×D11—81no—
225C2×D11—81no—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—84no—
237Dic11—81no—
238Dic11—81no—
239Dic11—81no—
240C22×D4—111no—
241C22×D4—221no—
242C23×C4—22no—
243C23×C4C22⋊D1111yescharacteristic
244C23×C4C22⋊D1111yescharacteristic
245C23×C4C22×D1111yescharacteristic
246C22×C8—222no—
247#123—444no—
248#121—222no—
249#121—222no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C22⋊C4—221no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42C4×D1111yescharacteristic
264C2×C42C4×D1111yescharacteristic
265C2×C42D4411yescharacteristic
266C2×C42D4411yescharacteristic
267C4⋊C8—224no—
268C22⋊C8—114no—
269C22⋊C8—222no—
270#97—224no—
271#95—24no—
272#95—22no—
273#95—22no—
274#95—42no—
275#95—221no—
276#95—221no—
277#95—221no—
278C2×C11—22no—
279C2×C11—22no—
280C2×C11#150511yescharacteristic
281C2×C11#150911yescharacteristic
282C2×C11#151211yescharacteristic
283C2×C11#151411yescharacteristic
284C2×C11#187111yescharacteristic
285C2×C11#189511yescharacteristic
286C2×C11#189911yescharacteristic
287D11—161no—
288C24—221no—
289C24C2×C22⋊D1111yescharacteristic
290C2×D4—222no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—442no—
295C2×D4—441no—
296C2×D4—442no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4(C2×D11)⋊C411yescharacteristic
317C22×C4(C2×D11)⋊C411yescharacteristic
318C22×C4(C2×D11)⋊C411yescharacteristic
319C22×C4(C2×D11)⋊C411yescharacteristic
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4C2×D4411yescharacteristic
322C22×C4D4×D1112yes—
323C22×C4#434112yes—
324C2×C8—224no—
325C2×C8—442no—
326C2×C8—442no—
327C4⋊C4—222no—
328C4⋊C4—441no—
329C4⋊C4—441no—
330C4⋊C4—442no—
331C4⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C22⋊C4—442no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C42—22no—
340C42—22no—
341C42—21no—
342C42—21no—
343C42—21no—
344C42—21no—
345C11#911811yescharacteristic, complemented, Sylow
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—441no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23C2×(C2×D11)⋊C411yescharacteristic
358C23#6698511yescharacteristic
359C23#6699212yes—
360C23#6699511yescharacteristic
361C23#6700212yes—
362D4—882no—
363D4—882no—
364D4—882no—
365C2×C4—21no—
366C2×C4—21no—
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—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—82no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4#6686912yes—
402C2×C4(C22⋊D11)⋊C412yes—
403C2×C4#6693511yescharacteristic
404C2×C4#6693911yescharacteristic
405C8—444no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22—881no—
418C22—881no—
419C22—881no—
420C22—881no—
421C22C2×#6686911yescharacteristic
422C22#1062257111yescharacteristic
423C22#1062257911yescharacteristic
424C22#1062261411yescharacteristic
425C22#1062261811yescharacteristic
426C22#1062261911yescharacteristic
427C22#1062261911yescharacteristic
428C22#1062265212yes—
429C22#1062266212yes—
430C4—21no—
431C4—22no—
432C4—21no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—41no—
437C4—84no—
438C4—881no—
439C4—881no—
440C4—881no—
441C2—22no—
442C2—22no—
443C2—1761no—
444C2#1306712311yescharacteristic
445C2#1306713911yescharacteristic
446C2#1306715211yescharacteristic
447C2#1306716211yescharacteristic
448C2#1306891611yescharacteristic
449C2#1306905211yescharacteristic
450C2#1306907211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#9118
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
1. C2×#10622539C2semidirect
4. #13066495C2semidirect
5. C11×#1434C2semidirect
17. #10622552C4semidirect
18. #10622552C4semidirect
19. #10622541C4semidirect
20. #10622541C4semidirect
124. #1434D11semidirect
345. C11#9118semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130769472
C2×#106220892
#130664952
C11×#14342
#911811