Finite Group Databasebeta

← #14644667

Subgroups — #14644667

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068378C211yesmaximal, characteristic, complemented
2C2×#10622175C212yesmaximal
3C4×C11⋊#95C211yesmaximal, characteristic, complemented
4#13066494C212yesmaximal, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C2×C11×#121C2211yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C411yescharacteristic, complemented
9C22×C42×C11C2211yescharacteristic
10C22×C4×Dic11—21no—
11C11×#390C411yescharacteristic, complemented
12C11×#389C411yescharacteristic, complemented
13C11×#388—21no—
14C11×#386—21no—
15C11×#380C2211yescharacteristic
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C4×C11×C22⋊C4—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66867—21no—
22#10622175C418yescomplemented
23#10622162—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—22no—
31C11×#121—22no—
32C11×#121C2×C414yes—
33C4×D4×C11—42no—
34C4×D4×C11—44no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C42×C11—21no—
45C2×C42×C11—42no—
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C4×Dic11—24no—
51C2×C4×Dic11—42no—
52C2×C4×Dic11—42no—
53C22×C11⋊C8—22no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11⋊#95—24no—
58C11⋊#95—22no—
59C11⋊#95C2×C414yescomplemented
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)C2×C414yescomplemented
62#66867—42no—
63#8218—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—24no—
67C2×D4×C11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11C4212yescomplemented
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4112yes—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4C4212yescomplemented
109C11×C22⋊C4—24no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11—42no—
119C4×Dic11—48no—
120C2×C11⋊C8—24no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C4×#121D1111yescharacteristic
124#1749—111no—
125C2×#327—112no—
126C4×#95—111no—
127#1294—112no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11C2×C22⋊C411yescharacteristic
140C23×C11C4×D412yes—
141C23×C11AGL(1,ℤ/8)12yes—
142C23×C11AGL(1,ℤ/8)11yescharacteristic
143C23×C11#13711yescharacteristic
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—44no—
147D4×C11—44no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
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—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—44no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—84no—
176C2×C4×C11#9912yes—
177C2×C4×C11#10412yes—
178C2×C4×C11#10412yes—
179C2×C4×C11C2×C4211yescharacteristic
180C2×C4×C11#11711yescharacteristic
181C2×C4×C11C4×D412yes—
182C2×Dic11—28no—
183C2×Dic11—44no—
184C2×Dic11—44no—
185C2×Dic11—44no—
186C2×Dic11—44no—
187C2×Dic11—44no—
188C2×Dic11—44no—
189C11⋊C8—44no—
190C2×#121C2×D1111yescharacteristic
191C2×C4×D4—21no—
192C2×C4×D4Dic1111yescharacteristic, complemented
193C22×C42—221no—
194C22×C42C2×D1111yescharacteristic
195C2×C22⋊C8—112no—
196C2×#97—221no—
197#390Dic1111yescharacteristic, complemented
198#389Dic1111yescharacteristic, complemented
199#388—21no—
200#386—21no—
201#380C2×D1111yescharacteristic
202C4×C4⋊C4Dic1111yescharacteristic, complemented
203C4×C22⋊C4—21no—
204C2×#95—112no—
205C2×#95—221no—
206#336—221no—
207#327—118no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11—81no—
223C22×C11C4×C22⋊C411yescharacteristic
224C22×C11C2×#9911yescharacteristic
225C22×C11#41011yescharacteristic
226C22×C11#41711yescharacteristic
227C22×C11#41811yescharacteristic
228C22×C11C2×#10411yescharacteristic
229C22×C11C2×#10411yescharacteristic
230C22×C11#44012yes—
231C22×C11#44212yes—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—42no—
239C4×C11—41no—
240C4×C11—81no—
241C4×C11—81no—
242Dic11—48no—
243C22×D4—21no—
244C22×D4C2×Dic1111yescharacteristic
245C23×C4—21no—
246C23×C4—222no—
247C23×C4C22⋊D1111yescharacteristic
248C23×C4C22⋊D1111yescharacteristic
249C23×C4C22×D1111yescharacteristic
250C22×C8—222no—
251#121—22no—
252#121C4×D1114yes—
253C4×D4—42no—
254C4×D4—44no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C2×Dic1111yescharacteristic
257C2×C4⋊C4C2×Dic1111yescharacteristic
258C2×C4⋊C4C2×Dic1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C42—21no—
265C2×C42—42no—
266C2×C42—224no—
267C2×C42—442no—
268C2×C42—442no—
269C2×C42C2×Dic1111yescharacteristic
270C2×C42C2×Dic1111yescharacteristic
271C2×C42C22⋊D1111yescharacteristic
272C2×C42C22⋊D1111yescharacteristic
273C22⋊C8—114no—
274C22⋊C8—222no—
275#97—442no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—114no—
280#95—224no—
281#95—222no—
282C2×C11—22no—
283C2×C11—22no—
284C2×C11—82no—
285C2×C11#150411yescharacteristic
286C2×C11#150511yescharacteristic
287C2×C11#150711yescharacteristic
288C2×C11#150911yescharacteristic
289C2×C11C4×#9911yescharacteristic
290C2×C11C4×#10411yescharacteristic
291C2×C11#176211yescharacteristic
292C24—21no—
293C24C2×C22⋊D1111yescharacteristic
294C2×D4—24no—
295C2×D4—21no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4C4×Dic1112yescomplemented
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—224no—
318C22×C4—224no—
319C22×C4—224no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4C22⋊Dic1111yescharacteristic
325C22×C4C22⋊Dic1111yescharacteristic
326C22×C4C22⋊Dic1111yescharacteristic
327C22×C4C22⋊Dic1111yescharacteristic
328C22×C4C2×C4×D1112yes—
329C22×C4#433912yes—
330C22×C4C22×Dic1111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332C2×C8—224no—
333C2×C8—442no—
334C2×C8—442no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4C4×Dic1112yescomplemented
340C22⋊C4—24no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C42—22no—
346C42—22no—
347C42—41no—
348C42—41no—
349C42—42no—
350C42—448no—
351C11#821811yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23C4×C22⋊D1112yes—
364C23#6698512yes—
365C23#6700211yescharacteristic
366C23#6700411yescharacteristic
367C23C2×C22⋊Dic1111yescharacteristic
368D4—42no—
369D4—42no—
370D4—44no—
371D4—44no—
372C2×C4—24no—
373C2×C4—24no—
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—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—84no—
400C2×C4—228no—
401C2×C4—444no—
402C2×C4—444no—
403C2×C4—444no—
404C2×C4—444no—
405C2×C4—444no—
406C2×C4—444no—
407C2×C4#6689812yes—
408C2×C4#6690112yes—
409C2×C4#6690112yes—
410C2×C4C2×C4×Dic1111yescharacteristic
411C2×C4#6697911yescharacteristic
412C2×C4C4×C22⋊D1112yes—
413C8—444no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22#1062262712yes—
430C22#1062263112yes—
431C22C4×C22⋊Dic1111yescharacteristic
432C22#1062282811yescharacteristic
433C22C2×#6689811yescharacteristic
434C22#1062284511yescharacteristic
435C22C2×#6690111yescharacteristic
436C22C2×#6690111yescharacteristic
437C22#1062285311yescharacteristic
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—21no—
443C4—22no—
444C4—41no—
445C4—42no—
446C4—81no—
447C4—81no—
448C4—448no—
449C2—22no—
450C2—22no—
451C2—82no—
452C2#1306712011yescharacteristic
453C2#1306712411yescharacteristic
454C2#1306713211yescharacteristic
455C2#1306714111yescharacteristic
456C2C4×#6689811yescharacteristic
457C2C4×#6690111yescharacteristic
458C2#1306844111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC4×C11×#121C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC4×#121D11
hypocenterC11#8218
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13068378C2semidirect
3. C4×C11⋊#95C2semidirect
4. #13066494C2semidirect
8. C2×C4×D4×C11C4semidirect
11. C11×#390C4semidirect
12. C11×#389C4semidirect
16. C4×C11×C4⋊C4C4semidirect
22. #10622175C4semidirect
59. C11⋊#95C2×C4semidirect
61. C22⋊(C11⋊C8)C2×C4semidirect
73. C2×D4×C11C42semidirect
108. C11×C4⋊C4C42semidirect
192. C2×C4×D4Dic11semidirect
197. #390Dic11semidirect
198. #389Dic11semidirect
202. C4×C4⋊C4Dic11semidirect
301. C2×D4C4×Dic11semidirect
339. C4⋊C4C4×Dic11semidirect
351. C11#8218semidirect

Maximal subgroups

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

subgroupindex
#130683782
C2×#106221752
C4×C11⋊#952
#130664942
C4×C11×#1212
#821811