Finite Group Databasebeta

← #14772078

Subgroups — #14772078

Order 2816.

974 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
1C2×#10622502C212yesmaximal
2C2×C4×#4314C211yesmaximal, characteristic
3#13071533C211yesmaximal, characteristic, complemented
4#13071524C211yesmaximal, characteristic
5#13069357C212yesmaximal, complemented
6#13068881C212yesmaximal, complemented
7#13068874C212yesmaximal
8#13068628C211yesmaximal, characteristic, complemented
9#13068623C211yesmaximal, characteristic
10#13068483C211yesmaximal, characteristic, complemented
11C11×#1846C211yesmaximal, characteristic, complemented
12C22×#4314C2211yescharacteristic
13C2×#66946C2212yes—
14C2×#66940C2212yes—
15C2×C4×D44C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#107C2212yes—
18C2×C11×#106C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#382C2211yescharacteristic
21C11×#382C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66881C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66879C2212yes—
26#10622586C2212yes—
27#10622586C2212yes—
28C2×#66874C2212yes—
29C2×#66873C2212yes—
30C4×C4⋊Dic11C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622502—28no—
33C4×#4314C418yescomplemented
34#10622281—22no—
35#10622280—21no—
36D11×#95—21no—
37#10622263—21no—
38#10622262—21no—
39#10622260—22no—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—22no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11D412yes—
55C2×C4⋊Dic11C2311yescharacteristic
56C2×C4⋊Dic11C2311yescharacteristic
57C2×Dic11⋊C4—21no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11C2312yes—
64C22×C11⋊C8C2312yes—
65C2×#4314C2×C414yes—
66C2×#4314D414yes—
67C2×#4314Q814yes—
68#66946—24no—
69#66946—42no—
70#66940—24no—
71#66940—42no—
72C4×D44—22no—
73C4×D44C2×C414yes—
74C4×Dic22—22no—
75C4×Dic22C2×C414yescomplemented
76C11×#107—24no—
77C11×#106—42no—
78C4×C8×C11C2×C414yescomplemented
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—21no—
82C11×#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95D411yescharacteristic
86C11⋊#95D411yescharacteristic
87#66885C2×C414yes—
88#66881C2×C414yescomplemented
89#66880C2×C414yescomplemented
90#66879—24no—
91#66874—24no—
92#66873—24no—
93C4⋊(C11⋊C8)—22no—
94#22673—111nomaximal, Sylow
95C23×D11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11C2×D412yes—
105C22×Dic11C2×D412yes—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44C22×C412yes—
110C2×D44C2×D412yes—
111C2×D44C2×Q812yes—
112C2×C4×D11—24no—
113C2×C4×D11—44no—
114C2×C4×D11—44no—
115C2×C4×D11—82no—
116C2×C4×D11—82no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22C22×C412yes—
121C2×Dic22C2×D412yes—
122C2×Dic22C2×Q812yes—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11C22×C412yes—
126C2×C8×C11C22×C412yes—
127C2×C8×C11C2×D412yes—
128C2×C8×C11C2×Q812yes—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C42×C11C22×C412yes—
134C42×C11#4112yes—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—44no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—42no—
140C4⋊Dic11C22×C412yes—
141C4⋊Dic11C22×C412yes—
142Dic11⋊C4—24no—
143Dic11⋊C4—44no—
144Dic11⋊C4—44no—
145Dic11⋊C4—82no—
146C4×Dic11—24no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—44no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153#4314C4⋊C4116yescomplemented
154C2×#440—112no—
155C2×C4×SD16—111no—
156#2351—111no—
157#2349—111no—
158#1944—112no—
159#1865—112no—
160#1864—112no—
161#1846D1111yescharacteristic, complemented
162#1805—111no—
163#1804—111no—
164#1770—111no—
165C23×C11C22×D411yescharacteristic
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—42no—
170C22×D11—42no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11C4×D412yes—
180C2×C4×C11C4×D412yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×C4×C112−1+411yescharacteristic
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200D44—22no—
201D44—22no—
202D44—22no—
203D44C2×C4⋊C414yes—
204C4×D11—84no—
205C4×D11—88no—
206Dic22—22no—
207Dic22—22no—
208Dic22—22no—
209Dic22C2×C4⋊C414yes—
210C8×C11—22no—
211C8×C11C2×C4⋊C414yes—
212C11⋊C8—42no—
213C22×SD16—111no—
214C2×C4×Q8—112no—
215C2×C4×Q8—111no—
216C2×C4×D4—112no—
217C2×C4×D4—111no—
218#440—228no—
219C4×SD16—118no—
220C2×#107C2×D1112yes—
221C2×#106—111no—
222C2×#106C2×D1112yes—
223C2×C4⋊C8—111no—
224C2×#103—111no—
225C2×#103—112no—
226C2×#102—111no—
227C2×#102—112no—
228C2×#97—112no—
229C2×C4×C8C2×D1111yescharacteristic
230#389—112no—
231#389—112no—
232#389—222no—
233#385—222no—
234#382—221no—
235#382C2×D1111yescharacteristic
236#382C2×D1111yescharacteristic
237#380—221no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4—221no—
240C2×#95—221no—
241#340—112no—
242#340—112no—
243#336—112no—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11D4211yescharacteristic
246C22×C11D4×Q811yescharacteristic
247C22×C11#57512yes—
248C22×C11#57712yes—
249C2×D11—24no—
250C2×D11—44no—
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—44no—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—82no—
257C4×C11—82no—
258C4×C11C22×C4⋊C411yescharacteristic
259C4×C11#52011yescharacteristic
260C4×C11#54711yescharacteristic
261C4×C11#55411yescharacteristic
262Dic11—24no—
263Dic11—42no—
264Dic11—42no—
265Dic11—42no—
266Dic11—42no—
267C22×Q8—111no—
268C22×D4—111no—
269C23×C4—222no—
270C23×C4—221no—
271C2×SD16—114no—
272C2×SD16—114no—
273C2×SD16—114no—
274C22×C8—112no—
275C22×C8C22×D1111yescharacteristic
276C22×C8C22×D1111yescharacteristic
277C4×Q8—114no—
278C4×Q8—222no—
279C4×Q8—224no—
280C4×Q8—442no—
281C4×D4—114no—
282C4×D4—224no—
283C4×D4—222no—
284C4×D4—442no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—222no—
296C2×C42—112no—
297C2×C42—221no—
298C2×C42—222no—
299C2×C42C22×D1111yescharacteristic
300#107—24no—
301#106—42no—
302#106—114no—
303C4⋊C8—222no—
304#103—114no—
305#103—224no—
306#102—114no—
307#102—224no—
308#97—224no—
309C4×C8C4×D1114yescomplemented
310#95—21no—
311#95—21no—
312#95—21no—
313#95—21no—
314#95—111no—
315#95—111no—
316#95—222no—
317#95—222no—
318C2×C11D4×C4⋊C411yescharacteristic
319C2×C11#294311yescharacteristic
320C2×C11#294911yescharacteristic
321C2×C11#327512yes—
322C2×C11#338812yes—
323D11—44no—
324C24—221no—
325C2×Q8—112no—
326C2×Q8—112no—
327C2×Q8—112no—
328C2×Q8—221no—
329C2×Q8—221no—
330C2×Q8—221no—
331C2×D4—112no—
332C2×D4—112no—
333C2×D4—112no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—224no—
345C22×C4—444no—
346C22×C4—444no—
347C22×C4—882no—
348C22×C4—882no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352SD16—1116no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8C2×C4×D1112yes—
359C2×C8C2×C4×D1112yes—
360C2×C8D4×D1112yes—
361C2×C8Q8×D1112yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—112no—
367C4⋊C4—112no—
368C4⋊C4—224no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—442no—
372C4⋊C4—444no—
373C4⋊C4—444no—
374C4⋊C4—882no—
375C22⋊C4—224no—
376C22⋊C4—444no—
377C42—224no—
378C42—222no—
379C42—222no—
380C42—444no—
381C42C2×C4×D1112yes—
382C42#434312yes—
383C11#2267311yescharacteristic, complemented, Sylow
384C23—222no—
385C23—222no—
386C23—222no—
387C23—442no—
388C23—442no—
389C23C2×D4×D1111yescharacteristic
390Q8—114no—
391Q8—222no—
392Q8—222no—
393Q8—222no—
394D4—114no—
395D4—222no—
396D4—222no—
397D4—222no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—884no—
420C2×C4—888no—
421C2×C4#6694612yes—
422C2×C4#6694612yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×D4×D1111yescharacteristic
425C2×C4#6703711yescharacteristic
426C2×C4C2×Q8×D1111yescharacteristic
427C2×C4C2×#434311yescharacteristic
428C2×C4#6704011yescharacteristic
429C8—22no—
430C8—442no—
431C8C4⋊C4×D1114yes—
432C22—224no—
433C22—442no—
434C22—444no—
435C22—444no—
436C22—442no—
437C22C2×#6694611yescharacteristic
438C22#1062324811yescharacteristic
439C22#1062325811yescharacteristic
440C22#1062329912yes—
441C22#1062330112yes—
442C4—22no—
443C4—22no—
444C4—82no—
445C4—82no—
446C4—224no—
447C4—442no—
448C4—442no—
449C4—442no—
450C4—442no—
451C4C2×C4⋊C4×D1111yescharacteristic
452C4#1062303511yescharacteristic
453C4#1062325711yescharacteristic
454C4#1062326111yescharacteristic
455C2—444no—
456C2#1307151611yescharacteristic
457C2#1307741611yescharacteristic
458C2#1307747411yescharacteristic
459C2#1308024612yes—
460C2#1308156712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1846C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1846D11
hypocenterC11#22673
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1846

Complements

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

NH ≅ G/Ntype
3. #13071533C2semidirect
5. #13069357C2semidirect
6. #13068881C2semidirect
8. #13068628C2semidirect
10. #13068483C2semidirect
11. C11×#1846C2semidirect
33. C4×#4314C4semidirect
75. C4×Dic22C2×C4semidirect
78. C4×C8×C11C2×C4semidirect
88. #66881C2×C4semidirect
89. #66880C2×C4semidirect
153. #4314C4⋊C4semidirect
161. #1846D11semidirect
309. C4×C8C4×D11semidirect
383. C11#22673semidirect

Maximal subgroups

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

subgroupindex
C2×#106225022
C2×C4×#43142
#130715332
#130715242
#130693572
#130688812
#130688742
#130686282
#130686232
#130684832
C11×#18462
#2267311