Finite Group Databasebeta

← #14758997

Subgroups — #14758997

Order 2816.

1230 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66867C211yesmaximal, characteristic, complemented
2#13071023C211yesmaximal, characteristic, complemented
3#13069586C212yesmaximal, complemented
4#13069433C212yesmaximal, complemented
5#13069045C212yesmaximal
6#13069040C212yesmaximal, complemented
7#13068446C212yesmaximal, complemented
8#13068441C212yesmaximal, complemented
9C2×C11×#529C211yesmaximal, characteristic
10C11×#529—24no—
11C11×#529C418yescomplemented
12C2×C11×#126—21no—
13C2×C11×#125C2211yescharacteristic
14C2×C11×#124C2211yescharacteristic
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117—21no—
22C22×C42×C11C2211yescharacteristic
23C2×#66979—21no—
24C23×C11⋊C8C2212yes—
25C2×#66899C2214yes—
26C2×#66896C2214yes—
27#10622825—21no—
28#10622825C2212yes—
29#10622549—21no—
30#10622548C2212yes—
31C4×C4⋊Dic11—21no—
32C4×C4⋊Dic11C2212yes—
33C2×#66867—24no—
34C2×#66867C2212yes—
35C2×#66867C2212yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11C2311yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C11×#126—28no—
46C11×#125—22no—
47C11×#125C2×C414yes—
48C11×#124—22no—
49C11×#124C2×C414yes—
50C11×#123—28no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8C2×C414yes—
53C11×#121—22no—
54C11×#121C2×C414yes—
55C4×Q8×C11—22no—
56C4×Q8×C11C2×C414yes—
57C4×D4×C11—28no—
58C4×D4×C11—22no—
59C4×D4×C11C2×C414yes—
60C11×#117—28no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2×C414yes—
74C2×C42×C11D411yescharacteristic
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D414yes—
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80#66979—44no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11C2314yes—
84C2×C4×Dic11—22no—
85C22×C11⋊C8—24no—
86C22×C11⋊C8—28no—
87C22×C11⋊C8C2314yes—
88#66899—28no—
89#66896—28no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92#66867—24no—
93#66867—24no—
94#21406—111nomaximal, Sylow
95C24×C11—21no—
96C24×C11C2×D411yescharacteristic
97C2×Q8×C11—21no—
98C2×Q8×C11—24no—
99C2×Q8×C11C22×C412yes—
100C2×D4×C11—24no—
101C2×D4×C11—21no—
102C2×D4×C11—24no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11C22×C412yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—24no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—42no—
114C22×C4×C11—44no—
115C22×C4×C11C22⋊C414yes—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4C22×C412yes—
133C11×C4⋊C4C22×C412yes—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C11×C22⋊C4—24no—
139C42×C11—24no—
140C42×C11C22⋊C414yes—
141C42×C11C22⋊C414yes—
142C42×C11C22×C412yes—
143C42×C11C22×C412yes—
144C42×C11C2×D412yes—
145C42×C11C2×D412yes—
146C22⋊Dic11—44no—
147C4⋊Dic11—24no—
148C4⋊Dic11—24no—
149C4⋊Dic11—44no—
150C4⋊Dic11—44no—
151C4×Dic11—44no—
152C2×C11⋊C8—216no—
153C2×C11⋊C8—24no—
154C2×C11⋊C8—24no—
155C2×C11⋊C8#4118yes—
156C2×#529D1111yescharacteristic
157C22×#97—111no—
158#2285—111no—
159#1992—112no—
160#1959—112no—
161#1893—112no—
162#1892—112no—
163#1763—112no—
164#1762—112no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—42no—
172C23×C11C2×C22⋊C412yes—
173C23×C11AGL(1,ℤ/8)12yes—
174C23×C11#13712yes—
175C23×C11C22×D411yescharacteristic
176Q8×C11—24no—
177Q8×C11—42no—
178D4×C11—24no—
179D4×C11—48no—
180D4×C11—42no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—28no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—44no—
195C2×C4×C11—48no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C2×C22⋊C412yes—
203C2×C4×C11C2×C22⋊C412yes—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4114yes—
208C2×Dic11—44no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211C11⋊C8—28no—
212C23×C8—112no—
213#529—24no—
214#529Dic1118yescomplemented
215C2×#126—21no—
216C2×#125C2×D1111yescharacteristic
217C2×#124C2×D1111yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8C2×D1111yescharacteristic
220C2×#121C2×D1111yescharacteristic
221C2×C4×Q8C2×D1111yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4C2×D1111yescharacteristic
224C2×#117—21no—
225C2×#117—221no—
226C22×C42C2×D1111yescharacteristic
227C2×#103—114no—
228C2×#102—114no—
229C2×#97—112no—
230C2×#97—112no—
231C2×#97—224no—
232#384—112no—
233#382—221no—
234#380—112no—
235#380—221no—
236C4×C4⋊C4—112no—
237C4×C4⋊C4—221no—
238#340—114no—
239#340—114no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11—22no—
244C22×C11—42no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11#41714yes—
250C22×C11C22×C22⋊C411yescharacteristic
251C22×C11#53212yes—
252C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C11C2×#13711yescharacteristic
254C22×C11#57512yes—
255C4×C11—22no—
256C4×C11—22no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11C4×#4112yes—
264C4×C11#52512yes—
265Dic11—84no—
266C22×Q8C22×D1111yescharacteristic
267C22×D4—21no—
268C22×D4C22×D1111yescharacteristic
269C23×C4—21no—
270C23×C4C22⋊D1111yescharacteristic
271C23×C4C22⋊D1111yescharacteristic
272C23×C4C22×D1111yescharacteristic
273C22×C8—114no—
274C22×C8—228no—
275C22×C8—224no—
276#126—28no—
277#125—22no—
278#125C2×Dic1114yes—
279#124—22no—
280#124C2×Dic1114yes—
281#123—28no—
282C22⋊Q8—22no—
283C22⋊Q8C2×Dic1114yes—
284#121—22no—
285#121C2×Dic1114yes—
286C4×Q8—22no—
287C4×Q8C2×Dic1114yes—
288C4×D4—28no—
289C4×D4—22no—
290C4×D4C2×Dic1114yes—
291#117—28no—
292#117—444no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—114no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—222no—
300C2×C4⋊C4C22×D1111yescharacteristic
301C2×C4⋊C4C22×D1111yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—222no—
308C2×C42—21no—
309C2×C42—222no—
310C2×C42C2×Dic1114yes—
311C2×C42C22⋊D1111yescharacteristic
312C2×C42C22⋊D1111yescharacteristic
313C2×C42C22⋊D1114yes—
314C2×C42C22×D1111yescharacteristic
315C2×C42C22×D1111yescharacteristic
316#103—228no—
317#102—228no—
318#97—224no—
319#97—224no—
320#95—222no—
321#95—222no—
322C2×C11—24no—
323C2×C11—82no—
324C2×C11#229711yescharacteristic
325C2×C11C2×#41711yescharacteristic
326C2×C11#289611yescharacteristic
327C2×C11#318012yes—
328C2×C11#318112yes—
329C24—21no—
330C24C2×C22⋊D1111yescharacteristic
331C2×Q8—21no—
332C2×Q8—24no—
333C2×Q8C22×Dic1112yes—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—42no—
338C2×D4—42no—
339C2×D4C22×Dic1112yes—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—24no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—224no—
350C22×C4C22⋊Dic1114yes—
351C22×C4C22⋊Dic1114yes—
352C22×C4C22×Dic1112yes—
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1112yes—
359C22×C4C23×D1111yescharacteristic
360C2×C8—118no—
361C2×C8—2216no—
362C2×C8—224no—
363C2×C8—224no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—224no—
371C4⋊C4—224no—
372C4⋊C4—444no—
373C4⋊C4—444no—
374C4⋊C4C22×Dic1112yes—
375C4⋊C4C22×Dic1112yes—
376C22⋊C4—24no—
377C22⋊C4—24no—
378C22⋊C4—24no—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—444no—
382C42—24no—
383C42—444no—
384C42C22⋊Dic1114yes—
385C42C22⋊Dic1114yes—
386C42C22×Dic1112yes—
387C42C22×Dic1112yes—
388C42C2×C22⋊D1112yes—
389C42C2×C22⋊D1112yes—
390C11#2140611yescharacteristic, complemented, Sylow
391C23—22no—
392C23—22no—
393C23—22no—
394C23—41no—
395C23—42no—
396C23—41no—
397C23—42no—
398C23#6700212yes—
399C23#6700412yes—
400C23C2×C22⋊Dic1112yes—
401C23C22×C22⋊D1111yescharacteristic
402Q8—24no—
403Q8—42no—
404D4—24no—
405D4—48no—
406D4—42no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—28no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—44no—
421C2×C4—48no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—444no—
427C2×C4—444no—
428C2×C4—444no—
429C2×C4C2×C22⋊Dic1112yes—
430C2×C4C2×C22⋊Dic1112yes—
431C2×C4C2×C22⋊Dic1112yes—
432C2×C4C2×C22⋊Dic1112yes—
433C2×C4C2×C22⋊Dic1112yes—
434C2×C4#41×D1114yes—
435C2×C4C23×Dic1111yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—228no—
438C22—22no—
439C22—24no—
440C22—24no—
441C22—22no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—82no—
446C22—82no—
447C22#1062284514yes—
448C22C2×#6700211yescharacteristic
449C22#1062335312yes—
450C22C2×#6700411yescharacteristic
451C22#1062336312yes—
452C22C22×C22⋊Dic1111yescharacteristic
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—884no—
462C4#41×Dic1112yes—
463C4#1062335912yes—
464C2—24no—
465C2—82no—
466C2#1307110711yescharacteristic
467C2C2×#1062284511yescharacteristic
468C2#1307713511yescharacteristic
469C2#1307931512yes—
470C2#1307932612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#529D11
hypocenterC11#21406
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C22×#66867C2semidirect
2. #13071023C2semidirect
3. #13069586C2semidirect
4. #13069433C2semidirect
6. #13069040C2semidirect
7. #13068446C2semidirect
8. #13068441C2semidirect
11. C11×#529C4semidirect
214. #529Dic11semidirect
390. C11#21406semidirect

Maximal subgroups

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

subgroupindex
C22×#668672
#130710232
#130695862
#130694332
#130690452
#130690402
#130684462
#130684412
C2×C11×#5292
#2140611