Finite Group Databasebeta

← #14770962

Subgroups — #14770962

Order 2816.

974 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
1C22×#66874C211yesmaximal, characteristic
2#13071493C211yesmaximal, characteristic
3#13071448C211yesmaximal, characteristic
4#13069293C212yesmaximal, complemented
5#13069255C212yesmaximal, complemented
6#13068871C212yesmaximal, complemented
7#13068643C211yesmaximal, characteristic
8#13068552C211yesmaximal, characteristic
9#13068435C212yesmaximal, complemented
10#13068390C211yesmaximal, characteristic
11C11×#1824C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×#66940C2212yes—
16C2×C11×C22⋊C8C2211yescharacteristic
17C11×#380C2211yescharacteristic
18#10622825—21no—
19#10622825C2211yescharacteristic
20C4×C22⋊Dic11—21no—
21C4×C22⋊Dic11C2211yescharacteristic
22C2×#66880C2212yes—
23C2×#66880C2212yes—
24C2×C8×Dic11C2212yes—
25#10622598C2212yes—
26#10622594—22no—
27C4⋊C4×Dic11C2212yes—
28#10622587C2212yes—
29C2×#66874C418yescomplemented
30C2×#66874C2211yescharacteristic
31C2×#66874C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66871C2212yes—
35#10622555—21no—
36C22⋊C4×Dic11—21no—
37#10622259—22no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C22×Dic22—24no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—42no—
49C22×Dic22C2×C414yes—
50C22×Dic22C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D411yescharacteristic
62C2×C22⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2312yes—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2312yes—
69C22×C11⋊C8—42no—
70C22×C11⋊C8C2×C414yes—
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73#66940—24no—
74#66940—42no—
75C11×C22⋊C8—22no—
76C11×#95—21no—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95D412yes—
83#66880—24no—
84#66880—42no—
85C8×Dic11—42no—
86#66874C2×C414yes—
87#66874C2×C414yes—
88#66874C2×C414yes—
89#66874C2×C414yes—
90#66871—42no—
91#22575—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—82no—
100C22×C4×C11C22×C412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4112yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—24no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11—44no—
109C22×Dic11C2×D412yes—
110C22×Dic11C2×D412yes—
111C2×Dic22—28no—
112C2×Dic22—24no—
113C2×Dic22—21no—
114C2×Dic22—22no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—44no—
119C2×Dic22—48no—
120C2×Dic22—44no—
121C2×Dic22C22×C412yes—
122C2×Dic22C22×C412yes—
123C2×Dic22#4114yes—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C22×C412yes—
133C11×C4⋊C4C22×C412yes—
134C11×C22⋊C4—42no—
135C22⋊Dic11—22no—
136C22⋊Dic11—42no—
137C22⋊Dic11Q1614yes—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—82no—
141Dic11⋊C4—44no—
142C4×Dic11—22no—
143C4×Dic11—22no—
144C4×Dic11—44no—
145C4×Dic11—82no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—44no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C22×#103—111no—
152#2345—111no—
153Q8×C22⋊C4—111no—
154#1933—112no—
155#1928—112no—
156#1863—112no—
157#1824D1111yescharacteristic
158#1808—111no—
159#1787—111no—
160C4×#103—112no—
161C8×C22⋊C4—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C4×D412yes—
165C23×C11C2×Q1612yes—
166C23×C11#13512yes—
167C23×C11C22×D411yescharacteristic
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—84no—
180C2×C4×C11C4×D412yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4112yes—
184C2×C4×C11H(5,𝔽2)12yes—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—48no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11C2×Q1614yes—
199Dic22—22no—
200Dic22—24no—
201Dic22—22no—
202Dic22—22no—
203Dic22—48no—
204Dic22—42no—
205Dic22#11714yes—
206C8×C11—42no—
207C11⋊C8—22no—
208C11⋊C8—22no—
209C23×Q8—111no—
210C23×C8—111no—
211C2×C4×Q8—112no—
212C22×C4⋊C4C2×D1111yescharacteristic
213C2×#107—112no—
214C2×#103—111no—
215C2×#103—111no—
216C2×#103—111no—
217C2×#103—111no—
218C2×#103—118no—
219C2×#103—112no—
220C2×#103—112no—
221C2×C22⋊C8C2×D1111yescharacteristic
222C2×C4×C8—112no—
223#391—112no—
224#391—222no—
225#389—112no—
226#387—222no—
227#380—111no—
228#380—221no—
229#380—221no—
230#380C2×D1111yescharacteristic
231C4×C4⋊C4—112no—
232C4×C22⋊C4—111no—
233C4×C22⋊C4—221no—
234C4×C22⋊C4—221no—
235#340—112no—
236#340C2×D1112yes—
237#340C2×D1112yes—
238#336—112no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11C4×Q1614yes—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#54612yes—
246C22×C11C22×Q1611yescharacteristic
247C22×C11C2×#13511yescharacteristic
248C22×C11#57712yes—
249C4×C11—22no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—82no—
253C4×C11C2×#11711yescharacteristic
254C4×C11#51811yescharacteristic
255C4×C11#55112yes—
256Dic11—24no—
257Dic11—24no—
258Dic11—42no—
259Dic11—42no—
260Dic11—82no—
261C22×Q8—114no—
262C22×Q8—111no—
263C22×Q8—111no—
264C22×Q8—224no—
265C22×Q8—221no—
266C22×Q8—222no—
267C22×Q8—442no—
268C23×C4—21no—
269C23×C4—221no—
270C23×C4C22×D1111yescharacteristic
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—114no—
274C22×C8—442no—
275C22×C8C22×D1112yes—
276C4×Q8—224no—
277C4×Q8—442no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—112no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4C4×D1114yes—
284C2×C4⋊C4C22×D1112yes—
285C2×C4⋊C4C22×D1111yescharacteristic
286C2×C4⋊C4C22×D1111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C22⋊C4—111no—
289C2×C22⋊C4—111no—
290C2×C22⋊C4—221no—
291C2×C42—112no—
292C2×C42—222no—
293C2×C42—222no—
294#107—442no—
295#103—114no—
296#103—114no—
297#103—114no—
298#103—114no—
299#103—224no—
300#103—442no—
301C22⋊C8—22no—
302C4×C8—442no—
303#95—21no—
304#95—112no—
305#95—222no—
306#95—222no—
307#95—222no—
308#95—222no—
309#95—221no—
310C2×C11—24no—
311C2×C11#234211yescharacteristic
312C2×C11C2×C4×Q1611yescharacteristic
313C2×C11#294911yescharacteristic
314C2×C11#329912yes—
315C2×C11#330112yes—
316C24D4×D1111yescharacteristic
317C2×Q8—112no—
318C2×Q8—112no—
319C2×Q8—114no—
320C2×Q8—228no—
321C2×Q8—224no—
322C2×Q8—221no—
323C2×Q8—221no—
324C2×Q8—222no—
325C2×Q8—222no—
326C2×Q8—222no—
327C2×Q8—444no—
328C2×Q8—444no—
329C2×Q8—448no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—82no—
337C22×C4—112no—
338C22×C4—112no—
339C22×C4—221no—
340C22×C4—224no—
341C22×C4—221no—
342C22×C4—222no—
343C22×C4—444no—
344C22×C4C2×C4×D1112yes—
345C22×C4D4×D1111yescharacteristic
346C22×C4#434112yes—
347C22×C4C23×D1111yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—112no—
352C2×C8—112no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—444no—
356C4⋊C4—24no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—222no—
362C4⋊C4—222no—
363C4⋊C4—444no—
364C4⋊C4—882no—
365C4⋊C4C2×C4×D1112yes—
366C4⋊C4C2×C4×D1112yes—
367C22⋊C4—42no—
368C22⋊C4—114no—
369C22⋊C4—222no—
370C22⋊C4—442no—
371C42—222no—
372C42—222no—
373C42—444no—
374C42—882no—
375C11#2257511yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23(C22⋊D11)⋊C412yes—
379C23#6696912yes—
380C23Q16×D1112yes—
381C23C2×D4×D1111yescharacteristic
382Q8—114no—
383Q8—222no—
384Q8—224no—
385Q8—222no—
386Q8—222no—
387Q8—448no—
388Q8—442no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—84no—
401C2×C4—114no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—224no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—448no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4(C22⋊D11)⋊C412yes—
416C2×C4C22×C4×D1111yescharacteristic
417C2×C4C2×#434111yescharacteristic
418C2×C4#41×D1112yes—
419C2×C4#6704212yes—
420C8—42no—
421C8—222no—
422C8—222no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22#1062240314yes—
428C22C2×(C22⋊D11)⋊C411yescharacteristic
429C22#1062318512yes—
430C22C2×#6696911yescharacteristic
431C22C2×Q16×D1111yescharacteristic
432C22#1062330612yes—
433C4—22no—
434C4—42no—
435C4—42no—
436C4—82no—
437C4—224no—
438C4—224no—
439C4—442no—
440C4—442no—
441C4—882no—
442C4D11×#11711yescharacteristic
443C4#1062305211yescharacteristic
444C4#1062318912yes—
445C2—24no—
446C2#1307145811yescharacteristic
447C2C2×#1062240311yescharacteristic
448C2#1307747811yescharacteristic
449C2#1308049012yes—
450C2#1308051612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1824C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1824D11
hypocenterC11#22575
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13069293C2semidirect
5. #13069255C2semidirect
6. #13068871C2semidirect
9. #13068435C2semidirect
29. C2×#66874C4semidirect
375. C11#22575semidirect

Maximal subgroups

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

subgroupindex
C22×#668742
#130714932
#130714482
#130692932
#130692552
#130688712
#130686432
#130685522
#130684352
#130683902
C11×#18242
#2257511