Finite Group Databasebeta

← #14770840

Subgroups — #14770840

Order 2816.

990 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
1C22×#66880C211yesmaximal, characteristic
2#13071483C211yesmaximal, characteristic
3C22⋊C4×Dic22C211yesmaximal, characteristic
4#13069306C212yesmaximal, complemented
5#13069258C212yesmaximal, complemented
6#13068873C212yesmaximal, complemented
7#13068703C211yesmaximal, characteristic
8#13068645C211yesmaximal, characteristic
9#13068552C211yesmaximal, characteristic
10#13068447C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×#66930—21no—
16C2×C4×Dic22C2212yes—
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×#97C2212yes—
19C4×C11×C22⋊C4C2211yescharacteristic
20#10622825C2211yescharacteristic
21#10622825C2211yescharacteristic
22C2×#66882C2212yes—
23C2×#66880C418yescomplemented
24C2×#66880C2212yes—
25C2×#66880C2212yes—
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30#10622556—21no—
31#10622555—21no—
32C22⋊C4×Dic11—21no—
33C4×C4⋊Dic11C2212yes—
34#10622542C2212yes—
35#10622541C2212yes—
36#10622266—22no—
37#10622259—22no—
38C11×#336C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×Dic22—24no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—42no—
49C22×Dic22C2×C414yes—
50C22×Dic22C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C22×C8×C11—42no—
53C22×C8×C11C2×C414yes—
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C2×C11×C22⋊C4D411yescharacteristic
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C42×C11C2312yes—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2×C414yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73#66930—44no—
74C4×Dic22—24no—
75C4×Dic22—42no—
76C11×C22⋊C8—22no—
77C11×#97—42no—
78C11×#95D412yes—
79C11⋊#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66882—42no—
86#66880—24no—
87#66880—42no—
88#66880C2×C414yes—
89#66880C2×C414yes—
90#66880C2×C414yes—
91#66880C2×C414yes—
92#22563—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4112yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—44no—
111C22×Dic11—42no—
112C22×Dic11—42no—
113C2×Dic22—28no—
114C2×Dic22—24no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—44no—
121C2×Dic22—48no—
122C2×Dic22—44no—
123C2×Dic22C22×C412yes—
124C2×Dic22C22×C412yes—
125C2×Dic22#4114yes—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—44no—
132C2×C8×C11C22×C412yes—
133C2×C8×C11C22×C412yes—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C42×C11—22no—
137C42×C11—22no—
138C22⋊Dic11—42no—
139C22⋊Dic11—42no—
140C4⋊Dic11—24no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11C22×C412yes—
148C4⋊Dic11C22×C412yes—
149Dic11⋊C4—44no—
150Dic11⋊C4—44no—
151C4×Dic11—44no—
152C4×Dic11—44no—
153C22×#103—111no—
154#2344—111no—
155Q8×C22⋊C4—111no—
156#1935—112no—
157#1928—112no—
158#1863—112no—
159#1823—111no—
160#1808—111no—
161#1787—111no—
162#1763—112no—
163#1752D1111yescharacteristic
164C23×C11—22no—
165C23×C11—22no—
166C23×C11C4×D412yes—
167C23×C11AGL(1,ℤ/8)12yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
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—24no—
187C2×Dic11—22no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—48no—
191C2×Dic11—42no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—48no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203Dic22—22no—
204Dic22—24no—
205Dic22—22no—
206Dic22—22no—
207Dic22—48no—
208Dic22—42no—
209Dic22#11714yescomplemented
210C8×C11—22no—
211C8×C11—22no—
212C8×C11—42no—
213C23×Q8—111no—
214C23×C8C2×D1111yescharacteristic
215C2×C4×Q8—112no—
216C2×#117—221no—
217C22×C4⋊C4—111no—
218C2×#107—112no—
219C2×#103—111no—
220C2×#103—111no—
221C2×#103—111no—
222C2×#103—111no—
223C2×#103—118no—
224C2×#103—112no—
225C2×#103—112no—
226C2×C22⋊C8C2×D1111yescharacteristic
227C2×#97C2×D1112yes—
228#391—112no—
229#391—222no—
230#389—112no—
231#387—222no—
232#381—221no—
233#380—111no—
234#380—111no—
235#380—221no—
236C4×C4⋊C4—112no—
237C4×C22⋊C4—221no—
238C4×C22⋊C4C2×D1111yescharacteristic
239#340—112no—
240#340—112no—
241#340—112no—
242#336C2×D1112yes—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11#44014yes—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54612yes—
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11#57812yes—
253C4×C11—22no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11C2×#11711yescharacteristic
257C4×C11#51811yescharacteristic
258C4×C11#55112yes—
259Dic11—24no—
260Dic11—42no—
261Dic11—42no—
262Dic11—42no—
263Dic11—82no—
264Dic11—82no—
265C22×Q8—114no—
266C22×Q8—111no—
267C22×Q8—111no—
268C22×Q8—224no—
269C22×Q8—221no—
270C22×Q8—222no—
271C22×Q8—442no—
272C23×C4—221no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C22×C8—42no—
276C22×C8C4×D1114yes—
277C22×C8C22×D1112yes—
278C22×C8C22×D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280C4×Q8—224no—
281C4×Q8—442no—
282#117—444no—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4D4411yescharacteristic
295C2×C22⋊C4D4411yescharacteristic
296C2×C42—222no—
297C2×C42—222no—
298C2×C42C22×D1112yes—
299#107—442no—
300#103—114no—
301#103—114no—
302#103—114no—
303#103—114no—
304#103—224no—
305#103—442no—
306C22⋊C8—22no—
307#97—42no—
308#95—222no—
309#95—222no—
310#95—221no—
311#95—221no—
312#95—222no—
313#95—222no—
314#95D4412yes—
315C2×C11—24no—
316C2×C11#234211yescharacteristic
317C2×C11C2×#44011yescharacteristic
318C2×C11#295011yescharacteristic
319C2×C11#330812yes—
320C2×C11#331212yes—
321C24C2×D4411yescharacteristic
322C2×Q8—112no—
323C2×Q8—112no—
324C2×Q8—114no—
325C2×Q8—228no—
326C2×Q8—224no—
327C2×Q8—221no—
328C2×Q8—221no—
329C2×Q8—222no—
330C2×Q8—222no—
331C2×Q8—222no—
332C2×Q8—444no—
333C2×Q8—444no—
334C2×Q8—448no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—221no—
338C22×C4—224no—
339C22×C4—224no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—444no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4C2×C4×D1112yes—
349C22×C4C2×D4412yes—
350C22×C4C2×D4412yes—
351C22×C4C2×D4411yescharacteristic
352C22×C4#433912yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—44no—
360C2×C8C2×C4×D1112yes—
361C2×C8C2×C4×D1112yes—
362C4⋊C4—112no—
363C4⋊C4—112no—
364C4⋊C4—224no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—444no—
372C4⋊C4—444no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—442no—
376C22⋊C4—442no—
377C42—22no—
378C42—22no—
379C42—444no—
380C42—444no—
381C11#2256311yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23C4×D4412yes—
385C23#6696112yes—
386C23#6696212yes—
387C23C22×D4411yescharacteristic
388Q8—114no—
389Q8—222no—
390Q8—224no—
391Q8—222no—
392Q8—222no—
393Q8—448no—
394Q8—442no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—222no—
406C2×C4—224no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—448no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—448no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4C4×D4412yes—
424C2×C4C22×C4×D1111yescharacteristic
425C2×C4C2×#433911yescharacteristic
426C2×C4#6703712yes—
427C2×C4#41×D1112yes—
428C8—22no—
429C8—22no—
430C8—42no—
431C22—24no—
432C22—24no—
433C22—22no—
434C22—22no—
435C22#1062232314yes—
436C22C2×C4×D4411yescharacteristic
437C22#1062308512yes—
438C22C2×#6696111yescharacteristic
439C22C2×#6696211yescharacteristic
440C22#1062328412yes—
441C4—22no—
442C4—42no—
443C4—42no—
444C4—224no—
445C4—442no—
446C4—442no—
447C4—442no—
448C4—882no—
449C4—882no—
450C4#1062301711yescharacteristic
451C4D11×#11711yescharacteristic
452C4#1062308712yes—
453C2—24no—
454C2#1307146811yescharacteristic
455C2C2×#1062232311yescharacteristic
456C2#1307748511yescharacteristic
457C2#1308060912yes—
458C2#1308066912yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
4. #13069306C2semidirect
5. #13069258C2semidirect
6. #13068873C2semidirect
10. #13068447C2semidirect
23. C2×#66880C4semidirect
209. Dic22#117semidirect
381. C11#22563semidirect

Maximal subgroups

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

subgroupindex
C22×#668802
#130714832
C22⋊C4×Dic222
#130693062
#130692582
#130688732
#130687032
#130686452
#130685522
#130684472
C11×#17522
#2256311