Finite Group Databasebeta

← #14764045

Subgroups — #14764045

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊(C11⋊C8)C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic
3#13068815C214yesmaximal, complemented
4#13068808C212yesmaximal, complemented
5#13068803C212yesmaximal, complemented
6#13068643C212yesmaximal, complemented
7#13068639C212yesmaximal, complemented
8C11×#2280C211yesmaximal, characteristic
9C24×C4×C11C2211yescharacteristic
10C2×C11×#117C2212yes—
11C22×C22⋊Dic11—21no—
12C22×C4⋊Dic11C2212yes—
13C23×C11⋊C8C2212yes—
14C11×#381—21no—
15C11×#380C2212yes—
16C11×#380C2211yescharacteristic
17C11×#380C2211yescharacteristic
18C11×#379—21no—
19C4×C11×C22⋊C4—21no—
20C4×C11×C22⋊C4—21no—
21#10622825—21no—
22#10622825—21no—
23#10622825C2212yes—
24#10622825C2212yes—
25C2×C11⋊#95—21no—
26C2×C22⋊(C11⋊C8)C418yescomplemented
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×#66872C2214yescomplemented
31C2×#66871C2214yescomplemented
32#10622167C2214yescomplemented
33#10622167C2214yescomplemented
34C25×C11D411yescharacteristic
35C23×C4×C11—44no—
36C23×C4×C11C2×C414yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11Q814yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—22no—
45C11×#117—44no—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C42×C11—22no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—44no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—44no—
58C2×C4⋊Dic11C2314yes—
59C22×C11⋊C8—44no—
60C22×C11⋊C8C2×C418yescomplemented
61C22×C11⋊C8C2312yes—
62C22×C11⋊C8C2312yes—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—22no—
66C11⋊#95—22no—
67C11⋊#95—22no—
68C22⋊(C11⋊C8)C2×C414yes—
69C22⋊(C11⋊C8)C2×C414yes—
70C22⋊(C11⋊C8)C2×C418yescomplemented
71#66872—44no—
72#66871—44no—
73#21941—111nomaximal, Sylow
74C24×C11—24no—
75C24×C11—22no—
76C24×C11—22no—
77C24×C11—42no—
78C24×C11C4⋊C414yes—
79C24×C11C2×D411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C24×C11C2×D411yescharacteristic
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—48no—
88C22×C4×C11—48no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11C4⋊C414yes—
93C22×C4×C11C4⋊C414yes—
94C22×C4×C11C4⋊C414yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C22×C412yes—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—24no—
106C22×Dic11—44no—
107C22×Dic11—44no—
108C22×Dic11—44no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C22⋊C4—44no—
112C11×C22⋊C4—44no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C42×C11—44no—
116C22⋊Dic11—44no—
117C22⋊Dic11—44no—
118C4⋊Dic11—24no—
119C4⋊Dic11—24no—
120C4⋊Dic11—44no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—48no—
124C2×C11⋊C8C22×C414yes—
125C2×C11⋊C8C22×C414yes—
126C22×C22⋊C8—111no—
127#2280D1111yescharacteristic
128C2×#380—111no—
129#1854—114no—
130#1853—112no—
131#1852—112no—
132#1808—112no—
133#1807—112no—
134C23×C11—22no—
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—28no—
144C23×C11—28no—
145C23×C11—44no—
146C23×C11—48no—
147C23×C11—48no—
148C23×C11C2×C4⋊C412yes—
149C23×C11C2×C4⋊C412yes—
150C23×C11C2×C4⋊C412yes—
151C23×C11#13514yes—
152C23×C11AGL(1,ℤ/8)12yes—
153C23×C11#13712yes—
154C23×C11C22×D411yescharacteristic
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—24no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11—44no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11C2×C4⋊C412yes—
174C2×C4×C11C2×C4⋊C412yes—
175C2×C4×C11C2×C4⋊C412yes—
176C2×C4×C11C23×C411yescharacteristic
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11H(5,𝔽2)14yes—
179C2×Dic11—44no—
180C2×Dic11—44no—
181C2×Dic11—44no—
182C2×Dic11—88no—
183C11⋊C8—24no—
184C11⋊C8—24no—
185C24×C4C2×D1111yescharacteristic
186C23×C8—112no—
187C2×#117C2×D1112yes—
188C22×C4⋊C4—112no—
189C22×C22⋊C4—221no—
190C2×#107—114no—
191C2×#106—114no—
192C2×C22⋊C8—111no—
193C2×C22⋊C8—111no—
194C2×C22⋊C8—112no—
195C2×C22⋊C8—118no—
196#381—21no—
197#380—112no—
198#380—112no—
199#380—221no—
200#380—221no—
201#380C2×D1111yescharacteristic
202#380C2×D1111yescharacteristic
203#380C2×D1112yes—
204#379—21no—
205C4×C22⋊C4—21no—
206C4×C22⋊C4—21no—
207C2×#95—221no—
208#340—114no—
209#340—114no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—24no—
215C22×C11—24no—
216C22×C11—24no—
217C22×C11—24no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—22no—
221C22×C11—416no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11#42714yes—
225C22×C11#42814yes—
226C22×C11C22×C4⋊C411yescharacteristic
227C22×C11#53412yes—
228C22×C11C2×#13512yes—
229C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—22no—
234C4×C11—82no—
235C4×C11—82no—
236C4×C11#51812yes—
237C4×C11#54312yes—
238Dic11—84no—
239C25C22⋊D1111yescharacteristic
240C23×C4—44no—
241C23×C4—222no—
242C23×C4Dic2214yes—
243C23×C4C4×D1114yes—
244C23×C4C22⋊D1111yescharacteristic
245C23×C4C22⋊D1111yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C23×C4C22×D1111yescharacteristic
249C23×C4C22×D1111yescharacteristic
250C22×C8—112no—
251C22×C8—112no—
252C22×C8—118no—
253C22×C8—444no—
254#117—44no—
255C2×C4⋊C4—114no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4—444no—
258C2×C4⋊C4C22×D1112yes—
259C2×C4⋊C4C22×D1112yes—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—222no—
265C2×C22⋊C4—222no—
266C2×C22⋊C4—444no—
267C2×C42—22no—
268#107—444no—
269#106—444no—
270C22⋊C8—114no—
271C22⋊C8—114no—
272C22⋊C8—118no—
273#95—21no—
274#95—21no—
275#95—22no—
276#95—222no—
277#95—222no—
278C2×C11—24no—
279C2×C11—24no—
280C2×C11—42no—
281C2×C11#231511yescharacteristic
282C2×C11C2×#42711yescharacteristic
283C2×C11C2×#42811yescharacteristic
284C2×C11#318812yes—
285C2×C11#319012yes—
286C24—22no—
287C24—24no—
288C24—22no—
289C24—42no—
290C24Dic11⋊C414yes—
291C24C2×C22⋊D1111yescharacteristic
292C24C2×C22⋊D1111yescharacteristic
293C24C2×C22⋊D1111yescharacteristic
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—48no—
300C22×C4—48no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—224no—
305C22×C4—444no—
306C22×C4—444no—
307C22×C4—444no—
308C22×C4Dic11⋊C414yes—
309C22×C4Dic11⋊C414yes—
310C22×C4Dic11⋊C414yes—
311C22×C4C2×Dic2212yes—
312C22×C4C2×Dic2212yes—
313C22×C4C2×Dic2212yes—
314C22×C4C2×C4×D1112yes—
315C22×C4C2×C4×D1112yes—
316C22×C4C2×C4×D1112yes—
317C22×C4C2×C22⋊D1111yescharacteristic
318C22×C4C2×C22⋊D1111yescharacteristic
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321C2×C8—114no—
322C2×C8—114no—
323C2×C8—224no—
324C2×C8—224no—
325C2×C8—448no—
326C4⋊C4—24no—
327C4⋊C4—24no—
328C4⋊C4—224no—
329C4⋊C4—224no—
330C4⋊C4—444no—
331C22⋊C4—44no—
332C22⋊C4—42no—
333C22⋊C4—44no—
334C22⋊C4—42no—
335C22⋊C4—444no—
336C22⋊C4—444no—
337C42—44no—
338C11#2194111yescharacteristic, complemented, Sylow
339C23—22no—
340C23—22no—
341C23—21no—
342C23—22no—
343C23—21no—
344C23—22no—
345C23—21no—
346C23—22no—
347C23—21no—
348C23—28no—
349C23—28no—
350C23—44no—
351C23—48no—
352C23—48no—
353C23C2×Dic11⋊C412yes—
354C23C2×Dic11⋊C412yes—
355C23C2×Dic11⋊C412yes—
356C23#6700212yes—
357C23#6700314yes—
358C23#6700412yes—
359C23C22×C22⋊D1111yescharacteristic
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—444no—
379C2×C4—444no—
380C2×C4—444no—
381C2×C4—888no—
382C2×C4C2×Dic11⋊C412yes—
383C2×C4C2×Dic11⋊C412yes—
384C2×C4C2×Dic11⋊C412yes—
385C2×C4C22×Dic2211yescharacteristic
386C2×C4C22×C4×D1111yescharacteristic
387C2×C4#6703714yes—
388C8—224no—
389C8—224no—
390C22—24no—
391C22—24no—
392C22—24no—
393C22—24no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—416no—
402C22—42no—
403C22—42no—
404C22#1062260814yes—
405C22#1062261114yes—
406C22C22×Dic11⋊C411yescharacteristic
407C22#1062333512yes—
408C22C2×#6700211yescharacteristic
409C22C2×#6700312yes—
410C22C2×#6700411yescharacteristic
411C4—22no—
412C4—22no—
413C4—22no—
414C4—82no—
415C4—82no—
416C4—884no—
417C4#1062301412yes—
418C4#1062301712yes—
419C2—24no—
420C2—24no—
421C2—42no—
422C2#1307122811yescharacteristic
423C2C2×#1062261111yescharacteristic
424C2C2×#1062260811yescharacteristic
425C2#1307937712yes—
426C2#1307939312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2280C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenter#2280D11
hypocenterC11#21941
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13068815C2semidirect
4. #13068808C2semidirect
5. #13068803C2semidirect
6. #13068643C2semidirect
7. #13068639C2semidirect
26. C2×C22⋊(C11⋊C8)C4semidirect
30. C2×#66872C22semidirect
31. C2×#66871C22semidirect
32. #10622167C22semidirect
33. #10622167C22semidirect
60. C22×C11⋊C8C2×C4semidirect
70. C22⋊(C11⋊C8)C2×C4semidirect
338. C11#21941semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊(C11⋊C8)2
C2×#106228252
#130688152
#130688082
#130688032
#130686432
#130686392
C11×#22802
#2194111