Finite Group Databasebeta

← #14764067

Subgroups — #14764067

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic
2#13070999C211yesmaximal, characteristic
3#13068813C214yesmaximal, complemented
4#13068809C212yesmaximal, complemented
5#13068804C212yesmaximal, complemented
6#13068647C214yesmaximal, complemented
7C2×C11×#380C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C22×C11×C4⋊C4C2212yes—
10C22×C11×C22⋊C4—21no—
11C2×#66979C2212yes—
12C22×#4318C2212yes—
13C11×#380—21no—
14C11×#380—21no—
15C11×#380C2212yes—
16C11×#380C2212yes—
17C2×C11×#95—21no—
18#10622860—21no—
19#10622825C2211yescharacteristic
20#10622825C2211yescharacteristic
21#10622825C2212yes—
22#10622824—21no—
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11—21no—
25#10622820C418yescomplemented
26C2×C22⋊(C11⋊C8)C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28C2×#66872C2214yescomplemented
29C2×#66871C2214yescomplemented
30#10622167C2214yescomplemented
31#10622167C2214yescomplemented
32C25×C11D411yescharacteristic
33C23×C4×C11—22no—
34C23×C4×C11—44no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D411yescharacteristic
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11Q814yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—44no—
45C2×C11×C4⋊C4C2314yes—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—44no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—22no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53#66979—44no—
54C2×C4⋊Dic11C2312yes—
55C2×C4⋊Dic11C2312yes—
56C2×C4×Dic11—22no—
57C2×#4318—44no—
58C2×#4318C2×C418yescomplemented
59C22×C11⋊C8C2314yes—
60C11×#95—22no—
61C11×#95—22no—
62C11⋊#95—22no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C22⋊(C11⋊C8)C2×C418yes—
66C22⋊(C11⋊C8)C2×C418yescomplemented
67#66872—44no—
68#66871—44no—
69#21944—111nomaximal, Sylow
70C24×C11—22no—
71C24×C11—22no—
72C24×C11—42no—
73C24×C11—42no—
74C24×C11C4⋊C414yes—
75C24×C11C2×D411yescharacteristic
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11—24no—
81C22×C4×C11—24no—
82C22×C4×C11—48no—
83C22×C4×C11—48no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—44no—
88C22×C4×C11—44no—
89C22×C4×C11—44no—
90C22×C4×C11C4⋊C414yes—
91C22×C4×C11C4⋊C414yes—
92C22×C4×C11C4⋊C414yes—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C22×C412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×Q812yes—
100C22×C4×C11C2×Q812yes—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—24no—
107C11×C4⋊C4—44no—
108C11×C22⋊C4—44no—
109C11×C22⋊C4—44no—
110C22⋊Dic11—44no—
111C22⋊Dic11—44no—
112C22⋊Dic11—42no—
113C22⋊Dic11—42no—
114C4⋊Dic11—24no—
115C4⋊Dic11—24no—
116C4×Dic11—44no—
117#4318—48no—
118C2×C11⋊C8—24no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8C22×C418yes—
121C2×#407—111no—
122#2280—111no—
123C2×#380D1111yescharacteristic
124#1854—114no—
125#1853—112no—
126#1852—112no—
127#1809—114no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—22no—
137C23×C11—22no—
138C23×C11—28no—
139C23×C11—44no—
140C23×C11—44no—
141C23×C11—48no—
142C23×C11—48no—
143C23×C11C2×C4⋊C412yes—
144C23×C11C2×C4⋊C412yes—
145C23×C11C2×C4⋊C412yes—
146C23×C11AGL(1,ℤ/8)12yes—
147C23×C11#13712yes—
148C23×C11C22×D411yescharacteristic
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—24no—
157C2×C4×C11—24no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11—44no—
163C2×C4×C11—44no—
164C2×C4×C11—88no—
165C2×C4×C11C2×C4⋊C412yes—
166C2×C4×C11C2×C4⋊C412yes—
167C2×C4×C11C2×C4⋊C412yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C22×Q811yescharacteristic
170C2×C4×C11H(5,𝔽2)14yes—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C11⋊C8—28no—
178C24×C4C2×D1111yescharacteristic
179C22×M16—112no—
180C2×#117—112no—
181C22×C4⋊C4C2×D1112yes—
182C22×C22⋊C4—21no—
183C2×#107—114no—
184C2×#106—114no—
185#407—118no—
186C2×C22⋊C8—112no—
187C2×C22⋊C8—112no—
188#381—221no—
189#380—21no—
190#380—21no—
191#380—112no—
192#380—111no—
193#380—111no—
194#380C2×D1112yes—
195#380C2×D1112yes—
196#379—221no—
197C4×C22⋊C4—221no—
198C4×C22⋊C4—221no—
199C2×#95—21no—
200#340—114no—
201#340—114no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—24no—
205C22×C11—24no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—416no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11#42814yes—
218C22×C11C22×C4⋊C411yescharacteristic
219C22×C11#53412yes—
220C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C11C2×#13711yescharacteristic
222C22×C11#57512yes—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—84no—
227C4×C11#51812yes—
228C4×C11#54312yes—
229Dic11—82no—
230Dic11—82no—
231C25C22⋊D1111yescharacteristic
232C23×C4—22no—
233C23×C4—44no—
234C23×C4Dic2214yes—
235C23×C4C4×D1114yes—
236C23×C4C22⋊D1111yescharacteristic
237C23×C4C22⋊D1111yescharacteristic
238C23×C4C22⋊D1111yescharacteristic
239C23×C4C22×D1111yescharacteristic
240C23×C4C22×D1111yescharacteristic
241C23×C4C22×D1111yescharacteristic
242C2×M16—118no—
243C2×M16—444no—
244C22×C8—114no—
245#117—444no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—44no—
248C2×C4⋊C4—112no—
249C2×C4⋊C4—112no—
250C2×C4⋊C4C22×D1114yes—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—44no—
254C2×C22⋊C4—222no—
255C2×C22⋊C4—222no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C42—222no—
259#107—444no—
260#106—444no—
261C22⋊C8—118no—
262C22⋊C8—118no—
263#95—22no—
264#95—22no—
265#95—222no—
266#95—221no—
267#95—221no—
268C2×C11—24no—
269C2×C11—42no—
270C2×C11—42no—
271C2×C11#231511yescharacteristic
272C2×C11C2×#42811yescharacteristic
273C2×C11#291111yescharacteristic
274C2×C11#319412yes—
275C2×C11#319612yes—
276C24—22no—
277C24—22no—
278C24—42no—
279C24—42no—
280C24Dic11⋊C414yes—
281C24C2×C22⋊D1111yescharacteristic
282C24C2×C22⋊D1111yescharacteristic
283C24C2×C22⋊D1111yescharacteristic
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—48no—
289C22×C4—48no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—222no—
297C22×C4—222no—
298C22×C4Dic11⋊C414yes—
299C22×C4Dic11⋊C414yes—
300C22×C4Dic11⋊C414yes—
301C22×C4C2×Dic2212yes—
302C22×C4C2×Dic2212yes—
303C22×C4C2×Dic2212yes—
304C22×C4C2×C4×D1112yes—
305C22×C4C2×C4×D1112yes—
306C22×C4C2×C4×D1112yes—
307C22×C4C2×C22⋊D1111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C2×C22⋊D1111yescharacteristic
310C22×C4C23×D1111yescharacteristic
311M16—448no—
312C2×C8—118no—
313C2×C8—224no—
314C2×C8—224no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—44no—
318C4⋊C4—224no—
319C4⋊C4—224no—
320C22⋊C4—44no—
321C22⋊C4—44no—
322C22⋊C4—444no—
323C22⋊C4—444no—
324C22⋊C4—442no—
325C22⋊C4—442no—
326C42—444no—
327C11#2194411yescharacteristic, complemented, Sylow
328C23—22no—
329C23—22no—
330C23—21no—
331C23—21no—
332C23—22no—
333C23—22no—
334C23—21no—
335C23—21no—
336C23—28no—
337C23—22no—
338C23—22no—
339C23—44no—
340C23—44no—
341C23—48no—
342C23—48no—
343C23C2×Dic11⋊C412yes—
344C23C2×Dic11⋊C412yes—
345C23C2×Dic11⋊C412yes—
346C23#6698512yes—
347C23#6699512yes—
348C23C22×C22⋊D1111yescharacteristic
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—88no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4C2×Dic11⋊C412yes—
372C2×C4C2×Dic11⋊C412yes—
373C2×C4C2×Dic11⋊C412yes—
374C2×C4C22×Dic2211yescharacteristic
375C2×C4C22×C4×D1111yescharacteristic
376C2×C4#6703714yes—
377C8—228no—
378C22—22no—
379C22—24no—
380C22—24no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—416no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22#1062257714yes—
394C22C22×Dic11⋊C411yescharacteristic
395C22C2×#6698511yescharacteristic
396C22#1062333512yes—
397C22C2×#6699511yescharacteristic
398C22#1062335312yes—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—84no—
403C4—882no—
404C4—882no—
405C4#1062301412yes—
406C4#1062301712yes—
407C2—24no—
408C2—42no—
409C2—42no—
410C2#1307122811yescharacteristic
411C2C2×#1062257711yescharacteristic
412C2#1307720511yescharacteristic
413C2#1307943012yes—
414C2#1307944612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#380C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC2×#380D11
hypocenterC11#21944
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. #13068813C2semidirect
4. #13068809C2semidirect
5. #13068804C2semidirect
6. #13068647C2semidirect
25. #10622820C4semidirect
28. C2×#66872C22semidirect
29. C2×#66871C22semidirect
30. #10622167C22semidirect
31. #10622167C22semidirect
58. C2×#4318C2×C4semidirect
66. C22⋊(C11⋊C8)C2×C4semidirect
327. C11#21944semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130688132
#130688092
#130688042
#130686472
C2×C11×#3802
#2194411