Finite Group Databasebeta

← #14753985

Subgroups — #14753985

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×Dic11C211yesmaximal, characteristic
2#13071019C211yesmaximal, characteristic
3C2×#10622589C211yesmaximal, characteristic
4#13068748C214yesmaximal, complemented
5#13068742C214yesmaximal, complemented
6#13068337C211yesmaximal, characteristic
7#13068336C211yesmaximal, characteristic
8#13068335C211yesmaximal, characteristic
9C11×#1736C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4—22no—
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18M16×Dic11C418yescomplemented
19C2×#66879C2212yes—
20C2×C8×Dic11C2212yes—
21#10622590C2212yes—
22#10622589—22no—
23#10622589C2212yes—
24#10622589C2212yes—
25#10622589C2212yes—
26#10622555—22no—
27C4×Dic11⋊C4—22no—
28C11×#340C2214yes—
29#10622189C2214yes—
30#10622167C2214yes—
31#10622167C2214yes—
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11D412yes—
36C2×C11×M16—22no—
37C2×C11×M16—22no—
38C2×C11×M16C2×C414yes—
39C22×C8×C11C2312yes—
40C11×#117—22no—
41C11×#117—22no—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C4⋊C4C2312yes—
47C2×C11×C22⋊C4—21no—
48C2×C42×C11—21no—
49C2×C22⋊Dic11—21no—
50#66979—22no—
51#66979—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11C2312yes—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—24no—
61C2×Dic11⋊C4—48no—
62C2×C4×Dic11—21no—
63C2×C4×Dic11C2×C414yes—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11Q814yes—
66C2×C4×Dic11C2311yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C2×#4318—22no—
69C2×#4318—22no—
70C2×#4318C2×C414yes—
71C22×C11⋊C8C2312yes—
72C11⋊#95—24no—
73#66879C2×C418yescomplemented
74C8×Dic11C2×C418yescomplemented
75#20764—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—44no—
80C22×C4×C11—42no—
81C22×C4×C11C22×C412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×Q812yes—
84C22×C4×C11#4112yes—
85C22×C4×C11#4112yes—
86C22×C4×C11#4112yes—
87C22×C4×C11#4112yes—
88C22×C4×C11C2411yescharacteristic
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—44no—
94C22×Dic11—42no—
95C22×Dic11C4⋊C418yes—
96C22×Dic11C2×D412yes—
97C22×Dic11C2×D412yes—
98C11×M16—28no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11C22×C414yes—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—42no—
107C11×C22⋊C4—42no—
108C42×C11—42no—
109C22⋊Dic11—42no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—22no—
114C4⋊Dic11—42no—
115Dic11⋊C4—48no—
116Dic11⋊C4—44no—
117Dic11⋊C4—48no—
118Dic11⋊C4—44no—
119C4×Dic11—42no—
120C4×Dic11C4⋊C418yes—
121C4×Dic11C22×C412yes—
122C4×Dic11C22×C412yes—
123C4×Dic11C2×Q812yes—
124C4×Dic11C2×Q812yes—
125#4318—28no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8C22×C414yes—
129C2×C4×M16—111no—
130#2285—111no—
131C2×#384—111no—
132#1836—114no—
133#1834—114no—
134#1736—111no—
135#1736—111no—
136#1736—111no—
137#1736D1111yescharacteristic
138C23×C11—22no—
139C23×C11—22no—
140C23×C11C2×C4⋊C412yes—
141C23×C11#12412yes—
142C23×C11#12412yes—
143C23×C11C22×D411yescharacteristic
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—84no—
150C2×C4×C11C2×C4⋊C412yes—
151C2×C4×C11#11714yes—
152C2×C4×C11#11714yes—
153C2×C4×C11#12412yes—
154C2×C4×C11#12412yes—
155C2×C4×C11#12514yes—
156C2×C4×C11#12514yes—
157C2×C4×C11C23×C411yescharacteristic
158C2×C4×C11C22×Q811yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C2×C4×C11C2×#4111yescharacteristic
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—216no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—44no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—84no—
172C2×Dic11C2×C4⋊C414yes—
173C2×Dic11C2×C4⋊C414yes—
174C2×Dic11AGL(1,ℤ/8)14yes—
175C2×Dic11#13714yes—
176C8×C11—24no—
177C11⋊C8—24no—
178C22×M16—111no—
179C22×M16C2×D1111yescharacteristic
180C2×#117—111no—
181C2×#117C2×D1111yescharacteristic
182C22×C4⋊C4—111no—
183C22×C4⋊C4—222no—
184C22×C4⋊C4C2×D1111yescharacteristic
185C22×C42—111no—
186C4×M16—118no—
187C2×#97—112no—
188C2×C4×C8—112no—
189#384—112no—
190#384—112no—
191#384—112no—
192#384—222no—
193#382—112no—
194#380—222no—
195C4×C4⋊C4—222no—
196#340—114no—
197#340—114no—
198#340—114no—
199#340C2×D1114yes—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—24no—
203C22×C11—24no—
204C22×C11#38214yes—
205C22×C11C22×C4⋊C411yescharacteristic
206C22×C11C2×#12411yescharacteristic
207C22×C11C2×#12411yescharacteristic
208C22×C11C2×AGL(1,ℤ/8)12yes—
209C22×C11C2×#13712yes—
210C4×C11—82no—
211C4×C11—82no—
212C4×C11#38214yes—
213C4×C11C2×#11711yescharacteristic
214C4×C11C2×#11711yescharacteristic
215C4×C11C2×#12511yescharacteristic
216C4×C11C2×#12511yescharacteristic
217Dic11—24no—
218Dic11—82no—
219Dic11—82no—
220Dic11#42818yes—
221C23×C4—21no—
222C23×C4—112no—
223C23×C4—221no—
224C23×C4C22×D1111yescharacteristic
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—114no—
228C2×M16—222no—
229C2×M16—222no—
230C2×M16C4×D1114yes—
231C22×C8—112no—
232C22×C8C22×D1112yes—
233#117—22no—
234#117—22no—
235#117—222no—
236#117—222no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—112no—
242C2×C4⋊C4—222no—
243C2×C4⋊C4—222no—
244C2×C4⋊C4—224no—
245C2×C4⋊C4—224no—
246C2×C4⋊C4—222no—
247C2×C4⋊C4—222no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—448no—
250C2×C4⋊C4C22×D1112yes—
251C2×C4⋊C4C22×D1112yes—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—221no—
254C2×C42—21no—
255C2×C42—114no—
256C2×C42—112no—
257C2×C42—114no—
258C2×C42—111no—
259C2×C42—111no—
260C2×C42—221no—
261#97—118no—
262C4×C8—118no—
263#95—224no—
264C2×C11—24no—
265C2×C11C2×#38211yescharacteristic
266C2×C11C2×#42812yes—
267C2×C11#313811yescharacteristic
268C2×C11#313911yescharacteristic
269C2×C11#314112yes—
270C24D4×D1111yescharacteristic
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—44no—
274C22×C4—42no—
275C22×C4—112no—
276C22×C4—118no—
277C22×C4—112no—
278C22×C4—224no—
279C22×C4—224no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—444no—
283C22×C4—442no—
284C22×C4C2×C4×D1112yes—
285C22×C4#433912yes—
286C22×C4#433912yes—
287C22×C4D4×D1111yescharacteristic
288C22×C4#434112yes—
289C22×C4#434112yes—
290C22×C4Q8×D1112yes—
291C22×C4C23×D1111yescharacteristic
292M16—28no—
293M16—228no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—114no—
297C2×C8—222no—
298C2×C8—222no—
299C2×C8C2×C4×D1114yes—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—42no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—222no—
309C4⋊C4—448no—
310C4⋊C4—444no—
311C4⋊C4—444no—
312C4⋊C4—448no—
313C4⋊C4—442no—
314C22⋊C4—42no—
315C22⋊C4—442no—
316C42—42no—
317C42—118no—
318C42—112no—
319C42—112no—
320C42—112no—
321C42—112no—
322C42—442no—
323C11#2076411yescharacteristic, complemented, Sylow
324C23—22no—
325C23—22no—
326C23#6693812yes—
327C23#6693812yes—
328C23C4⋊C4×D1112yes—
329C23C2×D4×D1111yescharacteristic
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—84no—
336C2×C4—114no—
337C2×C4—114no—
338C2×C4—114no—
339C2×C4—114no—
340C2×C4—2216no—
341C2×C4—222no—
342C2×C4—222no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—444no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—884no—
349C2×C4#6692514yes—
350C2×C4#6693014yes—
351C2×C4#6693812yes—
352C2×C4#6693812yes—
353C2×C4#6694214yes—
354C2×C4#6694214yes—
355C2×C4C4⋊C4×D1112yes—
356C2×C4C22×C4×D1111yescharacteristic
357C2×C4C2×#433911yescharacteristic
358C2×C4C2×#433911yescharacteristic
359C2×C4C2×#434111yescharacteristic
360C2×C4C2×#434111yescharacteristic
361C2×C4C2×Q8×D1111yescharacteristic
362C8—24no—
363C8—224no—
364C22—22no—
365C22—24no—
366C22—22no—
367C22—24no—
368C22#1062226314yes—
369C22C2×#6693811yescharacteristic
370C22C2×#6693811yescharacteristic
371C22C2×C4⋊C4×D1111yescharacteristic
372C22D11×AGL(1,ℤ/8)12yes—
373C22D11×#13712yes—
374C4—82no—
375C4—82no—
376C4—118no—
377C4—224no—
378C4—882no—
379C4—882no—
380C4#1062226314yes—
381C4C2×#6692511yescharacteristic
382C4C2×#6693011yescharacteristic
383C4C2×#6694211yescharacteristic
384C4C2×#6694211yescharacteristic
385C2—24no—
386C2C2×#1062226311yescharacteristic
387C2D11×#42812yes—
388C2#1307898811yescharacteristic
389C2#1307899411yescharacteristic
390C2#1307900712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20764
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13068748C2semidirect
5. #13068742C2semidirect
18. M16×Dic11C4semidirect
73. #66879C2×C4semidirect
74. C8×Dic11C2×C4semidirect
323. C11#20764semidirect

Maximal subgroups

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

subgroupindex
C2×M16×Dic112
#130710192
C2×#106225892
#130687482
#130687422
#130683372
#130683362
#130683352
C11×#17362
#2076411