Finite Group Databasebeta

← #14668746

Subgroups — #14668746

Order 2816.

1026 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C212yesmaximal
2#13066741C214yesmaximal, complemented
3C11×#2309C211yesmaximal, characteristic
4C23×D4×C11C2211yescharacteristic
5C2×C11×#117C411yescharacteristic, complemented
6C2×C11×#117C411yescharacteristic, complemented
7C22×C22⋊Dic11—22no—
8C11×#390—22no—
9C11×#390C412yescomplemented
10C11×#390C2212yes—
11C11×#379—22no—
12C2×#66898—22no—
13C2×#66898—24no—
14C2×#66898C418yescomplemented
15C2×#66898C2214yes—
16C25×C11D412yes—
17C22×D4×C11—42no—
18C22×D4×C11—42no—
19C22×D4×C11C2×C414yes—
20C22×D4×C11C2×C411yescharacteristic
21C22×D4×C11D412yes—
22C22×D4×C11D412yes—
23C22×D4×C11Q812yes—
24C22×D4×C11C2311yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×Dic11—42no—
27C11×#117—42no—
28C11×#117—42no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C412yescomplemented
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—24no—
34C2×C11×C22⋊C4—24no—
35C2×C42×C11—21no—
36C2×C42×C11C2×C412yescomplemented
37C2×C22⋊Dic11—28no—
38C2×C22⋊Dic11—24no—
39C2×C22⋊Dic11—42no—
40C2×C22⋊Dic11—44no—
41#66898—28no—
42#66898—24no—
43#66898C2×C418yescomplemented
44#12582—111nomaximal, Sylow
45C24×C11—22no—
46C24×C11—24no—
47C24×C11—22no—
48C24×C11—84no—
49C24×C11C22⋊C412yes—
50C24×C11C22⋊C414yes—
51C24×C11C22⋊C411yescharacteristic
52C24×C11C4⋊C414yes—
53C24×C11C2×D412yes—
54C2×D4×C11—44no—
55C2×D4×C11—44no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—44no—
59C2×D4×C11—42no—
60C2×D4×C11—42no—
61C2×D4×C11—44no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11C4212yes—
65C2×D4×C11C22⋊C414yes—
66C2×D4×C11C4⋊C414yes—
67C2×D4×C11C4⋊C412yes—
68C2×D4×C11C22×C412yes—
69C2×D4×C11C2×D411yescharacteristic
70C2×D4×C11C2×Q811yescharacteristic
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11C4212yes—
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C4⋊C412yes—
78C22×C4×C11C22×C411yescharacteristic
79C22×Dic11—48no—
80C22×Dic11—44no—
81C22×Dic11—88no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C22⋊C4—42no—
85C11×C22⋊C4—42no—
86C11×C22⋊C4—84no—
87C11×C22⋊C4—84no—
88C42×C11—42no—
89C42×C11—42no—
90C22⋊Dic11—28no—
91C22⋊Dic11—48no—
92C22⋊Dic11—44no—
93C22×#99—112no—
94#2309D1111yescharacteristic
95#1393—114no—
96C23×C11—24no—
97C23×C11—24no—
98C23×C11—22no—
99C23×C11—22no—
100C23×C11—24no—
101C23×C11—24no—
102C23×C11—22no—
103C23×C11—22no—
104C23×C11—42no—
105C23×C11—48no—
106C23×C11—44no—
107C23×C11—44no—
108C23×C11—84no—
109C23×C11—84no—
110C23×C11—84no—
111C23×C11—88no—
112C23×C11#9514yes—
113C23×C11#9512yes—
114C23×C11#9912yes—
115C23×C11#9912yes—
116C23×C11C2×C22⋊C412yes—
117C23×C11C2×C22⋊C411yescharacteristic
118C23×C11C2×C4⋊C412yes—
119D4×C11—42no—
120D4×C11—44no—
121D4×C11—44no—
122D4×C11—42no—
123D4×C11—42no—
124D4×C11—41no—
125D4×C11—41no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—44no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11#9512yes—
138C2×C4×C11C2×C4211yescharacteristic
139C2×C4×C11C2×C4⋊C411yescharacteristic
140C2×Dic11—48no—
141C2×Dic11—816no—
142C2×Dic11—88no—
143C23×D4C2×D1111yescharacteristic
144C2×#117Dic1111yescharacteristic, complemented
145C2×#117Dic1111yescharacteristic, complemented
146C22×C22⋊C4—222no—
147C2×#99—114no—
148C2×#99—118no—
149C2×#99—224no—
150C2×#99—222no—
151#390—22no—
152#390Dic1112yescomplemented
153#390C2×D1112yes—
154#379—22no—
155C22×C11—22no—
156C22×C11—24no—
157C22×C11—24no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—44no—
163C22×C11—42no—
164C22×C11—42no—
165C22×C11—48no—
166C22×C11—48no—
167C22×C11—44no—
168C22×C11—44no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11—84no—
172C22×C11—84no—
173C22×C11#34214yes—
174C22×C11C2×#9511yescharacteristic
175C22×C11C2×#9911yescharacteristic
176C22×C11C2×#9911yescharacteristic
177C4×C11—22no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—82no—
181C4×C11—82no—
182Dic11—88no—
183C25C22⋊D1112yes—
184C22×D4—42no—
185C22×D4—42no—
186C22×D4Dic2212yes—
187C22×D4C4×D1114yes—
188C22×D4D4412yes—
189C22×D4C2×Dic1111yescharacteristic
190C22×D4C22⋊D1112yes—
191C22×D4C22×D1111yescharacteristic
192C23×C4—442no—
193C23×C4C2×Dic1111yescharacteristic
194#117—42no—
195#117—42no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic1112yescomplemented
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—228no—
203C2×C22⋊C4—224no—
204C2×C22⋊C4—444no—
205C2×C22⋊C4—442no—
206C2×C42—21no—
207C2×C42C2×Dic1112yescomplemented
208#99—118no—
209#99—228no—
210#99—224no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11—24no—
214C2×C11—42no—
215C2×C11—44no—
216C2×C11—42no—
217C2×C11C2×#34211yescharacteristic
218C2×C11#212712yes—
219C24—22no—
220C24—22no—
221C24—24no—
222C24—84no—
223C24Dic11⋊C414yes—
224C24(C2×D11)⋊C414yes—
225C24C22⋊Dic1112yes—
226C24C22⋊Dic1111yescharacteristic
227C24C2×C22⋊D1112yes—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4—44no—
233C2×D4—44no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4C4×Dic1112yes—
239C2×D4Dic11⋊C414yes—
240C2×D4C4⋊Dic1112yes—
241C2×D4(C2×D11)⋊C414yes—
242C2×D4C2×Dic2211yescharacteristic
243C2×D4C2×C4×D1112yes—
244C2×D4C2×D4411yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—444no—
250C22×C4—448no—
251C22×C4—888no—
252C22×C4C4×Dic1112yes—
253C22×C4C4⋊Dic1112yes—
254C22×C4C22⋊Dic1111yescharacteristic
255C22×C4C22×Dic1111yescharacteristic
256C4⋊C4—42no—
257C4⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—84no—
261C22⋊C4—84no—
262C22⋊C4—228no—
263C22⋊C4—444no—
264C22⋊C4—448no—
265C42—42no—
266C42—42no—
267C11#1258211yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—24no—
271C23—24no—
272C23—22no—
273C23—22no—
274C23—24no—
275C23—24no—
276C23—42no—
277C23—48no—
278C23—44no—
279C23—44no—
280C23—84no—
281C23—84no—
282C23—84no—
283C23—88no—
284C23C11⋊#9514yes—
285C23C11⋊#9512yes—
286C23#6689812yes—
287C23#6689812yes—
288C23C2×Dic11⋊C412yes—
289C23C2×(C2×D11)⋊C412yes—
290C23C2×C22⋊Dic1111yescharacteristic
291D4—42no—
292D4—44no—
293D4—42no—
294D4—44no—
295D4—41no—
296D4—42no—
297D4—41no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—448no—
310C2×C4—8816no—
311C2×C4—888no—
312C2×C4C11⋊#9512yes—
313C2×C4C2×C4×Dic1111yescharacteristic
314C2×C4C2×C4⋊Dic1111yescharacteristic
315C22—22no—
316C22—24no—
317C22—22no—
318C22—24no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—44no—
323C22—42no—
324C22—42no—
325C22—48no—
326C22—48no—
327C22—44no—
328C22—44no—
329C22—82no—
330C22—82no—
331C22—84no—
332C22—84no—
333C22#1062216414yes—
334C22C2×C11⋊#9511yescharacteristic
335C22C2×#6689811yescharacteristic
336C22C2×#6689811yescharacteristic
337C4—22no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—82no—
342C4—888no—
343C2—21no—
344C2—21no—
345C2—24no—
346C2—42no—
347C2—44no—
348C2—42no—
349C2C2×#1062216411yescharacteristic
350C2#1307028512yes—
subgroupG/H
centerC22C2×#66898
commutatorC2×C4×C11C2×C42
FrattiniC22×D4C22×D11
FittingC11×#2309C2
socleC22×C11C2×#99
prime radicalC23×D4×C11C22
cosocleC22×D4×C11C23
hypercenter#2309D11
hypocenterC11#12582
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #13066741C2semidirect
5. C2×C11×#117C4semidirect
6. C2×C11×#117C4semidirect
9. C11×#390C4semidirect
14. C2×#66898C4semidirect
30. C2×C11×C4⋊C4C2×C4semidirect
36. C2×C42×C11C2×C4semidirect
43. #66898C2×C4semidirect
144. C2×#117Dic11semidirect
145. C2×#117Dic11semidirect
152. #390Dic11semidirect
197. C2×C4⋊C4C2×Dic11semidirect
207. C2×C42C2×Dic11semidirect
267. C11#12582semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130667412
C11×#23092
#1258211