Finite Group Databasebeta

← #14752214

Subgroups — #14752214

Order 2816.

1234 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C212yesmaximal
2C2×C4×#4318C212yesmaximal, complemented
3C4⋊C4×C11⋊C8C212yesmaximal, complemented
4#13068469C211yesmaximal, characteristic, complemented
5#13068400C214yesmaximal, complemented
6#13068378C212yesmaximal, complemented
7C4×#66867C211yesmaximal, characteristic, complemented
8C42×D4×C11C211yesmaximal, characteristic
9C2×C4×D4×C11C412yes—
10C2×C4×D4×C11C2211yescharacteristic
11C22×C42×C11C2212yes—
12C22×#4318C2214yes—
13C4×C11×C4⋊C4C412yes—
14C4×C11×C4⋊C4C2211yescharacteristic
15C4×C11×C22⋊C4C414yes—
16C4×C11×C22⋊C4C2212yes—
17C43×C11C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2214yes—
19#10622625C4116yescomplemented
20C2×C4⋊(C11⋊C8)C2212yes—
21C4×#4318—28no—
22C2×#66867C2211yescharacteristic
23C2×#66867C2212yes—
24C2×#66867C2212yes—
25C2×#66867C2211yescharacteristic
26C2×C4×C11⋊C8C2214yes—
27C2×C4×C11⋊C8C2212yes—
28#10622162C2214yes—
29#10622162C2212yes—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C414yes—
32C23×C4×C11C2312yes—
33C4×D4×C11—28no—
34C4×D4×C11C2×C418yes—
35C2×C11×C4⋊C4C2×C411yescharacteristic
36C2×C11×C4⋊C4C2×C412yes—
37C2×C11×C22⋊C4C2×C414yes—
38C2×C11×C22⋊C4C2×C412yes—
39C2×C42×C11—24no—
40C2×C42×C11—24no—
41C2×C42×C11C2×C414yes—
42C2×C42×C11C2×C412yes—
43C2×C42×C11C2×C412yes—
44C2×C42×C11C2312yes—
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C2×#4318—28no—
49C2×#4318—28no—
50C2×#4318C2×C4116yescomplemented
51C22×C11⋊C8C2312yes—
52C22×C11⋊C8C2314yes—
53C22×C11⋊C8C2312yes—
54C11×#95C2×C412yes—
55C11×#95C2×C414yes—
56C22⋊(C11⋊C8)C2×C4116yescomplemented
57C4⋊(C11⋊C8)C2×C418yescomplemented
58#66867—24no—
59#66867—22no—
60#66867—24no—
61#66867D414yescomplemented
62C4×C11⋊C8—28no—
63C4×C11⋊C8C2×C418yescomplemented
64#20494—111nomaximal, Sylow
65C24×C11C22×C412yes—
66C2×D4×C11—24no—
67C2×D4×C11C4214yes—
68C22×C4×C11—22no—
69C22×C4×C11—24no—
70C22×C4×C11—22no—
71C22×C4×C11—28no—
72C22×C4×C11—28no—
73C22×C4×C11—44no—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C412yes—
77C22×C4×C11C22×C418yes—
78C22×C4×C11C22×C412yes—
79C22×C4×C11C22×C414yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2411yescharacteristic
82C11×C4⋊C4C4214yes—
83C11×C4⋊C4M1618yescomplemented
84C11×C22⋊C4—28no—
85C11×C22⋊C4C4218yes—
86C42×C11—28no—
87C42×C11—24no—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11—22no—
91C42×C11—42no—
92C42×C11C22×C414yes—
93C42×C11C2×D412yes—
94C42×C11#4112yes—
95#4318—232no—
96C2×C11⋊C8—24no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—24no—
100C2×C11⋊C8C22×C414yes—
101C2×C11⋊C8C22×C418yes—
102C2×C11⋊C8C22×C414yes—
103C2×C11⋊C8C2×D414yes—
104C2×C11⋊C8#4114yes—
105C2×#436—112no—
106C2×C4×M16—112no—
107C42×D4D1111yescharacteristic
108C8×C4⋊C4—112no—
109#1767—111no—
110#1753—114no—
111#1749—112no—
112C4×#97—111no—
113C23×C11—22no—
114C23×C11—22no—
115C23×C11—24no—
116C23×C11—24no—
117C23×C11C2×C4214yes—
118C23×C11C23×C411yescharacteristic
119D4×C11—28no—
120C2×C4×C11—24no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11—28no—
128C2×C4×C11—28no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—416no—
133C2×C4×C11C2×C4212yes—
134C2×C4×C11C2×C4214yes—
135C2×C4×C11C2×C4212yes—
136C2×C4×C11C4×D414yes—
137C2×C4×C11C2×M1618yes—
138C2×C4×C11C2×M1614yes—
139C2×C4×C11C23×C412yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C2×#4111yescharacteristic
142C2×C4×C11C2×#4112yes—
143C11⋊C8—28no—
144C11⋊C8—24no—
145C11⋊C8C4×D418yescomplemented
146C22×M16—114no—
147C2×C4×D4Dic1112yes—
148C2×C4×D4C2×D1111yescharacteristic
149C22×C42C2×D1112yes—
150#436—1116no—
151C2×C4⋊C8—112no—
152C2×C22⋊C8—114no—
153C4×M16—228no—
154C2×#97—111no—
155C2×#97—112no—
156C2×#97—111no—
157C2×#97—112no—
158C2×C4×C8—112no—
159C2×C4×C8—114no—
160C4×C4⋊C4Dic1112yes—
161C4×C4⋊C4C2×D1111yescharacteristic
162C4×C22⋊C4Dic1114yes—
163C4×C22⋊C4C2×D1112yes—
164C43C2×D1111yescharacteristic
165#336—114no—
166#336—112no—
167C22×C11—24no—
168C22×C11—24no—
169C22×C11—24no—
170C22×C11—44no—
171C22×C11—44no—
172C22×C11C22×C4211yescharacteristic
173C22×C11C2×C4×D411yescharacteristic
174C22×C11C4×#4111yescharacteristic
175C22×C11C22×M1612yes—
176C22×C11#56812yes—
177C4×C11—22no—
178C4×C11—24no—
179C4×C11—28no—
180C4×C11—24no—
181C4×C11—42no—
182C4×C11C4×M1614yescomplemented
183C4×C11C2×C4×D412yes—
184C4×C11C4×#4112yes—
185C22×D4C2×Dic1111yescharacteristic
186C23×C4C2×Dic1114yes—
187C23×C4C22×D1112yes—
188C2×M16—1116no—
189C2×M16—228no—
190C2×M16—228no—
191C22×C8—112no—
192C22×C8—114no—
193C22×C8—112no—
194C4×D4—28no—
195C4×D4C4×D1118yes—
196C2×C4⋊C4C2×Dic1112yes—
197C2×C4⋊C4C2×Dic1111yescharacteristic
198C2×C22⋊C4C2×Dic1114yes—
199C2×C22⋊C4C2×Dic1112yes—
200C2×C42—24no—
201C2×C42—24no—
202C2×C42C2×Dic1112yes—
203C2×C42C2×Dic1114yes—
204C2×C42C2×Dic1112yes—
205C2×C42C22×D1111yescharacteristic
206C2×C42C22×D1112yes—
207C2×C42C22×D1111yescharacteristic
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—118no—
210C22⋊C8—1116no—
211#97—114no—
212#97—224no—
213#97—224no—
214#97—222no—
215C4×C8—118no—
216C4×C8—228no—
217#95C2×Dic1112yes—
218#95C2×Dic1114yes—
219C2×C11—44no—
220C2×C11C42×D411yescharacteristic
221C2×C11C2×C4×M1611yescharacteristic
222C2×C11#287511yescharacteristic
223C2×C11D4×M1612yes—
224C2×C11#297112yes—
225C24C22×Dic1112yes—
226C2×D4—24no—
227C2×D4C4×Dic1114yes—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—28no—
232C22×C4—28no—
233C22×C4—44no—
234C22×C4C2×C4×D1118yes—
235C22×C4C22×Dic1112yes—
236C22×C4C22×Dic1114yes—
237C22×C4C22×Dic1111yescharacteristic
238C22×C4C22×Dic1112yes—
239C22×C4C22×Dic1112yes—
240C22×C4C22×Dic1111yescharacteristic
241C22×C4C23×D1111yescharacteristic
242M16—2232no—
243C2×C8—114no—
244C2×C8—114no—
245C2×C8—114no—
246C2×C8—114no—
247C2×C8—118no—
248C2×C8—224no—
249C2×C8—222no—
250C2×C8—222no—
251C2×C8—224no—
252C4⋊C4#431818yescomplemented
253C4⋊C4C4×Dic1114yes—
254C22⋊C4—28no—
255C22⋊C4C4×Dic1118yes—
256C42—24no—
257C42—28no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—42no—
262C42C2×C4×D1114yes—
263C42D4×D1112yes—
264C42#434112yes—
265C11#2049411yescharacteristic, complemented, Sylow
266C23—24no—
267C23—22no—
268C23—24no—
269C23—22no—
270C23C2×C4×Dic1114yes—
271C23C23×Dic1111yescharacteristic
272D4—28no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—28no—
281C2×C4—28no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—416no—
286C2×C4C2×#431818yes—
287C2×C4C2×#431814yes—
288C2×C4C2×C4×Dic1112yes—
289C2×C4C2×C4×Dic1114yes—
290C2×C4C2×C4×Dic1112yes—
291C2×C4D4×Dic1114yes—
292C2×C4C22×C4×D1112yes—
293C2×C4C2×D4×D1111yescharacteristic
294C2×C4C2×#434111yescharacteristic
295C2×C4#41×D1112yes—
296C8—118no—
297C8—224no—
298C8—228no—
299C22—24no—
300C22—24no—
301C22—24no—
302C22—44no—
303C22—44no—
304C22C22×#431812yes—
305C22C22×C4×Dic1111yescharacteristic
306C22C2×D4×Dic1111yescharacteristic
307C22#1062335012yes—
308C22#41×Dic1111yescharacteristic
309C4—22no—
310C4—24no—
311C4—28no—
312C4—24no—
313C4—42no—
314C4C4×#431814yescomplemented
315C4C4×#434112yes—
316C4C4×D4×D1112yes—
317C2—44no—
318C2C4×D4×Dic1111yescharacteristic
319C2C2×C4×#431811yescharacteristic
320C2#1307704411yescharacteristic
321C2D4×#431812yes—
322C2#1307763612yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC42×D4×C11C2
socleC23×C11C23×C4
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC42×D4D11
hypocenterC11#20494
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4318C2semidirect
3. C4⋊C4×C11⋊C8C2semidirect
4. #13068469C2semidirect
5. #13068400C2semidirect
6. #13068378C2semidirect
7. C4×#66867C2semidirect
19. #10622625C4semidirect
50. C2×#4318C2×C4semidirect
56. C22⋊(C11⋊C8)C2×C4semidirect
57. C4⋊(C11⋊C8)C2×C4semidirect
61. #66867D4semidirect
63. C4×C11⋊C8C2×C4semidirect
83. C11×C4⋊C4M16semidirect
145. C11⋊C8C4×D4semidirect
182. C4×C11C4×M16semidirect
252. C4⋊C4#4318semidirect
265. C11#20494semidirect
314. C4C4×#4318semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×C4×#43182
C4⋊C4×C11⋊C82
#130684692
#130684002
#130683782
C4×#668672
C42×D4×C112
#2049411