Finite Group Databasebeta

← #14664061

Subgroups — #14664061

Order 2816.

448 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074437C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066636C214yesmaximal
4C11×#1740C211yesmaximal, characteristic
5C2×C11×#117—21no—
6C2×C11×#117C2211yescharacteristic
7C2×#66922C411yescharacteristic, complemented
8#10622825—21no—
9#10622599—21no—
10#10622592C412yescomplemented
11#10622562—21no—
12#10622560C2212yes—
13#10622549C411yescharacteristic, complemented
14#10622541—21no—
15#10622538—21no—
16C11×#342—21no—
17C11×#342C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×Dic22C2×C412yes—
22C11×#117—24no—
23C11×#117—41no—
24C11×#117—41no—
25C11×#117—42no—
26C2×C11×C4⋊C4—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2311yescharacteristic
32C2×C42×C11—41no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C22⋊Dic11—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×Dic11⋊C4—22no—
40#66922—41no—
41#66922—41no—
42C11⋊#95—21no—
43C11⋊#95—22no—
44C11⋊#95—22no—
45C11⋊#95C2×C412yes—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—41no—
48C4×C11⋊C8—41no—
49#11717—111nomaximal, Sylow
50C24×C11C2×D411yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11—42no—
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C22⋊C411yescharacteristic
58C22×C4×C11C22⋊C411yescharacteristic
59C22×C4×C11SD1612yes—
60C22×C4×C11Q1612yes—
61C22×C4×C11C22×C411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C22×Dic11—22no—
65C2×Dic22—42no—
66C2×Dic22—82no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—44no—
70C11×C22⋊C4—24no—
71C11×C22⋊C4—41no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—42no—
74C42×C11—21no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—44no—
79C22⋊Dic11—82no—
80C4⋊Dic11—42no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—42no—
84Dic11⋊C4—82no—
85C2×C11⋊C8—42no—
86#2628—111no—
87#1740D1111yescharacteristic
88#1458—111no—
89#1351—114no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11C2×C22⋊C411yescharacteristic
95C23×C11C2×SD1611yescharacteristic
96C23×C11C2×Q1611yescharacteristic
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—22no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—44no—
112C2×C4×C11—82no—
113C2×C4×C11—82no—
114C2×C4×C11#9911yescharacteristic
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#10312yes—
117C2×C4×C11#10312yes—
118C2×C4×C11#10412yes—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125Dic22—84no—
126C11⋊C8—82no—
127C2×C4⋊Q8—111no—
128C2×#117—21no—
129C2×#117C2×D1111yescharacteristic
130#431—221no—
131#400—221no—
132#399—221no—
133#395—112no—
134#393—112no—
135#389—221no—
136#382—111no—
137#380—221no—
138#342—21no—
139#342C2×D1112yes—
140#324—221no—
141#323—112no—
142C22×C11—21no—
143C22×C11—21no—
144C22×C11—21no—
145C22×C11—21no—
146C22×C11—41no—
147C22×C11—41no—
148C22×C11—41no—
149C22×C11—41no—
150C22×C11—81no—
151C22×C11C2×#9911yescharacteristic
152C22×C11C2×#10311yescharacteristic
153C22×C11C2×#10411yescharacteristic
154C4×C11—22no—
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—41no—
158C4×C11—41no—
159C4×C11—84no—
160C4×C11#32812yes—
161C4×C11#32812yes—
162Dic11—82no—
163Dic11—82no—
164C22×Q8—112no—
165C23×C4C22⋊D1111yescharacteristic
166C4⋊Q8—441no—
167C4⋊Q8—441no—
168#117—24no—
169#117—41no—
170#117—41no—
171#117—42no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—221no—
175C2×C4⋊C4—221no—
176C2×C4⋊C4—222no—
177C2×C4⋊C4C4×D1111yescharacteristic
178C2×C4⋊C4D4411yescharacteristic
179C2×C22⋊C4—22no—
180C2×C22⋊C4—222no—
181C2×C22⋊C4C22⋊D1111yescharacteristic
182C2×C22⋊C4C22×D1111yescharacteristic
183C2×C42—41no—
184C2×C42C4×D1111yescharacteristic
185C2×C42D4411yescharacteristic
186C4⋊C8—441no—
187C22⋊C8—222no—
188C4×C8—441no—
189#95—112no—
190#95—222no—
191#95—221no—
192#95—222no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—41no—
196C2×C11—41no—
197C2×C11C2×#32811yescharacteristic
198C2×C11#212211yescharacteristic
199C2×C11#212911yescharacteristic
200C24C2×C22⋊D1111yescharacteristic
201C2×Q8—442no—
202C2×Q8—882no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—222no—
208C22×C4—222no—
209C22×C4(C2×D11)⋊C411yescharacteristic
210C22×C4(C2×D11)⋊C411yescharacteristic
211C22×C4(C2×D11)⋊C411yescharacteristic
212C22×C4(C2×D11)⋊C411yescharacteristic
213C22×C4#432412yes—
214C22×C4#432612yes—
215C22×C4C2×C4×D1111yescharacteristic
216C22×C4C2×D4411yescharacteristic
217C2×C8—442no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—44no—
221C4⋊C4—442no—
222C4⋊C4—442no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—882no—
226C22⋊C4—24no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—42no—
230C22⋊C4—882no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—44no—
236C11#1171711yescharacteristic, complemented, Sylow
237C23—21no—
238C23—21no—
239C23—41no—
240C23—41no—
241C23C2×(C2×D11)⋊C411yescharacteristic
242C23C2×#432411yescharacteristic
243C23C2×#432611yescharacteristic
244Q8—884no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—44no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—442no—
263C2×C4—442no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4—442no—
267C2×C4—442no—
268C2×C4#6686912yes—
269C2×C4#6687011yescharacteristic
270C2×C4#6687011yescharacteristic
271C2×C4#6687412yes—
272C2×C4#6687412yes—
273C8—882no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—81no—
283C22C2×#6686911yescharacteristic
284C22C2×#6687011yescharacteristic
285C22C2×#6687411yescharacteristic
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—84no—
292C4—882no—
293C4—882no—
294C4#1062209012yes—
295C4#1062209012yes—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2C2×#1062209011yescharacteristic
301C2#1307026511yescharacteristic
302C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1740C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1740D11
hypocenterC11#11717
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
7. C2×#66922C4semidirect
10. #10622592C4semidirect
13. #10622549C4semidirect
236. C11#11717semidirect

Maximal subgroups

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

subgroupindex
#130744372
#130669302
#130666362
C11×#17402
#1171711