Finite Group Databasebeta

← #14662937

Subgroups — #14662937

Order 2816.

434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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#13071236C211yesmaximal, characteristic
2#13066930C211yesmaximal, characteristic
3#13066559C214yesmaximal, complemented
4C11×#1458C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C2×#66979C411yescharacteristic
7C22×C4⋊Dic11C411yescharacteristic
8C11×#431—21no—
9#10622590C2212yes—
10#10622589C412yes—
11#10622559—21no—
12#10622559—21no—
13#10622541—21no—
14#10622541—21no—
15#10622538—21no—
16C11×#324C2212yes—
17C11×#323—21no—
18#10622166C2212yes—
19#10622163—21no—
20C23×C4×C11C2×C411yescharacteristic
21C23×Dic11—21no—
22C11×#117—41no—
23C11×#117—41no—
24C2×C11×C4⋊C4C2×C411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C11×C22⋊C4D411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—21no—
31#66979—22no—
32#66979C814yescomplemented
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—41no—
36C2×C4⋊Dic11—41no—
37C2×C4⋊Dic11C2×C412yes—
38C2×Dic11⋊C4—22no—
39C2×Dic11⋊C4—22no—
40C2×C4×Dic11C2×C412yes—
41C11×C4⋊C8—41no—
42C11×C22⋊C8—22no—
43C4×C8×C11—41no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C22⋊(C11⋊C8)—22no—
47C4⋊(C11⋊C8)—41no—
48C4×C11⋊C8—41no—
49#11449—111nomaximal, Sylow
50C24×C11C22⋊C411yescharacteristic
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11C22⋊C411yescharacteristic
55C22×C4×C11C22⋊C411yescharacteristic
56C22×C4×C11C22⋊C411yescharacteristic
57C22×C4×C11C2×C812yes—
58C22×C4×C11M1612yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C22×Dic11—42no—
65C22×Dic11—82no—
66C2×C8×C11—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C22⋊C4—41no—
70C11×C22⋊C4—41no—
71C42×C11—21no—
72C42×C11—21no—
73C42×C11—21no—
74C42×C11—21no—
75C22⋊Dic11—24no—
76C4⋊Dic11—24no—
77C4⋊Dic11—42no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—82no—
81Dic11⋊C4—82no—
82C4×Dic11—22no—
83C4×Dic11C2×C814yes—
84C2×C11⋊C8—42no—
85#2317—111no—
86#1458—111no—
87#1458D1111yescharacteristic
88#1324—114no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—41no—
92C23×C11—41no—
93C23×C11C22⋊C812yes—
94C23×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11C22⋊C812yes—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#9911yescharacteristic
112C2×C4×C11#10112yes—
113C2×C4×C11C22×C811yescharacteristic
114C2×C4×C11C2×M1611yescharacteristic
115C2×Dic11—24no—
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—84no—
122C8×C11—82no—
123C11⋊C8—82no—
124C2×#117—111no—
125C2×#117C2×D1111yescharacteristic
126C22×C4⋊C4—111no—
127#431—21no—
128#431—221no—
129#389—221no—
130#389—221no—
131#385—221no—
132#385—221no—
133#384—112no—
134#382—112no—
135#324—112no—
136#324C2×D1112yes—
137#323—21no—
138#323—221no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—22no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11C2×C22⋊C811yescharacteristic
147C22×C11C2×#9911yescharacteristic
148C22×C11C2×#10111yescharacteristic
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—41no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11#32412yes—
156C4×C11#32412yes—
157Dic11—44no—
158Dic11—82no—
159C23×C4—221no—
160C23×C4C4×D1111yescharacteristic
161#117—41no—
162#117—41no—
163#117—114no—
164#117—222no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4—221no—
167C2×C4⋊C4—221no—
168C2×C4⋊C4—222no—
169C2×C4⋊C4—222no—
170C2×C4⋊C4—441no—
171C2×C4⋊C4—441no—
172C2×C4⋊C4C4×D1111yescharacteristic
173C2×C4⋊C4C22×D1111yescharacteristic
174C2×C22⋊C4—221no—
175C2×C22⋊C4D4411yescharacteristic
176C2×C22⋊C4C22⋊D1111yescharacteristic
177C2×C42—112no—
178C2×C42D4411yescharacteristic
179C2×C42C22⋊D1111yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—441no—
182C22⋊C8—22no—
183C22⋊C8—222no—
184C4×C8—41no—
185C4×C8—441no—
186#95—222no—
187#95—222no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—42no—
191C2×C11C2×#32411yescharacteristic
192C2×C11#212911yescharacteristic
193C2×C11#213411yescharacteristic
194C24(C2×D11)⋊C411yescharacteristic
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4—442no—
201C22×C4—882no—
202C22×C4C8×D1112yes—
203C22×C4#431312yes—
204C22×C4(C2×D11)⋊C411yescharacteristic
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4C2×C4×D1111yescharacteristic
208C22×C4C2×D4411yescharacteristic
209C22×C4C2×C22⋊D1111yescharacteristic
210C2×C8—42no—
211C2×C8—442no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—224no—
215C4⋊C4—442no—
216C4⋊C4—441no—
217C4⋊C4—441no—
218C4⋊C4—882no—
219C4⋊C4—882no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—224no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—114no—
228C42—222no—
229C11#1144911yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—41no—
233C23—41no—
234C23(C2×D11)⋊C812yes—
235C23C2×(C2×D11)⋊C411yescharacteristic
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—224no—
251C2×C4—442no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—884no—
257C2×C4#6687011yescharacteristic
258C2×C4#6687011yescharacteristic
259C2×C4(C2×D11)⋊C812yes—
260C2×C4#6688812yes—
261C2×C4C2×C8×D1111yescharacteristic
262C2×C4C2×#431311yescharacteristic
263C8—82no—
264C8—882no—
265C22—21no—
266C22—21no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—41no—
271C22—41no—
272C22C2×#6687011yescharacteristic
273C22C2×(C2×D11)⋊C811yescharacteristic
274C22C2×#6688811yescharacteristic
275C4—21no—
276C4—21no—
277C4—41no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—444no—
282C4—882no—
283C4#1062210712yes—
284C4#1062210712yes—
285C2—21no—
286C2—21no—
287C2—42no—
288C2C2×#1062210711yescharacteristic
289C2#1307029011yescharacteristic
290C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC2×C4×C11C22×C8
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1458D11
hypocenterC11#11449
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13066559C2semidirect
32. #66979C8semidirect
229. C11#11449semidirect

Maximal subgroups

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

subgroupindex
#130712362
#130669302
#130665592
C11×#14582
#1144911