Finite Group Databasebeta

← #14664089

Subgroups — #14664089

Order 2816.

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

normal subgroups only

This group has 432 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#13068355C211yesmaximal, characteristic
3#13066644C214yesmaximal, complemented
4C11×#1458C211yesmaximal, characteristic
5C2×C11×#117C2211yescharacteristic
6C22×#4318—21no—
7C2×#66922C411yescharacteristic
8C11×#431—21no—
9#10622825—21no—
10#10622599C2212yes—
11#10622592—21no—
12#10622562C412yes—
13#10622560—21no—
14#10622549C411yescharacteristic
15#10622541—21no—
16C11×#324C2212yes—
17C11×#323—21no—
18#10622168—21no—
19#10622168C2212yes—
20C23×C4×C11D411yescharacteristic
21C22×Dic22—21no—
22C11×#117—41no—
23C11×#117—41no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C4⋊C4C2311yescharacteristic
26C2×C11×C22⋊C4C2×C411yescharacteristic
27C2×C11×C22⋊C4D411yescharacteristic
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×C22⋊Dic11—22no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×Dic11⋊C4—22no—
35C2×#4318—24no—
36C2×#4318—22no—
37C2×#4318—41no—
38C2×#4318—42no—
39C22×C11⋊C8—41no—
40#66922—41no—
41#66922—41no—
42C11×C4⋊C8—41no—
43C11×C22⋊C8—22no—
44C4×C8×C11—41no—
45C11⋊#95—21no—
46C11⋊#95—22no—
47C11⋊#95—22no—
48C11⋊#95C2×C412yes—
49#11723—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×C11SD1612yes—
58C22×C4×C11Q1612yes—
59C22×C4×C11C22×C411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×Dic11—22no—
63C22×Dic11—22no—
64C2×Dic22—42no—
65C2×Dic22—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—82no—
76C4⋊Dic11—42no—
77C4⋊Dic11—41no—
78C4⋊Dic11—41no—
79C4⋊Dic11—42no—
80Dic11⋊C4—82no—
81#4318—24no—
82#4318—44no—
83#4318—42no—
84C2×C11⋊C8—42no—
85C2×C11⋊C8—44no—
86#2628—111no—
87#1742—111no—
88#1458D1111yescharacteristic
89#1353—114no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11#10312yes—
95C23×C11C2×C22⋊C411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11#9911yescharacteristic
111C2×C4×C11#9911yescharacteristic
112C2×C4×C11#10312yes—
113C2×C4×C11#10412yes—
114C2×C4×C11C2×SD1611yescharacteristic
115C2×C4×C11C2×Q1611yescharacteristic
116C2×Dic11—42no—
117C2×Dic11—42no—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—42no—
121C2×Dic11—42no—
122Dic22—84no—
123C8×C11—82no—
124C11⋊C8—44no—
125C22×M16—221no—
126C2×C4⋊Q8—111no—
127C2×#117C2×D1111yescharacteristic
128#431—21no—
129#400—112no—
130#399—112no—
131#395—221no—
132#393—221no—
133#389—221no—
134#382—111no—
135#380—221no—
136#343—112no—
137#343—221no—
138#324C2×D1112yes—
139#323—21no—
140C22×C11—21no—
141C22×C11—21no—
142C22×C11—22no—
143C22×C11—42no—
144C22×C11—41no—
145C22×C11—41no—
146C22×C11—81no—
147C22×C11C2×#9911yescharacteristic
148C22×C11C2×#10311yescharacteristic
149C22×C11C2×#10411yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11#32812yes—
157C4×C11#32812yes—
158Dic11—82no—
159Dic11—82no—
160C22×Q8—221no—
161C23×C4D4411yescharacteristic
162C2×M16—224no—
163C2×M16—222no—
164C2×M16—441no—
165C2×M16—442no—
166C22×C8—441no—
167C4⋊Q8—441no—
168C4⋊Q8—441no—
169#117—41no—
170#117—41no—
171C2×C4⋊C4—112no—
172C2×C4⋊C4—221no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4—222no—
175C2×C4⋊C4D4411yescharacteristic
176C2×C4⋊C4C22×D1111yescharacteristic
177C2×C22⋊C4—222no—
178C2×C22⋊C4C4×D1111yescharacteristic
179C2×C22⋊C4C22⋊D1111yescharacteristic
180C2×C42C4×D1111yescharacteristic
181C2×C42C22⋊D1111yescharacteristic
182C4⋊C8—41no—
183C22⋊C8—22no—
184C4×C8—41no—
185#95—112no—
186#95—221no—
187#95—222no—
188#95—222no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11—42no—
192C2×C11C2×#32811yescharacteristic
193C2×C11#212311yescharacteristic
194C2×C11#213411yescharacteristic
195C24(C2×D11)⋊C411yescharacteristic
196C2×Q8—442no—
197C2×Q8—882no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—222no—
202C22×C4—222no—
203C22×C4#431412yes—
204C22×C4Dic4412yes—
205C22×C4(C2×D11)⋊C411yescharacteristic
206C22×C4(C2×D11)⋊C411yescharacteristic
207C22×C4(C2×D11)⋊C411yescharacteristic
208C22×C4C2×C4×D1111yescharacteristic
209C22×C4C2×D4411yescharacteristic
210C22×C4C2×C22⋊D1111yescharacteristic
211M16—224no—
212M16—444no—
213M16—442no—
214C2×C8—42no—
215C2×C8—442no—
216C2×C8—444no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—442no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—442no—
223C4⋊C4—882no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—882no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C11#1172311yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23#6688012yes—
237C23C2×(C2×D11)⋊C411yescharacteristic
238Q8—884no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—442no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4#6687011yescharacteristic
260C2×C4#6687011yescharacteristic
261C2×C4#6688012yes—
262C2×C4#6688912yes—
263C2×C4C2×#431411yescharacteristic
264C2×C4C2×Dic4411yescharacteristic
265C8—82no—
266C8—444no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#6687011yescharacteristic
275C22C2×#6688011yescharacteristic
276C22C2×#6688911yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—882no—
284C4—882no—
285C4#1062210512yes—
286C4#1062210512yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#1062210511yescharacteristic
291C2#1307026911yescharacteristic
292C2#1307030711yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1458C2
socleC22×C11C2×#99
prime radicalC24×C11C22⋊C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1458D11
hypocenterC11#11723
LCSG ▷ C22×C4×C11 ▷ C23×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. #13066644C2semidirect
231. C11#11723semidirect

Maximal subgroups

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

subgroupindex
#130744372
#130683552
#130666442
C11×#14582
#1172311