Finite Group Databasebeta

← #14647188

Subgroups — #14647188

Order 2816.

630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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
1D11×#384C211yesmaximal, characteristic
2#13068593C212yesmaximal
3#13066500C212yesmaximal, complemented
4#13066499C211yesmaximal, characteristic, complemented
5C11×#1296C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D11—22no—
7C2×C4⋊C4×D11C412yes—
8C2×C42×D11C2211yescharacteristic
9C2×C11×C4⋊C8C2212yes—
10C11×#384C2211yescharacteristic
11C2×(C2×D11)⋊C8—22no—
12#10622589—22no—
13#10622589C412yes—
14#10622548C2211yescharacteristic
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622188—22no—
17C22×C4×D11—22no—
18C22×C4×D11C2×C411yescharacteristic
19C22×C4×D11D412yes—
20C22×C8×C11—22no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4C2×C412yes—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11C2×C412yes—
26C2×Dic11⋊C4—24no—
27C2×Dic11⋊C4—22no—
28C2×C4×Dic11C2×C411yescharacteristic
29C2×C4×Dic11D412yes—
30C22×C11⋊C8—22no—
31C4⋊C4×D11—44no—
32C4⋊C4×D11—44no—
33C4⋊C4×D11—44no—
34C42×D11—22no—
35C42×D11—21no—
36C42×D11—21no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39(C2×D11)⋊C8—44no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42#8723—111nomaximal, Sylow
43C23×D11C22⋊C411yescharacteristic
44C22×C4×C11—22no—
45C22×C4×C11C22×C411yescharacteristic
46C22×C4×C11C2×D412yes—
47C22×Dic11—22no—
48C22×Dic11C22⋊C411yescharacteristic
49C22×Dic11C22⋊C412yes—
50C2×C4×D11—22no—
51C2×C4×D11—22no—
52C2×C4×D11—21no—
53C2×C4×D11—21no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—22no—
58C2×C4×D11—44no—
59C2×C4×D11—48no—
60C2×C4×D11D814yes—
61C2×C4×D11SD1614yes—
62C2×C8×C11—42no—
63C2×C8×C11—42no—
64C2×C8×C11—42no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—42no—
68C42×C11#4112yes—
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C4⋊Dic11—42no—
74Dic11⋊C4—44no—
75Dic11⋊C4—48no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11—22no—
79C4×Dic11—22no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×#384—111no—
84#1797—112no—
85#1296—112no—
86#1296—111no—
87#1296D1111yescharacteristic, complemented
88C23×C11C2×C22⋊C411yescharacteristic
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—22no—
92C22×D11#10012yes—
93C22×D11#10214yes—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—42no—
97C2×C4×C11—44no—
98C2×C4×C11#11711yescharacteristic
99C2×C4×C11#11711yescharacteristic
100C2×C4×C11#12312yes—
101C2×C4×C11#12312yes—
102C2×C4×C11C2×D812yes—
103C2×C4×C11C2×SD1612yes—
104C2×C4×C11#13712yes—
105C2×C4×C11#13712yes—
106C2×Dic11—21no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—22no—
110C2×Dic11—42no—
111C2×Dic11—44no—
112C2×Dic11#10112yes—
113C2×Dic11#10214yes—
114C4×D11—24no—
115C4×D11—24no—
116C4×D11—24no—
117C4×D11—24no—
118C4×D11—24no—
119C4×D11—24no—
120C4×D11—88no—
121C8×C11—82no—
122C11⋊C8—82no—
123C22×C4⋊C4—112no—
124C22×C4⋊C4—222no—
125C22×C42—111no—
126C2×C4⋊C8—112no—
127C2×C4⋊C8C2×D1112yes—
128C2×C22⋊C8—222no—
129#384—112no—
130#384—111no—
131#384—222no—
132#384C2×D1111yescharacteristic
133#336—222no—
134C22×C11#38111yescharacteristic
135C22×C11C2×#10011yescharacteristic
136C22×C11C2×#10111yescharacteristic
137C22×C11C2×#10212yes—
138C22×C11#41912yes—
139C2×D11—24no—
140C2×D11—22no—
141C2×D11—22no—
142C2×D11—24no—
143C2×D11#33114yes—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—82no—
147C4×C11#48012yes—
148C4×C11#48012yes—
149C4×C11#48312yes—
150C4×C11#48312yes—
151Dic11—22no—
152Dic11—24no—
153Dic11—82no—
154C23×C4—112no—
155C23×C4—111no—
156C23×C4—222no—
157C22×C8—22no—
158C22×C8—222no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—222no—
162C2×C4⋊C4—224no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4—444no—
165C2×C4⋊C4—444no—
166C2×C4⋊C4—444no—
167C2×C4⋊C4C4×D1112yes—
168C2×C42—111no—
169C2×C42—112no—
170C2×C42—222no—
171C2×C42—221no—
172C2×C42—221no—
173C2×C42C22×D1111yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—222no—
177C4⋊C8—222no—
178C22⋊C8—444no—
179C2×C11C2×#33111yescharacteristic
180C2×C11#154612yes—
181C2×C11#155811yescharacteristic
182C2×C11#182111yescharacteristic
183C2×C11#182312yes—
184D11—24no—
185C24—111no—
186C22×C4—22no—
187C22×C4—111no—
188C22×C4—112no—
189C22×C4—114no—
190C22×C4—114no—
191C22×C4—222no—
192C22×C4—222no—
193C22×C4—221no—
194C22×C4—222no—
195C22×C4—221no—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4—448no—
201C22×C4—444no—
202C22×C4C2×C4×D1111yescharacteristic
203C22×C4D4×D1112yes—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—442no—
208C2×C8—442no—
209C2×C8—442no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—442no—
214C4⋊C4—448no—
215C4⋊C4—444no—
216C4⋊C4—442no—
217C4⋊C4—442no—
218C42—221no—
219C42—222no—
220C42—221no—
221C42—222no—
222C42#433912yes—
223C42#434111yescharacteristic
224C42#434311yescharacteristic
225C11#872311yescharacteristic, complemented, Sylow
226C23—112no—
227C23—114no—
228C23—221no—
229C23—221no—
230C23—222no—
231C23C22⋊C4×D1111yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—44no—
236C2×C4—112no—
237C2×C4—114no—
238C2×C4—224no—
239C2×C4—224no—
240C2×C4—221no—
241C2×C4—222no—
242C2×C4—221no—
243C2×C4—222no—
244C2×C4—224no—
245C2×C4—224no—
246C2×C4—224no—
247C2×C4—224no—
248C2×C4—442no—
249C2×C4—444no—
250C2×C4—888no—
251C2×C4#6692511yescharacteristic
252C2×C4#6693612yes—
253C2×C4#6694511yescharacteristic
254C2×C4#6694712yes—
255C2×C4D8×D1112yes—
256C2×C4SD16×D1112yes—
257C2×C4#6696812yes—
258C2×C4#6697112yes—
259C8—82no—
260C8—882no—
261C22—114no—
262C22—224no—
263C22—222no—
264C22—222no—
265C22—224no—
266C22#1062227711yescharacteristic
267C22D11×#10011yescharacteristic
268C22D11×#10111yescharacteristic
269C22D11×#10212yes—
270C22#1062241512yes—
271C4—21no—
272C4—21no—
273C4—82no—
274C4—222no—
275C4—224no—
276C4—882no—
277C4#1062238712yes—
278C4#1062241812yes—
279C4#1062247512yes—
280C4#1062249512yes—
281C2—224no—
282C2D11×#33111yescharacteristic
283C2#1306728612yes—
284C2#1306734011yescharacteristic
285C2#1306869511yescharacteristic
286C2#1306870112yes—
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1296D11
hypocenterC11#8723
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #13066500C2semidirect
4. #13066499C2semidirect
5. C11×#1296C2semidirect
87. #1296D11semidirect
225. C11#8723semidirect

Maximal subgroups

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

subgroupindex
D11×#3842
#130685932
#130665002
#130664992
C11×#12962
#872311