Finite Group Databasebeta

← #14670586

Subgroups — #14670586

Order 2816.

424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077683C211yesmaximal, characteristic
2#13070281C211yesmaximal, characteristic
3#13068902C212yesmaximal, complemented
4#13066736C212yesmaximal, complemented
5C11×#1884C211yesmaximal, characteristic
6C11×#568C2211yescharacteristic
7C11×#532C2211yescharacteristic
8C11×#421—21no—
9C11×#410C2211yescharacteristic
10#10622853C2212yes—
11#10622847—21no—
12#10622847C2212yes—
13#10622732—22no—
14#10622625—22no—
15D4×C11⋊C8—22no—
16#10622538—21no—
17C11×#339—21no—
18#10622194—22no—
19#10622183C412yescomplemented
20#10622179C412yescomplemented
21C2×C11×#41D411yescharacteristic
22C2×C11×#41C2311yescharacteristic
23C11×#131—42no—
24C2×C11×M16—22no—
25C2×C11×M16—21no—
26C11×C4⋊Q8Q811yescharacteristic
27C11×#127C2×C411yescharacteristic
28C11×#124C2×C411yescharacteristic
29C11×#124Q811yescharacteristic
30C11×#121—22no—
31C4×D4×C11—22no—
32C11×#117—21no—
33C2×C42×C11D411yescharacteristic
34#66979—22no—
35C2×#4318—21no—
36C2×#4318D412yes—
37C22×C11⋊C8—21no—
38C22×C11⋊C8D412yes—
39C11×#104—42no—
40C11×#99—22no—
41#66898—22no—
42#66898C2×C414yes—
43C22⋊(C11⋊C8)—22no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46Dic11⋊C8—44no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4×C11⋊C8—22no—
50#12968—111nomaximal, Sylow
51C11×#41—41no—
52C11×#41—41no—
53C11×#41—41no—
54C11×#41—41no—
55C2×Q8×C11C4⋊C411yescharacteristic
56C2×Q8×C11C2×Q811yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—21no—
59C2×D4×C11C4⋊C411yescharacteristic
60C2×D4×C11C22×C411yescharacteristic
61C2×D4×C11#4112yes—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C11×M16—22no—
67C11×M16—42no—
68C11×M16—41no—
69C2×C8×C11—24no—
70C2×C8×C11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—41no—
76C42×C11—21no—
77C42×C11—41no—
78C42×C11C4⋊C411yescharacteristic
79C42×C11C4⋊C411yescharacteristic
80C22⋊Dic11—24no—
81C4⋊Dic11—42no—
82C4×Dic11—42no—
83#4318—42no—
84#4318—81no—
85C2×C11⋊C8—22no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—42no—
88C2×C11⋊C8—81no—
89#2979—111no—
90#2126—111no—
91#1884D1111yescharacteristic
92#1868—112no—
93#1391—112no—
94C23×C11—21no—
95C23×C11C4×D412yes—
96C23×C11#12311yescharacteristic
97Q8×C11—41no—
98Q8×C11—41no—
99D4×C11—41no—
100D4×C11—42no—
101D4×C11—41no—
102D4×C11—44no—
103D4×C11—81no—
104C2×C4×C11—21no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—42no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—81no—
115C2×C4×C11C2×C4⋊C411yescharacteristic
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11C22⋊Q812yes—
118C2×Dic11—44no—
119C8×C11—42no—
120C11⋊C8—42no—
121C11⋊C8—42no—
122#568C2×D1111yescharacteristic
123#532C2×D1111yescharacteristic
124#436—222no—
125C8×D4—222no—
126#431—221no—
127#424—222no—
128#421—21no—
129#410—112no—
130#410C2×D1111yescharacteristic
131#408—112no—
132#408—221no—
133#354—112no—
134#353—112no—
135#344—222no—
136#339—21no—
137C22×C11—21no—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—41no—
143C22×C11#38511yescharacteristic
144C4×C11—22no—
145C4×C11—21no—
146C4×C11—22no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11—161no—
150C4×C11B(4,𝔽2)11yescharacteristic
151C4×C11#45811yescharacteristic
152Dic11—84no—
153C2×#41C22⋊D1111yescharacteristic
154C2×#41C22×D1111yescharacteristic
155#131—42no—
156C2×M16—22no—
157C2×M16—21no—
158C2×M16—112no—
159C2×M16—221no—
160C22×C8—112no—
161C22×C8—221no—
162C4⋊Q8Dic2211yescharacteristic
163#127C4×D1111yescharacteristic
164#124Dic2211yescharacteristic
165#124C4×D1111yescharacteristic
166#121—22no—
167C4×D4—22no—
168#117—21no—
169#117—222no—
170C2×C42C22⋊D1111yescharacteristic
171C4⋊C8—221no—
172C4⋊C8—221no—
173C4⋊C8—444no—
174#104—42no—
175#99—22no—
176#99—114no—
177#99—222no—
178C22⋊C8—222no—
179C22⋊C8—222no—
180C22⋊C8—222no—
181C4×C8—222no—
182C2×C11—21no—
183C2×C11—42no—
184C2×C11—41no—
185C2×C11—81no—
186C2×C11#186711yescharacteristic
187#41—41no—
188#41—41no—
189#41—41no—
190#41—41no—
191C2×Q8Dic11⋊C411yescharacteristic
192C2×Q8C2×Dic2211yescharacteristic
193C2×D4—22no—
194C2×D4—21no—
195C2×D4Dic11⋊C411yescharacteristic
196C2×D4C2×C4×D1111yescharacteristic
197C2×D4#434112yes—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4D4×D1112yes—
201C22×C4C2×C22⋊D1111yescharacteristic
202M16—22no—
203M16—42no—
204M16—41no—
205M16—442no—
206M16—881no—
207C2×C8—24no—
208C2×C8—41no—
209C2×C8—222no—
210C2×C8—222no—
211C2×C8—442no—
212C2×C8—881no—
213C4⋊C4—22no—
214C4⋊C4—41no—
215C4⋊C4—442no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—41no—
219C22⋊C4—224no—
220C42—21no—
221C42—41no—
222C42—442no—
223C42Dic11⋊C411yescharacteristic
224C42Dic11⋊C411yescharacteristic
225C11#1296811yescharacteristic, complemented, Sylow
226C23—21no—
227C23(C22⋊D11)⋊C412yes—
228C23#6698811yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—42no—
233D4—41no—
234D4—44no—
235D4—81no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—444no—
248C2×C4#6693112yes—
249C2×C4C2×Dic11⋊C411yescharacteristic
250C2×C4#6699011yescharacteristic
251C8—42no—
252C8—442no—
253C8—442no—
254C22—21no—
255C22—22no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22#1062255911yescharacteristic
261C4—22no—
262C4—22no—
263C4—21no—
264C4—41no—
265C4—41no—
266C4—161no—
267C4—884no—
268C4#1062264511yescharacteristic
269C4#1062266611yescharacteristic
270C2—21no—
271C2—41no—
272C2—42no—
273C2—81no—
274C2#1306889611yescharacteristic
subgroupG/H
centerC4#10622645
commutatorC2×D4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1884C2
socleC2×C11#1867
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#1884D11
hypocenterC11#12968
LCSG ▷ C2×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1884

Complements

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

NH ≅ G/Ntype
3. #13068902C2semidirect
4. #13066736C2semidirect
19. #10622183C4semidirect
20. #10622179C4semidirect
225. C11#12968semidirect

Maximal subgroups

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

subgroupindex
#130776832
#130702812
#130689022
#130667362
C11×#18842
#1296811