Finite Group Databasebeta

← #14651203

Subgroups — #14651203

Order 2816.

554 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 119 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#13073615C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic, complemented
3#13067283C212yesmaximal
4#13066518C212yesmaximal, complemented
5C11×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#67000—21no—
8C2×#66927C2211yescharacteristic
9C11×#446—24no—
10C11×#432—22no—
11C11×#431C2212yes—
12C2×#66900—21no—
13#10622604C414yes—
14#10622601—21no—
15#10622552—22no—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622537C2212yes—
18#10622168—21no—
19#10622123—24no—
20C22×Q8×C11D411yescharacteristic
21C22×D44—21no—
22C22×D44—21no—
23C22×D44C2×C412yes—
24C4×Q8×C11—22no—
25C4×Q8×C11—22no—
26C2×C11×C4⋊C4C2×C412yes—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30#67000—44no—
31C2×(C2×D11)⋊C4—24no—
32C2×(C2×D11)⋊C4—24no—
33C2×C4⋊Dic11—21no—
34C2×C4×Dic11—21no—
35C2×#4318—22no—
36#66927—22no—
37#66927—22no—
38C11×C4⋊C8—24no—
39C11×C4⋊C8D414yes—
40C11×C22⋊C8—22no—
41C11×#97—24no—
42C4×C8×C11—22no—
43#66900—42no—
44C11⋊#95C2×C412yes—
45C4⋊(C11⋊C8)—22no—
46C4⋊(C11⋊C8)—22no—
47#9406—111nomaximal, Sylow
48C23×D11—22no—
49C2×Q8×C11—22no—
50C2×Q8×C11—21no—
51C2×Q8×C11—22no—
52C2×Q8×C11—21no—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22⋊C412yes—
55C22×C4×C11C22×C411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×Dic11—22no—
59C2×D44—24no—
60C2×D44—44no—
61C2×D44—41no—
62C2×D44—42no—
63C2×D44—41no—
64C2×D44—42no—
65C2×D44—41no—
66C2×D44—41no—
67C2×D44—82no—
68C2×C8×C11—24no—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—22no—
71C42×C11—22no—
72C42×C11—22no—
73C42×C11C2×D412yes—
74C42×C11#4112yes—
75(C2×D11)⋊C4—48no—
76(C2×D11)⋊C4—84no—
77C4⋊Dic11—42no—
78C4×Dic11—42no—
79#4318—42no—
80#4318—42no—
81C2×C11⋊C8—42no—
82#2983D1111yescharacteristic, complemented
83#2548—111no—
84#1801—111no—
85#1545—112no—
86#1303—112no—
87C23×C11C2×C22⋊C411yescharacteristic
88C22×D11—44no—
89C22×D11—44no—
90C22×D11—42no—
91C22×D11—42no—
92C22×D11—42no—
93Q8×C11—42no—
94Q8×C11—42no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—41no—
101C2×C4×C11—42no—
102C2×C4×C11C4×D412yes—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11#12112yes—
105C2×C4×C11#12311yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)12yes—
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C11#13711yescharacteristic
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112D44—84no—
113D44—82no—
114D44—82no—
115D44—82no—
116D44—82no—
117C8×C11—44no—
118C11⋊C8—82no—
119C2×#127—111no—
120C2×#124—221no—
121C2×C4×Q8C2×D1111yescharacteristic
122#446—24no—
123#432—22no—
124#431C2×D1112yes—
125#423—112no—
126C2×#101—221no—
127#394—114no—
128#390—221no—
129#390—222no—
130C4×C4⋊C4—111no—
131#343—221no—
132#331—224no—
133C22×C11—21no—
134C22×C11—21no—
135C22×C11#38611yescharacteristic
136C22×C11#41711yescharacteristic
137C22×C11#41811yescharacteristic
138C2×D11—84no—
139C2×D11—84no—
140C2×D11—82no—
141C2×D11—82no—
142C2×D11—82no—
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—42no—
147C4×C11#45412yes—
148C4×C11#46812yes—
149C4×C11#46912yes—
150Dic11—82no—
151C22×Q8D4411yescharacteristic
152C22×D4—112no—
153C22×D4—221no—
154C22×D4—221no—
155C2×M16—222no—
156#127—222no—
157#127—222no—
158#124—444no—
159C4×Q8—22no—
160C4×Q8—22no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4C4×D1112yes—
163C2×C4⋊C4D4411yescharacteristic
164C2×C22⋊C4—224no—
165C2×C22⋊C4—224no—
166C2×C42—221no—
167C2×C42C22⋊D1112yes—
168C2×C42C22×D1111yescharacteristic
169C4⋊C8—24no—
170C4⋊C8—222no—
171C4⋊C8—222no—
172C4⋊C8C22⋊D1114yes—
173#101—442no—
174C22⋊C8—22no—
175#97—24no—
176C4×C8—22no—
177#95—112no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11#188811yescharacteristic
181C2×C11#189511yescharacteristic
182C2×C11#191411yescharacteristic
183D11—162no—
184C24—222no—
185C2×Q8—21no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—22no—
189C2×D4—224no—
190C2×D4—444no—
191C2×D4—442no—
192C2×D4—441no—
193C2×D4—441no—
194C2×D4—441no—
195C2×D4—442no—
196C2×D4—441no—
197C2×D4—882no—
198C22×C4—222no—
199C22×C4(C2×D11)⋊C412yes—
200C22×C4(C2×D11)⋊C412yes—
201C22×C4C2×C4×D1111yescharacteristic
202C22×C4C2×D4411yescharacteristic
203C22×C4C2×C22⋊D1111yescharacteristic
204M16—442no—
205M16—442no—
206C2×C8—24no—
207C2×C8—442no—
208C4⋊C4—24no—
209C4⋊C4—22no—
210C4⋊C4—442no—
211C22⋊C4—448no—
212C22⋊C4—884no—
213C42—22no—
214C42—22no—
215C42—442no—
216C42#433912yes—
217C42C2×C22⋊D1112yes—
218C11#940611yescharacteristic, complemented, Sylow
219C23—444no—
220C23—444no—
221C23—442no—
222C23—442no—
223C23—442no—
224C23C2×(C2×D11)⋊C411yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—884no—
228D4—882no—
229D4—882no—
230D4—882no—
231D4—882no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—442no—
240C2×C4—442no—
241C2×C4—442no—
242C2×C4#6696112yes—
243C2×C4#6696111yescharacteristic
244C2×C4#6696211yescharacteristic
245C2×C4C4×C22⋊D1112yes—
246C2×C4#6698211yescharacteristic
247C2×C4#6698312yes—
248C2×C4#6700611yescharacteristic
249C8—44no—
250C8—882no—
251C22—21no—
252C22—21no—
253C22—884no—
254C22—884no—
255C22—882no—
256C22—882no—
257C22—882no—
258C22#1062274411yescharacteristic
259C22#1062274611yescharacteristic
260C22#1062282611yescharacteristic
261C4—22no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—882no—
266C4#1062274712yes—
267C4#1062274812yes—
268C4#1062285812yes—
269C2—21no—
270C2—21no—
271C2—1762no—
272C2#1306901911yescharacteristic
273C2#1306905411yescharacteristic
274C2#1306916311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2983C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#2983D11
hypocenterC11#9406
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #13068612C2semidirect
4. #13066518C2semidirect
5. C11×#2983C2semidirect
82. #2983D11semidirect
218. C11#9406semidirect

Maximal subgroups

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

subgroupindex
#130736152
#130686122
#130672832
#130665182
C11×#29832
#940611