Finite Group Databasebeta

← #13068992

Subgroups — #13068992

Order 1408.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C11×#520C211yesmaximal, characteristic, complemented
2C2×#67002C211yesmaximal, characteristic
3C2×#66901C211yesmaximal, characteristic, complemented
4#10622614C211yesmaximal, characteristic, complemented
5#10622601C211yesmaximal, characteristic, complemented
6#10622170C211yesmaximal, characteristic, complemented
7#10622168C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C4×Q8×C11—21no—
11C4×D4×C11—21no—
12C4×D4×C11—22no—
13C11×#117—21no—
14C11×#117C2211yescharacteristic
15C2×C11×C4⋊C4—21no—
16C2×C11×C4⋊C4C2211yescharacteristic
17#67002—22no—
18#67002C414yescomplemented
19C2×#4325—21no—
20C2×#4323—21no—
21C2×(C2×D11)⋊C4—22no—
22C2×C4×Dic11C2211yescharacteristic
23C2×#4318C2211yescharacteristic
24C2×#4318C2211yescharacteristic
25#66901—22no—
26#66873—21no—
27#66873—21no—
28C23×D11—21no—
29C11×#41—21no—
30C11×#41—21no—
31C11×#41C2×C412yes—
32C11×#41D412yes—
33C2×Q8×C11D411yescharacteristic
34C2×D4×C11—21no—
35C2×D4×C11D411yescharacteristic
36C22×C4×C11—21no—
37C22×C4×C11—22no—
38C22×C4×C11D412yes—
39C22×C4×C11C2311yescharacteristic
40C22×Dic11—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44—21no—
45C2×D44—21no—
46C2×D44C2×C412yescomplemented
47C11×C4⋊C4—22no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4D411yescharacteristic
51C11×C4⋊C4D411yescharacteristic
52C11×C22⋊C4—22no—
53C11×C22⋊C4—21no—
54C42×C11—22no—
55C42×C11—21no—
56#4325—24no—
57#4323—24no—
58(C2×D11)⋊C4—44no—
59C4×Dic11—21no—
60C4×Dic11—21no—
61#4318—21no—
62#4318—21no—
63#4318—21no—
64#4318C2×C412yescomplemented
65C2×C11⋊C8—21no—
66C2×C11⋊C8—21no—
67#1883—111nomaximal, Sylow
68C23×C11—21no—
69C23×C11C2×D411yescharacteristic
70C22×D11—22no—
71C22×D11—42no—
72C22×D11—42no—
73C22×D11—41no—
74C22×D11—41no—
75Q8×C11—21no—
76Q8×C11C22⋊C412yescomplemented
77D4×C11—22no—
78D4×C11—22no—
79D4×C11—21no—
80D4×C11C22⋊C412yescomplemented
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—42no—
88C2×C4×C11—82no—
89C2×C4×C11C22×C411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11#4111yescharacteristic
94C2×C4×C11#4111yescharacteristic
95C2×Dic11—22no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98D44—22no—
99D44—22no—
100D44—41no—
101D44—41no—
102C11⋊C8—22no—
103C11⋊C8—41no—
104C2×AGL(1,ℤ/8)—111no—
105#520D1111yescharacteristic, complemented
106C2×#104—111no—
107#418—111no—
108#390—111no—
109#343—111no—
110#339—111no—
111C22×C11—21no—
112C22×C11—21no—
113C22×C11—22no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11C4×D411yescharacteristic
117C22×C11#12011yescharacteristic
118C22×C11#12111yescharacteristic
119C2×D11—44no—
120C2×D11—42no—
121C2×D11—82no—
122C2×D11—81no—
123C2×D11—81no—
124C4×C11—22no—
125C4×C11—42no—
126C4×C11—41no—
127C4×C11—41no—
128C4×C11C2×C22⋊C411yescharacteristic
129C4×C11C4×D411yescharacteristic
130C4×C11#12111yescharacteristic
131C4×C11#12311yescharacteristic
132Dic11—42no—
133C2×#41C2×D1111yescharacteristic
134C22×D4—111no—
135AGL(1,ℤ/8)—114no—
136AGL(1,ℤ/8)—222no—
137C2×SD16—221no—
138C2×D8—221no—
139C2×M16—111no—
140C2×M16—111no—
141C4×Q8—21no—
142C4×D4—21no—
143C4×D4—22no—
144#117—21no—
145#117C2×D1111yescharacteristic
146C2×C4⋊C4—21no—
147C2×C4⋊C4C2×D1111yescharacteristic
148C2×C22⋊C4—222no—
149C2×C42—111no—
150#104—222no—
151#102—221no—
152#102—221no—
153C2×C11—21no—
154C2×C11—21no—
155C2×C11—42no—
156C2×C11#38611yescharacteristic
157C2×C11#45311yescharacteristic
158C2×C11#45411yescharacteristic
159D11—82no—
160C24—221no—
161#41—21no—
162#41—21no—
163#41C4×D1112yes—
164#41D4412yes—
165C2×Q8C22⋊D1111yescharacteristic
166C2×D4—21no—
167C2×D4—112no—
168C2×D4—221no—
169C2×D4—221no—
170C2×D4—221no—
171C2×D4—221no—
172C2×D4—221no—
173C2×D4C22⋊D1111yescharacteristic
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—221no—
177C22×C4C22⋊D1112yes—
178C22×C4C22×D1111yescharacteristic
179SD16—224no—
180D8—224no—
181M16—112no—
182M16—221no—
183M16—221no—
184M16—221no—
185C2×C8—221no—
186C2×C8—221no—
187C4⋊C4—22no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4C22⋊D1111yescharacteristic
191C4⋊C4C22⋊D1111yescharacteristic
192C22⋊C4—22no—
193C22⋊C4—21no—
194C22⋊C4—444no—
195C42—22no—
196C42—21no—
197C42—221no—
198C42—221no—
199C11#188311yescharacteristic, complemented, Sylow
200C23—21no—
201C23—222no—
202C23—442no—
203C23—442no—
204C23—441no—
205C23—441no—
206C23C2×C22⋊D1111yescharacteristic
207Q8—21no—
208Q8(C2×D11)⋊C412yescomplemented
209D4—22no—
210D4—22no—
211D4—21no—
212D4—222no—
213D4—222no—
214D4—441no—
215D4—441no—
216D4(C2×D11)⋊C412yescomplemented
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—222no—
226C2×C4—441no—
227C2×C4—441no—
228C2×C4C2×C4×D1111yescharacteristic
229C2×C4C2×D4411yescharacteristic
230C2×C4#433911yescharacteristic
231C2×C4#433911yescharacteristic
232C2×C4C2×C22⋊D1111yescharacteristic
233C2×C4C2×C22⋊D1111yescharacteristic
234C8—222no—
235C8—441no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—444no—
242C22—442no—
243C22—882no—
244C22—881no—
245C22—881no—
246C22C4×C22⋊D1111yescharacteristic
247C22#6698311yescharacteristic
248C22#6700611yescharacteristic
249C4—22no—
250C4—42no—
251C4—41no—
252C4—41no—
253C4—442no—
254C4C2×(C2×D11)⋊C411yescharacteristic
255C4C4×C22⋊D1111yescharacteristic
256C4#6698211yescharacteristic
257C4#6698311yescharacteristic
258C2—21no—
259C2—21no—
260C2—42no—
261C2—882no—
262C2#1062282611yescharacteristic
263C2#1062285411yescharacteristic
264C2#1062285811yescharacteristic
subgroupG/H
centerC22#67006
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#520C2
socleC22×C11#120
prime radicalC2×#67002C2
cosocleC22×C4×C11C23
hypercenter#520D11
hypocenterC11#1883
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C11×#520C2semidirect
3. C2×#66901C2semidirect
4. #10622614C2semidirect
5. #10622601C2semidirect
6. #10622170C2semidirect
7. #10622168C2semidirect
18. #67002C4semidirect
46. C2×D44C2×C4semidirect
64. #4318C2×C4semidirect
76. Q8×C11C22⋊C4semidirect
80. D4×C11C22⋊C4semidirect
105. #520D11semidirect
199. C11#1883semidirect
208. Q8(C2×D11)⋊C4semidirect
216. D4(C2×D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C11×#5202
C2×#670022
C2×#669012
#106226142
#106226012
#106221702
#106221682
#188311