Finite Group Databasebeta

← #13069828

Subgroups — #13069828

Order 1408.

326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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#10623056C211yesmaximal, characteristic
2C11×#428C211yesmaximal, characteristic, complemented
3C2×#66889C211yesmaximal, characteristic, complemented
4C2×#66887C211yesmaximal, characteristic, complemented
5#10622601C211yesmaximal, characteristic, complemented
6#10622579C211yesmaximal, characteristic, complemented
7#10622170C211yesmaximal, characteristic, complemented
8C2×#4339C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C11×#117C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C4—22no—
14C2×C4×Dic11C2211yescharacteristic
15C2×#4318C2211yescharacteristic
16#66948—21no—
17#66948—21no—
18#66935—22no—
19#66928—21no—
20#66927—21no—
21C11×#107—21no—
22C11×#106—21no—
23#66889—22no—
24#66887—22no—
25#66874—21no—
26#66873—21no—
27C23×D11D412yes—
28C22×C4×C11—21no—
29C22×C4×C11C2311yescharacteristic
30C2×C22⋊D11—21no—
31C22×Dic11—21no—
32#4339—21no—
33#4339—21no—
34#4339—21no—
35#4339—21no—
36C2×D44—22no—
37C2×D44—22no—
38C2×D44—21no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44D411yescharacteristic
45C2×C4×D11—21no—
46C2×Dic22D411yescharacteristic
47C11×M16—21no—
48C11×M16D412yescomplemented
49C2×C8×C11—21no—
50C11×C4⋊C4—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4D411yescharacteristic
53C11×C4⋊C4D411yescharacteristic
54C11×C22⋊C4—21no—
55C42×C11—21no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—44no—
59C4×Dic11—21no—
60C4×Dic11—21no—
61#4318—21no—
62#4318—21no—
63C2×C11⋊C8—21no—
64#2037—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67C22×D11—21no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—42no—
71C22×D11—42no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—42no—
75C2×C4×C11—41no—
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11#4111yescharacteristic
80C2×C4×C11#4111yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C22⋊D11—41no—
83C22⋊D11—41no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—41no—
87C2×Dic11—41no—
88D44—21no—
89D44—21no—
90D44—41no—
91D44—41no—
92D44—41no—
93D44—41no—
94D44—82no—
95D44—82no—
96C4×D11—41no—
97C4×D11—41no—
98Dic22—21no—
99Dic22—21no—
100C8×C11—22no—
101C11⋊C8—41no—
102#535—111no—
103#428D1111yescharacteristic, complemented
104C2×#104—111no—
105#417—111no—
106C2×#100—111no—
107#390—111no—
108#339—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11#12011yescharacteristic
112C22×C11#12111yescharacteristic
113C22×C11#12311yescharacteristic
114C2×D11—44no—
115C2×D11—42no—
116C2×D11—41no—
117C2×D11—42no—
118C2×D11—41no—
119C2×D11—42no—
120C2×D11—41no—
121C2×D11—82no—
122C4×C11—41no—
123C4×C11—41no—
124C4×C11—81no—
125C4×C11#12111yescharacteristic
126C4×C11#12111yescharacteristic
127C4×C11#12311yescharacteristic
128C4×C11#12411yescharacteristic
129Dic11—42no—
130Dic11—41no—
131C2×#41—111no—
132C22×D4—111no—
133C2×M16—111no—
134C2×M16C2×D1111yescharacteristic
135#127—221no—
136#124—221no—
137#121—221no—
138#121—221no—
139#120—222no—
140#117C2×D1111yescharacteristic
141C2×C4⋊C4C2×D1111yescharacteristic
142C2×C22⋊C4—222no—
143C2×C42—111no—
144#107—21no—
145#106—21no—
146#104—222no—
147#103—221no—
148#102—221no—
149#100—222no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11#39411yescharacteristic
153C2×C11#45311yescharacteristic
154C2×C11#45511yescharacteristic
155D11—81no—
156D11—82no—
157C24—112no—
158#41—221no—
159#41—221no—
160#41—221no—
161#41—221no—
162C2×Q8—111no—
163C2×D4—111no—
164C2×D4—222no—
165C2×D4—222no—
166C2×D4—221no—
167C2×D4—221no—
168C2×D4—221no—
169C2×D4—221no—
170C2×D4—221no—
171C2×D4—221no—
172C2×D4—221no—
173C22×C4—21no—
174C22×C4—221no—
175C22×C4—221no—
176C22×C4C22×D1111yescharacteristic
177M16—21no—
178M16—221no—
179M16—221no—
180M16D4412yescomplemented
181C2×C8—21no—
182C2×C8—221no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4C22⋊D1111yescharacteristic
186C4⋊C4C22⋊D1111yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C22⋊C4—444no—
191C42—21no—
192C42—221no—
193C42—221no—
194C11#203711yescharacteristic, complemented, Sylow
195C23—222no—
196C23—222no—
197C23—221no—
198C23—222no—
199C23—442no—
200C23—442no—
201C23D4×D1111yescharacteristic
202Q8—221no—
203Q8—221no—
204D4—221no—
205D4—221no—
206D4—441no—
207D4—441no—
208D4—441no—
209D4—441no—
210D4—441no—
211D4—441no—
212D4—882no—
213D4—882no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—222no—
219C2×C4—221no—
220C2×C4—441no—
221C2×C4—441no—
222C2×C4—441no—
223C2×C4—441no—
224C2×C4C2×D4411yescharacteristic
225C2×C4#433911yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4#434311yescharacteristic
228C2×C4#434311yescharacteristic
229C2×C4C2×C22⋊D1111yescharacteristic
230C8—22no—
231C8—441no—
232C22—21no—
233C22—21no—
234C22—444no—
235C22—441no—
236C22—442no—
237C22—441no—
238C22—442no—
239C22—441no—
240C22—442no—
241C22—882no—
242C22#6694711yescharacteristic
243C22#6694811yescharacteristic
244C22#6699011yescharacteristic
245C4—41no—
246C4—41no—
247C4—81no—
248C4—442no—
249C4—441no—
250C4#6694711yescharacteristic
251C4#6694811yescharacteristic
252C4#6698311yescharacteristic
253C4#6700011yescharacteristic
254C2—21no—
255C2—21no—
256C2—882no—
257C2—881no—
258C2#1062260411yescharacteristic
259C2#1062281111yescharacteristic
260C2#1062281511yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#428C2
socleC22×C11#120
prime radical#10623056C2
hypercenter#428D11
hypocenterC11#2037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C11×#428C2semidirect
3. C2×#66889C2semidirect
4. C2×#66887C2semidirect
5. #10622601C2semidirect
6. #10622579C2semidirect
7. #10622170C2semidirect
48. C11×M16D4semidirect
103. #428D11semidirect
180. M16D44semidirect
194. C11#2037semidirect

Maximal subgroups

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

subgroupindex
#106230562
C11×#4282
C2×#668892
C2×#668872
#106226012
#106225792
#106221702
#203711