Finite Group Databasebeta

← #13069825

Subgroups — #13069825

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#10623361C211yesmaximal, characteristic
2C2×C11×#104C211yesmaximal, characteristic, complemented
3#10622845C211yesmaximal, characteristic, complemented
4C2×#66887C211yesmaximal, characteristic, complemented
5#10622734C211yesmaximal, characteristic, complemented
6#10622552C211yesmaximal, characteristic, complemented
7#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D44C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12#67000—21no—
13#66993—21no—
14#66990—22no—
15#66983—21no—
16#66983—21no—
17C2×(C2×D11)⋊C4—22no—
18#66979C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×#4318C2211yescharacteristic
21C11×#104—22no—
22#66899—21no—
23#66896—21no—
24#66887—22no—
25#66882—21no—
26#66881—21no—
27C23×D11D412yes—
28C11×#41—21no—
29C11×#41—21no—
30C11×#41—21no—
31C11×#41—21no—
32C2×Q8×C11D411yescharacteristic
33C2×D4×C11—21no—
34C2×D4×C11D411yescharacteristic
35C22×C4×C11—21no—
36C22×C4×C11—21no—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—22no—
39C2×C22⋊D11—22no—
40C22×Dic11—21no—
41C2×D44—21no—
42C2×D44—21no—
43C2×D44—21no—
44C2×D44—21no—
45C2×D44—21no—
46C2×D44—21no—
47C11×M16—21no—
48C11×M16D412yescomplemented
49C2×C8×C11—21no—
50C42×C11—21no—
51C42×C11—21no—
52C22⋊Dic11—21no—
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—44no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11D411yescharacteristic
59C4⋊Dic11D411yescharacteristic
60C4×Dic11—21no—
61#4318—21no—
62#4318—21no—
63C2×C11⋊C8—21no—
64#2037—111nomaximal, Sylow
65C23×C11—21no—
66C23×C11C2×D411yescharacteristic
67C22×D11—22no—
68C22×D11—22no—
69C22×D11—22no—
70C22×D11—42no—
71C22×D11—42no—
72Q8×C11—21no—
73Q8×C11—21no—
74D4×C11—21no—
75D4×C11—21no—
76D4×C11—41no—
77D4×C11—41no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11#4111yescharacteristic
88C2×C4×C11#4111yescharacteristic
89C2×C4×C11#4111yescharacteristic
90C22⋊D11—82no—
91C22⋊D11—82no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—42no—
95C2×Dic11—41no—
96D44—41no—
97D44—41no—
98D44—41no—
99D44—41no—
100C8×C11—22no—
101C11⋊C8—41no—
102#535—111no—
103#428—111no—
104C2×#104D1111yescharacteristic, complemented
105#417—111no—
106C2×#100—111no—
107#390—111no—
108#339—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11#12011yescharacteristic
115C22×C11#12111yescharacteristic
116C22×C11#12311yescharacteristic
117C2×D11—44no—
118C2×D11—42no—
119C2×D11—42no—
120C2×D11—42no—
121C2×D11—82no—
122C4×C11—42no—
123C4×C11—41no—
124C4×C11#12111yescharacteristic
125C4×C11#12111yescharacteristic
126C4×C11#12311yescharacteristic
127C4×C11#12411yescharacteristic
128Dic11—41no—
129Dic11—41no—
130Dic11—81no—
131C2×#41C2×D1111yescharacteristic
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#117—111no—
141C2×C4⋊C4—111no—
142C2×C22⋊C4—222no—
143C2×C42C2×D1111yescharacteristic
144#107—221no—
145#106—221no—
146#104—22no—
147#103—221no—
148#102—221no—
149#100—222no—
150C2×C11—21no—
151C2×C11—21no—
152C2×C11—81no—
153C2×C11#39411yescharacteristic
154C2×C11#45311yescharacteristic
155C2×C11#45511yescharacteristic
156D11—82no—
157C24—112no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8D4411yescharacteristic
163C2×D4—21no—
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×D4D4411yescharacteristic
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—221no—
176C22×C4C22×D1111yescharacteristic
177M16—21no—
178M16—221no—
179M16—221no—
180M16C22⋊D1112yescomplemented
181C2×C8—21no—
182C2×C8—221no—
183C4⋊C4—111no—
184C4⋊C4—111no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C22⋊C4—222no—
188C22⋊C4—222no—
189C22⋊C4—221no—
190C22⋊C4—444no—
191C42—21no—
192C42—21no—
193C42—221no—
194C11#203711yescharacteristic, complemented, Sylow
195C23—21no—
196C23—222no—
197C23—222no—
198C23—222no—
199C23—442no—
200C23—442no—
201C23D4×D1111yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—441no—
209D4—441no—
210D4—441no—
211D4—441no—
212D4—882no—
213D4—882no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—221no—
221C2×C4—221no—
222C2×C4—442no—
223C2×C4—441no—
224C2×C4C2×D4411yescharacteristic
225C2×C4#433911yescharacteristic
226C2×C4D4×D1111yescharacteristic
227C2×C4#434111yescharacteristic
228C2×C4#434111yescharacteristic
229C2×C4C2×C22⋊D1111yescharacteristic
230C8—22no—
231C8—441no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—444no—
238C22—442no—
239C22—442no—
240C22—442no—
241C22—882no—
242C22#6693511yescharacteristic
243C22#6693611yescharacteristic
244C22#6699111yescharacteristic
245C4—42no—
246C4—41no—
247C4—441no—
248C4—441no—
249C4—881no—
250C4#6693811yescharacteristic
251C4#6693911yescharacteristic
252C4#6698311yescharacteristic
253C4#6699211yescharacteristic
254C2—21no—
255C2—21no—
256C2—81no—
257C2—882no—
258C2#1062243511yescharacteristic
259C2#1062243811yescharacteristic
260C2#1062257411yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#104C2
socleC22×C11#120
prime radical#10623361C2
hypercenterC2×#104D11
hypocenterC11#2037
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C11×#104C2semidirect
3. #10622845C2semidirect
4. C2×#66887C2semidirect
5. #10622734C2semidirect
6. #10622552C2semidirect
7. #10622161C2semidirect
48. C11×M16D4semidirect
104. C2×#104D11semidirect
180. M16C22⋊D11semidirect
194. C11#2037semidirect

Maximal subgroups

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

subgroupindex
#106233612
C2×C11×#1042
#106228452
C2×#668872
#106227342
#106225522
#106221612
#203711