Finite Group Databasebeta

← #13069843

Subgroups — #13069843

Order 1408.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#10623364C211yesmaximal, characteristic
2C11×#417C211yesmaximal, characteristic, complemented
3C2×#66901C211yesmaximal, characteristic, complemented
4C2×#66889C211yesmaximal, characteristic, complemented
5#10622590C211yesmaximal, characteristic, complemented
6#10622579C211yesmaximal, characteristic, complemented
7#10622192C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12#66999—21no—
13#66992—22no—
14#66991—21no—
15#66983—21no—
16C2×C4⋊Dic11C2211yescharacteristic
17#66977—21no—
18C2×C4×Dic11C2211yescharacteristic
19C2×#4318C2211yescharacteristic
20C11×#103—21no—
21C11×#102—21no—
22#66901—22no—
23C11⋊#95—22no—
24#66889—22no—
25#66874—21no—
26#66873—21no—
27C11×#41—21no—
28C11×#41—21no—
29C11×#41—21no—
30C11×#41—21no—
31C2×Q8×C11D411yescharacteristic
32C2×D4×C11—21no—
33C2×D4×C11D411yescharacteristic
34C22×C4×C11—21no—
35C22×C4×C11—21no—
36C22×C4×C11C2311yescharacteristic
37C2×C22⋊D11—22no—
38C2×C22⋊D11—21no—
39C22×Dic11—21no—
40C22×Dic11D412yes—
41#4339—21no—
42#4339—21no—
43#4339—21no—
44#4339—21no—
45C2×D44D411yescharacteristic
46C2×C4×D11—21no—
47C2×Dic22D411yescharacteristic
48C11×M16—21no—
49C11×M16—21no—
50C2×C8×C11—21no—
51C11×C4⋊C4—21no—
52C11×C4⋊C4—21no—
53C22⋊Dic11—22no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57Dic11⋊C4—22no—
58C4×Dic11—21no—
59C4×Dic11D412yescomplemented
60#4318—21no—
61#4318—21no—
62C2×C11⋊C8—21no—
63#2040—111nomaximal, Sylow
64C23×C11—21no—
65C23×C11C2×D411yescharacteristic
66C22×D11—21no—
67Q8×C11—21no—
68Q8×C11—21no—
69D4×C11—21no—
70D4×C11—21no—
71D4×C11—41no—
72D4×C11—41no—
73C2×C4×C11—21no—
74C2×C4×C11—41no—
75C2×C4×C11—41no—
76C2×C4×C11—42no—
77C2×C4×C11—41no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11#4111yescharacteristic
82C2×C4×C11#4111yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C22⋊D11—41no—
85C22⋊D11—41no—
86C22⋊D11—82no—
87C2×Dic11—21no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—41no—
91C2×Dic11—41no—
92C2×Dic11—42no—
93D44—21no—
94D44—21no—
95C4×D11—41no—
96C4×D11—41no—
97Dic22—21no—
98Dic22—21no—
99C8×C11—41no—
100C11⋊C8—41no—
101#537—111no—
102C2×#104—111no—
103C2×#104—111no—
104#417—111no—
105#417D1111yescharacteristic, complemented
106#382—111no—
107#343—111no—
108C22×C11—21no—
109C22×C11—21no—
110C22×C11—41no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11#12011yescharacteristic
114C22×C11#12111yescharacteristic
115C22×C11#12411yescharacteristic
116C2×D11—41no—
117C2×D11—41no—
118C2×D11—41no—
119C4×C11—41no—
120C4×C11—81no—
121C4×C11#12111yescharacteristic
122C4×C11#12111yescharacteristic
123C4×C11#12311yescharacteristic
124C4×C11#12311yescharacteristic
125Dic11—42no—
126Dic11—41no—
127Dic11—42no—
128C2×#41—111no—
129C2×#41C2×D1111yescharacteristic
130C2×M16—111no—
131C2×M16C2×D1111yescharacteristic
132C22⋊Q8—221no—
133C22⋊Q8—221no—
134#121—221no—
135#121—222no—
136#121—221no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4C2×D1111yescharacteristic
139C2×C42—111no—
140#104—222no—
141#104—222no—
142#103—21no—
143#103—221no—
144#102—21no—
145#102—221no—
146#95—222no—
147C2×C11—21no—
148C2×C11—21no—
149C2×C11—81no—
150C2×C11#39411yescharacteristic
151C2×C11#45411yescharacteristic
152C2×C11#45511yescharacteristic
153D11—81no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—221no—
159#41—221no—
160#41—221no—
161#41—221no—
162C2×Q8—111no—
163C2×Q8C22⋊D1111yescharacteristic
164C2×D4—21no—
165C2×D4—111no—
166C2×D4—221no—
167C2×D4—222no—
168C2×D4C22⋊D1111yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—112no—
172C22×C4—221no—
173C22×C4—221no—
174C22×C4C22×D1111yescharacteristic
175M16—21no—
176M16—21no—
177M16—221no—
178M16—221no—
179C2×C8—21no—
180C2×C8—221no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C22⋊C4—222no—
187C22⋊C4—222no—
188C42—112no—
189C42—221no—
190C11#204011yescharacteristic, complemented, Sylow
191C23—21no—
192C23—221no—
193C23D4×D1111yescharacteristic
194Q8—21no—
195Q8—21no—
196Q8—221no—
197Q8—221no—
198D4—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—221no—
203D4—221no—
204D4—441no—
205D4—441no—
206D4—882no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—442no—
220C2×C4#433911yescharacteristic
221C2×C4#433911yescharacteristic
222C2×C4D4×D1111yescharacteristic
223C2×C4D4×D1111yescharacteristic
224C2×C4#434111yescharacteristic
225C2×C4C2×C22⋊D1111yescharacteristic
226C8—41no—
227C8—441no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—441no—
234C22—441no—
235C22—441no—
236C22#6693711yescharacteristic
237C22#6693811yescharacteristic
238C22#6699011yescharacteristic
239C4—41no—
240C4—81no—
241C4—442no—
242C4—442no—
243C4—441no—
244C4#6693611yescharacteristic
245C4#6693711yescharacteristic
246C4#6698211yescharacteristic
247C4#6699211yescharacteristic
248C2—21no—
249C2—21no—
250C2—81no—
251C2—881no—
252C2#1062257211yescharacteristic
253C2#1062281411yescharacteristic
254C2#1062281511yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#417C2
socleC22×C11#120
prime radical#10623364C2
hypercenter#417D11
hypocenterC11#2040
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C11×#417C2semidirect
3. C2×#66901C2semidirect
4. C2×#66889C2semidirect
5. #10622590C2semidirect
6. #10622579C2semidirect
7. #10622192C2semidirect
59. C4×Dic11D4semidirect
105. #417D11semidirect
190. C11#2040semidirect

Maximal subgroups

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

subgroupindex
#106233642
C11×#4172
C2×#669012
C2×#668892
#106225902
#106225792
#106221922
#204011