Finite Group Databasebeta

← #13069839

Subgroups — #13069839

Order 1408.

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

normal subgroups only

This group has 306 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#10623364C211yesmaximal, characteristic
2C2×C11×#104C211yesmaximal, characteristic, complemented
3#10622845C211yesmaximal, characteristic, complemented
4#10622746C211yesmaximal, characteristic, complemented
5#10622548C211yesmaximal, characteristic, complemented
6C2×#66869C211yesmaximal, characteristic, complemented
7#10622192C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C2×#4339C2211yescharacteristic
10C2×C11×M16C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12#66999—21no—
13#66992—22no—
14#66991—21no—
15#66983—21no—
16C2×C4⋊Dic11—22no—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19#66977—21no—
20C2×#4318C2211yescharacteristic
21C11×#104—22no—
22#66899—21no—
23#66896—21no—
24#66885—21no—
25#66880—21no—
26#66869—22no—
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—
51C42×C11—21no—
52C42×C11D412yescomplemented
53C22⋊Dic11—22no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11—44no—
60Dic11⋊C4—22no—
61#4318—21no—
62#4318—21no—
63C2×C11⋊C8—21no—
64#2039—111nomaximal, Sylow
65C23×C11—21no—
66C23×C11C2×D411yescharacteristic
67C22×D11—21no—
68Q8×C11—21no—
69Q8×C11—21no—
70D4×C11—21no—
71D4×C11—21no—
72D4×C11—41no—
73D4×C11—41no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C2×C4×C11#4111yescharacteristic
85C2×C4×C11#4111yescharacteristic
86C22⋊D11—41no—
87C22⋊D11—41no—
88C22⋊D11—82no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11—42no—
92C2×Dic11—42no—
93C2×Dic11—41no—
94D44—21no—
95D44—21no—
96C4×D11—41no—
97C4×D11—41no—
98Dic22—21no—
99Dic22—21no—
100C8×C11—41no—
101C11⋊C8—41no—
102#537—111no—
103C2×#104—111no—
104C2×#104D1111yescharacteristic, complemented
105#417—111no—
106#417—111no—
107#384—111no—
108#343—111no—
109C22×C11—21no—
110C22×C11—21no—
111C22×C11—41no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11#12011yescharacteristic
115C22×C11#12111yescharacteristic
116C22×C11#12411yescharacteristic
117C2×D11—41no—
118C2×D11—41no—
119C2×D11—41no—
120C4×C11—24no—
121C4×C11—41no—
122C4×C11#12111yescharacteristic
123C4×C11#12111yescharacteristic
124C4×C11#12311yescharacteristic
125C4×C11#12311yescharacteristic
126Dic11—41no—
127Dic11—42no—
128Dic11—81no—
129C2×#41—111no—
130C2×#41C2×D1111yescharacteristic
131C2×M16—111no—
132C2×M16C2×D1111yescharacteristic
133C22⋊Q8—221no—
134C22⋊Q8—221no—
135#121—221no—
136#121—222no—
137#121—221no—
138C2×C4⋊C4—111no—
139C2×C4⋊C4—111no—
140C2×C4⋊C4—222no—
141C2×C42C2×D1111yescharacteristic
142#104—22no—
143#104—222no—
144#103—221no—
145#103—221no—
146#102—221no—
147#102—221no—
148C2×C11—21no—
149C2×C11—21no—
150C2×C11—81no—
151C2×C11#39411yescharacteristic
152C2×C11#45311yescharacteristic
153C2×C11#45611yescharacteristic
154D11—81no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—221no—
160#41—221no—
161#41—221no—
162#41—221no—
163C2×Q8—111no—
164C2×Q8D4411yescharacteristic
165C2×D4—21no—
166C2×D4—111no—
167C2×D4—221no—
168C2×D4—222no—
169C2×D4D4411yescharacteristic
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—112no—
173C22×C4—221no—
174C22×C4—221no—
175C22×C4C22×D1111yescharacteristic
176M16—21no—
177M16—21no—
178M16—221no—
179M16—221no—
180C2×C8—21no—
181C2×C8—221no—
182C4⋊C4—222no—
183C4⋊C4—221no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C4⋊C4—444no—
188C22⋊C4—222no—
189C22⋊C4—222no—
190C42—21no—
191C42C22⋊D1112yescomplemented
192C11#203911yescharacteristic, complemented, Sylow
193C23—21no—
194C23—221no—
195C23D4×D1111yescharacteristic
196Q8—21no—
197Q8—21no—
198Q8—221no—
199Q8—221no—
200D4—21no—
201D4—21no—
202D4—41no—
203D4—41no—
204D4—221no—
205D4—221no—
206D4—441no—
207D4—441no—
208D4—882no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—222no—
216C2×C4—221no—
217C2×C4—441no—
218C2×C4—441no—
219C2×C4—442no—
220C2×C4—442no—
221C2×C4—441no—
222C2×C4C2×D4411yescharacteristic
223C2×C4#433911yescharacteristic
224C2×C4D4×D1111yescharacteristic
225C2×C4#434111yescharacteristic
226C2×C4#434111yescharacteristic
227C2×C4C2×C22⋊D1111yescharacteristic
228C8—41no—
229C8—441no—
230C22—21no—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—441no—
236C22—441no—
237C22—441no—
238C22#6693511yescharacteristic
239C22#6693811yescharacteristic
240C22#6699211yescharacteristic
241C4—24no—
242C4—41no—
243C4—441no—
244C4—442no—
245C4—881no—
246C4#6693611yescharacteristic
247C4#6693911yescharacteristic
248C4#6698311yescharacteristic
249C4#6699111yescharacteristic
250C2—21no—
251C2—21no—
252C2—81no—
253C2—881no—
254C2#1062243511yescharacteristic
255C2#1062243911yescharacteristic
256C2#1062257411yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#104C2
socleC22×C11#120
prime radical#10623364C2
hypercenterC2×#104D11
hypocenterC11#2039
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. #10622746C2semidirect
5. #10622548C2semidirect
6. C2×#66869C2semidirect
7. #10622192C2semidirect
52. C42×C11D4semidirect
104. C2×#104D11semidirect
191. C42C22⋊D11semidirect
192. C11#2039semidirect

Maximal subgroups

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

subgroupindex
#106233642
C2×C11×#1042
#106228452
#106227462
#106225482
C2×#668692
#106221922
#203911