Finite Group Databasebeta

← #13078585

Subgroups — #13078585

Order 1408.

386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 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
2#10623356C211yesmaximal, characteristic
3#10622847C211yesmaximal, characteristic
4#10622617C211yesmaximal, characteristic, complemented
5#10622611C211yesmaximal, characteristic, complemented
6#10622609C212yesmaximal, complemented
7#10622609C212yesmaximal, complemented
8#10622584C212yesmaximal, complemented
9#10622583C212yesmaximal, complemented
10C2×#66874C211yesmaximal, characteristic, complemented
11#10622577C211yesmaximal, characteristic, complemented
12C2×C11×#41C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C4×Q8×C11—21no—
15C4×D4×C11—22no—
16C4×D4×C11—21no—
17C11×#117C2212yes—
18C11×#117C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2212yes—
21#66997—21no—
22#66989—21no—
23#66988—22no—
24#66979C2211yescharacteristic
25#66977C2212yes—
26#66977C2212yes—
27C2×#4318C2211yescharacteristic
28C22×C11⋊C8C2211yescharacteristic
29C22⋊(C11⋊C8)C2212yes—
30C22⋊(C11⋊C8)C2212yes—
31#66874C2212yes—
32#66874C2212yes—
33#66874C2212yes—
34#66874C2212yes—
35#66872C2212yes—
36#66872C2211yescharacteristic
37#66872C2211yescharacteristic
38#66871C2212yes—
39#66871C2211yescharacteristic
40#66871C2211yescharacteristic
41C11×#41—22no—
42C11×#41—22no—
43C2×Q8×C11D411yescharacteristic
44C2×D4×C11D412yes—
45C2×D4×C11D411yescharacteristic
46C22×C4×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11C2312yes—
49C22×C4×C11C2311yescharacteristic
50C22×Dic11—21no—
51C2×Dic22—21no—
52C2×Dic22—22no—
53C2×Dic22—22no—
54C2×Dic22C2312yes—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2312yes—
58C11×C4⋊C4C2311yescharacteristic
59C11×C4⋊C4C2311yescharacteristic
60C11×C22⋊C4—22no—
61C11×C22⋊C4—21no—
62C42×C11—22no—
63C42×C11—21no—
64C22⋊Dic11—22no—
65C22⋊Dic11—22no—
66C22⋊Dic11—21no—
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2311yescharacteristic
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71C4×Dic11—21no—
72#4318—22no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2312yes—
76C2×C11⋊C8C2311yescharacteristic
77#3097—111nomaximal, Sylow
78C23×C11C2×D412yes—
79C23×C11C2×D411yescharacteristic
80Q8×C11—22no—
81D4×C11—24no—
82D4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—81no—
89C2×C4×C11—82no—
90C2×C4×C11C2×D412yes—
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11#4112yes—
93C2×C4×C11#4112yes—
94C2×C4×C11C2411yescharacteristic
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—22no—
98C2×Dic11—42no—
99Dic22—22no—
100Dic22—22no—
101Dic22—42no—
102C11⋊C8—21no—
103C11⋊C8—21no—
104C11⋊C8—22no—
105#536—111no—
106#520D1111yescharacteristic
107#485—112no—
108#485—112no—
109#484—112no—
110#483—112no—
111#428—111no—
112#427—111no—
113#419—111no—
114C2×#103—111no—
115#408—111no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11#12312yes—
122C22×C11C22×D411yescharacteristic
123C4×C11—22no—
124C4×C11—42no—
125C4×C11—41no—
126C4×C11—41no—
127C4×C11#12312yes—
128C4×C11C2×#4111yescharacteristic
129C4×C11C2×#4111yescharacteristic
130Dic11—42no—
131Dic11—41no—
132Dic11—41no—
133C2×#41C2×D1111yescharacteristic
134C22×Q8—111no—
135C2×M16—111no—
136C22×C8—111no—
137C4⋊Q8—221no—
138#124—221no—
139#123—222no—
140C22⋊Q8—112no—
141C22⋊Q8—112no—
142C4×Q8—21no—
143C4×D4—22no—
144C4×D4—21no—
145#117—111no—
146#117C2×D1111yescharacteristic
147#117C2×D1112yes—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C4⋊C4C2×D1112yes—
150#107—111no—
151#107—111no—
152#107—112no—
153#106—111no—
154#106—111no—
155#106—112no—
156#103—112no—
157#103—112no—
158#103—112no—
159#103—112no—
160C22⋊C8—112no—
161C22⋊C8—112no—
162C2×C11—22no—
163C2×C11—42no—
164C2×C11C2×#12311yescharacteristic
165C2×C11#57711yescharacteristic
166C2×C11#57811yescharacteristic
167#41—22no—
168#41—22no—
169C2×Q8—112no—
170C2×Q8—221no—
171C2×Q8—222no—
172C2×Q8—222no—
173C2×Q8C22⋊D1111yescharacteristic
174C2×D4C22⋊D1112yes—
175C2×D4C22⋊D1111yescharacteristic
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—221no—
179C22×C4C22×D1112yes—
180C22×C4C22×D1111yescharacteristic
181M16—222no—
182C2×C8—111no—
183C2×C8—112no—
184C2×C8—111no—
185C2×C8—222no—
186C4⋊C4—22no—
187C4⋊C4—21no—
188C4⋊C4—111no—
189C4⋊C4—111no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4C22×D1112yes—
193C4⋊C4C22×D1111yescharacteristic
194C4⋊C4C22×D1111yescharacteristic
195C22⋊C4—22no—
196C22⋊C4—21no—
197C22⋊C4—221no—
198C22⋊C4—222no—
199C22⋊C4—222no—
200C42—22no—
201C42—21no—
202C42—221no—
203C11#309711yescharacteristic, complemented, Sylow
204C23C2×C22⋊D1112yes—
205C23C2×C22⋊D1111yescharacteristic
206Q8—22no—
207Q8—222no—
208Q8—222no—
209Q8—442no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—81no—
218C2×C4—82no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—222no—
222C2×C4—442no—
223C2×C4#433912yes—
224C2×C4#433912yes—
225C2×C4C2×C22⋊D1112yes—
226C2×C4C2×C22⋊D1111yescharacteristic
227C2×C4C23×D1111yescharacteristic
228C8—221no—
229C8—221no—
230C8—222no—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22#6698212yes—
237C22C22×C22⋊D1111yescharacteristic
238C4—22no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—442no—
243C4—441no—
244C4—441no—
245C4#6698212yes—
246C4C2×#433911yescharacteristic
247C4C2×#433911yescharacteristic
248C2—22no—
249C2—42no—
250C2C2×#6698211yescharacteristic
251C2#1062336711yescharacteristic
252C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#520C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#520D11
hypocenterC11#3097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
4. #10622617C2semidirect
5. #10622611C2semidirect
6. #10622609C2semidirect
7. #10622609C2semidirect
8. #10622584C2semidirect
9. #10622583C2semidirect
10. C2×#66874C2semidirect
11. #10622577C2semidirect
203. C11#3097semidirect

Maximal subgroups

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

subgroupindex
C11×#5202
#106233562
#106228472
#106226172
#106226112
#106226092
#106225842
#106225832
C2×#668742
#106225772
#309711