Finite Group Databasebeta

← #13079783

Subgroups — #13079783

Order 1408.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623131C211yesmaximal, characteristic
2C2×#66943C211yesmaximal, characteristic, complemented
3C11×#481C211yesmaximal, characteristic
4#10622646C211yesmaximal, characteristic
5#10622583C211yesmaximal, characteristic, complemented
6#10622471C212yesmaximal, complemented
7#10622470C212yesmaximal, complemented
8#10622381C212yesmaximal, complemented
9#10622376C212yesmaximal, complemented
10#10622334C211yesmaximal, characteristic, complemented
11#10622331C211yesmaximal, characteristic, complemented
12C11×#121C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14#66989C2211yescharacteristic
15#66988—21no—
16D4×Dic11—21no—
17D4×Dic11C2211yescharacteristic
18C2×C4⋊Dic11—21no—
19C2×C4⋊Dic11C2211yescharacteristic
20#66977C2211yescharacteristic
21C2×Dic11⋊C4—21no—
22C2×C4×Dic11C2211yescharacteristic
23#66943—21no—
24#66943—21no—
25#66943C2212yes—
26#66943C2211yescharacteristic
27#66943C2212yes—
28#66940C2211yescharacteristic
29#66932—21no—
30#66930—21no—
31C11×#106C2212yes—
32C11×#102C2212yes—
33C11×C22⋊C8C2211yescharacteristic
34#66896C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36#66881C2212yes—
37#66880C2212yes—
38Dic11⋊C8C2212yes—
39C8×Dic11C2212yes—
40#66874C2212yes—
41#66871C2212yes—
42#66871C2212yes—
43C2×D4×C11—21no—
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—21no—
48C22×Dic11—21no—
49C22×Dic11D411yescharacteristic
50C22×Dic11D411yescharacteristic
51C2×Dic22C2311yescharacteristic
52C2×C8×C11C2312yes—
53C11×C4⋊C4—21no—
54C11×C4⋊C4C2311yescharacteristic
55C11×C4⋊C4C2312yes—
56C11×C22⋊C4—21no—
57C22⋊Dic11—21no—
58C22⋊Dic11—21no—
59C22⋊Dic11—21no—
60C22⋊Dic11—21no—
61C4⋊Dic11—21no—
62C4⋊Dic11—22no—
63C4⋊Dic11—22no—
64C4⋊Dic11—21no—
65C4⋊Dic11C2311yescharacteristic
66C4⋊Dic11C2312yes—
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—21no—
72C4×Dic11—21no—
73C4×Dic11D411yescharacteristic
74C4×Dic11D411yescharacteristic
75C4×Dic11C2311yescharacteristic
76C4×Dic11C2311yescharacteristic
77C2×C11⋊C8C2312yes—
78#3232—111nomaximal, Sylow
79C23×C11—21no—
80C23×C11C2×D411yescharacteristic
81D4×C11—22no—
82D4×C11—42no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—42no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—22no—
90C2×Dic11—21no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11—41no—
94C2×Dic11—42no—
95C2×Dic11—42no—
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99C2×Dic11C2×D411yescharacteristic
100Dic22—22no—
101C8×C11—22no—
102C11⋊C8—22no—
103#529—111no—
104C2×#125—111no—
105#499—112no—
106#488—112no—
107#484—111no—
108#483—111no—
109#481D1111yescharacteristic
110#480—111no—
111#479—112no—
112#478—112no—
113#431—111no—
114C22×C11—21no—
115C22×C11—21no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11#13512yes—
120C22×C11C22×D411yescharacteristic
121C4×C11—21no—
122C4×C11—41no—
123C4×C11—42no—
124C4×C112−1+412yes—
125Dic11—21no—
126Dic11—21no—
127Dic11—21no—
128Dic11—21no—
129Dic11—41no—
130Dic11—42no—
131Dic11—41no—
132#126—221no—
133#125—112no—
134#125—112no—
135#125—111no—
136#125—221no—
137#125—221no—
138#124—111no—
139#123—221no—
140C22⋊Q8—111no—
141#121C2×D1111yescharacteristic
142C4×Q8—111no—
143C4×D4—111no—
144C4×D4—221no—
145#117—221no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—221no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C42—111no—
151#107—112no—
152#107—112no—
153#106—112no—
154#106C2×D1112yes—
155C4⋊C8—112no—
156#103—112no—
157#103—112no—
158#102—112no—
159#102C2×D1112yes—
160C22⋊C8—111no—
161C22⋊C8C2×D1111yescharacteristic
162C4×C8—112no—
163C2×C11—22no—
164C2×C11—81no—
165C2×C11#53611yescharacteristic
166C2×C11C2×#13511yescharacteristic
167C2×C11#57511yescharacteristic
168C2×Q8—111no—
169C2×D4—21no—
170C2×D4C22×D1111yescharacteristic
171C22×C4—21no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—221no—
175C22×C4—221no—
176C22×C4C22×D1111yescharacteristic
177C2×C8—112no—
178C2×C8C22×D1112yes—
179C4⋊C4—21no—
180C4⋊C4—112no—
181C4⋊C4—111no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4C22×D1112yes—
192C4⋊C4C22×D1111yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—221no—
195C22⋊C4—221no—
196C22⋊C4—221no—
197C22⋊C4—221no—
198C42—111no—
199C42—111no—
200C42—111no—
201C42—111no—
202C42—221no—
203C11#323211yescharacteristic, complemented, Sylow
204C23—21no—
205C23D4×D1111yescharacteristic
206Q8—222no—
207D4—22no—
208D4—42no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—111no—
214C2×C4—111no—
215C2×C4—111no—
216C2×C4—111no—
217C2×C4—222no—
218C2×C4—221no—
219C2×C4—221no—
220C2×C4—222no—
221C2×C4—441no—
222C2×C4—442no—
223C2×C4—442no—
224C2×C4D4×D1111yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—22no—
227C8—222no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22#6696912yes—
234C22C2×D4×D1111yescharacteristic
235C4—21no—
236C4—41no—
237C4—42no—
238C4—221no—
239C4—221no—
240C4—221no—
241C4—221no—
242C4—442no—
243C4—441no—
244C4—441no—
245C4#6704312yes—
246C2—22no—
247C2—81no—
248C2#1062317911yescharacteristic
249C2C2×#6696911yescharacteristic
250C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#481C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#481D11
hypocenterC11#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#66943C2semidirect
5. #10622583C2semidirect
6. #10622471C2semidirect
7. #10622470C2semidirect
8. #10622381C2semidirect
9. #10622376C2semidirect
10. #10622334C2semidirect
11. #10622331C2semidirect
203. C11#3232semidirect

Maximal subgroups

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

subgroupindex
#106231312
C2×#669432
C11×#4812
#106226462
#106225832
#106224712
#106224702
#106223812
#106223762
#106223342
#106223312
#323211