Finite Group Databasebeta

← #13079784

Subgroups — #13079784

Order 1408.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×C11×#125C211yesmaximal, characteristic, complemented
2#10623010C211yesmaximal, characteristic
3#10622681C212yesmaximal, complemented
4#10622679C212yesmaximal, complemented
5#10622677C212yesmaximal, complemented
6#10622676C212yesmaximal, complemented
7#10622584C211yesmaximal, characteristic, complemented
8#10622583C211yesmaximal, characteristic, complemented
9#10622581C211yesmaximal, characteristic
10#10622580C211yesmaximal, characteristic
11#10622538C211yesmaximal, characteristic, complemented
12C11×#125—21no—
13C11×#125—21no—
14C11×#125C2212yes—
15C11×#125C2212yes—
16C2×C11×C4⋊C4—21no—
17C2×C11×C4⋊C4—21no—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C42×C11C2211yescharacteristic
21#66983C2211yescharacteristic
22#66982—21no—
23C4×C22⋊D11—21no—
24#66977C2211yescharacteristic
25#66929—21no—
26#66928C2211yescharacteristic
27C4×D44C2211yescharacteristic
28#66925—21no—
29#66923C2211yescharacteristic
30C4×Dic22C2211yescharacteristic
31C22⋊(C11⋊C8)C2211yescharacteristic
32C22⋊(C11⋊C8)C2211yescharacteristic
33#66874C2212yes—
34#66874C2212yes—
35#66873C2212yes—
36#66873C2212yes—
37#66872C2212yes—
38#66872C2212yes—
39#66871C2212yes—
40#66871C2212yes—
41C4⋊(C11⋊C8)C2212yes—
42C4×C11⋊C8C2212yes—
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11D411yescharacteristic
46C22×C4×C11D411yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—21no—
49C2×D44C2311yescharacteristic
50C2×C4×D11—21no—
51C2×Dic22C2311yescharacteristic
52C11×C4⋊C4—22no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2312yes—
59C11×C4⋊C4C2312yes—
60C42×C11D411yescharacteristic
61C42×C11D411yescharacteristic
62C42×C11C2311yescharacteristic
63C42×C11C2311yescharacteristic
64C22⋊Dic11—21no—
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4—21no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—21no—
69C4⋊Dic11C2311yescharacteristic
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75C4×Dic11—21no—
76C2×C11⋊C8C2312yes—
77C2×C11⋊C8C2312yes—
78#3232—111nomaximal, Sylow
79C23×C11C2×D411yescharacteristic
80C22×D11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—41no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2411yescharacteristic
94C22⋊D11—42no—
95C2×Dic11—21no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98D44—22no—
99C4×D11—42no—
100Dic22—22no—
101C11⋊C8—22no—
102C11⋊C8—22no—
103#529—111no—
104C2×#125D1111yescharacteristic, complemented
105#499—112no—
106#488—112no—
107#484—111no—
108#483—111no—
109#481—111no—
110#480—111no—
111#479—112no—
112#478—112no—
113#431—111no—
114C22×C11—21no—
115C22×C11—21no—
116C22×C11#13512yes—
117C22×C11C22×D411yescharacteristic
118C2×D11—41no—
119C2×D11—41no—
120C2×D11—41no—
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—42no—
127C4×C11—42no—
128C4×C112−1+412yes—
129Dic11—41no—
130Dic11—41no—
131Dic11—41no—
132#126—221no—
133#125—21no—
134#125—21no—
135#125—111no—
136#125C2×D1112yes—
137#125C2×D1112yes—
138#124—111no—
139#123—221no—
140C22⋊Q8—111no—
141#121—111no—
142C4×Q8—111no—
143C4×D4—111no—
144C4×D4—221no—
145#117—221no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C42C2×D1111yescharacteristic
151#107—112no—
152#107—112no—
153#106—112no—
154#106—112no—
155C4⋊C8—112no—
156#103—112no—
157#103—112no—
158#102—112no—
159#102—112no—
160C22⋊C8—111no—
161C22⋊C8—111no—
162C4×C8—112no—
163C2×C11—22no—
164C2×C11#53611yescharacteristic
165C2×C11C2×#13511yescharacteristic
166C2×C11#57511yescharacteristic
167D11—81no—
168C2×Q8—111no—
169C2×D4—111no—
170C2×D4—221no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—221no—
174C22×C4C22⋊D1111yescharacteristic
175C22×C4C22⋊D1111yescharacteristic
176C22×C4C22×D1111yescharacteristic
177C2×C8—112no—
178C2×C8—112no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—111no—
186C4⋊C4—111no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4C22×D1112yes—
192C4⋊C4C22×D1112yes—
193C22⋊C4—221no—
194C22⋊C4—221no—
195C22⋊C4—221no—
196C22⋊C4—221no—
197C22⋊C4—221no—
198C42—221no—
199C42C22⋊D1111yescharacteristic
200C42C22⋊D1111yescharacteristic
201C42C22×D1111yescharacteristic
202C42C22×D1111yescharacteristic
203C11#323211yescharacteristic, complemented, Sylow
204C23—221no—
205C23C2×C22⋊D1111yescharacteristic
206Q8—222no—
207D4—222no—
208D4—442no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—221no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—442no—
220C2×C4C2×C22⋊D1111yescharacteristic
221C2×C4C2×C22⋊D1111yescharacteristic
222C2×C4C2×C22⋊D1111yescharacteristic
223C2×C4C2×C22⋊D1111yescharacteristic
224C2×C4C2×C22⋊D1111yescharacteristic
225C2×C4C23×D1111yescharacteristic
226C8—222no—
227C8—222no—
228C22—21no—
229C22—21no—
230C22—441no—
231C22—441no—
232C22—441no—
233C22#6700312yes—
234C22C22×C22⋊D1111yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—441no—
243C4—441no—
244C4—441no—
245C4#6704012yes—
246C2—22no—
247C2—881no—
248C2#1062334711yescharacteristic
249C2C2×#6700311yescharacteristic
250C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC2×C11×#125C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenterC2×#125D11
hypocenterC11#3232
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C11×#125C2semidirect
3. #10622681C2semidirect
4. #10622679C2semidirect
5. #10622677C2semidirect
6. #10622676C2semidirect
7. #10622584C2semidirect
8. #10622583C2semidirect
11. #10622538C2semidirect
104. C2×#125D11semidirect
203. C11#3232semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
#106230102
#106226812
#106226792
#106226772
#106226762
#106225842
#106225832
#106225812
#106225802
#106225382
#323211