Finite Group Databasebeta

← #13079758

Subgroups — #13079758

Order 1408.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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#10623153C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic
3C11×#483C211yesmaximal, characteristic
4#10622656C211yesmaximal, characteristic
5#10622584C211yesmaximal, characteristic
6#10622468C212yesmaximal, complemented
7#10622467C212yesmaximal, complemented
8#10622405C212yesmaximal, complemented
9#10622404C212yesmaximal, complemented
10#10622334C211yesmaximal, characteristic
11#10622331C211yesmaximal, characteristic
12C22×Dic22—21no—
13C11×C22⋊Q8C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15Q8×Dic11C2211yescharacteristic
16#66997C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18#66977C2211yescharacteristic
19C2×Dic11⋊C4—21no—
20C2×C4×Dic11C2211yescharacteristic
21#66942—21no—
22#66941—21no—
23#66941—21no—
24#66941C2212yes—
25#66941C2211yescharacteristic
26#66941C2212yes—
27#66940—21no—
28#66940C2211yescharacteristic
29#66931—21no—
30#66930—21no—
31C11×#106C2212yes—
32C11×#103C2212yes—
33C11×C22⋊C8C2211yescharacteristic
34#66899C2212yes—
35C22⋊(C11⋊C8)C2211yescharacteristic
36#66881C2212yes—
37#66880C2212yes—
38Dic11⋊C8C2212yes—
39C8×Dic11C2212yes—
40#66874C2212yes—
41#66872C2212yes—
42#66872C2212yes—
43C2×Q8×C11C2311yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2311yescharacteristic
46C22×Dic11—21no—
47C22×Dic11D411yescharacteristic
48C22×Dic11D411yescharacteristic
49C2×Dic22—21no—
50C2×Dic22—22no—
51C2×Dic22—22no—
52C2×Dic22—44no—
53C2×Dic22C2311yescharacteristic
54C2×C8×C11C2312yes—
55C11×C4⋊C4—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4C2311yescharacteristic
58C11×C4⋊C4C2312yes—
59C11×C22⋊C4—21no—
60C22⋊Dic11—21no—
61C4⋊Dic11—21no—
62C4⋊Dic11—21no—
63C4⋊Dic11C2311yescharacteristic
64C4⋊Dic11C2312yes—
65Dic11⋊C4—21no—
66Dic11⋊C4—21no—
67Dic11⋊C4—21no—
68Dic11⋊C4—21no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—21no—
72C4×Dic11—21no—
73C4×Dic11—21no—
74C4×Dic11D411yescharacteristic
75C4×Dic11D411yescharacteristic
76C4×Dic11C2311yescharacteristic
77C4×Dic11C2311yescharacteristic
78C2×C11⋊C8C2312yes—
79#3229—111nomaximal, Sylow
80C23×C11C2×D411yescharacteristic
81Q8×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
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—21no—
92C2×Dic11—22no—
93C2×Dic11—42no—
94C2×Dic11SD1614yes—
95C2×Dic11C2×D411yescharacteristic
96C2×Dic11C2×D411yescharacteristic
97C2×Dic11C2×D411yescharacteristic
98C2×Dic11C2×D411yescharacteristic
99Dic22—22no—
100Dic22—44no—
101Dic22—44no—
102Dic22—42no—
103C8×C11—22no—
104C11⋊C8—22no—
105#533—111no—
106C2×C4⋊Q8—111no—
107#498—112no—
108#487—112no—
109#483—111no—
110#483—111no—
111#483—111no—
112#483D1111yescharacteristic
113#475—112no—
114#475—112no—
115#431—111no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11C2×SD1612yes—
119C22×C11C22×D411yescharacteristic
120C4×C11—21no—
121C4×C11—41no—
122C4×C11—42no—
123C4×C11—41no—
124C4×C112−1+412yes—
125Dic11—21no—
126Dic11—41no—
127Dic11—42no—
128Dic11—41no—
129Dic11C2×SD1612yes—
130Dic11C2×SD1612yes—
131Dic11#13712yes—
132C22×Q8—221no—
133C4⋊Q8—112no—
134C4⋊Q8—112no—
135C4⋊Q8—111no—
136C4⋊Q8—111no—
137C4⋊Q8—221no—
138C4⋊Q8—221no—
139#125—221no—
140C22⋊Q8—111no—
141C22⋊Q8—221no—
142C22⋊Q8C2×D1111yescharacteristic
143C4×Q8—111no—
144C4×Q8—111no—
145C4×Q8—221no—
146#117—221no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C42—111no—
151#106—112no—
152#106—112no—
153#106—112no—
154#106C2×D1112yes—
155C4⋊C8—112no—
156#103—112no—
157#103—112no—
158#103—112no—
159#103C2×D1112yes—
160C22⋊C8—111no—
161C22⋊C8C2×D1111yescharacteristic
162C4×C8—112no—
163C2×C11—22no—
164C2×C11#53611yescharacteristic
165C2×C11C22×SD1611yescharacteristic
166C2×C11C2×#13711yescharacteristic
167C2×Q8—111no—
168C2×Q8—221no—
169C2×Q8—222no—
170C2×Q8—222no—
171C2×Q8—444no—
172C2×Q8C22×D1111yescharacteristic
173C22×C4—21no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—221no—
177C22×C4C22×D1111yescharacteristic
178C2×C8—112no—
179C2×C8C22×D1112yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—112no—
183C4⋊C4—111no—
184C4⋊C4—222no—
185C4⋊C4—222no—
186C4⋊C4—221no—
187C4⋊C4—221no—
188C4⋊C4—221no—
189C4⋊C4—221no—
190C4⋊C4—221no—
191C4⋊C4—221no—
192C4⋊C4—221no—
193C4⋊C4C22×D1112yes—
194C4⋊C4C22×D1111yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—221no—
197C42—111no—
198C42—111no—
199C42—111no—
200C42—111no—
201C42—221no—
202C42—221no—
203C11#322911yescharacteristic, complemented, Sylow
204C23D4×D1111yescharacteristic
205Q8—22no—
206Q8—222no—
207Q8—444no—
208Q8—444no—
209Q8—442no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—114no—
216C2×C4—111no—
217C2×C4—111no—
218C2×C4—111no—
219C2×C4—111no—
220C2×C4—222no—
221C2×C4—221no—
222C2×C4—221no—
223C2×C4—222no—
224C2×C4—442no—
225C2×C4D4×D1111yescharacteristic
226C2×C4C23×D1111yescharacteristic
227C8—22no—
228C8—222no—
229C22—21no—
230C22—21no—
231C22SD16×D1112yes—
232C22C2×D4×D1111yescharacteristic
233C4—21no—
234C4—42no—
235C4—41no—
236C4—41no—
237C4—112no—
238C4—112no—
239C4—112no—
240C4—221no—
241C4—442no—
242C4—441no—
243C4—441no—
244C4#6704312yes—
245C2—22no—
246C2#1062317911yescharacteristic
247C2C2×SD16×D1111yescharacteristic
248C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#483C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#483D11
hypocenterC11#3229
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
6. #10622468C2semidirect
7. #10622467C2semidirect
8. #10622405C2semidirect
9. #10622404C2semidirect
203. C11#3229semidirect

Maximal subgroups

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

subgroupindex
#106231532
C2×#669412
C11×#4832
#106226562
#106225842
#106224682
#106224672
#106224052
#106224042
#106223342
#106223312
#322911