Finite Group Databasebeta

← #13081029

Subgroups — #13081029

Order 1408.

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

normal subgroups only

This group has 352 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
1C11×#555C211yesmaximal, characteristic
2#10623073C211yesmaximal, characteristic, complemented
3#10622704C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5#10622654C212yesmaximal, complemented
6#10622648C212yesmaximal, complemented
7C4×#4324C211yesmaximal, characteristic, complemented
8D4×C11⋊C8C211yesmaximal, characteristic, complemented
9#10622620C211yesmaximal, characteristic, complemented
10#10622611C212yesmaximal, complemented
11#10622609C212yesmaximal, complemented
12C11×C4⋊Q8C2211yescharacteristic
13C11×#124—22no—
14C11×#121—21no—
15C11×#121C2212yes—
16C4×D4×C11C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18C11×#117—21no—
19C11×#117C2212yes—
20#66989—21no—
21C2×#4324C2211yescharacteristic
22#66979C2212yes—
23#66977C2212yes—
24C22×C11⋊C8C2212yes—
25#66940—21no—
26#66932—22no—
27#66922C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29#66896C2212yes—
30#66896C2211yescharacteristic
31C22⋊(C11⋊C8)C2212yes—
32#66874C2211yescharacteristic
33#66874C2212yes—
34#66872C2212yes—
35#66872C2211yescharacteristic
36#66872C2212yes—
37#66871C2212yes—
38#66871C2212yes—
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11—22no—
43C2×D4×C11D411yescharacteristic
44C2×D4×C11C2311yescharacteristic
45C22×C4×C11—21no—
46C22×C4×C11C2312yes—
47C2×Dic22—21no—
48C2×Dic22C2311yescharacteristic
49C11×C4⋊C4—21no—
50C11×C4⋊C4D411yescharacteristic
51C11×C4⋊C4C2311yescharacteristic
52C11×C4⋊C4C2312yes—
53C11×C22⋊C4—22no—
54C11×C22⋊C4—22no—
55C11×C22⋊C4—21no—
56C11×C22⋊C4D412yes—
57C42×C11—22no—
58C42×C11C2311yescharacteristic
59C22⋊Dic11—22no—
60C22⋊Dic11—22no—
61#4324—22no—
62C4⋊Dic11—21no—
63C4⋊Dic11C2311yescharacteristic
64C4⋊Dic11C2312yes—
65Dic11⋊C4—21no—
66Dic11⋊C4—22no—
67C4×Dic11—21no—
68C4×Dic11—22no—
69C2×C11⋊C8—24no—
70C2×C11⋊C8C2311yescharacteristic
71C2×C11⋊C8C2312yes—
72C2×C11⋊C8C2311yescharacteristic
73#3340—111nomaximal, Sylow
74C23×C11—21no—
75C23×C11C2×D412yes—
76Q8×C11—81no—
77D4×C11—22no—
78D4×C11—21no—
79D4×C11—21no—
80D4×C11—82no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—42no—
86C2×C4×C11C2×D412yes—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93Dic22—21no—
94Dic22—21no—
95Dic22—42no—
96C11⋊C8—22no—
97C11⋊C8—21no—
98C11⋊C8#4112yes—
99#556—111no—
100#555D1111yescharacteristic
101#498—111no—
102#485—112no—
103#482—112no—
104#477—111no—
105#474—111no—
106#465—112no—
107C4×SD16—111no—
108C8×D4—111no—
109#427—112no—
110C22×C11—22no—
111C22×C11—22no—
112C22×C11—22no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11—41no—
116C22×C11C22×D411yescharacteristic
117C4×C11—22no—
118C4×C11—21no—
119C4×C11—41no—
120C4×C11—42no—
121C4×C11#13512yes—
122C4×C11C2×#4111yescharacteristic
123C4×C112−1+411yescharacteristic
124Dic11—41no—
125Dic11—42no—
126Dic11—41no—
127C2×SD16—111no—
128C22×C8—112no—
129C4⋊Q8—111no—
130C4⋊Q8C2×D1111yescharacteristic
131#126—222no—
132#124—22no—
133#124—221no—
134C22⋊Q8—112no—
135#121—21no—
136#121C2×D1112yes—
137C4×Q8—111no—
138C4×Q8—221no—
139C4×D4C2×D1111yescharacteristic
140C4×D4C2×D1111yescharacteristic
141#117—21no—
142#117—112no—
143#117C2×D1112yes—
144#107—112no—
145#107—112no—
146#106—111no—
147#106—112no—
148#106—112no—
149C4⋊C8—111no—
150#103—111no—
151#103—112no—
152#102—111no—
153#102—112no—
154C22⋊C8—112no—
155C4×C8—111no—
156C2×C11—42no—
157C2×C11—81no—
158C2×C11#54711yescharacteristic
159C2×C11C2×#13511yescharacteristic
160C2×C11#57711yescharacteristic
161C2×Q8—21no—
162C2×Q8—111no—
163C2×Q8—221no—
164C2×D4—22no—
165C2×D4C22⋊D1111yescharacteristic
166C2×D4C22×D1111yescharacteristic
167C22×C4—21no—
168C22×C4C22×D1112yes—
169SD16—222no—
170C2×C8—111no—
171C2×C8—111no—
172C2×C8—112no—
173C2×C8—224no—
174C4⋊C4—21no—
175C4⋊C4—112no—
176C4⋊C4—111no—
177C4⋊C4—221no—
178C4⋊C4—222no—
179C4⋊C4—221no—
180C4⋊C4C22⋊D1111yescharacteristic
181C4⋊C4C22×D1112yes—
182C4⋊C4C22×D1111yescharacteristic
183C22⋊C4—22no—
184C22⋊C4—22no—
185C22⋊C4—21no—
186C22⋊C4—222no—
187C22⋊C4—222no—
188C22⋊C4C22⋊D1112yes—
189C42—22no—
190C42—222no—
191C42—221no—
192C42C22×D1111yescharacteristic
193C11#334011yescharacteristic, complemented, Sylow
194C23—21no—
195C23C2×C22⋊D1112yes—
196Q8—81no—
197Q8—221no—
198Q8—221no—
199Q8—442no—
200D4—22no—
201D4—21no—
202D4—21no—
203D4—82no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—221no—
210C2×C4—222no—
211C2×C4—221no—
212C2×C4C2×C22⋊D1112yes—
213C2×C4C2×C22⋊D1111yescharacteristic
214C2×C4C2×C22⋊D1111yescharacteristic
215C2×C4C23×D1111yescharacteristic
216C8—112no—
217C8—222no—
218C8—221no—
219C22—22no—
220C22—22no—
221C22—22no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22C22×C22⋊D1111yescharacteristic
226C4—22no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—442no—
231C4—441no—
232C4—441no—
233C4#6700312yes—
234C4#41×D1111yescharacteristic
235C4#6704311yescharacteristic
236C2—42no—
237C2—81no—
238C2C2×#6700311yescharacteristic
239C2#1062335511yescharacteristic
240C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#555C2
socleC22×C11C22×D4
hypercenter#555D11
hypocenterC11#3340
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
2. #10623073C2semidirect
3. #10622704C2semidirect
4. #10622692C2semidirect
5. #10622654C2semidirect
6. #10622648C2semidirect
7. C4×#4324C2semidirect
8. D4×C11⋊C8C2semidirect
9. #10622620C2semidirect
10. #10622611C2semidirect
11. #10622609C2semidirect
193. C11#3340semidirect

Maximal subgroups

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

subgroupindex
C11×#5552
#106230732
#106227042
#106226922
#106226542
#106226482
C4×#43242
D4×C11⋊C82
#106226202
#106226112
#106226092
#334011