Finite Group Databasebeta

← #13070554

Subgroups — #13070554

Order 1408.

220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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×#66957C211yesmaximal, characteristic
2C11×#467C211yesmaximal, characteristic, complemented
3C2×#66893C211yesmaximal, characteristic, complemented
4C2×#66892C211yesmaximal, characteristic, complemented
5C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#10622130C211yesmaximal, characteristic, complemented
7#10622129C211yesmaximal, characteristic, complemented
8C2×#4339—21no—
9C2×C11×Q16C2211yescharacteristic
10C22×C8×C11C2211yescharacteristic
11C11×C22⋊Q8—21no—
12C2×Dic44C2211yescharacteristic
13#66957—22no—
14#66957—22no—
15C2×D88C2211yescharacteristic
16C2×#4314—21no—
17C11×#107C2211yescharacteristic
18C11×#103—21no—
19#66893—22no—
20#66892—22no—
21C2×C11⋊C16C2211yescharacteristic
22C2×C11⋊C16C2211yescharacteristic
23C2×Q8×C11—21no—
24C22×C4×C11D411yescharacteristic
25C2×C22⋊D11—41no—
26#4339—24no—
27#4339—42no—
28C2×D44—21no—
29C2×C4×D11—41no—
30C2×Dic22—21no—
31C11×Q16—21no—
32C11×Q16—21no—
33C2×C8×C11—21no—
34C2×C8×C11—21no—
35C2×C8×C11D411yescharacteristic
36C2×C8×C11C2311yescharacteristic
37C11×C4⋊C4—21no—
38C11×C4⋊C4—41no—
39C11×C22⋊C4—41no—
40Dic44—21no—
41Dic44D412yes—
42D88—21no—
43D88D412yes—
44#4314—24no—
45C11⋊C16—21no—
46C11⋊C16—21no—
47#2189—111nomaximal, Sylow
48C23×C11D811yescharacteristic
49C22×D11—41no—
50Q8×C11—41no—
51Q8×C11—41no—
52C2×C4×C11—21no—
53C2×C4×C11—21no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11D811yescharacteristic
57C2×C4×C11C2×D411yescharacteristic
58C22⋊D11—44no—
59C2×Dic11—41no—
60D44—22no—
61D44—41no—
62C4×D11—44no—
63Dic22—22no—
64Dic22—41no—
65C8×C11—21no—
66C8×C11C2×D411yescharacteristic
67C8×C11C2×D411yescharacteristic
68C2×#135—111no—
69C2×Q32—111no—
70C2×SD32—111no—
71#467D1111yescharacteristic, complemented
72#358—111no—
73#357—111no—
74C22⋊C16—111no—
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11C2×D811yescharacteristic
79C2×D11—42no—
80C2×D11—81no—
81C2×D11—81no—
82C4×C11—21no—
83C4×C11—81no—
84C4×C11—81no—
85C4×C11#12011yescharacteristic
86C4×C11AGL(1,ℤ/8)11yescharacteristic
87Dic11—42no—
88C2×#41—221no—
89#135—222no—
90#135—222no—
91C2×Q16—111no—
92C2×Q16C2×D1111yescharacteristic
93C2×SD16—221no—
94C2×D8—111no—
95C22×C8C2×D1111yescharacteristic
96C22⋊Q8—21no—
97Q32—222no—
98SD32—222no—
99C2×C16—111no—
100C2×C16—111no—
101#107C2×D1111yescharacteristic
102#103—21no—
103C2×C11—41no—
104C2×C11#44711yescharacteristic
105C2×C11#50811yescharacteristic
106C2×C11#51011yescharacteristic
107D11—82no—
108#41—224no—
109#41—442no—
110C2×Q8—21no—
111C2×Q8—221no—
112C2×D4—221no—
113C2×D4—441no—
114C22×C4—441no—
115C22×C4C22⋊D1111yescharacteristic
116Q16—21no—
117Q16—21no—
118Q16—112no—
119Q16—221no—
120SD16—224no—
121D8—112no—
122D8—221no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8C22⋊D1111yescharacteristic
126C2×C8C22×D1111yescharacteristic
127C4⋊C4—21no—
128C4⋊C4—41no—
129C22⋊C4—41no—
130C16—221no—
131C16—221no—
132C11#218911yescharacteristic, complemented, Sylow
133C23—441no—
134C23#432311yescharacteristic
135Q8—41no—
136Q8—41no—
137Q8—222no—
138Q8—441no—
139D4—222no—
140D4—444no—
141D4—441no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—444no—
147C2×C4—441no—
148C2×C4#432311yescharacteristic
149C2×C4C2×C22⋊D1111yescharacteristic
150C8—21no—
151C8D4×D1111yescharacteristic
152C8D4×D1111yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—442no—
157C22—881no—
158C22—881no—
159C22C2×#432311yescharacteristic
160C4—21no—
161C4—81no—
162C4—81no—
163C4—442no—
164C4#6699011yescharacteristic
165C4#6700211yescharacteristic
166C2—41no—
167C2—882no—
168C2#1062264911yescharacteristic
169C2#1062279211yescharacteristic
170C2#1062280711yescharacteristic
subgroupG/H
centerC22C2×#4323
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#467C2
socleC22×C11C2×D8
prime radicalC2×#66957C2
hypercenter#467D11
hypocenterC11#2189
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
2. C11×#467C2semidirect
3. C2×#66893C2semidirect
4. C2×#66892C2semidirect
5. C22⋊(C11⋊C16)C2semidirect
6. #10622130C2semidirect
7. #10622129C2semidirect
71. #467D11semidirect
132. C11#2189semidirect

Maximal subgroups

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

subgroupindex
C2×#669572
C11×#4672
C2×#668932
C2×#668922
C22⋊(C11⋊C16)2
#106221302
#106221292
#218911