Finite Group Databasebeta

← #13070577

Subgroups — #13070577

Order 1408.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#10623302C211yesmaximal, characteristic, complemented
2C11×#509C211yesmaximal, characteristic, complemented
3#10622773C211yesmaximal, characteristic, complemented
4C2×#66891C211yesmaximal, characteristic, complemented
5#10622205C211yesmaximal, characteristic, complemented
6#10622155C211yesmaximal, characteristic, complemented
7#10622153C211yesmaximal, characteristic, complemented
8#67043—21no—
9C11×#135C2211yescharacteristic
10C2×C11×D8C2211yescharacteristic
11#67004—21no—
12#66985—21no—
13Q16×D11—21no—
14#66968—22no—
15#66965—21no—
16C2×Dic44C2211yescharacteristic
17#66954C2211yescharacteristic
18C11×SD32—21no—
19C11×D16—21no—
20C11×M32C2211yescharacteristic
21#66897—21no—
22#66891—22no—
23#66883C2211yescharacteristic
24C2×C11⋊C16C2211yescharacteristic
25C11×#41—21no—
26C2×D4×C11—21no—
27Q8×D11—22no—
28#4341—22no—
29#4341—42no—
30#4339—41no—
31#4339D411yescharacteristic
32C2×Dic22—21no—
33C2×Dic22—41no—
34C11×Q16D411yescharacteristic
35C11×SD16—21no—
36C11×D8—21no—
37C11×D8—21no—
38C11×D8D411yescharacteristic
39C2×C8×C11C2311yescharacteristic
40#4326—22no—
41#4324—22no—
42#4324—41no—
43#4323—41no—
44#4318—21no—
45#4318D411yescharacteristic
46Dic44—21no—
47Dic44D412yes—
48#4313—21no—
49C8×D11—21no—
50C11×C16—21no—
51C11⋊C16—21no—
52#2193—111nomaximal, Sylow
53C23×C11—41no—
54Q8×C11—21no—
55D4×C11—21no—
56D4×C11—41no—
57D4×C11—41no—
58D4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11C2×D411yescharacteristic
61C22⋊D11—21no—
62C22⋊D11—42no—
63C2×Dic11—42no—
64C2×Dic11—41no—
65D44D811yescharacteristic
66C4×D11—21no—
67C4×D11—42no—
68Dic22—22no—
69Dic22—42no—
70Dic22—41no—
71Dic22D811yescharacteristic
72C8×C11C2×D411yescharacteristic
73C8×C11C2×D411yescharacteristic
74C11⋊C8—21no—
75C11⋊C8—41no—
76#578—111no—
77#509D1111yescharacteristic, complemented
78C2×SD32—111no—
79#472—111no—
80#362—111no—
81#359—111no—
82#350—111no—
83C22×C11—41no—
84C22×C11—81no—
85C22×C11—161no—
86C22×C11AGL(1,ℤ/8)11yescharacteristic
87C2×D11—21no—
88C4×C11—41no—
89C4×C11#12011yescharacteristic
90C4×C11C2×D811yescharacteristic
91Dic11—21no—
92Dic11—42no—
932−1+4—221no—
94#137—221no—
95#137—222no—
96AGL(1,ℤ/8)—221no—
97#135—221no—
98#135C2×D1111yescharacteristic
99C2×Q16—111no—
100C2×Q16—221no—
101C2×D8C2×D1111yescharacteristic
102#131—111no—
103SD32—21no—
104SD32—222no—
105D16—21no—
106M32C2×D1111yescharacteristic
107C2×C16—111no—
108#108—111no—
109#100—221no—
110C2×C11—21no—
111C2×C11—81no—
112C2×C11—161no—
113C2×C11#44711yescharacteristic
114D11—41no—
115#41—21no—
116#41—111no—
117#41—222no—
118#41—441no—
119#41—442no—
120C2×Q8—222no—
121C2×Q8—221no—
122C2×Q8—441no—
123C2×D4—21no—
124Q16—112no—
125Q16—222no—
126Q16—221no—
127Q16C22⋊D1111yescharacteristic
128SD16—21no—
129SD16—222no—
130SD16—441no—
131D8—21no—
132D8—21no—
133D8—441no—
134D8C22⋊D1111yescharacteristic
135M16—111no—
136M16—221no—
137M16—221no—
138C2×C8—221no—
139C2×C8C22×D1111yescharacteristic
140C16—21no—
141C16—221no—
142C11#219311yescharacteristic, complemented, Sylow
143C23—41no—
144Q8—21no—
145Q8—111no—
146Q8—222no—
147Q8—442no—
148Q8—441no—
149D4—21no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—111no—
154D4—221no—
155D4—442no—
156C2×C4—41no—
157C2×C4—221no—
158C2×C4—442no—
159C2×C4—442no—
160C2×C4—441no—
161C2×C4D4×D1111yescharacteristic
162C8—221no—
163C8—441no—
164C8D4×D1111yescharacteristic
165C8C2×C22⋊D1111yescharacteristic
166C22—41no—
167C22—81no—
168C22—161no—
169C22—221no—
170C22#6696411yescharacteristic
171C4—41no—
172C4—221no—
173C4—442no—
174C4D8×D1111yescharacteristic
175C4#6699011yescharacteristic
176C2—21no—
177C2—81no—
178C2—161no—
179C2—441no—
180C2#1062276911yescharacteristic
subgroupG/H
centerC2#10622769
commutator, cosocleC2×C8×C11C23
FrattiniC2×C8C22×D11
FittingC11×#509C2
socleC2×C11#447
hypercenter#509D11
hypocenterC11#2193
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #10623302C2semidirect
2. C11×#509C2semidirect
3. #10622773C2semidirect
4. C2×#66891C2semidirect
5. #10622205C2semidirect
6. #10622155C2semidirect
7. #10622153C2semidirect
77. #509D11semidirect
142. C11#2193semidirect

Maximal subgroups

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

subgroupindex
#106233022
C11×#5092
#106227732
C2×#668912
#106222052
#106221552
#106221532
#219311