Finite Group Databasebeta

← #13069772

Subgroups — #13069772

Order 1408.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#10623031C211yesmaximal, characteristic, complemented
2C11×#390C211yesmaximal, characteristic
3#10622828C212yesmaximal
4#10622168C211yesmaximal, characteristic, complemented
5#10622161C212yesmaximal, complemented
6C22×D4×C11C2211yescharacteristic
7C2×C11×C4⋊C4C2211yescharacteristic
8C2×C11×C22⋊C4—22no—
9C2×C42×C11C2211yescharacteristic
10#66979C2212yes—
11#66977—22no—
12C2×#4318C2212yes—
13#66943—22no—
14#66941—22no—
15#66896—22no—
16#66896—22no—
17C24×C11—21no—
18C2×D4×C11—22no—
19C2×D4×C11—22no—
20C2×D4×C11—21no—
21C2×D4×C11Q812yescomplemented
22C22×C4×C11—21no—
23C22×C4×C11D412yes—
24C22×C4×C11C2311yescharacteristic
25C2×Dic22—22no—
26C11×C4⋊C4—22no—
27C11×C22⋊C4—44no—
28C42×C11—22no—
29C22⋊Dic11—22no—
30C4⋊Dic11—22no—
31C4⋊Dic11D412yes—
32C4⋊Dic11D412yes—
33Dic11⋊C4—24no—
34C4×Dic11—22no—
35#4318—22no—
36#4318—22no—
37C2×C11⋊C8—22no—
38#2027—111nomaximal, Sylow
39C23×C11—22no—
40C23×C11—42no—
41C23×C11—42no—
42C23×C11—41no—
43C23×C11—41no—
44C23×C11C2×D411yescharacteristic
45D4×C11—24no—
46D4×C11—42no—
47C2×C4×C11—22no—
48C2×C4×C11—22no—
49C2×C4×C11—41no—
50C2×C4×C11—41no—
51C2×C4×C11—42no—
52C2×C4×C11C2×D412yes—
53C2×C4×C11C2×Q811yescharacteristic
54C2×C4×C11#4111yescharacteristic
55C2×C4×C11#4112yes—
56C2×Dic11—22no—
57C2×Dic11—22no—
58Dic22—82no—
59C11⋊C8—42no—
60#544—111no—
61#418—112no—
62#390D1111yescharacteristic
63#343—111no—
64#339—112no—
65C22×C11—21no—
66C22×C11—21no—
67C22×C11—44no—
68C22×C11—42no—
69C22×C11—82no—
70C22×C11—81no—
71C22×C11—81no—
72C22×C11#12011yescharacteristic
73C22×C11C22⋊Q811yescharacteristic
74C22×C11#12411yescharacteristic
75C4×C11—42no—
76C4×C11—42no—
77C4×C11C22⋊Q812yes—
78C4×C11#12412yes—
79Dic11—42no—
80Dic11—42no—
81C22×D4C2×D1111yescharacteristic
82C2×M16—112no—
83C4⋊Q8—222no—
84#125—222no—
85C22⋊Q8—222no—
86#117—112no—
87C2×C4⋊C4C2×D1111yescharacteristic
88C2×C22⋊C4—22no—
89C2×C42C2×D1111yescharacteristic
90#102—222no—
91#102—222no—
92C2×C11—21no—
93C2×C11—21no—
94C2×C11—82no—
95C2×C11#39311yescharacteristic
96C2×C11#45311yescharacteristic
97C2×C11#45411yescharacteristic
98C24—21no—
99C2×Q8—222no—
100C2×D4—21no—
101C2×D4—22no—
102C2×D4—22no—
103C2×D4Dic2212yescomplemented
104C22×C4—21no—
105C22×C4C22⋊D1112yes—
106C22×C4C22×D1111yescharacteristic
107M16—222no—
108M16—222no—
109C2×C8—222no—
110C4⋊C4—22no—
111C4⋊C4—112no—
112C4⋊C4—112no—
113C4⋊C4—222no—
114C4⋊C4—224no—
115C22⋊C4—44no—
116C22⋊C4—222no—
117C42—22no—
118C42—222no—
119C11#202711yescharacteristic, complemented, Sylow
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×C22⋊D1111yescharacteristic
126Q8—882no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—222no—
135C2×C4—222no—
136C2×C4C2×Dic2211yescharacteristic
137C2×C4#433911yescharacteristic
138C2×C4D4×D1112yes—
139C2×C4#434112yes—
140C8—442no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22#6697711yescharacteristic
149C22#6698911yescharacteristic
150C22#6699011yescharacteristic
151C4—42no—
152C4—42no—
153C4—442no—
154C4—442no—
155C4#6693112yes—
156C4#6693812yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2#1062256011yescharacteristic
161C2#1062267511yescharacteristic
162C2#1062269011yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#390C2
socleC22×C11#120
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #10623031C2semidirect
4. #10622168C2semidirect
5. #10622161C2semidirect
21. C2×D4×C11Q8semidirect
103. C2×D4Dic22semidirect
119. C11#2027semidirect

Maximal subgroups

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

subgroupindex
#106230312
C11×#3902
#106228282
#106221682
#106221612
#202711