Finite Group Databasebeta

← #26018802

Subgroups — #26018802

Order 11392.

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

normal subgroups only

This group has 208 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#19152155C211yesmaximal, characteristic
2#19151655C211yesmaximal, characteristic
3#19151334C214yesmaximal
4#383×C89C211yesmaximal, characteristic
5#15668012C411yescharacteristic, complemented
6#15668012C411yescharacteristic, complemented
7#15668004—21no—
8#15667991—21no—
9#15667991C2212yes—
10C4×Dic178—21no—
11C4×Dic178C412yescomplemented
12#15667971—21no—
13C4⋊#10623494—21no—
14C22⋊#10623494C2212yes—
15#15667923—21no—
16C2×C42×C89C2211yescharacteristic
17#95×C89—21no—
18#95×C89—21no—
19#95×C89C2212yes—
20C2×Dic178—21no—
21C2×Dic178C2×C412yes—
22C2×#10623494—22no—
23C4⋊Dic89—21no—
24C4⋊Dic89—21no—
25C4⋊Dic89—21no—
26C4⋊Dic89C2×C412yes—
27#13083553—22no—
28#13083553—22no—
29C22⋊Dic89—22no—
30C4×Dic89—22no—
31C22×C4×C89—22no—
32C22×C4×C89D411yescharacteristic
33C22×C4×C89D411yescharacteristic
34C22×C4×C89C2311yescharacteristic
35C42×C89C2×C411yescharacteristic
36C42×C89C2×C411yescharacteristic
37C42×C89D411yescharacteristic
38C42×C89D411yescharacteristic
39C23×C89C2×D411yescharacteristic
40C2×C4×C89—22no—
41C2×C4×C89—41no—
42C2×C4×C89—41no—
43C2×C4×C89—42no—
44C2×C4×C89—42no—
45C2×C4×C89—42no—
46C2×C4×C89C22⋊C411yescharacteristic
47C2×C4×C89C22⋊C411yescharacteristic
48C2×C4×C89C22⋊C411yescharacteristic
49C2×C4×C89C22⋊C411yescharacteristic
50C2×C4×C89C22×C411yescharacteristic
51C2×C4×C89C2×D411yescharacteristic
52C2×Dic89—22no—
53C2×Dic89—22no—
54Dic178—42no—
55Dic178—42no—
56#10623494—42no—
57C22×C89—21no—
58C22×C89—21no—
59C22×C89C2×C22⋊C411yescharacteristic
60C22×C89#13712yes—
61C4×C89—21no—
62C4×C89—21no—
63C4×C89—21no—
64C4×C89—21no—
65C4×C89—21no—
66C4×C89—21no—
67C4×C89—82no—
68Dic89—42no—
69Dic89—42no—
70C2×C89—22no—
71C2×C89#41011yescharacteristic
72C2×C89#41911yescharacteristic
73C2×C89#42111yescharacteristic
74#1515—891nomaximal, Sylow
75C89#151511yescharacteristic, complemented, Sylow
76#533—891no—
77#432—891no—
78#383D8911yescharacteristic
79#328—894no—
80C4⋊Q8—891no—
81C4⋊Q8—891no—
82#125—1781no—
83C22⋊Q8—892no—
84C22⋊Q8—1781no—
85C4×Q8—892no—
86C4×Q8—1781no—
87#117—1781no—
88C2×C42C2×D8911yescharacteristic
89C4⋊C8—1781no—
90C22⋊C8—892no—
91#97—1781no—
92#95—21no—
93#95—21no—
94#95C2×D8912yes—
95C2×Q8—892no—
96C2×Q8—1781no—
97C22×C4—22no—
98C22×C4C22⋊D8911yescharacteristic
99C22×C4C22⋊D8911yescharacteristic
100C22×C4C22×D8911yescharacteristic
101C2×C8—1782no—
102C4⋊C4—892no—
103C4⋊C4—1781no—
104C4⋊C4—1781no—
105C4⋊C4—1782no—
106C4⋊C4—1781no—
107C4⋊C4—1782no—
108C22⋊C4—1782no—
109C42—1782no—
110C42C4×D8911yescharacteristic
111C42C4×D8911yescharacteristic
112C42D35611yescharacteristic
113C42D35611yescharacteristic
114C23C2×C22⋊D8911yescharacteristic
115Q8—3562no—
116Q8—3562no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—1782no—
124C2×C4—1782no—
125C2×C4#1308355111yescharacteristic
126C2×C4#1308355111yescharacteristic
127C2×C4#1308355111yescharacteristic
128C2×C4#1308355111yescharacteristic
129C2×C4C2×C4×D8911yescharacteristic
130C2×C4C2×D35611yescharacteristic
131C8—3562no—
132C22—21no—
133C22—21no—
134C22C2×#1308355111yescharacteristic
135C22#1566804212yes—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—82no—
143C4—3562no—
144C4—3562no—
145C2—22no—
146C2#1915157111yescharacteristic
147C2#1915160611yescharacteristic
148C2#1915161611yescharacteristic
subgroupG/H
centerC22C2×#13083551
commutatorC2×C4×C89C22×C4
FrattiniC22×C4C22×D89
Fitting#383×C89C2
socleC22×C89C2×C22⋊C4
prime radicalC23×C89C2×D4
cosocleC22×C4×C89C23
hypercenter#383D89
hypocenterC89#1515
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
5. #15668012C4semidirect
6. #15668012C4semidirect
11. C4×Dic178C4semidirect
75. C89#1515semidirect

Maximal subgroups

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

subgroupindex
#191521552
#191516552
#191513342
#383×C892
#151589