Finite Group Databasebeta

← #26019388

Subgroups — #26019388

Order 11392.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#19152305C211yesmaximal, characteristic
2#19151978C211yesmaximal, characteristic, complemented
3#19151894C211yesmaximal, characteristic, complemented
4#19151888C211yesmaximal, characteristic
5#19151346C211yesmaximal, characteristic, complemented
6#19151330C211yesmaximal, characteristic, complemented
7D4⋊C8×C89C211yesmaximal, characteristic
8C2×Dic356—22no—
9#15668012C2211yescharacteristic
10#15668012C2211yescharacteristic
11#15668003—21no—
12#15667991—21no—
13#15667989—22no—
14C4×Dic178C2211yescharacteristic
15D4×Dic89—21no—
16C2×C4⋊Dic89—21no—
17#15667946—21no—
18#15667943—21no—
19C4⋊#10623494C2211yescharacteristic
20#15667937—21no—
21#15667933—21no—
22C4×D4×C89C2211yescharacteristic
23C4⋊C8×C89C2211yescharacteristic
24C4×C8×C89C2211yescharacteristic
25C2×Dic178—21no—
26C2×Dic178D411yescharacteristic
27C2×Dic178D412yes—
28C22×Dic89—22no—
29Dic356—44no—
30C2×#10623494—21no—
31C4⋊Dic89—22no—
32C4⋊Dic89—21no—
33C4⋊Dic89—21no—
34C4⋊Dic89—21no—
35C4⋊Dic89—21no—
36C4⋊Dic89D411yescharacteristic
37#13083553—22no—
38#13083553—21no—
39C22⋊Dic89—22no—
40C4×Dic89—21no—
41C2×D4×C89D411yescharacteristic
42C22×C4×C89—21no—
43C2×C8×C89—21no—
44C2×C8×C89—21no—
45C4⋊C4×C89D411yescharacteristic
46C22⋊C4×C89—21no—
47C42×C89C2311yescharacteristic
48C23×C89—21no—
49D4×C89—21no—
50D4×C89Q1612yescomplemented
51C2×C4×C89—21no—
52C2×C4×C89—41no—
53C2×C4×C89—41no—
54C2×C4×C89C2×D411yescharacteristic
55C2×C4×C89C2×D411yescharacteristic
56C2×C4×C89C2×D411yescharacteristic
57C2×Dic89—21no—
58C2×Dic89—21no—
59C2×Dic89—22no—
60C2×Dic89—41no—
61C2×Dic89—82no—
62Dic178—21no—
63Dic178—21no—
64Dic178—42no—
65Dic178—42no—
66C8×C89—22no—
67C8×C89—41no—
68#10623494—41no—
69C22×C89—22no—
70C22×C89—41no—
71C22×C89—41no—
72C22×C89#12011yescharacteristic
73C4×C89—21no—
74C4×C89—41no—
75C4×C89C2×Q1611yescharacteristic
76C4×C89#13511yescharacteristic
77C4×C89#13711yescharacteristic
78C4×C89#13711yescharacteristic
79Dic89—41no—
80Dic89—42no—
81Dic89—41no—
82Dic89—81no—
83C2×C89—42no—
84C2×C89#45111yescharacteristic
85C2×C89#45211yescharacteristic
86C2×C89#45311yescharacteristic
87#1632—891nomaximal, Sylow
88C89#163211yescharacteristic, complemented, Sylow
89#554—891no—
90#494—891no—
91#477—891no—
92#476—891no—
93#333—891no—
94Q8⋊C8—891no—
95D4⋊C8D8911yescharacteristic
96C2×Q16—1782no—
97C4⋊Q8—891no—
98C4⋊Q8—891no—
99#125—1781no—
100C22⋊Q8—1782no—
101C22⋊Q8—1781no—
102C4×Q8—891no—
103C4×D4—1781no—
104C4×D4C2×D8911yescharacteristic
105C2×C4⋊C4—1781no—
106#107—1781no—
107#106—1781no—
108C4⋊C8—891no—
109C4⋊C8C2×D8911yescharacteristic
110#103—1781no—
111#102—1781no—
112C4×C8C2×D8911yescharacteristic
113C2×Q8—892no—
114C2×Q8—891no—
115C2×Q8—1781no—
116C2×D4D35611yescharacteristic
117C22×C4—21no—
118C22×C4—1782no—
119Q16—3564no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1781no—
123C4⋊C4—891no—
124C4⋊C4—1782no—
125C4⋊C4—1782no—
126C4⋊C4—1781no—
127C4⋊C4—1781no—
128C4⋊C4—1781no—
129C4⋊C4—1781no—
130C4⋊C4—1781no—
131C4⋊C4D35611yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1782no—
134C42—1781no—
135C42C22×D8911yescharacteristic
136C23—21no—
137Q8—3562no—
138Q8—3562no—
139Q8—1781no—
140Q8—1781no—
141D4—21no—
142D4Dic35612yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—3561no—
147C2×C4—1781no—
148C2×C4—1781no—
149C2×C4—1782no—
150C2×C4—7122no—
151C2×C4D4×D8911yescharacteristic
152C2×C4D4×D8911yescharacteristic
153C2×C4C2×D35611yescharacteristic
154C8—22no—
155C8—41no—
156C8—3561no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1566798211yescharacteristic
161C4—21no—
162C4—41no—
163C4—3561no—
164C4—3561no—
165C4—3562no—
166C4—7121no—
167C4C2×Dic35611yescharacteristic
168C4#1566803111yescharacteristic
169C4#1566804111yescharacteristic
170C4#1566804511yescharacteristic
171C2—42no—
172C2#1915175611yescharacteristic
173C2#1915176111yescharacteristic
174C2#1915176711yescharacteristic
subgroupG/H
centerC22#15667982
commutator, cosocleC42×C89C23
FrattiniC42C22×D89
FittingD4⋊C8×C89C2
socleC22×C89#120
prime radicalC2×D4×C89D4
hypercenterD4⋊C8D89
hypocenterC89#1632
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #19151978C2semidirect
3. #19151894C2semidirect
5. #19151346C2semidirect
6. #19151330C2semidirect
50. D4×C89Q16semidirect
88. C89#1632semidirect
142. D4Dic356semidirect

Maximal subgroups

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

subgroupindex
#191523052
#191519782
#191518942
#191518882
#191513462
#191513302
D4⋊C8×C892
#163289