Finite Group Databasebeta

← #26019383

Subgroups — #26019383

Order 11392.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#19152309C211yesmaximal, characteristic
2#19151890C211yesmaximal, characteristic, complemented
3#19151885C211yesmaximal, characteristic
4#19151347C211yesmaximal, characteristic, complemented
5#19151330C211yesmaximal, characteristic, complemented
6#19151327C211yesmaximal, characteristic
7#494×C89C211yesmaximal, characteristic, complemented
8#15668003—21no—
9#15667992—21no—
10#15667988—22no—
11C4×Dic178C2211yescharacteristic
12C4×D356C2211yescharacteristic
13#15667974—21no—
14C4⋊C4×D89—21no—
15#15667945—21no—
16#15667943—21no—
17C4⋊#10623494C2211yescharacteristic
18C4⋊#10623494C2211yescharacteristic
19#15667935—21no—
20#15667932—21no—
21C2×Q16×C89—22no—
22C4⋊Q8×C89C2211yescharacteristic
23C4⋊Q8×C89C2211yescharacteristic
24C4×C8×C89C2211yescharacteristic
25C2×Dic178D411yescharacteristic
26C2×D356D411yescharacteristic
27C2×C4×D89—21no—
28C2×C4×D89—22no—
29C2×#10623494—21no—
30C2×#10623494—21no—
31C4⋊Dic89—22no—
32C4⋊Dic89D411yescharacteristic
33C4⋊Dic89D411yescharacteristic
34#13083553—22no—
35#13083553—21no—
36#13083551—22no—
37#13083551—21no—
38C4×Dic89—21no—
39C2×Q8×C89—21no—
40C2×Q8×C89D412yes—
41Q16×C89—44no—
42C2×C8×C89—21no—
43C4⋊C4×C89—21no—
44C4⋊C4×C89—21no—
45C4⋊C4×C89—21no—
46C4⋊C4×C89—21no—
47C42×C89C2311yescharacteristic
48C22×D89—21no—
49Q8×C89—42no—
50Q8×C89—42no—
51C2×C4×C89—22no—
52C2×C4×C89—41no—
53C2×C4×C89C2×D411yescharacteristic
54C2×C4×C89C2×D411yescharacteristic
55C2×C4×C89C2×D411yescharacteristic
56C2×Dic89—21no—
57C2×Dic89—21no—
58C2×Dic89—21no—
59D356—21no—
60D356Q1612yescomplemented
61C4×D89—41no—
62C4×D89—41no—
63C4×D89—82no—
64Dic178—21no—
65Dic178—21no—
66C8×C89—22no—
67#10623494—41no—
68#10623494—41no—
69C22×C89#12011yescharacteristic
70C2×D89—22no—
71C2×D89—41no—
72C2×D89—41no—
73C4×C89—21no—
74C4×C89—42no—
75C4×C89—81no—
76C4×C89C2×Q1611yescharacteristic
77C4×C89#13511yescharacteristic
78C4×C89#13711yescharacteristic
79C4×C89#13711yescharacteristic
80Dic89—41no—
81Dic89—41no—
82Dic89—41no—
83C2×C89#45111yescharacteristic
84C2×C89#45211yescharacteristic
85C2×C89#45311yescharacteristic
86D89—42no—
87#1632—891nomaximal, Sylow
88C89#163211yescharacteristic, complemented, Sylow
89#554—891no—
90#494D8911yescharacteristic, complemented
91#477—891no—
92#476—891no—
93#333—891no—
94Q8⋊C8—891no—
95D4⋊C8—891no—
96C2×Q16—22no—
97C4⋊Q8C2×D8911yescharacteristic
98C4⋊Q8C2×D8911yescharacteristic
99#125—1781no—
100C22⋊Q8—1781no—
101C22⋊Q8—1782no—
102C4×Q8—891no—
103C4×D4—891no—
104C4×D4—1781no—
105C2×C4⋊C4—1781no—
106#107—1781no—
107#106—1781no—
108C4⋊C8—891no—
109C4⋊C8—891no—
110#103—1781no—
111#102—1781no—
112C4×C8C2×D8911yescharacteristic
113C2×Q8—21no—
114C2×Q8—891no—
115C2×Q8C22⋊D8912yes—
116C2×D4—891no—
117C22×C4—1782no—
118C22×C4—1781no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—1781no—
122C2×C8—1781no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—891no—
128C4⋊C4—891no—
129C4⋊C4—1782no—
130C4⋊C4—1782no—
131C4⋊C4—1781no—
132C22⋊C4—1782no—
133C22⋊C4—1781no—
134C42—1781no—
135C42C22×D8911yescharacteristic
136C23—1781no—
137Q8—42no—
138Q8—42no—
139Q8—1781no—
140Q8—1781no—
141D4—892no—
142D4—1781no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—3561no—
146C2×C4—3561no—
147C2×C4—1781no—
148C2×C4—1781no—
149C2×C4—1781no—
150C2×C4—7122no—
151C2×C4D4×D8911yescharacteristic
152C2×C4D4×D8911yescharacteristic
153C2×C4C2×C22⋊D8911yescharacteristic
154C8—22no—
155C8—3561no—
156C8—3561no—
157C22—3561no—
158C22—3561no—
159C22—1782no—
160C22#1566798011yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—3561no—
165C4—3561no—
166C4—3561no—
167C4Q16×D8911yescharacteristic
168C4#1566803511yescharacteristic
169C4#1566804411yescharacteristic
170C4#1566804411yescharacteristic
171C2—3562no—
172C2#1915175211yescharacteristic
173C2#1915175911yescharacteristic
174C2#1915176511yescharacteristic
subgroupG/H
centerC22#15667980
commutator, cosocleC42×C89C23
FrattiniC42C22×D89
Fitting#494×C89C2
socleC22×C89#120
prime radicalC2×D356D4
hypercenter#494D89
hypocenterC89#1632
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #19151890C2semidirect
4. #19151347C2semidirect
5. #19151330C2semidirect
7. #494×C89C2semidirect
60. D356Q16semidirect
88. C89#1632semidirect
90. #494D89semidirect

Maximal subgroups

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

subgroupindex
#191523092
#191518902
#191518852
#191513472
#191513302
#191513272
#494×C892
#163289