Finite Group Databasebeta

← #26018874

Subgroups — #26018874

Order 11392.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D89C211yesmaximal, characteristic
2#19151653C212yesmaximal, complemented
3#19151338C211yesmaximal, characteristic, complemented
4#19151337C212yesmaximal, complemented
5#329×C89C211yesmaximal, characteristic, complemented
6C2×Q8×D89C411yescharacteristic
7C2×D4×D89C411yescharacteristic
8#15668001C411yescharacteristic
9#15668000C2211yescharacteristic
10#15667999C411yescharacteristic
11#15667998—22no—
12C22⋊C4×D89—22no—
13C42×D89C2211yescharacteristic
14#15667941—22no—
15#15667924—22no—
16#15667923C2212yescomplemented
17#124×C89C2211yescharacteristic
18#97×C89C2212yescomplemented
19C23×D89—21no—
20C2×Dic178—21no—
21C2×Dic178C2×C411yescharacteristic
22Q8×D89—42no—
23C2×D356C2×C411yescharacteristic
24C2×C22⋊D89—21no—
25D4×D89—42no—
26C2×C4×D89—21no—
27C2×C4×D89C2×C411yescharacteristic
28C2×C4×D89D412yes—
29C2×#10623494—22no—
30C22⋊Dic89—22no—
31#13083551—22no—
32#13083551—22no—
33C4×Dic89C2×C411yescharacteristic
34C4×Dic89D412yes—
35C2×Q8×C89C2×C411yescharacteristic
36C2×D4×C89C2×C411yescharacteristic
37C2×C8×C89—22no—
38C22⋊C4×C89—22no—
39C42×C89C2311yescharacteristic
40C23×C89—21no—
41C22×D89—21no—
42C22×D89—44no—
43C22×D89—42no—
44C22×D89C22⋊C411yescharacteristic
45Q8×C89—41no—
46D4×C89—41no—
47C2×C4×C89—21no—
48C2×C4×C89C22×C411yescharacteristic
49C2×C4×C89C2×D412yes—
50C22⋊D89—42no—
51C2×Dic89—21no—
52C2×Dic89C22⋊C412yes—
53C2×Dic89C22⋊C411yescharacteristic
54D356—41no—
55C4×D89—22no—
56C4×D89—42no—
57C4×D89—42no—
58Dic178—42no—
59Dic178—41no—
60C8×C89—42no—
61#10623494—42no—
62C22×C89—41no—
63C22×C89—42no—
64C22×C89C2×C22⋊C411yescharacteristic
65C2×D89—22no—
66C2×D89—41no—
67C2×D89—42no—
68C2×D89—84no—
69C2×D89#10012yes—
70C4×C89—21no—
71C4×C89—22no—
72C4×C89—41no—
73Dic89—21no—
74Dic89—22no—
75Dic89—41no—
76C2×C89—81no—
77C2×C89C2×#10011yescharacteristic
78C2×C89#42112yes—
79D89—22no—
80D89—81no—
81#1533—891nomaximal, Sylow
82C89#153311yescharacteristic, complemented, Sylow
83C2×#124—891no—
84#432—892no—
85#329—891no—
86#329—892no—
87#329D8911yescharacteristic, complemented
88C22×Q8—891no—
89C22×D4—891no—
90#124—891no—
91#124—891no—
92#124—891no—
93#124—1782no—
94#124C2×D8911yescharacteristic
95C2×C22⋊C4—1782no—
96C2×C42—891no—
97C4⋊C8—1782no—
98C22⋊C8—1782no—
99#97—892no—
100#97C2×D8912yescomplemented
101C24—1781no—
102C2×Q8—891no—
103C2×Q8—3562no—
104C2×Q8—1781no—
105C2×Q8C4×D8911yescharacteristic
106C2×D4—891no—
107C2×D4—3562no—
108C2×D4—1781no—
109C2×D4C4×D8911yescharacteristic
110C22×C4—892no—
111C22×C4—891no—
112C22×C4—1781no—
113C2×C8—22no—
114C2×C8—1782no—
115C22⋊C4—22no—
116C22⋊C4—1782no—
117C22⋊C4—1782no—
118C22⋊C4—1782no—
119C42—891no—
120C42—892no—
121C42C22×D8911yescharacteristic
122C23—21no—
123C23—891no—
124C23—3562no—
125C23—3564no—
126C23—1781no—
127Q8—41no—
128Q8—3561no—
129Q8—3562no—
130D4—41no—
131D4—3561no—
132D4—3562no—
133C2×C4—21no—
134C2×C4—892no—
135C2×C4—891no—
136C2×C4—3562no—
137C2×C4—3562no—
138C2×C4—1782no—
139C2×C4—1781no—
140C2×C4C2×C4×D8911yescharacteristic
141C2×C4D4×D8912yes—
142C8—42no—
143C8—3562no—
144C22—41no—
145C22—42no—
146C22—892no—
147C22—3561no—
148C22—3562no—
149C22—1782no—
150C22—7124no—
151C22C22⋊C4×D8911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—3561no—
156C4—1781no—
157C4—1782no—
158C2—81no—
159C2—1782no—
160C2—7121no—
161C2#100×D8911yescharacteristic
162C2#1915161312yes—
subgroupG/H
centerC22C22⋊C4×D89
commutatorC2×C4×C89C22×C4
FrattiniC42C22×D89
Fitting#329×C89C2
socleC22×C89C2×C22⋊C4
prime radicalC2×D4×D89C4
cosocleC42×C89C23
hypercenter#329D89
hypocenterC89#1533
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #19151653C2semidirect
3. #19151338C2semidirect
4. #19151337C2semidirect
5. #329×C89C2semidirect
16. #15667923C22semidirect
18. #97×C89C22semidirect
82. C89#1533semidirect
87. #329D89semidirect
100. #97C2×D89semidirect

Maximal subgroups

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

subgroupindex
#124×D892
#191516532
#191513382
#191513372
#329×C892
#153389