Finite Group Databasebeta

← #26021918

Subgroups — #26021918

Order 11392.

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

normal subgroups only

This group has 286 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#19152161C211yesmaximal, characteristic
2#99×D89C212yesmaximal, complemented
3#19151392C212yesmaximal, complemented
4#19151391C211yesmaximal, characteristic, complemented
5#353×C89C211yesmaximal, characteristic, complemented
6C2×#13083573C411yescharacteristic, complemented
7C2×D4×D89C2211yescharacteristic
8#15668008C411yescharacteristic, complemented
9#15668000C411yescharacteristic, complemented
10#15667999C2211yescharacteristic
11#15667984—22no—
12#15667980—22no—
13#15667969C411yescharacteristic, complemented
14C22⋊C4×D89—22no—
15#15667927C2212yes—
16#15667926—22no—
17#127×C89C2211yescharacteristic
18#99×C89C2212yes—
19C23×D89D412yes—
20#13083573—42no—
21C2×Dic178C2×C411yescharacteristic, complemented
22C2×D356C2×C411yescharacteristic
23C2×C22⋊D89—21no—
24C2×C22⋊D89—22no—
25C2×C22⋊D89D412yes—
26D4×D89—42no—
27C22×Dic89—21no—
28C2×C4×D89—42no—
29C2×C4×D89C2×C411yescharacteristic
30#13083553—21no—
31C22⋊Dic89—22no—
32C22⋊Dic89—22no—
33#13083551—21no—
34#13083551—22no—
35#13083551—42no—
36C4×Dic89C2×C411yescharacteristic, complemented
37C2×D4×C89—22no—
38C2×D4×C89C2×C411yescharacteristic, complemented
39C2×D4×C89C2311yescharacteristic
40C22⋊C4×C89—22no—
41C42×C89C2×C411yescharacteristic, complemented
42C23×C89—21no—
43C23×C89C2×D412yes—
44C22×D89—22no—
45C22×D89—22no—
46C22×D89—82no—
47C22×D89C22⋊C412yes—
48C22×D89C22⋊C411yescharacteristic
49D4×C89—41no—
50D4×C89—41no—
51D4×C89—82no—
52C2×C4×C89—21no—
53C2×C4×C89—42no—
54C2×C4×C89C22×C411yescharacteristic
55C22⋊D89—42no—
56C22⋊D89—42no—
57C22⋊D89—82no—
58C2×Dic89—21no—
59C2×Dic89—21no—
60C2×Dic89—42no—
61C2×Dic89—42no—
62C2×Dic89C22⋊C411yescharacteristic
63D356—41no—
64C4×D89—22no—
65C4×D89—84no—
66Dic178—41no—
67C22×C89—22no—
68C22×C89—42no—
69C22×C89—42no—
70C22×C89—41no—
71C22×C89C2×C22⋊C411yescharacteristic
72C2×D89—22no—
73C2×D89—41no—
74C2×D89—44no—
75C2×D89—42no—
76C2×D89—82no—
77C2×D89#9912yes—
78C4×C89—21no—
79C4×C89—41no—
80C4×C89—82no—
81Dic89—21no—
82Dic89—41no—
83Dic89—41no—
84Dic89—82no—
85C2×C89—21no—
86C2×C89—42no—
87C2×C89—81no—
88C2×C89C2×#9911yescharacteristic
89D89—22no—
90D89—42no—
91#2127—891nomaximal, Sylow
92C89#212711yescharacteristic, complemented, Sylow
93#535—891no—
94C2×#99—892no—
95#354—892no—
96#353—891no—
97#353D8911yescharacteristic, complemented
98C2×#41—891no—
99C22×D4—891no—
100#127—891no—
101#127C2×D8911yescharacteristic
102#124—891no—
103#124—891no—
104#121—1782no—
105#120—1782no—
106#117—891no—
107C2×C22⋊C4—1782no—
108#99—892no—
109#99—1782no—
110#99C2×D8912yes—
111C24—892no—
112#41—3562no—
113C2×Q8—891no—
114C2×D4—22no—
115C2×D4—892no—
116C2×D4—891no—
117C2×D4—3562no—
118C2×D4—1781no—
119C2×D4—1782no—
120C2×D4C4×D8911yescharacteristic, complemented
121C2×D4C22×D8911yescharacteristic
122C22×C4—891no—
123C22×C4—3562no—
124C22×C4—1781no—
125C4⋊C4—1781no—
126C22⋊C4—22no—
127C22⋊C4—3562no—
128C22⋊C4—1781no—
129C22⋊C4—1782no—
130C22⋊C4—1782no—
131C22⋊C4—1782no—
132C42—891no—
133C42C4×D8911yescharacteristic, complemented
134C23—21no—
135C23—891no—
136C23—892no—
137C23—1782no—
138C23—1782no—
139C23—7122no—
140C23D4×D8912yes—
141Q8—3561no—
142D4—41no—
143D4—41no—
144D4—82no—
145D4—3561no—
146D4—3562no—
147D4—3562no—
148D4—7122no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—891no—
152C2×C4—3562no—
153C2×C4—3562no—
154C2×C4—1782no—
155C2×C4—1781no—
156C2×C4—1781no—
157C2×C4—7124no—
158C2×C4C2×C4×D8911yescharacteristic
159C22—22no—
160C22—42no—
161C22—42no—
162C22—41no—
163C22—892no—
164C22—3562no—
165C22—3561no—
166C22—3564no—
167C22—1782no—
168C22—7122no—
169C22C22⋊C4×D8911yescharacteristic
170C4—21no—
171C4—41no—
172C4—82no—
173C4—3561no—
174C4—3561no—
175C4—1781no—
176C4—7122no—
177C2—21no—
178C2—42no—
179C2—81no—
180C2—3562no—
181C2—1782no—
182C2#99×D8911yescharacteristic
subgroupG/H
centerC2#99×D89
commutatorC2×C4×C89C22×C4
FrattiniC2×D4C22×D89
Fitting#353×C89C2
socleC2×C89C2×#99
prime radical#19152161C2
cosocleC2×D4×C89C23
hypercenter#353D89
hypocenterC89#2127
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D89C2semidirect
3. #19151392C2semidirect
4. #19151391C2semidirect
5. #353×C89C2semidirect
6. C2×#13083573C4semidirect
8. #15668008C4semidirect
9. #15668000C4semidirect
13. #15667969C4semidirect
21. C2×Dic178C2×C4semidirect
36. C4×Dic89C2×C4semidirect
38. C2×D4×C89C2×C4semidirect
41. C42×C89C2×C4semidirect
92. C89#2127semidirect
97. #353D89semidirect
120. C2×D4C4×D89semidirect
133. C42C4×D89semidirect

Maximal subgroups

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

subgroupindex
#191521612
#99×D892
#191513922
#191513912
#353×C892
#212789