Finite Group Databasebeta

← #26019414

Subgroups — #26019414

Order 11392.

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

normal subgroups only

This group has 228 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#19152263C211yesmaximal, characteristic
2#19151890C211yesmaximal, characteristic, complemented
3#19151885C211yesmaximal, characteristic
4#19151344C211yesmaximal, characteristic, complemented
5#19151330C211yesmaximal, characteristic, complemented
6#19151327C211yesmaximal, characteristic
7#487×C89C211yesmaximal, characteristic, complemented
8C2×Q8×D89—21no—
9#15668011—21no—
10#15667990—22no—
11#15667988—21no—
12C4×Dic178C2211yescharacteristic
13C4×D356C2211yescharacteristic
14#15667974—21no—
15#15667945—21no—
16#15667943—21no—
17C4⋊#10623494C2211yescharacteristic
18C4⋊#10623494C2211yescharacteristic
19#15667935—21no—
20#15667932—21no—
21C4⋊Q8×C89C2211yescharacteristic
22C4⋊Q8×C89C2211yescharacteristic
23#103×C89—22no—
24C4×C8×C89C2211yescharacteristic
25C2×Dic178—22no—
26C2×Dic178D411yescharacteristic
27Q8×D89—42no—
28Q8×D89—42no—
29C2×D356D411yescharacteristic
30C2×C4×D89—22no—
31C2×C4×D89—21no—
32C2×#10623494—21no—
33C2×#10623494—21no—
34C4⋊Dic89D411yescharacteristic
35C4⋊Dic89D411yescharacteristic
36#13083553—22no—
37#13083553—21no—
38#13083551—22no—
39#13083551—21no—
40C4×Dic89—21no—
41C2×Q8×C89—21no—
42C2×Q8×C89—21no—
43C2×C8×C89—21no—
44C4⋊C4×C89—21no—
45C4⋊C4×C89—21no—
46C4⋊C4×C89—21no—
47C4⋊C4×C89D412yes—
48C42×C89C2311yescharacteristic
49C22×D89—21no—
50Q8×C89—42no—
51Q8×C89—41no—
52Q8×C89—41no—
53C2×C4×C89—22no—
54C2×C4×C89—41no—
55C2×C4×C89C2×D411yescharacteristic
56C2×C4×C89C2×D411yescharacteristic
57C2×C4×C89C2×D411yescharacteristic
58C2×Dic89—21no—
59C2×Dic89—21no—
60C2×Dic89—21no—
61D356—21no—
62D356Q1612yes—
63C4×D89—44no—
64C4×D89—41no—
65C4×D89—41no—
66Dic178—21no—
67Dic178—44no—
68Dic178SD1612yes—
69C8×C89—41no—
70#10623494—41no—
71#10623494—41no—
72C22×C89#12011yescharacteristic
73C2×D89—22no—
74C2×D89—41no—
75C2×D89—41no—
76C4×C89—21no—
77C4×C89—42no—
78C4×C89—81no—
79C4×C89C2×SD1611yescharacteristic
80C4×C89C2×Q1611yescharacteristic
81C4×C89AGL(1,ℤ/8)11yescharacteristic
82C4×C89#13711yescharacteristic
83Dic89—22no—
84Dic89—41no—
85Dic89—41no—
86C2×C89#45011yescharacteristic
87C2×C89#45111yescharacteristic
88C2×C89#45411yescharacteristic
89D89—42no—
90#1637—891nomaximal, Sylow
91C89#163711yescharacteristic, complemented, Sylow
92D4×Q8—891no—
93#487D8911yescharacteristic, complemented
94#477—891no—
95#476—891no—
96#332—891no—
97Q8⋊C8—891no—
98D4⋊C8—891no—
99C22×Q8—1781no—
100C4⋊Q8—1781no—
101C4⋊Q8C2×D8911yescharacteristic
102C4⋊Q8C2×D8911yescharacteristic
103C22⋊Q8—1781no—
104C22⋊Q8—1782no—
105C4×Q8—891no—
106C4×D4—891no—
107C4×D4—1781no—
108#107—1781no—
109#106—1781no—
110C4⋊C8—891no—
111C4⋊C8—891no—
112#103—22no—
113#103—1781no—
114#102—1781no—
115C4×C8C2×D8911yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—891no—
119C2×Q8—3562no—
120C2×Q8—3562no—
121C2×Q8—1782no—
122C2×D4—891no—
123C22×C4—1782no—
124C22×C4—1781no—
125C2×C8—21no—
126C2×C8—1781no—
127C2×C8—1781no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—891no—
132C4⋊C4—891no—
133C4⋊C4—1782no—
134C4⋊C4—1781no—
135C4⋊C4C22⋊D8912yes—
136C22⋊C4—1782no—
137C22⋊C4—1781no—
138C42—1781no—
139C42C22×D8911yescharacteristic
140C23—1781no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—892no—
145Q8—3564no—
146Q8—1781no—
147D4—892no—
148D4—1781no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—3564no—
152C2×C4—3561no—
153C2×C4—3561no—
154C2×C4—1781no—
155C2×C4—1781no—
156C2×C4—1781no—
157C2×C4D4×D8911yescharacteristic
158C2×C4D4×D8911yescharacteristic
159C2×C4C2×C22⋊D8911yescharacteristic
160C8—41no—
161C8—3561no—
162C8—3561no—
163C22—3561no—
164C22—3561no—
165C22—1782no—
166C22#1566798011yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—3561no—
171C4—3561no—
172C4—1782no—
173C4SD16×D8911yescharacteristic
174C4Q16×D8911yescharacteristic
175C4#1566803911yescharacteristic
176C4#1566804411yescharacteristic
177C2—3562no—
178C2#1915174711yescharacteristic
179C2#1915175211yescharacteristic
180C2#1915177011yescharacteristic
subgroupG/H
centerC22#15667980
commutator, cosocleC42×C89C23
FrattiniC42C22×D89
Fitting#487×C89C2
socleC22×C89#120
prime radicalC2×D356D4
hypercenter#487D89
hypocenterC89#1637
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #19151890C2semidirect
4. #19151344C2semidirect
5. #19151330C2semidirect
7. #487×C89C2semidirect
91. C89#1637semidirect
93. #487D89semidirect

Maximal subgroups

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

subgroupindex
#191522632
#191518902
#191518852
#191513442
#191513302
#191513272
#487×C892
#163789