Finite Group Databasebeta

← #26018973

Subgroups — #26018973

Order 11392.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#19152149C211yesmaximal, characteristic
2#19151654C211yesmaximal, characteristic, complemented
3#19151620C211yesmaximal, characteristic, complemented
4#19151344C211yesmaximal, characteristic, complemented
5#19151341C211yesmaximal, characteristic, complemented
6#19151341C211yesmaximal, characteristic, complemented
7#332×C89C211yesmaximal, characteristic, complemented
8C2×#13083575—21no—
9C2×#13083557—21no—
10#15668009C2211yescharacteristic
11#15668001—21no—
12#15667987—21no—
13#15667987C412yes—
14#15667974—21no—
15#15667974C412yes—
16C42×D89C2211yescharacteristic
17C4⋊#10623494C2211yescharacteristic
18C4⋊#10623494C2211yescharacteristic
19#15667941—21no—
20#15667924—21no—
21#15667922—21no—
22C4⋊Q8×C89C2211yescharacteristic
23C4⋊C8×C89C2211yescharacteristic
24C4⋊C8×C89C2211yescharacteristic
25#13083575—42no—
26#13083575—42no—
27C2×D356—22no—
28C2×D356—21no—
29C2×D356—21no—
30C2×D356C2×C412yes—
31C2×C4×D89—22no—
32C2×C4×D89C2×C411yescharacteristic
33C2×C4×D89D411yescharacteristic
34C2×C4×D89D411yescharacteristic
35#13083557—42no—
36C2×#10623494—21no—
37C2×#10623494—21no—
38#13083551—22no—
39#13083551—22no—
40C4×Dic89C2×C411yescharacteristic
41C4×Dic89D411yescharacteristic
42C4×Dic89D411yescharacteristic
43C2×Q8×C89—21no—
44C2×C8×C89—21no—
45C2×C8×C89—21no—
46C4⋊C4×C89—21no—
47C4⋊C4×C89C2×C412yes—
48C42×C89C2311yescharacteristic
49C22×D89—22no—
50C22×D89C22⋊C411yescharacteristic
51Q8×C89—41no—
52Q8×C89—41no—
53C2×C4×C89—22no—
54C2×C4×C89C22×C411yescharacteristic
55C2×C4×C89C2×D411yescharacteristic
56C2×C4×C89C2×D411yescharacteristic
57C2×Dic89C22⋊C411yescharacteristic
58C2×Dic89C22⋊C411yescharacteristic
59C2×Dic89C22⋊C411yescharacteristic
60D356—42no—
61D356—44no—
62D356—41no—
63D356—41no—
64D356—41no—
65D356—41no—
66C4×D89—21no—
67C4×D89—21no—
68C4×D89—21no—
69C4×D89—21no—
70C4×D89—41no—
71C4×D89—44no—
72C8×C89—41no—
73C8×C89—41no—
74#10623494—41no—
75#10623494—41no—
76C22×C89C2×C22⋊C411yescharacteristic
77C2×D89—21no—
78C2×D89—21no—
79C2×D89—21no—
80C2×D89—42no—
81C2×D89—42no—
82C2×D89—42no—
83C4×C89—21no—
84C4×C89—42no—
85C4×C89AGL(1,ℤ/8)11yescharacteristic
86C4×C89AGL(1,ℤ/8)11yescharacteristic
87C4×C89AGL(1,ℤ/8)11yescharacteristic
88C4×C89#13711yescharacteristic
89Dic89—21no—
90Dic89—21no—
91Dic89—21no—
92C2×C89#41311yescharacteristic
93C2×C89#41711yescharacteristic
94C2×C89#41811yescharacteristic
95D89—41no—
96D89—82no—
97#1557—891nomaximal, Sylow
98C89#155711yescharacteristic, complemented, Sylow
99#532—891no—
100#432—891no—
101#423—891no—
102#332—891no—
103#332D8911yescharacteristic, complemented
104#331—891no—
105#331—891no—
106C2×#41—1781no—
107C2×M16—1781no—
108C4⋊Q8C2×D8911yescharacteristic
109#127—891no—
110#124—1781no—
111#121—892no—
112#121—1781no—
113C4×D4—892no—
114C4×D4—1781no—
115C2×C42—891no—
116C4⋊C8—891no—
117C4⋊C8—891no—
118C4⋊C8—1781no—
119C4⋊C8C2×D8911yescharacteristic
120C4⋊C8C2×D8911yescharacteristic
121C22⋊C8—1781no—
122#97—1781no—
123#41—3562no—
124#41—3562no—
125C2×Q8—21no—
126C2×D4—892no—
127C2×D4—1782no—
128C2×D4—1781no—
129C2×D4—1781no—
130C22×C4—891no—
131C22×C4—891no—
132C22×C4—891no—
133C22×C4—1782no—
134M16—3562no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—1781no—
138C2×C8—1781no—
139C4⋊C4—21no—
140C4⋊C4C4×D8912yes—
141C22⋊C4—1782no—
142C22⋊C4—1782no—
143C42—891no—
144C42—891no—
145C42—891no—
146C42C22×D8911yescharacteristic
147C23—891no—
148C23—1782no—
149Q8—41no—
150Q8—41no—
151D4—3562no—
152D4—3564no—
153D4—3561no—
154D4—3561no—
155D4—3561no—
156D4—3561no—
157C2×C4—22no—
158C2×C4—891no—
159C2×C4—891no—
160C2×C4—891no—
161C2×C4—3561no—
162C2×C4—3564no—
163C2×C4—1781no—
164C2×C4—1781no—
165C2×C4—1781no—
166C2×C4—1781no—
167C2×C4C2×C4×D8911yescharacteristic
168C2×C4D4×D8911yescharacteristic
169C2×C4D4×D8911yescharacteristic
170C8—41no—
171C8—41no—
172C8—3561no—
173C8—3561no—
174C22—3562no—
175C22—3562no—
176C22—3562no—
177C22—1781no—
178C22—1781no—
179C22—1781no—
180C22C22⋊C4×D8911yescharacteristic
181C4—21no—
182C4—42no—
183C4—1781no—
184C4—1781no—
185C4—1781no—
186C4#1566803611yescharacteristic
187C4#1566803911yescharacteristic
188C4#1566803911yescharacteristic
189C4#1566804411yescharacteristic
190C2—3561no—
191C2—7122no—
192C2#1915158111yescharacteristic
193C2#1915159811yescharacteristic
194C2#1915160111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D89
commutatorC2×C4×C89C22×C4
FrattiniC42C22×D89
Fitting#332×C89C2
socleC22×C89C2×C22⋊C4
prime radical#19152149C2
cosocleC42×C89C23
hypercenter#332D89
hypocenterC89#1557
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #19151654C2semidirect
3. #19151620C2semidirect
4. #19151344C2semidirect
5. #19151341C2semidirect
6. #19151341C2semidirect
7. #332×C89C2semidirect
98. C89#1557semidirect
103. #332D89semidirect

Maximal subgroups

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

subgroupindex
#191521492
#191516542
#191516202
#191513442
#191513412
#332×C892
#155789