Finite Group Databasebeta

← #38767376

Subgroups — #38767376

Order 25472.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#27164552C211yesmaximal, characteristic
2C4×C4⋊Dic199C211yesmaximal, characteristic, complemented
3#27163756C212yesmaximal, complemented
4#27163753C212yesmaximal
5#432×C199C211yesmaximal, characteristic, complemented
6#20263949—21no—
7#20263947C411yescharacteristic, complemented
8#20263943C411yescharacteristic, complemented
9#20263938—21no—
10#20263934C2211yescharacteristic
11#20263929C2211yescharacteristic
12C4×Dic398C411yescharacteristic, complemented
13C4×D796C411yescharacteristic, complemented
14C4×C22⋊D199—21no—
15#20263912—21no—
16C2×C4⋊Dic199—21no—
17C2×C4×Dic199—21no—
18C199⋊#95C2212yes—
19C2×C42×C199C2211yescharacteristic
20C4⋊C8×C199—21no—
21C22⋊C8×C199C2212yes—
22#97×C199—21no—
23C2×Dic398C2×C411yescharacteristic
24C2×D796C2×C411yescharacteristic
25C2×C22⋊D199—21no—
26C22×Dic199—22no—
27C2×C4×D199—21no—
28C4⋊Dic199—24no—
29C4⋊Dic199C2×C411yescharacteristic
30C4⋊Dic199C2×C411yescharacteristic
31Dic199⋊C4—21no—
32Dic199⋊C4—21no—
33Dic199⋊C4—21no—
34Dic199⋊C4—21no—
35C22⋊Dic199—21no—
36(C2×D199)⋊C4—21no—
37(C2×D199)⋊C4—21no—
38(C2×D199)⋊C4—21no—
39(C2×D199)⋊C4—21no—
40C4×Dic199—21no—
41C4×Dic199—42no—
42C22×C4×C199D411yescharacteristic
43C22×C4×C199D411yescharacteristic
44C22×C4×C199C2311yescharacteristic
45C2×C8×C199—22no—
46C42×C199C2×C411yescharacteristic
47C42×C199C2×C411yescharacteristic
48C42×C199D411yescharacteristic
49C42×C199D411yescharacteristic
50C22×D199—21no—
51Dic398—41no—
52D796—41no—
53C22⋊D199—41no—
54C22⋊D199—41no—
55C2×Dic199—24no—
56C2×Dic199—21no—
57C2×Dic199—21no—
58C2×Dic199—21no—
59C2×Dic199—42no—
60C2×Dic199—42no—
61C4×D199—42no—
62C23×C199C2×D411yescharacteristic
63C2×C4×C199—21no—
64C2×C4×C199—21no—
65C2×C4×C199—22no—
66C2×C4×C199—41no—
67C2×C4×C199C22⋊C411yescharacteristic
68C2×C4×C199C22⋊C411yescharacteristic
69C2×C4×C199C22⋊C411yescharacteristic
70C2×C4×C199C22⋊C411yescharacteristic
71C2×C4×C199C22×C411yescharacteristic
72C2×C4×C199C2×D411yescharacteristic
73C8×C199—42no—
74C22×C199—21no—
75C22×C199—21no—
76C22×C199C2×C22⋊C411yescharacteristic
77C22×C199AGL(1,ℤ/8)11yescharacteristic
78C22×C199#13711yescharacteristic
79C2×D199—41no—
80C2×D199—41no—
81C2×D199—41no—
82C4×C199—21no—
83C4×C199—21no—
84C4×C199—21no—
85C4×C199—21no—
86C4×C199—21no—
87C4×C199#10412yes—
88Dic199—44no—
89Dic199—41no—
90Dic199—41no—
91Dic199—41no—
92C2×C199—21no—
93C2×C199—21no—
94C2×C199#41011yescharacteristic
95C2×C199#41711yescharacteristic
96C2×C199C2×#10411yescharacteristic
97D199—81no—
98C199#150911yescharacteristic, complemented, Sylow
99#1509—1991nomaximal, Sylow
100#529—1991no—
101#432D19911yescharacteristic, complemented
102C4×C4⋊C4—1991no—
103#328—1992no—
104#327—1992no—
105#126—3981no—
106#125—1991no—
107#124—1991no—
108#123—3981no—
109C22⋊Q8—1991no—
110#121—1991no—
111C4×Q8—1991no—
112C4×D4—3981no—
113C4×D4—1991no—
114#117—3981no—
115C2×C4⋊C4—3981no—
116C2×C42—3981no—
117C2×C42C2×D19911yescharacteristic
118C4⋊C8—21no—
119C22⋊C8C2×D19912yes—
120#97—21no—
121#95—1992no—
122C2×Q8—1991no—
123C2×D4—3981no—
124C2×D4—1991no—
125C22×C4—3982no—
126C22×C4—3981no—
127C22×C4D79611yescharacteristic
128C22×C4D79611yescharacteristic
129C22×C4C22×D19911yescharacteristic
130C2×C8—22no—
131C4⋊C4—3984no—
132C4⋊C4—3981no—
133C4⋊C4—3981no—
134C4⋊C4—3981no—
135C4⋊C4—3981no—
136C4⋊C4—1991no—
137C4⋊C4—1991no—
138C22⋊C4—3981no—
139C22⋊C4—3981no—
140C22⋊C4—3981no—
141C22⋊C4—3981no—
142C22⋊C4—3981no—
143C42—7962no—
144C42—3981no—
145C42C4×D19911yescharacteristic
146C42C4×D19911yescharacteristic
147C42C22⋊D19911yescharacteristic
148C42C22⋊D19911yescharacteristic
149C23—3981no—
150C23C2×D79611yescharacteristic
151Q8—7961no—
152D4—7961no—
153D4—7961no—
154D4—7961no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—7962no—
160C2×C4—7962no—
161C2×C4—7962no—
162C2×C4—3984no—
163C2×C4—3981no—
164C2×C4—3981no—
165C2×C4—3981no—
166C2×C4(C2×D199)⋊C411yescharacteristic
167C2×C4(C2×D199)⋊C411yescharacteristic
168C2×C4(C2×D199)⋊C411yescharacteristic
169C2×C4(C2×D199)⋊C411yescharacteristic
170C2×C4C2×C4×D19911yescharacteristic
171C2×C4C2×C22⋊D19911yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—7961no—
176C22—7961no—
177C22—7961no—
178C22C2×(C2×D199)⋊C411yescharacteristic
179C22#2026398311yescharacteristic
180C22#2026398811yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—7964no—
187C4—7961no—
188C4—7961no—
189C4—7961no—
190C4#2026388112yes—
191C2—21no—
192C2—21no—
193C2—15921no—
194C2#2716399111yescharacteristic
195C2#2716402011yescharacteristic
196C2C2×#2026388111yescharacteristic
subgroupG/H
centerC22C2×(C2×D199)⋊C4
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#432×C199C2
socleC22×C199C2×C22⋊C4
prime radical#20263929C22
cosocleC22×C4×C199C23
hypercenter#432D199
hypocenterC199#1509
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic199C2semidirect
3. #27163756C2semidirect
5. #432×C199C2semidirect
7. #20263947C4semidirect
8. #20263943C4semidirect
12. C4×Dic398C4semidirect
13. C4×D796C4semidirect
98. C199#1509semidirect
101. #432D199semidirect

Maximal subgroups

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

subgroupindex
#271645522
C4×C4⋊Dic1992
#271637562
#271637532
#432×C1992
#1509199