Finite Group Databasebeta

← #38767449

Subgroups — #38767449

Order 25472.

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

normal subgroups only

This group has 264 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
1C2×#20263943C211yesmaximal, characteristic
2C4×#15691870C211yesmaximal, characteristic, complemented
3#27163757C214yesmaximal, complemented
4#432×C199C211yesmaximal, characteristic, complemented
5C22×Dic398C411yescharacteristic
6C22×D796C411yescharacteristic
7C2×#15691870—21no—
8#20263943—21no—
9#20263943—21no—
10#20263943C412yes—
11#20263943C2212yes—
12C2×(C2×D199)⋊C4—21no—
13C2×(C2×D199)⋊C4—21no—
14#20263866C2212yescomplemented
15C4×C199⋊C8—21no—
16C2×C42×C199C2211yescharacteristic
17C4⋊C8×C199—21no—
18C22⋊C8×C199—21no—
19#97×C199C2212yescomplemented
20C23×D199—21no—
21C2×Dic398—21no—
22C2×Dic398—42no—
23C2×Dic398C2×C412yes—
24C2×D796—21no—
25C2×D796—42no—
26C2×D796C2×C412yes—
27C22×Dic199—21no—
28#15691870—24no—
29C2×C199⋊C8—22no—
30(C2×D199)⋊C4—22no—
31(C2×D199)⋊C4—22no—
32(C2×D199)⋊C4—22no—
33(C2×D199)⋊C4—22no—
34C22×C4×C199C2×C411yescharacteristic
35C22×C4×C199D411yescharacteristic
36C22×C4×C199D411yescharacteristic
37C2×C8×C199—22no—
38C42×C199C2×C411yescharacteristic
39C42×C199D411yescharacteristic
40C42×C199D411yescharacteristic
41C42×C199C2311yescharacteristic
42C22×D199—22no—
43C22×D199—42no—
44C22×D199—42no—
45C22×D199—42no—
46Dic398—42no—
47Dic398—42no—
48D796—42no—
49D796—42no—
50C2×Dic199—22no—
51C2×Dic199—42no—
52C199⋊C8—24no—
53C23×C199C22⋊C411yescharacteristic
54C2×C4×C199—22no—
55C2×C4×C199—22no—
56C2×C4×C199—41no—
57C2×C4×C199C22⋊C411yescharacteristic
58C2×C4×C199C22⋊C411yescharacteristic
59C2×C4×C199C22⋊C411yescharacteristic
60C2×C4×C199C22×C411yescharacteristic
61C2×C4×C199C2×D411yescharacteristic
62C2×C4×C199C2×D411yescharacteristic
63C8×C199—42no—
64C22×C199—21no—
65C22×C199—21no—
66C22×C199#10412yes—
67C22×C199C2×C22⋊C411yescharacteristic
68C2×D199—42no—
69C2×D199—42no—
70C2×D199—42no—
71C2×D199—84no—
72C4×C199—21no—
73C4×C199—21no—
74C4×C199—21no—
75C4×C199—21no—
76C4×C199—21no—
77C4×C199#10012yes—
78Dic199—42no—
79C2×C199—22no—
80C2×C199C2×#10011yescharacteristic
81C2×C199C2×#10411yescharacteristic
82C2×C199#42111yescharacteristic
83D199—82no—
84C199#152711yescharacteristic, complemented, Sylow
85#1527—1991nomaximal, Sylow
86C2×#124—1991no—
87#432D19911yescharacteristic, complemented
88C4×M16—1991no—
89#329—1994no—
90C22×Q8—1991no—
91C22×D4—1991no—
92C2×M16—3981no—
93#124—3981no—
94#124—3981no—
95#124—1992no—
96#124—1992no—
97C2×C22⋊C4—3981no—
98C2×C22⋊C4—3981no—
99C2×C42C2×D19911yescharacteristic
100C4⋊C8—21no—
101C22⋊C8—21no—
102#97—1992no—
103#97C2×D19912yescomplemented
104C4×C8—3981no—
105C24—3981no—
106C2×Q8—7962no—
107C2×Q8—3981no—
108C2×Q8—1992no—
109C2×D4—7962no—
110C2×D4—3981no—
111C2×D4—1992no—
112C22×C4—3981no—
113C22×C4C4×D19911yescharacteristic
114C22×C4C22⋊D19911yescharacteristic
115C22×C4D79611yescharacteristic
116M16—3984no—
117C2×C8—22no—
118C2×C8—3982no—
119C22⋊C4—3982no—
120C22⋊C4—3982no—
121C22⋊C4—3982no—
122C22⋊C4—3982no—
123C42C4×D19911yescharacteristic
124C42C22⋊D19911yescharacteristic
125C42D79611yescharacteristic
126C42C22×D19911yescharacteristic
127C23—7962no—
128C23—7962no—
129C23—7962no—
130C23—3982no—
131C23(C2×D199)⋊C411yescharacteristic
132Q8—7962no—
133Q8—7962no—
134D4—7962no—
135D4—7962no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—7962no—
140C2×C4—3982no—
141C2×C4(C2×D199)⋊C411yescharacteristic
142C2×C4(C2×D199)⋊C411yescharacteristic
143C2×C4(C2×D199)⋊C411yescharacteristic
144C2×C4C2×C4×D19911yescharacteristic
145C2×C4C2×C22⋊D19911yescharacteristic
146C2×C4C2×D79611yescharacteristic
147C8—42no—
148C8—3984no—
149C22—21no—
150C22—21no—
151C22—7962no—
152C22—7962no—
153C22—7962no—
154C22—15924no—
155C22#2026388112yes—
156C22C2×(C2×D199)⋊C411yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—7962no—
163C4#2026387112yes—
164C2—22no—
165C2—15922no—
166C2C2×#2026387111yescharacteristic
167C2C2×#2026388111yescharacteristic
168C2#2716403611yescharacteristic
subgroupG/H
centerC22C2×(C2×D199)⋊C4
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#432×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D796C4
cosocleC42×C199C23
hypercenter#432D199
hypocenterC199#1527
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×#15691870C2semidirect
3. #27163757C2semidirect
4. #432×C199C2semidirect
14. #20263866C22semidirect
19. #97×C199C22semidirect
84. C199#1527semidirect
87. #432D199semidirect
103. #97C2×D199semidirect

Maximal subgroups

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

subgroupindex
C2×#202639432
C4×#156918702
#271637572
#432×C1992
#1527199