Finite Group Databasebeta

← #38767579

Subgroups — #38767579

Order 25472.

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

normal subgroups only

This group has 202 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#27164573C211yesmaximal, characteristic
2#27164074C211yesmaximal, characteristic
3#27164040C211yesmaximal, characteristic
4#27163766C211yesmaximal, characteristic, complemented
5#27163766C211yesmaximal, characteristic, complemented
6#27163764C211yesmaximal, characteristic, complemented
7#332×C199C211yesmaximal, characteristic, complemented
8C2×#15691869—21no—
9#20263955C2211yescharacteristic
10#20263946—21no—
11#20263935C412yes—
12#20263931—21no—
13Q8×Dic199—21no—
14#20263920C412yes—
15#20263913—21no—
16C42×D199C2211yescharacteristic
17C4⋊(C199⋊C8)C2211yescharacteristic
18C4⋊(C199⋊C8)C2211yescharacteristic
19Dic199⋊C8—21no—
20(C2×D199)⋊C8—21no—
21#20263865—21no—
22C4⋊Q8×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24C4⋊C8×C199C2211yescharacteristic
25C2×Dic398C2×C412yes—
26C2×C4×D199C2×C411yescharacteristic
27C2×C4×D199D411yescharacteristic
28C2×C4×D199D411yescharacteristic
29#15691869—42no—
30C2×C199⋊C8—21no—
31C2×C199⋊C8—21no—
32C4⋊Dic199—22no—
33C4⋊Dic199—21no—
34C4⋊Dic199—21no—
35Dic199⋊C4—22no—
36(C2×D199)⋊C4—22no—
37C4×Dic199—22no—
38C4×Dic199C2×C411yescharacteristic
39C4×Dic199D411yescharacteristic
40C4×Dic199D411yescharacteristic
41C2×Q8×C199—21no—
42C2×C8×C199—21no—
43C2×C8×C199—21no—
44C4⋊C4×C199—21no—
45C4⋊C4×C199C2×C412yes—
46C42×C199C2311yescharacteristic
47C22×D199C22⋊C411yescharacteristic
48Dic398—42no—
49C2×Dic199—22no—
50C2×Dic199C22⋊C411yescharacteristic
51C2×Dic199C22⋊C411yescharacteristic
52C2×Dic199C22⋊C411yescharacteristic
53C4×D199—21no—
54C4×D199—21no—
55C4×D199—21no—
56C4×D199—21no—
57C4×D199—41no—
58C199⋊C8—41no—
59C199⋊C8—41no—
60Q8×C199—41no—
61Q8×C199—41no—
62C2×C4×C199—22no—
63C2×C4×C199C22×C411yescharacteristic
64C2×C4×C199C2×D411yescharacteristic
65C2×C4×C199C2×D411yescharacteristic
66C8×C199—41no—
67C8×C199—41no—
68C22×C199C2×C22⋊C411yescharacteristic
69C2×D199—21no—
70C2×D199—21no—
71C2×D199—21no—
72C4×C199—21no—
73C4×C199—42no—
74C4×C199AGL(1,ℤ/8)11yescharacteristic
75C4×C199#13711yescharacteristic
76C4×C199#13711yescharacteristic
77C4×C199#13711yescharacteristic
78Dic199—21no—
79Dic199—21no—
80Dic199—21no—
81Dic199—42no—
82C2×C199#41311yescharacteristic
83C2×C199#41711yescharacteristic
84C2×C199#41911yescharacteristic
85D199—41no—
86C199#155911yescharacteristic, complemented, Sylow
87#1559—1991nomaximal, Sylow
88#533—1991no—
89#432—1991no—
90#423—1991no—
91#333—1991no—
92#333—1991no—
93#332—1991no—
94#332D19911yescharacteristic, complemented
95C2×M16—3981no—
96C4⋊Q8—1991no—
97C4⋊Q8C2×D19911yescharacteristic
98#125—3981no—
99C22⋊Q8—3981no—
100C22⋊Q8—1992no—
101C4×Q8—3981no—
102C4×Q8—1992no—
103#117—3981no—
104C2×C42—1991no—
105C4⋊C8—3981no—
106C4⋊C8—1991no—
107C4⋊C8—1991no—
108C4⋊C8C2×D19911yescharacteristic
109C4⋊C8C2×D19911yescharacteristic
110C22⋊C8—3981no—
111#97—3981no—
112C2×Q8—21no—
113C2×Q8—1992no—
114C22×C4—1991no—
115C22×C4—1991no—
116C22×C4—1991no—
117M16—7962no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—3981no—
121C2×C8—3981no—
122C4⋊C4—21no—
123C4⋊C4—3982no—
124C4⋊C4—3982no—
125C4⋊C4—3981no—
126C4⋊C4—3981no—
127C4⋊C4C4×D19912yes—
128C22⋊C4—3982no—
129C42—3982no—
130C42—1991no—
131C42—1991no—
132C42—1991no—
133C42C22×D19911yescharacteristic
134C23—1991no—
135Q8—41no—
136Q8—41no—
137Q8—7962no—
138C2×C4—22no—
139C2×C4—7961no—
140C2×C4—3982no—
141C2×C4—3981no—
142C2×C4—3981no—
143C2×C4—3981no—
144C2×C4—3981no—
145C2×C4—1991no—
146C2×C4—1991no—
147C2×C4—1991no—
148C2×C4C2×C4×D19911yescharacteristic
149C2×C4D4×D19911yescharacteristic
150C2×C4D4×D19911yescharacteristic
151C8—41no—
152C8—41no—
153C8—7961no—
154C8—7961no—
155C22—3981no—
156C22—3981no—
157C22—3981no—
158C22C22⋊C4×D19911yescharacteristic
159C4—21no—
160C4—42no—
161C4—7962no—
162C4—3981no—
163C4—3981no—
164C4—3981no—
165C4#2026397911yescharacteristic
166C4#2026398411yescharacteristic
167C4#2026398411yescharacteristic
168C4#2026398711yescharacteristic
169C2—7961no—
170C2#2716400111yescharacteristic
171C2#2716401611yescharacteristic
172C2#2716402511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#332×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D199C22⋊C4
cosocleC42×C199C23
hypercenter#332D199
hypocenterC199#1559
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #27163766C2semidirect
5. #27163766C2semidirect
6. #27163764C2semidirect
7. #332×C199C2semidirect
86. C199#1559semidirect
94. #332D199semidirect

Maximal subgroups

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

subgroupindex
#271645732
#271640742
#271640402
#271637662
#271637642
#332×C1992
#1559199