Finite Group Databasebeta

← #38767443

Subgroups — #38767443

Order 25472.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#27164574C211yesmaximal, characteristic
2#27163970C212yesmaximal
3#27163760C211yesmaximal, characteristic, complemented
4#27163759C212yesmaximal, complemented
5#330×C199C211yesmaximal, characteristic, complemented
6C2×#15691869—22no—
7#20263954C412yes—
8#20263947C2211yescharacteristic
9#20263933—22no—
10#20263920—22no—
11#20263913C412yes—
12C42×D199C2211yescharacteristic
13#20263866C2212yes—
14C8×Dic199—22no—
15#125×C199C2211yescharacteristic
16#97×C199C2212yes—
17C2×Dic398—22no—
18C2×C4×D199C2×C411yescharacteristic
19C2×C4×D199D412yes—
20#15691869—28no—
21C2×C199⋊C8—22no—
22C4⋊Dic199C2×C412yes—
23Dic199⋊C4—22no—
24Dic199⋊C4—22no—
25(C2×D199)⋊C4—22no—
26C4×Dic199—22no—
27C4×Dic199C2×C411yescharacteristic
28C4×Dic199D412yes—
29C2×C8×C199—22no—
30C4⋊C4×C199—22no—
31C4⋊C4×C199C2×C412yes—
32C42×C199C2311yescharacteristic
33C22×D199C22⋊C411yescharacteristic
34Dic398—44no—
35C2×Dic199—22no—
36C2×Dic199C22⋊C411yescharacteristic
37C2×Dic199C22⋊C412yes—
38C4×D199—22no—
39C4×D199—24no—
40C199⋊C8—24no—
41C2×C4×C199—22no—
42C2×C4×C199C22×C411yescharacteristic
43C2×C4×C199C2×D412yes—
44C8×C199—24no—
45C22×C199C2×C22⋊C411yescharacteristic
46C2×D199—21no—
47C2×D199—22no—
48C4×C199—21no—
49C4×C199—22no—
50C4×C199—42no—
51Dic199—42no—
52Dic199#10112yes—
53Dic199#10414yes—
54C2×C199C2×#10111yescharacteristic
55C2×C199C2×#10412yes—
56D199—41no—
57C199#152611yescharacteristic, complemented, Sylow
58#1526—1991nomaximal, Sylow
59#533—1991no—
60C4×M16—1992no—
61#330—1991no—
62#330—1992no—
63#330D19911yescharacteristic, complemented
64C2×M16—3982no—
65C4⋊Q8—1992no—
66#125—1991no—
67#125C2×D19911yescharacteristic
68C22⋊Q8—3982no—
69C4×Q8—3982no—
70#117—1992no—
71C2×C42—1991no—
72#97—1992no—
73#97C2×D19912yes—
74C4×C8—3982no—
75C2×Q8—3982no—
76C22×C4—1991no—
77C22×C4—1992no—
78M16—3988no—
79C2×C8—22no—
80C2×C8—3982no—
81C4⋊C4—22no—
82C4⋊C4—3982no—
83C4⋊C4—3982no—
84C4⋊C4—1992no—
85C4⋊C4C4×D19912yes—
86C22⋊C4—3982no—
87C42—3982no—
88C42—1991no—
89C42—1992no—
90C42C22×D19911yescharacteristic
91C23—1991no—
92Q8—7964no—
93C2×C4—22no—
94C2×C4—3984no—
95C2×C4—3982no—
96C2×C4—3982no—
97C2×C4—1991no—
98C2×C4—1992no—
99C2×C4C2×C4×D19911yescharacteristic
100C2×C4D4×D19912yes—
101C8—24no—
102C8—3984no—
103C22—3981no—
104C22—3982no—
105C22C22⋊C4×D19911yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—7962no—
110C4—1992no—
111C4—1994no—
112C2—7961no—
113C2#101×D19911yescharacteristic
114C2#104×D19912yes—
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D199C22⋊C4
cosocleC42×C199C23
hypercenter#330D199
hypocenterC199#1526
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #27163760C2semidirect
4. #27163759C2semidirect
5. #330×C199C2semidirect
57. C199#1526semidirect
63. #330D199semidirect

Maximal subgroups

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

subgroupindex
#271645742
#271639702
#271637602
#271637592
#330×C1992
#1526199