Finite Group Databasebeta

← #38767860

Subgroups — #38767860

Order 25472.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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#27164649C211yesmaximal, characteristic
2#27164349C212yesmaximal
3#27163948C211yesmaximal, characteristic
4#27163756C212yesmaximal
5#324×C199C211yesmaximal, characteristic
6#20263954—22no—
7#20263946—22no—
8#20263934—21no—
9#20263934C2212yes—
10#20263914—21no—
11C2×C4⋊Dic199C2211yescharacteristic
12C2×Dic199⋊C4—21no—
13#20263887—22no—
14#20263880—22no—
15C199⋊#95—21no—
16C199⋊#95C2211yescharacteristic
17C2×C4⋊C4×C199C2211yescharacteristic
18C22⋊C8×C199C2212yes—
19C2×Dic398—21no—
20C2×Dic398D412yes—
21C22×Dic199—21no—
22C22×Dic199—21no—
23C4⋊Dic199—21no—
24C4⋊Dic199—21no—
25C4⋊Dic199—21no—
26C4⋊Dic199—22no—
27C4⋊Dic199D412yes—
28Dic199⋊C4—22no—
29Dic199⋊C4—22no—
30Dic199⋊C4—42no—
31C22⋊Dic199—22no—
32C4×Dic199—22no—
33C22×C4×C199D411yescharacteristic
34C22×C4×C199D411yescharacteristic
35C22×C4×C199C2311yescharacteristic
36C2×C8×C199—22no—
37C4⋊C4×C199—22no—
38Dic398—42no—
39Dic398—81no—
40C2×Dic199—22no—
41C2×Dic199—22no—
42C2×Dic199—22no—
43C2×Dic199—41no—
44C2×Dic199—41no—
45C2×Dic199—41no—
46C2×Dic199—41no—
47C2×Dic199—41no—
48C23×C199C2×D411yescharacteristic
49C2×C4×C199—21no—
50C2×C4×C199—21no—
51C2×C4×C199—21no—
52C2×C4×C199—41no—
53C2×C4×C199—41no—
54C2×C4×C199SD1612yes—
55C2×C4×C199C2×D412yes—
56C8×C199—42no—
57C22×C199—21no—
58C22×C199—21no—
59C22×C199#12011yescharacteristic
60C22×C199C2×SD1611yescharacteristic
61C22×C199#13711yescharacteristic
62C4×C199—22no—
63C4×C199—22no—
64C4×C199—41no—
65Dic199—42no—
66Dic199—42no—
67Dic199—42no—
68Dic199—81no—
69C2×C199—21no—
70C2×C199—21no—
71C2×C199#44811yescharacteristic
72C2×C199#45611yescharacteristic
73C2×C199#45811yescharacteristic
74C199#161111yescharacteristic, complemented, Sylow
75#1611—1991nomaximal, Sylow
76#544—1991no—
77#483—1992no—
78#398—1991no—
79#328—1992no—
80#324D19911yescharacteristic
81C4⋊Q8—3982no—
82#125—3982no—
83C22⋊Q8—3981no—
84C22⋊Q8—1992no—
85#117—3981no—
86C2×C4⋊C4—3981no—
87C2×C4⋊C4—1991no—
88C2×C4⋊C4C2×D19911yescharacteristic
89#106—3982no—
90#103—3982no—
91C22⋊C8C2×D19912yes—
92#95—3981no—
93#95—1991no—
94C2×Q8—3981no—
95C2×Q8—1992no—
96C22×C4—3981no—
97C22×C4—3981no—
98C22×C4D79611yescharacteristic
99C22×C4D79611yescharacteristic
100C22×C4C22×D19911yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—7962no—
104C4⋊C4—3982no—
105C4⋊C4—3981no—
106C4⋊C4—3981no—
107C4⋊C4—3981no—
108C4⋊C4—3982no—
109C4⋊C4—3982no—
110C4⋊C4—1992no—
111C22⋊C4—3982no—
112C42—3982no—
113C23C2×D79611yescharacteristic
114Q8—7962no—
115Q8—15921no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—7961no—
122C2×C4—7961no—
123C2×C4—7961no—
124C2×C4—7961no—
125C2×C4—7961no—
126C2×C4—3982no—
127C2×C4—3982no—
128C2×C4—3982no—
129C2×C4#1569187512yes—
130C2×C4D4×D19912yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#2026392511yescharacteristic
135C22C2×#1569187511yescharacteristic
136C22#2026398811yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—7962no—
141C4—7962no—
142C4—7962no—
143C4—15921no—
144C2—21no—
145C2—21no—
146C2#2716415911yescharacteristic
147C2#2716420311yescharacteristic
148C2#2716420911yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#324×C199C2
socleC22×C199#120
prime radicalC23×C199C2×D4
hypercenter#324D199
hypocenterC199#1611
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
74. C199#1611semidirect

Maximal subgroups

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

subgroupindex
#271646492
#271643492
#271639482
#271637562
#324×C1992
#1611199