Finite Group Databasebeta

← #38767894

Subgroups — #38767894

Order 25472.

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

normal subgroups only

This group has 202 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#27164354C212yesmaximal
3#27163957C211yesmaximal, characteristic
4#27163756C212yesmaximal
5#324×C199C211yesmaximal, characteristic
6#20263954—22no—
7#20263946—22no—
8#20263934—21no—
9#20263934C2212yes—
10#20263914—21no—
11C2×C4⋊Dic199C2211yescharacteristic
12#20263889—22no—
13#20263880—22no—
14C199⋊#95—21no—
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—
30C22⋊Dic199—22no—
31C4×Dic199—22no—
32C22×C4×C199D411yescharacteristic
33C22×C4×C199D411yescharacteristic
34C22×C4×C199C2311yescharacteristic
35C2×C8×C199—22no—
36C4⋊C4×C199—22no—
37Dic398—42no—
38Dic398—81no—
39C2×Dic199—22no—
40C2×Dic199—22no—
41C2×Dic199—41no—
42C2×Dic199—41no—
43C2×Dic199—42no—
44C2×Dic199—41no—
45C2×Dic199—41no—
46C23×C199C2×D411yescharacteristic
47C2×C4×C199—21no—
48C2×C4×C199—21no—
49C2×C4×C199—21no—
50C2×C4×C199—41no—
51C2×C4×C199—41no—
52C2×C4×C199Q1612yes—
53C2×C4×C199C2×D412yes—
54C8×C199—42no—
55C22×C199—21no—
56C22×C199—21no—
57C22×C199#12011yescharacteristic
58C22×C199C2×Q1611yescharacteristic
59C22×C199#13711yescharacteristic
60C4×C199—22no—
61C4×C199—22no—
62C4×C199—41no—
63Dic199—42no—
64Dic199—42no—
65Dic199—81no—
66Dic199—81no—
67C2×C199—21no—
68C2×C199—21no—
69C2×C199#45111yescharacteristic
70C2×C199#45411yescharacteristic
71C2×C199#45811yescharacteristic
72C199#161711yescharacteristic, complemented, Sylow
73#1617—1991nomaximal, Sylow
74#544—1991no—
75#484—1992no—
76#400—1991no—
77#328—1992no—
78#324D19911yescharacteristic
79C4⋊Q8—3982no—
80#125—3982no—
81C22⋊Q8—3981no—
82C22⋊Q8—1992no—
83#117—3981no—
84C2×C4⋊C4—1991no—
85C2×C4⋊C4C2×D19911yescharacteristic
86#107—3982no—
87#103—3982no—
88C22⋊C8C2×D19912yes—
89#95—3981no—
90#95—3981no—
91#95—1991no—
92C2×Q8—3981no—
93C2×Q8—1992no—
94C22×C4—3981no—
95C22×C4—3981no—
96C22×C4D79611yescharacteristic
97C22×C4D79611yescharacteristic
98C22×C4C22×D19911yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—3982no—
102C4⋊C4—3981no—
103C4⋊C4—3981no—
104C4⋊C4—3981no—
105C4⋊C4—3982no—
106C4⋊C4—3982no—
107C4⋊C4—1992no—
108C22⋊C4—3982no—
109C42—3982no—
110C23C2×D79611yescharacteristic
111Q8—7962no—
112Q8—15921no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—7961no—
119C2×C4—7961no—
120C2×C4—7962no—
121C2×C4—7961no—
122C2×C4—7961no—
123C2×C4—3982no—
124C2×C4—3982no—
125C2×C4Dic79612yes—
126C2×C4D4×D19912yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#2026392511yescharacteristic
131C22C2×Dic79611yescharacteristic
132C22#2026398811yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—7962no—
137C4—7962no—
138C4—15921no—
139C4—15921no—
140C2—21no—
141C2—21no—
142C2#2716417611yescharacteristic
143C2#2716419311yescharacteristic
144C2#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#1617
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
72. C199#1617semidirect

Maximal subgroups

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

subgroupindex
#271646492
#271643542
#271639572
#271637562
#324×C1992
#1617199