Finite Group Databasebeta

← #38767886

Subgroups — #38767886

Order 25472.

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

normal subgroups only

This group has 246 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#27164599C211yesmaximal, characteristic
2#27164336C212yesmaximal, complemented
3#27163751C212yesmaximal, complemented
4#27163744C211yesmaximal, characteristic, complemented
5#400×C199C211yesmaximal, characteristic, complemented
6C2×#15691886—21no—
7#20263935—22no—
8#20263930—22no—
9#20263929—21no—
10#20263929C2212yes—
11#20263886—22no—
12#20263875—22no—
13C22⋊(C199⋊C8)C2212yes—
14C2×C4⋊C4×C199C2211yescharacteristic
15C2×C4⋊C4×C199C2211yescharacteristic
16#95×C199—21no—
17#95×C199—21no—
18#95×C199C2211yescharacteristic
19#15691886—42no—
20#15691886—42no—
21C2×Dic398—21no—
22C2×D796—21no—
23C2×D796—21no—
24C2×D796D412yes—
25C2×C22⋊D199—22no—
26C2×C4×D199—22no—
27C2×C199⋊C8—22no—
28C4⋊Dic199—21no—
29C4⋊Dic199D412yes—
30(C2×D199)⋊C4—22no—
31(C2×D199)⋊C4—22no—
32C22×C4×C199—21no—
33C22×C4×C199—21no—
34C22×C4×C199D411yescharacteristic
35C22×C4×C199D411yescharacteristic
36C22×C4×C199C2311yescharacteristic
37C4⋊C4×C199—22no—
38C4⋊C4×C199—22no—
39C22×D199—22no—
40Dic398—42no—
41D796—42no—
42D796—42no—
43D796—81no—
44C22⋊D199—42no—
45C22⋊D199—42no—
46C2×Dic199—22no—
47C4×D199—44no—
48C199⋊C8—42no—
49C23×C199C2×D411yescharacteristic
50C2×C4×C199—21no—
51C2×C4×C199—21no—
52C2×C4×C199—21no—
53C2×C4×C199—41no—
54C2×C4×C199—41no—
55C2×C4×C199—41no—
56C2×C4×C199—41no—
57C2×C4×C199—42no—
58C2×C4×C199—41no—
59C2×C4×C199—41no—
60C2×C4×C199SD1612yes—
61C2×C4×C199C2×D412yes—
62C22×C199—21no—
63C22×C199—21no—
64C22×C199#12011yescharacteristic
65C22×C199C2×SD1611yescharacteristic
66C22×C199AGL(1,ℤ/8)11yescharacteristic
67C2×D199—42no—
68C2×D199—42no—
69C2×D199—42no—
70C4×C199—22no—
71C4×C199—22no—
72C4×C199—41no—
73C4×C199—81no—
74C4×C199—81no—
75Dic199—42no—
76C2×C199—21no—
77C2×C199—21no—
78C2×C199#45011yescharacteristic
79C2×C199#45411yescharacteristic
80C2×C199#45811yescharacteristic
81D199—82no—
82C199#161611yescharacteristic, complemented, Sylow
83#1616—1991nomaximal, Sylow
84#537—1991no—
85#481—1992no—
86#400D19911yescharacteristic, complemented
87#327—1992no—
88#324—1991no—
89C2×#41—3981no—
90C22⋊Q8—3982no—
91#121—3982no—
92#121—3981no—
93#121—1992no—
94C2×C4⋊C4C2×D19911yescharacteristic
95C2×C4⋊C4C2×D19911yescharacteristic
96#106—3982no—
97#102—3982no—
98C22⋊C8—1992no—
99#95—21no—
100#95—21no—
101#95C2×D19911yescharacteristic
102#41—7962no—
103#41—7962no—
104C2×Q8—3981no—
105C2×D4—3981no—
106C2×D4—3981no—
107C2×D4—3982no—
108C2×D4—1992no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—3982no—
112C22×C4C22⋊D19911yescharacteristic
113C22×C4C22⋊D19911yescharacteristic
114C22×C4C22×D19911yescharacteristic
115C2×C8—3982no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—3981no—
119C4⋊C4—1992no—
120C22⋊C4—3982no—
121C22⋊C4—3982no—
122C23—3982no—
123C23C2×C22⋊D19911yescharacteristic
124Q8—7962no—
125D4—7962no—
126D4—7962no—
127D4—7962no—
128D4—7962no—
129D4—15921no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—7964no—
141C2×C4—3982no—
142C2×C4#1569187312yes—
143C2×C4D4×D19912yes—
144C8—7962no—
145C22—21no—
146C22—21no—
147C22—7962no—
148C22—7962no—
149C22—7962no—
150C22#2026392311yescharacteristic
151C22C2×#1569187311yescharacteristic
152C22#2026398011yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—7962no—
159C2—21no—
160C2—21no—
161C2—15922no—
162C2#2716416811yescharacteristic
163C2#2716419011yescharacteristic
164C2#2716420711yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#400×C199C2
socleC22×C199#120
prime radical#27164599C2
hypercenter#400D199
hypocenterC199#1616
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #27164336C2semidirect
3. #27163751C2semidirect
4. #27163744C2semidirect
5. #400×C199C2semidirect
82. C199#1616semidirect
86. #400D199semidirect

Maximal subgroups

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

subgroupindex
#271645992
#271643362
#271637512
#271637442
#400×C1992
#1616199