Finite Group Databasebeta

← #38770798

Subgroups — #38770798

Order 25472.

226 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 49 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#27164818C211yesmaximal, characteristic, complemented
2#27164456C212yesmaximal, complemented
3#27164271C211yesmaximal, characteristic, complemented
4#27163829C212yesmaximal, complemented
5#349×C199C211yesmaximal, characteristic, complemented
6C2×#15691886—21no—
7#20263988—22no—
8#20263983—22no—
9#20263977—21no—
10#20263977C2212yes—
11C2×D1592C2211yescharacteristic, complemented
12#20263929—21no—
13#20263900—22no—
14D3184—22no—
15#20263887C2211yescharacteristic, complemented
16#20263877—21no—
17C2×M16×C199C2211yescharacteristic
18M32×C199C2212yescomplemented
19#15691886—22no—
20#15691886—22no—
21#15691886—41no—
22#15691886—41no—
23C2×Dic398—21no—
24C2×D796—21no—
25C2×D796—21no—
26C2×C22⋊D199—41no—
27C2×C22⋊D199—41no—
28C2×C4×D199—41no—
29Dic796—21no—
30Dic796D412yescomplemented
31#15691875—22no—
32#15691875—22no—
33D1592—21no—
34D1592—22no—
35D1592D412yescomplemented
36C4⋊Dic199—21no—
37(C2×D199)⋊C4—41no—
38C22×C4×C199D411yescharacteristic
39M16×C199—22no—
40C2×C8×C199D411yescharacteristic
41C2×C8×C199C2311yescharacteristic
42C16×C199—22no—
43C22×D199—41no—
44C22×D199—41no—
45Dic398—22no—
46Dic398—41no—
47D796—22no—
48D796—41no—
49D796—41no—
50D796—41no—
51C22⋊D199—42no—
52C22⋊D199—42no—
53C22⋊D199—82no—
54C2×Dic199—41no—
55C2×Dic199—41no—
56C4×D199—42no—
57C4×D199—42no—
58C23×C199D811yescharacteristic
59C2×C4×C199—21no—
60C2×C4×C199—21no—
61C2×C4×C199D811yescharacteristic
62C2×C4×C199C2×D411yescharacteristic
63C8×C199—21no—
64C8×C199C2×D412yes—
65C22×C199—21no—
66C22×C199—41no—
67C22×C199C2×D811yescharacteristic
68C2×D199—42no—
69C2×D199—82no—
70C2×D199—81no—
71C2×D199—81no—
72C2×D199—81no—
73C4×C199—21no—
74C4×C199#12011yescharacteristic
75C4×C199AGL(1,ℤ/8)11yescharacteristic
76Dic199—42no—
77Dic199—81no—
78C2×C199—21no—
79C2×C199—41no—
80C2×C199#44711yescharacteristic
81D199—82no—
82D199—161no—
83C199#219011yescharacteristic, complemented, Sylow
84#2190—1991nomaximal, Sylow
85#575—1991no—
86#509—1992no—
87#469—1991no—
88#360—1992no—
89#349D19911yescharacteristic, complemented
90C2×#41—3981no—
91#137—3982no—
92AGL(1,ℤ/8)—3982no—
93#135—3981no—
94#135—1992no—
95C2×D8—1991no—
96C2×M16C2×D19911yescharacteristic
97#121—3981no—
98SD32—3982no—
99D16—3982no—
100M32C2×D19912yescomplemented
101#106—1991no—
102#102—3981no—
103#41—7961no—
104#41—7961no—
105#41—3982no—
106#41—3982no—
107C2×Q8—3981no—
108C2×D4—7961no—
109C2×D4—7961no—
110C2×D4—3981no—
111C2×D4—3981no—
112C22×C4—7961no—
113C22×C4D79611yescharacteristic
114Q16—3981no—
115Q16—1992no—
116SD16—3982no—
117SD16—3982no—
118D8—3981no—
119D8—3982no—
120D8—1992no—
121M16—22no—
122C2×C8D79611yescharacteristic
123C2×C8C22×D19911yescharacteristic
124C4⋊C4—3981no—
125C22⋊C4—7961no—
126C16—22no—
127C23—7961no—
128C23—7961no—
129C23D159211yescharacteristic
130Q8—7961no—
131Q8—3982no—
132D4—7961no—
133D4—7962no—
134D4—7962no—
135D4—7961no—
136D4—7961no—
137D4—15922no—
138D4—3982no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—7962no—
142C2×C4—7961no—
143C2×C4—7962no—
144C2×C4—7961no—
145C2×C4D159211yescharacteristic
146C2×C4C2×D79611yescharacteristic
147C8—21no—
148C8D4×D19912yes—
149C22—21no—
150C22—41no—
151C22—7962no—
152C22—15921no—
153C22—15921no—
154C22—15922no—
155C22—15921no—
156C22C2×D159211yescharacteristic
157C4—21no—
158C4—7962no—
159C4—15921no—
160C4#2026392511yescharacteristic
161C4#2026398311yescharacteristic
162C2—21no—
163C2—41no—
164C2—15922no—
165C2—31841no—
166C2#2716415411yescharacteristic
subgroupG/H
centerC2#27164154
commutator, cosocleC2×C8×C199C23
FrattiniC2×C8C22×D199
Fitting#349×C199C2
socleC2×C199#447
hypercenter#349D199
hypocenterC199#2190
LCSG ▷ C2×C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
1. #27164818C2semidirect
2. #27164456C2semidirect
3. #27164271C2semidirect
4. #27163829C2semidirect
5. #349×C199C2semidirect
11. C2×D1592C22semidirect
15. #20263887C22semidirect
18. M32×C199C22semidirect
30. Dic796D4semidirect
35. D1592D4semidirect
83. C199#2190semidirect
89. #349D199semidirect
100. M32C2×D199semidirect

Maximal subgroups

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

subgroupindex
#271648182
#271644562
#271642712
#271638292
#349×C1992
#2190199