Finite Group Databasebeta

← #38770925

Subgroups — #38770925

Order 25472.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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#27164456C211yesmaximal, characteristic, complemented
2#27164454C211yesmaximal, characteristic, complemented
3#27164393C211yesmaximal, characteristic, complemented
4#27164134C211yesmaximal, characteristic, complemented
5#27163838C211yesmaximal, characteristic, complemented
6#27163830C211yesmaximal, characteristic, complemented
7#361×C199C211yesmaximal, characteristic, complemented
8#20263977C2211yescharacteristic
9C2×D1592C2211yescharacteristic
10C2×#15691871—21no—
11#20263963—21no—
12#20263951—21no—
13#20263900—21no—
14#20263899—21no—
15D3184—21no—
16#20263896—21no—
17#20263895C2211yescharacteristic
18#20263881—21no—
19C8×Dic199C2211yescharacteristic
20C2×D8×C199C2211yescharacteristic
21M32×C199C2211yescharacteristic
22#108×C199C2211yescharacteristic
23#15691886—21no—
24C2×D796—21no—
25C2×C22⋊D199—42no—
26Dic796D411yescharacteristic, complemented
27#15691875—21no—
28D1592—21no—
29D1592—21no—
30D1592D411yescharacteristic, complemented
31#15691871—41no—
32#15691871—41no—
33#15691869—41no—
34C2×C199⋊C8D411yescharacteristic
35C8×D199—41no—
36C4×Dic199D411yescharacteristic
37C199⋊C16—21no—
38C2×D4×C199—21no—
39D8×C199—21no—
40D8×C199—21no—
41M16×C199—21no—
42C2×C8×C199C2311yescharacteristic
43C16×C199—21no—
44C22×D199—41no—
45Dic398—21no—
46D796—21no—
47D796—41no—
48D796—41no—
49C22⋊D199—41no—
50C22⋊D199—84no—
51C2×Dic199—21no—
52C4×D199—41no—
53C199⋊C8D811yescharacteristic
54C199⋊C8D811yescharacteristic
55C23×C199—41no—
56D4×C199—41no—
57D4×C199—41no—
58C2×C4×C199C2×D411yescharacteristic
59C8×C199—41no—
60C8×C199C2×D411yescharacteristic
61C8×C199#4111yescharacteristic
62C22×C199—82no—
63C22×C199—81no—
64C22×C199AGL(1,ℤ/8)11yescharacteristic
65C2×D199—41no—
66C2×D199—82no—
67C2×D199—81no—
68C4×C199#12111yescharacteristic
69C4×C199C2×D811yescharacteristic
70Dic199—22no—
71Dic199—41no—
72C2×C199—21no—
73C2×C199—161no—
74C2×C199#45911yescharacteristic
75D199—81no—
76D199—161no—
77C199#221311yescharacteristic, complemented, Sylow
78#2213—1991nomaximal, Sylow
79#509—1991no—
80#509—1991no—
81#493—1991no—
82#443—1991no—
83#364—1991no—
84#361—1991no—
85#361D19911yescharacteristic, complemented
86#135—1991no—
87C2×D8—3981no—
88C2×D8—1991no—
89C2×D8C2×D19911yescharacteristic
90#131—3981no—
91#127—3981no—
92SD32—3981no—
93SD32—3981no—
94D16—3981no—
95D16—3981no—
96M32—1991no—
97M32C2×D19911yescharacteristic
98#108C2×D19911yescharacteristic
99#104—3981no—
100C4×C8—1991no—
101#41—3981no—
102C2×D4—21no—
103C2×D4—7962no—
104C2×D4—3981no—
105Q16—1991no—
106SD16—3981no—
107D8—21no—
108D8—21no—
109D8—7961no—
110D8—7961no—
111D8—3981no—
112D8—3981no—
113D8—1991no—
114M16—21no—
115M16—7961no—
116C2×C8—7961no—
117C2×C8—1991no—
118C2×C8C22×D19911yescharacteristic
119C42—1991no—
120C16—21no—
121C16—3981no—
122C23—41no—
123C23—7961no—
124Q8—3981no—
125D4—41no—
126D4—41no—
127D4—7961no—
128D4—7961no—
129D4—7961no—
130D4—15924no—
131D4—3981no—
132C2×C4—7961no—
133C2×C4—3981no—
134C2×C4D4×D19911yescharacteristic
135C8—41no—
136C8—1991no—
137C8—1991no—
138C8D4×D19911yescharacteristic
139C8#1569188611yescharacteristic
140C22—82no—
141C22—81no—
142C22—7961no—
143C22—15922no—
144C22—15921no—
145C22#2026398211yescharacteristic
146C4—7961no—
147C4—3982no—
148C4#2026392811yescharacteristic
149C4D8×D19911yescharacteristic
150C2—21no—
151C2—161no—
152C2—15921no—
153C2—31841no—
154C2#2716421211yescharacteristic
subgroupG/H
centerC2#27164212
commutator, cosocleC2×C8×C199C23
FrattiniC2×C8C22×D199
Fitting#361×C199C2
socleC2×C199#459
hypercenter#361D199
hypocenterC199#2213
LCSG ▷ C2×C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #27164456C2semidirect
2. #27164454C2semidirect
3. #27164393C2semidirect
4. #27164134C2semidirect
5. #27163838C2semidirect
6. #27163830C2semidirect
7. #361×C199C2semidirect
26. Dic796D4semidirect
30. D1592D4semidirect
77. C199#2213semidirect
85. #361D199semidirect

Maximal subgroups

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

subgroupindex
#271644562
#271644542
#271643932
#271641342
#271638382
#271638302
#361×C1992
#2213199