Finite Group Databasebeta

← #44486623

Subgroups — #44486623

Order 30592.

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#29505210C211yesmaximal, characteristic, complemented
2#29505208C211yesmaximal, characteristic, complemented
3#29505147C211yesmaximal, characteristic, complemented
4#29504888C211yesmaximal, characteristic, complemented
5#29504592C211yesmaximal, characteristic, complemented
6#29504584C211yesmaximal, characteristic, complemented
7#361×C239C211yesmaximal, characteristic, complemented
8#21439982C2211yescharacteristic
9C2×D1912C2211yescharacteristic
10C2×#16838533—21no—
11#21439968—21no—
12#21439956—21no—
13#21439905—21no—
14#21439904—21no—
15D3824—21no—
16#21439901—21no—
17#21439900C2211yescharacteristic
18#21439886—21no—
19C8×Dic239C2211yescharacteristic
20C2×D8×C239C2211yescharacteristic
21M32×C239C2211yescharacteristic
22#108×C239C2211yescharacteristic
23#16838548—21no—
24C2×D956—21no—
25C2×C22⋊D239—42no—
26Dic956D411yescharacteristic, complemented
27#16838537—21no—
28D1912—21no—
29D1912—21no—
30D1912D411yescharacteristic, complemented
31#16838533—41no—
32#16838533—41no—
33#16838531—41no—
34C2×C239⋊C8D411yescharacteristic
35C8×D239—41no—
36C4×Dic239D411yescharacteristic
37C239⋊C16—21no—
38C2×D4×C239—21no—
39D8×C239—21no—
40D8×C239—21no—
41M16×C239—21no—
42C2×C8×C239C2311yescharacteristic
43C16×C239—21no—
44C22×D239—41no—
45Dic478—21no—
46D956—21no—
47D956—41no—
48D956—41no—
49C22⋊D239—41no—
50C22⋊D239—84no—
51C2×Dic239—21no—
52C4×D239—41no—
53C239⋊C8D811yescharacteristic
54C239⋊C8D811yescharacteristic
55C23×C239—41no—
56D4×C239—41no—
57D4×C239—41no—
58C2×C4×C239C2×D411yescharacteristic
59C8×C239—41no—
60C8×C239C2×D411yescharacteristic
61C8×C239#4111yescharacteristic
62C22×C239—82no—
63C22×C239—81no—
64C22×C239AGL(1,ℤ/8)11yescharacteristic
65C2×D239—41no—
66C2×D239—82no—
67C2×D239—81no—
68C4×C239#12111yescharacteristic
69C4×C239C2×D811yescharacteristic
70Dic239—22no—
71Dic239—41no—
72C2×C239—21no—
73C2×C239—161no—
74C2×C239#45911yescharacteristic
75D239—81no—
76D239—161no—
77C239#221311yescharacteristic, complemented, Sylow
78#2213—2391nomaximal, Sylow
79#509—2391no—
80#509—2391no—
81#493—2391no—
82#443—2391no—
83#364—2391no—
84#361—2391no—
85#361D23911yescharacteristic, complemented
86#135—2391no—
87C2×D8—4781no—
88C2×D8—2391no—
89C2×D8C2×D23911yescharacteristic
90#131—4781no—
91#127—4781no—
92SD32—4781no—
93SD32—4781no—
94D16—4781no—
95D16—4781no—
96M32—2391no—
97M32C2×D23911yescharacteristic
98#108C2×D23911yescharacteristic
99#104—4781no—
100C4×C8—2391no—
101#41—4781no—
102C2×D4—21no—
103C2×D4—9562no—
104C2×D4—4781no—
105Q16—2391no—
106SD16—4781no—
107D8—21no—
108D8—21no—
109D8—9561no—
110D8—9561no—
111D8—4781no—
112D8—4781no—
113D8—2391no—
114M16—21no—
115M16—9561no—
116C2×C8—9561no—
117C2×C8—2391no—
118C2×C8C22×D23911yescharacteristic
119C42—2391no—
120C16—21no—
121C16—4781no—
122C23—41no—
123C23—9561no—
124Q8—4781no—
125D4—41no—
126D4—41no—
127D4—19124no—
128D4—9561no—
129D4—9561no—
130D4—9561no—
131D4—4781no—
132C2×C4—9561no—
133C2×C4—4781no—
134C2×C4D4×D23911yescharacteristic
135C8—41no—
136C8—2391no—
137C8—2391no—
138C8D4×D23911yescharacteristic
139C8#1683854811yescharacteristic
140C22—82no—
141C22—81no—
142C22—19122no—
143C22—19121no—
144C22—9561no—
145C22#2143998711yescharacteristic
146C4—9561no—
147C4—4782no—
148C4#2143993311yescharacteristic
149C4D8×D23911yescharacteristic
150C2—21no—
151C2—161no—
152C2—19121no—
153C2—38241no—
154C2#2950496611yescharacteristic
subgroupG/H
centerC2#29504966
commutator, cosocleC2×C8×C239C23
FrattiniC2×C8C22×D239
Fitting#361×C239C2
socleC2×C239#459
hypercenter#361D239
hypocenterC239#2213
LCSG ▷ C2×C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #29505210C2semidirect
2. #29505208C2semidirect
3. #29505147C2semidirect
4. #29504888C2semidirect
5. #29504592C2semidirect
6. #29504584C2semidirect
7. #361×C239C2semidirect
26. Dic956D4semidirect
30. D1912D4semidirect
77. C239#2213semidirect
85. #361D239semidirect

Maximal subgroups

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

subgroupindex
#295052102
#295052082
#295051472
#295048882
#295045922
#295045842
#361×C2392
#2213239