Finite Group Databasebeta

← #49123336

Subgroups — #49123336

Order 36224.

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#31826903C211yesmaximal, characteristic, complemented
2#31826901C211yesmaximal, characteristic, complemented
3#31826840C211yesmaximal, characteristic, complemented
4#31826581C211yesmaximal, characteristic, complemented
5#31826285C211yesmaximal, characteristic, complemented
6#31826277C211yesmaximal, characteristic, complemented
7#361×C283C211yesmaximal, characteristic, complemented
8#22583632C2211yescharacteristic
9C2×D2264C2211yescharacteristic
10C2×#17985377—21no—
11#22583618—21no—
12#22583606—21no—
13#22583555—21no—
14#22583554—21no—
15D4528—21no—
16#22583551—21no—
17#22583550C2211yescharacteristic
18#22583536—21no—
19C8×Dic283C2211yescharacteristic
20C2×D8×C283C2211yescharacteristic
21M32×C283C2211yescharacteristic
22#108×C283C2211yescharacteristic
23#17985392—21no—
24C2×D1132—21no—
25C2×C22⋊D283—42no—
26Dic1132D411yescharacteristic, complemented
27#17985381—21no—
28D2264—21no—
29D2264—21no—
30D2264D411yescharacteristic, complemented
31#17985377—41no—
32#17985377—41no—
33#17985375—41no—
34C2×C283⋊C8D411yescharacteristic
35C8×D283—41no—
36C4×Dic283D411yescharacteristic
37C283⋊C16—21no—
38C2×D4×C283—21no—
39D8×C283—21no—
40D8×C283—21no—
41M16×C283—21no—
42C2×C8×C283C2311yescharacteristic
43C16×C283—21no—
44C22×D283—41no—
45Dic566—21no—
46D1132—21no—
47D1132—41no—
48D1132—41no—
49C22⋊D283—41no—
50C22⋊D283—84no—
51C2×Dic283—21no—
52C4×D283—41no—
53C283⋊C8D811yescharacteristic
54C283⋊C8D811yescharacteristic
55C23×C283—41no—
56D4×C283—41no—
57D4×C283—41no—
58C2×C4×C283C2×D411yescharacteristic
59C8×C283—41no—
60C8×C283C2×D411yescharacteristic
61C8×C283#4111yescharacteristic
62C22×C283—82no—
63C22×C283—81no—
64C22×C283AGL(1,ℤ/8)11yescharacteristic
65C2×D283—41no—
66C2×D283—82no—
67C2×D283—81no—
68C4×C283#12111yescharacteristic
69C4×C283C2×D811yescharacteristic
70Dic283—22no—
71Dic283—41no—
72C2×C283—21no—
73C2×C283—161no—
74C2×C283#45911yescharacteristic
75D283—81no—
76D283—161no—
77C283#221311yescharacteristic, complemented, Sylow
78#2213—2831nomaximal, Sylow
79#509—2831no—
80#509—2831no—
81#493—2831no—
82#443—2831no—
83#364—2831no—
84#361—2831no—
85#361D28311yescharacteristic, complemented
86#135—2831no—
87C2×D8—2831no—
88C2×D8—5661no—
89C2×D8C2×D28311yescharacteristic
90#131—5661no—
91#127—5661no—
92SD32—5661no—
93SD32—5661no—
94D16—5661no—
95D16—5661no—
96M32—2831no—
97M32C2×D28311yescharacteristic
98#108C2×D28311yescharacteristic
99#104—5661no—
100C4×C8—2831no—
101#41—5661no—
102C2×D4—21no—
103C2×D4—5661no—
104C2×D4—11322no—
105Q16—2831no—
106SD16—5661no—
107D8—21no—
108D8—21no—
109D8—2831no—
110D8—5661no—
111D8—5661no—
112D8—11321no—
113D8—11321no—
114M16—21no—
115M16—11321no—
116C2×C8—2831no—
117C2×C8—11321no—
118C2×C8C22×D28311yescharacteristic
119C42—2831no—
120C16—21no—
121C16—5661no—
122C23—41no—
123C23—11321no—
124Q8—5661no—
125D4—41no—
126D4—41no—
127D4—5661no—
128D4—11321no—
129D4—11321no—
130D4—11321no—
131D4—22644no—
132C2×C4—5661no—
133C2×C4—11321no—
134C2×C4D4×D28311yescharacteristic
135C8—41no—
136C8—2831no—
137C8—2831no—
138C8D4×D28311yescharacteristic
139C8#1798539211yescharacteristic
140C22—82no—
141C22—81no—
142C22—11321no—
143C22—22642no—
144C22—22641no—
145C22#2258363711yescharacteristic
146C4—5662no—
147C4—11321no—
148C4#2258358311yescharacteristic
149C4D8×D28311yescharacteristic
150C2—21no—
151C2—161no—
152C2—45281no—
153C2—22641no—
154C2#3182665911yescharacteristic
subgroupG/H
centerC2#31826659
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
Fitting#361×C283C2
socleC2×C283#459
hypercenter#361D283
hypocenterC283#2213
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #31826903C2semidirect
2. #31826901C2semidirect
3. #31826840C2semidirect
4. #31826581C2semidirect
5. #31826285C2semidirect
6. #31826277C2semidirect
7. #361×C283C2semidirect
26. Dic1132D4semidirect
30. D2264D4semidirect
77. C283#2213semidirect
85. #361D283semidirect

Maximal subgroups

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

subgroupindex
#318269032
#318269012
#318268402
#318265812
#318262852
#318262772
#361×C2832
#2213283