Finite Group Databasebeta

← #37511075

Subgroups — #37511075

Order 22912.

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#26038877C211yesmaximal, characteristic, complemented
2#26038875C211yesmaximal, characteristic, complemented
3#26038814C211yesmaximal, characteristic, complemented
4#26038555C211yesmaximal, characteristic, complemented
5#26038259C211yesmaximal, characteristic, complemented
6#26038251C211yesmaximal, characteristic, complemented
7#361×C179C211yesmaximal, characteristic, complemented
8#19153135C2211yescharacteristic
9C2×D1432C2211yescharacteristic
10C2×#15668244—21no—
11#19153121—21no—
12#19153109—21no—
13#19153058—21no—
14#19153057—21no—
15D2864—21no—
16#19153054—21no—
17#19153053C2211yescharacteristic
18#19153039—21no—
19C8×Dic179C2211yescharacteristic
20C2×D8×C179C2211yescharacteristic
21M32×C179C2211yescharacteristic
22#108×C179C2211yescharacteristic
23#15668259—21no—
24C2×D716—21no—
25C2×C22⋊D179—42no—
26Dic716D411yescharacteristic, complemented
27#15668248—21no—
28D1432—21no—
29D1432—21no—
30D1432D411yescharacteristic, complemented
31#15668244—41no—
32#15668244—41no—
33#15668242—41no—
34C2×C179⋊C8D411yescharacteristic
35C8×D179—41no—
36C4×Dic179D411yescharacteristic
37C179⋊C16—21no—
38C2×D4×C179—21no—
39D8×C179—21no—
40D8×C179—21no—
41M16×C179—21no—
42C2×C8×C179C2311yescharacteristic
43C16×C179—21no—
44C22×D179—41no—
45Dic358—21no—
46D716—21no—
47D716—41no—
48D716—41no—
49C22⋊D179—41no—
50C22⋊D179—84no—
51C2×Dic179—21no—
52C4×D179—41no—
53C179⋊C8D811yescharacteristic
54C179⋊C8D811yescharacteristic
55C23×C179—41no—
56D4×C179—41no—
57D4×C179—41no—
58C2×C4×C179C2×D411yescharacteristic
59C8×C179—41no—
60C8×C179C2×D411yescharacteristic
61C8×C179#4111yescharacteristic
62C22×C179—82no—
63C22×C179—81no—
64C22×C179AGL(1,ℤ/8)11yescharacteristic
65C2×D179—41no—
66C2×D179—82no—
67C2×D179—81no—
68C4×C179#12111yescharacteristic
69C4×C179C2×D811yescharacteristic
70Dic179—22no—
71Dic179—41no—
72C2×C179—21no—
73C2×C179—161no—
74C2×C179#45911yescharacteristic
75D179—81no—
76D179—161no—
77C179#221311yescharacteristic, complemented, Sylow
78#2213—1791nomaximal, Sylow
79#509—1791no—
80#509—1791no—
81#493—1791no—
82#443—1791no—
83#364—1791no—
84#361—1791no—
85#361D17911yescharacteristic, complemented
86#135—1791no—
87C2×D8—3581no—
88C2×D8—1791no—
89C2×D8C2×D17911yescharacteristic
90#131—3581no—
91#127—3581no—
92SD32—3581no—
93SD32—3581no—
94D16—3581no—
95D16—3581no—
96M32—1791no—
97M32C2×D17911yescharacteristic
98#108C2×D17911yescharacteristic
99#104—3581no—
100C4×C8—1791no—
101#41—3581no—
102C2×D4—21no—
103C2×D4—3581no—
104C2×D4—7162no—
105Q16—1791no—
106SD16—3581no—
107D8—21no—
108D8—21no—
109D8—3581no—
110D8—3581no—
111D8—1791no—
112D8—7161no—
113D8—7161no—
114M16—21no—
115M16—7161no—
116C2×C8—1791no—
117C2×C8—7161no—
118C2×C8C22×D17911yescharacteristic
119C42—1791no—
120C16—21no—
121C16—3581no—
122C23—41no—
123C23—7161no—
124Q8—3581no—
125D4—41no—
126D4—41no—
127D4—3581no—
128D4—14324no—
129D4—7161no—
130D4—7161no—
131D4—7161no—
132C2×C4—3581no—
133C2×C4—7161no—
134C2×C4D4×D17911yescharacteristic
135C8—41no—
136C8—1791no—
137C8—1791no—
138C8D4×D17911yescharacteristic
139C8#1566825911yescharacteristic
140C22—82no—
141C22—81no—
142C22—14322no—
143C22—14321no—
144C22—7161no—
145C22#1915314011yescharacteristic
146C4—3582no—
147C4—7161no—
148C4#1915308611yescharacteristic
149C4D8×D17911yescharacteristic
150C2—21no—
151C2—161no—
152C2—28641no—
153C2—14321no—
154C2#2603863311yescharacteristic
subgroupG/H
centerC2#26038633
commutator, cosocleC2×C8×C179C23
FrattiniC2×C8C22×D179
Fitting#361×C179C2
socleC2×C179#459
hypercenter#361D179
hypocenterC179#2213
LCSG ▷ C2×C8×C179 ▷ C4×C179 ▷ C2×C179 ▷ C179
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #26038877C2semidirect
2. #26038875C2semidirect
3. #26038814C2semidirect
4. #26038555C2semidirect
5. #26038259C2semidirect
6. #26038251C2semidirect
7. #361×C179C2semidirect
26. Dic716D4semidirect
30. D1432D4semidirect
77. C179#2213semidirect
85. #361D179semidirect

Maximal subgroups

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

subgroupindex
#260388772
#260388752
#260388142
#260385552
#260382592
#260382512
#361×C1792
#2213179