Finite Group Databasebeta

← #49120559

Subgroups — #49120559

Order 36224.

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

normal subgroups only

This group has 206 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#31826855C211yesmaximal, characteristic
2#31826831C212yesmaximal, complemented
3#31826207C212yesmaximal, complemented
4#31826205C211yesmaximal, characteristic, complemented
5#563×C283C211yesmaximal, characteristic, complemented
6C2×#17985379—21no—
7C2×#17985377—21no—
8#22583607C2211yescharacteristic
9#22583530—22no—
10#22583530—22no—
11#22583521C2212yes—
12#22583521C2211yescharacteristic
13C4⋊Q8×C283—21no—
14#126×C283—22no—
15#125×C283C2212yes—
16#124×C283C2211yescharacteristic
17#123×C283—21no—
18C22⋊Q8×C283—22no—
19C2×D1132—21no—
20C2×D1132—22no—
21#17985379—42no—
22#17985377—42no—
23C2×C283⋊C8—21no—
24C2×C283⋊C8—22no—
25C2×Q8×C283—21no—
26C2×Q8×C283D411yescharacteristic
27C2×D4×C283D411yescharacteristic
28C22×C4×C283—21no—
29C4⋊C4×C283—22no—
30C4⋊C4×C283—22no—
31C4⋊C4×C283—22no—
32C4⋊C4×C283D412yes—
33C4⋊C4×C283D412yes—
34C22⋊C4×C283—22no—
35C22⋊C4×C283—21no—
36C22⋊C4×C283—22no—
37C42×C283—21no—
38C42×C283C2311yescharacteristic
39C22×D283—41no—
40D1132—41no—
41D1132—41no—
42D1132—44no—
43C283⋊C8—22no—
44C283⋊C8—42no—
45C23×C283—21no—
46Q8×C283—41no—
47Q8×C283—81no—
48D4×C283—41no—
49C2×C4×C283—22no—
50C2×C4×C283—21no—
51C2×C4×C283—22no—
52C2×C4×C283—81no—
53C2×C4×C283C2×D412yes—
54C2×C4×C283C2×D411yescharacteristic
55C22×C283—41no—
56C22×C283—42no—
57C22×C283#12011yescharacteristic
58C2×D283—81no—
59C2×D283—82no—
60C4×C283—21no—
61C4×C283—22no—
62C4×C283—42no—
63C4×C283—41no—
64C4×C283—42no—
65C2×C283—81no—
66C2×C283#45311yescharacteristic
67C2×C283#45412yes—
68D283—161no—
69C283#165711yescharacteristic, complemented, Sylow
70#1657—2831nomaximal, Sylow
71#563D28311yescharacteristic, complemented
72#496—2831no—
73#490—2832no—
74#330—2832no—
75#329—2831no—
76C2×SD16—5661no—
77C2×D8—5661no—
78C4⋊Q8—21no—
79#127—2831no—
80#126—22no—
81#125C2×D28312yes—
82#124C2×D28311yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—5662no—
86#102—5662no—
87#97—2832no—
88#97—2831no—
89C2×Q8—21no—
90C2×Q8C22⋊D28311yescharacteristic
91C2×D4—5662no—
92C2×D4—5661no—
93C2×D4C22⋊D28311yescharacteristic
94C22×C4—21no—
95SD16—11322no—
96D8—11322no—
97C2×C8—5661no—
98C2×C8—5662no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D28312yes—
103C4⋊C4C22⋊D28312yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D28311yescharacteristic
109C23—21no—
110C23—11321no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—11321no—
115D4—11321no—
116D4—11324no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D28312yes—
122C2×C4C2×C22⋊D28311yescharacteristic
123C8—5662no—
124C8—11322no—
125C22—41no—
126C22—42no—
127C22—22641no—
128C22—22642no—
129C22#2258357911yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—45281no—
137C2#3182663311yescharacteristic
138C2#3182663812yes—
subgroupG/H
centerC22#22583579
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#563×C283C2
socleC22×C283#120
prime radical#31826855C2
hypercenter#563D283
hypocenterC283#1657
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #31826831C2semidirect
3. #31826207C2semidirect
4. #31826205C2semidirect
5. #563×C283C2semidirect
69. C283#1657semidirect
71. #563D283semidirect

Maximal subgroups

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

subgroupindex
#318268552
#318268312
#318262072
#318262052
#563×C2832
#1657283