Finite Group Databasebeta

← #49120557

Subgroups — #49120557

Order 36224.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#31827215C211yesmaximal, characteristic, complemented
2#31826829C212yesmaximal, complemented
3#31826206C212yesmaximal, complemented
4#31826205C211yesmaximal, characteristic, complemented
5#496×C283C211yesmaximal, characteristic
6#22583608—21no—
7#22583603—22no—
8#22583602C2212yes—
9#22583591—21no—
10#22583587—22no—
11#22583531—22no—
12#22583531—22no—
13#22583521C2212yes—
14C2×SD16×C283—21no—
15C2×D8×C283—21no—
16#127×C283C2211yescharacteristic
17#124×C283C2211yescharacteristic
18#97×C283C2211yescharacteristic
19C2×Dic566—21no—
20C22×Dic283—21no—
21C2×C283⋊C8—22no—
22C4⋊Dic283D412yes—
23C4⋊Dic283D412yes—
24Dic283⋊C4—22no—
25Dic283⋊C4—22no—
26Dic283⋊C4—22no—
27C22⋊Dic283—22no—
28C22⋊Dic283—21no—
29C4×Dic283—21no—
30C2×Q8×C283D411yescharacteristic
31C2×D4×C283—21no—
32C2×D4×C283—22no—
33C2×D4×C283D411yescharacteristic
34SD16×C283—42no—
35D8×C283—42no—
36C2×C8×C283—21no—
37C22⋊C4×C283—22no—
38C42×C283C2311yescharacteristic
39Dic566—81no—
40C2×Dic283—22no—
41C2×Dic283—22no—
42C2×Dic283—81no—
43C283⋊C8—42no—
44C23×C283—21no—
45C23×C283—41no—
46Q8×C283—41no—
47D4×C283—41no—
48D4×C283—41no—
49D4×C283—41no—
50D4×C283—44no—
51C2×C4×C283—21no—
52C2×C4×C283C2×D412yes—
53C2×C4×C283C2×D411yescharacteristic
54C8×C283—22no—
55C22×C283—41no—
56C22×C283—42no—
57C22×C283—81no—
58C22×C283—82no—
59C22×C283#12011yescharacteristic
60C4×C283—21no—
61C4×C283—22no—
62C4×C283—41no—
63Dic283—42no—
64Dic283—42no—
65C2×C283—81no—
66C2×C283—161no—
67C2×C283#45311yescharacteristic
68C2×C283#45412yes—
69C283#165711yescharacteristic, complemented, Sylow
70#1657—2831nomaximal, Sylow
71#563—2831no—
72#496D28311yescharacteristic
73#490—2832no—
74#330—2832no—
75#329—2831no—
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—5661no—
79#127C2×D28311yescharacteristic
80#126—5662no—
81#125—2832no—
82#124C2×D28311yescharacteristic
83#123—5661no—
84C22⋊Q8—5662no—
85#102—5662no—
86#102—5662no—
87#97—2832no—
88#97C2×D28311yescharacteristic
89C2×Q8—5661no—
90C2×Q8C22⋊D28311yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D28311yescharacteristic
94C22×C4—5661no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—5662no—
99C4⋊C4—2832no—
100C4⋊C4—2832no—
101C4⋊C4—5662no—
102C4⋊C4—5662no—
103C4⋊C4—5662no—
104C22⋊C4—22no—
105C22⋊C4—5662no—
106C22⋊C4—5661no—
107C42—5661no—
108C42C22×D28311yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—22641no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—5662no—
119C2×C4—5662no—
120C2×C4—22641no—
121C2×C4D4×D28312yes—
122C2×C4C2×C22⋊D28311yescharacteristic
123C8—22no—
124C8—11322no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#2258357811yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—11322no—
134C4—11322no—
135C2—81no—
136C2—161no—
137C2#3182663211yescharacteristic
138C2#3182663612yes—
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting, prime radical#496×C283C2
socleC22×C283#120
hypercenter#496D283
hypocenterC283#1657
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #31827215C2semidirect
2. #31826829C2semidirect
3. #31826206C2semidirect
4. #31826205C2semidirect
69. C283#1657semidirect

Maximal subgroups

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

subgroupindex
#318272152
#318268292
#318262062
#318262052
#496×C2832
#1657283