Finite Group Databasebeta

← #49121305

Subgroups — #49121305

Order 36224.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#22583617C211yesmaximal, characteristic
2#31826501C212yesmaximal, complemented
3#31826439C211yesmaximal, characteristic
4#31826221C212yesmaximal, complemented
5#410×C283C211yesmaximal, characteristic
6#22583617—22no—
7#22583617—22no—
8C2×#17985376C412yescomplemented
9C2×#17985376C2211yescharacteristic
10C22×C283⋊C8C412yescomplemented
11C22×C283⋊C8C2211yescharacteristic
12#22583569C2212yes—
13#22583543—22no—
14#22583541—22no—
15#22583525—22no—
16C2×#41×C283C2211yescharacteristic
17#117×C283C2212yes—
18#99×C283—22no—
19#17985376—24no—
20#17985376—22no—
21C2×C283⋊C8—22no—
22C2×C283⋊C8—22no—
23C2×C283⋊C8C2×C412yes—
24C2×C283⋊C8C2×C411yescharacteristic
25C2×C283⋊C8C2×C411yescharacteristic
26C2×C283⋊C8D412yes—
27C2×C283⋊C8D412yes—
28C4⋊Dic283—22no—
29C22⋊Dic283—22no—
30C4×Dic283—22no—
31#41×C283—22no—
32#41×C283—22no—
33C2×Q8×C283Q811yescharacteristic
34C2×D4×C283D412yes—
35C2×D4×C283Q811yescharacteristic
36C22×C4×C283C2×C412yes—
37C22×C4×C283C2311yescharacteristic
38C4⋊C4×C283—22no—
39C22⋊C4×C283—22no—
40C42×C283—22no—
41C2×Dic283—42no—
42C283⋊C8—22no—
43C283⋊C8C22⋊C411yescharacteristic
44C283⋊C8C22⋊C411yescharacteristic
45C283⋊C8C22⋊C412yes—
46C23×C283C4⋊C412yes—
47C23×C283C2×D411yescharacteristic
48Q8×C283—22no—
49D4×C283—24no—
50D4×C283—22no—
51C2×C4×C283—22no—
52C2×C4×C283—22no—
53C2×C4×C283—42no—
54C2×C4×C283C4⋊C412yes—
55C2×C4×C283C22×C411yescharacteristic
56C2×C4×C283C2×D412yes—
57C2×C4×C283C2×Q811yescharacteristic
58C2×C4×C283#4112yes—
59C22×C283—22no—
60C22×C283—41no—
61C22×C283—42no—
62C22×C283C2×C4⋊C411yescharacteristic
63C22×C283#12112yes—
64C4×C283—22no—
65C4×C283—82no—
66C4×C283C2×C22⋊C411yescharacteristic
67C4×C283#11711yescharacteristic
68C4×C283C22⋊Q812yes—
69Dic283—82no—
70C2×C283—22no—
71C2×C283—21no—
72C2×C283—42no—
73C2×C283#38011yescharacteristic
74C283#181211yescharacteristic, complemented, Sylow
75#1812—2831nomaximal, Sylow
76C2×#131—2831no—
77#427—2832no—
78#410—2831no—
79#410D28311yescharacteristic
80H(3,ℤ/4)—2832no—
81C2×#41C2×D28311yescharacteristic
82#131—5662no—
83#131—5662no—
84C2×M16—2832no—
85C2×M16—2831no—
86C22×C8—2831no—
87C22×C8—2832no—
88#117—2832no—
89#117C2×D28312yes—
90#107—5662no—
91#106—5662no—
92#99—22no—
93#99—5662no—
94#41—22no—
95#41—22no—
96C2×Q8Dic56611yescharacteristic
97C2×D4C22⋊D28312yes—
98C2×D4Dic56611yescharacteristic
99C22×C4C4×D28312yes—
100C22×C4C22×D28311yescharacteristic
101M16—5664no—
102M16—5662no—
103C2×C8—2831no—
104C2×C8—2831no—
105C2×C8—2832no—
106C2×C8—2832no—
107C2×C8—2832no—
108C2×C8—5662no—
109C2×C8—5662no—
110C4⋊C4—22no—
111C4⋊C4—5662no—
112C22⋊C4—22no—
113C22⋊C4—5662no—
114C42—22no—
115C42—5662no—
116C23Dic283⋊C412yes—
117C23C2×C22⋊D28311yescharacteristic
118Q8—22no—
119D4—24no—
120D4—22no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—42no—
124C2×C4—11322no—
125C2×C4Dic283⋊C412yes—
126C2×C4C2×C4×D28311yescharacteristic
127C2×C4D4×D28312yes—
128C2×C4C2×Dic56611yescharacteristic
129C2×C4#1798539112yes—
130C8—2831no—
131C8—2831no—
132C8—2832no—
133C8—5662no—
134C22—22no—
135C22—41no—
136C22—42no—
137C22C2×Dic283⋊C411yescharacteristic
138C22#2258358212yes—
139C4—22no—
140C4—82no—
141C4—22642no—
142C4C22⋊C4×D28311yescharacteristic
143C4#2258356611yescharacteristic
144C4#2258358712yes—
145C2—22no—
146C2—21no—
147C2—42no—
148C2#3182632311yescharacteristic
subgroupG/H
centerC4#22583566
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#410×C283C2
socleC2×C283#380
prime radicalC2×#41×C283C22
cosocleC22×C4×C283C23
hypercenter#410D283
hypocenterC283#1812
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #31826501C2semidirect
4. #31826221C2semidirect
8. C2×#17985376C4semidirect
10. C22×C283⋊C8C4semidirect
74. C283#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#225836172
#318265012
#318264392
#318262212
#410×C2832
#1812283