Finite Group Databasebeta

← #49121788

Subgroups — #49121788

Order 36224.

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

normal subgroups only

This group has 344 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
1#31827029C211yesmaximal, characteristic
2#31826471C212yesmaximal, complemented
3#31826439C211yesmaximal, characteristic, complemented
4#31826222C212yesmaximal, complemented
5#568×C283C211yesmaximal, characteristic, complemented
6C22×D1132C2211yescharacteristic
7#22583606C412yescomplemented
8#22583599C412yescomplemented
9#22583584—22no—
10#22583578—22no—
11#22583569C2212yes—
12#22583569C2211yescharacteristic
13#22583532—24no—
14#22583525—22no—
15C2×#41×C283C2211yescharacteristic
16#131×C283—24no—
17C2×M16×C283—22no—
18C2×M16×C283C2212yes—
19C23×D283—21no—
20C2×D1132—22no—
21C2×D1132—21no—
22C2×D1132—22no—
23C2×D1132C2×C412yes—
24C2×C22⋊D283—24no—
25C4⋊Dic283—21no—
26C4⋊Dic283—22no—
27C22⋊Dic283—21no—
28C22⋊Dic283—22no—
29(C2×D283)⋊C4—24no—
30C4×Dic283—22no—
31C4×Dic283C2×C412yes—
32#41×C283—22no—
33#41×C283—22no—
34C2×Q8×C283C2×C411yescharacteristic
35C2×D4×C283C2×C411yescharacteristic
36C2×D4×C283D412yes—
37C22×C4×C283D412yes—
38C22×C4×C283C2311yescharacteristic
39M16×C283—24no—
40M16×C283—22no—
41M16×C283—22no—
42C2×C8×C283—24no—
43C2×C8×C283D414yescomplemented
44C22×D283—22no—
45C22×D283—42no—
46C22×D283—82no—
47D1132—24no—
48D1132—41no—
49D1132—41no—
50C22⋊D283—84no—
51C2×Dic283—22no—
52C2×Dic283—42no—
53C23×C283C22⋊C412yes—
54C23×C283C2×D411yescharacteristic
55Q8×C283—22no—
56D4×C283—24no—
57D4×C283—22no—
58C2×C4×C283—22no—
59C2×C4×C283—22no—
60C2×C4×C283C22⋊C412yes—
61C2×C4×C283C22×C411yescharacteristic
62C2×C4×C283C2×D412yes—
63C2×C4×C283C2×D411yescharacteristic
64C2×C4×C283#4112yes—
65C8×C283—24no—
66C22×C283—22no—
67C22×C283—41no—
68C22×C283—42no—
69C22×C283C2×C22⋊C411yescharacteristic
70C22×C283#12112yes—
71C2×D283—44no—
72C2×D283—42no—
73C2×D283—84no—
74C4×C283—22no—
75C4×C283C4×D412yes—
76C4×C283#12011yescharacteristic
77C4×C283#12311yescharacteristic
78Dic283—42no—
79Dic283—82no—
80C2×C283—21no—
81C2×C283—22no—
82C2×C283—42no—
83C2×C283#38611yescharacteristic
84D283—82no—
85C283#191011yescharacteristic, complemented, Sylow
86#1910—2831nomaximal, Sylow
87#568D28311yescharacteristic, complemented
88#535—2831no—
89#418—2832no—
90#410—2831no—
91H(3,ℤ/4)—2832no—
92C2×#41C2×D28311yescharacteristic
93C22×D4—2831no—
94#131—24no—
95C2×M16—22no—
96C2×M16C2×D28312yes—
97#127—2832no—
98#124—2832no—
99#121—5662no—
100#120—5662no—
101#117—2831no—
102#117—2832no—
103#102—5664no—
104#99—5662no—
105C24—5661no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D28311yescharacteristic
109C2×D4—2832no—
110C2×D4—5664no—
111C2×D4—5662no—
112C2×D4—5661no—
113C2×D4—5662no—
114C2×D4C4×D28311yescharacteristic
115C2×D4D113212yes—
116C22×C4C22⋊D28312yes—
117C22×C4C22×D28311yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D28314yescomplemented
123C4⋊C4—5661no—
124C4⋊C4—5662no—
125C22⋊C4—5661no—
126C22⋊C4—5664no—
127C22⋊C4—5662no—
128C42—2832no—
129C42—5662no—
130C23—5662no—
131C23—11322no—
132C23—22642no—
133C23(C2×D283)⋊C412yes—
134C23C2×D113211yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—5664no—
139D4—11321no—
140D4—11321no—
141D4—22644no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—5662no—
145C2×C4—11322no—
146C2×C4(C2×D283)⋊C412yes—
147C2×C4C2×C4×D28311yescharacteristic
148C2×C4C2×C22⋊D28312yes—
149C2×C4C2×C22⋊D28311yescharacteristic
150C2×C4#1798539212yes—
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—11324no—
156C22—11322no—
157C22—22644no—
158C22C2×(C2×D283)⋊C411yescharacteristic
159C22#2258358412yes—
160C4—22no—
161C4—11322no—
162C4—22642no—
163C4C4×C22⋊D28312yes—
164C4#2258357911yescharacteristic
165C4#2258359311yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—22642no—
170C2#3182634411yescharacteristic
subgroupG/H
centerC2#31826344
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#568×C283C2
socleC2×C283#386
prime radical#31827029C2
cosocleC22×C4×C283C23
hypercenter#568D283
hypocenterC283#1910
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #31826471C2semidirect
3. #31826439C2semidirect
4. #31826222C2semidirect
5. #568×C283C2semidirect
7. #22583606C4semidirect
8. #22583599C4semidirect
43. C2×C8×C283D4semidirect
85. C283#1910semidirect
87. #568D283semidirect
122. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318270292
#318264712
#318264392
#318262222
#568×C2832
#1910283