Finite Group Databasebeta

← #49121808

Subgroups — #49121808

Order 36224.

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

normal subgroups only

This group has 340 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#31826449C211yesmaximal, characteristic, complemented
3C2×#22583526C212yesmaximal, complemented
4#31826237C212yesmaximal, complemented
5#568×C283C211yesmaximal, characteristic, complemented
6C22×D1132C2211yescharacteristic
7C2×#17985376C2212yes—
8#22583606—21no—
9#22583599—21no—
10#22583584—22no—
11#22583578C414yes—
12#22583569C2211yescharacteristic
13#22583529—21no—
14#22583527—21no—
15#22583526—24no—
16C2×#41×C283C2211yescharacteristic
17#131×C283—24no—
18C2×M16×C283—22no—
19C2×M16×C283C2212yes—
20C23×D283C2×C412yes—
21C2×D1132—21no—
22C2×D1132—21no—
23C2×D1132—22no—
24C2×D1132—22no—
25C2×C22⋊D283—24no—
26#17985376—22no—
27#17985376—22no—
28C2×C283⋊C8—22no—
29C4⋊Dic283—21no—
30C22⋊Dic283C2×C412yes—
31(C2×D283)⋊C4—24no—
32C4×Dic283—21no—
33#41×C283—22no—
34#41×C283—22no—
35C2×Q8×C283D411yescharacteristic
36C2×D4×C283C2×C412yes—
37C2×D4×C283D411yescharacteristic
38C22×C4×C283D412yes—
39C22×C4×C283C2311yescharacteristic
40M16×C283—24no—
41M16×C283—22no—
42M16×C283D414yescomplemented
43C2×C8×C283—24no—
44C2×C8×C283—22no—
45C22×D283—22no—
46C22×D283—24no—
47C22×D283—82no—
48D1132—41no—
49D1132—42no—
50D1132—41no—
51C22⋊D283—84no—
52C2×Dic283—22no—
53C283⋊C8—42no—
54C23×C283C22⋊C412yes—
55C23×C283C22×C411yescharacteristic
56Q8×C283—22no—
57D4×C283—24no—
58D4×C283—22no—
59C2×C4×C283—22no—
60C2×C4×C283—22no—
61C2×C4×C283C22⋊C412yes—
62C2×C4×C283C2×D412yes—
63C2×C4×C283C2×D411yescharacteristic
64C2×C4×C283C2×D411yescharacteristic
65C2×C4×C283#4112yes—
66C8×C283—24no—
67C22×C283—22no—
68C22×C283—41no—
69C22×C283—42no—
70C22×C283C2×C22⋊C411yescharacteristic
71C22×C283C4×D412yes—
72C2×D283—44no—
73C2×D283—42no—
74C2×D283—84no—
75C4×C283—22no—
76C4×C283#12011yescharacteristic
77C4×C283#12112yes—
78C4×C283#12311yescharacteristic
79Dic283—42no—
80C2×C283—21no—
81C2×C283—22no—
82C2×C283—42no—
83C2×C283#38611yescharacteristic
84D283—82no—
85C283#191411yescharacteristic, complemented, Sylow
86#1914—2831nomaximal, Sylow
87#568D28311yescharacteristic, complemented
88#535—2831no—
89#413—2831no—
90C2×#100—2832no—
91#344—2832no—
92C2×#41C2×D28311yescharacteristic
93C22×D4—2831no—
94#131—24no—
95C2×M16—22no—
96C2×M16—2832no—
97C2×M16C2×D28312yes—
98#127—5661no—
99#124—5661no—
100#121—5662no—
101#120—2834no—
102#117—2831no—
103#101—5661no—
104#100—5661no—
105#100—5664no—
106C24—2832no—
107#41—22no—
108#41—22no—
109C2×Q8D113211yescharacteristic
110C2×D4—5664no—
111C2×D4—5662no—
112C2×D4—5661no—
113C2×D4—5661no—
114C2×D4—5662no—
115C2×D4C4×D28312yes—
116C2×D4D113211yescharacteristic
117C22×C4C22⋊D28312yes—
118C22×C4C22×D28311yescharacteristic
119M16—24no—
120M16—22no—
121M16—5662no—
122M16—5662no—
123M16C22⋊D28314yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—5662no—
127C4⋊C4—5661no—
128C22⋊C4—2832no—
129C22⋊C4—5664no—
130C42—5661no—
131C23—5662no—
132C23—5664no—
133C23—22642no—
134C23(C2×D283)⋊C412yes—
135C23C2×C4×D28311yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—11321no—
140D4—11322no—
141D4—11321no—
142D4—22644no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—5662no—
146C2×C4(C2×D283)⋊C412yes—
147C2×C4C2×C22⋊D28312yes—
148C2×C4C2×C22⋊D28311yescharacteristic
149C2×C4C2×D113211yescharacteristic
150C2×C4#1798539212yes—
151C8—24no—
152C8—11322no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—11324no—
157C22—11322no—
158C22—22644no—
159C22C2×(C2×D283)⋊C411yescharacteristic
160C22C4×C22⋊D28312yes—
161C4—22no—
162C4—11322no—
163C4#2258357911yescharacteristic
164C4#2258358412yes—
165C4#2258359311yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—22642no—
170C2#3182634411yescharacteristic
subgroupG/H
centerC2#31826344
commutatorC23×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#568×C283C2
socleC2×C283#386
prime radical#31827029C2
cosocleC22×C4×C283C23
hypercenter#568D283
hypocenterC283#1914
LCSG ▷ C23×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #31826449C2semidirect
3. C2×#22583526C2semidirect
4. #31826237C2semidirect
5. #568×C283C2semidirect
42. M16×C283D4semidirect
85. C283#1914semidirect
87. #568D283semidirect
123. M16C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318270292
#318264492
C2×#225835262
#318262372
#568×C2832
#1914283