Finite Group Databasebeta

← #44484592

Subgroups — #44484592

Order 30592.

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×#21439967C211yesmaximal, characteristic
2#29504808C212yesmaximal, complemented
3#29504746C211yesmaximal, characteristic
4#29504528C212yesmaximal, complemented
5#410×C239C211yesmaximal, characteristic
6#21439967—22no—
7#21439967—22no—
8C2×#16838532C412yescomplemented
9C2×#16838532C2211yescharacteristic
10C22×C239⋊C8C412yescomplemented
11C22×C239⋊C8C2211yescharacteristic
12#21439919C2212yes—
13#21439893—22no—
14#21439891—22no—
15#21439875—22no—
16C2×#41×C239C2211yescharacteristic
17#117×C239C2212yes—
18#99×C239—22no—
19#16838532—24no—
20#16838532—22no—
21C2×C239⋊C8—22no—
22C2×C239⋊C8—22no—
23C2×C239⋊C8C2×C412yes—
24C2×C239⋊C8C2×C411yescharacteristic
25C2×C239⋊C8C2×C411yescharacteristic
26C2×C239⋊C8D412yes—
27C2×C239⋊C8D412yes—
28C4⋊Dic239—22no—
29C22⋊Dic239—22no—
30C4×Dic239—22no—
31#41×C239—22no—
32#41×C239—22no—
33C2×Q8×C239Q811yescharacteristic
34C2×D4×C239D412yes—
35C2×D4×C239Q811yescharacteristic
36C22×C4×C239C2×C412yes—
37C22×C4×C239C2311yescharacteristic
38C4⋊C4×C239—22no—
39C22⋊C4×C239—22no—
40C42×C239—22no—
41C2×Dic239—42no—
42C239⋊C8—22no—
43C239⋊C8C22⋊C411yescharacteristic
44C239⋊C8C22⋊C411yescharacteristic
45C239⋊C8C22⋊C412yes—
46C23×C239C4⋊C412yes—
47C23×C239C2×D411yescharacteristic
48Q8×C239—22no—
49D4×C239—24no—
50D4×C239—22no—
51C2×C4×C239—22no—
52C2×C4×C239—22no—
53C2×C4×C239—42no—
54C2×C4×C239C4⋊C412yes—
55C2×C4×C239C22×C411yescharacteristic
56C2×C4×C239C2×D412yes—
57C2×C4×C239C2×Q811yescharacteristic
58C2×C4×C239#4112yes—
59C22×C239—22no—
60C22×C239—41no—
61C22×C239—42no—
62C22×C239C2×C4⋊C411yescharacteristic
63C22×C239#12112yes—
64C4×C239—22no—
65C4×C239—82no—
66C4×C239C2×C22⋊C411yescharacteristic
67C4×C239#11711yescharacteristic
68C4×C239C22⋊Q812yes—
69Dic239—82no—
70C2×C239—22no—
71C2×C239—21no—
72C2×C239—42no—
73C2×C239#38011yescharacteristic
74C239#181211yescharacteristic, complemented, Sylow
75#1812—2391nomaximal, Sylow
76C2×#131—2391no—
77#427—2392no—
78#410—2391no—
79#410D23911yescharacteristic
80H(3,ℤ/4)—2392no—
81C2×#41C2×D23911yescharacteristic
82#131—4782no—
83#131—4782no—
84C2×M16—2392no—
85C2×M16—2391no—
86C22×C8—2392no—
87C22×C8—2391no—
88#117—2392no—
89#117C2×D23912yes—
90#107—4782no—
91#106—4782no—
92#99—22no—
93#99—4782no—
94#41—22no—
95#41—22no—
96C2×Q8Dic47811yescharacteristic
97C2×D4C22⋊D23912yes—
98C2×D4Dic47811yescharacteristic
99C22×C4C4×D23912yes—
100C22×C4C22×D23911yescharacteristic
101M16—4782no—
102M16—4784no—
103C2×C8—4782no—
104C2×C8—4782no—
105C2×C8—2392no—
106C2×C8—2391no—
107C2×C8—2391no—
108C2×C8—2392no—
109C2×C8—2392no—
110C4⋊C4—22no—
111C4⋊C4—4782no—
112C22⋊C4—22no—
113C22⋊C4—4782no—
114C42—22no—
115C42—4782no—
116C23Dic239⋊C412yes—
117C23C2×C22⋊D23911yescharacteristic
118Q8—22no—
119D4—24no—
120D4—22no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—42no—
124C2×C4—9562no—
125C2×C4Dic239⋊C412yes—
126C2×C4C2×C4×D23911yescharacteristic
127C2×C4D4×D23912yes—
128C2×C4C2×Dic47811yescharacteristic
129C2×C4#1683854712yes—
130C8—4782no—
131C8—2391no—
132C8—2391no—
133C8—2392no—
134C22—22no—
135C22—41no—
136C22—42no—
137C22C2×Dic239⋊C411yescharacteristic
138C22#2143993212yes—
139C4—22no—
140C4—82no—
141C4—19122no—
142C4C22⋊C4×D23911yescharacteristic
143C4#2143991611yescharacteristic
144C4#2143993712yes—
145C2—22no—
146C2—21no—
147C2—42no—
148C2#2950463011yescharacteristic
subgroupG/H
centerC4#21439916
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#410×C239C2
socleC2×C239#380
prime radicalC2×#41×C239C22
cosocleC22×C4×C239C23
hypercenter#410D239
hypocenterC239#1812
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #29504808C2semidirect
4. #29504528C2semidirect
8. C2×#16838532C4semidirect
10. C22×C239⋊C8C4semidirect
74. C239#1812semidirect

Maximal subgroups

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

subgroupindex
C2×#214399672
#295048082
#295047462
#295045282
#410×C2392
#1812239