Finite Group Databasebeta

← #44483816

Subgroups — #44483816

Order 30592.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#29505495C211yesmaximal, characteristic
2#29505168C211yesmaximal, characteristic, complemented
3#29505049C211yesmaximal, characteristic
4#29504517C211yesmaximal, characteristic, complemented
5Q8⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic
7#462×C239C211yesmaximal, characteristic, complemented
8#21439960C2211yescharacteristic
9#21439955—22no—
10#21439948—21no—
11#21439936—21no—
12C4×Dic478—21no—
13C4×D956C2211yescharacteristic
14#21439918—21no—
15#21439893—21no—
16#21439891—22no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18#21439880—21no—
19C4×C239⋊C8C2211yescharacteristic
20C2×Q16×C239—21no—
21C4⋊Q8×C239C2211yescharacteristic
22C4×Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24#103×C239—21no—
25C2×Dic478—21no—
26C2×D956D411yescharacteristic
27C2×C4×D239—21no—
28C2×C239⋊C8—21no—
29C2×C239⋊C8—21no—
30C4⋊Dic239—21no—
31C4⋊Dic239D412yes—
32C4⋊Dic239D411yescharacteristic
33Dic239⋊C4—22no—
34(C2×D239)⋊C4—22no—
35(C2×D239)⋊C4—22no—
36(C2×D239)⋊C4—21no—
37C4×Dic239—22no—
38C2×Q8×C239—21no—
39C2×Q8×C239D411yescharacteristic
40Q16×C239—42no—
41C2×C8×C239—21no—
42C4⋊C4×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239D411yescharacteristic
46C42×C239—21no—
47C42×C239C2311yescharacteristic
48C22×D239—21no—
49Dic478—41no—
50Dic478—41no—
51D956—21no—
52D956—21no—
53C2×Dic239—21no—
54C2×Dic239—22no—
55C4×D239—41no—
56C4×D239—41no—
57C239⋊C8—22no—
58C239⋊C8—41no—
59Q8×C239—21no—
60Q8×C239—21no—
61Q8×C239—41no—
62Q8×C239—41no—
63C2×C4×C239—21no—
64C2×C4×C239—21no—
65C2×C4×C239—41no—
66C2×C4×C239C2×D411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C2×C4×C239C2×D411yescharacteristic
69C8×C239—41no—
70C22×C239#12011yescharacteristic
71C2×D239—41no—
72C2×D239—41no—
73C2×D239—41no—
74C4×C239—21no—
75C4×C239—41no—
76C4×C239—41no—
77C4×C239—81no—
78C4×C239#13511yescharacteristic
79C4×C239#13511yescharacteristic
80C4×C239AGL(1,ℤ/8)11yescharacteristic
81C4×C239#13711yescharacteristic
82Dic239—41no—
83Dic239—42no—
84C2×C239#44911yescharacteristic
85C2×C239#45211yescharacteristic
86C2×C239#45611yescharacteristic
87D239—81no—
88C239#165211yescharacteristic, complemented, Sylow
89#1652—2391nomaximal, Sylow
90#556—2391no—
91#498—2391no—
92#474—2391no—
93#462D23911yescharacteristic, complemented
94#332—2391no—
95Q8⋊C8—2391no—
96D4⋊C8—2391no—
97C2×Q16—21no—
98C4⋊Q8—2391no—
99C4⋊Q8C2×D23911yescharacteristic
100#126—4782no—
101#124—4781no—
102C22⋊Q8—4781no—
103C4×Q8—4781no—
104C4×Q8C2×D23911yescharacteristic
105C4×D4—2391no—
106#117—4781no—
107#107—4781no—
108#106—4782no—
109C4⋊C8—2391no—
110C4⋊C8C2×D23911yescharacteristic
111#103—21no—
112#102—4781no—
113C4×C8—2391no—
114C2×Q8—21no—
115C2×Q8—4781no—
116C2×Q8C22⋊D23911yescharacteristic
117C2×D4—2391no—
118C22×C4—4781no—
119Q16—42no—
120C2×C8—21no—
121C2×C8—4781no—
122C2×C8—4781no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—4782no—
127C4⋊C4—4781no—
128C4⋊C4—2392no—
129C4⋊C4—2391no—
130C4⋊C4C22⋊D23911yescharacteristic
131C22⋊C4—4782no—
132C22⋊C4—4782no—
133C22⋊C4—4781no—
134C42—21no—
135C42—4782no—
136C42C22×D23911yescharacteristic
137C23—4781no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—9561no—
143Q8—9561no—
144D4—4781no—
145D4—4781no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—9561no—
150C2×C4—9561no—
151C2×C4—4781no—
152C2×C4—4782no—
153C2×C4D4×D23911yescharacteristic
154C2×C4D4×D23911yescharacteristic
155C2×C4C2×C22⋊D23911yescharacteristic
156C8—41no—
157C8—9561no—
158C8—4782no—
159C22—9561no—
160C22—9561no—
161C22—9561no—
162C22#2143992811yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—9561no—
168C4—9562no—
169C4#2143998011yescharacteristic
170C4#2143998311yescharacteristic
171C4#2143998611yescharacteristic
172C4#2143999211yescharacteristic
173C2—19121no—
174C2#2950491511yescharacteristic
175C2#2950493311yescharacteristic
176C2#2950495311yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#462×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#462D239
hypocenterC239#1652
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #29505168C2semidirect
4. #29504517C2semidirect
5. Q8⋊(C239⋊C8)C2semidirect
7. #462×C239C2semidirect
88. C239#1652semidirect
93. #462D239semidirect

Maximal subgroups

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

subgroupindex
#295054952
#295051682
#295050492
#295045172
Q8⋊(C239⋊C8)2
#295044992
#462×C2392
#1652239