Finite Group Databasebeta

← #44483754

Subgroups — #44483754

Order 30592.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#29505482C211yesmaximal, characteristic
2#29505124C211yesmaximal, characteristic, complemented
3#29504974C211yesmaximal, characteristic
4#29504520C211yesmaximal, characteristic, complemented
5Q8⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic
7#475×C239C211yesmaximal, characteristic, complemented
8C2×#16838535—21no—
9#21439960C2211yescharacteristic
10#21439952—21no—
11#21439938—22no—
12#21439936—21no—
13C4×D956—21no—
14C4×D956C2211yescharacteristic
15C4⋊C4×D239—21no—
16C4⋊(C239⋊C8)C2211yescharacteristic
17#21439884—21no—
18#21439883—22no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×Q8×C239C2211yescharacteristic
22#106×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#103×C239—21no—
25C2×Dic478D412yes—
26C2×D956D411yescharacteristic
27C2×C4×D239—22no—
28C2×C4×D239—21no—
29#16838535—42no—
30C2×C239⋊C8—21no—
31C2×C239⋊C8—21no—
32C4⋊Dic239—21no—
33C4⋊Dic239—21no—
34C4⋊Dic239D411yescharacteristic
35Dic239⋊C4—22no—
36Dic239⋊C4—22no—
37(C2×D239)⋊C4—22no—
38(C2×D239)⋊C4—21no—
39C2×Q8×C239—21no—
40C2×Q8×C239D411yescharacteristic
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—42no—
50D956—21no—
51D956SD1612yes—
52C2×Dic239—21no—
53C2×Dic239—22no—
54C4×D239—41no—
55C4×D239—41no—
56C4×D239—82no—
57C239⋊C8—41no—
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—22no—
72C2×D239—41no—
73C2×D239—41no—
74C4×C239—21no—
75C4×C239—41no—
76C4×C239—41no—
77C4×C239—81no—
78C4×C239C2×SD1611yescharacteristic
79C4×C239#13511yescharacteristic
80C4×C239#13711yescharacteristic
81C4×C239#13711yescharacteristic
82Dic239—41no—
83Dic239—42no—
84C2×C239#44811yescharacteristic
85C2×C239#45211yescharacteristic
86C2×C239#45511yescharacteristic
87D239—42no—
88C239#164311yescharacteristic, complemented, Sylow
89#1643—2391nomaximal, Sylow
90#554—2391no—
91#487—2391no—
92#475D23911yescharacteristic, complemented
93#461—2391no—
94#333—2391no—
95Q8⋊C8—2391no—
96D4⋊C8—2391no—
97C2×SD16—4781no—
98C4⋊Q8—2391no—
99C4⋊Q8C2×D23911yescharacteristic
100#125—4781no—
101C22⋊Q8—4782no—
102C22⋊Q8—4781no—
103C4×Q8C2×D23911yescharacteristic
104C4×D4—4781no—
105C4×D4—2391no—
106C2×C4⋊C4—4781no—
107#106—21no—
108C4⋊C8—2391no—
109C4⋊C8C2×D23911yescharacteristic
110#103—21no—
111#103—4782no—
112#103—4781no—
113C4×C8—2391no—
114C2×Q8—21no—
115C2×Q8—2392no—
116C2×Q8C22⋊D23911yescharacteristic
117C2×D4—2391no—
118C22×C4—4782no—
119C22×C4—4781no—
120SD16—9562no—
121C2×C8—21no—
122C2×C8—4781no—
123C2×C8—4781no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—4782no—
128C4⋊C4—4782no—
129C4⋊C4—4781no—
130C4⋊C4—4781no—
131C4⋊C4—2391no—
132C4⋊C4C22⋊D23911yescharacteristic
133C22⋊C4—4782no—
134C22⋊C4—4781no—
135C42—21no—
136C42C22×D23911yescharacteristic
137C23—4781no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—9562no—
143D4—4781no—
144D4—2392no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—19122no—
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—9561no—
159C22—9561no—
160C22—9561no—
161C22—4782no—
162C22#2143992811yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—9561no—
168C4—9562no—
169C4SD16×D23911yescharacteristic
170C4#2143998011yescharacteristic
171C4#2143998911yescharacteristic
172C4#2143999111yescharacteristic
173C2—9562no—
174C2#2950490911yescharacteristic
175C2#2950493211yescharacteristic
176C2#2950494811yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#475×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#475D239
hypocenterC239#1643
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #29505124C2semidirect
4. #29504520C2semidirect
5. Q8⋊(C239⋊C8)C2semidirect
7. #475×C239C2semidirect
88. C239#1643semidirect
92. #475D239semidirect

Maximal subgroups

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

subgroupindex
#295054822
#295051242
#295049742
#295045202
Q8⋊(C239⋊C8)2
#295044992
#475×C2392
#1643239