Finite Group Databasebeta

← #44483721

Subgroups — #44483721

Order 30592.

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

normal subgroups only

This group has 194 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#29505496C211yesmaximal, characteristic
2#29505124C211yesmaximal, characteristic, complemented
3#29505068C211yesmaximal, characteristic, complemented
4#29505063C211yesmaximal, characteristic
5#29504502C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic
7#332×C239C211yesmaximal, characteristic, complemented
8#21439960C2211yescharacteristic
9#21439955—22no—
10#21439949—21no—
11#21439940—21no—
12Q8×Dic239—21no—
13C4×Dic478C2211yescharacteristic
14C4×D956C2211yescharacteristic
15#21439918—21no—
16#21439894—21no—
17#21439892—21no—
18#21439885—21no—
19#21439883—22no—
20#21439882—21no—
21C4×C239⋊C8C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25C2×Dic478—21no—
26C2×Dic478D411yescharacteristic
27C2×D956D411yescharacteristic
28C2×C4×D239—21no—
29C2×C239⋊C8—21no—
30C4⋊Dic239—22no—
31C4⋊Dic239—21no—
32C4⋊Dic239—21no—
33C4⋊Dic239D411yescharacteristic
34C4⋊Dic239D411yescharacteristic
35Dic239⋊C4—21no—
36(C2×D239)⋊C4—22no—
37(C2×D239)⋊C4—22no—
38(C2×D239)⋊C4—21no—
39C4×Dic239—22no—
40C4×Dic239—21no—
41C2×Q8×C239—21no—
42C2×C8×C239—21no—
43C2×C8×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239D412yes—
46C42×C239C2311yescharacteristic
47C22×D239—21no—
48Dic478—21no—
49Dic478—21no—
50Dic478—42no—
51D956—21no—
52D956—21no—
53C2×Dic239—21no—
54C2×Dic239—21no—
55C2×Dic239—21no—
56C2×Dic239—41no—
57C4×D239—41no—
58C4×D239—41no—
59C239⋊C8—41no—
60Q8×C239—41no—
61Q8×C239—41no—
62C2×C4×C239—22no—
63C2×C4×C239C2×D411yescharacteristic
64C2×C4×C239C2×D411yescharacteristic
65C2×C4×C239C2×D411yescharacteristic
66C8×C239—41no—
67C8×C239—41no—
68C22×C239#12011yescharacteristic
69C2×D239—41no—
70C2×D239—41no—
71C2×D239—41no—
72C4×C239—21no—
73C4×C239—42no—
74C4×C239#13511yescharacteristic
75C4×C239#13511yescharacteristic
76C4×C239#13711yescharacteristic
77C4×C239#13711yescharacteristic
78Dic239—41no—
79Dic239—41no—
80Dic239—41no—
81Dic239—81no—
82C2×C239#45211yescharacteristic
83C2×C239#45211yescharacteristic
84C2×C239#45411yescharacteristic
85D239—81no—
86C239#163811yescharacteristic, complemented, Sylow
87#1638—2391nomaximal, Sylow
88#556—2391no—
89#487—2391no—
90#477—2391no—
91#476—2391no—
92#332D23911yescharacteristic, complemented
93Q8⋊C8—2391no—
94D4⋊C8—2391no—
95C4⋊Q8—2391no—
96C4⋊Q8C2×D23911yescharacteristic
97#126—4782no—
98#124—4781no—
99C22⋊Q8—4781no—
100C4×Q8—4781no—
101C4×Q8—2391no—
102C4×D4—2391no—
103#117—4781no—
104#107—4781no—
105#106—4781no—
106C4⋊C8C2×D23911yescharacteristic
107C4⋊C8C2×D23911yescharacteristic
108#103—4781no—
109#103—4782no—
110#102—4781no—
111C4×C8—2391no—
112C2×Q8—21no—
113C2×Q8—4781no—
114C2×Q8—2391no—
115C2×D4—2391no—
116C22×C4—4781no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—4781no—
120C4⋊C4—21no—
121C4⋊C4—4782no—
122C4⋊C4—4781no—
123C4⋊C4—4781no—
124C4⋊C4—4781no—
125C4⋊C4—2391no—
126C4⋊C4—2391no—
127C4⋊C4D95612yes—
128C22⋊C4—4782no—
129C22⋊C4—4782no—
130C22⋊C4—4781no—
131C42—4782no—
132C42—4781no—
133C42C22×D23911yescharacteristic
134C23—4781no—
135Q8—41no—
136Q8—41no—
137Q8—9562no—
138Q8—4781no—
139Q8—4781no—
140D4—4781no—
141D4—4781no—
142C2×C4—22no—
143C2×C4—9561no—
144C2×C4—9561no—
145C2×C4—9561no—
146C2×C4—4781no—
147C2×C4—4781no—
148C2×C4—4781no—
149C2×C4D4×D23911yescharacteristic
150C2×C4D4×D23911yescharacteristic
151C2×C4C2×D95611yescharacteristic
152C8—41no—
153C8—41no—
154C8—9561no—
155C22—9561no—
156C22—9561no—
157C22—9561no—
158C22#2143993011yescharacteristic
159C4—21no—
160C4—42no—
161C4—19121no—
162C4—9561no—
163C4—9561no—
164C4—9561no—
165C4#2143997911yescharacteristic
166C4#2143998111yescharacteristic
167C4#2143998911yescharacteristic
168C4#2143999211yescharacteristic
169C2—19121no—
170C2#2950493511yescharacteristic
171C2#2950493711yescharacteristic
172C2#2950494711yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#332×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#332D239
hypocenterC239#1638
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #29505124C2semidirect
3. #29505068C2semidirect
5. #29504502C2semidirect
7. #332×C239C2semidirect
86. C239#1638semidirect
92. #332D239semidirect

Maximal subgroups

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

subgroupindex
#295054962
#295051242
#295050682
#295050632
#295045022
#295044992
#332×C2392
#1638239