Finite Group Databasebeta

← #44483718

Subgroups — #44483718

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#29505492C211yesmaximal, characteristic
2#29505122C211yesmaximal, characteristic, complemented
3#29505064C211yesmaximal, characteristic, complemented
4#29504519C211yesmaximal, characteristic, complemented
5#29504502C211yesmaximal, characteristic, complemented
6D4⋊(C239⋊C8)C211yesmaximal, characteristic
7#476×C239C211yesmaximal, characteristic
8#21439960C2211yescharacteristic
9#21439953—22no—
10#21439947—21no—
11#21439939—21no—
12C4×Dic478C2211yescharacteristic
13#21439925—21no—
14#21439919—21no—
15#21439893—21no—
16C4⋊(C239⋊C8)C2211yescharacteristic
17#21439884—22no—
18#21439883—21no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×D4×C239C2211yescharacteristic
22#106×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#102×C239—21no—
25C2×Dic478—21no—
26C2×Dic478D411yescharacteristic
27C2×C239⋊C8—21no—
28C2×C239⋊C8—21no—
29C4⋊Dic239—21no—
30C4⋊Dic239D412yes—
31C4⋊Dic239D411yescharacteristic
32Dic239⋊C4—22no—
33Dic239⋊C4—21no—
34C22⋊Dic239—22no—
35C22⋊Dic239—22no—
36C4×Dic239—22no—
37C4×Dic239—21no—
38C2×Q8×C239—21no—
39C2×D4×C239D411yescharacteristic
40C22×C4×C239—21no—
41C2×C8×C239—21no—
42C4⋊C4×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239D411yescharacteristic
45C22⋊C4×C239—21no—
46C42×C239C2311yescharacteristic
47Dic478—21no—
48Dic478—21no—
49Dic478—41no—
50Dic478—41no—
51C2×Dic239—21no—
52C2×Dic239—21no—
53C2×Dic239—22no—
54C239⋊C8—41no—
55C239⋊C8—41no—
56C23×C239—21no—
57Q8×C239—42no—
58D4×C239—21no—
59D4×C239—21no—
60C2×C4×C239—21no—
61C2×C4×C239—41no—
62C2×C4×C239—41no—
63C2×C4×C239—41no—
64C2×C4×C239C2×D411yescharacteristic
65C2×C4×C239C2×D411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C8×C239—41no—
68C22×C239—41no—
69C22×C239—41no—
70C22×C239—41no—
71C22×C239#12011yescharacteristic
72C4×C239—21no—
73C4×C239—41no—
74C4×C239—81no—
75C4×C239#13511yescharacteristic
76C4×C239#13511yescharacteristic
77C4×C239#13711yescharacteristic
78C4×C239#13711yescharacteristic
79Dic239—41no—
80Dic239—42no—
81Dic239—41no—
82C2×C239—81no—
83C2×C239#45211yescharacteristic
84C2×C239#45211yescharacteristic
85C2×C239#45411yescharacteristic
86C239#163811yescharacteristic, complemented, Sylow
87#1638—2391nomaximal, Sylow
88#556—2391no—
89#487—2391no—
90#477—2391no—
91#476D23911yescharacteristic
92#332—2391no—
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×D4C2×D23911yescharacteristic
103#117—4781no—
104#107—4781no—
105#106—21no—
106C4⋊C8—2391no—
107C4⋊C8C2×D23911yescharacteristic
108#103—4781no—
109#103—4782no—
110#102—21no—
111C4×C8—2391no—
112C2×Q8—21no—
113C2×Q8—4781no—
114C2×Q8—2391no—
115C2×D4C22⋊D23911yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—4781no—
119C2×C8—4781no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—4782no—
123C4⋊C4—4781no—
124C4⋊C4—4781no—
125C4⋊C4—2392no—
126C4⋊C4—2391no—
127C4⋊C4C22⋊D23911yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—4782no—
130C22⋊C4—4782no—
131C42—4782no—
132C42—4781no—
133C42C22×D23911yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—9561no—
137Q8—9561no—
138Q8—4781no—
139Q8—4781no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—4781no—
147C2×C4—4781no—
148C2×C4—4782no—
149C2×C4D4×D23911yescharacteristic
150C2×C4D4×D23911yescharacteristic
151C2×C4C2×C22⋊D23911yescharacteristic
152C8—41no—
153C8—9561no—
154C8—9561no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2143992811yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—9561no—
163C4—9562no—
164C4—9561no—
165C4#2143998011yescharacteristic
166C4#2143998111yescharacteristic
167C4#2143998911yescharacteristic
168C4#2143999111yescharacteristic
169C2—81no—
170C2#2950493111yescharacteristic
171C2#2950493211yescharacteristic
172C2#2950494311yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#476×C239C2
socleC22×C239#120
prime radicalC2×D4×C239D4
hypercenter#476D239
hypocenterC239#1638
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #29505122C2semidirect
3. #29505064C2semidirect
4. #29504519C2semidirect
5. #29504502C2semidirect
86. C239#1638semidirect

Maximal subgroups

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

subgroupindex
#295054922
#295051222
#295050642
#295045192
#295045022
D4⋊(C239⋊C8)2
#476×C2392
#1638239