Finite Group Databasebeta

← #44483831

Subgroups — #44483831

Order 30592.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#29505426C211yesmaximal, characteristic
2#29505168C211yesmaximal, characteristic, complemented
3#29504974C211yesmaximal, characteristic, complemented
4#29504519C211yesmaximal, characteristic, complemented
5D4⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#474×C239C211yesmaximal, characteristic, complemented
8C2×#16838547—21no—
9C2×#16838535—21no—
10#21439960C2211yescharacteristic
11#21439944—22no—
12#21439940—21no—
13#21439934—21no—
14C4×D956C2211yescharacteristic
15C2×C4⋊Dic239—21no—
16#21439891—22no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18#21439884—21no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×D4×C239C2211yescharacteristic
22#107×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#102×C239—21no—
25#16838547—42no—
26#16838547—42no—
27C2×Dic478—21no—
28C2×D956D411yescharacteristic
29C2×C22⋊D239—22no—
30C22×Dic239—22no—
31C2×C4×D239—21no—
32#16838535—42no—
33C2×C239⋊C8—21no—
34C2×C239⋊C8—21no—
35C4⋊Dic239—22no—
36C4⋊Dic239—21no—
37C4⋊Dic239D411yescharacteristic
38C4⋊Dic239D412yes—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C2×Q8×C239—21no—
42C2×D4×C239D411yescharacteristic
43C22×C4×C239—21no—
44C2×C8×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C4⋊C4×C239D411yescharacteristic
48C22⋊C4×C239—21no—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51Dic478—41no—
52Dic478—41no—
53D956—21no—
54D956—21no—
55C22⋊D239—44no—
56C2×Dic239—21no—
57C2×Dic239—22no—
58C2×Dic239—44no—
59C4×D239—41no—
60C4×D239—41no—
61C239⋊C8—22no—
62C239⋊C8—41no—
63C23×C239—21no—
64Q8×C239—41no—
65Q8×C239—41no—
66D4×C239—21no—
67D4×C239SD1612yescomplemented
68C2×C4×C239—21no—
69C2×C4×C239—41no—
70C2×C4×C239—41no—
71C2×C4×C239—41no—
72C2×C4×C239C2×D411yescharacteristic
73C2×C4×C239C2×D411yescharacteristic
74C2×C4×C239C2×D411yescharacteristic
75C8×C239—41no—
76C22×C239—22no—
77C22×C239—41no—
78C22×C239—41no—
79C22×C239#12011yescharacteristic
80C2×D239—41no—
81C2×D239—41no—
82C2×D239—41no—
83C4×C239—21no—
84C4×C239—41no—
85C4×C239—81no—
86C4×C239C2×SD1611yescharacteristic
87C4×C239#13511yescharacteristic
88C4×C239AGL(1,ℤ/8)11yescharacteristic
89C4×C239AGL(1,ℤ/8)11yescharacteristic
90Dic239—41no—
91Dic239—42no—
92C2×C239—42no—
93C2×C239#44911yescharacteristic
94C2×C239#45011yescharacteristic
95C2×C239#45611yescharacteristic
96D239—81no—
97C239#165411yescharacteristic, complemented, Sylow
98#1654—2391nomaximal, Sylow
99#547—2391no—
100#498—2391no—
101#474D23911yescharacteristic, complemented
102#461—2391no—
103#332—2391no—
104D4⋊C8—2391no—
105D4⋊C8—2391no—
106C2×#41—4781no—
107C2×SD16—4781no—
108C4⋊Q8—2391no—
109C4⋊Q8C2×D23911yescharacteristic
110#123—4782no—
111C22⋊Q8—4781no—
112#121—4781no—
113C4×D4—2391no—
114C4×D4C2×D23911yescharacteristic
115C2×C4⋊C4—4781no—
116#107—21no—
117#106—4782no—
118C4⋊C8—2391no—
119C4⋊C8C2×D23911yescharacteristic
120#103—4781no—
121#102—21no—
122C4×C8—2391no—
123#41—9562no—
124#41—9562no—
125C2×Q8—21no—
126C2×Q8—4781no—
127C2×D4—4782no—
128C2×D4—2391no—
129C2×D4C22⋊D23911yescharacteristic
130C22×C4—21no—
131C22×C4—4782no—
132C22×C4—4781no—
133SD16—9562no—
134C2×C8—21no—
135C2×C8—4781no—
136C2×C8—4781no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—4782no—
140C4⋊C4—4781no—
141C4⋊C4—2391no—
142C4⋊C4—2392no—
143C4⋊C4C22⋊D23911yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—4782no—
146C22⋊C4—4781no—
147C42C22×D23911yescharacteristic
148C23—21no—
149C23—4781no—
150Q8—41no—
151Q8—41no—
152Q8—9561no—
153Q8—9561no—
154D4—21no—
155D4—9564no—
156D4—4781no—
157D4—4781no—
158D4#1683853512yescomplemented
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—9564no—
164C2×C4—9561no—
165C2×C4—9561no—
166C2×C4—4781no—
167C2×C4—4782no—
168C2×C4D4×D23911yescharacteristic
169C2×C4D4×D23911yescharacteristic
170C2×C4C2×C22⋊D23911yescharacteristic
171C8—41no—
172C8—9561no—
173C8—4782no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—9561no—
178C22—9561no—
179C22—9561no—
180C22#2143992811yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—9561no—
185C4—9562no—
186C4C2×#1683853511yescharacteristic
187C4#2143997911yescharacteristic
188C4#2143998411yescharacteristic
189C4#2143998511yescharacteristic
190C2—42no—
191C2—19121no—
192C2#2950491411yescharacteristic
193C2#2950492211yescharacteristic
194C2#2950495311yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#474×C239C2
socleC22×C239#120
prime radical#29505426C2
hypercenter#474D239
hypocenterC239#1654
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #29505168C2semidirect
3. #29504974C2semidirect
4. #29504519C2semidirect
5. D4⋊(C239⋊C8)C2semidirect
6. #29504499C2semidirect
7. #474×C239C2semidirect
67. D4×C239SD16semidirect
97. C239#1654semidirect
101. #474D239semidirect
158. D4#16838535semidirect

Maximal subgroups

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

subgroupindex
#295054262
#295051682
#295049742
#295045192
D4⋊(C239⋊C8)2
#295044992
#474×C2392
#1654239