Finite Group Databasebeta

← #44483748

Subgroups — #44483748

Order 30592.

250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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#29505118C211yesmaximal, characteristic, complemented
2#29505057C211yesmaximal, characteristic, complemented
3#29504977C211yesmaximal, characteristic, complemented
4#29504516C211yesmaximal, characteristic, complemented
5Q8⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
7#550×C239C211yesmaximal, characteristic
8C2×#16838536—21no—
9#21439960C2211yescharacteristic
10#21439891—21no—
11C4⋊(C239⋊C8)C2211yescharacteristic
12C4⋊(C239⋊C8)C2211yescharacteristic
13#21439884—21no—
14#21439883—21no—
15#21439881—22no—
16C4×C239⋊C8C2211yescharacteristic
17C2×#41×C239—21no—
18#127×C239—21no—
19#127×C239C2211yescharacteristic
20#121×C239—22no—
21#121×C239—21no—
22C4×Q8×C239C2211yescharacteristic
23C4×D4×C239—21no—
24C4×D4×C239C2211yescharacteristic
25C2×Dic478—21no—
26#16838536—42no—
27C2×C239⋊C8—21no—
28C2×C239⋊C8—21no—
29C2×C239⋊C8—21no—
30C4⋊Dic239—21no—
31C4⋊Dic239—21no—
32#41×C239—42no—
33#41×C239—42no—
34C2×Q8×C239D411yescharacteristic
35C2×D4×C239—22no—
36C2×D4×C239—22no—
37C2×D4×C239—21no—
38C2×D4×C239—21no—
39C2×D4×C239D411yescharacteristic
40C2×D4×C239D412yes—
41C22×C4×C239—22no—
42C22×C4×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239D411yescharacteristic
45C4⋊C4×C239D411yescharacteristic
46C22⋊C4×C239—22no—
47C22⋊C4×C239—21no—
48C42×C239—21no—
49C42×C239C2311yescharacteristic
50Dic478—41no—
51Dic478—41no—
52C2×Dic239—41no—
53C239⋊C8—41no—
54C239⋊C8—41no—
55C239⋊C8—41no—
56C23×C239—21no—
57C23×C239—22no—
58Q8×C239—21no—
59Q8×C239SD1612yescomplemented
60D4×C239—21no—
61D4×C239—21no—
62D4×C239—44no—
63D4×C239—42no—
64D4×C239—41no—
65D4×C239—41no—
66D4×C239—41no—
67D4×C239—41no—
68D4×C239—82no—
69C2×C4×C239—21no—
70C2×C4×C239—21no—
71C2×C4×C239—21no—
72C2×C4×C239—44no—
73C2×C4×C239—41no—
74C2×C4×C239—41no—
75C2×C4×C239C2×D411yescharacteristic
76C2×C4×C239C2×D411yescharacteristic
77C2×C4×C239C2×D411yescharacteristic
78C22×C239—41no—
79C22×C239—42no—
80C22×C239—42no—
81C22×C239—41no—
82C22×C239—42no—
83C22×C239—41no—
84C22×C239#12011yescharacteristic
85C4×C239—22no—
86C4×C239—21no—
87C4×C239—41no—
88C4×C239—41no—
89C4×C239C2×SD1611yescharacteristic
90C4×C239#13511yescharacteristic
91C4×C239AGL(1,ℤ/8)11yescharacteristic
92C4×C239AGL(1,ℤ/8)11yescharacteristic
93Dic239—81no—
94C2×C239—81no—
95C2×C239—82no—
96C2×C239#44911yescharacteristic
97C2×C239#45011yescharacteristic
98C2×C239#45511yescharacteristic
99C239#164211yescharacteristic, complemented, Sylow
100#1642—2391nomaximal, Sylow
101#550D23911yescharacteristic
102#486—2391no—
103#475—2391no—
104#461—2391no—
105#331—2391no—
106Q8⋊C8—2391no—
107D4⋊C8—2391no—
108C2×#41—21no—
109C2×SD16—4781no—
110C4⋊Q8—2391no—
111#127—21no—
112#127C2×D23911yescharacteristic
113#121—22no—
114#121—21no—
115C4×Q8C2×D23911yescharacteristic
116C4×D4—21no—
117C4×D4C2×D23911yescharacteristic
118#106—4781no—
119C4⋊C8—2391no—
120C4⋊C8—2391no—
121#103—4781no—
122#103—4781no—
123#102—4782no—
124C4×C8—2391no—
125#41—42no—
126#41—42no—
127C2×Q8—4781no—
128C2×Q8C22⋊D23911yescharacteristic
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D23911yescharacteristic
134C2×D4C22⋊D23912yes—
135C22×C4—22no—
136C22×C4—21no—
137SD16—9562no—
138C2×C8—4781no—
139C2×C8—4781no—
140C2×C8—4781no—
141C4⋊C4—21no—
142C4⋊C4—4781no—
143C4⋊C4—4781no—
144C4⋊C4C22⋊D23911yescharacteristic
145C4⋊C4C22⋊D23911yescharacteristic
146C22⋊C4—22no—
147C22⋊C4—21no—
148C42—21no—
149C42C22×D23911yescharacteristic
150C23—21no—
151C23—22no—
152Q8—21no—
153Q8—9561no—
154Q8—9561no—
155Q8#1683853612yescomplemented
156D4—21no—
157D4—21no—
158D4—42no—
159D4—44no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—44no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—9561no—
172C2×C4C2×C22⋊D23911yescharacteristic
173C2×C4C2×C22⋊D23911yescharacteristic
174C2×C4C2×C22⋊D23911yescharacteristic
175C8—9561no—
176C8—9561no—
177C8—9561no—
178C22—41no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22—42no—
183C22—41no—
184C22#2143992911yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—41no—
189C4—19121no—
190C4C2×#1683853611yescharacteristic
191C4#2143998011yescharacteristic
192C4#2143998511yescharacteristic
193C4#2143998611yescharacteristic
194C2—81no—
195C2—82no—
196C2#2950491711yescharacteristic
197C2#2950492311yescharacteristic
198C2#2950495011yescharacteristic
subgroupG/H
centerC22#21439929
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting, prime radical#550×C239C2
socleC22×C239#120
hypercenter#550D239
hypocenterC239#1642
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #29505118C2semidirect
2. #29505057C2semidirect
3. #29504977C2semidirect
4. #29504516C2semidirect
5. Q8⋊(C239⋊C8)C2semidirect
6. D4⋊(C239⋊C8)C2semidirect
59. Q8×C239SD16semidirect
99. C239#1642semidirect
155. Q8#16838536semidirect

Maximal subgroups

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

subgroupindex
#295051182
#295050572
#295049772
#295045162
Q8⋊(C239⋊C8)2
D4⋊(C239⋊C8)2
#550×C2392
#1642239