Finite Group Databasebeta

← #44483747

Subgroups — #44483747

Order 30592.

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

normal subgroups only

This group has 250 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#29505444C211yesmaximal, characteristic
2#29505120C211yesmaximal, characteristic, complemented
3#29504974C211yesmaximal, characteristic, complemented
4#29504515C211yesmaximal, characteristic, complemented
5Q8⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#475×C239C211yesmaximal, characteristic, complemented
8C2×#16838549—21no—
9C2×#16838535—21no—
10#21439957—21no—
11#21439957C2211yescharacteristic
12#21439935—22no—
13#21439935—21no—
14C4×D956—21no—
15C4×D956C2211yescharacteristic
16C4⋊(C239⋊C8)C2211yescharacteristic
17#21439884—21no—
18#21439880—22no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×Q8×C239C2211yescharacteristic
22#106×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#103×C239—21no—
25#16838549—42no—
26#16838549—42no—
27C2×D956—22no—
28C2×D956—22no—
29C2×D956—21no—
30C2×D956—21no—
31C2×D956D411yescharacteristic
32C2×D956D412yes—
33C2×C4×D239—22no—
34C2×C4×D239—21no—
35#16838535—42no—
36C2×C239⋊C8—21no—
37C2×C239⋊C8—21no—
38C4⋊Dic239D411yescharacteristic
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C2×Q8×C239—21no—
42C2×Q8×C239D411yescharacteristic
43C2×C8×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C4⋊C4×C239D411yescharacteristic
48C42×C239—21no—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51C22×D239—22no—
52D956—21no—
53D956—21no—
54D956—44no—
55D956—42no—
56D956—41no—
57D956—41no—
58D956—41no—
59D956—41no—
60D956—82no—
61C2×Dic239—21no—
62C4×D239—44no—
63C4×D239—41no—
64C4×D239—41no—
65C239⋊C8—41no—
66C239⋊C8—41no—
67Q8×C239—21no—
68Q8×C239—41no—
69Q8×C239—41no—
70Q8×C239SD1612yescomplemented
71C2×C4×C239—21no—
72C2×C4×C239—21no—
73C2×C4×C239—41no—
74C2×C4×C239C2×D411yescharacteristic
75C2×C4×C239C2×D411yescharacteristic
76C2×C4×C239C2×D411yescharacteristic
77C8×C239—41no—
78C22×C239#12011yescharacteristic
79C2×D239—41no—
80C2×D239—42no—
81C2×D239—42no—
82C2×D239—41no—
83C2×D239—42no—
84C2×D239—41no—
85C4×C239—22no—
86C4×C239—21no—
87C4×C239—41no—
88C4×C239—81no—
89C4×C239C2×SD1611yescharacteristic
90C4×C239#13511yescharacteristic
91C4×C239AGL(1,ℤ/8)11yescharacteristic
92C4×C239AGL(1,ℤ/8)11yescharacteristic
93Dic239—41no—
94C2×C239#44911yescharacteristic
95C2×C239#45011yescharacteristic
96C2×C239#45511yescharacteristic
97D239—81no—
98D239—82no—
99C239#164211yescharacteristic, complemented, Sylow
100#1642—2391nomaximal, Sylow
101#550—2391no—
102#486—2391no—
103#475D23911yescharacteristic, complemented
104#461—2391no—
105#331—2391no—
106Q8⋊C8—2391no—
107D4⋊C8—2391no—
108C2×#41—4781no—
109C2×SD16—4781no—
110C4⋊Q8C2×D23911yescharacteristic
111#127—4781no—
112#127—2391no—
113#121—4782no—
114#121—4781no—
115C4×Q8C2×D23911yescharacteristic
116C4×D4—4781no—
117C4×D4—2391no—
118#106—21no—
119C4⋊C8—2391no—
120C4⋊C8C2×D23911yescharacteristic
121#103—21no—
122#103—4781no—
123#102—4782no—
124C4×C8—2391no—
125#41—9562no—
126#41—9562no—
127C2×Q8—21no—
128C2×Q8C22⋊D23911yescharacteristic
129C2×D4—4782no—
130C2×D4—4782no—
131C2×D4—4781no—
132C2×D4—4781no—
133C2×D4—2392no—
134C2×D4—2391no—
135C22×C4—4782no—
136C22×C4—4781no—
137SD16—9562no—
138C2×C8—21no—
139C2×C8—4781no—
140C2×C8—4781no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—2391no—
145C4⋊C4C22⋊D23911yescharacteristic
146C22⋊C4—4782no—
147C22⋊C4—4781no—
148C42—21no—
149C42C22×D23911yescharacteristic
150C23—4782no—
151C23—4781no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1683853512yescomplemented
156D4—19122no—
157D4—9562no—
158D4—9564no—
159D4—9561no—
160D4—9561no—
161D4—9561no—
162D4—9561no—
163D4—4781no—
164D4—4781no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—9564no—
169C2×C4—9561no—
170C2×C4—9561no—
171C2×C4—4781no—
172C2×C4D4×D23911yescharacteristic
173C2×C4D4×D23911yescharacteristic
174C2×C4C2×C22⋊D23911yescharacteristic
175C8—41no—
176C8—9561no—
177C8—9561no—
178C22—9562no—
179C22—9561no—
180C22—9562no—
181C22—9561no—
182C22—9561no—
183C22—9562no—
184C22#2143992811yescharacteristic
185C4—22no—
186C4—21no—
187C4—41no—
188C4—81no—
189C4—9561no—
190C4C2×#1683853511yescharacteristic
191C4#2143998111yescharacteristic
192C4#2143998511yescharacteristic
193C4#2143998711yescharacteristic
194C2—19122no—
195C2—19121no—
196C2#2950491611yescharacteristic
197C2#2950492211yescharacteristic
198C2#2950494811yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#475×C239C2
socleC22×C239#120
prime radical#29505444C2
hypercenter#475D239
hypocenterC239#1642
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. #29505120C2semidirect
3. #29504974C2semidirect
4. #29504515C2semidirect
5. Q8⋊(C239⋊C8)C2semidirect
6. #29504499C2semidirect
7. #475×C239C2semidirect
70. Q8×C239SD16semidirect
99. C239#1642semidirect
103. #475D239semidirect
155. Q8#16838535semidirect

Maximal subgroups

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

subgroupindex
#295054442
#295051202
#295049742
#295045152
Q8⋊(C239⋊C8)2
#295044992
#475×C2392
#1642239