Finite Group Databasebeta

← #44483657

Subgroups — #44483657

Order 30592.

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

normal subgroups only

This group has 216 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#29505495C211yesmaximal, characteristic, complemented
2#29505118C211yesmaximal, characteristic, complemented
3#29504964C211yesmaximal, characteristic
4#29504517C211yesmaximal, characteristic, complemented
5Q8⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#460×C239C211yesmaximal, characteristic, complemented
8C2×#16838533—21no—
9#21439960C2211yescharacteristic
10#21439955—22no—
11#21439948—21no—
12#21439936—21no—
13C4×Dic478—21no—
14C4×D956C2211yescharacteristic
15#21439918—21no—
16C4⋊(C239⋊C8)C2211yescharacteristic
17#21439881—22no—
18#21439881—21no—
19C4×C239⋊C8C2211yescharacteristic
20C2×SD16×C239—21no—
21#127×C239C2211yescharacteristic
22C4×Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24#102×C239—21no—
25C2×Dic478—21no—
26C2×D956D411yescharacteristic
27C2×C4×D239—21no—
28#16838533—42no—
29C2×C239⋊C8—21no—
30C2×C239⋊C8—21no—
31C4⋊Dic239—21no—
32C4⋊Dic239D411yescharacteristic
33C4⋊Dic239D412yes—
34Dic239⋊C4—22no—
35(C2×D239)⋊C4—22no—
36(C2×D239)⋊C4—22no—
37(C2×D239)⋊C4—21no—
38C4×Dic239—22no—
39C2×Q8×C239D411yescharacteristic
40C2×D4×C239—21no—
41C2×D4×C239—21no—
42C2×D4×C239—21no—
43SD16×C239—42no—
44C2×C8×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239D411yescharacteristic
47C42×C239—21no—
48C42×C239C2311yescharacteristic
49C22×D239—21no—
50Dic478—41no—
51Dic478—41no—
52D956—21no—
53D956—21no—
54C2×Dic239—21no—
55C2×Dic239—22no—
56C4×D239—41no—
57C4×D239—41no—
58C239⋊C8—41no—
59C239⋊C8—41no—
60C23×C239—41no—
61Q8×C239—21no—
62Q8×C239—21no—
63D4×C239—42no—
64D4×C239—41no—
65D4×C239—41no—
66D4×C239—41no—
67D4×C239—41no—
68C2×C4×C239—21no—
69C2×C4×C239—21no—
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C8×C239—41no—
74C22×C239—81no—
75C22×C239—81no—
76C22×C239—81no—
77C22×C239#12011yescharacteristic
78C2×D239—41no—
79C2×D239—41no—
80C2×D239—41no—
81C4×C239—21no—
82C4×C239—41no—
83C4×C239—41no—
84C4×C239#13511yescharacteristic
85C4×C239#13511yescharacteristic
86C4×C239AGL(1,ℤ/8)11yescharacteristic
87C4×C239AGL(1,ℤ/8)11yescharacteristic
88Dic239—41no—
89Dic239—42no—
90C2×C239—161no—
91C2×C239#44911yescharacteristic
92C2×C239#44911yescharacteristic
93C2×C239#45411yescharacteristic
94D239—81no—
95C239#162811yescharacteristic, complemented, Sylow
96#1628—2391nomaximal, Sylow
97#556—2391no—
98#486—2391no—
99#460D23911yescharacteristic, complemented
100#459—2391no—
101#332—2391no—
102Q8⋊C8—2391no—
103D4⋊C8—2391no—
104C2×SD16—21no—
105C2×D8—4781no—
106C4⋊Q8—2391no—
107#127C2×D23911yescharacteristic
108#126—4782no—
109#124—4781no—
110C22⋊Q8—4781no—
111C4×Q8—4781no—
112C4×Q8C2×D23911yescharacteristic
113C4×D4—2391no—
114#117—4781no—
115C4⋊C8—2391no—
116C4⋊C8C2×D23911yescharacteristic
117#102—21no—
118#102—4781no—
119#102—4782no—
120C4×C8—2391no—
121C2×Q8—4781no—
122C2×Q8C22⋊D23911yescharacteristic
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—2391no—
127C22×C4—4781no—
128SD16—42no—
129D8—9562no—
130C2×C8—21no—
131C2×C8—4781no—
132C2×C8—4781no—
133C4⋊C4—21no—
134C4⋊C4—4782no—
135C4⋊C4—4781no—
136C4⋊C4—2391no—
137C4⋊C4—2392no—
138C4⋊C4C22⋊D23911yescharacteristic
139C22⋊C4—4782no—
140C22⋊C4—4782no—
141C22⋊C4—4781no—
142C42—21no—
143C42—4782no—
144C42C22×D23911yescharacteristic
145C23—41no—
146C23—4781no—
147Q8—21no—
148Q8—21no—
149Q8—9561no—
150Q8—9561no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—4781no—
157D4—4781no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—9561no—
161C2×C4—9561no—
162C2×C4—4781no—
163C2×C4—4782no—
164C2×C4D4×D23911yescharacteristic
165C2×C4D4×D23911yescharacteristic
166C2×C4C2×C22⋊D23911yescharacteristic
167C8—41no—
168C8—9561no—
169C8—9561no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—9561no—
174C22—9561no—
175C22—9561no—
176C22#2143992811yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—9561no—
181C4—9562no—
182C4#2143998011yescharacteristic
183C4#2143998111yescharacteristic
184C4#2143998611yescharacteristic
185C4#2143998711yescharacteristic
186C2—161no—
187C2—19121no—
188C2#2950491511yescharacteristic
189C2#2950491611yescharacteristic
190C2#2950494311yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#460×C239C2
socleC22×C239#120
prime radical#29504964C2
hypercenter#460D239
hypocenterC239#1628
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #29505495C2semidirect
2. #29505118C2semidirect
4. #29504517C2semidirect
5. Q8⋊(C239⋊C8)C2semidirect
6. #29504499C2semidirect
7. #460×C239C2semidirect
95. C239#1628semidirect
99. #460D239semidirect

Maximal subgroups

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

subgroupindex
#295054952
#295051182
#295049642
#295045172
Q8⋊(C239⋊C8)2
#295044992
#460×C2392
#1628239