Finite Group Databasebeta

← #44483692

Subgroups — #44483692

Order 30592.

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

normal subgroups only

This group has 218 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#29505487C211yesmaximal, characteristic
2#29505151C211yesmaximal, characteristic, complemented
3#29505059C211yesmaximal, characteristic, complemented
4#29504520C211yesmaximal, characteristic, complemented
5D4⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#476×C239C211yesmaximal, characteristic, complemented
8C2×#16838538—22no—
9#21439960C2211yescharacteristic
10#21439946—22no—
11#21439934—21no—
12#21439931—21no—
13C4×D956C2211yescharacteristic
14#21439919—21no—
15#21439918—21no—
16#21439891—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18#21439880—21no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×D4×C239C2211yescharacteristic
22#106×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#102×C239—21no—
25C2×Dic478D412yes—
26C2×D956D411yescharacteristic
27C2×C22⋊D239—22no—
28C2×C4×D239—21no—
29#16838538—44no—
30C2×C239⋊C8—21no—
31C2×C239⋊C8—21no—
32C4⋊Dic239—21no—
33C4⋊Dic239—21no—
34C4⋊Dic239D411yescharacteristic
35C22⋊Dic239—22no—
36(C2×D239)⋊C4—22no—
37(C2×D239)⋊C4—21no—
38C4×Dic239—22no—
39C2×Q8×C239—21no—
40C2×D4×C239D411yescharacteristic
41C22×C4×C239—21no—
42C2×C8×C239—21no—
43C4⋊C4×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239D411yescharacteristic
46C22⋊C4×C239—21no—
47C42×C239C2311yescharacteristic
48C22×D239—21no—
49Dic478—42no—
50D956—21no—
51D956—21no—
52C22⋊D239—82no—
53C2×Dic239—21no—
54C2×Dic239—22no—
55C4×D239—41no—
56C4×D239—41no—
57C239⋊C8—22no—
58C239⋊C8—41no—
59C23×C239—21no—
60Q8×C239—42no—
61D4×C239—21no—
62D4×C239—21no—
63C2×C4×C239—21no—
64C2×C4×C239—41no—
65C2×C4×C239—41no—
66C2×C4×C239—41no—
67C2×C4×C239C2×D411yescharacteristic
68C2×C4×C239C2×D411yescharacteristic
69C2×C4×C239C2×D411yescharacteristic
70C8×C239—41no—
71C22×C239—41no—
72C22×C239—41no—
73C22×C239—41no—
74C22×C239#12011yescharacteristic
75C2×D239—41no—
76C2×D239—41no—
77C2×D239—41no—
78C4×C239—21no—
79C4×C239—41no—
80C4×C239—81no—
81C4×C239#13511yescharacteristic
82C4×C239#13511yescharacteristic
83C4×C239#13711yescharacteristic
84C4×C239#13711yescharacteristic
85Dic239—41no—
86Dic239—42no—
87C2×C239—81no—
88C2×C239#45211yescharacteristic
89C2×C239#45211yescharacteristic
90C2×C239#45311yescharacteristic
91D239—81no—
92C239#163411yescharacteristic, complemented, Sylow
93#1634—2391nomaximal, Sylow
94#555—2391no—
95#494—2391no—
96#476—2391no—
97#476D23911yescharacteristic, complemented
98#333—2391no—
99D4⋊C8—2391no—
100D4⋊C8—2391no—
101C2×Q16—4782no—
102C4⋊Q8—2391no—
103C4⋊Q8C2×D23911yescharacteristic
104#124—4782no—
105#121—4781no—
106#121—4781no—
107C4×D4—2391no—
108C4×D4C2×D23911yescharacteristic
109#117—4781no—
110#117—4781no—
111#106—21no—
112#106—4781no—
113C4⋊C8—2391no—
114C4⋊C8C2×D23911yescharacteristic
115#102—21no—
116#102—4781no—
117C4×C8—2391no—
118C2×Q8—21no—
119C2×Q8—2392no—
120C2×D4—4782no—
121C2×D4—2391no—
122C2×D4C22⋊D23911yescharacteristic
123C22×C4—21no—
124C22×C4—4781no—
125Q16—9564no—
126C2×C8—21no—
127C2×C8—4781no—
128C2×C8—4781no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—4781no—
132C4⋊C4—4781no—
133C4⋊C4—2391no—
134C4⋊C4C22⋊D23911yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—4782no—
137C22⋊C4—4782no—
138C22⋊C4—4781no—
139C42—4782no—
140C42C22×D23911yescharacteristic
141C23—21no—
142C23—4781no—
143Q8—42no—
144Q8—9562no—
145D4—21no—
146D4—21no—
147D4—19122no—
148D4—4781no—
149D4—4781no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—9561no—
155C2×C4—9561no—
156C2×C4—4781no—
157C2×C4—4782no—
158C2×C4D4×D23911yescharacteristic
159C2×C4D4×D23911yescharacteristic
160C2×C4C2×C22⋊D23911yescharacteristic
161C8—41no—
162C8—9561no—
163C8—4782no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—9561no—
168C22—9561no—
169C22—9561no—
170C22#2143992811yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—9561no—
175C4—9562no—
176C4#2143998011yescharacteristic
177C4#2143998111yescharacteristic
178C4#2143998911yescharacteristic
179C4#2143999111yescharacteristic
180C2—81no—
181C2—19121no—
182C2#2950493111yescharacteristic
183C2#2950493211yescharacteristic
184C2#2950493811yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#476×C239C2
socleC22×C239#120
prime radical#29505487C2
hypercenter#476D239
hypocenterC239#1634
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. #29505151C2semidirect
3. #29505059C2semidirect
4. #29504520C2semidirect
5. D4⋊(C239⋊C8)C2semidirect
6. #29504499C2semidirect
7. #476×C239C2semidirect
92. C239#1634semidirect
97. #476D239semidirect

Maximal subgroups

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

subgroupindex
#295054872
#295051512
#295050592
#295045202
D4⋊(C239⋊C8)2
#295044992
#476×C2392
#1634239