Finite Group Databasebeta

← #44483680

Subgroups — #44483680

Order 30592.

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

normal subgroups only

This group has 214 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#29505479C211yesmaximal, characteristic
2#29505151C211yesmaximal, characteristic, complemented
3#29505064C211yesmaximal, characteristic, complemented
4#29504520C211yesmaximal, characteristic, complemented
5#29504502C211yesmaximal, characteristic, complemented
6D4⋊(C239⋊C8)C211yesmaximal, characteristic
7#476×C239C211yesmaximal, characteristic
8C2×#16838538—22no—
9#21439960C2211yescharacteristic
10#21439951—21no—
11#21439939—21no—
12#21439937—22no—
13C4×Dic478C2211yescharacteristic
14D4×Dic239—21no—
15C2×C4⋊Dic239—21no—
16#21439893—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic
18#21439883—21no—
19C4×C239⋊C8C2211yescharacteristic
20C4⋊Q8×C239C2211yescharacteristic
21C4×D4×C239C2211yescharacteristic
22#106×C239—21no—
23C4⋊C8×C239C2211yescharacteristic
24#102×C239—21no—
25C2×Dic478D411yescharacteristic
26C2×Dic478D412yes—
27C22×Dic239—22no—
28#16838538—44no—
29C2×C239⋊C8—21no—
30C2×C239⋊C8—21no—
31C4⋊Dic239—22no—
32C4⋊Dic239—21no—
33C4⋊Dic239—21no—
34C4⋊Dic239D411yescharacteristic
35Dic239⋊C4—22no—
36Dic239⋊C4—21no—
37C22⋊Dic239—22no—
38C4×Dic239—21no—
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
48Dic478—21no—
49Dic478—21no—
50Dic478—42no—
51C2×Dic239—21no—
52C2×Dic239—21no—
53C2×Dic239—22no—
54C2×Dic239—82no—
55C239⋊C8—22no—
56C239⋊C8—41no—
57C23×C239—21no—
58Q8×C239—42no—
59D4×C239—21no—
60D4×C239Q1612yescomplemented
61C2×C4×C239—21no—
62C2×C4×C239—41no—
63C2×C4×C239—41no—
64C2×C4×C239—41no—
65C2×C4×C239C2×D411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C8×C239—41no—
69C22×C239—22no—
70C22×C239—41no—
71C22×C239—41no—
72C22×C239#12011yescharacteristic
73C4×C239—21no—
74C4×C239—41no—
75C4×C239—81no—
76C4×C239C2×Q1611yescharacteristic
77C4×C239#13511yescharacteristic
78C4×C239#13711yescharacteristic
79C4×C239#13711yescharacteristic
80Dic239—41no—
81Dic239—41no—
82Dic239—42no—
83C2×C239—42no—
84C2×C239#45111yescharacteristic
85C2×C239#45211yescharacteristic
86C2×C239#45311yescharacteristic
87C239#163211yescharacteristic, complemented, Sylow
88#1632—2391nomaximal, Sylow
89#554—2391no—
90#494—2391no—
91#477—2391no—
92#476D23911yescharacteristic
93#333—2391no—
94Q8⋊C8—2391no—
95D4⋊C8—2391no—
96C2×Q16—4782no—
97C4⋊Q8—2391no—
98C4⋊Q8C2×D23911yescharacteristic
99#125—4781no—
100C22⋊Q8—4782no—
101C22⋊Q8—4781no—
102C4×Q8—2391no—
103C4×D4—4781no—
104C4×D4C2×D23911yescharacteristic
105C2×C4⋊C4—4781no—
106#107—4781no—
107#106—21no—
108C4⋊C8—2391no—
109C4⋊C8C2×D23911yescharacteristic
110#103—4781no—
111#102—21no—
112C4×C8—2391no—
113C2×Q8—21no—
114C2×Q8—2392no—
115C2×Q8—2391no—
116C2×D4C22⋊D23911yescharacteristic
117C22×C4—21no—
118C22×C4—4782no—
119Q16—9564no—
120C2×C8—21no—
121C2×C8—4781no—
122C2×C8—4781no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—4782no—
126C4⋊C4—4782no—
127C4⋊C4—4781no—
128C4⋊C4—4781no—
129C4⋊C4—4781no—
130C4⋊C4—2391no—
131C4⋊C4C22⋊D23911yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—4782no—
134C42—4781no—
135C42C22×D23911yescharacteristic
136C23—21no—
137Q8—42no—
138Q8—9562no—
139Q8—4781no—
140Q8—4781no—
141D4—21no—
142D4#1683853812yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—19122no—
148C2×C4—4781no—
149C2×C4—4781no—
150C2×C4—4782no—
151C2×C4D4×D23911yescharacteristic
152C2×C4D4×D23911yescharacteristic
153C2×C4C2×C22⋊D23911yescharacteristic
154C8—41no—
155C8—9561no—
156C8—4782no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2143992811yescharacteristic
161C4—21no—
162C4—41no—
163C4—81no—
164C4—9561no—
165C4—9561no—
166C4—9562no—
167C4C2×#1683853811yescharacteristic
168C4#2143998111yescharacteristic
169C4#2143998911yescharacteristic
170C4#2143999011yescharacteristic
171C2—42no—
172C2#2950492711yescharacteristic
173C2#2950493111yescharacteristic
174C2#2950493811yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#476×C239C2
socleC22×C239#120
prime radicalC2×D4×C239D4
hypercenter#476D239
hypocenterC239#1632
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. #29505064C2semidirect
4. #29504520C2semidirect
5. #29504502C2semidirect
60. D4×C239Q16semidirect
87. C239#1632semidirect
142. D4#16838538semidirect

Maximal subgroups

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

subgroupindex
#295054792
#295051512
#295050642
#295045202
#295045022
D4⋊(C239⋊C8)2
#476×C2392
#1632239