Finite Group Databasebeta

← #44483684

Subgroups — #44483684

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#29505152C211yesmaximal, characteristic, complemented
3#29505068C211yesmaximal, characteristic, complemented
4#29505062C211yesmaximal, characteristic
5#29504520C211yesmaximal, characteristic, complemented
6#29504504C211yesmaximal, characteristic, complemented
7D4⋊C8×C239C211yesmaximal, characteristic
8C2×Dic956—22no—
9#21439960C2211yescharacteristic
10#21439960C2211yescharacteristic
11#21439951—21no—
12#21439939—21no—
13#21439937—22no—
14C4×Dic478C2211yescharacteristic
15D4×Dic239—21no—
16C2×C4⋊Dic239—21no—
17#21439894—21no—
18#21439891—21no—
19C4⋊(C239⋊C8)C2211yescharacteristic
20#21439885—21no—
21#21439881—21no—
22C4×D4×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4×C8×C239C2211yescharacteristic
25C2×Dic478—21no—
26C2×Dic478D411yescharacteristic
27C2×Dic478D412yes—
28C22×Dic239—22no—
29Dic956—44no—
30C2×C239⋊C8—21no—
31C4⋊Dic239—22no—
32C4⋊Dic239—21no—
33C4⋊Dic239—21no—
34C4⋊Dic239—21no—
35C4⋊Dic239—21no—
36C4⋊Dic239D411yescharacteristic
37Dic239⋊C4—22no—
38Dic239⋊C4—21no—
39C22⋊Dic239—22no—
40C4×Dic239—21no—
41C2×D4×C239D411yescharacteristic
42C22×C4×C239—21no—
43C2×C8×C239—21no—
44C2×C8×C239—21no—
45C4⋊C4×C239D411yescharacteristic
46C22⋊C4×C239—21no—
47C42×C239C2311yescharacteristic
48Dic478—21no—
49Dic478—21no—
50Dic478—42no—
51Dic478—42no—
52C2×Dic239—21no—
53C2×Dic239—21no—
54C2×Dic239—22no—
55C2×Dic239—41no—
56C2×Dic239—82no—
57C239⋊C8—41no—
58C23×C239—21no—
59D4×C239—21no—
60D4×C239Q1612yescomplemented
61C2×C4×C239—21no—
62C2×C4×C239—41no—
63C2×C4×C239—41no—
64C2×C4×C239C2×D411yescharacteristic
65C2×C4×C239C2×D411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C8×C239—22no—
68C8×C239—41no—
69C22×C239—22no—
70C22×C239—41no—
71C22×C239—41no—
72C22×C239#12011yescharacteristic
73C4×C239—21no—
74C4×C239—41no—
75C4×C239C2×Q1611yescharacteristic
76C4×C239#13511yescharacteristic
77C4×C239#13711yescharacteristic
78C4×C239#13711yescharacteristic
79Dic239—41no—
80Dic239—41no—
81Dic239—42no—
82Dic239—81no—
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#476—2391no—
93#333—2391no—
94Q8⋊C8—2391no—
95D4⋊C8D23911yescharacteristic
96C2×Q16—4782no—
97C4⋊Q8—2391no—
98C4⋊Q8—2391no—
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—4781no—
108C4⋊C8—2391no—
109C4⋊C8C2×D23911yescharacteristic
110#103—4781no—
111#102—4781no—
112C4×C8C2×D23911yescharacteristic
113C2×Q8—4781no—
114C2×Q8—2392no—
115C2×Q8—2391no—
116C2×D4D95611yescharacteristic
117C22×C4—21no—
118C22×C4—4782no—
119Q16—9564no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—4781no—
123C4⋊C4—4782no—
124C4⋊C4—4782no—
125C4⋊C4—4781no—
126C4⋊C4—4781no—
127C4⋊C4—4781no—
128C4⋊C4—4781no—
129C4⋊C4—4781no—
130C4⋊C4—2391no—
131C4⋊C4D95611yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—4782no—
134C42—4781no—
135C42C22×D23911yescharacteristic
136C23—21no—
137Q8—9562no—
138Q8—9562no—
139Q8—4781no—
140Q8—4781no—
141D4—21no—
142D4Dic95612yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—19122no—
147C2×C4—9561no—
148C2×C4—4781no—
149C2×C4—4781no—
150C2×C4—4782no—
151C2×C4D4×D23911yescharacteristic
152C2×C4D4×D23911yescharacteristic
153C2×C4C2×D95611yescharacteristic
154C8—22no—
155C8—41no—
156C8—9561no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2143993011yescharacteristic
161C4—21no—
162C4—41no—
163C4—19121no—
164C4—9561no—
165C4—9561no—
166C4—9562no—
167C4C2×Dic95611yescharacteristic
168C4#2143997911yescharacteristic
169C4#2143998911yescharacteristic
170C4#2143999311yescharacteristic
171C2—42no—
172C2#2950493011yescharacteristic
173C2#2950493511yescharacteristic
174C2#2950494111yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
FittingD4⋊C8×C239C2
socleC22×C239#120
prime radicalC2×D4×C239D4
hypercenterD4⋊C8D239
hypocenterC239#1632
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29505152C2semidirect
3. #29505068C2semidirect
5. #29504520C2semidirect
6. #29504504C2semidirect
60. D4×C239Q16semidirect
87. C239#1632semidirect
142. D4Dic956semidirect

Maximal subgroups

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

subgroupindex
#295054792
#295051522
#295050682
#295050622
#295045202
#295045042
D4⋊C8×C2392
#1632239