Finite Group Databasebeta

← #44483716

Subgroups — #44483716

Order 30592.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic478C211yesmaximal, characteristic
2#29505123C211yesmaximal, characteristic, complemented
3#29505068C211yesmaximal, characteristic, complemented
4#29505062C211yesmaximal, characteristic
5#29504519C211yesmaximal, characteristic, complemented
6#29504504C211yesmaximal, characteristic, complemented
7D4⋊C8×C239C211yesmaximal, characteristic
8C22×Dic478—21no—
9#21439960C2211yescharacteristic
10#21439960C2211yescharacteristic
11#21439959—21no—
12#21439939—21no—
13#21439937—22no—
14C4×Dic478C2211yescharacteristic
15D4×Dic239—21no—
16#21439894—21no—
17#21439891—21no—
18C4⋊(C239⋊C8)C2211yescharacteristic
19#21439885—21no—
20#21439885—22no—
21#21439881—21no—
22C4×D4×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4×C8×C239C2211yescharacteristic
25C2×Dic478—22no—
26C2×Dic478—21no—
27C2×Dic478—21no—
28C2×Dic478—42no—
29C2×Dic478—42no—
30C2×Dic478D411yescharacteristic
31C22×Dic239—22no—
32C2×C239⋊C8—21no—
33C4⋊Dic239—21no—
34C4⋊Dic239—21no—
35C4⋊Dic239—21no—
36C4⋊Dic239D412yes—
37C4⋊Dic239D411yescharacteristic
38Dic239⋊C4—22no—
39Dic239⋊C4—21no—
40C22⋊Dic239—22no—
41C4×Dic239—21no—
42C2×D4×C239D411yescharacteristic
43C22×C4×C239—21no—
44C2×C8×C239—21no—
45C2×C8×C239—21no—
46C4⋊C4×C239D411yescharacteristic
47C22⋊C4×C239—21no—
48C42×C239C2311yescharacteristic
49Dic478—21no—
50Dic478—44no—
51Dic478—41no—
52Dic478—41no—
53Dic478—42no—
54Dic478SD1612yes—
55C2×Dic239—21no—
56C2×Dic239—21no—
57C2×Dic239—22no—
58C2×Dic239—44no—
59C2×Dic239—41no—
60C239⋊C8—41no—
61C23×C239—21no—
62D4×C239—21no—
63D4×C239Q1612yes—
64C2×C4×C239—21no—
65C2×C4×C239—41no—
66C2×C4×C239—41no—
67C2×C4×C239C2×D411yescharacteristic
68C2×C4×C239C2×D411yescharacteristic
69C2×C4×C239C2×D411yescharacteristic
70C8×C239—41no—
71C8×C239—41no—
72C22×C239—22no—
73C22×C239—41no—
74C22×C239—41no—
75C22×C239#12011yescharacteristic
76C4×C239—21no—
77C4×C239—41no—
78C4×C239C2×SD1611yescharacteristic
79C4×C239C2×Q1611yescharacteristic
80C4×C239AGL(1,ℤ/8)11yescharacteristic
81C4×C239#13711yescharacteristic
82Dic239—22no—
83Dic239—42no—
84Dic239—41no—
85Dic239—81no—
86C2×C239—42no—
87C2×C239#45011yescharacteristic
88C2×C239#45111yescharacteristic
89C2×C239#45411yescharacteristic
90C239#163711yescharacteristic, complemented, Sylow
91#1637—2391nomaximal, Sylow
92D4×Q8—2391no—
93#487—2391no—
94#477—2391no—
95#476—2391no—
96#332—2391no—
97Q8⋊C8—2391no—
98D4⋊C8D23911yescharacteristic
99C22×Q8—4781no—
100C4⋊Q8—4781no—
101C4⋊Q8—2391no—
102C4⋊Q8—2391no—
103C22⋊Q8—4782no—
104C22⋊Q8—4781no—
105C4×Q8—2391no—
106C4×D4—4781no—
107C4×D4C2×D23911yescharacteristic
108#107—4781no—
109#106—4781no—
110C4⋊C8—2391no—
111C4⋊C8C2×D23911yescharacteristic
112#103—4781no—
113#103—4782no—
114#102—4781no—
115C4×C8C2×D23911yescharacteristic
116C2×Q8—9562no—
117C2×Q8—9562no—
118C2×Q8—4782no—
119C2×Q8—4781no—
120C2×Q8—4781no—
121C2×Q8—2391no—
122C2×D4D95611yescharacteristic
123C22×C4—21no—
124C22×C4—4782no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—4781no—
128C4⋊C4—4782no—
129C4⋊C4—4781no—
130C4⋊C4—4781no—
131C4⋊C4—4781no—
132C4⋊C4—4781no—
133C4⋊C4—2392no—
134C4⋊C4—2391no—
135C4⋊C4D95611yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—4782no—
138C42—4781no—
139C42C22×D23911yescharacteristic
140C23—21no—
141Q8—9562no—
142Q8—9564no—
143Q8—9561no—
144Q8—9561no—
145Q8—4781no—
146Q8—2392no—
147D4—21no—
148D4Dic95612yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—9561no—
153C2×C4—9564no—
154C2×C4—4781no—
155C2×C4—4782no—
156C2×C4—4781no—
157C2×C4D4×D23911yescharacteristic
158C2×C4D4×D23911yescharacteristic
159C2×C4C2×D95611yescharacteristic
160C8—41no—
161C8—41no—
162C8—9561no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2143993011yescharacteristic
167C4—21no—
168C4—41no—
169C4—19121no—
170C4—9562no—
171C4—9561no—
172C4—4782no—
173C4SD16×D23911yescharacteristic
174C4C2×Dic95611yescharacteristic
175C4#2143998411yescharacteristic
176C4#2143999311yescharacteristic
177C2—42no—
178C2#2950492411yescharacteristic
179C2#2950493011yescharacteristic
180C2#2950494611yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
FittingD4⋊C8×C239C2
socleC22×C239#120
prime radicalC2×D4×C239D4
hypercenterD4⋊C8D239
hypocenterC239#1637
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. #29505123C2semidirect
3. #29505068C2semidirect
5. #29504519C2semidirect
6. #29504504C2semidirect
90. C239#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic4782
#295051232
#295050682
#295050622
#295045192
#295045042
D4⋊C8×C2392
#1637239