Finite Group Databasebeta

← #44483763

Subgroups — #44483763

Order 30592.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#29505483C211yesmaximal, characteristic
2#29505122C211yesmaximal, characteristic, complemented
3#29505053C211yesmaximal, characteristic
4#29504983C211yesmaximal, characteristic, complemented
5#29504502C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic
7#333×C239C211yesmaximal, characteristic, complemented
8C2×Dic956—21no—
9#21439960C2211yescharacteristic
10#21439951—21no—
11#21439940—21no—
12#21439936—22no—
13C4×Dic478C2211yescharacteristic
14C4×D956C2211yescharacteristic
15#21439922—21no—
16C4⋊C4×D239—21no—
17#21439894—21no—
18#21439885—21no—
19#21439884—22no—
20#21439882—21no—
21C4×C239⋊C8C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25C2×Dic478—21no—
26C2×Dic478D411yescharacteristic
27C2×D956D411yescharacteristic
28C2×C4×D239—22no—
29C2×C4×D239—21no—
30Dic956—42no—
31C2×C239⋊C8—21no—
32C4⋊Dic239—22no—
33C4⋊Dic239—21no—
34C4⋊Dic239—21no—
35C4⋊Dic239D411yescharacteristic
36C4⋊Dic239D411yescharacteristic
37Dic239⋊C4—22no—
38Dic239⋊C4—21no—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C4×Dic239—21no—
42C2×Q8×C239D412yes—
43C2×C8×C239—21no—
44C2×C8×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C42×C239C2311yescharacteristic
48C22×D239—21no—
49Dic478—21no—
50Dic478—21no—
51Dic478—41no—
52Dic478—41no—
53D956—21no—
54D956Q1612yescomplemented
55C2×Dic239—21no—
56C2×Dic239—21no—
57C2×Dic239—21no—
58C2×Dic239—41no—
59C4×D239—41no—
60C4×D239—41no—
61C4×D239—82no—
62C239⋊C8—41no—
63Q8×C239—42no—
64C2×C4×C239—22no—
65C2×C4×C239C2×D411yescharacteristic
66C2×C4×C239C2×D411yescharacteristic
67C2×C4×C239C2×D411yescharacteristic
68C8×C239—41no—
69C8×C239—41no—
70C22×C239#12011yescharacteristic
71C2×D239—22no—
72C2×D239—41no—
73C2×D239—41no—
74C4×C239—21no—
75C4×C239—42no—
76C4×C239C2×Q1611yescharacteristic
77C4×C239#13511yescharacteristic
78C4×C239AGL(1,ℤ/8)11yescharacteristic
79C4×C239#13711yescharacteristic
80Dic239—41no—
81Dic239—41no—
82Dic239—41no—
83Dic239—81no—
84C2×C239#44911yescharacteristic
85C2×C239#45111yescharacteristic
86C2×C239#45511yescharacteristic
87D239—42no—
88C239#164411yescharacteristic, complemented, Sylow
89#1644—2391nomaximal, Sylow
90#554—2391no—
91#487—2391no—
92#474—2391no—
93#462—2391no—
94#333D23911yescharacteristic, complemented
95Q8⋊C8—2391no—
96D4⋊C8—2391no—
97C2×Q16—4781no—
98C4⋊Q8—2391no—
99C4⋊Q8C2×D23911yescharacteristic
100#125—4781no—
101C22⋊Q8—4781no—
102C22⋊Q8—4782no—
103C4×Q8—2391no—
104C4×D4—4781no—
105C4×D4—2391no—
106C2×C4⋊C4—4781no—
107#107—4781no—
108C4⋊C8C2×D23911yescharacteristic
109C4⋊C8C2×D23911yescharacteristic
110#103—4782no—
111#103—4781no—
112#102—4781no—
113C4×C8—2391no—
114C2×Q8—4781no—
115C2×Q8—2391no—
116C2×Q8D95612yes—
117C2×D4—2391no—
118C22×C4—4782no—
119C22×C4—4781no—
120Q16—9562no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—4781no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—4782no—
127C4⋊C4—4782no—
128C4⋊C4—4781no—
129C4⋊C4—4781no—
130C4⋊C4—4781no—
131C4⋊C4—2391no—
132C4⋊C4—2391no—
133C22⋊C4—4782no—
134C22⋊C4—4781no—
135C42—4781no—
136C42C22×D23911yescharacteristic
137C23—4781no—
138Q8—42no—
139Q8—9561no—
140Q8—9561no—
141Q8—4781no—
142Q8—4781no—
143D4—4781no—
144D4—2392no—
145C2×C4—22no—
146C2×C4—19122no—
147C2×C4—9561no—
148C2×C4—9561no—
149C2×C4—9561no—
150C2×C4—4781no—
151C2×C4—4781no—
152C2×C4—4781no—
153C2×C4D4×D23911yescharacteristic
154C2×C4D4×D23911yescharacteristic
155C2×C4C2×D95611yescharacteristic
156C8—41no—
157C8—41no—
158C8—9561no—
159C22—9561no—
160C22—9561no—
161C22—4782no—
162C22#2143993011yescharacteristic
163C4—21no—
164C4—42no—
165C4—19121no—
166C4—9561no—
167C4—9561no—
168C4—9561no—
169C4Q16×D23911yescharacteristic
170C4#2143998311yescharacteristic
171C4#2143998711yescharacteristic
172C4#2143998911yescharacteristic
173C2—9562no—
174C2#2950492011yescharacteristic
175C2#2950492911yescharacteristic
176C2#2950495211yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#333×C239C2
socleC22×C239#120
prime radicalC2×D956D4
hypercenter#333D239
hypocenterC239#1644
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #29505122C2semidirect
4. #29504983C2semidirect
5. #29504502C2semidirect
7. #333×C239C2semidirect
54. D956Q16semidirect
88. C239#1644semidirect
94. #333D239semidirect

Maximal subgroups

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

subgroupindex
#295054832
#295051222
#295050532
#295049832
#295045022
#295044992
#333×C2392
#1644239