Finite Group Databasebeta

← #44483774

Subgroups — #44483774

Order 30592.

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

normal subgroups only

This group has 212 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#29505124C211yesmaximal, characteristic, complemented
3#29505049C211yesmaximal, characteristic, complemented
4#29504520C211yesmaximal, characteristic, complemented
5D4⋊(C239⋊C8)C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#461×C239C211yesmaximal, characteristic, complemented
8#21439960C2211yescharacteristic
9#21439946—22no—
10#21439934—21no—
11#21439931—21no—
12C4×D956C2211yescharacteristic
13#21439919—21no—
14#21439918—21no—
15#21439893—21no—
16C4⋊(C239⋊C8)C2211yescharacteristic
17#21439883—22no—
18#21439880—21no—
19C4×C239⋊C8C2211yescharacteristic
20C2×SD16×C239—21no—
21C4⋊Q8×C239C2211yescharacteristic
22C4×D4×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24#103×C239—21no—
25C2×Dic478D412yes—
26C2×D956D411yescharacteristic
27C2×C22⋊D239—22no—
28C2×C4×D239—21no—
29C2×C239⋊C8—21no—
30C2×C239⋊C8—21no—
31C4⋊Dic239—21no—
32C4⋊Dic239—21no—
33C4⋊Dic239D411yescharacteristic
34C22⋊Dic239—22no—
35(C2×D239)⋊C4—22no—
36(C2×D239)⋊C4—21no—
37C4×Dic239—22no—
38C2×Q8×C239—21no—
39C2×D4×C239D411yescharacteristic
40C22×C4×C239—21no—
41SD16×C239—42no—
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—41no—
58C239⋊C8—41no—
59C23×C239—21no—
60Q8×C239—41no—
61Q8×C239—41no—
62D4×C239—21no—
63D4×C239—21no—
64C2×C4×C239—21no—
65C2×C4×C239—41no—
66C2×C4×C239—41no—
67C2×C4×C239—41no—
68C2×C4×C239C2×D411yescharacteristic
69C2×C4×C239C2×D411yescharacteristic
70C2×C4×C239C2×D411yescharacteristic
71C8×C239—41no—
72C22×C239—41no—
73C22×C239—41no—
74C22×C239—41no—
75C22×C239#12011yescharacteristic
76C2×D239—41no—
77C2×D239—41no—
78C2×D239—41no—
79C4×C239—21no—
80C4×C239—41no—
81C4×C239—81no—
82C4×C239#13511yescharacteristic
83C4×C239#13511yescharacteristic
84C4×C239AGL(1,ℤ/8)11yescharacteristic
85C4×C239#13711yescharacteristic
86Dic239—41no—
87Dic239—42no—
88C2×C239—81no—
89C2×C239#44911yescharacteristic
90C2×C239#45211yescharacteristic
91C2×C239#45511yescharacteristic
92D239—81no—
93C239#164611yescharacteristic, complemented, Sylow
94#1646—2391nomaximal, Sylow
95#555—2391no—
96#487—2391no—
97#474—2391no—
98#461D23911yescharacteristic, complemented
99#333—2391no—
100D4⋊C8—2391no—
101D4⋊C8—2391no—
102C2×SD16—21no—
103C4⋊Q8—2391no—
104C4⋊Q8C2×D23911yescharacteristic
105#124—4782no—
106#121—4781no—
107#121—4781no—
108C4×D4—2391no—
109C4×D4C2×D23911yescharacteristic
110#117—4781no—
111#117—4781no—
112#107—4781no—
113C4⋊C8—2391no—
114C4⋊C8C2×D23911yescharacteristic
115#103—21no—
116#103—4782no—
117#102—4781no—
118C4×C8—2391no—
119C2×Q8—21no—
120C2×Q8—2392no—
121C2×D4—4782no—
122C2×D4—2391no—
123C2×D4C22⋊D23911yescharacteristic
124C22×C4—21no—
125C22×C4—4781no—
126SD16—42no—
127C2×C8—21no—
128C2×C8—4781no—
129C2×C8—4781no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—4781no—
133C4⋊C4—4781no—
134C4⋊C4—2391no—
135C4⋊C4C22⋊D23911yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—4782no—
138C22⋊C4—4782no—
139C22⋊C4—4781no—
140C42—4782no—
141C42C22×D23911yescharacteristic
142C23—21no—
143C23—4781no—
144Q8—41no—
145Q8—41no—
146Q8—9562no—
147D4—21no—
148D4—21no—
149D4—19122no—
150D4—4781no—
151D4—4781no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—9561no—
157C2×C4—9561no—
158C2×C4—4781no—
159C2×C4—4782no—
160C2×C4D4×D23911yescharacteristic
161C2×C4D4×D23911yescharacteristic
162C2×C4C2×C22⋊D23911yescharacteristic
163C8—41no—
164C8—9561no—
165C8—9561no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—9561no—
170C22—9561no—
171C22—9561no—
172C22#2143992811yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—9561no—
177C4—9562no—
178C4#2143998011yescharacteristic
179C4#2143998111yescharacteristic
180C4#2143998611yescharacteristic
181C4#2143998911yescharacteristic
182C2—81no—
183C2—19121no—
184C2#2950491511yescharacteristic
185C2#2950493111yescharacteristic
186C2#2950494811yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#461×C239C2
socleC22×C239#120
prime radical#29505487C2
hypercenter#461D239
hypocenterC239#1646
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #29505124C2semidirect
3. #29505049C2semidirect
4. #29504520C2semidirect
5. D4⋊(C239⋊C8)C2semidirect
6. #29504499C2semidirect
7. #461×C239C2semidirect
93. C239#1646semidirect
98. #461D239semidirect

Maximal subgroups

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

subgroupindex
#295054872
#295051242
#295050492
#295045202
D4⋊(C239⋊C8)2
#295044992
#461×C2392
#1646239