Finite Group Databasebeta

← #44506628

Subgroups — #44506628

Order 30848.

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#29508453C211yesmaximal, characteristic
2#29507999C211yesmaximal, characteristic, complemented
3#29507924C211yesmaximal, characteristic, complemented
4#29507461C211yesmaximal, characteristic
5#29507449C211yesmaximal, characteristic, complemented
6#29507449C211yesmaximal, characteristic, complemented
7#486×C241C211yesmaximal, characteristic
8C2×#16838760—21no—
9#21440629—21no—
10#21440629—21no—
11#21440623—22no—
12C4×Dic482C2211yescharacteristic
13C4×Dic482C2211yescharacteristic
14D4×Dic241—21no—
15D4×Dic241—21no—
16#21440573—21no—
17C4⋊#14515349C2211yescharacteristic
18C4⋊#14515349C2211yescharacteristic
19#21440566—21no—
20#21440565—21no—
21C4⋊Q8×C241C2211yescharacteristic
22#127×C241C2211yescharacteristic
23#102×C241—22no—
24C4×C8×C241C2211yescharacteristic
25C2×Dic482D411yescharacteristic
26C2×Dic482D411yescharacteristic
27C22×Dic241—22no—
28#16838760—42no—
29C2×#14515349—21no—
30C2×#14515349—21no—
31C4⋊Dic241D411yescharacteristic
32C4⋊Dic241D411yescharacteristic
33#16838749—21no—
34#16838749—21no—
35C22⋊Dic241—22no—
36C22⋊Dic241—22no—
37C22⋊Dic241—22no—
38C4×Dic241—21no—
39C4×Dic241—21no—
40C2×Q8×C241—21no—
41C2×D4×C241—21no—
42C2×D4×C241—21no—
43C2×D4×C241D412yes—
44C2×C8×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48Dic482—21no—
49Dic482—21no—
50Dic482—21no—
51Dic482—21no—
52C2×Dic241—21no—
53C2×Dic241—21no—
54C2×Dic241—21no—
55C2×Dic241—21no—
56C2×Dic241—82no—
57#14515349—41no—
58#14515349—41no—
59C23×C241—22no—
60Q8×C241—41no—
61Q8×C241—41no—
62D4×C241—42no—
63D4×C241—41no—
64D4×C241—41no—
65D4×C241—41no—
66D4×C241—41no—
67C2×C4×C241—41no—
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C8×C241—41no—
72C22×C241—42no—
73C22×C241—42no—
74C22×C241—42no—
75C22×C241#12011yescharacteristic
76C4×C241—21no—
77C4×C241—81no—
78C4×C241#13511yescharacteristic
79C4×C241#13511yescharacteristic
80C4×C241AGL(1,ℤ/8)11yescharacteristic
81C4×C241#13711yescharacteristic
82Dic241—41no—
83Dic241—41no—
84Dic241—41no—
85Dic241—41no—
86C2×C241—82no—
87C2×C241#44911yescharacteristic
88C2×C241#45211yescharacteristic
89C2×C241#45511yescharacteristic
90C241#164011yescharacteristic, complemented, Sylow
91#1640—2411nomaximal, Sylow
92#559—2411no—
93#486D24111yescharacteristic
94#475—2411no—
95#462—2411no—
96#331—2411no—
97Q8⋊C8—2411no—
98Q8⋊C8—2411no—
99C2×Q16—4821no—
100C4⋊Q8C2×D24111yescharacteristic
101#127C2×D24111yescharacteristic
102#124—4821no—
103#124—4821no—
104#123—4822no—
105C4×Q8—2411no—
106C4×Q8—2411no—
107C4×D4—4821no—
108C4×D4—4821no—
109#106—4821no—
110C4⋊C8—2411no—
111C4⋊C8—2411no—
112#103—4821no—
113#103—4821no—
114#102—22no—
115C4×C8C2×D24111yescharacteristic
116C2×Q8—21no—
117C2×Q8—2411no—
118C2×Q8—2411no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D24112yes—
122C22×C4—4822no—
123Q16—9642no—
124C2×C8—21no—
125C2×C8—4821no—
126C2×C8—4821no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—4821no—
130C4⋊C4—4821no—
131C4⋊C4—2411no—
132C4⋊C4—2411no—
133C22⋊C4—4822no—
134C22⋊C4—4822no—
135C22⋊C4—4822no—
136C42—4821no—
137C42—4821no—
138C42C22×D24111yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—4821no—
143Q8—4821no—
144Q8—4821no—
145Q8—4821no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—19282no—
153C2×C4—4821no—
154C2×C4—4821no—
155C2×C4—4821no—
156C2×C4—4821no—
157C2×C4D4×D24111yescharacteristic
158C2×C4D4×D24111yescharacteristic
159C2×C4C2×C22⋊D24111yescharacteristic
160C8—41no—
161C8—9641no—
162C8—9641no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#2144061011yescharacteristic
167C4—21no—
168C4—81no—
169C4—9641no—
170C4—9641no—
171C4—9641no—
172C4—9641no—
173C4#2144066111yescharacteristic
174C4#2144066311yescharacteristic
175C4#2144066611yescharacteristic
176C4#2144067111yescharacteristic
177C2—82no—
178C2#2950785911yescharacteristic
179C2#2950787611yescharacteristic
180C2#2950789411yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#486×C241C2
socleC22×C241#120
prime radical#127×C241C22
hypercenter#486D241
hypocenterC241#1640
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #29507999C2semidirect
3. #29507924C2semidirect
5. #29507449C2semidirect
6. #29507449C2semidirect
90. C241#1640semidirect

Maximal subgroups

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

subgroupindex
#295084532
#295079992
#295079242
#295074612
#295074492
#486×C2412
#1640241