Finite Group Databasebeta

← #44506699

Subgroups — #44506699

Order 30848.

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

normal subgroups only

This group has 200 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#29508437C211yesmaximal, characteristic
2#29508120C211yesmaximal, characteristic, complemented
3#29507999C211yesmaximal, characteristic, complemented
4#29507464C211yesmaximal, characteristic, complemented
5#29507447C211yesmaximal, characteristic, complemented
6D4⋊#14515349C211yesmaximal, characteristic
7#461×C241C211yesmaximal, characteristic
8#21440642C2211yescharacteristic
9#21440635—22no—
10#21440629—21no—
11#21440621—21no—
12C4×Dic482C2211yescharacteristic
13#21440607—21no—
14#21440601—21no—
15#21440575—22no—
16#21440573—21no—
17C4⋊#14515349C2211yescharacteristic
18#21440565—21no—
19C4×#14515349C2211yescharacteristic
20C2×SD16×C241—21no—
21C4⋊Q8×C241C2211yescharacteristic
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24#103×C241—21no—
25C2×Dic482—21no—
26C2×Dic482D411yescharacteristic
27C2×#14515349—21no—
28C2×#14515349—21no—
29C4⋊Dic241—21no—
30C4⋊Dic241D411yescharacteristic
31C4⋊Dic241D412yes—
32#16838749—22no—
33#16838749—21no—
34C22⋊Dic241—22no—
35C22⋊Dic241—22no—
36C4×Dic241—22no—
37C4×Dic241—21no—
38C2×Q8×C241—21no—
39C2×D4×C241D411yescharacteristic
40C22×C4×C241—21no—
41SD16×C241—42no—
42C2×C8×C241—21no—
43C4⋊C4×C241—21no—
44C4⋊C4×C241—21no—
45C4⋊C4×C241D411yescharacteristic
46C22⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48Dic482—21no—
49Dic482—21no—
50Dic482—41no—
51Dic482—41no—
52C2×Dic241—21no—
53C2×Dic241—21no—
54C2×Dic241—22no—
55#14515349—22no—
56#14515349—41no—
57C23×C241—21no—
58Q8×C241—41no—
59Q8×C241—41no—
60D4×C241—21no—
61D4×C241—21no—
62C2×C4×C241—21no—
63C2×C4×C241—41no—
64C2×C4×C241—41no—
65C2×C4×C241—41no—
66C2×C4×C241C2×D411yescharacteristic
67C2×C4×C241C2×D411yescharacteristic
68C2×C4×C241C2×D411yescharacteristic
69C8×C241—41no—
70C22×C241—41no—
71C22×C241—41no—
72C22×C241—41no—
73C22×C241#12011yescharacteristic
74C4×C241—21no—
75C4×C241—41no—
76C4×C241—81no—
77C4×C241#13511yescharacteristic
78C4×C241#13511yescharacteristic
79C4×C241AGL(1,ℤ/8)11yescharacteristic
80C4×C241#13711yescharacteristic
81Dic241—42no—
82Dic241—41no—
83Dic241—41no—
84C2×C241—81no—
85C2×C241#44911yescharacteristic
86C2×C241#45211yescharacteristic
87C2×C241#45611yescharacteristic
88C241#165011yescharacteristic, complemented, Sylow
89#1650—2411nomaximal, Sylow
90#556—2411no—
91#500—2411no—
92#475—2411no—
93#461D24111yescharacteristic
94#332—2411no—
95Q8⋊C8—2411no—
96D4⋊C8—2411no—
97C2×SD16—21no—
98C4⋊Q8—2411no—
99C4⋊Q8C2×D24111yescharacteristic
100#126—4822no—
101#124—4821no—
102C22⋊Q8—4821no—
103C4×Q8—4821no—
104C4×Q8—2411no—
105C4×D4C2×D24111yescharacteristic
106#117—4821no—
107#107—4822no—
108#106—4821no—
109C4⋊C8—2411no—
110C4⋊C8C2×D24111yescharacteristic
111#103—21no—
112#103—4821no—
113C4×C8—2411no—
114C2×Q8—21no—
115C2×Q8—4821no—
116C2×Q8—2411no—
117C2×D4C22⋊D24111yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—4821no—
122C2×C8—4821no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—4822no—
126C4⋊C4—4821no—
127C4⋊C4—4821no—
128C4⋊C4—2411no—
129C4⋊C4—2412no—
130C4⋊C4C22⋊D24111yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—4822no—
133C22⋊C4—4822no—
134C42—4822no—
135C42—4821no—
136C42C22×D24111yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—9641no—
141Q8—9641no—
142Q8—4821no—
143Q8—4821no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—4821no—
151C2×C4—4821no—
152C2×C4—4822no—
153C2×C4D4×D24111yescharacteristic
154C2×C4D4×D24111yescharacteristic
155C2×C4C2×C22⋊D24111yescharacteristic
156C8—41no—
157C8—9641no—
158C8—4822no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#2144061011yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—9642no—
167C4—9641no—
168C4—9641no—
169C4#2144066211yescharacteristic
170C4#2144066311yescharacteristic
171C4#2144066811yescharacteristic
172C4#2144067111yescharacteristic
173C2—81no—
174C2#2950786011yescharacteristic
175C2#2950787611yescharacteristic
176C2#2950789811yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#461×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenter#461D241
hypocenterC241#1650
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #29508120C2semidirect
3. #29507999C2semidirect
4. #29507464C2semidirect
5. #29507447C2semidirect
88. C241#1650semidirect

Maximal subgroups

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

subgroupindex
#295084372
#295081202
#295079992
#295074642
#295074472
D4⋊#145153492
#461×C2412
#1650241