Finite Group Databasebeta

← #44506671

Subgroups — #44506671

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#29508432C211yesmaximal, characteristic
2#29508069C211yesmaximal, characteristic, complemented
3#29507994C211yesmaximal, characteristic, complemented
4#29507465C211yesmaximal, characteristic, complemented
5D4⋊#14515349C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7#461×C241C211yesmaximal, characteristic, complemented
8#21440642C2211yescharacteristic
9#21440628—22no—
10#21440616—21no—
11#21440613—21no—
12C4×D964C2211yescharacteristic
13#21440601—21no—
14#21440600—21no—
15#21440575—21no—
16C4⋊#14515349C2211yescharacteristic
17#21440565—22no—
18#21440562—21no—
19C4×#14515349C2211yescharacteristic
20C2×SD16×C241—21no—
21C4⋊Q8×C241C2211yescharacteristic
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24#103×C241—21no—
25C2×Dic482D412yes—
26C2×D964D411yescharacteristic
27C2×C22⋊D241—22no—
28C2×C4×D241—21no—
29C2×#14515349—21no—
30C2×#14515349—21no—
31C4⋊Dic241—21no—
32C4⋊Dic241—21no—
33C4⋊Dic241D411yescharacteristic
34C22⋊Dic241—22no—
35#16838747—22no—
36#16838747—21no—
37C4×Dic241—22no—
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
48C22×D241—21no—
49Dic482—42no—
50D964—21no—
51D964—21no—
52C22⋊D241—82no—
53C2×Dic241—21no—
54C2×Dic241—22no—
55C4×D241—41no—
56C4×D241—41no—
57#14515349—41no—
58#14515349—41no—
59C23×C241—21no—
60Q8×C241—41no—
61Q8×C241—41no—
62D4×C241—21no—
63D4×C241—21no—
64C2×C4×C241—21no—
65C2×C4×C241—41no—
66C2×C4×C241—41no—
67C2×C4×C241—41no—
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C8×C241—41no—
72C22×C241—41no—
73C22×C241—41no—
74C22×C241—41no—
75C22×C241#12011yescharacteristic
76C2×D241—41no—
77C2×D241—41no—
78C2×D241—41no—
79C4×C241—21no—
80C4×C241—41no—
81C4×C241—81no—
82C4×C241#13511yescharacteristic
83C4×C241#13511yescharacteristic
84C4×C241AGL(1,ℤ/8)11yescharacteristic
85C4×C241#13711yescharacteristic
86Dic241—41no—
87Dic241—42no—
88C2×C241—81no—
89C2×C241#44911yescharacteristic
90C2×C241#45211yescharacteristic
91C2×C241#45511yescharacteristic
92D241—81no—
93C241#164611yescharacteristic, complemented, Sylow
94#1646—2411nomaximal, Sylow
95#555—2411no—
96#487—2411no—
97#474—2411no—
98#461D24111yescharacteristic, complemented
99#333—2411no—
100D4⋊C8—2411no—
101D4⋊C8—2411no—
102C2×SD16—21no—
103C4⋊Q8—2411no—
104C4⋊Q8C2×D24111yescharacteristic
105#124—4822no—
106#121—4821no—
107#121—4821no—
108C4×D4—2411no—
109C4×D4C2×D24111yescharacteristic
110#117—4821no—
111#117—4821no—
112#107—4821no—
113C4⋊C8—2411no—
114C4⋊C8C2×D24111yescharacteristic
115#103—21no—
116#103—4822no—
117#102—4821no—
118C4×C8—2411no—
119C2×Q8—21no—
120C2×Q8—2412no—
121C2×D4—4822no—
122C2×D4—2411no—
123C2×D4C22⋊D24111yescharacteristic
124C22×C4—21no—
125C22×C4—4821no—
126SD16—42no—
127C2×C8—21no—
128C2×C8—4821no—
129C2×C8—4821no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—4821no—
133C4⋊C4—4821no—
134C4⋊C4—2411no—
135C4⋊C4C22⋊D24111yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—4822no—
138C22⋊C4—4822no—
139C22⋊C4—4821no—
140C42—4822no—
141C42C22×D24111yescharacteristic
142C23—21no—
143C23—4821no—
144Q8—41no—
145Q8—41no—
146Q8—9642no—
147D4—21no—
148D4—21no—
149D4—19282no—
150D4—4821no—
151D4—4821no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—9641no—
157C2×C4—9641no—
158C2×C4—4821no—
159C2×C4—4822no—
160C2×C4D4×D24111yescharacteristic
161C2×C4D4×D24111yescharacteristic
162C2×C4C2×C22⋊D24111yescharacteristic
163C8—41no—
164C8—9641no—
165C8—9641no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—9641no—
170C22—9641no—
171C22—9641no—
172C22#2144061011yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—9641no—
177C4—9642no—
178C4#2144066211yescharacteristic
179C4#2144066311yescharacteristic
180C4#2144066811yescharacteristic
181C4#2144067111yescharacteristic
182C2—81no—
183C2—19281no—
184C2#2950786011yescharacteristic
185C2#2950787611yescharacteristic
186C2#2950789311yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#461×C241C2
socleC22×C241#120
prime radical#29508432C2
hypercenter#461D241
hypocenterC241#1646
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. #29508069C2semidirect
3. #29507994C2semidirect
4. #29507465C2semidirect
5. D4⋊#14515349C2semidirect
6. #29507444C2semidirect
7. #461×C241C2semidirect
93. C241#1646semidirect
98. #461D241semidirect

Maximal subgroups

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

subgroupindex
#295084322
#295080692
#295079942
#295074652
D4⋊#145153492
#295074442
#461×C2412
#1646241