Finite Group Databasebeta

← #44507888

Subgroups — #44507888

Order 30848.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#29508228C211yesmaximal, characteristic
2C2×#21440570C212yesmaximal, complemented
3#29507681C211yesmaximal, characteristic, complemented
4#29507477C212yesmaximal, complemented
5C22×C42×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2211yescharacteristic
7C2×#16838754C2212yes—
8#21440625—21no—
9#21440621C412yescomplemented
10#21440616C412yescomplemented
11#21440611—21no—
12C4×C22⋊D241—22no—
13#21440601C2211yescharacteristic
14#21440570—24no—
15C22⋊#14515349—22no—
16C23×C4×C241—21no—
17C23×C4×C241C2211yescharacteristic
18C2×C42×C241—21no—
19C2×C42×C241—24no—
20C2×C42×C241C2212yes—
21#16838770—22no—
22#16838770—22no—
23C2×Dic482C2×C411yescharacteristic, complemented
24C2×D964C2×C411yescharacteristic, complemented
25C2×C22⋊D241—22no—
26C2×C22⋊D241—21no—
27C2×C4×D241—21no—
28#16838754—22no—
29#16838754—22no—
30C2×#14515349—22no—
31C4⋊Dic241C2×C412yescomplemented
32#16838749—22no—
33C22⋊Dic241—22no—
34C22⋊Dic241—21no—
35#16838747—22no—
36C4×Dic241—21no—
37C24×C241D411yescharacteristic
38C22×C4×C241—24no—
39C22×C4×C241—28no—
40C22×C4×C241—22no—
41C22×C4×C241—22no—
42C22×C4×C241—22no—
43C22×C4×C241C2×C412yes—
44C22×C4×C241D411yescharacteristic
45C22×C4×C241D412yes—
46C22×C4×C241C2311yescharacteristic
47C42×C241—24no—
48C42×C241—22no—
49C42×C241D414yescomplemented
50C22×D241—21no—
51Dic482—22no—
52D964—22no—
53C22⋊D241—44no—
54C22⋊D241—41no—
55C22⋊D241—41no—
56C2×Dic241—22no—
57C2×Dic241—21no—
58C4×D241—42no—
59#14515349—42no—
60C23×C241—24no—
61C23×C241—21no—
62C23×C241—21no—
63C23×C241C22⋊C412yes—
64C23×C241C2×D411yescharacteristic
65C2×C4×C241—216no—
66C2×C4×C241—28no—
67C2×C4×C241—21no—
68C2×C4×C241—24no—
69C2×C4×C241—21no—
70C2×C4×C241—24no—
71C2×C4×C241—24no—
72C2×C4×C241C22⋊C412yes—
73C2×C4×C241C22×C411yescharacteristic
74C2×C4×C241C2×D412yes—
75C2×C4×C241C2×D411yescharacteristic
76C2×C4×C241#4112yes—
77C22×C241—24no—
78C22×C241—24no—
79C22×C241—22no—
80C22×C241—22no—
81C22×C241—22no—
82C22×C241#10414yescomplemented
83C22×C241C2×C22⋊C411yescharacteristic
84C22×C241#12011yescharacteristic
85C22×C241#12311yescharacteristic
86C2×D241—41no—
87C2×D241—42no—
88C4×C241—28no—
89C4×C241—22no—
90C4×C241C4×D412yes—
91C4×C241#12112yes—
92Dic241—41no—
93Dic241—42no—
94C2×C241—21no—
95C2×C241—24no—
96C2×C241—21no—
97C2×C241#38611yescharacteristic
98C2×C241C2×#10412yes—
99D241—81no—
100C241#189611yescharacteristic, complemented, Sylow
101#1896—2411nomaximal, Sylow
102#525—2411no—
103C22×C42D24111yescharacteristic, complemented
104C2×#104—2412no—
105#407—2411no—
106#339—2412no—
107C2×#41—2411no—
108C23×C4—21no—
109C23×C4C2×D24111yescharacteristic
110C2×M16—2412no—
111#123—4821no—
112C22⋊Q8—2412no—
113#121—2412no—
114#120—4821no—
115C4×D4—4822no—
116#117—2411no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D24112yes—
120#104—4824no—
121C22⋊C8—4822no—
122C24C22⋊D24111yescharacteristic
123#41—4822no—
124#41—4822no—
125C2×Q8—2411no—
126C2×D4—4822no—
127C2×D4—4821no—
128C2×D4—2411no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—4821no—
135C22×C4C4×D24112yes—
136C22×C4C22⋊D24111yescharacteristic
137C22×C4D96412yes—
138C22×C4C22×D24111yescharacteristic
139M16—4822no—
140M16—4822no—
141C2×C8—4822no—
142C4⋊C4—4822no—
143C4⋊C4—2412no—
144C22⋊C4—4822no—
145C22⋊C4—4821no—
146C22⋊C4—4822no—
147C42—24no—
148C42—22no—
149C42—4821no—
150C42C22⋊D24114yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—4821no—
155C23#1683874712yes—
156C23C2×C22⋊D24111yescharacteristic
157Q8—4822no—
158D4—9644no—
159D4—9641no—
160D4—9641no—
161D4—4822no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—9642no—
170C2×C4—4822no—
171C2×C4—4821no—
172C2×C4#1683874712yes—
173C2×C4C2×C4×D24111yescharacteristic
174C2×C4C2×C22⋊D24112yes—
175C2×C4C2×D96411yescharacteristic
176C2×C4#1683877012yes—
177C8—9642no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—9641no—
184C22—9642no—
185C22#2144057014yescomplemented
186C22C2×#1683874711yescharacteristic
187C22#2144061111yescharacteristic
188C22#2144062511yescharacteristic
189C4—28no—
190C4—22no—
191C4—9641no—
192C4—9642no—
193C4C4×C22⋊D24112yes—
194C4#2144061612yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—19281no—
199C2#2950759611yescharacteristic
200C2C2×#2144057012yes—
subgroupG/H
centerC2×C4C2×D964
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingC22×C42×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508228C2
cosocleC22×C4×C241C23
hypercenterC22×C42D241
hypocenterC241#1896
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#21440570C2semidirect
3. #29507681C2semidirect
4. #29507477C2semidirect
5. C22×C42×C241C2semidirect
9. #21440621C4semidirect
10. #21440616C4semidirect
23. C2×Dic482C2×C4semidirect
24. C2×D964C2×C4semidirect
31. C4⋊Dic241C2×C4semidirect
49. C42×C241D4semidirect
82. C22×C241#104semidirect
100. C241#1896semidirect
103. C22×C42D241semidirect
150. C42C22⋊D241semidirect
185. C22#21440570semidirect

Maximal subgroups

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

subgroupindex
#295082282
C2×#214405702
#295076812
#295074772
C22×C42×C2412
#1896241