Finite Group Databasebeta

← #44507977

Subgroups — #44507977

Order 30848.

362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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#29508284C211yesmaximal, characteristic
2#29507735C212yesmaximal, complemented
3C2×#21440559C211yesmaximal, characteristic, complemented
4#29507473C212yesmaximal, complemented
5#518×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2211yescharacteristic
7C2×#16838754C2212yes—
8#21440638C412yescomplemented
9#21440629C412yescomplemented
10#21440613—22no—
11#21440611—22no—
12#21440601C2211yescharacteristic
13#21440570—24no—
14#21440559—22no—
15C22×D4×C241C2211yescharacteristic
16C4×D4×C241—24no—
17#117×C241C2212yes—
18C2×C22⋊C4×C241—22no—
19#16838770—22no—
20#16838770—22no—
21C2×Dic482C2×C411yescharacteristic, complemented
22C2×D964C2×C411yescharacteristic, complemented
23C2×C22⋊D241—24no—
24C2×C22⋊D241—21no—
25C2×C4×D241—21no—
26#16838754—22no—
27#16838754—22no—
28C2×#14515349—22no—
29C4⋊Dic241—21no—
30C22⋊Dic241—24no—
31C22⋊Dic241—21no—
32C4×Dic241C2×C412yescomplemented
33C24×C241D412yes—
34C2×D4×C241—22no—
35C2×D4×C241—22no—
36C2×D4×C241C2×C412yes—
37C2×D4×C241D412yes—
38C22×C4×C241—24no—
39C22×C4×C241C2311yescharacteristic
40C4⋊C4×C241—22no—
41C22⋊C4×C241—24no—
42C22⋊C4×C241—22no—
43C42×C241D414yescomplemented
44C22×D241—21no—
45Dic482—22no—
46D964—22no—
47C22⋊D241—41no—
48C22⋊D241—41no—
49C22⋊D241—84no—
50C2×Dic241—22no—
51C2×Dic241—21no—
52C4×D241—42no—
53#14515349—42no—
54C23×C241—22no—
55C23×C241—22no—
56C23×C241—82no—
57C23×C241C22⋊C414yes—
58C23×C241C2×D411yescharacteristic
59D4×C241—24no—
60D4×C241—24no—
61C2×C4×C241—24no—
62C2×C4×C241—84no—
63C2×C4×C241C22×C411yescharacteristic
64C2×C4×C241C2×D412yes—
65C2×C4×C241C2×D411yescharacteristic
66C2×C4×C241#4112yes—
67C22×C241—24no—
68C22×C241—41no—
69C22×C241—44no—
70C22×C241—44no—
71C22×C241—82no—
72C22×C241C2×C22⋊C411yescharacteristic
73C22×C241#12011yescharacteristic
74C22×C241#12311yescharacteristic
75C2×D241—42no—
76C2×D241—41no—
77C4×C241—44no—
78C4×C241C4×D412yes—
79C4×C241#12112yes—
80Dic241—42no—
81Dic241—41no—
82C2×C241—21no—
83C2×C241—21no—
84C2×C241—21no—
85C2×C241—44no—
86C2×C241#38611yescharacteristic
87D241—81no—
88C241#191111yescharacteristic, complemented, Sylow
89#1911—2411nomaximal, Sylow
90#535—2411no—
91#518D24111yescharacteristic, complemented
92#421—2412no—
93C2×#100—2411no—
94H(3,ℤ/4)—2412no—
95C2×#41—2411no—
96C22×D4C2×D24111yescharacteristic
97C2×M16—2412no—
98#127—2412no—
99#124—2412no—
100#121—4822no—
101#120—4822no—
102C4×D4—24no—
103#117—2411no—
104#117C2×D24112yes—
105C2×C22⋊C4—22no—
106#104—4824no—
107#100—4822no—
108C24C22⋊D24112yes—
109#41—4822no—
110#41—4822no—
111C2×Q8—2411no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—4824no—
115C2×D4—4821no—
116C2×D4—2411no—
117C2×D4C4×D24112yes—
118C2×D4D96412yes—
119C22×C4—24no—
120C22×C4—4821no—
121C22×C4C22×D24111yescharacteristic
122M16—4822no—
123M16—4822no—
124C2×C8—4822no—
125C4⋊C4—22no—
126C4⋊C4—4821no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—4824no—
130C22⋊C4—4821no—
131C42—2412no—
132C42C22⋊D24114yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—4821no—
137C23#1683874714yes—
138C23C2×C22⋊D24111yescharacteristic
139Q8—4822no—
140D4—24no—
141D4—24no—
142D4—19284no—
143D4—9641no—
144D4—9641no—
145D4—4822no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—9642no—
149C2×C4—4822no—
150C2×C4—4821no—
151C2×C4C2×C4×D24111yescharacteristic
152C2×C4C2×C22⋊D24112yes—
153C2×C4C2×D96411yescharacteristic
154C2×C4#1683877012yes—
155C8—9642no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—9642no—
162C22—9641no—
163C22C2×#1683874711yescharacteristic
164C22#2144061111yescharacteristic
165C22#2144062511yescharacteristic
166C4—44no—
167C4—9642no—
168C4—9641no—
169C4C4×C22⋊D24112yes—
170C4#2144061612yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—19281no—
176C2#2950759611yescharacteristic
subgroupG/H
centerC2#29507596
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#518×C241C2
socleC2×C241#386
prime radical#29508284C2
cosocleC22×C4×C241C23
hypercenter#518D241
hypocenterC241#1911
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #29507735C2semidirect
3. C2×#21440559C2semidirect
4. #29507473C2semidirect
5. #518×C241C2semidirect
8. #21440638C4semidirect
9. #21440629C4semidirect
21. C2×Dic482C2×C4semidirect
22. C2×D964C2×C4semidirect
32. C4×Dic241C2×C4semidirect
43. C42×C241D4semidirect
88. C241#1911semidirect
91. #518D241semidirect
132. C42C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082842
#295077352
C2×#214405592
#295074732
#518×C2412
#1911241