Finite Group Databasebeta

← #44507972

Subgroups — #44507972

Order 30848.

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

normal subgroups only

This group has 344 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#29508281C211yesmaximal, characteristic
2#29507723C212yesmaximal, complemented
3#29507691C211yesmaximal, characteristic, complemented
4#29507474C212yesmaximal, complemented
5#568×C241C211yesmaximal, characteristic, complemented
6C22×D964C2211yescharacteristic
7#21440638C412yescomplemented
8#21440631C412yescomplemented
9#21440616—22no—
10#21440610—22no—
11#21440601C2212yes—
12#21440601C2211yescharacteristic
13#21440564—24no—
14#21440557—22no—
15C2×#41×C241C2211yescharacteristic
16#131×C241—24no—
17C2×M16×C241—22no—
18C2×M16×C241C2212yes—
19C23×D241—21no—
20C2×D964—22no—
21C2×D964—21no—
22C2×D964—22no—
23C2×D964C2×C412yes—
24C2×C22⋊D241—24no—
25C4⋊Dic241—21no—
26C4⋊Dic241—22no—
27C22⋊Dic241—21no—
28C22⋊Dic241—22no—
29#16838747—24no—
30C4×Dic241—22no—
31C4×Dic241C2×C412yes—
32#41×C241—22no—
33#41×C241—22no—
34C2×Q8×C241C2×C411yescharacteristic
35C2×D4×C241C2×C411yescharacteristic
36C2×D4×C241D412yes—
37C22×C4×C241D412yes—
38C22×C4×C241C2311yescharacteristic
39M16×C241—24no—
40M16×C241—22no—
41M16×C241—22no—
42C2×C8×C241—24no—
43C2×C8×C241D414yescomplemented
44C22×D241—22no—
45C22×D241—42no—
46C22×D241—82no—
47D964—24no—
48D964—41no—
49D964—41no—
50C22⋊D241—84no—
51C2×Dic241—22no—
52C2×Dic241—42no—
53C23×C241C22⋊C412yes—
54C23×C241C2×D411yescharacteristic
55Q8×C241—22no—
56D4×C241—24no—
57D4×C241—22no—
58C2×C4×C241—22no—
59C2×C4×C241—22no—
60C2×C4×C241C22⋊C412yes—
61C2×C4×C241C22×C411yescharacteristic
62C2×C4×C241C2×D412yes—
63C2×C4×C241C2×D411yescharacteristic
64C2×C4×C241#4112yes—
65C8×C241—24no—
66C22×C241—22no—
67C22×C241—41no—
68C22×C241—42no—
69C22×C241C2×C22⋊C411yescharacteristic
70C22×C241#12112yes—
71C2×D241—44no—
72C2×D241—42no—
73C2×D241—84no—
74C4×C241—22no—
75C4×C241C4×D412yes—
76C4×C241#12011yescharacteristic
77C4×C241#12311yescharacteristic
78Dic241—42no—
79Dic241—82no—
80C2×C241—21no—
81C2×C241—22no—
82C2×C241—42no—
83C2×C241#38611yescharacteristic
84D241—82no—
85C241#191011yescharacteristic, complemented, Sylow
86#1910—2411nomaximal, Sylow
87#568D24111yescharacteristic, complemented
88#535—2411no—
89#418—2412no—
90#410—2411no—
91H(3,ℤ/4)—2412no—
92C2×#41C2×D24111yescharacteristic
93C22×D4—2411no—
94#131—24no—
95C2×M16—22no—
96C2×M16C2×D24112yes—
97#127—2412no—
98#124—2412no—
99#121—4822no—
100#120—4822no—
101#117—2412no—
102#117—2411no—
103#102—4824no—
104#99—4822no—
105C24—4821no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D24111yescharacteristic
109C2×D4—4824no—
110C2×D4—4821no—
111C2×D4—4822no—
112C2×D4—4822no—
113C2×D4—2412no—
114C2×D4C4×D24111yescharacteristic
115C2×D4D96412yes—
116C22×C4C22⋊D24112yes—
117C22×C4C22×D24111yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D24114yescomplemented
123C4⋊C4—4822no—
124C4⋊C4—4821no—
125C22⋊C4—4822no—
126C22⋊C4—4821no—
127C22⋊C4—4824no—
128C42—4822no—
129C42—2412no—
130C23—19282no—
131C23—9642no—
132C23—4822no—
133C23#1683874712yes—
134C23C2×D96411yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—19284no—
139D4—9641no—
140D4—9641no—
141D4—4824no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—9642no—
145C2×C4—4822no—
146C2×C4#1683874712yes—
147C2×C4C2×C4×D24111yescharacteristic
148C2×C4C2×C22⋊D24112yes—
149C2×C4C2×C22⋊D24111yescharacteristic
150C2×C4#1683877012yes—
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—19284no—
156C22—9644no—
157C22—9642no—
158C22C2×#1683874711yescharacteristic
159C22#2144061612yes—
160C4—22no—
161C4—19282no—
162C4—9642no—
163C4C4×C22⋊D24112yes—
164C4#2144061111yescharacteristic
165C4#2144062511yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—19282no—
170C2#2950759611yescharacteristic
subgroupG/H
centerC2#29507596
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#568×C241C2
socleC2×C241#386
prime radical#29508281C2
cosocleC22×C4×C241C23
hypercenter#568D241
hypocenterC241#1910
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #29507723C2semidirect
3. #29507691C2semidirect
4. #29507474C2semidirect
5. #568×C241C2semidirect
7. #21440638C4semidirect
8. #21440631C4semidirect
43. C2×C8×C241D4semidirect
85. C241#1910semidirect
87. #568D241semidirect
122. C2×C8C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295082812
#295077232
#295076912
#295074742
#568×C2412
#1910241