Finite Group Databasebeta

← #44507843

Subgroups — #44507843

Order 30848.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#21440638C211yesmaximal, characteristic
2#29507721C212yesmaximal, complemented
3C2×#21440559C211yesmaximal, characteristic, complemented
4#29507476C212yesmaximal, complemented
5#518×C241C211yesmaximal, characteristic, complemented
6C22×D964C2211yescharacteristic
7C22×C22⋊D241—22no—
8C2×#16838754C2212yes—
9#21440638—22no—
10#21440638C414yescomplemented
11C2×C4×Dic241C2211yescharacteristic
12#21440562—24no—
13#21440559—22no—
14C22×D4×C241C2211yescharacteristic
15C4×D4×C241—24no—
16#117×C241C2212yes—
17C2×C22⋊C4×C241—22no—
18C23×D241—21no—
19C2×D964—22no—
20C2×D964—21no—
21C2×D964—22no—
22C2×D964C2×C412yescomplemented
23C2×C22⋊D241—28no—
24C2×C22⋊D241—48no—
25C22×Dic241—21no—
26#16838754—22no—
27#16838754—22no—
28C2×#14515349—22no—
29C4×Dic241—21no—
30C4×Dic241C2×C412yescomplemented
31C24×C241D412yes—
32C2×D4×C241—22no—
33C2×D4×C241—22no—
34C2×D4×C241C2×C412yes—
35C2×D4×C241D412yes—
36C22×C4×C241—24no—
37C22×C4×C241C2311yescharacteristic
38C4⋊C4×C241D414yescomplemented
39C22⋊C4×C241—24no—
40C22⋊C4×C241—22no—
41C42×C241—22no—
42C22×D241—22no—
43C22×D241—44no—
44C22×D241—41no—
45C22×D241—41no—
46D964—24no—
47D964—42no—
48C22⋊D241—416no—
49C2×Dic241—24no—
50C2×Dic241—22no—
51#14515349—42no—
52C23×C241—22no—
53C23×C241—22no—
54C23×C241—44no—
55C23×C241C22⋊C414yes—
56C23×C241C2×D411yescharacteristic
57D4×C241—24no—
58D4×C241—24no—
59C2×C4×C241—24no—
60C2×C4×C241—84no—
61C2×C4×C241C22×C411yescharacteristic
62C2×C4×C241C2×D412yes—
63C2×C4×C241C2×D411yescharacteristic
64C2×C4×C241#4112yes—
65C22×C241—22no—
66C22×C241—24no—
67C22×C241—44no—
68C22×C241—44no—
69C22×C241—82no—
70C22×C241C2×C22⋊C411yescharacteristic
71C22×C241#12011yescharacteristic
72C22×C241#12311yescharacteristic
73C2×D241—44no—
74C2×D241—42no—
75C2×D241—82no—
76C2×D241—82no—
77C4×C241—44no—
78C4×C241C4×D412yes—
79C4×C241#12112yes—
80Dic241—24no—
81C2×C241—21no—
82C2×C241—21no—
83C2×C241—44no—
84C2×C241#38611yescharacteristic
85C2×C241#45312yes—
86D241—82no—
87C241#188711yescharacteristic, complemented, Sylow
88#1887—2411nomaximal, Sylow
89C2×#127—2411no—
90#518D24111yescharacteristic, complemented
91#418—2412no—
92C2×#100—2411no—
93#339—2412no—
94C22×D4—4822no—
95C22×D4—2411no—
96C22×D4C2×D24111yescharacteristic
97C2×M16—2412no—
98#127—4822no—
99#127—2414no—
100C4×D4—24no—
101#117C2×D24112yes—
102C2×C22⋊C4—22no—
103C2×C42—2411no—
104#102—4824no—
105#100—4822no—
106C24—4821no—
107C24C22⋊D24112yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—9648no—
111C2×D4—4828no—
112C2×D4—4822no—
113C2×D4—4821no—
114C2×D4—4822no—
115C2×D4—2412no—
116C2×D4C4×D24112yes—
117C2×D4D96412yes—
118C22×C4—24no—
119C22×C4—4821no—
120C22×C4C22×D24111yescharacteristic
121M16—4822no—
122M16—4822no—
123C2×C8—4822no—
124C4⋊C4C22⋊D24114yescomplemented
125C22⋊C4—24no—
126C22⋊C4—22no—
127C42—22no—
128C42—4821no—
129C42—2412no—
130C23—22no—
131C23—22no—
132C23—44no—
133C23—9644no—
134C23—9641no—
135C23—9641no—
136C23—4822no—
137C23#1683874714yes—
138C23C2×C22⋊D24111yescharacteristic
139D4—24no—
140D4—24no—
141D4—96416no—
142D4—9642no—
143D4—4824no—
144C2×C4—24no—
145C2×C4—84no—
146C2×C4—4824no—
147C2×C4—4822no—
148C2×C4C2×C4×D24111yescharacteristic
149C2×C4C2×C22⋊D24112yes—
150C2×C4C2×D96411yescharacteristic
151C2×C4#1683877012yes—
152C8—9642no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—82no—
158C22—19282no—
159C22—19282no—
160C22—9644no—
161C22—9642no—
162C22C2×#1683874711yescharacteristic
163C22#2144061111yescharacteristic
164C22#2144062511yescharacteristic
165C4—44no—
166C4—4824no—
167C4C4×C22⋊D24112yes—
168C4#2144061612yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—19282no—
173C2#2950759611yescharacteristic
174C2#2950788512yes—
subgroupG/H
centerC22#21440611
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#518×C241C2
socleC22×C241#120
prime radicalC2×#21440638C2
cosocleC22×C4×C241C23
hypercenter#518D241
hypocenterC241#1887
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #29507721C2semidirect
3. C2×#21440559C2semidirect
4. #29507476C2semidirect
5. #518×C241C2semidirect
10. #21440638C4semidirect
22. C2×D964C2×C4semidirect
30. C4×Dic241C2×C4semidirect
38. C4⋊C4×C241D4semidirect
87. C241#1887semidirect
90. #518D241semidirect
124. C4⋊C4C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406382
#295077212
C2×#214405592
#295074762
#518×C2412
#1887241