Finite Group Databasebeta

← #44507844

Subgroups — #44507844

Order 30848.

444 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 97 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#29508192C211yesmaximal, characteristic, complemented
2#29507722C212yesmaximal, complemented
3C2×#21440559C211yesmaximal, characteristic, complemented
4#29507477C212yesmaximal, complemented
5C2×#127×C241C211yesmaximal, characteristic
6C2×#16838754C2212yes—
7D4×Dic241—24no—
8#21440601C2212yes—
9C2×C22⋊Dic241—22no—
10#21440563—24no—
11#21440559—22no—
12C22×D4×C241—22no—
13C22×D4×C241C2211yescharacteristic
14C22×D4×C241C2211yescharacteristic
15#127×C241—22no—
16#127×C241C414yescomplemented
17C2×C42×C241C2211yescharacteristic
18C22×Dic241—24no—
19#16838754—22no—
20#16838754—22no—
21C2×#14515349—22no—
22C4⋊Dic241D414yescomplemented
23C22⋊Dic241—24no—
24C22⋊Dic241—22no—
25C4×Dic241—22no—
26C24×C241—21no—
27C24×C241D412yes—
28C2×D4×C241—28no—
29C2×D4×C241—22no—
30C2×D4×C241—22no—
31C2×D4×C241—21no—
32C2×D4×C241—22no—
33C2×D4×C241—22no—
34C2×D4×C241—48no—
35C2×D4×C241C2×C412yes—
36C2×D4×C241C2×C412yescomplemented
37C2×D4×C241D412yes—
38C22×C4×C241—21no—
39C22×C4×C241C2311yescharacteristic
40C42×C241—21no—
41C42×C241C2×C412yescomplemented
42C2×Dic241—24no—
43C2×Dic241—84no—
44#14515349—42no—
45C23×C241—22no—
46C23×C241—22no—
47C23×C241—22no—
48C23×C241—44no—
49C23×C241—44no—
50C23×C241—41no—
51C23×C241—41no—
52C23×C241C22⋊C414yes—
53C23×C241C2×D411yescharacteristic
54D4×C241—24no—
55D4×C241—24no—
56D4×C241—24no—
57D4×C241—416no—
58D4×C241—42no—
59C2×C4×C241—24no—
60C2×C4×C241—22no—
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—44no—
70C22×C241—42no—
71C22×C241—82no—
72C22×C241—82no—
73C22×C241—82no—
74C22×C241C2×C22⋊C411yescharacteristic
75C22×C241#12011yescharacteristic
76C22×C241#12311yescharacteristic
77C4×C241—24no—
78C4×C241C4×D412yes—
79C4×C241#12112yes—
80Dic241—44no—
81C2×C241—21no—
82C2×C241—21no—
83C2×C241—44no—
84C2×C241—82no—
85C2×C241#38611yescharacteristic
86C2×C241#45312yes—
87C241#188711yescharacteristic, complemented, Sylow
88#1887—2411nomaximal, Sylow
89C2×#127D24111yescharacteristic
90#518—2411no—
91#418—2412no—
92C2×#100—2411no—
93#339—2412no—
94C22×D4—22no—
95C22×D4C2×D24111yescharacteristic
96C22×D4C2×D24111yescharacteristic
97C2×M16—2412no—
98#127—22no—
99#127Dic24114yescomplemented
100C4×D4—4824no—
101#117—2412no—
102C2×C22⋊C4—4822no—
103C2×C42C2×D24111yescharacteristic
104#102—4824no—
105#100—4822no—
106C24—21no—
107C24C22⋊D24112yes—
108C2×D4—28no—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—48no—
115C2×D4C2×Dic24112yes—
116C2×D4C2×Dic24112yescomplemented
117C2×D4C22⋊D24112yes—
118C22×C4—21no—
119C22×C4—4824no—
120C22×C4C22×D24111yescharacteristic
121M16—4822no—
122M16—4822no—
123C2×C8—4822no—
124C4⋊C4—2414no—
125C22⋊C4—4824no—
126C22⋊C4—4822no—
127C42—21no—
128C42—4822no—
129C42C2×Dic24112yescomplemented
130C23—22no—
131C23—22no—
132C23—22no—
133C23—44no—
134C23—44no—
135C23—41no—
136C23—41no—
137C23C22⋊Dic24114yes—
138C23C2×C22⋊D24111yescharacteristic
139D4—24no—
140D4—24no—
141D4—24no—
142D4—416no—
143D4—42no—
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—19284no—
147C2×C4—4824no—
148C2×C4C22×Dic24111yescharacteristic
149C2×C4D4×D24112yes—
150C2×C4C2×C22⋊D24111yescharacteristic
151C2×C4#1683876912yes—
152C8—9642no—
153C22—22no—
154C22—24no—
155C22—44no—
156C22—44no—
157C22—44no—
158C22—42no—
159C22—82no—
160C22—82no—
161C22—82no—
162C22C2×C22⋊Dic24111yescharacteristic
163C22#2144061011yescharacteristic
164C22#2144062311yescharacteristic
165C4—24no—
166C4—9644no—
167C4D4×Dic24112yes—
168C4#2144061412yes—
169C2—21no—
170C2—21no—
171C2—44no—
172C2—82no—
173C2#2950759711yescharacteristic
174C2#2950788412yes—
subgroupG/H
centerC22#21440610
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting, prime radicalC2×#127×C241C2
socleC22×C241#120
cosocleC22×C4×C241C23
hypercenterC2×#127D241
hypocenterC241#1887
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #29508192C2semidirect
2. #29507722C2semidirect
3. C2×#21440559C2semidirect
4. #29507477C2semidirect
16. #127×C241C4semidirect
22. C4⋊Dic241D4semidirect
36. C2×D4×C241C2×C4semidirect
41. C42×C241C2×C4semidirect
87. C241#1887semidirect
99. #127Dic241semidirect
116. C2×D4C2×Dic241semidirect
129. C42C2×Dic241semidirect

Maximal subgroups

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

subgroupindex
#295081922
#295077222
C2×#214405592
#295074772
C2×#127×C2412
#1887241