Finite Group Databasebeta

← #44506775

Subgroups — #44506775

Order 30848.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C241⋊#564C211yesmaximal, characteristic
2#29508127C211yesmaximal, characteristic
3#29508126C211yesmaximal, characteristic
4#29508086C211yesmaximal, characteristic
5#29507458C211yesmaximal, characteristic
6#29507458C211yesmaximal, characteristic
7#330×C241C211yesmaximal, characteristic
8#21440642C2211yescharacteristic
9#21440634C2211yescharacteristic
10#21440634C2211yescharacteristic
11#21440633—21no—
12#21440633—21no—
13#21440632—21no—
14#21440632—21no—
15#21440632—21no—
16#21440632—21no—
17#21440576—21no—
18#21440575—21no—
19#21440574—21no—
20#21440573—21no—
21#21440567—21no—
22#21440567—21no—
23#21440553C2211yescharacteristic
24#125×C241C2211yescharacteristic
25#97×C241C2211yescharacteristic
26#97×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×#14515349—21no—
29C4⋊Dic241—21no—
30C4⋊Dic241—21no—
31C4⋊Dic241—21no—
32C4⋊Dic241—21no—
33C4⋊Dic241D411yescharacteristic
34C4⋊Dic241D411yescharacteristic
35C4⋊Dic241D411yescharacteristic
36C4⋊Dic241D411yescharacteristic
37#16838749—21no—
38#16838749—21no—
39#16838749—21no—
40#16838749—21no—
41#16838749—21no—
42#16838749—21no—
43#16838749—21no—
44#16838749—21no—
45C4×Dic241—21no—
46C4×Dic241—21no—
47C2×C8×C241—21no—
48C2×C8×C241—21no—
49C4⋊C4×C241—21no—
50C4⋊C4×C241—21no—
51C4⋊C4×C241D411yescharacteristic
52C4⋊C4×C241D411yescharacteristic
53C42×C241C2311yescharacteristic
54Dic482—42no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—41no—
60#14515349—22no—
61C2×C4×C241—21no—
62C2×C4×C241—21no—
63C2×C4×C241C2×D411yescharacteristic
64C2×C4×C241C2×D411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C8×C241—22no—
67C8×C241—41no—
68C22×C241#12011yescharacteristic
69C4×C241—21no—
70C4×C241—21no—
71C4×C241—21no—
72C4×C241—41no—
73C4×C241—41no—
74Dic241—41no—
75Dic241—41no—
76Dic241—41no—
77Dic241—41no—
78Dic241—81no—
79C2×C241#45411yescharacteristic
80C2×C241#45611yescharacteristic
81C2×C241#45611yescharacteristic
82C241#166311yescharacteristic, complemented, Sylow
83#1663—2411nomaximal, Sylow
84#564—2411no—
85#501—2411no—
86#501—2411no—
87#491—2411no—
88#330—2411no—
89#330—2411no—
90#330D24111yescharacteristic
91C4⋊Q8—2411no—
92#125—4821no—
93#125—4821no—
94#125—4821no—
95#125—4821no—
96#125—4821no—
97#125—4821no—
98#125—2411no—
99#125—2411no—
100#125C2×D24111yescharacteristic
101#107—4821no—
102#107—4821no—
103#106—4821no—
104#106—4821no—
105#103—4821no—
106#103—4821no—
107#97—2411no—
108#97C2×D24111yescharacteristic
109#97C2×D24111yescharacteristic
110C2×Q8—4821no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—4821no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—4821no—
117C4⋊C4—4821no—
118C4⋊C4—4821no—
119C4⋊C4—4821no—
120C4⋊C4—4821no—
121C4⋊C4—4821no—
122C4⋊C4—4821no—
123C4⋊C4—4821no—
124C4⋊C4—4821no—
125C4⋊C4—4821no—
126C4⋊C4—4821no—
127C4⋊C4—4821no—
128C4⋊C4—2411no—
129C4⋊C4—2411no—
130C4⋊C4—2411no—
131C4⋊C4—2411no—
132C4⋊C4D96411yescharacteristic
133C4⋊C4D96411yescharacteristic
134C42—4821no—
135C42—4821no—
136C42C22×D24111yescharacteristic
137Q8—9642no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—9641no—
141C2×C4—4821no—
142C2×C4—4821no—
143C2×C4—4821no—
144C2×C4—4821no—
145C2×C4D4×D24111yescharacteristic
146C2×C4D4×D24111yescharacteristic
147C2×C4C2×D96411yescharacteristic
148C8—22no—
149C8—41no—
150C8—4822no—
151C22#2144061211yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—19281no—
158C4—9641no—
159C4—9641no—
160C4—9641no—
161C4—9641no—
162C2#2950789111yescharacteristic
163C2#2950790111yescharacteristic
164C2#2950790211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#330×C241C2
socle, prime radicalC22×C241#120
hypercenter#330D241
hypocenterC241#1663
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
82. C241#1663semidirect

Maximal subgroups

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

subgroupindex
C241⋊#5642
#295081272
#295081262
#295080862
#295074582
#330×C2412
#1663241