Finite Group Databasebeta

← #44506669

Subgroups — #44506669

Order 30848.

200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×Dic482C211yesmaximal, characteristic
2#29508068C211yesmaximal, characteristic
3#29508002C211yesmaximal, characteristic
4#29507928C211yesmaximal, characteristic
5#29507465C211yesmaximal, characteristic
6#29507449C211yesmaximal, characteristic
7Q8⋊C8×C241C211yesmaximal, characteristic
8C2×Dic964—21no—
9#21440642—21no—
10#21440642C2211yescharacteristic
11#21440642C2211yescharacteristic
12#21440641—22no—
13#21440641—21no—
14Q8×Dic241—21no—
15C4×Dic482—21no—
16C4×Dic482C2211yescharacteristic
17#21440573—21no—
18C4⋊#14515349C2211yescharacteristic
19#21440567—22no—
20#21440567—21no—
21#21440566—21no—
22C4×Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482—22no—
26C2×Dic482—21no—
27C2×Dic482D411yescharacteristic
28C2×Dic482D412yes—
29Dic964—42no—
30C2×#14515349—21no—
31C4⋊Dic241—22no—
32C4⋊Dic241—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241D411yescharacteristic
37#16838749—22no—
38#16838749—21no—
39C4×Dic241—22no—
40C4×Dic241—21no—
41C2×Q8×C241D411yescharacteristic
42C2×C8×C241—21no—
43C2×C8×C241—21no—
44C4⋊C4×C241—21no—
45C4⋊C4×C241D411yescharacteristic
46C42×C241—21no—
47C42×C241C2311yescharacteristic
48Dic482—21no—
49Dic482—42no—
50Dic482—41no—
51Dic482—41no—
52Dic482—82no—
53Dic482SD1612yes—
54C2×Dic241—21no—
55C2×Dic241—22no—
56C2×Dic241—21no—
57C2×Dic241—41no—
58#14515349—41no—
59Q8×C241—21no—
60Q8×C241Q1612yescomplemented
61C2×C4×C241—21no—
62C2×C4×C241—21no—
63C2×C4×C241C2×D411yescharacteristic
64C2×C4×C241C2×D411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C8×C241—41no—
67C8×C241—41no—
68C22×C241#12011yescharacteristic
69C4×C241—22no—
70C4×C241—21no—
71C4×C241—41no—
72C4×C241C2×SD1611yescharacteristic
73C4×C241C2×Q1611yescharacteristic
74C4×C241#13711yescharacteristic
75C4×C241#13711yescharacteristic
76Dic241—22no—
77Dic241—42no—
78Dic241—41no—
79Dic241—81no—
80C2×C241#44811yescharacteristic
81C2×C241#45111yescharacteristic
82C2×C241#45511yescharacteristic
83C241#164511yescharacteristic, complemented, Sylow
84#1645—2411nomaximal, Sylow
85Q82—2411no—
86#487—2411no—
87#475—2411no—
88#462—2411no—
89#333—2411no—
90Q8⋊C8—2411no—
91Q8⋊C8D24111yescharacteristic
92C2×Q16—4821no—
93C4⋊Q8—4821no—
94C4⋊Q8—4822no—
95C4⋊Q8—4821no—
96C4⋊Q8—2411no—
97C4⋊Q8—2411no—
98C4×Q8—4821no—
99C4×Q8—4821no—
100C4×Q8—2411no—
101C4×Q8C2×D24111yescharacteristic
102#106—4821no—
103C4⋊C8—2411no—
104C4⋊C8C2×D24111yescharacteristic
105#103—4822no—
106#103—4821no—
107#103—4821no—
108C4×C8C2×D24111yescharacteristic
109C2×Q8—4822no—
110C2×Q8—4821no—
111C2×Q8—2412no—
112C2×Q8—2411no—
113C2×Q8D96411yescharacteristic
114Q16—9642no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—4821no—
118C4⋊C4—21no—
119C4⋊C4—4822no—
120C4⋊C4—4822no—
121C4⋊C4—4821no—
122C4⋊C4—4821no—
123C4⋊C4—4821no—
124C4⋊C4—4821no—
125C4⋊C4—4821no—
126C4⋊C4—2411no—
127C4⋊C4D96411yescharacteristic
128C42—21no—
129C42—4822no—
130C42—4821no—
131C42C22×D24111yescharacteristic
132Q8—21no—
133Q8—19282no—
134Q8—9642no—
135Q8—9641no—
136Q8—9641no—
137Q8—4821no—
138Q8—2412no—
139Q8Dic96412yescomplemented
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—9641no—
143C2×C4—4822no—
144C2×C4—4821no—
145C2×C4—4821no—
146C2×C4D4×D24111yescharacteristic
147C2×C4D4×D24111yescharacteristic
148C2×C4C2×D96411yescharacteristic
149C8—41no—
150C8—41no—
151C8—9641no—
152C22#2144061211yescharacteristic
153C4—22no—
154C4—21no—
155C4—41no—
156C4—19281no—
157C4—9641no—
158C4—9642no—
159C4—4822no—
160C4SD16×D24111yescharacteristic
161C4C2×Dic96411yescharacteristic
162C4#2144067411yescharacteristic
163C4#2144067511yescharacteristic
164C2#2950785711yescharacteristic
165C2#2950787511yescharacteristic
166C2#2950789611yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingQ8⋊C8×C241C2
socle, prime radicalC22×C241#120
hypercenterQ8⋊C8D241
hypocenterC241#1645
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
60. Q8×C241Q16semidirect
83. C241#1645semidirect
139. Q8Dic964semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic4822
#295080682
#295080022
#295079282
#295074652
#295074492
Q8⋊C8×C2412
#1645241