Finite Group Databasebeta

← #44506581

Subgroups — #44506581

Order 30848.

214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508424C211yesmaximal, characteristic
2#29508097C211yesmaximal, characteristic, complemented
3#29508013C211yesmaximal, characteristic, complemented
4#29508007C211yesmaximal, characteristic
5#29507465C211yesmaximal, characteristic, complemented
6#29507449C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic
8C2×Dic964—22no—
9#21440642C2211yescharacteristic
10#21440642C2211yescharacteristic
11#21440633—21no—
12#21440621—21no—
13#21440619—22no—
14C4×Dic482C2211yescharacteristic
15D4×Dic241—21no—
16C2×C4⋊Dic241—21no—
17#21440576—21no—
18#21440573—21no—
19C4⋊#14515349C2211yescharacteristic
20#21440567—21no—
21#21440563—21no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×Dic482D411yescharacteristic
27C2×Dic482D412yes—
28C22×Dic241—22no—
29Dic964—44no—
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—
39C22⋊Dic241—22no—
40C4×Dic241—21no—
41C2×D4×C241D411yescharacteristic
42C22×C4×C241—21no—
43C2×C8×C241—21no—
44C2×C8×C241—21no—
45C4⋊C4×C241D411yescharacteristic
46C22⋊C4×C241—21no—
47C42×C241C2311yescharacteristic
48Dic482—21no—
49Dic482—21no—
50Dic482—42no—
51Dic482—42no—
52C2×Dic241—21no—
53C2×Dic241—21no—
54C2×Dic241—22no—
55C2×Dic241—41no—
56C2×Dic241—82no—
57#14515349—41no—
58C23×C241—21no—
59D4×C241—21no—
60D4×C241Q1612yescomplemented
61C2×C4×C241—21no—
62C2×C4×C241—41no—
63C2×C4×C241—41no—
64C2×C4×C241C2×D411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C2×C4×C241C2×D411yescharacteristic
67C8×C241—22no—
68C8×C241—41no—
69C22×C241—22no—
70C22×C241—41no—
71C22×C241—41no—
72C22×C241#12011yescharacteristic
73C4×C241—21no—
74C4×C241—41no—
75C4×C241C2×Q1611yescharacteristic
76C4×C241#13511yescharacteristic
77C4×C241#13711yescharacteristic
78C4×C241#13711yescharacteristic
79Dic241—41no—
80Dic241—41no—
81Dic241—42no—
82Dic241—81no—
83C2×C241—42no—
84C2×C241#45111yescharacteristic
85C2×C241#45211yescharacteristic
86C2×C241#45311yescharacteristic
87C241#163211yescharacteristic, complemented, Sylow
88#1632—2411nomaximal, Sylow
89#554—2411no—
90#494—2411no—
91#477—2411no—
92#476—2411no—
93#333—2411no—
94Q8⋊C8—2411no—
95D4⋊C8D24111yescharacteristic
96C2×Q16—4822no—
97C4⋊Q8—2411no—
98C4⋊Q8—2411no—
99#125—4821no—
100C22⋊Q8—4822no—
101C22⋊Q8—4821no—
102C4×Q8—2411no—
103C4×D4—4821no—
104C4×D4C2×D24111yescharacteristic
105C2×C4⋊C4—4821no—
106#107—4821no—
107#106—4821no—
108C4⋊C8—2411no—
109C4⋊C8C2×D24111yescharacteristic
110#103—4821no—
111#102—4821no—
112C4×C8C2×D24111yescharacteristic
113C2×Q8—4821no—
114C2×Q8—2412no—
115C2×Q8—2411no—
116C2×D4D96411yescharacteristic
117C22×C4—21no—
118C22×C4—4822no—
119Q16—9644no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—4821no—
123C4⋊C4—4822no—
124C4⋊C4—4822no—
125C4⋊C4—4821no—
126C4⋊C4—4821no—
127C4⋊C4—4821no—
128C4⋊C4—4821no—
129C4⋊C4—4821no—
130C4⋊C4—2411no—
131C4⋊C4D96411yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—4822no—
134C42—4821no—
135C42C22×D24111yescharacteristic
136C23—21no—
137Q8—9642no—
138Q8—9642no—
139Q8—4821no—
140Q8—4821no—
141D4—21no—
142D4Dic96412yescomplemented
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—19282no—
147C2×C4—9641no—
148C2×C4—4821no—
149C2×C4—4821no—
150C2×C4—4822no—
151C2×C4D4×D24111yescharacteristic
152C2×C4D4×D24111yescharacteristic
153C2×C4C2×D96411yescharacteristic
154C8—22no—
155C8—41no—
156C8—9641no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#2144061211yescharacteristic
161C4—21no—
162C4—41no—
163C4—19281no—
164C4—9641no—
165C4—9641no—
166C4—9642no—
167C4C2×Dic96411yescharacteristic
168C4#2144066111yescharacteristic
169C4#2144067111yescharacteristic
170C4#2144067511yescharacteristic
171C2—42no—
172C2#2950787511yescharacteristic
173C2#2950788011yescharacteristic
174C2#2950788611yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenterD4⋊C8D241
hypocenterC241#1632
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29508097C2semidirect
3. #29508013C2semidirect
5. #29507465C2semidirect
6. #29507449C2semidirect
60. D4×C241Q16semidirect
87. C241#1632semidirect
142. D4Dic964semidirect

Maximal subgroups

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

subgroupindex
#295084242
#295080972
#295080132
#295080072
#295074652
#295074492
D4⋊C8×C2412
#1632241