Finite Group Databasebeta

← #44506619

Subgroups — #44506619

Order 30848.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508437C211yesmaximal, characteristic
2#29508068C211yesmaximal, characteristic, complemented
3#29508013C211yesmaximal, characteristic, complemented
4#29508007C211yesmaximal, characteristic
5#29507462C211yesmaximal, characteristic, complemented
6#29507449C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic
8#21440642C2211yescharacteristic
9#21440642C2211yescharacteristic
10#21440635—22no—
11#21440629—21no—
12#21440621—21no—
13C4×Dic482C2211yescharacteristic
14#21440607—21no—
15#21440601—21no—
16#21440576—21no—
17#21440573—21no—
18C4⋊#14515349C2211yescharacteristic
19#21440567—21no—
20#21440567—22no—
21#21440563—21no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×Dic482—21no—
27C2×Dic482D411yescharacteristic
28C2×#14515349—21no—
29C4⋊Dic241—21no—
30C4⋊Dic241—21no—
31C4⋊Dic241—21no—
32C4⋊Dic241D412yes—
33C4⋊Dic241D411yescharacteristic
34#16838749—22no—
35#16838749—21no—
36C22⋊Dic241—22no—
37C22⋊Dic241—22no—
38C4×Dic241—22no—
39C4×Dic241—21no—
40C2×D4×C241D411yescharacteristic
41C22×C4×C241—21no—
42C2×C8×C241—21no—
43C2×C8×C241—21no—
44C4⋊C4×C241D411yescharacteristic
45C22⋊C4×C241—21no—
46C42×C241C2311yescharacteristic
47Dic482—21no—
48Dic482—21no—
49Dic482—41no—
50Dic482—41no—
51Dic482—42no—
52C2×Dic241—21no—
53C2×Dic241—21no—
54C2×Dic241—22no—
55C2×Dic241—41no—
56#14515349—41no—
57C23×C241—21no—
58D4×C241—21no—
59D4×C241—21no—
60C2×C4×C241—21no—
61C2×C4×C241—41no—
62C2×C4×C241—41no—
63C2×C4×C241C2×D411yescharacteristic
64C2×C4×C241C2×D411yescharacteristic
65C2×C4×C241C2×D411yescharacteristic
66C8×C241—41no—
67C8×C241—41no—
68C22×C241—41no—
69C22×C241—41no—
70C22×C241—41no—
71C22×C241#12011yescharacteristic
72C4×C241—21no—
73C4×C241—41no—
74C4×C241#13511yescharacteristic
75C4×C241#13511yescharacteristic
76C4×C241#13711yescharacteristic
77C4×C241#13711yescharacteristic
78Dic241—41no—
79Dic241—42no—
80Dic241—41no—
81Dic241—81no—
82C2×C241—81no—
83C2×C241#45211yescharacteristic
84C2×C241#45211yescharacteristic
85C2×C241#45411yescharacteristic
86C241#163811yescharacteristic, complemented, Sylow
87#1638—2411nomaximal, Sylow
88#556—2411no—
89#487—2411no—
90#477—2411no—
91#476—2411no—
92#332—2411no—
93Q8⋊C8—2411no—
94D4⋊C8D24111yescharacteristic
95C4⋊Q8—2411no—
96C4⋊Q8—2411no—
97#126—4822no—
98#124—4821no—
99C22⋊Q8—4821no—
100C4×Q8—4821no—
101C4×Q8—2411no—
102C4×D4C2×D24111yescharacteristic
103#117—4821no—
104#107—4821no—
105#106—4821no—
106C4⋊C8—2411no—
107C4⋊C8C2×D24111yescharacteristic
108#103—4821no—
109#103—4822no—
110#102—4821no—
111C4×C8C2×D24111yescharacteristic
112C2×Q8—4821no—
113C2×Q8—4821no—
114C2×Q8—2411no—
115C2×D4D96411yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—4821no—
120C4⋊C4—4822no—
121C4⋊C4—4821no—
122C4⋊C4—4821no—
123C4⋊C4—4821no—
124C4⋊C4—4821no—
125C4⋊C4—2412no—
126C4⋊C4—2411no—
127C4⋊C4D96411yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—4822no—
130C22⋊C4—4822no—
131C42—4822no—
132C42—4821no—
133C42C22×D24111yescharacteristic
134C23—21no—
135Q8—9642no—
136Q8—9641no—
137Q8—9641no—
138Q8—4821no—
139Q8—4821no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—9641no—
146C2×C4—4821no—
147C2×C4—4821no—
148C2×C4—4822no—
149C2×C4D4×D24111yescharacteristic
150C2×C4D4×D24111yescharacteristic
151C2×C4C2×D96411yescharacteristic
152C8—41no—
153C8—41no—
154C8—9641no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2144061211yescharacteristic
159C4—21no—
160C4—41no—
161C4—19281no—
162C4—9641no—
163C4—9642no—
164C4—9641no—
165C4#2144066111yescharacteristic
166C4#2144066411yescharacteristic
167C4#2144067111yescharacteristic
168C4#2144067511yescharacteristic
169C2—81no—
170C2#2950788011yescharacteristic
171C2#2950788111yescharacteristic
172C2#2950789111yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenterD4⋊C8D241
hypocenterC241#1638
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. #29508068C2semidirect
3. #29508013C2semidirect
5. #29507462C2semidirect
6. #29507449C2semidirect
86. C241#1638semidirect

Maximal subgroups

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

subgroupindex
#295084372
#295080682
#295080132
#295080072
#295074622
#295074492
D4⋊C8×C2412
#1638241