Finite Group Databasebeta

← #44506416

Subgroups — #44506416

Order 30848.

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

normal subgroups only

This group has 282 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#29508298C211yesmaximal, characteristic
2#29507858C212yesmaximal, complemented
3#29507637C211yesmaximal, characteristic, complemented
4#29507452C212yesmaximal, complemented
5#324×C241C211yesmaximal, characteristic, complemented
6C2×#16838770—21no—
7C22×Dic482C2211yescharacteristic
8C2×#16838759—22no—
9#21440622—22no—
10#21440617—22no—
11#21440616—21no—
12#21440616C2212yes—
13C2×#16838749—21no—
14#21440567—22no—
15#21440549—21no—
16#21440549C2211yescharacteristic
17C2×C4⋊C4×C241C2211yescharacteristic
18C22⋊C8×C241C2212yes—
19#16838770—42no—
20#16838770—42no—
21C2×Dic482—21no—
22C2×Dic482—22no—
23C2×Dic482—42no—
24C2×D964—21no—
25C2×D964—21no—
26C2×D964D412yes—
27C2×C22⋊D241—22no—
28C22×Dic241—21no—
29C22×Dic241—21no—
30C2×C4×D241—22no—
31#16838759—44no—
32C4⋊Dic241—21no—
33C4⋊Dic241D412yes—
34#16838749—42no—
35#16838747—22no—
36#16838747—22no—
37C22×C4×C241D411yescharacteristic
38C22×C4×C241D411yescharacteristic
39C22×C4×C241C2311yescharacteristic
40C2×C8×C241—22no—
41C4⋊C4×C241—22no—
42C22×D241—22no—
43Dic482—24no—
44Dic482—42no—
45Dic482—42no—
46D964—42no—
47D964—42no—
48D964—81no—
49C22⋊D241—42no—
50C22⋊D241—42no—
51C2×Dic241—22no—
52C2×Dic241—22no—
53C2×Dic241—22no—
54C2×Dic241—41no—
55C2×Dic241—41no—
56C2×Dic241—41no—
57C2×Dic241—41no—
58C4×D241—44no—
59C23×C241C2×D411yescharacteristic
60C2×C4×C241—21no—
61C2×C4×C241—21no—
62C2×C4×C241—21no—
63C2×C4×C241—41no—
64C2×C4×C241—41no—
65C2×C4×C241SD1612yescomplemented
66C2×C4×C241C2×D412yes—
67C8×C241—42no—
68C22×C241—21no—
69C22×C241—21no—
70C22×C241#12011yescharacteristic
71C22×C241C2×SD1611yescharacteristic
72C22×C241AGL(1,ℤ/8)11yescharacteristic
73C2×D241—42no—
74C2×D241—42no—
75C2×D241—42no—
76C4×C241—22no—
77C4×C241—22no—
78C4×C241—41no—
79Dic241—42no—
80Dic241—42no—
81Dic241—42no—
82C2×C241—21no—
83C2×C241—21no—
84C2×C241#45011yescharacteristic
85C2×C241#45611yescharacteristic
86C2×C241B(4,𝔽2)11yescharacteristic
87D241—82no—
88C241#160411yescharacteristic, complemented, Sylow
89#1604—2411nomaximal, Sylow
90#537—2411no—
91#448—2412no—
92#395—2411no—
93#327—2412no—
94#324D24111yescharacteristic, complemented
95C2×#41—4821no—
96C22×Q8—2411no—
97C2×SD16—4822no—
98C22⋊Q8—4822no—
99#121—4822no—
100#121—4821no—
101#121—2412no—
102C2×C4⋊C4—4821no—
103C2×C4⋊C4C2×D24111yescharacteristic
104#103—4822no—
105C22⋊C8C2×D24112yes—
106#95—4821no—
107#95—2411no—
108#41—9642no—
109#41—9642no—
110C2×Q8—9642no—
111C2×Q8—4821no—
112C2×Q8—4822no—
113C2×D4—4821no—
114C2×D4—4821no—
115C2×D4—4822no—
116C2×D4—2412no—
117C22×C4—4822no—
118C22×C4—4821no—
119C22×C4—4821no—
120C22×C4D96411yescharacteristic
121C22×C4D96411yescharacteristic
122C22×C4C22×D24111yescharacteristic
123SD16—9644no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—9642no—
127C4⋊C4—4821no—
128C4⋊C4—2412no—
129C22⋊C4—4822no—
130C22⋊C4—4822no—
131C23—4822no—
132C23C2×D96411yescharacteristic
133Q8—9642no—
134Q8—9642no—
135Q8—4824no—
136D4—19281no—
137D4—9642no—
138D4—9642no—
139D4—9642no—
140D4—9642no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—9644no—
147C2×C4—9641no—
148C2×C4—9641no—
149C2×C4—9641no—
150C2×C4—9641no—
151C2×C4—4822no—
152C2×C4—4822no—
153C2×C4—4822no—
154C2×C4#1683875912yescomplemented
155C2×C4D4×D24112yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—9642no—
160C22—9642no—
161C22—9642no—
162C22#2144061211yescharacteristic
163C22C2×#1683875911yescharacteristic
164C22#2144067011yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—9642no—
169C4—9642no—
170C4—9642no—
171C2—21no—
172C2—21no—
173C2—19282no—
174C2#2950787011yescharacteristic
175C2#2950790211yescharacteristic
176C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#324×C241C2
socleC22×C241#120
prime radical#29508298C2
hypercenter#324D241
hypocenterC241#1604
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #29507858C2semidirect
3. #29507637C2semidirect
4. #29507452C2semidirect
5. #324×C241C2semidirect
65. C2×C4×C241SD16semidirect
88. C241#1604semidirect
94. #324D241semidirect
154. C2×C4#16838759semidirect

Maximal subgroups

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

subgroupindex
#295082982
#295078582
#295076372
#295074522
#324×C2412
#1604241