Finite Group Databasebeta

← #44506484

Subgroups — #44506484

Order 30848.

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

normal subgroups only

This group has 246 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#29508036C212yesmaximal, complemented
3#29507656C211yesmaximal, characteristic, complemented
4#29507452C212yesmaximal, complemented
5#324×C241C211yesmaximal, characteristic, complemented
6C2×#16838770—21no—
7#21440622—22no—
8#21440617—22no—
9#21440616—21no—
10#21440616C2212yes—
11C2×C4⋊Dic241C2211yescharacteristic
12#21440574—22no—
13#21440564—22no—
14#21440549—21no—
15#21440549—21no—
16#21440549C2211yescharacteristic
17C2×C4⋊C4×C241C2211yescharacteristic
18C22⋊C8×C241C2212yes—
19#16838770—42no—
20#16838770—42no—
21C2×Dic482—21no—
22C2×D964—21no—
23C2×D964—21no—
24C2×D964D412yes—
25C2×C22⋊D241—22no—
26C22×Dic241—21no—
27C22×Dic241—21no—
28C2×C4×D241—22no—
29C4⋊Dic241—21no—
30C4⋊Dic241—22no—
31C4⋊Dic241D412yes—
32#16838747—22no—
33#16838747—22no—
34C22×C4×C241D411yescharacteristic
35C22×C4×C241D411yescharacteristic
36C22×C4×C241C2311yescharacteristic
37C2×C8×C241—22no—
38C4⋊C4×C241—22no—
39C22×D241—22no—
40Dic482—42no—
41D964—42no—
42D964—42no—
43D964—81no—
44C22⋊D241—42no—
45C22⋊D241—42no—
46C2×Dic241—22no—
47C2×Dic241—41no—
48C2×Dic241—41no—
49C2×Dic241—42no—
50C2×Dic241—41no—
51C2×Dic241—41no—
52C4×D241—44no—
53C23×C241C2×D411yescharacteristic
54C2×C4×C241—21no—
55C2×C4×C241—21no—
56C2×C4×C241—21no—
57C2×C4×C241—41no—
58C2×C4×C241—41no—
59C2×C4×C241SD1612yes—
60C2×C4×C241C2×D412yes—
61C8×C241—42no—
62C22×C241—21no—
63C22×C241—21no—
64C22×C241#12011yescharacteristic
65C22×C241C2×SD1611yescharacteristic
66C22×C241AGL(1,ℤ/8)11yescharacteristic
67C2×D241—42no—
68C2×D241—42no—
69C2×D241—42no—
70C4×C241—22no—
71C4×C241—22no—
72C4×C241—41no—
73Dic241—42no—
74Dic241—81no—
75Dic241—81no—
76C2×C241—21no—
77C2×C241—21no—
78C2×C241#45011yescharacteristic
79C2×C241#45411yescharacteristic
80C2×C241#45811yescharacteristic
81D241—82no—
82C241#161611yescharacteristic, complemented, Sylow
83#1616—2411nomaximal, Sylow
84#537—2411no—
85#481—2412no—
86#400—2411no—
87#327—2412no—
88#324D24111yescharacteristic, complemented
89C2×#41—4821no—
90C22⋊Q8—4822no—
91#121—4822no—
92#121—4821no—
93#121—2412no—
94C2×C4⋊C4—2411no—
95C2×C4⋊C4C2×D24111yescharacteristic
96#106—4822no—
97#102—4822no—
98C22⋊C8C2×D24112yes—
99#95—4821no—
100#95—4821no—
101#95—2411no—
102#41—9642no—
103#41—9642no—
104C2×Q8—4821no—
105C2×D4—4821no—
106C2×D4—4821no—
107C2×D4—4822no—
108C2×D4—2412no—
109C22×C4—4822no—
110C22×C4—4821no—
111C22×C4—4821no—
112C22×C4D96411yescharacteristic
113C22×C4D96411yescharacteristic
114C22×C4C22×D24111yescharacteristic
115C2×C8—22no—
116C4⋊C4—22no—
117C4⋊C4—4821no—
118C4⋊C4—4822no—
119C4⋊C4—2412no—
120C22⋊C4—4822no—
121C22⋊C4—4822no—
122C23—4822no—
123C23C2×D96411yescharacteristic
124Q8—9642no—
125D4—19281no—
126D4—9642no—
127D4—9642no—
128D4—9642no—
129D4—9642no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—9644no—
136C2×C4—9641no—
137C2×C4—9641no—
138C2×C4—9642no—
139C2×C4—9641no—
140C2×C4—9641no—
141C2×C4—4822no—
142C2×C4#1683875912yes—
143C2×C4D4×D24112yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—9642no—
148C22—9642no—
149C22—9642no—
150C22#2144061211yescharacteristic
151C22C2×#1683875911yescharacteristic
152C22#2144067011yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—19281no—
157C4—19281no—
158C4—9642no—
159C2—21no—
160C2—21no—
161C2—19282no—
162C2#2950787011yescharacteristic
163C2#2950789211yescharacteristic
164C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#324×C241C2
socleC22×C241#120
prime radical#29508298C2
hypercenter#324D241
hypocenterC241#1616
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. #29508036C2semidirect
3. #29507656C2semidirect
4. #29507452C2semidirect
5. #324×C241C2semidirect
82. C241#1616semidirect
88. #324D241semidirect

Maximal subgroups

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

subgroupindex
#295082982
#295080362
#295076562
#295074522
#324×C2412
#1616241