Finite Group Databasebeta

← #44505992

Subgroups — #44505992

Order 30848.

252 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 77 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#29507774C211yesmaximal, characteristic, complemented
2#29507585C211yesmaximal, characteristic, complemented
3#29507451C214yesmaximal, complemented
4#532×C241C211yesmaximal, characteristic
5C4⋊#14515349—21no—
6C22⋊#14515349C2212yes—
7#21440553—21no—
8#21440549—21no—
9#21440549—21no—
10#21440549C2212yes—
11C2×#41×C241—21no—
12C4⋊Q8×C241C411yescharacteristic, complemented
13#127×C241C411yescharacteristic, complemented
14#124×C241—21no—
15#121×C241—21no—
16#121×C241C2212yes—
17C4×D4×C241—21no—
18C4×D4×C241C412yescomplemented
19C2×C42×C241C2211yescharacteristic
20C22×Dic241—22no—
21C2×#14515349—22no—
22#41×C241—44no—
23C2×Q8×C241—21no—
24C2×D4×C241—22no—
25C2×D4×C241—21no—
26C2×D4×C241—21no—
27C2×D4×C241C2×C412yes—
28C22×C4×C241—22no—
29C22×C4×C241D411yescharacteristic
30C22×C4×C241D411yescharacteristic
31C22×C4×C241C2311yescharacteristic
32C4⋊C4×C241—21no—
33C4⋊C4×C241C2×C412yes—
34C22⋊C4×C241—22no—
35C22⋊C4×C241—22no—
36C42×C241C2×C411yescharacteristic
37C42×C241C2×C411yescharacteristic
38C42×C241D411yescharacteristic
39C42×C241D411yescharacteristic
40C2×Dic241—42no—
41C2×Dic241—42no—
42C2×Dic241—42no—
43#14515349—42no—
44C23×C241—22no—
45C23×C241C2×D411yescharacteristic
46Q8×C241—42no—
47D4×C241—42no—
48D4×C241—42no—
49D4×C241—42no—
50D4×C241—44no—
51C2×C4×C241—22no—
52C2×C4×C241—22no—
53C2×C4×C241—41no—
54C2×C4×C241—41no—
55C2×C4×C241—44no—
56C2×C4×C241C22⋊C411yescharacteristic
57C2×C4×C241C22⋊C411yescharacteristic
58C2×C4×C241C22⋊C411yescharacteristic
59C2×C4×C241C22⋊C411yescharacteristic
60C2×C4×C241C22×C411yescharacteristic
61C2×C4×C241C2×D411yescharacteristic
62C22×C241—21no—
63C22×C241—21no—
64C22×C241—42no—
65C22×C241—42no—
66C22×C241—42no—
67C22×C241C2×C22⋊C411yescharacteristic
68C22×C241AGL(1,ℤ/8)12yes—
69C4×C241—21no—
70C4×C241—21no—
71C4×C241—21no—
72C4×C241—21no—
73C4×C241—21no—
74C4×C241—21no—
75C4×C241—42no—
76Dic241—82no—
77C2×C241—22no—
78C2×C241—82no—
79C2×C241#41011yescharacteristic
80C2×C241#41811yescharacteristic
81C2×C241#42111yescharacteristic
82C241#151411yescharacteristic, complemented, Sylow
83#1514—2411nomaximal, Sylow
84#532D24111yescharacteristic
85#432—2411no—
86#383—2411no—
87#327—2414no—
88C2×#41—21no—
89C4⋊Q8Dic24111yescharacteristic, complemented
90#127Dic24111yescharacteristic, complemented
91#124—21no—
92#121—21no—
93#121C2×D24112yes—
94C4×D4—21no—
95C4×D4Dic24112yescomplemented
96C2×C42C2×D24111yescharacteristic
97C4⋊C8—4821no—
98C22⋊C8—2412no—
99#97—4821no—
100#95—4821no—
101#95—4821no—
102#95—2412no—
103#41—44no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—21no—
107C2×D4—21no—
108C2×D4C2×Dic24112yes—
109C22×C4—22no—
110C22×C4—4822no—
111C22×C4C22⋊D24111yescharacteristic
112C22×C4C22⋊D24111yescharacteristic
113C22×C4C22×D24111yescharacteristic
114C2×C8—4822no—
115C4⋊C4—21no—
116C4⋊C4C2×Dic24112yes—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C42C2×Dic24111yescharacteristic
120C42C2×Dic24111yescharacteristic
121C42C22⋊D24111yescharacteristic
122C42C22⋊D24111yescharacteristic
123C23—22no—
124C23C2×C22⋊D24111yescharacteristic
125Q8—42no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—44no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—44no—
135C2×C4—9642no—
136C2×C4—9642no—
137C2×C4—9642no—
138C2×C4C22⋊Dic24111yescharacteristic
139C2×C4C22⋊Dic24111yescharacteristic
140C2×C4C22⋊Dic24111yescharacteristic
141C2×C4C22⋊Dic24111yescharacteristic
142C2×C4C22×Dic24111yescharacteristic
143C2×C4C2×C22⋊D24111yescharacteristic
144C8—9642no—
145C22—21no—
146C22—21no—
147C22—42no—
148C22—42no—
149C22—42no—
150C22C2×C22⋊Dic24111yescharacteristic
151C22#2144066812yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—42no—
159C4—19282no—
160C2—22no—
161C2—82no—
162C2#2950769111yescharacteristic
163C2#2950772211yescharacteristic
164C2#2950773411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting, prime radical#532×C241C2
socleC22×C241C2×C22⋊C4
cosocleC22×C4×C241C23
hypercenter#532D241
hypocenterC241#1514
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #29507774C2semidirect
2. #29507585C2semidirect
3. #29507451C2semidirect
12. C4⋊Q8×C241C4semidirect
13. #127×C241C4semidirect
18. C4×D4×C241C4semidirect
82. C241#1514semidirect
89. C4⋊Q8Dic241semidirect
90. #127Dic241semidirect
95. C4×D4Dic241semidirect

Maximal subgroups

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

subgroupindex
#295077742
#295075852
#295074512
#532×C2412
#1514241