Finite Group Databasebeta

← #44505993

Subgroups — #44505993

Order 30848.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#29508267C211yesmaximal, characteristic
2#29507585C211yesmaximal, characteristic, complemented
3#29507452C214yesmaximal, complemented
4#432×C241C211yesmaximal, characteristic, complemented
5C2×#16838770—21no—
6#21440642C411yescharacteristic, complemented
7#21440639C411yescharacteristic, complemented
8#21440630—21no—
9#21440616—21no—
10#21440616C2212yes—
11C4×D964—21no—
12C4×D964C412yescomplemented
13#21440549—21no—
14#21440549—21no—
15#21440549C2212yes—
16C2×C42×C241C2211yescharacteristic
17C4⋊C8×C241—21no—
18C22⋊C8×C241C2212yes—
19#97×C241—21no—
20#16838770—44no—
21C2×Dic482—21no—
22C2×D964—21no—
23C2×D964—21no—
24C2×D964C2×C412yes—
25C2×C22⋊D241—22no—
26C22×Dic241—22no—
27C2×C4×D241—22no—
28C4⋊Dic241—21no—
29C4⋊Dic241C2×C412yes—
30#16838747—22no—
31#16838747—22no—
32C22×C4×C241D411yescharacteristic
33C22×C4×C241D411yescharacteristic
34C22×C4×C241C2311yescharacteristic
35C2×C8×C241—22no—
36C42×C241C2×C411yescharacteristic
37C42×C241C2×C411yescharacteristic
38C42×C241D411yescharacteristic
39C42×C241D411yescharacteristic
40C22×D241—22no—
41Dic482—42no—
42D964—42no—
43D964—42no—
44D964—42no—
45C22⋊D241—44no—
46C2×Dic241—22no—
47C2×Dic241—42no—
48C2×Dic241—42no—
49C2×Dic241—42no—
50C4×D241—44no—
51C23×C241C2×D411yescharacteristic
52C2×C4×C241—22no—
53C2×C4×C241—41no—
54C2×C4×C241—41no—
55C2×C4×C241C22⋊C411yescharacteristic
56C2×C4×C241C22⋊C411yescharacteristic
57C2×C4×C241C22⋊C411yescharacteristic
58C2×C4×C241C22⋊C411yescharacteristic
59C2×C4×C241C22×C411yescharacteristic
60C2×C4×C241C2×D411yescharacteristic
61C8×C241—42no—
62C22×C241—21no—
63C22×C241—21no—
64C22×C241C2×C22⋊C411yescharacteristic
65C22×C241AGL(1,ℤ/8)12yes—
66C2×D241—42no—
67C2×D241—42no—
68C2×D241—42no—
69C4×C241—21no—
70C4×C241—21no—
71C4×C241—21no—
72C4×C241—21no—
73C4×C241—21no—
74C4×C241—21no—
75Dic241—42no—
76Dic241—82no—
77C2×C241—22no—
78C2×C241#41011yescharacteristic
79C2×C241#41811yescharacteristic
80C2×C241#42111yescharacteristic
81D241—82no—
82C241#151411yescharacteristic, complemented, Sylow
83#1514—2411nomaximal, Sylow
84#532—2411no—
85#432D24111yescharacteristic, complemented
86#383—2411no—
87#327—2414no—
88C2×#41—4821no—
89C4⋊Q8—2411no—
90#127—2411no—
91#124—4821no—
92#121—4821no—
93#121—2412no—
94C4×D4—4821no—
95C4×D4—2412no—
96C2×C42C2×D24111yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C2×D24112yes—
99#97—21no—
100#95—4821no—
101#95—4821no—
102#95—2412no—
103#41—9644no—
104C2×Q8—4821no—
105C2×D4—4822no—
106C2×D4—4821no—
107C2×D4—4821no—
108C2×D4—2412no—
109C22×C4—4822no—
110C22×C4—4822no—
111C22×C4D96411yescharacteristic
112C22×C4D96411yescharacteristic
113C22×C4C22×D24111yescharacteristic
114C2×C8—22no—
115C4⋊C4—4821no—
116C4⋊C4—2412no—
117C22⋊C4—4822no—
118C22⋊C4—4822no—
119C42C4×D24111yescharacteristic
120C42C4×D24111yescharacteristic
121C42C22⋊D24111yescharacteristic
122C42C22⋊D24111yescharacteristic
123C23—4822no—
124C23C2×D96411yescharacteristic
125Q8—9642no—
126D4—9642no—
127D4—9642no—
128D4—9642no—
129D4—9644no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—9644no—
134C2×C4—9642no—
135C2×C4—9642no—
136C2×C4—9642no—
137C2×C4—4822no—
138C2×C4#1683874711yescharacteristic
139C2×C4#1683874711yescharacteristic
140C2×C4#1683874711yescharacteristic
141C2×C4#1683874711yescharacteristic
142C2×C4C2×C4×D24111yescharacteristic
143C2×C4C2×C22⋊D24111yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—9642no—
148C22—9642no—
149C22—9642no—
150C22C2×#1683874711yescharacteristic
151C22#2144067012yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—19282no—
159C4—9642no—
160C2—22no—
161C2—19282no—
162C2#2950769011yescharacteristic
163C2#2950772311yescharacteristic
164C2#2950773311yescharacteristic
subgroupG/H
centerC22C2×#16838747
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#432×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508267C2
cosocleC22×C4×C241C23
hypercenter#432D241
hypocenterC241#1514
LCSG ▷ C2×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #29507585C2semidirect
3. #29507452C2semidirect
4. #432×C241C2semidirect
6. #21440642C4semidirect
7. #21440639C4semidirect
12. C4×D964C4semidirect
82. C241#1514semidirect
85. #432D241semidirect

Maximal subgroups

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

subgroupindex
#295082672
#295075852
#295074522
#432×C2412
#1514241