Finite Group Databasebeta

← #44506421

Subgroups — #44506421

Order 30848.

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

normal subgroups only

This group has 238 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#29508348C211yesmaximal, characteristic
2#29507875C212yesmaximal
3#29507637C211yesmaximal, characteristic
4#29507455C212yesmaximal
5#324×C241C211yesmaximal, characteristic
6C22×Dic482C2211yescharacteristic
7C2×Dic964—22no—
8#21440641—22no—
9#21440633—22no—
10#21440621—21no—
11#21440621C2212yes—
12#21440601—21no—
13C2×#16838749—21no—
14#21440567—22no—
15#21440549—21no—
16#21440549C2211yescharacteristic
17C2×C4⋊C4×C241C2211yescharacteristic
18C22⋊C8×C241C2212yes—
19C2×Dic482—21no—
20C2×Dic482—22no—
21C2×Dic482—42no—
22C2×Dic482D412yes—
23C22×Dic241—21no—
24C22×Dic241—21no—
25Dic964—44no—
26C4⋊Dic241—21no—
27C4⋊Dic241—21no—
28C4⋊Dic241—21no—
29C4⋊Dic241D412yes—
30#16838749—22no—
31#16838749—22no—
32#16838749—42no—
33C22⋊Dic241—22no—
34C4×Dic241—22no—
35C22×C4×C241D411yescharacteristic
36C22×C4×C241D411yescharacteristic
37C22×C4×C241C2311yescharacteristic
38C2×C8×C241—22no—
39C4⋊C4×C241—22no—
40Dic482—24no—
41Dic482—42no—
42Dic482—42no—
43Dic482—81no—
44C2×Dic241—22no—
45C2×Dic241—22no—
46C2×Dic241—22no—
47C2×Dic241—22no—
48C2×Dic241—41no—
49C2×Dic241—41no—
50C2×Dic241—41no—
51C2×Dic241—41no—
52C23×C241C2×D411yescharacteristic
53C2×C4×C241—21no—
54C2×C4×C241—21no—
55C2×C4×C241—21no—
56C2×C4×C241—41no—
57C2×C4×C241—41no—
58C2×C4×C241Q1612yescomplemented
59C2×C4×C241C2×D412yes—
60C8×C241—42no—
61C22×C241—21no—
62C22×C241—21no—
63C22×C241#12011yescharacteristic
64C22×C241C2×Q1611yescharacteristic
65C22×C241#13711yescharacteristic
66C4×C241—22no—
67C4×C241—22no—
68C4×C241—41no—
69Dic241—42no—
70Dic241—42no—
71Dic241—42no—
72Dic241—42no—
73C2×C241—21no—
74C2×C241—21no—
75C2×C241#45111yescharacteristic
76C2×C241#45611yescharacteristic
77C2×C241B(4,𝔽2)11yescharacteristic
78C241#160511yescharacteristic, complemented, Sylow
79#1605—2411nomaximal, Sylow
80#544—2411no—
81#451—2412no—
82#395—2411no—
83#328—2412no—
84#324D24111yescharacteristic
85C22×Q8—2411no—
86C2×Q16—4822no—
87C4⋊Q8—4822no—
88#125—4822no—
89C22⋊Q8—4821no—
90C22⋊Q8—2412no—
91#117—4821no—
92C2×C4⋊C4—4821no—
93C2×C4⋊C4C2×D24111yescharacteristic
94#103—4822no—
95C22⋊C8C2×D24112yes—
96#95—4821no—
97#95—2411no—
98C2×Q8—9642no—
99C2×Q8—4821no—
100C2×Q8—4822no—
101C2×Q8—2412no—
102C22×C4—4821no—
103C22×C4—4821no—
104C22×C4D96411yescharacteristic
105C22×C4D96411yescharacteristic
106C22×C4C22×D24111yescharacteristic
107Q16—9644no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—9642no—
111C4⋊C4—4822no—
112C4⋊C4—4821no—
113C4⋊C4—4821no—
114C4⋊C4—4821no—
115C4⋊C4—4822no—
116C4⋊C4—2412no—
117C22⋊C4—4822no—
118C42—4822no—
119C23C2×D96411yescharacteristic
120Q8—19281no—
121Q8—9642no—
122Q8—9642no—
123Q8—4824no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—9641no—
130C2×C4—9641no—
131C2×C4—9641no—
132C2×C4—9641no—
133C2×C4—4822no—
134C2×C4—4822no—
135C2×C4—4822no—
136C2×C4—4822no—
137C2×C4Dic96412yescomplemented
138C2×C4D4×D24112yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#2144061211yescharacteristic
143C22C2×Dic96411yescharacteristic
144C22#2144067511yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—9642no—
149C4—9642no—
150C4—9642no—
151C4—9642no—
152C2—21no—
153C2—21no—
154C2#2950787511yescharacteristic
155C2#2950790211yescharacteristic
156C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#324×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#324D241
hypocenterC241#1605
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
58. C2×C4×C241Q16semidirect
78. C241#1605semidirect
137. C2×C4Dic964semidirect

Maximal subgroups

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

subgroupindex
#295083482
#295078752
#295076372
#295074552
#324×C2412
#1605241