Finite Group Databasebeta

← #44506478

Subgroups — #44506478

Order 30848.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#29508314C211yesmaximal, characteristic
2#29508053C211yesmaximal, characteristic, complemented
3#29508036C211yesmaximal, characteristic
4#29507656C211yesmaximal, characteristic, complemented
5#29507455C211yesmaximal, characteristic, complemented
6#29507452C211yesmaximal, characteristic
7#324×C241C211yesmaximal, characteristic, complemented
8#21440637—21no—
9#21440632—21no—
10#21440627—21no—
11#21440625—21no—
12#21440621C2211yescharacteristic
13#21440620—21no—
14#21440616C2211yescharacteristic
15C4×C22⋊D241—21no—
16C2×C4⋊Dic241C2211yescharacteristic
17#21440576—21no—
18#21440574—21no—
19#21440567—21no—
20#21440564—21no—
21#21440549—21no—
22#21440549—21no—
23#21440549C2211yescharacteristic
24C2×C4⋊C4×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26C22⋊C8×C241C2211yescharacteristic
27C2×Dic482D411yescharacteristic
28C2×D964D411yescharacteristic
29C2×C22⋊D241—21no—
30C22×Dic241—21no—
31C22×Dic241—21no—
32C2×C4×D241—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241D411yescharacteristic
36C4⋊Dic241D411yescharacteristic
37#16838749—21no—
38#16838749—21no—
39#16838749—21no—
40#16838749—21no—
41C22⋊Dic241—21no—
42#16838747—21no—
43#16838747—21no—
44#16838747—21no—
45#16838747—21no—
46C4×Dic241—21no—
47C22×C4×C241D411yescharacteristic
48C22×C4×C241D411yescharacteristic
49C22×C4×C241C2311yescharacteristic
50C2×C8×C241—21no—
51C2×C8×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241—21no—
54C22×D241—21no—
55Dic482—41no—
56D964—41no—
57C22⋊D241—41no—
58C22⋊D241—41no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64C2×Dic241—42no—
65C2×Dic241—41no—
66C2×Dic241—41no—
67C4×D241—81no—
68C23×C241C2×D411yescharacteristic
69C2×C4×C241—21no—
70C2×C4×C241—21no—
71C2×C4×C241—21no—
72C2×C4×C241—21no—
73C2×C4×C241—41no—
74C2×C4×C241—41no—
75C2×C4×C241C2×D411yescharacteristic
76C2×C4×C241C2×D411yescharacteristic
77C8×C241—41no—
78C8×C241—41no—
79C22×C241—21no—
80C22×C241—21no—
81C22×C241#12011yescharacteristic
82C22×C241#13511yescharacteristic
83C22×C241#13711yescharacteristic
84C2×D241—41no—
85C2×D241—41no—
86C2×D241—41no—
87C4×C241—21no—
88C4×C241—21no—
89C4×C241—41no—
90C4×C241—41no—
91Dic241—41no—
92Dic241—41no—
93Dic241—41no—
94Dic241—81no—
95Dic241—81no—
96C2×C241—21no—
97C2×C241—21no—
98C2×C241#45211yescharacteristic
99C2×C241#45411yescharacteristic
100C2×C241#45811yescharacteristic
101D241—81no—
102C241#161511yescharacteristic, complemented, Sylow
103#1615—2411nomaximal, Sylow
104#539—2411no—
105#484—2411no—
106#481—2411no—
107#400—2411no—
108#328—2411no—
109#327—2411no—
110#324D24111yescharacteristic, complemented
111#126—4821no—
112#125—4821no—
113#123—4821no—
114#123—4821no—
115C22⋊Q8—4821no—
116C22⋊Q8—2411no—
117#121—2411no—
118C4×D4—4821no—
119C2×C4⋊C4—2411no—
120C2×C4⋊C4C2×D24111yescharacteristic
121#107—4821no—
122#106—4821no—
123#103—4821no—
124#102—4821no—
125C22⋊C8C2×D24111yescharacteristic
126C22⋊C8C2×D24111yescharacteristic
127#95—4821no—
128#95—4821no—
129#95—2411no—
130C2×Q8—2411no—
131C2×D4—4821no—
132C2×D4—2411no—
133C22×C4—4821no—
134C22×C4—4821no—
135C22×C4—4821no—
136C22×C4D96411yescharacteristic
137C22×C4D96411yescharacteristic
138C22×C4C22×D24111yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—4821no—
144C4⋊C4—4821no—
145C4⋊C4—4821no—
146C4⋊C4—4821no—
147C4⋊C4—4821no—
148C4⋊C4—4821no—
149C4⋊C4—2411no—
150C4⋊C4—2411no—
151C22⋊C4—4821no—
152C22⋊C4—4821no—
153C22⋊C4—4821no—
154C22⋊C4—4821no—
155C22⋊C4—4821no—
156C42—4821no—
157C23—4821no—
158C23C2×D96411yescharacteristic
159Q8—9641no—
160D4—9641no—
161D4—9641no—
162D4—9641no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—19281no—
170C2×C4—9641no—
171C2×C4—9641no—
172C2×C4—9642no—
173C2×C4—9641no—
174C2×C4—9641no—
175C2×C4—4821no—
176C2×C4—4821no—
177C2×C4—4821no—
178C2×C4D4×D24111yescharacteristic
179C2×C4D4×D24111yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—9641no—
185C22—9641no—
186C22—9641no—
187C22#2144061211yescharacteristic
188C22#2144066411yescharacteristic
189C22#2144067511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—19281no—
195C4—19281no—
196C4—9641no—
197C4—9641no—
198C4—9641no—
199C2—21no—
200C2—21no—
201C2—19281no—
202C2#2950788111yescharacteristic
203C2#2950789211yescharacteristic
204C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#324×C241C2
socleC22×C241#120
prime radical#21440616C22
hypercenter#324D241
hypocenterC241#1615
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. #29508053C2semidirect
4. #29507656C2semidirect
5. #29507455C2semidirect
7. #324×C241C2semidirect
102. C241#1615semidirect
110. #324D241semidirect

Maximal subgroups

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

subgroupindex
#295083142
#295080532
#295080362
#295076562
#295074552
#295074522
#324×C2412
#1615241