Finite Group Databasebeta

← #44506454

Subgroups — #44506454

Order 30848.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#29508346C211yesmaximal, characteristic
2#29508048C211yesmaximal, characteristic
3#29508045C211yesmaximal, characteristic
4#29507649C211yesmaximal, characteristic
5#29507453C211yesmaximal, characteristic
6#29507442C211yesmaximal, characteristic
7#328×C241C211yesmaximal, characteristic
8#21440641—21no—
9#21440640—21no—
10#21440632—21no—
11#21440632—21no—
12#21440621C2211yescharacteristic
13#21440619—21no—
14#21440598—21no—
15C2×C4⋊Dic241—21no—
16C2×C4⋊Dic241C2211yescharacteristic
17C2×#16838749C2211yescharacteristic
18#21440574—21no—
19#21440573—21no—
20#21440567—21no—
21#21440566—21no—
22C22⋊#14515349C2211yescharacteristic
23#21440549—21no—
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482D411yescharacteristic
29C22×Dic241—21no—
30C22×Dic241D411yescharacteristic
31C22×Dic241D411yescharacteristic
32C2×#14515349—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241—42no—
37C4⋊Dic241D411yescharacteristic
38#16838749—21no—
39#16838749—21no—
40#16838749—21no—
41#16838749—21no—
42#16838749—21no—
43#16838749—21no—
44#16838749—21no—
45C22⋊Dic241—21no—
46C4×Dic241—21no—
47C4×Dic241—21no—
48C2×Q8×C241D411yescharacteristic
49C22×C4×C241—21no—
50C22×C4×C241C2311yescharacteristic
51C2×C8×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241D411yescharacteristic
54C22⋊C4×C241—21no—
55Dic482—41no—
56Dic482—81no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—21no—
60C2×Dic241—21no—
61C2×Dic241—21no—
62C2×Dic241—41no—
63C2×Dic241—41no—
64C2×Dic241—41no—
65C2×Dic241—41no—
66C2×Dic241SD1612yes—
67#14515349—41no—
68C23×C241C2×D411yescharacteristic
69Q8×C241—41no—
70C2×C4×C241—22no—
71C2×C4×C241—21no—
72C2×C4×C241—21no—
73C2×C4×C241—41no—
74C2×C4×C241—41no—
75C2×C4×C241—41no—
76C2×C4×C241C2×D411yescharacteristic
77C2×C4×C241C2×D411yescharacteristic
78C8×C241—41no—
79C22×C241—21no—
80C22×C241—21no—
81C22×C241#12011yescharacteristic
82C22×C241C2×SD1611yescharacteristic
83C22×C241#13711yescharacteristic
84C4×C241—21no—
85C4×C241—21no—
86C4×C241—42no—
87C4×C241—41no—
88C4×C241—41no—
89Dic241—22no—
90Dic241—41no—
91Dic241—41no—
92Dic241—41no—
93Dic241—81no—
94C2×C241—21no—
95C2×C241—21no—
96C2×C241#44811yescharacteristic
97C2×C241#45611yescharacteristic
98C2×C241#45811yescharacteristic
99C241#161111yescharacteristic, complemented, Sylow
100#1611—2411nomaximal, Sylow
101#544—2411no—
102#483—2411no—
103#483—2411no—
104#398—2411no—
105#328—2411no—
106#328D24111yescharacteristic
107#324—2411no—
108C4⋊Q8—4821no—
109C4⋊Q8—4821no—
110#125—4821no—
111#125—4821no—
112C22⋊Q8—4821no—
113C22⋊Q8—2411no—
114C22⋊Q8C2×D24111yescharacteristic
115#117—4821no—
116C2×C4⋊C4—4821no—
117C2×C4⋊C4—2411no—
118C2×C4⋊C4—2411no—
119#106—4821no—
120#106—4821no—
121#103—4821no—
122#103—4821no—
123C22⋊C8—2411no—
124C22⋊C8C2×D24111yescharacteristic
125#95—4821no—
126#95C2×D24111yescharacteristic
127C2×Q8—4821no—
128C2×Q8—2411no—
129C2×Q8D96411yescharacteristic
130C22×C4—21no—
131C22×C4—4821no—
132C22×C4—2411no—
133C22×C4—2411no—
134C22×C4C22×D24111yescharacteristic
135C2×C8—21no—
136C2×C8—4821no—
137C4⋊C4—21no—
138C4⋊C4—9642no—
139C4⋊C4—4821no—
140C4⋊C4—4821no—
141C4⋊C4—4821no—
142C4⋊C4—4821no—
143C4⋊C4—4821no—
144C4⋊C4—4821no—
145C4⋊C4—4821no—
146C4⋊C4—4821no—
147C4⋊C4—4821no—
148C4⋊C4—4821no—
149C4⋊C4—2411no—
150C4⋊C4D96411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—4821no—
153C42—4821no—
154C42—4821no—
155C23D4×D24111yescharacteristic
156Q8—41no—
157Q8—19281no—
158Q8—9641no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—9641no—
166C2×C4—9641no—
167C2×C4—9641no—
168C2×C4—9641no—
169C2×C4—4821no—
170C2×C4—4821no—
171C2×C4—4821no—
172C2×C4—4821no—
173C2×C4—4821no—
174C2×C4—2412no—
175C2×C4D4×D24111yescharacteristic
176C2×C4C2×D96411yescharacteristic
177C8—41no—
178C8—9641no—
179C22—21no—
180C22—21no—
181C22#2144061211yescharacteristic
182C22SD16×D24111yescharacteristic
183C22#2144067411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—19281no—
190C4—9641no—
191C4—9641no—
192C4—9641no—
193C4—4822no—
194C2—21no—
195C2—21no—
196C2#2950785711yescharacteristic
197C2#2950790111yescharacteristic
198C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#328D241
hypocenterC241#1611
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C241#1611semidirect

Maximal subgroups

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

subgroupindex
#295083462
#295080482
#295080452
#295076492
#295074532
#295074422
#328×C2412
#1611241