Finite Group Databasebeta

← #44506411

Subgroups — #44506411

Order 30848.

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

normal subgroups only

This group has 244 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#29508316C211yesmaximal, characteristic
2#29507872C211yesmaximal, characteristic, complemented
3#29507858C211yesmaximal, characteristic
4#29507638C211yesmaximal, characteristic, complemented
5#29507450C211yesmaximal, characteristic
6#29507442C211yesmaximal, characteristic, complemented
7#328×C241C211yesmaximal, characteristic, complemented
8C22×Dic482C2211yescharacteristic
9C2×#16838760—21no—
10C2×#16838759—21no—
11#21440637—21no—
12#21440633—21no—
13#21440627—21no—
14#21440626—21no—
15#21440618—21no—
16#21440616C2211yescharacteristic
17#21440602—21no—
18C2×C4⋊Dic241—21no—
19C2×#16838749C2211yescharacteristic
20#21440567—21no—
21#21440565—21no—
22C22⋊#14515349C2211yescharacteristic
23#21440549—21no—
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×Dic482—42no—
30C2×D964D411yescharacteristic
31C2×C22⋊D241—21no—
32C22×Dic241—21no—
33C22×Dic241D411yescharacteristic
34C22×Dic241D411yescharacteristic
35C2×C4×D241—21no—
36#16838760—42no—
37#16838759—42no—
38C2×#14515349—21no—
39C4⋊Dic241—21no—
40C4⋊Dic241—21no—
41C4⋊Dic241—42no—
42C4⋊Dic241D411yescharacteristic
43#16838749—21no—
44#16838749—21no—
45#16838749—21no—
46#16838747—21no—
47#16838747—21no—
48#16838747—21no—
49#16838747—21no—
50C4×Dic241—21no—
51C2×Q8×C241D411yescharacteristic
52C22×C4×C241—21no—
53C22×C4×C241C2311yescharacteristic
54C2×C8×C241—21no—
55C4⋊C4×C241—21no—
56C4⋊C4×C241D411yescharacteristic
57C22⋊C4×C241—21no—
58C22×D241—21no—
59Dic482—22no—
60Dic482—22no—
61Dic482—41no—
62Dic482—41no—
63D964—41no—
64C22⋊D241—41no—
65C22⋊D241—41no—
66C2×Dic241—22no—
67C2×Dic241—21no—
68C2×Dic241—21no—
69C2×Dic241—21no—
70C2×Dic241—21no—
71C2×Dic241—21no—
72C2×Dic241—41no—
73C2×Dic241—41no—
74C2×Dic241—41no—
75C4×D241—81no—
76#14515349—41no—
77C23×C241C2×D411yescharacteristic
78Q8×C241—41no—
79C2×C4×C241—22no—
80C2×C4×C241—21no—
81C2×C4×C241—21no—
82C2×C4×C241—41no—
83C2×C4×C241—41no—
84C2×C4×C241—41no—
85C2×C4×C241C2×D411yescharacteristic
86C2×C4×C241C2×D411yescharacteristic
87C8×C241—41no—
88C22×C241—21no—
89C22×C241—21no—
90C22×C241#12011yescharacteristic
91C22×C241#13511yescharacteristic
92C22×C241#13711yescharacteristic
93C2×D241—41no—
94C2×D241—41no—
95C2×D241—41no—
96C4×C241—21no—
97C4×C241—21no—
98C4×C241—42no—
99C4×C241—41no—
100C4×C241—41no—
101Dic241—41no—
102Dic241—41no—
103Dic241—41no—
104Dic241—42no—
105C2×C241—21no—
106C2×C241—21no—
107C2×C241#45211yescharacteristic
108C2×C241#45611yescharacteristic
109C2×C241B(4,𝔽2)11yescharacteristic
110D241—81no—
111C241#160311yescharacteristic, complemented, Sylow
112#1603—2411nomaximal, Sylow
113#539—2411no—
114#451—2411no—
115#448—2411no—
116#395—2411no—
117#328D24111yescharacteristic, complemented
118#327—2411no—
119#324—2411no—
120C22×Q8—2411no—
121C2×Q16—4821no—
122C2×SD16—4821no—
123#126—4821no—
124#125—4821no—
125#123—4821no—
126#123—4821no—
127C22⋊Q8—4821no—
128C22⋊Q8C2×D24111yescharacteristic
129#121—2411no—
130C4×D4—4821no—
131C2×C4⋊C4—4821no—
132C2×C4⋊C4—2411no—
133#103—4821no—
134#103—4821no—
135C22⋊C8—2411no—
136C22⋊C8C2×D24111yescharacteristic
137#95—4821no—
138#95C2×D24111yescharacteristic
139C2×Q8—9642no—
140C2×Q8—4821no—
141C2×Q8—4821no—
142C2×Q8D96411yescharacteristic
143C2×D4—4821no—
144C2×D4—2411no—
145C22×C4—21no—
146C22×C4—4821no—
147C22×C4—4821no—
148C22×C4—2411no—
149C22×C4—2411no—
150C22×C4C22×D24111yescharacteristic
151Q16—9642no—
152SD16—9642no—
153C2×C8—21no—
154C2×C8—4821no—
155C4⋊C4—21no—
156C4⋊C4—9642no—
157C4⋊C4—4821no—
158C4⋊C4—4821no—
159C4⋊C4—4821no—
160C4⋊C4—4821no—
161C4⋊C4—4821no—
162C4⋊C4—2411no—
163C4⋊C4D96411yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—4821no—
166C22⋊C4—4821no—
167C22⋊C4—4821no—
168C22⋊C4—4821no—
169C42—4821no—
170C23—4821no—
171C23D4×D24111yescharacteristic
172Q8—41no—
173Q8—9641no—
174Q8—9641no—
175Q8—4822no—
176Q8—4822no—
177D4—9641no—
178D4—9641no—
179D4—9641no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—19281no—
187C2×C4—9641no—
188C2×C4—9641no—
189C2×C4—9641no—
190C2×C4—4822no—
191C2×C4—4821no—
192C2×C4—4821no—
193C2×C4—4821no—
194C2×C4—4821no—
195C2×C4—4821no—
196C2×C4D4×D24111yescharacteristic
197C2×C4C2×D96411yescharacteristic
198C8—41no—
199C8—9641no—
200C22—21no—
201C22—21no—
202C22—9641no—
203C22—9641no—
204C22—9641no—
205C22#2144061211yescharacteristic
206C22#2144066311yescharacteristic
207C22#2144067411yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—9641no—
214C4—9641no—
215C4—9641no—
216C4—9642no—
217C2—21no—
218C2—21no—
219C2—19281no—
220C2#2950788211yescharacteristic
221C2#2950790111yescharacteristic
222C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241#120
prime radical#21440616C22
hypercenter#328D241
hypocenterC241#1603
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
2. #29507872C2semidirect
4. #29507638C2semidirect
6. #29507442C2semidirect
7. #328×C241C2semidirect
111. C241#1603semidirect
117. #328D241semidirect

Maximal subgroups

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

subgroupindex
#295083162
#295078722
#295078582
#295076382
#295074502
#295074422
#328×C2412
#1603241