Finite Group Databasebeta

← #44506366

Subgroups — #44506366

Order 30848.

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

normal subgroups only

This group has 316 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#29508342C211yesmaximal, characteristic, complemented
2#29507868C211yesmaximal, characteristic, complemented
3#29507625C211yesmaximal, characteristic
4#29507455C211yesmaximal, characteristic, complemented
5#29507454C211yesmaximal, characteristic, complemented
6#29507440C211yesmaximal, characteristic, complemented
7#450×C241C211yesmaximal, characteristic, complemented
8C22×C22⋊D241—21no—
9C2×#16838758—21no—
10#21440622—21no—
11#21440621C2211yescharacteristic
12#21440620—21no—
13#21440620—21no—
14#21440619—21no—
15#21440618—21no—
16C2×C22⋊Dic241—21no—
17C2×#16838747C2211yescharacteristic
18C22⋊C4×D241—21no—
19#21440563—21no—
20C22⋊#14515349C2211yescharacteristic
21#21440549C2211yescharacteristic
22C22×D4×C241C2211yescharacteristic
23C2×SD16×C241—21no—
24C22⋊Q8×C241C2211yescharacteristic
25#102×C241—21no—
26C22⋊C8×C241C2211yescharacteristic
27C23×D241D411yescharacteristic
28C2×Dic482—21no—
29C2×Dic482D411yescharacteristic, complemented
30C2×C22⋊D241—42no—
31C2×C22⋊D241—42no—
32C2×C22⋊D241—42no—
33C22×Dic241—21no—
34C22×Dic241D411yescharacteristic
35C2×C4×D241—21no—
36C2×C4×D241—21no—
37#16838758—42no—
38C2×#14515349—21no—
39C4⋊Dic241—21no—
40C4⋊Dic241D411yescharacteristic, complemented
41#16838749—21no—
42#16838749—21no—
43#16838749—21no—
44C22⋊Dic241—21no—
45C22⋊Dic241—42no—
46#16838747—21no—
47#16838747—21no—
48#16838747—21no—
49#16838747—21no—
50C24×C241—21no—
51C2×Q8×C241D411yescharacteristic, complemented
52C2×D4×C241—21no—
53C2×D4×C241—21no—
54C2×D4×C241—42no—
55C22×C4×C241C2311yescharacteristic
56SD16×C241—42no—
57C2×C8×C241—21no—
58C4⋊C4×C241—21no—
59C4⋊C4×C241D411yescharacteristic, complemented
60C22⋊C4×C241—21no—
61C22×D241—21no—
62C22×D241—21no—
63C22×D241—41no—
64C22×D241—41no—
65C22×D241SD1612yescomplemented
66Dic482—41no—
67Dic482—81no—
68C22⋊D241—48no—
69C2×Dic241—22no—
70C2×Dic241—21no—
71C2×Dic241—21no—
72C2×Dic241—21no—
73C2×Dic241—41no—
74C2×Dic241—41no—
75C2×Dic241—41no—
76C4×D241—81no—
77C4×D241—81no—
78#14515349—41no—
79C23×C241—22no—
80C23×C241—41no—
81C23×C241—41no—
82C23×C241—41no—
83C23×C241—41no—
84C23×C241—41no—
85C23×C241—41no—
86C23×C241C2×D411yescharacteristic
87Q8×C241—41no—
88D4×C241—22no—
89D4×C241—22no—
90D4×C241—41no—
91D4×C241—41no—
92C2×C4×C241—21no—
93C2×C4×C241—21no—
94C2×C4×C241—41no—
95C2×C4×C241C2×D411yescharacteristic
96C2×C4×C241C2×D411yescharacteristic
97C8×C241—41no—
98C22×C241—21no—
99C22×C241—21no—
100C22×C241—42no—
101C22×C241—42no—
102C22×C241—42no—
103C22×C241—81no—
104C22×C241—81no—
105C22×C241—81no—
106C22×C241—81no—
107C22×C241#12011yescharacteristic
108C22×C241C2×SD1611yescharacteristic
109C22×C241#13711yescharacteristic
110C2×D241—22no—
111C2×D241—41no—
112C2×D241—41no—
113C2×D241—42no—
114C2×D241—81no—
115C4×C241—21no—
116C4×C241—21no—
117C4×C241—41no—
118C4×C241—41no—
119Dic241—42no—
120Dic241—41no—
121Dic241—41no—
122Dic241—41no—
123C2×C241—21no—
124C2×C241—21no—
125C2×C241—82no—
126C2×C241#44811yescharacteristic
127C2×C241#45311yescharacteristic
128C2×C241B(4,𝔽2)11yescharacteristic
129D241—42no—
130C241#159611yescharacteristic, complemented, Sylow
131#1596—2411nomaximal, Sylow
132#543—2411no—
133#450—2411no—
134#450D24111yescharacteristic, complemented
135#392—2411no—
136#328—2411no—
137#328—2411no—
138#323—2411no—
139C22×D4—4821no—
140C22×D4C2×D24111yescharacteristic
141C2×SD16—21no—
142C2×SD16—4821no—
143C22⋊Q8—4821no—
144C22⋊Q8—4821no—
145C22⋊Q8—4821no—
146C22⋊Q8—4821no—
147C22⋊Q8—4821no—
148C22⋊Q8—2411no—
149C22⋊Q8C2×D24111yescharacteristic
150C2×C22⋊C4—4821no—
151C2×C22⋊C4—4821no—
152C2×C22⋊C4—2411no—
153#102—21no—
154#102—4821no—
155C22⋊C8—2411no—
156C22⋊C8C2×D24111yescharacteristic
157#95—2411no—
158C24—21no—
159C24—2411no—
160C2×Q8—4821no—
161C2×Q8—2411no—
162C2×Q8C22⋊D24111yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—42no—
166C2×D4—9642no—
167C2×D4—9642no—
168C2×D4—9642no—
169C22×C4—4821no—
170C22×C4—4821no—
171C22×C4—4821no—
172C22×C4—2411no—
173C22×C4C22×D24111yescharacteristic
174SD16—42no—
175SD16—9642no—
176C2×C8—21no—
177C2×C8—4821no—
178C4⋊C4—21no—
179C4⋊C4—4821no—
180C4⋊C4—4821no—
181C4⋊C4—4821no—
182C4⋊C4—4821no—
183C4⋊C4—2411no—
184C4⋊C4C22⋊D24111yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—9642no—
187C22⋊C4—4821no—
188C22⋊C4—4821no—
189C22⋊C4—4821no—
190C22⋊C4—4821no—
191C22⋊C4—4821no—
192C23—22no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—9641no—
200C23—9641no—
201C23—4821no—
202C23—4821no—
203C23—2412no—
204C23D4×D24111yescharacteristic
205Q8—41no—
206Q8—19281no—
207Q8—9641no—
208D4—22no—
209D4—22no—
210D4—41no—
211D4—41no—
212D4—9648no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—19281no—
217C2×C4—19281no—
218C2×C4—9641no—
219C2×C4—9641no—
220C2×C4—9641no—
221C2×C4—4822no—
222C2×C4—4821no—
223C2×C4—4821no—
224C2×C4—4821no—
225C2×C4D4×D24111yescharacteristic
226C2×C4C2×C22⋊D24111yescharacteristic
227C8—41no—
228C8—9641no—
229C22—21no—
230C22—21no—
231C22—42no—
232C22—42no—
233C22—42no—
234C22—81no—
235C22—81no—
236C22—81no—
237C22—81no—
238C22—19281no—
239C22—9642no—
240C22—9641no—
241C22—9641no—
242C22—4822no—
243C22#2144061011yescharacteristic
244C22SD16×D24111yescharacteristic
245C22#2144067111yescharacteristic
246C4—21no—
247C4—21no—
248C4—41no—
249C4—41no—
250C4—9642no—
251C4—9641no—
252C4—9641no—
253C4—9641no—
254C2—21no—
255C2—21no—
256C2—82no—
257C2—9642no—
258C2#2950785411yescharacteristic
259C2#2950788311yescharacteristic
260C2#2950790311yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#450×C241C2
socleC22×C241#120
prime radical#29507625C2
hypercenter#450D241
hypocenterC241#1596
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #29508342C2semidirect
2. #29507868C2semidirect
4. #29507455C2semidirect
5. #29507454C2semidirect
6. #29507440C2semidirect
7. #450×C241C2semidirect
29. C2×Dic482D4semidirect
40. C4⋊Dic241D4semidirect
51. C2×Q8×C241D4semidirect
59. C4⋊C4×C241D4semidirect
65. C22×D241SD16semidirect
130. C241#1596semidirect
134. #450D241semidirect
162. C2×Q8C22⋊D241semidirect
184. C4⋊C4C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295083422
#295078682
#295076252
#295074552
#295074542
#295074402
#450×C2412
#1596241