Finite Group Databasebeta

← #44508474

Subgroups — #44508474

Order 30848.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#21440673C211yesmaximal, characteristic, complemented
2#29508284C211yesmaximal, characteristic
3C2×#21440570C211yesmaximal, characteristic, complemented
4#29507726C211yesmaximal, characteristic, complemented
5C2×#21440559C211yesmaximal, characteristic, complemented
6#29507477C211yesmaximal, characteristic, complemented
7C2×#124×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9#21440673—22no—
10#21440673—22no—
11C2×#16838760—21no—
12C2×#16838757—21no—
13C2×#16838754C2211yescharacteristic
14C2×#16838754C2211yescharacteristic
15#21440638—21no—
16#21440629—21no—
17#21440613—22no—
18#21440611—22no—
19#21440601C2211yescharacteristic
20#21440570—22no—
21#21440566—22no—
22#21440559—22no—
23C22×Q8×C241C2211yescharacteristic
24C22×D4×C241C2211yescharacteristic
25#124×C241—22no—
26#124×C241—22no—
27C2×C22⋊C4×C241—22no—
28C2×C42×C241C2211yescharacteristic
29#16838770—21no—
30#16838770—21no—
31#16838770—21no—
32#16838770—21no—
33C2×Dic482D411yescharacteristic
34C2×D964D411yescharacteristic
35C2×C22⋊D241—24no—
36C2×C22⋊D241—21no—
37C2×C4×D241—21no—
38#16838760—24no—
39#16838757—24no—
40#16838754—21no—
41#16838754—21no—
42#16838754—21no—
43#16838754D412yescomplemented
44C2×#14515349—21no—
45C2×#14515349—21no—
46C4⋊Dic241D412yes—
47C22⋊Dic241—24no—
48C22⋊Dic241—21no—
49C4×Dic241—21no—
50C24×C241D412yes—
51C2×Q8×C241—21no—
52C2×Q8×C241—21no—
53C2×Q8×C241—21no—
54C2×Q8×C241—21no—
55C2×Q8×C241—21no—
56C2×Q8×C241D412yescomplemented
57C2×D4×C241—21no—
58C2×D4×C241—21no—
59C2×D4×C241—21no—
60C2×D4×C241—21no—
61C2×D4×C241—21no—
62C2×D4×C241—21no—
63C22×C4×C241—21no—
64C22×C4×C241—21no—
65C22×C4×C241C2311yescharacteristic
66C22⋊C4×C241—28no—
67C42×C241—21no—
68C42×C241D412yescomplemented
69C22×D241—21no—
70Dic482—21no—
71Dic482—21no—
72D964—21no—
73D964—21no—
74C22⋊D241—41no—
75C22⋊D241—41no—
76C22⋊D241—84no—
77C2×Dic241—22no—
78C2×Dic241—21no—
79C4×D241—41no—
80C4×D241—41no—
81#14515349—22no—
82#14515349—41no—
83C23×C241—22no—
84C23×C241—22no—
85C23×C241—22no—
86C23×C241—44no—
87C23×C241C2×D411yescharacteristic
88Q8×C241—22no—
89Q8×C241—22no—
90Q8×C241—41no—
91Q8×C241—41no—
92D4×C241—41no—
93D4×C241—41no—
94D4×C241—41no—
95D4×C241—41no—
96C2×C4×C241—22no—
97C2×C4×C241—22no—
98C2×C4×C241—42no—
99C2×C4×C241—41no—
100C2×C4×C241—41no—
101C2×C4×C241C2×D411yescharacteristic
102C2×C4×C241C2×D411yescharacteristic
103C2×C4×C241C2×D411yescharacteristic
104C2×C4×C241C2×D411yescharacteristic
105C2×C4×C241C2×D411yescharacteristic
106C2×C4×C241#4111yescharacteristic
107C22×C241—22no—
108C22×C241—44no—
109C22×C241—42no—
110C22×C241—44no—
111C22×C241—82no—
112C22×C241#12011yescharacteristic
113C22×C241#12011yescharacteristic
114C22×C241#12111yescharacteristic
115C2×D241—41no—
116C2×D241—42no—
117C4×C241—42no—
118C4×C241—42no—
119C4×C241#12011yescharacteristic
120C4×C241#12111yescharacteristic
121C4×C241#12111yescharacteristic
122C4×C241#12711yescharacteristic
123Dic241—41no—
124Dic241—42no—
125C2×C241—21no—
126C2×C241—21no—
127C2×C241—82no—
128C2×C241#39211yescharacteristic
129C2×C241#45512yes—
130D241—81no—
131C241#200411yescharacteristic, complemented, Sylow
132#2004—2411nomaximal, Sylow
133C2×#137—2411no—
134#535—2411no—
135C2×#124D24111yescharacteristic, complemented
136C2×#104—2411no—
137#419—2411no—
138C2×#100—2411no—
139#339—2411no—
140C2×#41—2411no—
141C22×Q8C2×D24111yescharacteristic
142C22×D4C2×D24111yescharacteristic
143#137—4822no—
144#137—4822no—
145C2×Q16—4821no—
146C2×SD16—4821no—
147C2×M16—2411no—
148C2×M16—2411no—
149#127—4821no—
150#124—22no—
151#124—22no—
152#124—4821no—
153#121—4822no—
154#120—4822no—
155#117—2411no—
156C2×C22⋊C4—22no—
157C2×C42C2×D24111yescharacteristic
158#104—4822no—
159#103—4822no—
160#100—4822no—
161C24C22⋊D24112yes—
162#41—4821no—
163#41—4821no—
164#41—4821no—
165#41—4821no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—2411no—
172C2×Q8C22⋊D24112yescomplemented
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—4824no—
180C2×D4—4821no—
181C2×D4—2411no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—4821no—
185C22×C4C22×D24111yescharacteristic
186Q16—4824no—
187SD16—4824no—
188M16—4821no—
189M16—4821no—
190M16—4821no—
191M16—2412no—
192C2×C8—4821no—
193C2×C8—4821no—
194C4⋊C4—2412no—
195C22⋊C4—28no—
196C22⋊C4—4824no—
197C22⋊C4—4821no—
198C42—21no—
199C42—4821no—
200C42C22⋊D24112yescomplemented
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—4821no—
206C23C2×C22⋊D24111yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—41no—
210Q8—41no—
211Q8—4821no—
212Q8—4821no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—19284no—
218D4—9641no—
219D4—9641no—
220D4—4821no—
221D4—4821no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—9641no—
228C2×C4—9641no—
229C2×C4—4822no—
230C2×C4—4821no—
231C2×C4D4×D24111yescharacteristic
232C2×C4D4×D24111yescharacteristic
233C2×C4D4×D24111yescharacteristic
234C2×C4C2×C22⋊D24111yescharacteristic
235C2×C4C2×C22⋊D24111yescharacteristic
236C2×C4#1683876911yescharacteristic
237C8—9641no—
238C8—4822no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—9641no—
245C22—9642no—
246C22#2144061011yescharacteristic
247C22#2144061111yescharacteristic
248C22#2144061411yescharacteristic
249C4—42no—
250C4—42no—
251C4—9641no—
252C4—9642no—
253C4#2144061011yescharacteristic
254C4#2144061311yescharacteristic
255C4#2144061411yescharacteristic
256C4#2144063811yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—19281no—
261C2#2950762511yescharacteristic
262C2#2950789412yes—
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
FittingC2×#124×C241C2
socleC22×C241#120
prime radical#29508284C2
hypercenterC2×#124D241
hypocenterC241#2004
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#21440673C2semidirect
3. C2×#21440570C2semidirect
4. #29507726C2semidirect
5. C2×#21440559C2semidirect
6. #29507477C2semidirect
7. C2×#124×C241C2semidirect
43. #16838754D4semidirect
56. C2×Q8×C241D4semidirect
68. C42×C241D4semidirect
131. C241#2004semidirect
135. C2×#124D241semidirect
172. C2×Q8C22⋊D241semidirect
200. C42C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406732
#295082842
C2×#214405702
#295077262
C2×#214405592
#295074772
C2×#124×C2412
#2004241