Finite Group Databasebeta

← #44508477

Subgroups — #44508477

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×#21440675C211yesmaximal, characteristic, complemented
2#29508286C211yesmaximal, characteristic
3C2×#21440630C211yesmaximal, characteristic, complemented
4C2×#21440570C211yesmaximal, characteristic, complemented
5#29507725C211yesmaximal, characteristic, complemented
6C2×#21440558C211yesmaximal, characteristic, complemented
7#339×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×Dic482C2211yescharacteristic
10C22×D964C2211yescharacteristic
11#21440675—22no—
12#21440675—22no—
13C2×Dic964—21no—
14C2×#16838759—21no—
15C2×#16838754C2211yescharacteristic
16#21440639—21no—
17#21440630—21no—
18#21440630—22no—
19#21440630—22no—
20#21440617—22no—
21#21440612—22no—
22C2×#16838747—22no—
23#21440570—22no—
24#21440565—22no—
25#21440558—22no—
26C2×M16×C241C2211yescharacteristic
27#117×C241C2211yescharacteristic
28C2×C42×C241C2211yescharacteristic
29C23×D241D412yes—
30#16838770—21no—
31#16838770—21no—
32#16838770—21no—
33#16838770—21no—
34C2×Dic482—21no—
35C2×Dic482—21no—
36C2×Dic482—21no—
37C2×Dic482—21no—
38C2×Dic482—21no—
39C2×Dic482D411yescharacteristic
40C2×Dic482D412yescomplemented
41C2×D964—24no—
42C2×D964—21no—
43C2×D964—21no—
44C2×D964—21no—
45C2×D964—21no—
46C2×D964—21no—
47C2×D964—21no—
48C2×D964D411yescharacteristic
49C2×C22⋊D241—21no—
50C22×Dic241—21no—
51C2×C4×D241—21no—
52Dic964—24no—
53#16838759—24no—
54#16838754—21no—
55#16838754—21no—
56C2×#14515349—21no—
57#16838747—28no—
58#16838747—24no—
59C22×C4×C241—21no—
60C22×C4×C241C2311yescharacteristic
61M16×C241—21no—
62M16×C241D412yescomplemented
63C2×C8×C241—21no—
64C4⋊C4×C241D412yes—
65C22⋊C4×C241—21no—
66C42×C241—21no—
67C42×C241—21no—
68C42×C241D412yescomplemented
69C22×D241—22no—
70C22×D241—22no—
71C22×D241—21no—
72C22×D241—22no—
73C22×D241—44no—
74Dic482—22no—
75Dic482—21no—
76Dic482—22no—
77Dic482—21no—
78Dic482—41no—
79Dic482—41no—
80D964—21no—
81D964—21no—
82D964—41no—
83D964—41no—
84D964—41no—
85D964—41no—
86D964—84no—
87C22⋊D241—41no—
88C22⋊D241—41no—
89C2×Dic241—21no—
90C2×Dic241—22no—
91C2×Dic241—41no—
92C2×Dic241—41no—
93C4×D241—41no—
94C4×D241—41no—
95#14515349—41no—
96C23×C241C2×D411yescharacteristic
97C2×C4×C241—22no—
98C2×C4×C241—22no—
99C2×C4×C241—42no—
100C2×C4×C241C2×D411yescharacteristic
101C2×C4×C241C2×D411yescharacteristic
102C2×C4×C241C2×D411yescharacteristic
103C2×C4×C241C2×D411yescharacteristic
104C2×C4×C241C2×D411yescharacteristic
105C2×C4×C241#4111yescharacteristic
106C8×C241—22no—
107C22×C241—22no—
108C22×C241#12011yescharacteristic
109C22×C241#12011yescharacteristic
110C22×C241#12111yescharacteristic
111C2×D241—44no—
112C2×D241—41no—
113C2×D241—42no—
114C2×D241—42no—
115C2×D241—44no—
116C2×D241—82no—
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#39211yescharacteristic
128C2×C241#45512yes—
129D241—81no—
130D241—82no—
131C241#200411yescharacteristic, complemented, Sylow
132#2004—2411nomaximal, Sylow
133C2×#137—2411no—
134#535—2411no—
135C2×#124—2411no—
136C2×#104—2411no—
137#419—2411no—
138C2×#100—2411no—
139#339D24111yescharacteristic, complemented
140C2×#41—2411no—
141C22×Q8—2411no—
142C22×D4—2411no—
143#137—4822no—
144#137—4822no—
145C2×Q16—4821no—
146C2×SD16—4821no—
147C2×M16—2411no—
148C2×M16C2×D24111yescharacteristic
149#127—4821no—
150#124—4822no—
151#124—4821no—
152#124—4822no—
153#121—4822no—
154#120—4822no—
155#117C2×D24111yescharacteristic
156C2×C22⋊C4—4822no—
157C2×C42C2×D24111yescharacteristic
158#104—4822no—
159#103—4822no—
160#100—4822no—
161C24—2412no—
162#41—4821no—
163#41—4821no—
164#41—4821no—
165#41—4821no—
166C2×Q8—4821no—
167C2×Q8—4821no—
168C2×Q8—4821no—
169C2×Q8—4821no—
170C2×Q8—4821no—
171C2×Q8—2411no—
172C2×Q8—2412no—
173C2×D4—4824no—
174C2×D4—4821no—
175C2×D4—4821no—
176C2×D4—4821no—
177C2×D4—4821no—
178C2×D4—4821no—
179C2×D4—4821no—
180C2×D4—4821no—
181C2×D4—2411no—
182C22×C4—21no—
183C22×C4—4821no—
184C22×C4—4821no—
185C22×C4C22×D24111yescharacteristic
186Q16—4824no—
187SD16—4824no—
188M16—21no—
189M16—4821no—
190M16—4821no—
191M16D96412yescomplemented
192C2×C8—21no—
193C2×C8—4821no—
194C4⋊C4D96412yes—
195C22⋊C4—21no—
196C22⋊C4—4828no—
197C22⋊C4—4824no—
198C42—21no—
199C42—21no—
200C42D96412yescomplemented
201C23—9644no—
202C23—4822no—
203C23—4822no—
204C23—4822no—
205C23—4821no—
206C23D4×D24111yescharacteristic
207Q8—9641no—
208Q8—9641no—
209Q8—4822no—
210Q8—4821no—
211Q8—4822no—
212Q8—4821no—
213D4—19284no—
214D4—9641no—
215D4—9641no—
216D4—9641no—
217D4—9641no—
218D4—9641no—
219D4—9641no—
220D4—4821no—
221D4—4821no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—9641no—
226C2×C4—9641no—
227C2×C4—9641no—
228C2×C4—9641no—
229C2×C4—4822no—
230C2×C4—4821no—
231C2×C4D4×D24111yescharacteristic
232C2×C4D4×D24111yescharacteristic
233C2×C4C2×D96411yescharacteristic
234C2×C4C2×D96411yescharacteristic
235C2×C4C2×D96411yescharacteristic
236C2×C4#1683877111yescharacteristic
237C8—22no—
238C8—9641no—
239C22—22no—
240C22—19282no—
241C22—9644no—
242C22—9641no—
243C22—9642no—
244C22—9642no—
245C22—9644no—
246C22#2144061211yescharacteristic
247C22#2144061211yescharacteristic
248C22#2144061711yescharacteristic
249C4—42no—
250C4—42no—
251C4—9641no—
252C4—9642no—
253C4#2144061211yescharacteristic
254C4#2144061711yescharacteristic
255C4#2144061711yescharacteristic
256C4#2144063911yescharacteristic
257C2—21no—
258C2—21no—
259C2—19282no—
260C2—19281no—
261C2#2950762711yescharacteristic
262C2#2950789612yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241#120
prime radical#29508286C2
hypercenter#339D241
hypocenterC241#2004
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#21440675C2semidirect
3. C2×#21440630C2semidirect
4. C2×#21440570C2semidirect
5. #29507725C2semidirect
6. C2×#21440558C2semidirect
7. #339×C241C2semidirect
40. C2×Dic482D4semidirect
62. M16×C241D4semidirect
68. C42×C241D4semidirect
131. C241#2004semidirect
139. #339D241semidirect
191. M16D964semidirect
200. C42D964semidirect

Maximal subgroups

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

subgroupindex
C2×#214406752
#295082862
C2×#214406302
C2×#214405702
#295077252
C2×#214405582
#339×C2412
#2004241