Finite Group Databasebeta

← #15682775

Subgroups — #15682775

Order 2944.

704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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#13093253C211yesmaximal, characteristic
2C2×#10625113C212yesmaximal, complemented
3#13092599C214yesmaximal, complemented
4#13092594C214yesmaximal, complemented
5#13092435C212yesmaximal, complemented
6#13092401C211yesmaximal, characteristic, complemented
7C23×#536C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9C22×Q8×C23C2211yescharacteristic, complemented
10#10625161—22no—
11#10625160—22no—
12#41×D23—24no—
13#10625158C2212yes—
14#10625155—22no—
15#10625155C2212yes—
16C2×#67288—22no—
17C2×#67288C2212yes—
18C23×C4⋊Q8C2212yescomplemented
19C23×#124C2212yescomplemented
20C23×#123—22no—
21C23×C22⋊Q8—22no—
22C23×#117C2211yescharacteristic, complemented
23C2×#67275—22no—
24#10625113—24no—
25#10625113C2218yescomplemented
26C2×#67274—22no—
27C2×#67267C2212yescomplemented
28#10625018C2212yescomplemented
29#10625015C2212yescomplemented
30#10624987C2218yescomplemented
31#41×C23—22no—
32#41×C23—22no—
33C2×Q8×C23—21no—
34C2×Q8×C23—22no—
35C2×Q8×C23—22no—
36C2×Q8×C23C2312yes—
37C2×Q8×C23C2311yescharacteristic
38C2×D4×C23D412yes—
39C2×D4×C23C2311yescharacteristic
40C22×C4×C23—21no—
41C22×C4×C23D412yes—
42C22×C4×C23C2311yescharacteristic
43C2×C22⋊D23—24no—
44C2×C22⋊D23—22no—
45#67292—24no—
46Q8×D23—24no—
47#67290—28no—
48#67290—24no—
49D4×D23—28no—
50D4×D23—24no—
51#67288—24no—
52#67288—24no—
53#67288—22no—
54#67288—24no—
55#67288—22no—
56#67288D414yes—
57#67288C2314yes—
58C2×D92—22no—
59C2×D92D412yes—
60C2×C4×D23—24no—
61C2×C4×D23—22no—
62C2×Dic46—22no—
63C2×Dic46D412yes—
64C4⋊C4×C23—21no—
65C4⋊C4×C23—24no—
66C22⋊C4×C23—21no—
67C22⋊C4×C23—24no—
68C42×C23C2312yes—
69#67275—28no—
70#67274—28no—
71#67267—22no—
72#67267C2314yes—
73C2×C23⋊C8—22no—
74C23×C23C2×D412yes—
75C23×C23C2×D411yescharacteristic
76C22×D23—24no—
77C22×D23—22no—
78Q8×C23—22no—
79Q8×C23—24no—
80Q8×C23—41no—
81Q8×C23—41no—
82D4×C23—24no—
83D4×C23—22no—
84C2×C4×C23—22no—
85C2×C4×C23—22no—
86C2×C4×C23—22no—
87C2×C4×C23—22no—
88C2×C4×C23—42no—
89C2×C4×C23C2×D412yes—
90C2×C4×C23C2×D412yes—
91C2×C4×C23C2×D412yes—
92C2×C4×C23C2×D411yescharacteristic
93C2×C4×C23C2411yescharacteristic
94C22⋊D23—28no—
95C22⋊D23—24no—
96C22⋊D23—24no—
97C2×Dic23—24no—
98C2×Dic23—22no—
99D92—24no—
100D92—22no—
101D92C2×D414yes—
102C4×D23—28no—
103C4×D23—24no—
104C4×D23—24no—
105Dic46—24no—
106Dic46—22no—
107Dic46C2×D414yes—
108C23⋊C8—24no—
109#3022—231nomaximal, Sylow
110C22×C23—22no—
111C22×C23—41no—
112C22×C23—42no—
113C22×C23#12012yes—
114C22×C23C22×D411yescharacteristic
115C2×D23—24no—
116C2×D23—82no—
117C2×D23—84no—
118C4×C23—22no—
119C4×C23—42no—
120C4×C23—42no—
121C4×C23#12011yescharacteristic
122C4×C23#12011yescharacteristic
123C4×C23C22×D412yes—
124Dic23—24no—
125#585—231no—
126C2×#137—232no—
127#536D2311yescharacteristic, complemented
128#456—234no—
129#455—234no—
130#421—232no—
131#413—231no—
132C2×C23—21no—
133C2×C23—22no—
134C2×C23—42no—
135C2×C23C2×#12011yescharacteristic
136D23—44no—
1372−1+4—232no—
1382−1+4—462no—
139H(5,𝔽2)—232no—
140H(5,𝔽2)—462no—
141H(5,𝔽2)—462no—
142C2×#41—232no—
143C2×#41—464no—
144C2×#41—462no—
145C2×#41C2×D2311yescharacteristic
146C22×Q8C2×D2311yescharacteristic, complemented
147#137—238no—
148#137—464no—
149C2×Q16—462no—
150C2×SD16—462no—
151C2×M16—232no—
152C4⋊Q8C2×D2312yescomplemented
153#124C2×D2312yescomplemented
154#123—22no—
155C22⋊Q8—22no—
156#117C2×D2311yescharacteristic, complemented
157#104—238no—
158#101—232no—
159#100—232no—
160C23#302211yescharacteristic, complemented, Sylow
161#41—22no—
162#41—22no—
163#41—234no—
164#41—234no—
165#41—464no—
166#41—464no—
167#41—464no—
168#41—468no—
169#41—464no—
170#41—462no—
171#41—462no—
172#41—464no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—232no—
177C2×Q8—462no—
178C2×Q8—464no—
179C2×Q8C22×D2312yes—
180C2×Q8C22×D2311yescharacteristic
181C2×D4—232no—
182C2×D4—462no—
183C2×D4—464no—
184C2×D4—468no—
185C2×D4—462no—
186C2×D4—464no—
187C2×D4C22⋊D2312yes—
188C2×D4C22×D2311yescharacteristic
189C22×C4—21no—
190C22×C4—464no—
191C22×C4—462no—
192C22×C4C22⋊D2312yes—
193C22×C4C22×D2311yescharacteristic
194Q16—468no—
195SD16—468no—
196M16—234no—
197M16—462no—
198C2×C8—462no—
199C4⋊C4—21no—
200C4⋊C4—24no—
201C22⋊C4—21no—
202C22⋊C4—24no—
203C42C22×D2312yes—
204C23—464no—
205C23—462no—
206C23C2×C22⋊D2312yes—
207C23C2×C22⋊D2311yescharacteristic
208Q8—22no—
209Q8—24no—
210Q8—41no—
211Q8—41no—
212Q8—234no—
213Q8—464no—
214Q8—462no—
215D4—24no—
216D4—22no—
217D4—234no—
218D4—464no—
219D4—468no—
220D4—464no—
221D4—464no—
222D4—462no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—468no—
229C2×C4—464no—
230C2×C4—462no—
231C2×C4—464no—
232C2×C4—464no—
233C2×C4D4×D2312yes—
234C2×C4D4×D2312yes—
235C2×C4C2×C22⋊D2312yes—
236C2×C4C2×C22⋊D2311yescharacteristic
237C2×C4C23×D2311yescharacteristic
238C8—464no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—464no—
243C22—1842no—
244C22—1844no—
245C22#1062510812yes—
246C22C22×C22⋊D2311yescharacteristic
247C4—22no—
248C4—42no—
249C4—42no—
250C4—464no—
251C4#1062510811yescharacteristic
252C4#1062510811yescharacteristic
253C4C2×D4×D2312yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—924no—
258C2C2×#1062510811yescharacteristic
subgroupG/H
centerC2C2×#10625108
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#536C2
socleC2×C23C2×#120
prime radical#13093253C2
hypercenter#536D23
hypocenterC23#3022
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#10625113C2semidirect
3. #13092599C2semidirect
4. #13092594C2semidirect
5. #13092435C2semidirect
6. #13092401C2semidirect
7. C23×#536C2semidirect
9. C22×Q8×C23C22semidirect
18. C23×C4⋊Q8C22semidirect
19. C23×#124C22semidirect
22. C23×#117C22semidirect
25. #10625113C22semidirect
27. C2×#67267C22semidirect
28. #10625018C22semidirect
29. #10625015C22semidirect
30. #10624987C22semidirect
127. #536D23semidirect
146. C22×Q8C2×D23semidirect
152. C4⋊Q8C2×D23semidirect
153. #124C2×D23semidirect
156. #117C2×D23semidirect
160. C23#3022semidirect

Maximal subgroups

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

subgroupindex
#130932532
C2×#106251132
#130925992
#130925942
#130924352
#130924012
C23×#5362
#302223