Finite Group Databasebeta

← #15682778

Subgroups — #15682778

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×#10625080C212yesmaximal, complemented
3#13092988C211yesmaximal, characteristic, complemented
4#13092602C214yesmaximal, complemented
5#13092597C214yesmaximal, complemented
6#13092433C212yesmaximal, complemented
7C23×#413C211yesmaximal, characteristic, complemented
8C2×#41×C23C2211yescharacteristic
9#10625161—22no—
10#10625160—22no—
11#41×D23—24no—
12#10625158C2212yes—
13#10625155—22no—
14#10625155C2212yes—
15C2×#67288—22no—
16C2×#67288C2212yes—
17C22×Dic46C2211yescharacteristic, complemented
18C2×M16×C23C2212yescomplemented
19#10625115C2212yescomplemented
20#10625107C2212yescomplemented
21#10625106—22no—
22#10625097C2211yescharacteristic, complemented
23#10625095—22no—
24#10625080—24no—
25#10625080C2218yescomplemented
26C2×Dic92—22no—
27C2×#67263—22no—
28C23×#101C2212yescomplemented
29C23×#100C2212yescomplemented
30#10625007C2218yescomplemented
31#41×C23—22no—
32#41×C23—22no—
33C2×Q8×C23C2311yescharacteristic
34C2×D4×C23D412yes—
35C2×D4×C23C2311yescharacteristic
36C22×C4×C23D412yes—
37C22×C4×C23C2311yescharacteristic
38C2×C22⋊D23—24no—
39C2×C22⋊D23—22no—
40C22×Dic23—21no—
41#67292—24no—
42Q8×D23—24no—
43#67290—28no—
44#67290—24no—
45D4×D23—28no—
46D4×D23—24no—
47#67288—24no—
48#67288—24no—
49#67288—22no—
50#67288—24no—
51#67288—22no—
52#67288D414yes—
53#67288C2314yes—
54C2×D92—22no—
55C2×D92D412yes—
56C2×C4×D23—24no—
57C2×C4×D23—22no—
58C2×Dic46—22no—
59C2×Dic46—22no—
60C2×Dic46—22no—
61C2×Dic46—21no—
62C2×Dic46D412yes—
63C2×Dic46C2312yes—
64M16×C23—22no—
65M16×C23C2314yes—
66C2×C8×C23—22no—
67C22⋊Dic23—24no—
68C22⋊Dic23—21no—
69C4⋊Dic23—21no—
70Dic23⋊C4—24no—
71C4×Dic23C2312yes—
72Dic92—28no—
73#67263—28no—
74C23×C23C2×D412yes—
75C23×C23C2×D411yescharacteristic
76C22×D23—24no—
77C22×D23—22no—
78Q8×C23—22no—
79D4×C23—24no—
80D4×C23—22no—
81C2×C4×C23—22no—
82C2×C4×C23—22no—
83C2×C4×C23C2×D412yes—
84C2×C4×C23C2×D411yescharacteristic
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2×D412yes—
87C2×C4×C23C2411yescharacteristic
88C22⋊D23—28no—
89C22⋊D23—24no—
90C22⋊D23—24no—
91C2×Dic23—24no—
92C2×Dic23—22no—
93C2×Dic23—22no—
94C2×Dic23—22no—
95C2×Dic23—42no—
96D92—24no—
97D92—22no—
98D92C2×D414yes—
99C4×D23—28no—
100C4×D23—24no—
101C4×D23—24no—
102Dic46—24no—
103Dic46—22no—
104Dic46—24no—
105Dic46—41no—
106Dic46—41no—
107Dic46C2×D414yes—
108C8×C23—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#12011yescharacteristic
120C4×C23#12011yescharacteristic
121C4×C23C22×D412yes—
122Dic23—24no—
123Dic23—42no—
124Dic23—42no—
125#585—231no—
126C2×#137—232no—
127#536—231no—
128#456—234no—
129#455—234no—
130#421—232no—
131#413D2311yescharacteristic, complemented
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×Q8—231no—
147#137—238no—
148#137—464no—
149C2×Q16—462no—
150C2×SD16—462no—
151C2×M16C2×D2312yescomplemented
152C4⋊Q8—232no—
153#124—232no—
154#123—462no—
155C22⋊Q8—462no—
156#117—231no—
157#104—238no—
158#101C2×D2312yescomplemented
159#100C2×D2312yescomplemented
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—464no—
172#41—462no—
173C2×Q8—232no—
174C2×Q8—232no—
175C2×Q8—462no—
176C2×Q8—464no—
177C2×Q8—461no—
178C2×Q8—462no—
179C2×Q8—462no—
180C2×Q8C22×D2311yescharacteristic
181C2×D4—232no—
182C2×D4—462no—
183C2×D4—464no—
184C2×D4—468no—
185C2×D4—462no—
186C2×D4—464no—
187C2×D4D9212yes—
188C2×D4C22×D2311yescharacteristic
189C22×C4—464no—
190C22×C4—462no—
191C22×C4—461no—
192C22×C4D9212yes—
193C22×C4C22×D2311yescharacteristic
194Q16—468no—
195SD16—468no—
196M16—22no—
197M16C22×D2314yes—
198C2×C8—22no—
199C4⋊C4—461no—
200C4⋊C4—464no—
201C22⋊C4—461no—
202C22⋊C4—464no—
203C42—232no—
204C23—464no—
205C23—462no—
206C23C2×D9212yes—
207C23C2×D9211yescharacteristic
208Q8—22no—
209Q8—234no—
210Q8—464no—
211Q8—462no—
212Q8—464no—
213Q8—921no—
214Q8—921no—
215D4—24no—
216D4—22no—
217D4—234no—
218D4—464no—
219D4—468no—
220D4—464no—
221D4—464no—
222D4—462no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—468no—
226C2×C4—464no—
227C2×C4—462no—
228C2×C4—464no—
229C2×C4—464no—
230C2×C4—462no—
231C2×C4—462no—
232C2×C4—922no—
233C2×C4C2×D9212yes—
234C2×C4C2×D9211yescharacteristic
235C2×C4D4×D2312yes—
236C2×C4D4×D2312yes—
237C2×C4C23×D2311yescharacteristic
238C8—24no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—464no—
243C22—1842no—
244C22—1844no—
245C22#1062505312yes—
246C22C22×D9211yescharacteristic
247C4—22no—
248C4—464no—
249C4—922no—
250C4—922no—
251C4#1062505311yescharacteristic
252C4#1062505311yescharacteristic
253C4C2×D4×D2312yes—
254C2—21no—
255C2—22no—
256C2—42no—
257C2—924no—
258C2C2×#1062505311yescharacteristic
subgroupG/H
centerC2C2×#10625053
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#413C2
socleC2×C23C2×#120
prime radical#13093253C2
hypercenter#413D23
hypocenterC23#3022
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. C2×#10625080C2semidirect
3. #13092988C2semidirect
4. #13092602C2semidirect
5. #13092597C2semidirect
6. #13092433C2semidirect
7. C23×#413C2semidirect
17. C22×Dic46C22semidirect
18. C2×M16×C23C22semidirect
19. #10625115C22semidirect
20. #10625107C22semidirect
22. #10625097C22semidirect
25. #10625080C22semidirect
28. C23×#101C22semidirect
29. C23×#100C22semidirect
30. #10625007C22semidirect
131. #413D23semidirect
151. C2×M16C2×D23semidirect
158. #101C2×D23semidirect
159. #100C2×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×#106250802
#130929882
#130926022
#130925972
#130924332
C23×#4132
#302223