Finite Group Databasebeta

← #15682804

Subgroups — #15682804

Order 2944.

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

normal subgroups only

This group has 716 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
2#13092993C212yesmaximal, complemented
3#13092988C211yesmaximal, characteristic, complemented
4#13092608C218yesmaximal, complemented
5#13092390C212yesmaximal, complemented
6C23×#410C211yesmaximal, characteristic, complemented
7C2×#41×C23C2211yescharacteristic
8#10625161—22no—
9#10625160—22no—
10#41×D23—24no—
11#10625158—21no—
12#10625155—21no—
13#10625155C2214yes—
14C2×#67288—22no—
15C2×#67288C2212yes—
16C22×Dic46C2211yescharacteristic, complemented
17C23×#117C2212yescomplemented
18#10625115—21no—
19#10625107—21no—
20#10625106C2214yescomplemented
21#10625097C2211yescharacteristic, complemented
22#10625095—22no—
23#10625068—24no—
24#10625057C2218yescomplemented
25#10625046—22no—
26#10625040—22no—
27C23×#99C2214yescomplemented
28#10624988C2218yescomplemented
29#41×C23—22no—
30#41×C23—22no—
31C2×Q8×C23D411yescharacteristic
32C2×D4×C23D411yescharacteristic
33C2×D4×C23C2312yes—
34C22×C4×C23D412yes—
35C22×C4×C23C2311yescharacteristic
36C2×C22⋊D23—24no—
37C2×C22⋊D23C2314yes—
38C22×Dic23C2312yes—
39#67292—24no—
40Q8×D23—24no—
41#67290—24no—
42#67290—28no—
43D4×D23—24no—
44D4×D23—28no—
45#67288—24no—
46#67288—24no—
47#67288—22no—
48#67288—24no—
49#67288—22no—
50#67288—22no—
51#67288—22no—
52C2×D92—22no—
53C2×D92D412yes—
54C2×C4×D23—24no—
55C2×C4×D23D414yes—
56C2×Dic46—22no—
57C2×Dic46—22no—
58C2×Dic46—22no—
59C2×Dic46—21no—
60C2×Dic46—21no—
61C2×Dic46D412yes—
62C4⋊C4×C23—22no—
63C22⋊C4×C23C2314yes—
64C42×C23—22no—
65C22⋊Dic23—24no—
66C22⋊Dic23C2312yes—
67(C2×D23)⋊C4—28no—
68C4⋊Dic23—21no—
69C4⋊Dic23—28no—
70Dic23⋊C4—24no—
71C4×Dic23—21no—
72C23×C23C2×D412yes—
73C23×C23C2411yescharacteristic
74C22×D23—24no—
75C22×D23C2×D414yes—
76Q8×C23—22no—
77D4×C23—24no—
78D4×C23—22no—
79C2×C4×C23—22no—
80C2×C4×C23—22no—
81C2×C4×C23—24no—
82C2×C4×C23C2×D412yes—
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2×D411yescharacteristic
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2×D412yes—
87C22⋊D23—28no—
88C22⋊D23—24no—
89C22⋊D23—24no—
90C2×Dic23—24no—
91C2×Dic23—22no—
92C2×Dic23—22no—
93C2×Dic23—24no—
94C2×Dic23C2×D414yes—
95D92—24no—
96D92—22no—
97D92—22no—
98C4×D23—28no—
99C4×D23—24no—
100C4×D23—24no—
101Dic46—24no—
102Dic46—22no—
103Dic46—22no—
104Dic46—41no—
105Dic46—42no—
106Dic46—41no—
107#3028—231nomaximal, Sylow
108C22×C23—22no—
109C22×C23—41no—
110C22×C23—42no—
111C22×C23C22×D411yescharacteristic
112C22×C23C22×D412yes—
113C2×D23—24no—
114C2×D23—44no—
115C2×D23—84no—
116C4×C23—22no—
117C4×C23—44no—
118C4×C23#12011yescharacteristic
119C4×C23#12012yes—
120C4×C23#12011yescharacteristic
121Dic23—24no—
122Dic23—42no—
123Dic23—42no—
124#585—231no—
125#536—231no—
126#536—232no—
127#458—238no—
128#410—232no—
129#410D2311yescharacteristic, complemented
130C2×C23—21no—
131C2×C23—22no—
132C2×C23—42no—
133C2×C23C2×#12011yescharacteristic
134D23—44no—
1352−1+4—462no—
1362−1+4—461no—
137H(5,𝔽2)—234no—
138H(5,𝔽2)—462no—
139H(5,𝔽2)—461no—
140C2×#41—232no—
141C2×#41—464no—
142C2×#41—462no—
143C2×#41C2×D2311yescharacteristic
144C22×Q8—231no—
145C4⋊Q8—462no—
146C4⋊Q8—461no—
147#124—462no—
148#124—461no—
149#123—234no—
150#123—238no—
151C22⋊Q8—464no—
152C22⋊Q8—462no—
153#117—231no—
154#117C2×D2312yescomplemented
155#99—238no—
156#99C2×D2314yescomplemented
157C23#302811yescharacteristic, complemented, Sylow
158#41—22no—
159#41—22no—
160#41—464no—
161#41—464no—
162#41—468no—
163#41—464no—
164#41—464no—
165#41—462no—
166#41—462no—
167#41—464no—
168#41—462no—
169#41—462no—
170C2×Q8—232no—
171C2×Q8—462no—
172C2×Q8—464no—
173C2×Q8—461no—
174C2×Q8—461no—
175C2×Q8—462no—
176C2×Q8—462no—
177C2×Q8D9211yescharacteristic
178C2×D4—234no—
179C2×D4—232no—
180C2×D4—462no—
181C2×D4—468no—
182C2×D4—464no—
183C2×D4—464no—
184C2×D4D9211yescharacteristic
185C2×D4C22×D2312yes—
186C22×C4—234no—
187C22×C4—232no—
188C22×C4—464no—
189C22×C4D9212yes—
190C22×C4C22×D2311yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—468no—
193C4⋊C4—461no—
194C4⋊C4—464no—
195C22⋊C4—232no—
196C22⋊C4—468no—
197C22⋊C4—464no—
198C22⋊C4C22×D2314yes—
199C42—22no—
200C42—461no—
201C23—234no—
202C23—464no—
203C23C2×D9212yes—
204C23C23×D2311yescharacteristic
205Q8—22no—
206Q8—464no—
207Q8—462no—
208Q8—462no—
209Q8—921no—
210Q8—921no—
211Q8—922no—
212D4—24no—
213D4—22no—
214D4—464no—
215D4—468no—
216D4—464no—
217D4—464no—
218D4—462no—
219D4—462no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—234no—
224C2×C4—468no—
225C2×C4—464no—
226C2×C4—464no—
227C2×C4—464no—
228C2×C4—462no—
229C2×C4—462no—
230C2×C4—464no—
231C2×C4C2×D9212yes—
232C2×C4C2×D9211yescharacteristic
233C2×C4C2×D9211yescharacteristic
234C2×C4D4×D2312yes—
235C2×C4D4×D2312yes—
236C22—22no—
237C22—41no—
238C22—42no—
239C22—464no—
240C22—924no—
241C22—1844no—
242C22C22×D9211yescharacteristic
243C22C2×D4×D2312yes—
244C4—22no—
245C4—44no—
246C4—464no—
247C4—922no—
248C4—922no—
249C4#1062505311yescharacteristic
250C4#1062505311yescharacteristic
251C4#1062505312yes—
252C2—22no—
253C2—21no—
254C2—42no—
255C2—924no—
256C2C2×#1062505311yescharacteristic
subgroupG/H
centerC2C2×#10625053
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC23×#410C2
socleC2×C23C2×#120
prime radical#13093253C2
hypercenter#410D23
hypocenterC23#3028
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #13092993C2semidirect
3. #13092988C2semidirect
4. #13092608C2semidirect
5. #13092390C2semidirect
6. C23×#410C2semidirect
16. C22×Dic46C22semidirect
17. C23×#117C22semidirect
20. #10625106C22semidirect
21. #10625097C22semidirect
24. #10625057C22semidirect
27. C23×#99C22semidirect
28. #10624988C22semidirect
129. #410D23semidirect
154. #117C2×D23semidirect
156. #99C2×D23semidirect
157. C23#3028semidirect

Maximal subgroups

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

subgroupindex
#130932532
#130929932
#130929882
#130926082
#130923902
C23×#4102
#302823