Finite Group Databasebeta

← #15682800

Subgroups — #15682800

Order 2944.

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

normal subgroups only

This group has 772 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, complemented
2#13092986C212yesmaximal, complemented
3#13092981C211yesmaximal, characteristic, complemented
4#13092605C218yesmaximal, 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×D92C2211yescharacteristic, complemented
17C23×#117C2212yescomplemented
18#10625118—21no—
19#10625111—21no—
20#10625108C2214yescomplemented
21#10625101—22no—
22#10625097C2211yescharacteristic, complemented
23#10625066—24no—
24#10625053C2218yescomplemented
25#10625046—22no—
26#10625045—22no—
27C23×#99C2214yescomplemented
28#10624988C2218yescomplemented
29C23×D23C2312yes—
30#41×C23—22no—
31#41×C23—22no—
32C2×Q8×C23D411yescharacteristic, complemented
33C2×D4×C23D411yescharacteristic, complemented
34C2×D4×C23C2312yes—
35C22×C4×C23D412yescomplemented
36C22×C4×C23C2311yescharacteristic
37C2×C22⋊D23—24no—
38C2×C22⋊D23—24no—
39C2×C22⋊D23C2314yes—
40#67292—24no—
41Q8×D23—24no—
42#67290—24no—
43#67290—28no—
44D4×D23—24no—
45D4×D23—28no—
46#67288—24no—
47#67288—24no—
48#67288—22no—
49#67288—24no—
50#67288—22no—
51#67288—22no—
52#67288—22no—
53C2×D92—22no—
54C2×D92—22no—
55C2×D92—22no—
56C2×D92—21no—
57C2×D92—21no—
58C2×D92—28no—
59C2×D92D412yescomplemented
60C2×C4×D23—24no—
61C2×C4×D23D414yescomplemented
62C2×Dic46—22no—
63C2×Dic46D412yescomplemented
64C4⋊C4×C23—22no—
65C22⋊C4×C23C2314yes—
66C42×C23—22no—
67C22⋊Dic23C2312yes—
68(C2×D23)⋊C4—24no—
69(C2×D23)⋊C4—28no—
70C4⋊Dic23—21no—
71C4×Dic23—21no—
72C23×C23C2×D412yes—
73C23×C23C2411yescharacteristic
74C22×D23—24no—
75C22×D23—24no—
76C22×D23—22no—
77C22×D23—82no—
78C22×D23C2×D414yes—
79Q8×C23—22no—
80D4×C23—24no—
81D4×C23—22no—
82C2×C4×C23—22no—
83C2×C4×C23—22no—
84C2×C4×C23—24no—
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2×D411yescharacteristic
87C2×C4×C23C2×D411yescharacteristic
88C2×C4×C23C2×D412yes—
89C2×C4×C23C2×D412yes—
90C22⋊D23—28no—
91C22⋊D23—24no—
92C22⋊D23—24no—
93C22⋊D23—84no—
94C2×Dic23—24no—
95C2×Dic23—22no—
96C2×Dic23C2×D414yes—
97D92—24no—
98D92—22no—
99D92—22no—
100D92—41no—
101D92—42no—
102D92—41no—
103D92—88no—
104C4×D23—28no—
105C4×D23—24no—
106C4×D23—24no—
107Dic46—24no—
108Dic46—22no—
109Dic46—22no—
110#3027—231nomaximal, Sylow
111C22×C23—22no—
112C22×C23—41no—
113C22×C23—42no—
114C22×C23C22×D411yescharacteristic
115C22×C23C22×D412yes—
116C2×D23—24no—
117C2×D23—44no—
118C2×D23—48no—
119C2×D23—44no—
120C2×D23—42no—
121C2×D23—84no—
122C4×C23—22no—
123C4×C23—44no—
124C4×C23#12011yescharacteristic
125C4×C23#12012yes—
126C4×C23#12011yescharacteristic
127Dic23—24no—
128Dic23—42no—
129#585—231no—
130#535—231no—
131#535—232no—
132B(4,𝔽2)—238no—
133#410—232no—
134#410D2311yescharacteristic, complemented
135C2×C23—21no—
136C2×C23—22no—
137C2×C23—42no—
138C2×C23C2×#12011yescharacteristic
139D23—44no—
140D23—82no—
1412−1+4—462no—
1422−1+4—461no—
143H(5,𝔽2)—234no—
144H(5,𝔽2)—462no—
145H(5,𝔽2)—461no—
146C2×#41—232no—
147C2×#41—464no—
148C2×#41—462no—
149C2×#41C2×D2311yescharacteristic
150C22×D4—231no—
151#127—462no—
152#127—461no—
153#124—462no—
154#124—461no—
155#121—464no—
156#121—462no—
157#120—234no—
158#120—238no—
159#117—231no—
160#117C2×D2312yescomplemented
161#99—238no—
162#99C2×D2314yescomplemented
163C23#302711yescharacteristic, complemented, Sylow
164C24—232no—
165#41—22no—
166#41—22no—
167#41—464no—
168#41—464no—
169#41—468no—
170#41—464no—
171#41—464no—
172#41—462no—
173#41—462no—
174#41—464no—
175#41—462no—
176#41—462no—
177C2×Q8—232no—
178C2×Q8—462no—
179C2×Q8—464no—
180C2×Q8D9211yescharacteristic, complemented
181C2×D4—234no—
182C2×D4—232no—
183C2×D4—462no—
184C2×D4—468no—
185C2×D4—468no—
186C2×D4—464no—
187C2×D4—464no—
188C2×D4—464no—
189C2×D4—461no—
190C2×D4—461no—
191C2×D4—462no—
192C2×D4—462no—
193C2×D4D9211yescharacteristic, complemented
194C2×D4C22×D2312yes—
195C22×C4—234no—
196C22×C4—464no—
197C22×C4D9212yescomplemented
198C22×C4C22×D2311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—461no—
201C22⋊C4—232no—
202C22⋊C4—468no—
203C22⋊C4—464no—
204C22⋊C4C22×D2314yes—
205C42—22no—
206C42—461no—
207C23—234no—
208C23—464no—
209C23—462no—
210C23—464no—
211C23—1842no—
212C23C2×D9212yes—
213C23C23×D2311yescharacteristic
214Q8—22no—
215Q8—464no—
216Q8—462no—
217Q8—462no—
218D4—24no—
219D4—22no—
220D4—464no—
221D4—468no—
222D4—464no—
223D4—464no—
224D4—462no—
225D4—462no—
226D4—921no—
227D4—921no—
228D4—922no—
229D4—1848no—
230D4—1844no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—234no—
235C2×C4—468no—
236C2×C4—464no—
237C2×C4—464no—
238C2×C4—464no—
239C2×C4—462no—
240C2×C4C2×D9212yes—
241C2×C4C2×D9211yescharacteristic
242C2×C4C2×D9211yescharacteristic
243C2×C4D4×D2312yes—
244C2×C4D4×D2312yes—
245C22—22no—
246C22—41no—
247C22—42no—
248C22—464no—
249C22—924no—
250C22—928no—
251C22—924no—
252C22—922no—
253C22—1844no—
254C22C22×D9211yescharacteristic
255C22C2×D4×D2312yes—
256C4—22no—
257C4—44no—
258C4—464no—
259C4—922no—
260C4#1062505311yescharacteristic
261C4#1062505311yescharacteristic
262C4#1062505312yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—924no—
267C2—1842no—
268C2C2×#1062505311yescharacteristic
subgroupG/H
centerC2C2×#10625053
commutator, cosocleC23×C23C24
FrattiniC23C23×D23
FittingC23×#410C2
socleC2×C23C2×#120
hypercenter#410D23
hypocenterC23#3027
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
1. #13093253C2semidirect
2. #13092986C2semidirect
3. #13092981C2semidirect
4. #13092605C2semidirect
5. #13092390C2semidirect
6. C23×#410C2semidirect
16. C22×D92C22semidirect
17. C23×#117C22semidirect
20. #10625108C22semidirect
22. #10625097C22semidirect
24. #10625053C22semidirect
27. C23×#99C22semidirect
28. #10624988C22semidirect
32. C2×Q8×C23D4semidirect
33. C2×D4×C23D4semidirect
35. C22×C4×C23D4semidirect
59. C2×D92D4semidirect
61. C2×C4×D23D4semidirect
63. C2×Dic46D4semidirect
134. #410D23semidirect
160. #117C2×D23semidirect
162. #99C2×D23semidirect
163. C23#3027semidirect
180. C2×Q8D92semidirect
193. C2×D4D92semidirect
197. C22×C4D92semidirect

Maximal subgroups

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

subgroupindex
#130932532
#130929862
#130929812
#130926052
#130923902
C23×#4102
#302723