Finite Group Databasebeta

← #15682761

Subgroups — #15682761

Order 2944.

698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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#13093215C212yesmaximal, complemented
2#13092991C211yesmaximal, characteristic, complemented
3#13092600C214yesmaximal, complemented
4#13092590C214yesmaximal, complemented
5#13092434C212yesmaximal, complemented
6C2×#10625018C211yesmaximal, characteristic, complemented
7C2×C23×2−1+4C211yesmaximal, characteristic, complemented
8C23×2−1+4—24no—
9C23×2−1+4—22no—
10C23×2−1+4C2214yes—
11C2×#41×C23—22no—
12C2×#41×C23—22no—
13C2×#41×C23C2212yes—
14C22×Q8×C23—22no—
15C22×Q8×C23C2211yescharacteristic
16C2×#67288C2211yescharacteristic
17#10625122C2214yescomplemented
18#10625121—24no—
19#10625120C2214yescomplemented
20#10625118C2212yescomplemented
21#10625117—22no—
22#10625115C2212yescomplemented
23#10625113—22no—
24#10625103—22no—
25#10625100—22no—
26#10625097C2211yescharacteristic
27C2×#67267C2212yes—
28#10625019C2218yescomplemented
29#10625018C2214yescomplemented
30#41×C23—28no—
31#41×C23—28no—
32#41×C23—28no—
33#41×C23—28no—
34#41×C23—22no—
35#41×C23—22no—
36#41×C23D414yes—
37#41×C23C2314yes—
38C2×Q8×C23—22no—
39C2×Q8×C23—28no—
40C2×Q8×C23—28no—
41C2×Q8×C23—22no—
42C2×Q8×C23—22no—
43C2×Q8×C23D412yes—
44C2×Q8×C23D412yes—
45C2×Q8×C23C2312yes—
46C2×D4×C23—22no—
47C2×D4×C23—22no—
48C2×D4×C23D412yes—
49C22×C4×C23—24no—
50C22×C4×C23—22no—
51C22×C4×C23D412yes—
52C22×C4×C23C2311yescharacteristic
53C2×C22⋊D23—21no—
54#67288—22no—
55#67288—22no—
56C2×D92C2311yescharacteristic
57C2×C4×D23—21no—
58C2×Dic46C2311yescharacteristic
59C22⋊Dic23—21no—
60#67275—24no—
61#67274—24no—
62#67273—24no—
63#67272—24no—
64(C2×D23)⋊C4—24no—
65C4⋊Dic23—21no—
66Dic23⋊C4—24no—
67C4×Dic23C2312yes—
68#67267—22no—
69#67267C2314yes—
70C2×C23⋊C8—22no—
71C23×C23—22no—
72C23×C23C2×D411yescharacteristic
73C22×D23—21no—
74Q8×C23—28no—
75Q8×C23—22no—
76Q8×C23—24no—
77Q8×C23—24no—
78Q8×C23C2×D414yes—
79D4×C23—28no—
80D4×C23—24no—
81D4×C23—24no—
82D4×C23—22no—
83D4×C23C2×D414yes—
84C2×C4×C23—216no—
85C2×C4×C23—22no—
86C2×C4×C23—22no—
87C2×C4×C23—22no—
88C2×C4×C23—24no—
89C2×C4×C23—24no—
90C2×C4×C23C2×D414yes—
91C2×C4×C23C2×D411yescharacteristic
92C2×C4×C23C2×D412yes—
93C2×C4×C23C2×D412yes—
94C2×C4×C23C2411yescharacteristic
95C22⋊D23—41no—
96C22⋊D23—41no—
97C2×Dic23—22no—
98C2×Dic23—21no—
99D92—22no—
100C4×D23—42no—
101Dic46—22no—
102C23⋊C8—24no—
103#3020—231nomaximal, Sylow
104C22×C23—24no—
105C22×C23—41no—
106C22×C23—44no—
107C22×C23#12011yescharacteristic
108C22×C23#12011yescharacteristic
109C22×C23C22×D411yescharacteristic
110C2×D23—42no—
111C2×D23—41no—
112C4×C23—24no—
113C4×C23—24no—
114C4×C23#12012yes—
115C4×C23C22×D412yes—
116Dic23—42no—
117Dic23—41no—
118C2×2−1+4D2311yescharacteristic, complemented
119#575—232no—
120#536—231no—
121#456—234no—
122#454—234no—
123#421—232no—
124C2×#101—231no—
125C2×C23—21no—
126C2×C23—21no—
127C2×C23—21no—
128C2×C23—44no—
129C2×C23C2×#12011yescharacteristic
130D23—81no—
1312−1+4—24no—
1322−1+4—22no—
1332−1+4C2×D2314yes—
134C2×#41—22no—
135C2×#41—22no—
136C2×#41—231no—
137C2×#41C2×D2312yes—
138C22×Q8—22no—
139C22×Q8C2×D2311yescharacteristic
140#137—234no—
141#137—462no—
142AGL(1,ℤ/8)—234no—
143AGL(1,ℤ/8)—462no—
144#135—464no—
145C2×M16—232no—
146C4⋊Q8—232no—
147#124—232no—
148#123—462no—
149C22⋊Q8—462no—
150#117—231no—
151#104—238no—
152#101—234no—
153C23#302011yescharacteristic, complemented, Sylow
154#41—28no—
155#41—28no—
156#41—28no—
157#41—28no—
158#41—22no—
159#41—22no—
160#41—462no—
161#41—462no—
162#41C22⋊D2314yes—
163#41C22×D2314yes—
164C2×Q8—22no—
165C2×Q8—28no—
166C2×Q8—28no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—231no—
170C2×Q8C22⋊D2312yes—
171C2×Q8C22⋊D2312yes—
172C2×Q8C22×D2312yes—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—231no—
176C2×D4—461no—
177C2×D4C22⋊D2312yes—
178C22×C4—24no—
179C22×C4—22no—
180C22×C4—461no—
181C22×C4C22⋊D2312yes—
182C22×C4C22×D2311yescharacteristic
183Q16—464no—
184SD16—464no—
185SD16—464no—
186D8—464no—
187M16—234no—
188M16—462no—
189C2×C8—462no—
190C4⋊C4—461no—
191C4⋊C4—464no—
192C22⋊C4—461no—
193C22⋊C4—464no—
194C42—232no—
195C23—22no—
196C23—461no—
197C23C2×C22⋊D2311yescharacteristic
198Q8—28no—
199Q8—22no—
200Q8—24no—
201Q8—24no—
202Q8—462no—
203Q8C2×C22⋊D2314yes—
204D4—28no—
205D4—24no—
206D4—24no—
207D4—22no—
208D4—462no—
209D4—921no—
210D4—921no—
211D4C2×C22⋊D2314yes—
212C2×C4—216no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—24no—
218C2×C4—462no—
219C2×C4—461no—
220C2×C4—922no—
221C2×C4C2×C22⋊D2314yes—
222C2×C4C2×C22⋊D2311yescharacteristic
223C2×C4C2×C22⋊D2312yes—
224C2×C4C2×C22⋊D2312yes—
225C2×C4C23×D2311yescharacteristic
226C8—464no—
227C22—24no—
228C22—41no—
229C22—44no—
230C22—922no—
231C22—921no—
232C22#1062512411yescharacteristic
233C22#1062512411yescharacteristic
234C22C22×C22⋊D2311yescharacteristic
235C4—24no—
236C4—24no—
237C4—922no—
238C4—921no—
239C4#1062512412yes—
240C4C22×C22⋊D2312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—44no—
245C2—1841no—
246C2C2×#1062512411yescharacteristic
subgroupG/H
centerC2C2×#10625124
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×2−1+4C2
socleC2×C23C2×#120
hypercenterC2×2−1+4D23
hypocenterC23#3020
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #13093215C2semidirect
2. #13092991C2semidirect
3. #13092600C2semidirect
4. #13092590C2semidirect
5. #13092434C2semidirect
6. C2×#10625018C2semidirect
7. C2×C23×2−1+4C2semidirect
17. #10625122C22semidirect
19. #10625120C22semidirect
20. #10625118C22semidirect
22. #10625115C22semidirect
28. #10625019C22semidirect
29. #10625018C22semidirect
118. C2×2−1+4D23semidirect
153. C23#3020semidirect

Maximal subgroups

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

subgroupindex
#130932152
#130929912
#130926002
#130925902
#130924342
C2×#106250182
C2×C23×2−1+42
#302023