Finite Group Databasebeta

← #15683878

Subgroups — #15683878

Order 2944.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#10625103C212yesmaximal, complemented
2C2×#10625075C211yesmaximal, characteristic, complemented
3#13092984C212yesmaximal, complemented
4#13092805C214yesmaximal, complemented
5#13092800C212yesmaximal, complemented
6#13092792C212yesmaximal, complemented
7#13092372C211yesmaximal, characteristic, complemented
8C22×D8×C23C211yesmaximal, characteristic, complemented
9C22×D4×C23C2212yes—
10C2×#67288C2212yes—
11C2×D8×C23—24no—
12C2×D8×C23C2212yes—
13C2×D8×C23C2212yes—
14C22×C8×C23C2211yescharacteristic
15#10625124—24no—
16#10625111C2214yescomplemented
17#10625109—24no—
18#10625107C2214yescomplemented
19C2×#67273C2214yescomplemented
20#10625103—28no—
21C2×#67272C2214yescomplemented
22#10625097C2211yescharacteristic
23C2×#67267C2211yescharacteristic
24C2×Dic92C2211yescharacteristic, complemented
25#10625075—24no—
26C2×D184C2211yescharacteristic, complemented
27C2×#67263C2212yescomplemented
28#10624997C2212yescomplemented
29C8×Dic23C2212yescomplemented
30C24×C23—22no—
31C2×D4×C23—24no—
32C2×D4×C23—24no—
33C2×D4×C23—22no—
34C2×D4×C23C2314yes—
35C22×C4×C23C2311yescharacteristic
36C2×C22⋊D23—22no—
37C2×C22⋊D23—28no—
38#67288—24no—
39#67288—24no—
40C2×D92C2312yes—
41C2×C4×D23—22no—
42C2×Dic46C2312yes—
43D8×C23—24no—
44D8×C23—24no—
45C2×C8×C23D414yescomplemented
46C2×C8×C23C2311yescharacteristic
47C2×C8×C23C2311yescharacteristic
48C22⋊Dic23—28no—
49C22⋊Dic23D412yes—
50#67273—28no—
51#67272—28no—
52C4⋊Dic23D412yes—
53C4×Dic23C2312yes—
54#67267D414yescomplemented
55C2×C23⋊C8C2312yes—
56Dic92—22no—
57D184—22no—
58#67263—24no—
59C23×C23—24no—
60C23×C23—44no—
61C23×C23—84no—
62C23×C23C2×D411yescharacteristic
63C22×D23—22no—
64D4×C23—24no—
65D4×C23—24no—
66D4×C23—44no—
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D412yes—
69C2×C4×C23C2×D412yes—
70C2×C4×C23C2411yescharacteristic
71C22⋊D23—44no—
72C22⋊D23—88no—
73C2×Dic23—22no—
74C2×Dic23C2×D414yes—
75D92—22no—
76D92—22no—
77C4×D23—44no—
78Dic46—22no—
79Dic46—22no—
80C8×C23C2×D412yes—
81C8×C23C2×D412yes—
82C23⋊C8C2×D414yes—
83#3155—231nomaximal, Sylow
84C22×C23—22no—
85C22×C23—44no—
86C22×C23—48no—
87C22×C23—88no—
88C22×C23#12712yes—
89C22×C23C22×D411yescharacteristic
90C2×D23—42no—
91C2×D23—44no—
92C4×C23#12712yes—
93C4×C23C22×D411yescharacteristic
94C4×C23C22×D411yescharacteristic
95Dic23—24no—
96Dic23—42no—
97C2×AGL(1,ℤ/8)—232no—
98C2×#135—231no—
99C22×D8D2311yescharacteristic, complemented
100#535—232no—
101#496—234no—
102#495—232no—
103#493—232no—
104#405—231no—
105C2×C23—22no—
106C2×C23—84no—
107C2×C23C2×#12711yescharacteristic
108C2×C23#57612yes—
109D23—82no—
110C2×#41—232no—
111C22×D4C2×D2312yes—
112AGL(1,ℤ/8)—468no—
113#135—464no—
114C2×Q16—231no—
115C2×SD16—234no—
116C2×SD16—232no—
117C2×D8—24no—
118C2×D8—234no—
119C2×D8—231no—
120C2×D8C2×D2312yes—
121C2×D8C2×D2312yes—
122C2×M16—231no—
123C22×C8C2×D2311yescharacteristic
124#127—234no—
125#124—234no—
126#121—464no—
127#120—464no—
128#117—231no—
129#97—232no—
130C4×C8—232no—
131C23#315511yescharacteristic, complemented, Sylow
132C24—22no—
133#41—464no—
134#41—464no—
135C2×Q8—232no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—232no—
140C2×D4—468no—
141C2×D4—462no—
142C2×D4C22×D2314yes—
143C22×C4—462no—
144C22×C4C22×D2311yescharacteristic
145Q16—462no—
146SD16—468no—
147SD16—464no—
148D8—24no—
149D8—24no—
150D8—468no—
151D8—462no—
152M16—234no—
153C2×C8—232no—
154C2×C8C22⋊D2314yescomplemented
155C2×C8C22×D2311yescharacteristic
156C2×C8C22×D2311yescharacteristic
157C4⋊C4—232no—
158C22⋊C4—232no—
159C22⋊C4—468no—
160C42—232no—
161C23—24no—
162C23—44no—
163C23—84no—
164C23—462no—
165C23D4×D2311yescharacteristic
166Q8—462no—
167Q8—462no—
168D4—24no—
169D4—24no—
170D4—44no—
171D4—462no—
172D4—462no—
173D4—924no—
174D4—1848no—
175C2×C4—234no—
176C2×C4—462no—
177C2×C4—924no—
178C2×C4D4×D2311yescharacteristic
179C2×C4D4×D2312yes—
180C2×C4C2×C22⋊D2312yes—
181C2×C4C23×D2311yescharacteristic
182C8—234no—
183C8C2×C22⋊D2312yes—
184C8C2×C22⋊D2312yes—
185C22—22no—
186C22—44no—
187C22—48no—
188C22—88no—
189C22—922no—
190C22—924no—
191C22#1062511112yes—
192C22C2×D4×D2311yescharacteristic
193C4—464no—
194C4—922no—
195C4#1062511112yes—
196C4C2×D4×D2311yescharacteristic
197C4C22×C22⋊D2311yescharacteristic
198C2—22no—
199C2—84no—
200C2—1842no—
201C2C2×#1062511111yescharacteristic
202C2#1309321812yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC22×D8×C23C2
socleC22×C23C22×D4
hypercenterC22×D8D23
hypocenterC23#3155
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C2×#10625075C2semidirect
3. #13092984C2semidirect
4. #13092805C2semidirect
5. #13092800C2semidirect
6. #13092792C2semidirect
7. #13092372C2semidirect
8. C22×D8×C23C2semidirect
16. #10625111C22semidirect
18. #10625107C22semidirect
19. C2×#67273C22semidirect
21. C2×#67272C22semidirect
24. C2×Dic92C22semidirect
26. C2×D184C22semidirect
27. C2×#67263C22semidirect
28. #10624997C22semidirect
29. C8×Dic23C22semidirect
45. C2×C8×C23D4semidirect
54. #67267D4semidirect
99. C22×D8D23semidirect
131. C23#3155semidirect
154. C2×C8C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C2×#106250752
#130929842
#130928052
#130928002
#130927922
#130923722
C22×D8×C232
#315523