Finite Group Databasebeta

← #15686530

Subgroups — #15686530

Order 2944.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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#135×D23C212yesmaximal, complemented
2#13092859C212yesmaximal, complemented
3#13092856C212yesmaximal, complemented
4#13092854C212yesmaximal, complemented
5#13092851C212yesmaximal, complemented
6#13092849C211yesmaximal, characteristic, complemented
7#13092847C212yesmaximal, complemented
8C2×#10624980C211yesmaximal, characteristic, complemented
9C23×#508C211yesmaximal, characteristic, complemented
10#41×D23—22no—
11C23×#135C2212yescomplemented
12#10625121—22no—
13#10625090C2212yes—
14Q16×D23C2212yescomplemented
15#10625087—22no—
16SD16×D23—22no—
17#10625083C2212yes—
18D8×D23C2212yescomplemented
19#10625075C2212yescomplemented
20C2×C8×D23C2211yescharacteristic
21C23×Q32C2211yescharacteristic, complemented
22C23×SD32C2212yescomplemented
23C23×D16C2211yescharacteristic, complemented
24C2×C16×C23C2211yescharacteristic, complemented
25#10625011C2212yescomplemented
26#10625010C2212yescomplemented
27#10625009C2212yescomplemented
28#10625008C2212yescomplemented
29C2×C23⋊C16C2211yescharacteristic, complemented
30Dic184C2211yescharacteristic, complemented
31#10624982C2212yescomplemented
32D368C2211yescharacteristic, complemented
33#10624980C2212yescomplemented
34#10624980C2212yescomplemented
35#41×C23—22no—
36#67292—22no—
37Q8×D23—22no—
38#67290—22no—
39#67290—42no—
40D4×D23—22no—
41D4×D23—42no—
42#67288—22no—
43#67288—42no—
44C2×C4×D23—42no—
45C2×C4×D23D411yescharacteristic
46Q16×C23C2312yes—
47SD16×C23—22no—
48D8×C23C2312yes—
49C2×C8×C23C2311yescharacteristic
50#67275—22no—
51#67274—22no—
52#67273—22no—
53#67272—22no—
54C2×C23⋊C8D411yescharacteristic
55Dic92C2312yes—
56D184C2312yes—
57#67263—22no—
58C8×D23D412yes—
59C8×D23C2312yes—
60C16×C23C2311yescharacteristic
61C16×C23C2311yescharacteristic
62C23⋊C16C2312yes—
63C22×D23—42no—
64C22×D23D811yescharacteristic
65Q8×C23—22no—
66D4×C23—22no—
67D4×C23—42no—
68C2×C4×C23—42no—
69C2×C4×C23C2×D411yescharacteristic
70C22⋊D23—42no—
71C22⋊D23—42no—
72C22⋊D23—42no—
73C2×Dic23—42no—
74C2×Dic23D811yescharacteristic
75D92—22no—
76D92—42no—
77C4×D23—42no—
78C4×D23—42no—
79C4×D23—42no—
80C4×D23D812yes—
81C4×D23C2×D412yes—
82Dic46—22no—
83Dic46—42no—
84C8×C23C2×D411yescharacteristic
85C8×C23C2411yescharacteristic
86C23⋊C8C2×D412yes—
87#3414—231nomaximal, Sylow
88C22×C23—42no—
89C22×C23C2×D811yescharacteristic
90C2×D23—41no—
91C2×D23—42no—
92C2×D23—84no—
93C2×D23C2×D812yes—
94C4×C23—42no—
95C4×C23C2×D811yescharacteristic
96C4×C23C22×D411yescharacteristic
97Dic23—42no—
98Dic23C2×D812yes—
99C2×#135—232no—
100#510—232no—
101#510—232no—
102#509—232no—
103#509—232no—
104#508—232no—
105#508—231no—
106#508D2311yescharacteristic, complemented
107C2×M32—231no—
108C2×C23—21no—
109C2×C23—82no—
110C2×C23C22×D811yescharacteristic
111D23—22no—
112D23—82no—
113C2×#41—462no—
114#135—232no—
115#135—232no—
116#135—232no—
117#135—462no—
118#135—462no—
119#135C2×D2312yescomplemented
120C2×Q16—232no—
121C2×SD16—462no—
122C2×D8—232no—
123C22×C8—231no—
124Q32—232no—
125Q32—231no—
126Q32C2×D2311yescharacteristic, complemented
127SD32—232no—
128SD32—232no—
129SD32—232no—
130SD32C2×D2312yescomplemented
131D16—232no—
132D16—231no—
133D16C2×D2311yescharacteristic, complemented
134M32—232no—
135M32—232no—
136C2×C16—231no—
137C2×C16C2×D2311yescharacteristic, complemented
138C23#341411yescharacteristic, complemented, Sylow
139#41—22no—
140#41—462no—
141#41—462no—
142#41—462no—
143#41—922no—
144#41—922no—
145C2×Q8—462no—
146C2×D4—462no—
147C2×D4—922no—
148C22×C4—231no—
149C22×C4—922no—
150Q16—232no—
151Q16—462no—
152Q16C22×D2312yes—
153SD16—22no—
154SD16—462no—
155SD16—462no—
156SD16—462no—
157D8—232no—
158D8—462no—
159D8C22×D2312yes—
160C2×C8—231no—
161C2×C8—232no—
162C2×C8—232no—
163C2×C8C22×D2311yescharacteristic
164C16—232no—
165C16C22×D2311yescharacteristic
166C16C22×D2311yescharacteristic
167C23—231no—
168C23—922no—
169Q8—22no—
170Q8—462no—
171Q8—922no—
172D4—22no—
173D4—42no—
174D4—462no—
175D4—922no—
176D4—922no—
177D4—922no—
178D4—922no—
179C2×C4—42no—
180C2×C4—231no—
181C2×C4—232no—
182C2×C4—232no—
183C2×C4—922no—
184C2×C4—922no—
185C2×C4—922no—
186C2×C4—922no—
187C2×C4D4×D2311yescharacteristic
188C8—232no—
189C8D4×D2311yescharacteristic
190C8C23×D2311yescharacteristic
191C22—42no—
192C22—232no—
193C22—921no—
194C22—922no—
195C22—1844no—
196C22D8×D2311yescharacteristic
197C4—42no—
198C4—232no—
199C4—922no—
200C4D8×D2311yescharacteristic
201C4C2×D4×D2311yescharacteristic
202C2—21no—
203C2—82no—
204C2—462no—
205C2—1842no—
206C2C2×D8×D2311yescharacteristic
subgroupG/H
centerC4D8×D23
commutator, cosocleC8×C23C24
FrattiniC8C23×D23
FittingC23×#508C2
socleC2×C23C22×D8
hypercenter#508D23
hypocenterC23#3414
LCSG ▷ C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D23C2semidirect
2. #13092859C2semidirect
3. #13092856C2semidirect
4. #13092854C2semidirect
5. #13092851C2semidirect
6. #13092849C2semidirect
7. #13092847C2semidirect
8. C2×#10624980C2semidirect
9. C23×#508C2semidirect
11. C23×#135C22semidirect
14. Q16×D23C22semidirect
18. D8×D23C22semidirect
19. #10625075C22semidirect
21. C23×Q32C22semidirect
22. C23×SD32C22semidirect
23. C23×D16C22semidirect
24. C2×C16×C23C22semidirect
25. #10625011C22semidirect
26. #10625010C22semidirect
27. #10625009C22semidirect
28. #10625008C22semidirect
29. C2×C23⋊C16C22semidirect
30. Dic184C22semidirect
31. #10624982C22semidirect
32. D368C22semidirect
33. #10624980C22semidirect
34. #10624980C22semidirect
106. #508D23semidirect
119. #135C2×D23semidirect
126. Q32C2×D23semidirect
130. SD32C2×D23semidirect
133. D16C2×D23semidirect
137. C2×C16C2×D23semidirect
138. C23#3414semidirect

Maximal subgroups

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

subgroupindex
#135×D232
#130928592
#130928562
#130928542
#130928512
#130928492
#130928472
C2×#106249802
C23×#5082
#341423