Finite Group Databasebeta

← #15683884

Subgroups — #15683884

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×#10625120C212yesmaximal, complemented
2C22×D184C211yesmaximal, characteristic, complemented
3#13092981C212yesmaximal, complemented
4#13092803C214yesmaximal, complemented
5#13092802C212yesmaximal, complemented
6#13092792C212yesmaximal, complemented
7#13092372C211yesmaximal, characteristic, complemented
8C2×C23×#135C211yesmaximal, characteristic, complemented
9C2×#41×C23C2212yes—
10C22×D92C2212yes—
11C23×#135—24no—
12C2×Q16×C23C2211yescharacteristic, complemented
13C2×SD16×C23C2212yescomplemented
14C2×D8×C23C2211yescharacteristic, complemented
15C22×C8×C23C2211yescharacteristic
16#10625120—28no—
17#10625118C2214yescomplemented
18C2×#67274C2214yescomplemented
19#10625111C2214yescomplemented
20#10625108—24no—
21C2×#67272C2214yescomplemented
22#10625101—24no—
23#10625097C2211yescharacteristic
24C2×#67267C2211yescharacteristic
25C2×D184—24no—
26C2×D184C2212yes—
27C2×D184C2212yes—
28#10624997C2212yescomplemented
29C8×Dic23C2212yescomplemented
30C23×D23—22no—
31#41×C23—24no—
32#41×C23—24no—
33C2×Q8×C23C2312yes—
34C2×D4×C23—22no—
35C2×D4×C23C2312yes—
36C22×C4×C23—22no—
37C22×C4×C23C2311yescharacteristic
38C2×C22⋊D23—28no—
39C2×D92—24no—
40C2×D92—24no—
41C2×D92—22no—
42C2×D92C2314yes—
43Q16×C23—22no—
44SD16×C23—24no—
45D8×C23—22no—
46C2×C8×C23D414yescomplemented
47C2×C8×C23C2311yescharacteristic
48C2×C8×C23C2311yescharacteristic
49C22⋊Dic23D412yes—
50#67274—28no—
51#67272—28no—
52(C2×D23)⋊C4—28no—
53C4⋊Dic23D412yes—
54C4×Dic23C2312yes—
55#67267D414yescomplemented
56C2×C23⋊C8C2312yes—
57D184—24no—
58D184—24no—
59C23×C23—22no—
60C23×C23C2×D411yescharacteristic
61C22×D23—24no—
62C22×D23—44no—
63C22×D23—84no—
64Q8×C23—22no—
65Q8×C23—22no—
66D4×C23—22no—
67D4×C23—22no—
68D4×C23—44no—
69C2×C4×C23—22no—
70C2×C4×C23—44no—
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D412yes—
73C2×C4×C23C2×D412yes—
74C2×C4×C23C2411yescharacteristic
75C22⋊D23—88no—
76C2×Dic23C2×D414yes—
77D92—24no—
78D92—24no—
79D92—44no—
80C8×C23C2×D412yes—
81C8×C23C2×D412yes—
82C23⋊C8C2×D414yes—
83#3155—231nomaximal, Sylow
84C22×C23—22no—
85C22×C23—42no—
86C22×C23—44no—
87C22×C23#12712yes—
88C22×C23C22×D411yescharacteristic
89C2×D23—44no—
90C2×D23—48no—
91C2×D23—88no—
92C4×C23—42no—
93C4×C23#12712yes—
94C4×C23C22×D411yescharacteristic
95C4×C23C22×D411yescharacteristic
96Dic23—24no—
97C2×AGL(1,ℤ/8)—232no—
98C2×#135D2311yescharacteristic, complemented
99C22×D8—231no—
100#535—232no—
101#496—234no—
102#495—232no—
103#493—232no—
104#405—231no—
105C2×C23—22no—
106C2×C23—82no—
107C2×C23C2×#12711yescharacteristic
108C2×C23#57612yes—
109D23—84no—
110C2×#41C2×D2312yes—
111C22×D4—232no—
112AGL(1,ℤ/8)—468no—
113#135—24no—
114C2×Q16C2×D2311yescharacteristic, complemented
115C2×SD16—234no—
116C2×SD16C2×D2312yescomplemented
117C2×D8—234no—
118C2×D8—232no—
119C2×D8—232no—
120C2×D8—464no—
121C2×D8C2×D2311yescharacteristic, complemented
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—462no—
133#41—24no—
134#41—24no—
135C2×Q8C22×D2312yes—
136C2×D4—22no—
137C2×D4—234no—
138C2×D4—468no—
139C2×D4—464no—
140C2×D4—462no—
141C2×D4—464no—
142C2×D4C22×D2312yes—
143C22×C4—22no—
144C22×C4C22×D2311yescharacteristic
145Q16—22no—
146SD16—24no—
147SD16—468no—
148D8—22no—
149D8—468no—
150D8—464no—
151D8—464no—
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—22no—
162C23—464no—
163C23—924no—
164C23—1844no—
165C23D4×D2311yescharacteristic
166Q8—22no—
167Q8—22no—
168D4—22no—
169D4—22no—
170D4—44no—
171D4—464no—
172D4—464no—
173D4—924no—
174D4—1848no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—234no—
178C2×C4D4×D2311yescharacteristic
179C2×C4D4×D2312yes—
180C2×C4C2×C22⋊D2312yes—
181C2×C4C23×D2311yescharacteristic
182C8—234no—
183C8C2×C22⋊D2312yes—
184C8C2×C22⋊D2312yes—
185C22—22no—
186C22—42no—
187C22—44no—
188C22—924no—
189C22—928no—
190C22—1848no—
191C22#1062511112yes—
192C22C2×D4×D2311yescharacteristic
193C4—42no—
194C4—464no—
195C4#1062511112yes—
196C4C2×D4×D2311yescharacteristic
197C4C22×C22⋊D2311yescharacteristic
198C2—22no—
199C2—82no—
200C2—1844no—
201C2C2×#1062511111yescharacteristic
202C2#1309321912yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#135C2
socleC22×C23C22×D4
hypercenterC2×#135D23
hypocenterC23#3155
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#10625120C2semidirect
2. C22×D184C2semidirect
3. #13092981C2semidirect
4. #13092803C2semidirect
5. #13092802C2semidirect
6. #13092792C2semidirect
7. #13092372C2semidirect
8. C2×C23×#135C2semidirect
12. C2×Q16×C23C22semidirect
13. C2×SD16×C23C22semidirect
14. C2×D8×C23C22semidirect
17. #10625118C22semidirect
18. C2×#67274C22semidirect
19. #10625111C22semidirect
21. C2×#67272C22semidirect
28. #10624997C22semidirect
29. C8×Dic23C22semidirect
46. C2×C8×C23D4semidirect
55. #67267D4semidirect
98. C2×#135D23semidirect
114. C2×Q16C2×D23semidirect
116. C2×SD16C2×D23semidirect
121. C2×D8C2×D23semidirect
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×#106251202
C22×D1842
#130929812
#130928032
#130928022
#130927922
#130923722
C2×C23×#1352
#315523