Finite Group Databasebeta

← #15675343

Subgroups — #15675343

Order 2944.

226 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 53 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#13092852C212yesmaximal, complemented
2#13092670C211yesmaximal, characteristic, complemented
3#13092227C212yesmaximal, complemented
4#13092199C211yesmaximal, characteristic, complemented
5C23×#575C211yesmaximal, characteristic, complemented
6C2×#41×C23—21no—
7C23×#137—22no—
8C23×AGL(1,ℤ/8)—22no—
9C23×#135—21no—
10C23×#135C2212yes—
11C2×M16×C23C2211yescharacteristic
12#10625101—21no—
13C2×D184C2211yescharacteristic, complemented
14#10625010—22no—
15#10625008—22no—
16#10625003—21no—
17#10624999C2211yescharacteristic, complemented
18#10624994C2212yescomplemented
19#41×C23—22no—
20#41×C23—22no—
21#41×C23—41no—
22#41×C23—41no—
23C2×Q8×C23—21no—
24C2×D4×C23—21no—
25C2×D4×C23—41no—
26C22×C4×C23—41no—
27C22×C4×C23D411yescharacteristic
28C2×C22⋊D23—41no—
29C2×D92—21no—
30Q16×C23—21no—
31Q16×C23D412yescomplemented
32SD16×C23—22no—
33SD16×C23—22no—
34D8×C23—21no—
35D8×C23D412yescomplemented
36M16×C23—22no—
37C2×C8×C23D411yescharacteristic
38C2×C8×C23C2311yescharacteristic
39(C2×D23)⋊C4—41no—
40C4⋊Dic23—21no—
41D184—22no—
42C23⋊C16—22no—
43C23×C23—41no—
44C23×C23D811yescharacteristic
45C22×D23—41no—
46Q8×C23—22no—
47Q8×C23—41no—
48D4×C23—22no—
49D4×C23—41no—
50D4×C23—42no—
51D4×C23—42no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—42no—
55C2×C4×C23—41no—
56C2×C4×C23—42no—
57C2×C4×C23D811yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C22⋊D23—82no—
60C2×Dic23—41no—
61D92—41no—
62D92—41no—
63C8×C23—21no—
64C8×C23C2×D412yes—
65#2190—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—41no—
68C22×C23—42no—
69C22×C23—82no—
70C22×C23C2×D811yescharacteristic
71C2×D23—81no—
72C2×D23—81no—
73C2×D23—81no—
74C4×C23—21no—
75C4×C23—42no—
76C4×C23#12011yescharacteristic
77C4×C23AGL(1,ℤ/8)11yescharacteristic
78Dic23—81no—
79#575D2311yescharacteristic, complemented
80#509—232no—
81#469—231no—
82#360—232no—
83#349—231no—
84C2×C23—21no—
85C2×C23—41no—
86C2×C23—82no—
87C2×C23#44711yescharacteristic
88D23—161no—
89C2×#41—21no—
90#137—22no—
91AGL(1,ℤ/8)—22no—
92#135—21no—
93#135C2×D2312yes—
94C2×D8—231no—
95C2×M16C2×D2311yescharacteristic
96#121—461no—
97SD32—462no—
98D16—462no—
99M32—232no—
100#106—231no—
101#102—461no—
102C23#219011yescharacteristic, complemented, Sylow
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—461no—
111C2×D4—921no—
112C22×C4—41no—
113C22×C4C22⋊D2311yescharacteristic
114Q16—21no—
115Q16C22⋊D2312yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—462no—
120D8C22⋊D2312yescomplemented
121M16—22no—
122C2×C8C22⋊D2311yescharacteristic
123C2×C8C22×D2311yescharacteristic
124C4⋊C4—461no—
125C22⋊C4—921no—
126C16—462no—
127C23—41no—
128C23—921no—
129C23#6727211yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—921no—
137D4—921no—
138D4—1842no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—921no—
145C2×C4#6727211yescharacteristic
146C2×C4C2×C22⋊D2311yescharacteristic
147C8—21no—
148C8C2×C22⋊D2312yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—1841no—
154C22—1841no—
155C22—1841no—
156C22C2×#6727211yescharacteristic
157C4—21no—
158C4—42no—
159C4—1841no—
160C4#1062510311yescharacteristic
161C4#1062512411yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—3681no—
166C2#1309255111yescharacteristic
subgroupG/H
centerC2#13092551
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#575C2
socleC2×C23#447
hypercenter#575D23
hypocenterC23#2190
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #13092852C2semidirect
2. #13092670C2semidirect
3. #13092227C2semidirect
4. #13092199C2semidirect
5. C23×#575C2semidirect
13. C2×D184C22semidirect
17. #10624999C22semidirect
18. #10624994C22semidirect
31. Q16×C23D4semidirect
35. D8×C23D4semidirect
79. #575D23semidirect
102. C23#2190semidirect
115. Q16C22⋊D23semidirect
120. D8C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130928522
#130926702
#130922272
#130921992
C23×#5752
#219023