Finite Group Databasebeta

← #15675348

Subgroups — #15675348

Order 2944.

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

normal subgroups only

This group has 216 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#13092857C212yesmaximal, complemented
2#13092675C211yesmaximal, characteristic, complemented
3#13092227C212yesmaximal, complemented
4#13092199C211yesmaximal, characteristic, complemented
5C23×#575C211yesmaximal, characteristic
6C2×#41×C23—21no—
7C23×#137—22no—
8C23×AGL(1,ℤ/8)—22no—
9C23×#135—21no—
10C23×#135C2212yes—
11C2×M16×C23C2211yescharacteristic
12#10625095—21no—
13C2×Dic92C2211yescharacteristic, complemented
14#10625011—22no—
15#10625009—22no—
16#10624999C2211yescharacteristic, complemented
17#10624998—21no—
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×Dic46—21no—
29Q16×C23—21no—
30Q16×C23D412yes—
31SD16×C23—22no—
32SD16×C23—22no—
33D8×C23—21no—
34D8×C23D412yes—
35M16×C23—22no—
36C2×C8×C23D411yescharacteristic
37C2×C8×C23C2311yescharacteristic
38C22⋊Dic23—41no—
39C4⋊Dic23—21no—
40Dic23⋊C4—41no—
41Dic92—22no—
42C23⋊C16—22no—
43C23×C23—41no—
44C23×C23D811yescharacteristic
45Q8×C23—22no—
46Q8×C23—41no—
47D4×C23—22no—
48D4×C23—41no—
49D4×C23—42no—
50D4×C23—42no—
51C2×C4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—42no—
54C2×C4×C23—41no—
55C2×C4×C23—42no—
56C2×C4×C23D811yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×Dic23—41no—
59C2×Dic23—41no—
60Dic46—41no—
61Dic46—41no—
62C8×C23—21no—
63C8×C23C2×D412yes—
64#2191—231nomaximal, Sylow
65C22×C23—21no—
66C22×C23—41no—
67C22×C23—42no—
68C22×C23—82no—
69C22×C23C2×D811yescharacteristic
70C4×C23—21no—
71C4×C23—42no—
72C4×C23#12011yescharacteristic
73C4×C23AGL(1,ℤ/8)11yescharacteristic
74Dic23—81no—
75Dic23—81no—
76#575D2311yescharacteristic
77#510—232no—
78#470—231no—
79#360—232no—
80#349—231no—
81C2×C23—21no—
82C2×C23—41no—
83C2×C23—82no—
84C2×C23#44711yescharacteristic
85C2×#41—21no—
86#137—22no—
87AGL(1,ℤ/8)—22no—
88#135—21no—
89#135C2×D2312yes—
90C2×Q16—231no—
91C2×M16C2×D2311yescharacteristic
92C22⋊Q8—461no—
93Q32—462no—
94SD32—462no—
95M32—232no—
96#106—231no—
97#103—461no—
98C23#219111yescharacteristic, complemented, Sylow
99#41—22no—
100#41—22no—
101#41—41no—
102#41—41no—
103C2×Q8—21no—
104C2×Q8—461no—
105C2×D4—21no—
106C2×D4—41no—
107C22×C4—41no—
108C22×C4C22⋊D2311yescharacteristic
109Q16—21no—
110Q16—462no—
111Q16C22⋊D2312yes—
112SD16—22no—
113SD16—22no—
114D8—21no—
115D8C22⋊D2312yes—
116M16—22no—
117C2×C8C22⋊D2311yescharacteristic
118C2×C8C22×D2311yescharacteristic
119C4⋊C4—461no—
120C4⋊C4—921no—
121C22⋊C4—921no—
122C16—462no—
123C23—41no—
124C23#6727211yescharacteristic
125Q8—22no—
126Q8—41no—
127Q8—921no—
128Q8—921no—
129D4—22no—
130D4—41no—
131D4—42no—
132D4—42no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—42no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—921no—
139C2×C4—921no—
140C2×C4#6727211yescharacteristic
141C2×C4C2×C22⋊D2311yescharacteristic
142C8—21no—
143C8C2×C22⋊D2312yes—
144C22—21no—
145C22—41no—
146C22—42no—
147C22—82no—
148C22C2×#6727211yescharacteristic
149C4—21no—
150C4—42no—
151C4—1841no—
152C4—1841no—
153C4#1062510311yescharacteristic
154C4#1062512411yescharacteristic
155C2—21no—
156C2—41no—
157C2—82no—
158C2#1309255111yescharacteristic
subgroupG/H
centerC2#13092551
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
Fitting, prime radicalC23×#575C2
socleC2×C23#447
hypercenter#575D23
hypocenterC23#2191
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. #13092857C2semidirect
2. #13092675C2semidirect
3. #13092227C2semidirect
4. #13092199C2semidirect
13. C2×Dic92C22semidirect
16. #10624999C22semidirect
18. #10624994C22semidirect
98. C23#2191semidirect

Maximal subgroups

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

subgroupindex
#130928572
#130926752
#130922272
#130921992
C23×#5752
#219123