Finite Group Databasebeta

← #104×D23 #13092428

Subgroups — #104×D23 #13092428

Order 1472.

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

normal subgroups only

This group has 170 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#41×D23C211yesmaximal, characteristic
2M16×D23C211yesmaximal, characteristic, complemented
3C42×D23C211yesmaximal, characteristic, complemented
4C23×#104C211yesmaximal, characteristic, complemented
5#10625019C211yesmaximal, characteristic, complemented
6#10625007C211yesmaximal, characteristic, complemented
7#10624987C211yesmaximal, characteristic, complemented
8#41×C23C2211yescharacteristic
9#67292C411yescharacteristic, complemented
10Q8×D23C411yescharacteristic, complemented
11#67290—21no—
12#67290C411yescharacteristic, complemented
13D4×D23—21no—
14D4×D23C411yescharacteristic, complemented
15#67288—21no—
16#67288C2211yescharacteristic
17C2×C4×D23—21no—
18C2×C4×D23—21no—
19C2×C4×D23C2211yescharacteristic
20M16×C23C2211yescharacteristic, complemented
21C42×C23C2211yescharacteristic, complemented
22C4×Dic23—21no—
23C4×Dic23C2211yescharacteristic, complemented
24#67267C2211yescharacteristic, complemented
25#67262—21no—
26C8×D23—21no—
27C22×D23—21no—
28C22×D23D411yescharacteristic
29Q8×C23C2×C411yescharacteristic, complemented
30D4×C23—21no—
31D4×C23C2×C411yescharacteristic, complemented
32C2×C4×C23—21no—
33C2×C4×C23—21no—
34C2×C4×C23C2311yescharacteristic
35C22⋊D23—21no—
36C22⋊D23—21no—
37C22⋊D23—21no—
38C2×Dic23—21no—
39C2×Dic23—21no—
40C2×Dic23D411yescharacteristic
41D92—21no—
42D92C2×C411yescharacteristic, complemented
43C4×D23—24no—
44C4×D23—21no—
45C4×D23—21no—
46C4×D23—21no—
47C4×D23C2×C411yescharacteristic
48C4×D23C2×C411yescharacteristic
49C4×D23D411yescharacteristic
50C4×D23D411yescharacteristic
51Dic46—21no—
52Dic46C2×C411yescharacteristic, complemented
53C8×C23—21no—
54C23⋊C8—21no—
55C22×C23—21no—
56C22×C23C2×D411yescharacteristic
57C2×D23—22no—
58C2×D23—21no—
59C2×D23—42no—
60C2×D23C22⋊C411yescharacteristic
61C2×D23C22⋊C411yescharacteristic
62C4×C23—22no—
63C4×C23—21no—
64C4×C23C22×C411yescharacteristic
65C4×C23C2×D411yescharacteristic
66Dic23—22no—
67Dic23—21no—
68Dic23C22⋊C411yescharacteristic
69Dic23C22⋊C411yescharacteristic
70C2×#104—231nomaximal, Sylow
71C2×C23—21no—
72C2×C23—41no—
73C2×C23C2×C22⋊C411yescharacteristic
74D23—21no—
75D23—41no—
76D23#10412yesdirect product factor
77C2×#41—231no—
78C2×M16—231no—
79C2×C42—231no—
80#104—231no—
81#104—231no—
82#104—231no—
83#104D2311yescharacteristic, direct product factor
84C23C2×#10411yescharacteristic, complemented, Sylow
85#41—231no—
86#41—231no—
87#41—231no—
88#41—461no—
89#41—461no—
90#41C2×D2311yescharacteristic
91C2×Q8—231no—
92C2×D4—231no—
93C2×D4—461no—
94C22×C4—231no—
95C22×C4—461no—
96C22×C4—461no—
97M16—231no—
98M16—461no—
99M16C2×D2311yescharacteristic, complemented
100C2×C8—461no—
101C42—231no—
102C42—461no—
103C42C2×D2311yescharacteristic, complemented
104C23—231no—
105C23—461no—
106Q8—231no—
107Q8—461no—
108Q8C4×D2311yescharacteristic, complemented
109D4—21no—
110D4—231no—
111D4—461no—
112D4—461no—
113D4—461no—
114D4—461no—
115D4C4×D2311yescharacteristic, complemented
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—231no—
119C2×C4—231no—
120C2×C4—231no—
121C2×C4—231no—
122C2×C4—231no—
123C2×C4—461no—
124C2×C4—461no—
125C2×C4—464no—
126C2×C4—461no—
127C2×C4—461no—
128C2×C4—461no—
129C2×C4C22×D2311yescharacteristic
130C8—21no—
131C8—461no—
132C22—21no—
133C22—231no—
134C22—231no—
135C22—462no—
136C22—461no—
137C22—922no—
138C22D4×D2311yescharacteristic
139C4—22no—
140C4—21no—
141C4—231no—
142C4—231no—
143C4—462no—
144C4—461no—
145C4C2×C4×D2311yescharacteristic
146C4D4×D2311yescharacteristic
147C2—21no—
148C2—41no—
149C2—232no—
150C2—461no—
151C2—921no—
152C2C22⋊C4×D2311yescharacteristic
subgroupG/H
centerC4D4×D23
commutatorC4×C23C22×C4
FrattiniC2×C4C22×D23
FittingC23×#104C2
socleC2×C23C2×C22⋊C4
prime radical#41×D23C2
cosocleC2×C4×C23C23
hypercenter#104D23
hypocenterC23C2×#104
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D23C2semidirect
3. C42×D23C2semidirect
4. C23×#104C2semidirect
5. #10625019C2semidirect
6. #10625007C2semidirect
7. #10624987C2semidirect
9. #67292C4semidirect
10. Q8×D23C4semidirect
12. #67290C4semidirect
14. D4×D23C4semidirect
20. M16×C23C22semidirect
21. C42×C23C22semidirect
23. C4×Dic23C22semidirect
24. #67267C22semidirect
29. Q8×C23C2×C4semidirect
31. D4×C23C2×C4semidirect
42. D92C2×C4semidirect
52. Dic46C2×C4semidirect
76. D23#104direct (N × H)
83. #104D23direct (N × H)
84. C23C2×#104semidirect
99. M16C2×D23semidirect
103. C42C2×D23semidirect
108. Q8C4×D23semidirect
115. D4C4×D23semidirect

Maximal subgroups

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

subgroupindex
#41×D232
M16×D232
C42×D232
C23×#1042
#106250192
#106250072
#106249872
C2×#10423