Finite Group Databasebeta

← #104×D373 #37559433

Subgroups — #104×D373 #37559433

Order 23872.

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×D373C211yesmaximal, characteristic
2M16×D373C211yesmaximal, characteristic, complemented
3C42×D373C211yesmaximal, characteristic, complemented
4#26045720C211yesmaximal, characteristic, complemented
5#26045719C211yesmaximal, characteristic, complemented
6#26045718C211yesmaximal, characteristic, complemented
7#104×C373C211yesmaximal, characteristic, complemented
8#20238611C411yescharacteristic, complemented
9#20238610—21no—
10#20238610C2211yescharacteristic
11#20238609—21no—
12#20238609C411yescharacteristic, complemented
13Q8×D373C411yescharacteristic, complemented
14D4×D373—21no—
15D4×D373C411yescharacteristic, complemented
16C2×C4×D373—21no—
17C2×C4×D373—21no—
18C2×C4×D373C2211yescharacteristic
19#20238594C2211yescharacteristic, complemented
20#20238593—21no—
21C8×D373—21no—
22C4×Dic373—21no—
23C4×Dic373C2211yescharacteristic, complemented
24#41×C373C2211yescharacteristic
25M16×C373C2211yescharacteristic, complemented
26C42×C373C2211yescharacteristic, complemented
27C22×D373—21no—
28C22×D373D411yescharacteristic
29Dic746—21no—
30Dic746C2×C411yescharacteristic, complemented
31D1492—21no—
32D1492C2×C411yescharacteristic, complemented
33C22⋊D373—21no—
34C22⋊D373—21no—
35C22⋊D373—21no—
36C2×Dic373—21no—
37C2×Dic373—21no—
38C2×Dic373D411yescharacteristic
39C4×D373—24no—
40C4×D373—21no—
41C4×D373—21no—
42C4×D373—21no—
43C4×D373C2×C411yescharacteristic
44C4×D373C2×C411yescharacteristic
45C4×D373D411yescharacteristic
46C4×D373D411yescharacteristic
47#15688412—21no—
48Q8×C373C2×C411yescharacteristic, complemented
49D4×C373—21no—
50D4×C373C2×C411yescharacteristic, complemented
51C2×C4×C373—21no—
52C2×C4×C373—21no—
53C2×C4×C373C2311yescharacteristic
54C8×C373—21no—
55C22×C373—21no—
56C22×C373C2×D411yescharacteristic
57C2×D373—22no—
58C2×D373—21no—
59C2×D373—42no—
60C2×D373C22⋊C411yescharacteristic
61C2×D373C22⋊C411yescharacteristic
62C4×C373—22no—
63C4×C373—21no—
64C4×C373C22×C411yescharacteristic
65C4×C373C2×D411yescharacteristic
66Dic373—22no—
67Dic373—21no—
68Dic373C22⋊C411yescharacteristic
69Dic373C22⋊C411yescharacteristic
70C2×C373—21no—
71C2×C373—41no—
72C2×C373C2×C22⋊C411yescharacteristic
73D373—21no—
74D373—41no—
75D373#10412yesdirect product factor
76C373C2×#10411yescharacteristic, complemented, Sylow
77C2×#104—3731nomaximal, Sylow
78C2×#41—3731no—
79C2×M16—3731no—
80C2×C42—3731no—
81#104—3731no—
82#104—3731no—
83#104—3731no—
84#104D37311yescharacteristic, direct product factor
85#41—3731no—
86#41—3731no—
87#41—3731no—
88#41—7461no—
89#41—7461no—
90#41C2×D37311yescharacteristic
91C2×Q8—3731no—
92C2×D4—3731no—
93C2×D4—7461no—
94C22×C4—3731no—
95C22×C4—7461no—
96C22×C4—7461no—
97M16—3731no—
98M16—7461no—
99M16C2×D37311yescharacteristic, complemented
100C2×C8—7461no—
101C42—3731no—
102C42—7461no—
103C42C2×D37311yescharacteristic, complemented
104C23—3731no—
105C23—7461no—
106Q8—3731no—
107Q8—7461no—
108Q8C4×D37311yescharacteristic, complemented
109D4—21no—
110D4—3731no—
111D4—7461no—
112D4—7461no—
113D4—7461no—
114D4—7461no—
115D4C4×D37311yescharacteristic, complemented
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—3731no—
119C2×C4—3731no—
120C2×C4—3731no—
121C2×C4—3731no—
122C2×C4—3731no—
123C2×C4—7461no—
124C2×C4—7461no—
125C2×C4—7464no—
126C2×C4—7461no—
127C2×C4—7461no—
128C2×C4—7461no—
129C2×C4C22×D37311yescharacteristic
130C8—21no—
131C8—7461no—
132C22—21no—
133C22—3731no—
134C22—3731no—
135C22—14922no—
136C22—7462no—
137C22—7461no—
138C22D4×D37311yescharacteristic
139C4—22no—
140C4—21no—
141C4—3731no—
142C4—3731no—
143C4—7462no—
144C4—7461no—
145C4C2×C4×D37311yescharacteristic
146C4D4×D37311yescharacteristic
147C2—21no—
148C2—41no—
149C2—3732no—
150C2—14921no—
151C2—7461no—
152C2C22⋊C4×D37311yescharacteristic
subgroupG/H
centerC4D4×D373
commutatorC4×C373C22×C4
FrattiniC2×C4C22×D373
Fitting#104×C373C2
socleC2×C373C2×C22⋊C4
prime radical#41×D373C2
cosocleC2×C4×C373C23
hypercenter#104D373
hypocenterC373C2×#104
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. M16×D373C2semidirect
3. C42×D373C2semidirect
4. #26045720C2semidirect
5. #26045719C2semidirect
6. #26045718C2semidirect
7. #104×C373C2semidirect
8. #20238611C4semidirect
12. #20238609C4semidirect
13. Q8×D373C4semidirect
15. D4×D373C4semidirect
19. #20238594C22semidirect
23. C4×Dic373C22semidirect
25. M16×C373C22semidirect
26. C42×C373C22semidirect
30. Dic746C2×C4semidirect
32. D1492C2×C4semidirect
48. Q8×C373C2×C4semidirect
50. D4×C373C2×C4semidirect
75. D373#104direct (N × H)
76. C373C2×#104semidirect
84. #104D373direct (N × H)
99. M16C2×D373semidirect
103. C42C2×D373semidirect
108. Q8C4×D373semidirect
115. D4C4×D373semidirect

Maximal subgroups

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

subgroupindex
#41×D3732
M16×D3732
C42×D3732
#260457202
#260457192
#260457182
#104×C3732
C2×#104373