Finite Group Databasebeta

← C37×#7348 #22628601

Subgroups — C37×#7348 #22628601

Order 9472.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C37×#1820C211yesmaximal, characteristic
2C37×#1317C212yesmaximal
3C2×#117×C37C411yescharacteristic
4C37×#381C411yescharacteristic
5C37×#381C2211yescharacteristic
6C37×#342—22no—
7C37×#323—22no—
8C23×C4×C37C2×C411yescharacteristic
9#117×C37—41no—
10#117×C37—41no—
11C2×C4⋊C4×C37—21no—
12C2×C22⋊C4×C37—21no—
13C2×C22⋊C4×C37—21no—
14C2×C22⋊C4×C37D412yes—
15C2×C42×C37C812yescomplemented
16C22⋊C8×C37—42no—
17#95×C37—41no—
18#95×C37—41no—
19C24×C37C22⋊C411yescharacteristic
20C22×C4×C37—21no—
21C22×C4×C37—21no—
22C22×C4×C37—22no—
23C22×C4×C37—22no—
24C22×C4×C37—42no—
25C22×C4×C37—41no—
26C22×C4×C37C2×C811yescharacteristic
27C22×C4×C37M1611yescharacteristic
28C2×C8×C37—82no—
29C4⋊C4×C37—42no—
30C22⋊C4×C37—41no—
31C22⋊C4×C37—41no—
32C22⋊C4×C37—42no—
33C22⋊C4×C37—42no—
34C42×C37—42no—
35C23×C37—22no—
36C23×C37—81no—
37C23×C37C22⋊C811yescharacteristic
38C23×C37#9911yescharacteristic
39C23×C37#10011yescharacteristic
40C2×C4×C37—21no—
41C2×C4×C37—21no—
42C2×C4×C37—42no—
43C2×C4×C37—42no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37—42no—
47C2×C4×C37—42no—
48C2×C4×C37—82no—
49C2×C4×C37—82no—
50C2×C4×C37—81no—
51C2×C4×C37—82no—
52C8×C37—162no—
53#7348C3711yesmaximal, characteristic, direct product factor, Sylow
54C22×C37—21no—
55C22×C37—21no—
56C22×C37—41no—
57C22×C37—41no—
58C22×C37—41no—
59C22×C37—82no—
60C22×C37#32311yescharacteristic
61C22×C37#35212yes—
62C4×C37—41no—
63C4×C37—41no—
64C4×C37—82no—
65C4×C37—82no—
66C4×C37—161no—
67#1820C2×C3711yescharacteristic
68#1317C2×C3712yes—
69C2×C37—21no—
70C2×C37—22no—
71C2×C37—41no—
72C2×C37—41no—
73C2×C37#131711yescharacteristic
74C2×#117C4×C3711yescharacteristic
75#381C4×C3711yescharacteristic
76#381C22×C3711yescharacteristic
77#342—22no—
78#323—22no—
79C37#734811yescharacteristic, direct product factor, Sylow
80C23×C4C2×C4×C3711yescharacteristic
81#117—41no—
82#117—41no—
83C2×C4⋊C4—21no—
84C2×C22⋊C4—21no—
85C2×C22⋊C4—21no—
86C2×C22⋊C4D4×C3712yes—
87C2×C42C8×C3712yescomplemented
88C22⋊C8—42no—
89#95—41no—
90#95—41no—
91C24C22⋊C4×C3711yescharacteristic
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—42no—
97C22×C4—41no—
98C22×C4C2×C8×C3711yescharacteristic
99C22×C4M16×C3711yescharacteristic
100C2×C8—82no—
101C4⋊C4—42no—
102C22⋊C4—41no—
103C22⋊C4—41no—
104C22⋊C4—42no—
105C22⋊C4—42no—
106C42—42no—
107C23—22no—
108C23—81no—
109C23C22⋊C8×C3711yescharacteristic
110C23#99×C3711yescharacteristic
111C23#100×C3711yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—42no—
119C2×C4—42no—
120C2×C4—82no—
121C2×C4—82no—
122C2×C4—81no—
123C2×C4—82no—
124C8—162no—
125C22—21no—
126C22—21no—
127C22—41no—
128C22—41no—
129C22—41no—
130C22—82no—
131C22C37×#32311yescharacteristic
132C22C37×#35212yes—
133C4—41no—
134C4—41no—
135C4—82no—
136C4—82no—
137C4—161no—
138C2—21no—
139C2—22no—
140C2—41no—
141C2—41no—
142C2C37×#131711yescharacteristic
subgroupG/H
center, socleC2×C37#1317
commutatorC22×C4C2×C8×C37
Frattini, cosocle#381C22×C37
prime radicalC24×C37C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C37 ◁ C23×C37 ◁ C24×C37 ◁ C37×#381 ◁ G

Complements

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

NH ≅ G/Ntype
15. C2×C42×C37C8semidirect
53. #7348C37direct (N × H)
79. C37#7348direct (N × H)
87. C2×C42C8×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#18202
C37×#13172
#734837