Finite Group Databasebeta

← #2397⋊C3 #73187

Subgroups — #2397⋊C3 #73187

Order 384.

175 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 175 conjugacy classes of subgroups — too many to draw. Only its 21 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#399⋊C3C211yesmaximal, characteristic, complemented
2#392⋊C3C211yesmaximal, characteristic, complemented
3#376⋊C3C211yesmaximal, characteristic, complemented
4#2397C311yesmaximal, characteristic, complemented, Sylow
5C2×C4×A4—41nomaximal
6#95⋊C3C2211yescharacteristic
7C2×C4×D4—31no—
8C2×C4×D4—31no—
9#399—31no—
10#399C2×C311yescharacteristic
11#392—31no—
12#392C2×C311yescharacteristic, complemented
13#376C2×C311yescharacteristic, complemented
14C22×A4—41no—
15C4×A4—41no—
16C4×A4—41no—
17C22×D4—31no—
18C22×D4—31no—
19C23×C4—31no—
20C23×C4A411yescharacteristic
21C4×D4—62no—
22C4×D4—62no—
23C4×D4—62no—
24C4×D4—62no—
25C2×C4⋊C4—31no—
26C2×C4⋊C4—31no—
27C2×C22⋊C4—32no—
28C2×C22⋊C4—31no—
29C2×C22⋊C4—31no—
30C2×C42—31no—
31#95—31no—
32#95C22×C311yescharacteristic
33C2×A4—42no—
34C2×A4—41no—
35C2×C3×C4—161no—
36C24—31no—
37C24C2×A411yescharacteristic
38C2×D4—62no—
39C2×D4—62no—
40C2×D4—62no—
41C2×D4—64no—
42C2×D4—62no—
43C22×C4—31no—
44C22×C4—31no—
45C22×C4—31no—
46C22×C4—61no—
47C22×C4—61no—
48C22×C4—62no—
49C22×C4—62no—
50C22×C4—61no—
51C22×C4—61no—
52C22×C4C2×A411yescharacteristic
53C22×C4C2×A411yescharacteristic
54C4⋊C4—62no—
55C4⋊C4—62no—
56C22⋊C4—62no—
57C22⋊C4—62no—
58C22⋊C4—64no—
59C42—32no—
60C42—32no—
61C22×C3—161no—
62A4—41no—
63C3×C4—161no—
64C3×C4—161no—
65C23—32no—
66C23—61no—
67C23—61no—
68C23—62no—
69C23—61no—
70C23—62no—
71C23—61no—
72C23#41⋊C312yes—
73C23C22×A411yescharacteristic
74D4—68no—
75D4—68no—
76C2×C4—31no—
77C2×C4—31no—
78C2×C4—32no—
79C2×C4—32no—
80C2×C4—41no—
81C2×C4—61no—
82C2×C4—62no—
83C2×C4—61no—
84C2×C4—61no—
85C2×C4—61no—
86C2×C4—62no—
87C2×C4—121no—
88C2×C4—121no—
89C2×C4—122no—
90C2×C4—121no—
91C2×C3—162no—
92C2×C3—161no—
93C22—31no—
94C22—31no—
95C22—41no—
96C22—62no—
97C22—64no—
98C22—62no—
99C22—121no—
100C22—121no—
101C22—122no—
102C22—121no—
103C22C2×#41⋊C311yescharacteristic
104C4—31no—
105C4—41no—
106C4—62no—
107C4—62no—
108C4—121no—
109C4#127⋊C311yescharacteristic
110C3—161noSylow
111C2—31no—
112C2—31no—
113C2—42no—
114C2—122no—
115C2C2×#127⋊C311yescharacteristic
subgroupG/H
center, hypercenterC4#127⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2397C3
LCSG ▷ #95
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. #399⋊C3C2semidirect
2. #392⋊C3C2semidirect
3. #376⋊C3C2semidirect
4. #2397C3semidirect
12. #392C2×C3semidirect
13. #376C2×C3semidirect

Maximal subgroups

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

subgroupindex
#399⋊C32
#392⋊C32
#376⋊C32
#23973
C2×C4×A44