Finite Group Databasebeta

← #2656⋊C3 #73196

Subgroups — #2656⋊C3 #73196

Order 384.

169 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 169 conjugacy classes of subgroups — too many to draw. Only its 19 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
3C2×#95⋊C3C211yesmaximal, characteristic, complemented
4#2656C311yesmaximal, characteristic, complemented, Sylow
5D4×A4—41nomaximal
6#95⋊C3C2211yescharacteristic
7C2×#121—31no—
8C2×#121—31no—
9#399—31no—
10#399C2×C311yescharacteristic, complemented
11#392—31no—
12#392C2×C311yescharacteristic, complemented
13C2×#95C2×C311yescharacteristic, complemented
14C22×A4—41no—
15C22×A4—41no—
16C4×A4—41no—
17C22×D4—31no—
18C22×D4—31no—
19C22×D4—31no—
20C22×D4A411yescharacteristic
21C23×C4—31no—
22#121—62no—
23#121—62no—
24#121—62no—
25#121—62no—
26C2×C4⋊C4—31no—
27C2×C4⋊C4—31no—
28C2×C22⋊C4—32no—
29C2×C22⋊C4—31no—
30C2×C22⋊C4—31no—
31#95—31no—
32#95C22×C311yescharacteristic
33C2×A4—41no—
34C2×A4—81no—
35C2×A4—81no—
36C3×D4—161no—
37C24—31no—
38C24C2×A411yescharacteristic
39C24C2×A411yescharacteristic
40C2×D4—62no—
41C2×D4—62no—
42C2×D4—61no—
43C2×D4—62no—
44C2×D4—61no—
45C2×D4—61no—
46C2×D4—62no—
47C2×D4—61no—
48C2×D4—122no—
49C2×D4—122no—
50C22×C4—31no—
51C22×C4—31no—
52C22×C4—32no—
53C22×C4—32no—
54C22×C4—31no—
55C22×C4—122no—
56C22×C4C2×A411yescharacteristic
57C4⋊C4—62no—
58C4⋊C4—62no—
59C22⋊C4—62no—
60C22⋊C4—62no—
61C22⋊C4—64no—
62C22×C3—161no—
63C22×C3—161no—
64A4—41no—
65C3×C4—161no—
66C23—21no—
67C23—21no—
68C23—31no—
69C23—31no—
70C23—61no—
71C23—61no—
72C23—61no—
73C23—61no—
74C23—62no—
75C23—62no—
76C23—61no—
77C23—61no—
78C23C22×A411yescharacteristic
79D4—41no—
80D4—121no—
81D4—124no—
82D4—124no—
83D4—121no—
84D4—122no—
85D4—121no—
86C2×C4—32no—
87C2×C4—32no—
88C2×C4—61no—
89C2×C4—62no—
90C2×C4—62no—
91C2×C4—61no—
92C2×C4—62no—
93C2×C4—122no—
94C2×C4—122no—
95C2×C3—161no—
96C2×C3—321no—
97C2×C3—321no—
98C22—31no—
99C22—31no—
100C22—31no—
101C22—41no—
102C22—61no—
103C22—61no—
104C22—61no—
105C22—61no—
106C22—121no—
107C22—121no—
108C22—121no—
109C22—122no—
110C22—121no—
111C22—122no—
112C22—121no—
113C22#127⋊C311yescharacteristic
114C222−1+4⋊C311yescharacteristic
115C4—41no—
116C4—62no—
117C4—62no—
118C4—121no—
119C3—161noSylow
120C2—21no—
121C2—31no—
122C2—31no—
123C2—61no—
124C2—81no—
125C2—241no—
126C2C2×#127⋊C311yescharacteristic
subgroupG/H
centerC2C2×#127⋊C3
commutator, cosocle, hypocenter#95C22×C3
Frattini, socleC23C22×A4
Fitting#2656C3
hypercenterC22#127⋊C3
LCSG ▷ #95
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. #399⋊C3C2semidirect
2. #392⋊C3C2semidirect
3. C2×#95⋊C3C2semidirect
4. #2656C3semidirect
10. #399C2×C3semidirect
12. #392C2×C3semidirect
13. C2×#95C2×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
C2×#95⋊C32
#26563
D4×A44