Finite Group Databasebeta

← #857⋊C4 #72993

Subgroups — #857⋊C4 #72993

Order 384.

147 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 147 conjugacy classes of subgroups — too many to draw. Only its 16 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
1C2×#857C211yesmaximal, characteristic
2#384⋊C3C211yesmaximal, characteristic, complemented
3#4623C211yesmaximal, characteristic, complemented
4#1859—31nomaximal, Sylow
5C4×S4—41nomaximal
6C2×C42⋊C3C2211yescharacteristic
7#857C412yescomplemented
8#520—31no—
9#428—31no—
10C2×#104—31no—
11#417—31no—
12#384D311yescharacteristic, complemented
13#343—31no—
14#339—31no—
15C2×S4—41no—
16C4×A4—41no—
17SL(2,ℤ/4)—41no—
18C42⋊C3C2×C411yescharacteristic, complemented
19C2×#41—31no—
20C2×M16—31no—
21C2×M16—31no—
22C4×Q8—61no—
23C4×D4—61no—
24C4×D4—61no—
25C4×D4—61no—
26#117—31no—
27#117—61no—
28C2×C4⋊C4—31no—
29C2×C4⋊C4—31no—
30C2×C4⋊C4—61no—
31C2×C42C2×D311yescharacteristic
32#107—61no—
33#106—61no—
34#104—32no—
35#104—32no—
36#103—61no—
37#102—61no—
38C2×A4—41no—
39S4—42no—
40C4×D3—161no—
41#41—32no—
42#41—32no—
43#41—61no—
44#41—61no—
45C2×Q8—31no—
46C2×D4—31no—
47C2×D4—61no—
48C22×C4—31no—
49C22×C4—31no—
50C22×C4—61no—
51C22×C4—61no—
52C22×C4—61no—
53C22×C4S411yescharacteristic
54M16—32no—
55M16—61no—
56M16—61no—
57M16—61no—
58C2×C8—61no—
59C2×C8—61no—
60C4⋊C4—31no—
61C4⋊C4—31no—
62C4⋊C4—61no—
63C4⋊C4—61no—
64C4⋊C4—61no—
65C4⋊C4—61no—
66C4⋊C4—61no—
67C4⋊C4—61no—
68C22⋊C4—61no—
69C22⋊C4—61no—
70C22⋊C4—61no—
71C42—31no—
72C42—61no—
73C42—61no—
74C42—61no—
75C42C4×D311yescharacteristic, complemented
76C2×D3—161no—
77A4—41no—
78C3×C4—161no—
79Dic3—161no—
80C23—61no—
81C23C2×S411yescharacteristic
82Q8—32no—
83Q8—61no—
84D4—32no—
85D4—61no—
86D4—62no—
87D4—62no—
88C2×C4—31no—
89C2×C4—31no—
90C2×C4—31no—
91C2×C4—31no—
92C2×C4—31no—
93C2×C4—31no—
94C2×C4—62no—
95C2×C4—62no—
96C2×C4—61no—
97C2×C4—61no—
98C2×C4—61no—
99C2×C4—61no—
100C2×C4—61no—
101C2×C4—121no—
102C2×C4—241no—
103C2×C4—241no—
104C8—62no—
105C8—121no—
106C2×C3—161no—
107D3—162no—
108C22—31no—
109C22—31no—
110C22—62no—
111C22—121no—
112C22—121no—
113C22C4×S411yescharacteristic
114C4—31no—
115C4—31no—
116C4—31no—
117C4—31no—
118C4—41no—
119C4—62no—
120C4—121no—
121C4—121no—
122C4—121no—
123C3—161noSylow
124C2—31no—
125C2—31no—
126C2—122no—
127C2#857⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#857⋊C2
commutator, hypocenterC42⋊C3C2×C4
Frattini, socleC23C2×S4
Fitting#384D3
prime radicalC2×#857C2
cosocleC2×C42⋊C3C22
LCSG ▷ C42⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #384⋊C3C2semidirect
3. #4623C2semidirect
7. #857C4semidirect
12. #384D3semidirect
18. C42⋊C3C2×C4semidirect
75. C42C4×D3semidirect

Maximal subgroups

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

subgroupindex
C2×#8572
#384⋊C32
#46232
#18593
C4×S44