Finite Group Databasebeta

← C127×#7284 #44570957

Subgroups — C127×#7284 #44570957

Order 32512.

298 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C127×#1985C211yesmaximal, characteristic
2C4×#101×C127C212yesmaximal
3C2×C4×Q8×C127C2211yescharacteristic
4C2×C4⋊C8×C127C411yescharacteristic
5C2×#101×C127—22no—
6C4×M16×C127—22no—
7C2×#97×C127C411yescharacteristic
8#343×C127C414yes—
9#336×C127—22no—
10C22×Q8×C127D411yescharacteristic
11C2×M16×C127—24no—
12C22×C8×C127—21no—
13C22×C8×C127—21no—
14C4×Q8×C127—41no—
15C4×Q8×C127—41no—
16C2×C4⋊C4×C127C2×C412yes—
17C2×C4⋊C4×C127Q811yescharacteristic
18C2×C42×C127C2×C411yescharacteristic
19C2×C42×C127D412yes—
20C4⋊C8×C127—41no—
21#101×C127—28no—
22#97×C127—42no—
23#97×C127—41no—
24C4×C8×C127—42no—
25C2×Q8×C127—24no—
26C2×Q8×C127—41no—
27C22×C4×C127C4211yescharacteristic
28C22×C4×C127C22⋊C412yes—
29C22×C4×C127C22⋊C411yescharacteristic
30C22×C4×C127C4⋊C411yescharacteristic
31C22×C4×C127C4⋊C412yes—
32M16×C127—28no—
33M16×C127—44no—
34C2×C8×C127—22no—
35C2×C8×C127—44no—
36C2×C8×C127—41no—
37C2×C8×C127—41no—
38C2×C8×C127—42no—
39C2×C8×C127—41no—
40C4⋊C4×C127—42no—
41C4⋊C4×C127—41no—
42C42×C127—21no—
43C42×C127—22no—
44C42×C127—22no—
45C42×C127—21no—
46C23×C127#9511yescharacteristic
47Q8×C127—44no—
48C2×C4×C127—22no—
49C2×C4×C127—22no—
50C2×C4×C127—21no—
51C2×C4×C127—21no—
52C2×C4×C127—22no—
53C2×C4×C127—21no—
54C2×C4×C127—22no—
55C2×C4×C127—21no—
56C2×C4×C127—41no—
57C2×C4×C127—42no—
58C2×C4×C127#9911yescharacteristic
59C2×C4×C127#9911yescharacteristic
60C2×C4×C127#10414yes—
61C8×C127—42no—
62C8×C127—48no—
63C8×C127—81no—
64C22×C127—21no—
65C22×C127—21no—
66C22×C127#33912yes—
67C22×C127#34211yescharacteristic
68C4×C127—24no—
69C4×C127—21no—
70C4×C127—41no—
71C4×C127—41no—
72C4×C127—42no—
73C4×C127#35511yescharacteristic
74C4×C127#35611yescharacteristic
75#7284C12711yesmaximal, characteristic, direct product factor, Sylow
76C2×C127—22no—
77C2×C127#129711yescharacteristic
78C2×C127#139211yescharacteristic
79C2×C127#139411yescharacteristic
80#1985C2×C12711yescharacteristic
81C4×#101C2×C12712yes—
82C127#728411yescharacteristic, direct product factor, Sylow
83C2×C4×Q8C22×C12711yescharacteristic
84C2×C4⋊C8C4×C12711yescharacteristic
85C2×#101—22no—
86C4×M16—22no—
87C2×#97C4×C12711yescharacteristic
88#343C4×C12714yes—
89#336—22no—
90C22×Q8D4×C12711yescharacteristic
91C2×M16—24no—
92C22×C8—21no—
93C22×C8—21no—
94C4×Q8—41no—
95C4×Q8—41no—
96C2×C4⋊C4C2×C4×C12712yes—
97C2×C4⋊C4Q8×C12711yescharacteristic
98C2×C42C2×C4×C12711yescharacteristic
99C2×C42D4×C12712yes—
100C4⋊C8—41no—
101#101—28no—
102#97—41no—
103#97—42no—
104C4×C8—42no—
105C2×Q8—24no—
106C2×Q8—41no—
107C22×C4C42×C12711yescharacteristic
108C22×C4C22⋊C4×C12711yescharacteristic
109C22×C4C22⋊C4×C12712yes—
110C22×C4C4⋊C4×C12711yescharacteristic
111C22×C4C4⋊C4×C12712yes—
112M16—28no—
113M16—44no—
114C2×C8—22no—
115C2×C8—44no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—42no—
119C2×C8—41no—
120C4⋊C4—42no—
121C4⋊C4—41no—
122C42—22no—
123C42—21no—
124C42—22no—
125C42—21no—
126C23#95×C12711yescharacteristic
127Q8—44no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4#99×C12711yescharacteristic
139C2×C4#99×C12711yescharacteristic
140C2×C4#104×C12714yes—
141C8—42no—
142C8—48no—
143C8—81no—
144C22—21no—
145C22—21no—
146C22#339×C12712yes—
147C22#342×C12711yescharacteristic
148C4—24no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—42no—
153C4#355×C12711yescharacteristic
154C4#356×C12711yescharacteristic
155C2—22no—
156C2C127×#129711yescharacteristic
157C2C127×#139211yescharacteristic
158C2C127×#139411yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C42×C127
Frattini, cosocleC2×C4×Q8C22×C127
socleC22×C127#342
prime radicalC23×C127#95
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
75. #7284C127direct (N × H)
82. C127#7284direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19852
C4×#101×C1272
#7284127