Finite Group Databasebeta

← C127×#7089 #44570762

Subgroups — C127×#7089 #44570762

Order 32512.

180 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 54 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×#2087C211yesmaximal, characteristic
2C127×#1322C211yesmaximal, characteristic
3C127×#1292C211yesmaximal, characteristic
4C2×#107×C127C411yescharacteristic
5#423×C127—21no—
6C2×C4⋊C8×C127C2211yescharacteristic
7#389×C127—21no—
8C22⋊C16×C127—21no—
9#340×C127—21no—
10#340×C127C411yescharacteristic
11C2×M16×C127—41no—
12C22×C8×C127C2×C411yescharacteristic
13C22×C8×C127D411yescharacteristic
14C2×C4⋊C4×C127—21no—
15C2×C4⋊C4×C127—21no—
16C2×C4⋊C4×C127—41no—
17C2×C42×C127D411yescharacteristic
18C2×C16×C127—41no—
19#107×C127—41no—
20C4⋊C8×C127—22no—
21C4⋊C8×C127—41no—
22C4⋊C8×C127—41no—
23#95×C127—41no—
24C22×C4×C127—41no—
25C22×C4×C127—41no—
26C22×C4×C127C22⋊C411yescharacteristic
27C22×C4×C127D811yescharacteristic
28C22×C4×C127SD1611yescharacteristic
29M16×C127—81no—
30M16×C127—81no—
31C2×C8×C127—21no—
32C2×C8×C127—21no—
33C2×C8×C127—41no—
34C2×C8×C127—41no—
35C2×C8×C127—42no—
36C4⋊C4×C127—22no—
37C4⋊C4×C127—41no—
38C4⋊C4×C127—41no—
39C4⋊C4×C127—41no—
40C4⋊C4×C127—82no—
41C42×C127—21no—
42C42×C127—21no—
43C16×C127—81no—
44C23×C127#10211yescharacteristic
45C2×C4×C127—21no—
46C2×C4×C127—21no—
47C2×C4×C127—21no—
48C2×C4×C127—21no—
49C2×C4×C127—21no—
50C2×C4×C127—41no—
51C2×C4×C127—42no—
52C2×C4×C127—81no—
53C2×C4×C127—81no—
54C2×C4×C127—81no—
55C2×C4×C127—81no—
56C2×C4×C127—81no—
57C2×C4×C127#9911yescharacteristic
58C2×C4×C127#10411yescharacteristic
59C2×C4×C127SD3211yescharacteristic
60C2×C4×C127Q3211yescharacteristic
61C8×C127—41no—
62C8×C127—41no—
63C8×C127—82no—
64C22×C127—21no—
65C22×C127—21no—
66C22×C127#32711yescharacteristic
67C22×C127#35811yescharacteristic
68C22×C127#36011yescharacteristic
69C4×C127—21no—
70C4×C127—21no—
71C4×C127—21no—
72C4×C127—41no—
73C4×C127—82no—
74C4×C127—161no—
75C4×C127#35211yescharacteristic
76C4×C127#35611yescharacteristic
77#7089C12711yesmaximal, characteristic, direct product factor, Sylow
78C2×C127—21no—
79C2×C127—21no—
80C2×C127#134111yescharacteristic
81C2×C127#134611yescharacteristic
82C2×C127#134811yescharacteristic
83#2087C2×C12711yescharacteristic
84#1322C2×C12711yescharacteristic
85#1292C2×C12711yescharacteristic
86C127#708911yescharacteristic, direct product factor, Sylow
87C2×#107C4×C12711yescharacteristic
88#423—21no—
89C2×C4⋊C8C22×C12711yescharacteristic
90#389—21no—
91C22⋊C16—21no—
92#340—21no—
93#340C4×C12711yescharacteristic
94C2×M16—41no—
95C22×C8C2×C4×C12711yescharacteristic
96C22×C8D4×C12711yescharacteristic
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—41no—
100C2×C42D4×C12711yescharacteristic
101C2×C16—41no—
102#107—41no—
103C4⋊C8—22no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106#95—41no—
107C22×C4—41no—
108C22×C4—41no—
109C22×C4C22⋊C4×C12711yescharacteristic
110C22×C4D8×C12711yescharacteristic
111C22×C4SD16×C12711yescharacteristic
112M16—81no—
113M16—81no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—41no—
117C2×C8—41no—
118C2×C8—42no—
119C4⋊C4—22no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—82no—
124C42—21no—
125C42—21no—
126C16—81no—
127C23#102×C12711yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—42no—
135C2×C4—81no—
136C2×C4—81no—
137C2×C4—81no—
138C2×C4—81no—
139C2×C4—81no—
140C2×C4#99×C12711yescharacteristic
141C2×C4#104×C12711yescharacteristic
142C2×C4SD32×C12711yescharacteristic
143C2×C4Q32×C12711yescharacteristic
144C8—41no—
145C8—41no—
146C8—82no—
147C22—21no—
148C22—21no—
149C22#327×C12711yescharacteristic
150C22#358×C12711yescharacteristic
151C22#360×C12711yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—82no—
157C4—161no—
158C4#352×C12711yescharacteristic
159C4#356×C12711yescharacteristic
160C2—21no—
161C2—21no—
162C2C127×#134111yescharacteristic
163C2C127×#134611yescharacteristic
164C2C127×#134811yescharacteristic
subgroupG/H
center, socleC22×C127#327
commutatorC22×C8C2×C4×C127
Frattini, cosocleC2×C4⋊C8C22×C127
prime radicalC23×C127#102
LCSG ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4⋊C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
77. #7089C127direct (N × H)
86. C127#7089direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#20872
C127×#13222
C127×#12922
#7089127