Finite Group Databasebeta

← C127×#7636 #44571309

Subgroups — C127×#7636 #44571309

Order 32512.

436 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C4×#125×C127C211yesmaximal, characteristic
2C127×#1767C212yesmaximal
3C127×#1271C214yesmaximal
4C2×#125×C127C411yescharacteristic
5C2×C4⋊C8×C127—22no—
6C2×#97×C127—22no—
7#389×C127C2212yes—
8#387×C127—22no—
9#382×C127C411yescharacteristic
10C4×C4⋊C4×C127—22no—
11C4×C4⋊C4×C127C412yes—
12C43×C127C2211yescharacteristic
13#336×C127C2214yes—
14C22×C8×C127—24no—
15#125×C127—24no—
16C2×C4⋊C4×C127—22no—
17C2×C4⋊C4×C127—22no—
18C2×C4⋊C4×C127C2×C412yes—
19C2×C4⋊C4×C127C2×C412yes—
20C2×C42×C127—22no—
21C2×C42×C127C2×C411yescharacteristic
22C2×C42×C127C2×C411yescharacteristic
23C2×C42×C127D412yes—
24C2×C42×C127D412yes—
25C2×C42×C127C2311yescharacteristic
26C4⋊C8×C127—28no—
27#97×C127—44no—
28#95×C127—22no—
29#95×C127—22no—
30#95×C127—22no—
31C22×C4×C127—22no—
32C22×C4×C127—22no—
33C22×C4×C127C22⋊C411yescharacteristic
34C22×C4×C127C22⋊C412yes—
35C22×C4×C127C22⋊C411yescharacteristic
36C22×C4×C127C22×C411yescharacteristic
37C22×C4×C127C2×D412yes—
38C2×C8×C127—28no—
39C2×C8×C127—44no—
40C2×C8×C127—44no—
41C4⋊C4×C127—28no—
42C4⋊C4×C127—22no—
43C4⋊C4×C127—42no—
44C4⋊C4×C127—42no—
45C4⋊C4×C127—42no—
46C4⋊C4×C127M1614yes—
47C42×C127—22no—
48C42×C127—24no—
49C42×C127—22no—
50C42×C127—22no—
51C42×C127—22no—
52C42×C127—41no—
53C42×C127—44no—
54C23×C127C2×C22⋊C411yescharacteristic
55C2×C4×C127—21no—
56C2×C4×C127—22no—
57C2×C4×C127—21no—
58C2×C4×C127—22no—
59C2×C4×C127—22no—
60C2×C4×C127—24no—
61C2×C4×C127—21no—
62C2×C4×C127—22no—
63C2×C4×C127—22no—
64C2×C4×C127—22no—
65C2×C4×C127—42no—
66C2×C4×C127—42no—
67C2×C4×C127—42no—
68C2×C4×C127—42no—
69C2×C4×C127—42no—
70C2×C4×C127#10112yes—
71C2×C4×C127#10414yes—
72C2×C4×C127C2×M1612yes—
73C2×C4×C127AGL(1,ℤ/8)12yes—
74C2×C4×C127#13712yes—
75C8×C127—48no—
76C22×C127#40711yescharacteristic
77C22×C127#41011yescharacteristic
78C22×C127C2×#10111yescharacteristic
79C22×C127#41712yes—
80C22×C127C2×#10412yes—
81C4×C127—22no—
82C4×C127—22no—
83C4×C127—22no—
84C4×C127—41no—
85C4×C127—42no—
86C4×C127—44no—
87C4×C127—82no—
88C4×C127#33014yes—
89#7636C12711yesmaximal, characteristic, direct product factor, Sylow
90C2×C127#146711yescharacteristic
91C2×C127#148912yes—
92C2×C127#150912yes—
93C2×C127C2×#33011yescharacteristic
94C2×C127#156111yescharacteristic
95C4×#125C2×C12711yescharacteristic
96#1767C2×C12712yes—
97#1271C2×C12714yes—
98C127#763611yescharacteristic, direct product factor, Sylow
99C2×#125C4×C12711yescharacteristic
100C2×C4⋊C8—22no—
101C2×#97—22no—
102#389C22×C12712yes—
103#387—22no—
104#382C4×C12711yescharacteristic
105C4×C4⋊C4—22no—
106C4×C4⋊C4C4×C12712yes—
107C43C22×C12711yescharacteristic
108#336C22×C12714yes—
109C22×C8—24no—
110#125—24no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4C2×C4×C12712yes—
114C2×C4⋊C4C2×C4×C12712yes—
115C2×C42—22no—
116C2×C42C2×C4×C12711yescharacteristic
117C2×C42C2×C4×C12711yescharacteristic
118C2×C42D4×C12712yes—
119C2×C42D4×C12712yes—
120C2×C42C23×C12711yescharacteristic
121C4⋊C8—28no—
122#97—44no—
123#95—22no—
124#95—22no—
125#95—22no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4C22⋊C4×C12711yescharacteristic
129C22×C4C22⋊C4×C12712yes—
130C22×C4C22⋊C4×C12711yescharacteristic
131C22×C4C22×C4×C12711yescharacteristic
132C22×C4C2×D4×C12712yes—
133C2×C8—28no—
134C2×C8—44no—
135C2×C8—44no—
136C4⋊C4—28no—
137C4⋊C4—22no—
138C4⋊C4—42no—
139C4⋊C4—42no—
140C4⋊C4—42no—
141C4⋊C4M16×C12714yes—
142C42—22no—
143C42—24no—
144C42—22no—
145C42—22no—
146C42—22no—
147C42—41no—
148C42—44no—
149C23C2×C22⋊C4×C12711yescharacteristic
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4#101×C12712yes—
166C2×C4#104×C12714yes—
167C2×C4C2×M16×C12712yes—
168C2×C4AGL(1,ℤ/8)×C12712yes—
169C2×C4#137×C12712yes—
170C8—48no—
171C22#407×C12711yescharacteristic
172C22#410×C12711yescharacteristic
173C22C2×#101×C12711yescharacteristic
174C22#417×C12712yes—
175C22C2×#104×C12712yes—
176C4—22no—
177C4—22no—
178C4—22no—
179C4—41no—
180C4—42no—
181C4—44no—
182C4—82no—
183C4#330×C12714yes—
184C2C127×#146711yescharacteristic
185C2C127×#148912yes—
186C2C127×#150912yes—
187C2C2×#330×C12711yescharacteristic
188C2C127×#156111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
89. #7636C127direct (N × H)
98. C127#7636direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#125×C1272
C127×#17672
C127×#12712
#7636127