Finite Group Databasebeta

← C127×#11990 #44575663

Subgroups — C127×#11990 #44575663

Order 32512.

268 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3177C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic
3C127×#2153C211yesmaximal, characteristic
4C127×#1366C212yesmaximal, complemented
5C127×#1358C212yesmaximal, complemented
6#541×C127C412yes—
7C2×M32×C127—21no—
8#499×C127C2211yescharacteristic
9#494×C127C2211yescharacteristic
10#491×C127C412yes—
11#470×C127—21no—
12#467×C127—21no—
13#441×C127—21no—
14C4×Q16×C127—21no—
15#405×C127C2211yescharacteristic
16#364×C127—21no—
17#364×C127C2212yes—
18#364×C127C2212yes—
19#349×C127—21no—
20#347×C127—21no—
21C2×Q16×C127—21no—
22C2×Q16×C127—21no—
23C2×M16×C127D411yescharacteristic
24C22×C8×C127D411yescharacteristic
25C4⋊Q8×C127C2×C412yes—
26#126×C127—42no—
27#125×C127—42no—
28#125×C127C2×C412yes—
29C22⋊Q8×C127—22no—
30C4×Q8×C127—22no—
31#117×C127C2×C411yescharacteristic
32M32×C127—22no—
33M32×C127—22no—
34M32×C127—41no—
35C2×C16×C127—41no—
36#107×C127—21no—
37#106×C127—21no—
38#103×C127—22no—
39#103×C127—22no—
40#97×C127C2×C411yescharacteristic
41#97×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127C2311yescharacteristic
44C2×Q8×C127—22no—
45C22×C4×C127C22⋊C411yescharacteristic
46Q16×C127—42no—
47Q16×C127—41no—
48Q16×C127—41no—
49M16×C127—22no—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×C8×C127C22⋊C411yescharacteristic
53C2×C8×C127C22⋊C411yescharacteristic
54C2×C8×C127C2×D411yescharacteristic
55C2×C8×C127C2×D411yescharacteristic
56C4⋊C4×C127—21no—
57C4⋊C4×C127—22no—
58C4⋊C4×C127—42no—
59C4⋊C4×C127—42no—
60C4⋊C4×C127—42no—
61C4⋊C4×C127—42no—
62C22⋊C4×C127—21no—
63C22⋊C4×C127—42no—
64C42×C127—42no—
65C42×C127C22⋊C411yescharacteristic
66C42×C127C22×C411yescharacteristic
67C16×C127—42no—
68C16×C127—42no—
69C23×C127#10011yescharacteristic
70Q8×C127—42no—
71Q8×C127—42no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—42no—
77C2×C4×C127—42no—
78C2×C4×C127#10011yescharacteristic
79C2×C4×C127C2×C22⋊C411yescharacteristic
80C8×C127—21no—
81C8×C127—21no—
82C8×C127#13512yes—
83C8×C127AGL(1,ℤ/8)11yescharacteristic
84C8×C127#13711yescharacteristic
85C22×C127—21no—
86C22×C127—41no—
87C22×C127C2×#10011yescharacteristic
88C4×C127—21no—
89C4×C127—41no—
90C4×C127—41no—
91C4×C127—82no—
92C4×C127—82no—
93C4×C127#41611yescharacteristic
94C4×C127#41711yescharacteristic
95#11990C12711yesmaximal, characteristic, direct product factor, Sylow
96C2×C127—21no—
97C2×C127—41no—
98C2×C127#155111yescharacteristic
99#3177C2×C12711yescharacteristic
100#2166C2×C12711yescharacteristic
101#2153C2×C12711yescharacteristic
102#1366C2×C12712yescomplemented
103#1358C2×C12712yescomplemented
104C127#1199011yescharacteristic, direct product factor, Sylow
105#541C4×C12712yes—
106C2×M32—21no—
107#499C22×C12711yescharacteristic
108#494C22×C12711yescharacteristic
109#491C4×C12712yes—
110#470—21no—
111#467—21no—
112#441—21no—
113C4×Q16—21no—
114#405C22×C12711yescharacteristic
115#364—21no—
116#364C22×C12712yes—
117#364C22×C12712yes—
118#349—21no—
119#347—21no—
120C2×Q16—21no—
121C2×Q16—21no—
122C2×M16D4×C12711yescharacteristic
123C22×C8D4×C12711yescharacteristic
124C4⋊Q8C2×C4×C12712yes—
125#126—42no—
126#125—42no—
127#125C2×C4×C12712yes—
128C22⋊Q8—22no—
129C4×Q8—22no—
130#117C2×C4×C12711yescharacteristic
131M32—22no—
132M32—22no—
133M32—41no—
134C2×C16—41no—
135#107—21no—
136#106—21no—
137#103—22no—
138#103—22no—
139#97C2×C4×C12711yescharacteristic
140#97D4×C12711yescharacteristic
141C4×C8D4×C12711yescharacteristic
142C4×C8C23×C12711yescharacteristic
143C2×Q8—22no—
144C22×C4C22⋊C4×C12711yescharacteristic
145Q16—42no—
146Q16—41no—
147Q16—41no—
148M16—22no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8C22⋊C4×C12711yescharacteristic
152C2×C8C22⋊C4×C12711yescharacteristic
153C2×C8C2×D4×C12711yescharacteristic
154C2×C8C2×D4×C12711yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C42—42no—
164C42C22⋊C4×C12711yescharacteristic
165C42C22×C4×C12711yescharacteristic
166C16—42no—
167C16—42no—
168C23#100×C12711yescharacteristic
169Q8—42no—
170Q8—42no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4#100×C12711yescharacteristic
178C2×C4C2×C22⋊C4×C12711yescharacteristic
179C8—21no—
180C8—21no—
181C8#135×C12712yes—
182C8AGL(1,ℤ/8)×C12711yescharacteristic
183C8#137×C12711yescharacteristic
184C22—21no—
185C22—41no—
186C22C2×#100×C12711yescharacteristic
187C4—21no—
188C4—41no—
189C4—41no—
190C4—82no—
191C4—82no—
192C4#416×C12711yescharacteristic
193C4#417×C12711yescharacteristic
194C2—21no—
195C2—41no—
196C2C127×#155111yescharacteristic
subgroupG/H
center, socleC2×C127#1551
commutatorC42C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC23×C127#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1366C2semidirect
5. C127×#1358C2semidirect
95. #11990C127direct (N × H)
102. #1366C2×C127semidirect
103. #1358C2×C127semidirect
104. C127#11990direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31772
C127×#21662
C127×#21532
C127×#13662
C127×#13582
#11990127