Finite Group Databasebeta

← C127×#11989 #44575662

Subgroups — C127×#11989 #44575662

Order 32512.

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

normal subgroups only

This group has 292 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×#3176C211yesmaximal, characteristic
2C127×#2166C211yesmaximal, characteristic, complemented
3C127×#2153C211yesmaximal, characteristic, complemented
4C127×#1366C212yesmaximal, complemented
5C127×#1357C212yesmaximal, complemented
6#540×C127C412yes—
7C2×M32×C127—21no—
8#499×C127C2211yescharacteristic
9#493×C127C2211yescharacteristic
10#490×C127C412yes—
11#469×C127—21no—
12#466×C127—21no—
13#442×C127—21no—
14C4×D8×C127—21no—
15#405×C127C2211yescharacteristic
16#364×C127—21no—
17#364×C127C2212yes—
18#364×C127C2212yes—
19#349×C127—21no—
20#347×C127—21no—
21C2×D8×C127—21no—
22C2×D8×C127—21no—
23C2×M16×C127D411yescharacteristic
24C22×C8×C127D411yescharacteristic
25#127×C127C2×C412yes—
26#125×C127C2×C412yes—
27#123×C127—42no—
28#121×C127—22no—
29#121×C127—42no—
30C4×D4×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#102×C127—22no—
39#102×C127—22no—
40#97×C127C2×C411yescharacteristic
41#97×C127D411yescharacteristic
42C4×C8×C127D411yescharacteristic
43C4×C8×C127C2311yescharacteristic
44C2×D4×C127—22no—
45C2×D4×C127—42no—
46C2×D4×C127—42no—
47C22×C4×C127—42no—
48C22×C4×C127C22⋊C411yescharacteristic
49D8×C127—42no—
50D8×C127—41no—
51D8×C127—41no—
52M16×C127—22no—
53C2×C8×C127—21no—
54C2×C8×C127—21no—
55C2×C8×C127C22⋊C411yescharacteristic
56C2×C8×C127C22⋊C411yescharacteristic
57C2×C8×C127C2×D411yescharacteristic
58C2×C8×C127C2×D411yescharacteristic
59C4⋊C4×C127—21no—
60C4⋊C4×C127—22no—
61C4⋊C4×C127—42no—
62C22⋊C4×C127—21no—
63C22⋊C4×C127—42no—
64C22⋊C4×C127—42no—
65C42×C127C22⋊C411yescharacteristic
66C42×C127C22×C411yescharacteristic
67C16×C127—42no—
68C16×C127—42no—
69C23×C127—42no—
70C23×C127#10011yescharacteristic
71D4×C127—42no—
72D4×C127—42no—
73D4×C127—162no—
74D4×C127—162no—
75C2×C4×C127—21no—
76C2×C4×C127—21no—
77C2×C4×C127—21no—
78C2×C4×C127—21no—
79C2×C4×C127—42no—
80C2×C4×C127—162no—
81C2×C4×C127#10011yescharacteristic
82C2×C4×C127C2×C22⋊C411yescharacteristic
83C8×C127—21no—
84C8×C127—21no—
85C8×C127#13512yes—
86C8×C127AGL(1,ℤ/8)11yescharacteristic
87C8×C127#13711yescharacteristic
88C22×C127—21no—
89C22×C127—41no—
90C22×C127—82no—
91C22×C127—82no—
92C22×C127—82no—
93C22×C127C2×#10011yescharacteristic
94C4×C127—21no—
95C4×C127—41no—
96C4×C127—41no—
97C4×C127—82no—
98C4×C127#41611yescharacteristic
99C4×C127#41711yescharacteristic
100#11989C12711yesmaximal, characteristic, direct product factor, Sylow
101C2×C127—21no—
102C2×C127—41no—
103C2×C127—162no—
104C2×C127#155111yescharacteristic
105#3176C2×C12711yescharacteristic
106#2166C2×C12711yescharacteristic, complemented
107#2153C2×C12711yescharacteristic, complemented
108#1366C2×C12712yescomplemented
109#1357C2×C12712yescomplemented
110C127#1198911yescharacteristic, direct product factor, Sylow
111#540C4×C12712yes—
112C2×M32—21no—
113#499C22×C12711yescharacteristic
114#493C22×C12711yescharacteristic
115#490C4×C12712yes—
116#469—21no—
117#466—21no—
118#442—21no—
119C4×D8—21no—
120#405C22×C12711yescharacteristic
121#364—21no—
122#364C22×C12712yes—
123#364C22×C12712yes—
124#349—21no—
125#347—21no—
126C2×D8—21no—
127C2×D8—21no—
128C2×M16D4×C12711yescharacteristic
129C22×C8D4×C12711yescharacteristic
130#127C2×C4×C12712yes—
131#125C2×C4×C12712yes—
132#123—42no—
133#121—22no—
134#121—42no—
135C4×D4—22no—
136#117C2×C4×C12711yescharacteristic
137M32—22no—
138M32—22no—
139M32—41no—
140C2×C16—41no—
141#107—21no—
142#106—21no—
143#102—22no—
144#102—22no—
145#97C2×C4×C12711yescharacteristic
146#97D4×C12711yescharacteristic
147C4×C8D4×C12711yescharacteristic
148C4×C8C23×C12711yescharacteristic
149C2×D4—22no—
150C2×D4—42no—
151C2×D4—42no—
152C22×C4—42no—
153C22×C4C22⋊C4×C12711yescharacteristic
154D8—42no—
155D8—41no—
156D8—41no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8C22⋊C4×C12711yescharacteristic
161C2×C8C22⋊C4×C12711yescharacteristic
162C2×C8C2×D4×C12711yescharacteristic
163C2×C8C2×D4×C12711yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—22no—
166C4⋊C4—42no—
167C22⋊C4—21no—
168C22⋊C4—42no—
169C22⋊C4—42no—
170C42C22⋊C4×C12711yescharacteristic
171C42C22×C4×C12711yescharacteristic
172C16—42no—
173C16—42no—
174C23—42no—
175C23#100×C12711yescharacteristic
176D4—42no—
177D4—42no—
178D4—162no—
179D4—162no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—42no—
185C2×C4—162no—
186C2×C4#100×C12711yescharacteristic
187C2×C4C2×C22⋊C4×C12711yescharacteristic
188C8—21no—
189C8—21no—
190C8#135×C12712yes—
191C8AGL(1,ℤ/8)×C12711yescharacteristic
192C8#137×C12711yescharacteristic
193C22—21no—
194C22—41no—
195C22—82no—
196C22—82no—
197C22—82no—
198C22C2×#100×C12711yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—82no—
203C4#416×C12711yescharacteristic
204C4#417×C12711yescharacteristic
205C2—21no—
206C2—41no—
207C2—162no—
208C2C127×#155111yescharacteristic
subgroupG/H
center, socleC2×C127#1551
commutatorC42C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radicalC127×#3176C2
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
2. C127×#2166C2semidirect
3. C127×#2153C2semidirect
4. C127×#1366C2semidirect
5. C127×#1357C2semidirect
100. #11989C127direct (N × H)
106. #2166C2×C127semidirect
107. #2153C2×C127semidirect
108. #1366C2×C127semidirect
109. #1357C2×C127semidirect
110. C127#11989direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31762
C127×#21662
C127×#21532
C127×#13662
C127×#13572
#11989127