Finite Group Databasebeta

← C127×#13447 #44577120

Subgroups — C127×#13447 #44577120

Order 32512.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3414C211yesmaximal, characteristic
2C127×#2151C211yesmaximal, characteristic, complemented
3C127×#2138C212yesmaximal, complemented
4C127×#1976C212yesmaximal, complemented
5C127×#1384C211yesmaximal, characteristic, complemented
6C2×#135×C127C2212yes—
7#510×C127—22no—
8#509×C127—22no—
9#508×C127—22no—
10C2×M32×C127C2211yescharacteristic
11C22×C16×C127C2211yescharacteristic
12#427×C127C2212yes—
13#421×C127—22no—
14#410×C127—22no—
15#405×C127C2211yescharacteristic
16C4⋊C16×C127—22no—
17#358×C127—22no—
18#357×C127—22no—
19C2×#41×C127—22no—
20#135×C127—22no—
21#135×C127—22no—
22#135×C127—22no—
23#135×C127—22no—
24C2×Q16×C127D412yes—
25C2×SD16×C127—22no—
26C2×D8×C127D412yes—
27C2×M16×C127D411yescharacteristic
28C22×C8×C127C2311yescharacteristic
29#117×C127—22no—
30#117×C127D411yescharacteristic
31Q32×C127—22no—
32SD32×C127—24no—
33D16×C127—22no—
34M32×C127—22no—
35C2×C16×C127—22no—
36C2×C16×C127—21no—
37C2×C16×C127D412yes—
38#107×C127—22no—
39#106×C127—22no—
40#104×C127—44no—
41#99×C127—44no—
42#97×C127—21no—
43C4×C8×C127—21no—
44#41×C127—42no—
45#41×C127—42no—
46#41×C127—42no—
47#41×C127—42no—
48C2×Q8×C127—22no—
49C2×D4×C127—22no—
50C2×D4×C127—42no—
51C22×C4×C127—42no—
52C22×C4×C127C2×D411yescharacteristic
53Q16×C127—22no—
54Q16×C127—22no—
55SD16×C127—42no—
56SD16×C127—42no—
57D8×C127—22no—
58D8×C127—22no—
59M16×C127—22no—
60C2×C8×C127—21no—
61C2×C8×C127C2×D412yes—
62C2×C8×C127C2×D411yescharacteristic
63C2×C8×C127#4111yescharacteristic
64C2×C8×C127#4112yes—
65C4⋊C4×C127—21no—
66C4⋊C4×C127—42no—
67C22⋊C4×C127—42no—
68C22⋊C4×C127D812yes—
69C42×C127—21no—
70C42×C127—42no—
71C16×C127—22no—
72C16×C127—41no—
73C23×C127—42no—
74C23×C127C2×D811yescharacteristic
75Q8×C127—42no—
76Q8×C127—42no—
77D4×C127—42no—
78D4×C127—42no—
79D4×C127—82no—
80D4×C127—82no—
81C2×C4×C127—22no—
82C2×C4×C127—42no—
83C2×C4×C127—82no—
84C2×C4×C127—82no—
85C2×C4×C127—82no—
86C2×C4×C127#12112yes—
87C2×C4×C127#12111yescharacteristic
88C2×C4×C127#13511yescharacteristic
89C2×C4×C127AGL(1,ℤ/8)12yes—
90C8×C127—41no—
91C8×C127#12011yescharacteristic
92C8×C127#12312yes—
93C8×C127#12411yescharacteristic
94C22×C127—41no—
95C22×C127—82no—
96C22×C127—162no—
97C22×C127#45912yes—
98C22×C127#46611yescharacteristic
99C4×C127—42no—
100C4×C127—82no—
101C4×C127—162no—
102C4×C127#39411yescharacteristic
103C4×C127#46312yes—
104C4×C127#46911yescharacteristic
105#13447C12711yesmaximal, characteristic, direct product factor, Sylow
106C2×C127—21no—
107C2×C127—22no—
108C2×C127—162no—
109C2×C127#205411yescharacteristic
110#3414C2×C12711yescharacteristic
111#2151C2×C12711yescharacteristic, complemented
112#2138C2×C12712yescomplemented
113#1976C2×C12712yescomplemented
114#1384C2×C12711yescharacteristic, complemented
115C127#1344711yescharacteristic, direct product factor, Sylow
116C2×#135C22×C12712yes—
117#510—22no—
118#509—22no—
119#508—22no—
120C2×M32C22×C12711yescharacteristic
121C22×C16C22×C12711yescharacteristic
122#427C22×C12712yes—
123#421—22no—
124#410—22no—
125#405C22×C12711yescharacteristic
126C4⋊C16—22no—
127#358—22no—
128#357—22no—
129C2×#41—22no—
130#135—22no—
131#135—22no—
132#135—22no—
133#135—22no—
134C2×Q16D4×C12712yes—
135C2×SD16—22no—
136C2×D8D4×C12712yes—
137C2×M16D4×C12711yescharacteristic
138C22×C8C23×C12711yescharacteristic
139#117—22no—
140#117D4×C12711yescharacteristic
141Q32—22no—
142SD32—24no—
143D16—22no—
144M32—22no—
145C2×C16—22no—
146C2×C16—21no—
147C2×C16D4×C12712yes—
148#107—22no—
149#106—22no—
150#104—44no—
151#99—44no—
152#97—21no—
153C4×C8—21no—
154#41—42no—
155#41—42no—
156#41—42no—
157#41—42no—
158C2×Q8—22no—
159C2×D4—22no—
160C2×D4—42no—
161C22×C4—42no—
162C22×C4C2×D4×C12711yescharacteristic
163Q16—22no—
164Q16—22no—
165SD16—42no—
166SD16—42no—
167D8—22no—
168D8—22no—
169M16—22no—
170C2×C8—21no—
171C2×C8C2×D4×C12712yes—
172C2×C8C2×D4×C12711yescharacteristic
173C2×C8#41×C12711yescharacteristic
174C2×C8#41×C12712yes—
175C4⋊C4—21no—
176C4⋊C4—42no—
177C22⋊C4—42no—
178C22⋊C4D8×C12712yes—
179C42—21no—
180C42—42no—
181C16—22no—
182C16—41no—
183C23—42no—
184C23C2×D8×C12711yescharacteristic
185Q8—42no—
186Q8—42no—
187D4—42no—
188D4—42no—
189D4—82no—
190D4—82no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—82no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4#121×C12712yes—
197C2×C4#121×C12711yescharacteristic
198C2×C4#135×C12711yescharacteristic
199C2×C4AGL(1,ℤ/8)×C12712yes—
200C8—41no—
201C8#120×C12711yescharacteristic
202C8#123×C12712yes—
203C8#124×C12711yescharacteristic
204C22—41no—
205C22—82no—
206C22—162no—
207C22#459×C12712yes—
208C22#466×C12711yescharacteristic
209C4—42no—
210C4—82no—
211C4—162no—
212C4#394×C12711yescharacteristic
213C4#463×C12712yes—
214C4#469×C12711yescharacteristic
215C2—21no—
216C2—22no—
217C2—162no—
218C2C127×#205411yescharacteristic
subgroupG/H
centerC4×C127#469
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2054
prime radicalC127×#3414C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2151C2semidirect
3. C127×#2138C2semidirect
4. C127×#1976C2semidirect
5. C127×#1384C2semidirect
105. #13447C127direct (N × H)
111. #2151C2×C127semidirect
112. #2138C2×C127semidirect
113. #1976C2×C127semidirect
114. #1384C2×C127semidirect
115. C127#13447direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34142
C127×#21512
C127×#21382
C127×#19762
C127×#13842
#13447127