Finite Group Databasebeta

← C127×#13444 #44577117

Subgroups — C127×#13444 #44577117

Order 32512.

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

normal subgroups only

This group has 392 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×#2150C211yesmaximal, characteristic, complemented
3C127×#2148C212yesmaximal, complemented
4C127×#1974C212yesmaximal, complemented
5C127×#1385C211yesmaximal, characteristic, complemented
6C2×#135×C127C2212yes—
7#510×C127—22no—
8#509×C127—22no—
9#508×C127—22no—
10C2×M32×C127C2211yescharacteristic
11C2×M32×C127C2211yescharacteristic
12C2×#108×C127C2212yes—
13C2×#104×C127—22no—
14#408×C127—22no—
15C2×C4×C8×C127C2211yescharacteristic
16C4⋊C16×C127—22no—
17#362×C127—22no—
18#361×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×C127—22no—
28C22×C8×C127D411yescharacteristic
29C22×C8×C127C2311yescharacteristic
30C2×C42×C127D411yescharacteristic
31Q32×C127—22no—
32SD32×C127—24no—
33D16×C127—22no—
34M32×C127—22no—
35M32×C127—22no—
36C2×C16×C127—21no—
37C2×C16×C127D412yes—
38#108×C127—22no—
39#108×C127—22no—
40#104×C127—42no—
41#104×C127—42no—
42C22⋊C8×C127—44no—
43C4×C8×C127—21no—
44C4×C8×C127—21no—
45#41×C127—42no—
46#41×C127—42no—
47#41×C127—42no—
48#41×C127—42no—
49C2×Q8×C127—22no—
50C2×D4×C127—22no—
51C2×D4×C127—42no—
52C22×C4×C127—21no—
53C22×C4×C127—42no—
54C22×C4×C127C2×D411yescharacteristic
55Q16×C127—22no—
56Q16×C127—22no—
57SD16×C127—42no—
58SD16×C127—42no—
59D8×C127—22no—
60D8×C127—22no—
61M16×C127—42no—
62M16×C127—42no—
63C2×C8×C127—21no—
64C2×C8×C127—22no—
65C2×C8×C127—42no—
66C2×C8×C127C2×D412yes—
67C2×C8×C127C2×D411yescharacteristic
68C2×C8×C127#4111yescharacteristic
69C2×C8×C127#4112yes—
70C42×C127—21no—
71C42×C127D811yescharacteristic
72C42×C127D811yescharacteristic
73C16×C127—22no—
74C16×C127—41no—
75C23×C127—42no—
76C23×C127#13511yescharacteristic
77Q8×C127—42no—
78Q8×C127—42no—
79D4×C127—42no—
80D4×C127—42no—
81D4×C127—82no—
82D4×C127—82no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—42no—
86C2×C4×C127—42no—
87C2×C4×C127—82no—
88C2×C4×C127—82no—
89C2×C4×C127#12112yes—
90C2×C4×C127#12111yescharacteristic
91C2×C4×C127C2×D811yescharacteristic
92C2×C4×C127AGL(1,ℤ/8)12yes—
93C8×C127—41no—
94C8×C127—82no—
95C8×C127#12011yescharacteristic
96C8×C127#12312yes—
97C8×C127#12411yescharacteristic
98C22×C127—41no—
99C22×C127—84no—
100C22×C127—82no—
101C22×C127#46312yes—
102C22×C127#46611yescharacteristic
103C4×C127—22no—
104C4×C127—41no—
105C4×C127—82no—
106C4×C127#39411yescharacteristic
107C4×C127#45912yes—
108C4×C127#46911yescharacteristic
109#13444C12711yesmaximal, characteristic, direct product factor, Sylow
110C2×C127—21no—
111C2×C127—22no—
112C2×C127—162no—
113C2×C127#205411yescharacteristic
114#3414C2×C12711yescharacteristic
115#2150C2×C12711yescharacteristic, complemented
116#2148C2×C12712yescomplemented
117#1974C2×C12712yescomplemented
118#1385C2×C12711yescharacteristic, complemented
119C127#1344411yescharacteristic, direct product factor, Sylow
120C2×#135C22×C12712yes—
121#510—22no—
122#509—22no—
123#508—22no—
124C2×M32C22×C12711yescharacteristic
125C2×M32C22×C12711yescharacteristic
126C2×#108C22×C12712yes—
127C2×#104—22no—
128#408—22no—
129C2×C4×C8C22×C12711yescharacteristic
130C4⋊C16—22no—
131#362—22no—
132#361—22no—
133C2×#41—22no—
134#135—22no—
135#135—22no—
136#135—22no—
137#135—22no—
138C2×Q16D4×C12712yes—
139C2×SD16—22no—
140C2×D8D4×C12712yes—
141C2×M16—22no—
142C22×C8D4×C12711yescharacteristic
143C22×C8C23×C12711yescharacteristic
144C2×C42D4×C12711yescharacteristic
145Q32—22no—
146SD32—24no—
147D16—22no—
148M32—22no—
149M32—22no—
150C2×C16—21no—
151C2×C16D4×C12712yes—
152#108—22no—
153#108—22no—
154#104—42no—
155#104—42no—
156C22⋊C8—44no—
157C4×C8—21no—
158C4×C8—21no—
159#41—42no—
160#41—42no—
161#41—42no—
162#41—42no—
163C2×Q8—22no—
164C2×D4—22no—
165C2×D4—42no—
166C22×C4—21no—
167C22×C4—42no—
168C22×C4C2×D4×C12711yescharacteristic
169Q16—22no—
170Q16—22no—
171SD16—42no—
172SD16—42no—
173D8—22no—
174D8—22no—
175M16—42no—
176M16—42no—
177C2×C8—21no—
178C2×C8—22no—
179C2×C8—42no—
180C2×C8C2×D4×C12712yes—
181C2×C8C2×D4×C12711yescharacteristic
182C2×C8#41×C12711yescharacteristic
183C2×C8#41×C12712yes—
184C42—21no—
185C42D8×C12711yescharacteristic
186C42D8×C12711yescharacteristic
187C16—22no—
188C16—41no—
189C23—42no—
190C23#135×C12711yescharacteristic
191Q8—42no—
192Q8—42no—
193D4—42no—
194D4—42no—
195D4—82no—
196D4—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—82no—
202C2×C4—82no—
203C2×C4#121×C12712yes—
204C2×C4#121×C12711yescharacteristic
205C2×C4C2×D8×C12711yescharacteristic
206C2×C4AGL(1,ℤ/8)×C12712yes—
207C8—41no—
208C8—82no—
209C8#120×C12711yescharacteristic
210C8#123×C12712yes—
211C8#124×C12711yescharacteristic
212C22—41no—
213C22—84no—
214C22—82no—
215C22#463×C12712yes—
216C22#466×C12711yescharacteristic
217C4—22no—
218C4—41no—
219C4—82no—
220C4#394×C12711yescharacteristic
221C4#459×C12712yes—
222C4#469×C12711yescharacteristic
223C2—21no—
224C2—22no—
225C2—162no—
226C2C127×#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 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2150C2semidirect
3. C127×#2148C2semidirect
4. C127×#1974C2semidirect
5. C127×#1385C2semidirect
109. #13444C127direct (N × H)
115. #2150C2×C127semidirect
116. #2148C2×C127semidirect
117. #1974C2×C127semidirect
118. #1385C2×C127semidirect
119. C127#13444direct (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×#21502
C127×#21482
C127×#19742
C127×#13852
#13444127