Finite Group Databasebeta

← C127×#13544 #44577217

Subgroups — C127×#13544 #44577217

Order 32512.

212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 94 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×#1953C211yesmaximal, characteristic
2C127×#1833C211yesmaximal, characteristic
3C127×#1389C211yesmaximal, characteristic
4C127×#1385C211yesmaximal, characteristic
5C127×#1382C211yesmaximal, characteristic
6C127×#1381C211yesmaximal, characteristic
7C127×#1379C211yesmaximal, characteristic
8C2×M32×C127C2211yescharacteristic
9C22×C16×C127C2211yescharacteristic
10#430×C127—21no—
11C2×#108×C127C2211yescharacteristic
12C2×#108×C127C2211yescharacteristic
13C2×#108×C127C2211yescharacteristic
14#427×C127C2211yescharacteristic
15#405×C127C2211yescharacteristic
16#344×C127—21no—
17#344×C127—21no—
18H(3,ℤ/4)×C127—21no—
19C2×M16×C127—21no—
20C2×M16×C127—21no—
21C2×M16×C127—21no—
22C2×M16×C127D411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24#117×C127—21no—
25#117×C127D411yescharacteristic
26M32×C127—21no—
27M32×C127—21no—
28C2×C16×C127—21no—
29C2×C16×C127—21no—
30C2×C16×C127—21no—
31C2×C16×C127—21no—
32#108×C127—21no—
33#108×C127—21no—
34#108×C127—21no—
35#108×C127—21no—
36#108×C127—21no—
37#108×C127—42no—
38#108×C127Q812yes—
39#107×C127—21no—
40#106×C127—21no—
41#97×C127—21no—
42C4×C8×C127—21no—
43C22×C4×C127C2×D411yescharacteristic
44M16×C127—22no—
45M16×C127—21no—
46M16×C127—21no—
47M16×C127—41no—
48M16×C127—41no—
49M16×C127—41no—
50M16×C127—41no—
51M16×C127—41no—
52C2×C8×C127—21no—
53C2×C8×C127—41no—
54C2×C8×C127—41no—
55C2×C8×C127—41no—
56C2×C8×C127C2×Q811yescharacteristic
57C2×C8×C127#4111yescharacteristic
58C2×C8×C127#4111yescharacteristic
59C2×C8×C127#4111yescharacteristic
60C2×C8×C127#4111yescharacteristic
61C2×C8×C127#4111yescharacteristic
62C4⋊C4×C127—21no—
63C4⋊C4×C127—41no—
64C22⋊C4×C127—21no—
65C22⋊C4×C127—41no—
66C42×C127—21no—
67C42×C127—41no—
68C16×C127—41no—
69C16×C127—41no—
70C23×C127#13711yescharacteristic
71C2×C4×C127—41no—
72C2×C4×C127—81no—
73C2×C4×C127C22⋊Q811yescharacteristic
74C2×C4×C127#12311yescharacteristic
75C2×C4×C127#12411yescharacteristic
76C2×C4×C127#13511yescharacteristic
77C2×C4×C127#13511yescharacteristic
78C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
79C8×C127—42no—
80C8×C127—41no—
81C8×C127—81no—
82C8×C127—81no—
83C8×C127#12511yescharacteristic
84C8×C127#12511yescharacteristic
85C8×C127#12611yescharacteristic
86C8×C127#12611yescharacteristic
87C22×C127—41no—
88C22×C127#47911yescharacteristic
89C22×C127#48511yescharacteristic
90C22×C127#48911yescharacteristic
91C4×C127—81no—
92C4×C127—161no—
93C4×C127#40011yescharacteristic
94C4×C127#47811yescharacteristic
95C4×C127#48211yescharacteristic
96C4×C127#48811yescharacteristic
97#13544C12711yesmaximal, characteristic, direct product factor, Sylow
98C2×C127—21no—
99C2×C127—21no—
100C2×C127—21no—
101C2×C127#210111yescharacteristic
102#1953C2×C12711yescharacteristic
103#1833C2×C12711yescharacteristic
104#1389C2×C12711yescharacteristic
105#1385C2×C12711yescharacteristic
106#1382C2×C12711yescharacteristic
107#1381C2×C12711yescharacteristic
108#1379C2×C12711yescharacteristic
109C127#1354411yescharacteristic, direct product factor, Sylow
110C2×M32C22×C12711yescharacteristic
111C22×C16C22×C12711yescharacteristic
112#430—21no—
113C2×#108C22×C12711yescharacteristic
114C2×#108C22×C12711yescharacteristic
115C2×#108C22×C12711yescharacteristic
116#427C22×C12711yescharacteristic
117#405C22×C12711yescharacteristic
118#344—21no—
119#344—21no—
120H(3,ℤ/4)—21no—
121C2×M16—21no—
122C2×M16—21no—
123C2×M16—21no—
124C2×M16D4×C12711yescharacteristic
125C22×C8C23×C12711yescharacteristic
126#117—21no—
127#117D4×C12711yescharacteristic
128M32—21no—
129M32—21no—
130C2×C16—21no—
131C2×C16—21no—
132C2×C16—21no—
133C2×C16—21no—
134#108—21no—
135#108—21no—
136#108—21no—
137#108—21no—
138#108—21no—
139#108—42no—
140#108Q8×C12712yes—
141#107—21no—
142#106—21no—
143#97—21no—
144C4×C8—21no—
145C22×C4C2×D4×C12711yescharacteristic
146M16—22no—
147M16—21no—
148M16—21no—
149M16—41no—
150M16—41no—
151M16—41no—
152M16—41no—
153M16—41no—
154C2×C8—21no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8C2×Q8×C12711yescharacteristic
159C2×C8#41×C12711yescharacteristic
160C2×C8#41×C12711yescharacteristic
161C2×C8#41×C12711yescharacteristic
162C2×C8#41×C12711yescharacteristic
163C2×C8#41×C12711yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—41no—
166C22⋊C4—21no—
167C22⋊C4—41no—
168C42—21no—
169C42—41no—
170C16—41no—
171C16—41no—
172C23#137×C12711yescharacteristic
173C2×C4—41no—
174C2×C4—81no—
175C2×C4C22⋊Q8×C12711yescharacteristic
176C2×C4#123×C12711yescharacteristic
177C2×C4#124×C12711yescharacteristic
178C2×C4#135×C12711yescharacteristic
179C2×C4#135×C12711yescharacteristic
180C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
181C8—42no—
182C8—41no—
183C8—81no—
184C8—81no—
185C8#125×C12711yescharacteristic
186C8#125×C12711yescharacteristic
187C8#126×C12711yescharacteristic
188C8#126×C12711yescharacteristic
189C22—41no—
190C22#479×C12711yescharacteristic
191C22#485×C12711yescharacteristic
192C22#489×C12711yescharacteristic
193C4—81no—
194C4—161no—
195C4#400×C12711yescharacteristic
196C4#478×C12711yescharacteristic
197C4#482×C12711yescharacteristic
198C4#488×C12711yescharacteristic
199C2—21no—
200C2—21no—
201C2—21no—
202C2C127×#210111yescharacteristic
subgroupG/H
centerC4×C127#482
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2101
prime radicalC23×C127#137
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
97. #13544C127direct (N × H)
109. C127#13544direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19532
C127×#18332
C127×#13892
C127×#13852
C127×#13822
C127×#13812
C127×#13792
#13544127