Finite Group Databasebeta

← C127×#13665 #44577338

Subgroups — C127×#13665 #44577338

Order 32512.

284 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C22×Q32×C127C211yesmaximal, characteristic
2C2×Q64×C127C212yesmaximal, complemented
3C127×#2216C211yesmaximal, characteristic
4C127×#1416C212yesmaximal, complemented
5C127×C22⋊C32C211yesmaximal, characteristic
6C22×Q16×C127—21no—
7C2×Q32×C127—24no—
8C2×Q32×C127—21no—
9C2×Q32×C127C2211yescharacteristic
10C2×Q32×C127C2212yes—
11C22×C16×C127C2211yescharacteristic
12#467×C127—21no—
13Q64×C127—24no—
14C2×C32×C127C2212yes—
15#366×C127C2211yescharacteristic
16#358×C127—21no—
17C22×Q8×C127—41no—
18C2×Q16×C127—24no—
19C2×Q16×C127—22no—
20C2×Q16×C127—21no—
21C2×Q16×C127—42no—
22C2×Q16×C127—41no—
23C22×C8×C127D411yescharacteristic
24C22⋊Q8×C127—41no—
25Q32×C127—24no—
26Q32×C127—22no—
27Q32×C127—22no—
28Q32×C127D414yes—
29C2×C16×C127—22no—
30C2×C16×C127D411yescharacteristic
31C2×C16×C127C2311yescharacteristic
32#107×C127—21no—
33#103×C127—41no—
34C32×C127—22no—
35C2×Q8×C127—44no—
36C2×Q8×C127—42no—
37C2×Q8×C127—41no—
38C2×Q8×C127—82no—
39C2×Q8×C127—81no—
40C22×C4×C127—81no—
41C22×C4×C127D811yescharacteristic
42Q16×C127—24no—
43Q16×C127—44no—
44Q16×C127—41no—
45Q16×C127—42no—
46Q16×C127—41no—
47C2×C8×C127—21no—
48C2×C8×C127—21no—
49C2×C8×C127D811yescharacteristic
50C2×C8×C127C2×D411yescharacteristic
51C4⋊C4×C127—41no—
52C4⋊C4×C127—81no—
53C22⋊C4×C127—81no—
54C16×C127—21no—
55C16×C127C2×D412yes—
56C23×C127D1611yescharacteristic
57Q8×C127—44no—
58Q8×C127—84no—
59Q8×C127—82no—
60Q8×C127—81no—
61Q8×C127—81no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—84no—
65C2×C4×C127—82no—
66C2×C4×C127—81no—
67C2×C4×C127—81no—
68C2×C4×C127D1611yescharacteristic
69C2×C4×C127C2×D811yescharacteristic
70C8×C127—21no—
71C8×C127#12011yescharacteristic
72C8×C127AGL(1,ℤ/8)11yescharacteristic
73C22×C127—21no—
74C22×C127—21no—
75C22×C127Q6412yescomplemented
76C22×C127C2×D1611yescharacteristic
77C4×C127—21no—
78C4×C127—84no—
79C4×C127—161no—
80C4×C127—161no—
81C4×C127#44711yescharacteristic
82C4×C127#50911yescharacteristic
83#13665C12711yesmaximal, characteristic, direct product factor, Sylow
84C2×C127—22no—
85C2×C127#218411yescharacteristic
86C2×C127C2×Q6411yescharacteristic
87C2×C127#226411yescharacteristic
88C22×Q32C2×C12711yescharacteristic
89C2×Q64C2×C12712yescomplemented
90#2216C2×C12711yescharacteristic
91#1416C2×C12712yescomplemented
92C22⋊C32C2×C12711yescharacteristic
93C127#1366511yescharacteristic, direct product factor, Sylow
94C22×Q16—21no—
95C2×Q32—24no—
96C2×Q32—21no—
97C2×Q32C22×C12711yescharacteristic
98C2×Q32C22×C12712yes—
99C22×C16C22×C12711yescharacteristic
100#467—21no—
101Q64—24no—
102C2×C32C22×C12712yes—
103#366C22×C12711yescharacteristic
104#358—21no—
105C22×Q8—41no—
106C2×Q16—24no—
107C2×Q16—22no—
108C2×Q16—21no—
109C2×Q16—42no—
110C2×Q16—41no—
111C22×C8D4×C12711yescharacteristic
112C22⋊Q8—41no—
113Q32—24no—
114Q32—22no—
115Q32—22no—
116Q32D4×C12714yes—
117C2×C16—22no—
118C2×C16D4×C12711yescharacteristic
119C2×C16C23×C12711yescharacteristic
120#107—21no—
121#103—41no—
122C32—22no—
123C2×Q8—44no—
124C2×Q8—42no—
125C2×Q8—41no—
126C2×Q8—82no—
127C2×Q8—81no—
128C22×C4—81no—
129C22×C4D8×C12711yescharacteristic
130Q16—24no—
131Q16—44no—
132Q16—41no—
133Q16—42no—
134Q16—41no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8D8×C12711yescharacteristic
138C2×C8C2×D4×C12711yescharacteristic
139C4⋊C4—41no—
140C4⋊C4—81no—
141C22⋊C4—81no—
142C16—21no—
143C16C2×D4×C12712yes—
144C23D16×C12711yescharacteristic
145Q8—44no—
146Q8—84no—
147Q8—82no—
148Q8—81no—
149Q8—81no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—84no—
153C2×C4—82no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4D16×C12711yescharacteristic
157C2×C4C2×D8×C12711yescharacteristic
158C8—21no—
159C8#120×C12711yescharacteristic
160C8AGL(1,ℤ/8)×C12711yescharacteristic
161C22—21no—
162C22—21no—
163C22Q64×C12712yescomplemented
164C22C2×D16×C12711yescharacteristic
165C4—21no—
166C4—84no—
167C4—161no—
168C4—161no—
169C4#447×C12711yescharacteristic
170C4#509×C12711yescharacteristic
171C2—22no—
172C2C127×#218411yescharacteristic
173C2C2×Q64×C12711yescharacteristic
174C2C127×#226411yescharacteristic
subgroupG/H
center, socleC22×C127C2×D16
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC23×C127D16
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C22×C8×C127 ◁ C22×C16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×Q64×C127C2semidirect
4. C127×#1416C2semidirect
75. C22×C127Q64semidirect
83. #13665C127direct (N × H)
89. C2×Q64C2×C127semidirect
91. #1416C2×C127semidirect
93. C127#13665direct (N × H)
163. C22Q64×C127semidirect

Maximal subgroups

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

subgroupindex
C22×Q32×C1272
C2×Q64×C1272
C127×#22162
C127×#14162
C127×C22⋊C322
#13665127