Finite Group Databasebeta

← C127×#13664 #44577337

Subgroups — C127×#13664 #44577337

Order 32512.

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

normal subgroups only

This group has 324 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×D16×C127C211yesmaximal, characteristic
2C2×SD64×C127C212yesmaximal, complemented
3C127×#2216C211yesmaximal, characteristic, complemented
4C127×#1415C212yesmaximal, complemented
5C127×C22⋊C32C211yesmaximal, characteristic, complemented
6C22×D8×C127—21no—
7C2×Q32×C127C2211yescharacteristic, complemented
8C2×D16×C127—24no—
9C2×D16×C127—21no—
10C2×D16×C127C2212yes—
11C22×C16×C127C2211yescharacteristic
12#467×C127—21no—
13SD64×C127—24no—
14C2×C32×C127C2212yescomplemented
15#366×C127C2211yescharacteristic, complemented
16#358×C127—21no—
17C22×D4×C127—41no—
18C2×Q16×C127—21no—
19C2×D8×C127—24no—
20C2×D8×C127—22no—
21C2×D8×C127—42no—
22C2×D8×C127—41no—
23C22×C8×C127D411yescharacteristic
24C22⋊Q8×C127—41no—
25Q32×C127—22no—
26D16×C127—24no—
27D16×C127—22no—
28D16×C127D414yes—
29C2×C16×C127—22no—
30C2×C16×C127D411yescharacteristic
31C2×C16×C127C2311yescharacteristic
32#107×C127—21no—
33#103×C127—41no—
34C32×C127—22no—
35C24×C127—81no—
36C2×Q8×C127—41no—
37C2×D4×C127—44no—
38C2×D4×C127—42no—
39C2×D4×C127—82no—
40C2×D4×C127—81no—
41C22×C4×C127D811yescharacteristic
42Q16×C127—41no—
43Q16×C127—41no—
44D8×C127—24no—
45D8×C127—44no—
46D8×C127—42no—
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×C127—84no—
57C23×C127—82no—
58C23×C127—162no—
59C23×C127—162no—
60C23×C127D1611yescharacteristic
61Q8×C127—81no—
62Q8×C127—81no—
63D4×C127—44no—
64D4×C127—84no—
65D4×C127—82no—
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—81no—
69C2×C4×C127—81no—
70C2×C4×C127D1611yescharacteristic
71C2×C4×C127C2×D811yescharacteristic
72C8×C127—21no—
73C8×C127#12011yescharacteristic
74C8×C127AGL(1,ℤ/8)11yescharacteristic
75C22×C127—21no—
76C22×C127—21no—
77C22×C127—84no—
78C22×C127—168no—
79C22×C127—162no—
80C22×C127—162no—
81C22×C127SD6412yescomplemented
82C22×C127C2×D1611yescharacteristic
83C4×C127—21no—
84C4×C127—161no—
85C4×C127—161no—
86C4×C127#44711yescharacteristic
87C4×C127#50911yescharacteristic
88#13664C12711yesmaximal, characteristic, direct product factor, Sylow
89C2×C127—22no—
90C2×C127—164no—
91C2×C127#218411yescharacteristic
92C2×C127C2×SD6411yescharacteristic
93C2×C127#226311yescharacteristic
94C22×D16C2×C12711yescharacteristic
95C2×SD64C2×C12712yescomplemented
96#2216C2×C12711yescharacteristic, complemented
97#1415C2×C12712yescomplemented
98C22⋊C32C2×C12711yescharacteristic, complemented
99C127#1366411yescharacteristic, direct product factor, Sylow
100C22×D8—21no—
101C2×Q32C22×C12711yescharacteristic, complemented
102C2×D16—24no—
103C2×D16—21no—
104C2×D16C22×C12712yes—
105C22×C16C22×C12711yescharacteristic
106#467—21no—
107SD64—24no—
108C2×C32C22×C12712yescomplemented
109#366C22×C12711yescharacteristic, complemented
110#358—21no—
111C22×D4—41no—
112C2×Q16—21no—
113C2×D8—24no—
114C2×D8—22no—
115C2×D8—42no—
116C2×D8—41no—
117C22×C8D4×C12711yescharacteristic
118C22⋊Q8—41no—
119Q32—22no—
120D16—24no—
121D16—22no—
122D16D4×C12714yes—
123C2×C16—22no—
124C2×C16D4×C12711yescharacteristic
125C2×C16C23×C12711yescharacteristic
126#107—21no—
127#103—41no—
128C32—22no—
129C24—81no—
130C2×Q8—41no—
131C2×D4—44no—
132C2×D4—42no—
133C2×D4—82no—
134C2×D4—81no—
135C22×C4D8×C12711yescharacteristic
136Q16—41no—
137Q16—41no—
138D8—24no—
139D8—44no—
140D8—42no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8D8×C12711yescharacteristic
144C2×C8C2×D4×C12711yescharacteristic
145C4⋊C4—41no—
146C4⋊C4—81no—
147C22⋊C4—81no—
148C16—21no—
149C16C2×D4×C12712yes—
150C23—84no—
151C23—82no—
152C23—162no—
153C23—162no—
154C23D16×C12711yescharacteristic
155Q8—81no—
156Q8—81no—
157D4—44no—
158D4—84no—
159D4—82no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4D16×C12711yescharacteristic
165C2×C4C2×D8×C12711yescharacteristic
166C8—21no—
167C8#120×C12711yescharacteristic
168C8AGL(1,ℤ/8)×C12711yescharacteristic
169C22—21no—
170C22—21no—
171C22—84no—
172C22—168no—
173C22—162no—
174C22—162no—
175C22SD64×C12712yescomplemented
176C22C2×D16×C12711yescharacteristic
177C4—21no—
178C4—161no—
179C4—161no—
180C4#447×C12711yescharacteristic
181C4#509×C12711yescharacteristic
182C2—22no—
183C2—164no—
184C2C127×#218411yescharacteristic
185C2C2×SD64×C12711yescharacteristic
186C2C127×#226311yescharacteristic
subgroupG/H
center, socleC22×C127C2×D16
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC22×D16×C127C2
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×SD64×C127C2semidirect
3. C127×#2216C2semidirect
4. C127×#1415C2semidirect
5. C127×C22⋊C32C2semidirect
7. C2×Q32×C127C22semidirect
14. C2×C32×C127C22semidirect
15. #366×C127C22semidirect
81. C22×C127SD64semidirect
88. #13664C127direct (N × H)
95. C2×SD64C2×C127semidirect
96. #2216C2×C127semidirect
97. #1415C2×C127semidirect
98. C22⋊C32C2×C127semidirect
99. C127#13664direct (N × H)
101. C2×Q32C22×C127semidirect
108. C2×C32C22×C127semidirect
109. #366C22×C127semidirect
175. C22SD64×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D16×C1272
C2×SD64×C1272
C127×#22162
C127×#14152
C127×C22⋊C322
#13664127