Finite Group Databasebeta

← C127×#13716 #44577389

Subgroups — C127×#13716 #44577389

Order 32512.

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2216C211yesmaximal, characteristic
2C127×#2158C211yesmaximal, characteristic
3C127×#1424C211yesmaximal, characteristic, complemented
4C127×#1423C211yesmaximal, characteristic, complemented
5C127×#1416C211yesmaximal, characteristic, complemented
6C127×#1416C211yesmaximal, characteristic, complemented
7C127×C22⋊C32C211yesmaximal, characteristic
8C2×Q32×C127C2211yescharacteristic
9C22×C16×C127C2211yescharacteristic
10#467×C127—21no—
11#427×C127—21no—
12C2×C32×C127C2211yescharacteristic
13C2×C32×C127C2211yescharacteristic
14#367×C127—21no—
15#366×C127C2211yescharacteristic
16#366×C127C2211yescharacteristic
17#366×C127C2211yescharacteristic
18#358×C127—21no—
19C2×Q16×C127—21no—
20C22×C8×C127D411yescharacteristic
21C22⋊Q8×C127—41no—
22#117×C127—41no—
23Q32×C127—21no—
24Q32×C127—21no—
25C2×C16×C127—21no—
26C2×C16×C127—21no—
27C2×C16×C127D411yescharacteristic
28C2×C16×C127C2311yescharacteristic
29#107×C127—21no—
30#107×C127—21no—
31#107×C127—21no—
32#106×C127—41no—
33#103×C127—41no—
34C32×C127—21no—
35C32×C127—21no—
36C2×Q8×C127—41no—
37C22×C4×C127D811yescharacteristic
38Q16×C127—41no—
39Q16×C127—41no—
40C2×C8×C127—21no—
41C2×C8×C127—21no—
42C2×C8×C127D811yescharacteristic
43C2×C8×C127C2×D411yescharacteristic
44C4⋊C4×C127—41no—
45C4⋊C4×C127—41no—
46C4⋊C4×C127—41no—
47C4⋊C4×C127—81no—
48C22⋊C4×C127—81no—
49C22⋊C4×C127—81no—
50C42×C127—81no—
51C16×C127—21no—
52C16×C127#4111yescharacteristic
53C16×C127#4111yescharacteristic
54C23×C127D1611yescharacteristic
55Q8×C127—81no—
56Q8×C127—81no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—81no—
60C2×C4×C127—81no—
61C2×C4×C127—81no—
62C2×C4×C127—81no—
63C2×C4×C127D1611yescharacteristic
64C2×C4×C127C2×D811yescharacteristic
65C8×C127—21no—
66C8×C127#12311yescharacteristic
67C8×C127#13711yescharacteristic
68C22×C127—21no—
69C22×C127—21no—
70C22×C127—21no—
71C22×C127C2×D1611yescharacteristic
72C4×C127—21no—
73C4×C127—161no—
74C4×C127—161no—
75C4×C127—161no—
76C4×C127—161no—
77C4×C127#48011yescharacteristic
78C4×C127#51011yescharacteristic
79#13716C12711yesmaximal, characteristic, direct product factor, Sylow
80C2×C127—41no—
81C2×C127#223211yescharacteristic
82C2×C127#226211yescharacteristic
83C2×C127#226411yescharacteristic
84#2216C2×C12711yescharacteristic
85#2158C2×C12711yescharacteristic
86#1424C2×C12711yescharacteristic, complemented
87#1423C2×C12711yescharacteristic, complemented
88#1416C2×C12711yescharacteristic, complemented
89#1416C2×C12711yescharacteristic, complemented
90C22⋊C32C2×C12711yescharacteristic
91C127#1371611yescharacteristic, direct product factor, Sylow
92C2×Q32C22×C12711yescharacteristic
93C22×C16C22×C12711yescharacteristic
94#467—21no—
95#427—21no—
96C2×C32C22×C12711yescharacteristic
97C2×C32C22×C12711yescharacteristic
98#367—21no—
99#366C22×C12711yescharacteristic
100#366C22×C12711yescharacteristic
101#366C22×C12711yescharacteristic
102#358—21no—
103C2×Q16—21no—
104C22×C8D4×C12711yescharacteristic
105C22⋊Q8—41no—
106#117—41no—
107Q32—21no—
108Q32—21no—
109C2×C16—21no—
110C2×C16—21no—
111C2×C16D4×C12711yescharacteristic
112C2×C16C23×C12711yescharacteristic
113#107—21no—
114#107—21no—
115#107—21no—
116#106—41no—
117#103—41no—
118C32—21no—
119C32—21no—
120C2×Q8—41no—
121C22×C4D8×C12711yescharacteristic
122Q16—41no—
123Q16—41no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8D8×C12711yescharacteristic
127C2×C8C2×D4×C12711yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—81no—
132C22⋊C4—81no—
133C22⋊C4—81no—
134C42—81no—
135C16—21no—
136C16#41×C12711yescharacteristic
137C16#41×C12711yescharacteristic
138C23D16×C12711yescharacteristic
139Q8—81no—
140Q8—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4D16×C12711yescharacteristic
148C2×C4C2×D8×C12711yescharacteristic
149C8—21no—
150C8#123×C12711yescharacteristic
151C8#137×C12711yescharacteristic
152C22—21no—
153C22—21no—
154C22—21no—
155C22C2×D16×C12711yescharacteristic
156C4—21no—
157C4—161no—
158C4—161no—
159C4—161no—
160C4—161no—
161C4#480×C12711yescharacteristic
162C4#510×C12711yescharacteristic
163C2—41no—
164C2C127×#223211yescharacteristic
165C2C127×#226211yescharacteristic
166C2C127×#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
3. C127×#1424C2semidirect
4. C127×#1423C2semidirect
5. C127×#1416C2semidirect
6. C127×#1416C2semidirect
79. #13716C127direct (N × H)
86. #1424C2×C127semidirect
87. #1423C2×C127semidirect
88. #1416C2×C127semidirect
89. #1416C2×C127semidirect
91. C127#13716direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22162
C127×#21582
C127×#14242
C127×#14232
C127×#14162
C127×C22⋊C322
#13716127