Finite Group Databasebeta

← C127×#12497 #44576170

Subgroups — C127×#12497 #44576170

Order 32512.

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

normal subgroups only

This group has 226 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
1C127×#2224C212yesmaximal
2C127×#1713C211yesmaximal, characteristic, complemented
3C127×#1589C211yesmaximal, characteristic
4C127×#1367C211yesmaximal, characteristic, complemented
5C127×#1364C212yesmaximal, complemented
6#500×C127—21no—
7#500×C127C2212yes—
8#494×C127—21no—
9C4×D8×C127C2211yescharacteristic
10#436×C127—21no—
11#366×C127—22no—
12C4⋊C16×C127C2212yes—
13#357×C127—22no—
14#335×C127C2211yescharacteristic
15D4⋊C8×C127—21no—
16C82×C127C2211yescharacteristic
17C2×Q16×C127—41no—
18C2×Q16×C127—41no—
19C2×D8×C127D411yescharacteristic
20C2×M16×C127—41no—
21C4⋊Q8×C127—22no—
22C4×D4×C127—21no—
23C2×C16×C127—22no—
24#107×C127—22no—
25#107×C127—22no—
26#107×C127—42no—
27#107×C127D411yescharacteristic
28C4⋊C8×C127—21no—
29#102×C127—21no—
30C22⋊C8×C127—41no—
31C4×C8×C127D411yescharacteristic
32C4×C8×C127D411yescharacteristic
33C4×C8×C127C2311yescharacteristic
34C2×Q8×C127—42no—
35C2×D4×C127—21no—
36C22×C4×C127—41no—
37Q16×C127—82no—
38Q16×C127—82no—
39D8×C127—22no—
40M16×C127—82no—
41C2×C8×C127—21no—
42C2×C8×C127—41no—
43C2×C8×C127D811yescharacteristic
44C2×C8×C127D811yescharacteristic
45C2×C8×C127C2×D411yescharacteristic
46C2×C8×C127#4111yescharacteristic
47C4⋊C4×C127—21no—
48C4⋊C4×C127—42no—
49C4⋊C4×C127—42no—
50C22⋊C4×C127—41no—
51C42×C127C2×D411yescharacteristic
52C16×C127—42no—
53C23×C127—41no—
54Q8×C127—82no—
55Q8×C127—82no—
56D4×C127—41no—
57D4×C127—41no—
58C2×C4×C127—41no—
59C2×C4×C127—81no—
60C2×C4×C127—81no—
61C2×C4×C127—82no—
62C2×C4×C127#12111yescharacteristic
63C2×C4×C127C2×D811yescharacteristic
64C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
65C8×C127—22no—
66C8×C127—21no—
67C8×C127—21no—
68C8×C127—81no—
69C8×C127D1612yes—
70C8×C127#13712yes—
71C22×C127—81no—
72C22×C127—81no—
73C22×C127—81no—
74C22×C127#45911yescharacteristic
75C4×C127—21no—
76C4×C127—81no—
77C4×C127—162no—
78C4×C127#47011yescharacteristic
79C4×C127#47311yescharacteristic
80C4×C127C2×D1611yescharacteristic
81C4×C127#50911yescharacteristic
82#12497C12711yesmaximal, characteristic, direct product factor, Sylow
83C2×C127—161no—
84C2×C127#168911yescharacteristic
85C2×C127#220611yescharacteristic
86C2×C127#221411yescharacteristic
87#2224C2×C12712yes—
88#1713C2×C12711yescharacteristic, complemented
89#1589C2×C12711yescharacteristic
90#1367C2×C12711yescharacteristic, complemented
91#1364C2×C12712yescomplemented
92C127#1249711yescharacteristic, direct product factor, Sylow
93#500—21no—
94#500C22×C12712yes—
95#494—21no—
96C4×D8C22×C12711yescharacteristic
97#436—21no—
98#366—22no—
99C4⋊C16C22×C12712yes—
100#357—22no—
101#335C22×C12711yescharacteristic
102D4⋊C8—21no—
103C82C22×C12711yescharacteristic
104C2×Q16—41no—
105C2×Q16—41no—
106C2×D8D4×C12711yescharacteristic
107C2×M16—41no—
108C4⋊Q8—22no—
109C4×D4—21no—
110C2×C16—22no—
111#107—22no—
112#107—22no—
113#107—42no—
114#107D4×C12711yescharacteristic
115C4⋊C8—21no—
116#102—21no—
117C22⋊C8—41no—
118C4×C8D4×C12711yescharacteristic
119C4×C8D4×C12711yescharacteristic
120C4×C8C23×C12711yescharacteristic
121C2×Q8—42no—
122C2×D4—21no—
123C22×C4—41no—
124Q16—82no—
125Q16—82no—
126D8—22no—
127M16—82no—
128C2×C8—21no—
129C2×C8—41no—
130C2×C8D8×C12711yescharacteristic
131C2×C8D8×C12711yescharacteristic
132C2×C8C2×D4×C12711yescharacteristic
133C2×C8#41×C12711yescharacteristic
134C4⋊C4—21no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C22⋊C4—41no—
138C42C2×D4×C12711yescharacteristic
139C16—42no—
140C23—41no—
141Q8—82no—
142Q8—82no—
143D4—41no—
144D4—41no—
145C2×C4—41no—
146C2×C4—81no—
147C2×C4—81no—
148C2×C4—82no—
149C2×C4#121×C12711yescharacteristic
150C2×C4C2×D8×C12711yescharacteristic
151C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
152C8—22no—
153C8—21no—
154C8—21no—
155C8—81no—
156C8D16×C12712yes—
157C8#137×C12712yes—
158C22—81no—
159C22—81no—
160C22—81no—
161C22#459×C12711yescharacteristic
162C4—21no—
163C4—81no—
164C4—162no—
165C4#470×C12711yescharacteristic
166C4#473×C12711yescharacteristic
167C4C2×D16×C12711yescharacteristic
168C4#509×C12711yescharacteristic
169C2—161no—
170C2C127×#168911yescharacteristic
171C2C127×#220611yescharacteristic
172C2C127×#221411yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC2×D8×C127D4
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1713C2semidirect
4. C127×#1367C2semidirect
5. C127×#1364C2semidirect
82. #12497C127direct (N × H)
88. #1713C2×C127semidirect
90. #1367C2×C127semidirect
91. #1364C2×C127semidirect
92. C127#12497direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22242
C127×#17132
C127×#15892
C127×#13672
C127×#13642
#12497127