Finite Group Databasebeta

← C127×#12499 #44576172

Subgroups — C127×#12499 #44576172

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×#2226C212yesmaximal
2C127×#1713C211yesmaximal, characteristic, complemented
3C127×#1589C211yesmaximal, characteristic
4C127×#1367C211yesmaximal, characteristic, complemented
5C127×#1365C212yesmaximal, complemented
6#500×C127—21no—
7#500×C127C2212yes—
8#494×C127—21no—
9C4×D8×C127C2211yescharacteristic
10#436×C127—21no—
11#367×C127—22no—
12C4⋊C16×C127C2212yes—
13#357×C127—22no—
14#335×C127C2211yescharacteristic
15D4⋊C8×C127—21no—
16C82×C127C2211yescharacteristic
17C2×Q16×C127—42no—
18C2×D8×C127D411yescharacteristic
19C2×M16×C127—41no—
20C4⋊Q8×C127—22no—
21C4×D4×C127—21no—
22C2×C16×C127—22no—
23#107×C127—22no—
24#107×C127—22no—
25#107×C127—41no—
26#107×C127—41no—
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—84no—
38D8×C127—22no—
39M16×C127—82no—
40C2×C8×C127—21no—
41C2×C8×C127—41no—
42C2×C8×C127D811yescharacteristic
43C2×C8×C127D811yescharacteristic
44C2×C8×C127C2×D411yescharacteristic
45C2×C8×C127#4111yescharacteristic
46C4⋊C4×C127—21no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127—42no—
49C22⋊C4×C127—41no—
50C42×C127C2×D411yescharacteristic
51C16×C127—42no—
52C23×C127—41no—
53Q8×C127—84no—
54D4×C127—41no—
55D4×C127—41no—
56C2×C4×C127—41no—
57C2×C4×C127—81no—
58C2×C4×C127—81no—
59C2×C4×C127—82no—
60C2×C4×C127#12111yescharacteristic
61C2×C4×C127C2×D811yescharacteristic
62C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
63C8×C127—22no—
64C8×C127—21no—
65C8×C127—21no—
66C8×C127—81no—
67C8×C127SD3212yes—
68C8×C127#13712yes—
69C22×C127—81no—
70C22×C127—81no—
71C22×C127—81no—
72C22×C127#45911yescharacteristic
73C4×C127—21no—
74C4×C127—81no—
75C4×C127—162no—
76C4×C127#47011yescharacteristic
77C4×C127#47311yescharacteristic
78C4×C127C2×SD3211yescharacteristic
79C4×C127#51011yescharacteristic
80#12499C12711yesmaximal, characteristic, direct product factor, Sylow
81C2×C127—161no—
82C2×C127#168911yescharacteristic
83C2×C127#220811yescharacteristic
84C2×C127#221311yescharacteristic
85#2226C2×C12712yes—
86#1713C2×C12711yescharacteristic, complemented
87#1589C2×C12711yescharacteristic
88#1367C2×C12711yescharacteristic, complemented
89#1365C2×C12712yescomplemented
90C127#1249911yescharacteristic, direct product factor, Sylow
91#500—21no—
92#500C22×C12712yes—
93#494—21no—
94C4×D8C22×C12711yescharacteristic
95#436—21no—
96#367—22no—
97C4⋊C16C22×C12712yes—
98#357—22no—
99#335C22×C12711yescharacteristic
100D4⋊C8—21no—
101C82C22×C12711yescharacteristic
102C2×Q16—42no—
103C2×D8D4×C12711yescharacteristic
104C2×M16—41no—
105C4⋊Q8—22no—
106C4×D4—21no—
107C2×C16—22no—
108#107—22no—
109#107—22no—
110#107—41no—
111#107—41no—
112#107D4×C12711yescharacteristic
113C4⋊C8—21no—
114#102—21no—
115C22⋊C8—41no—
116C4×C8D4×C12711yescharacteristic
117C4×C8D4×C12711yescharacteristic
118C4×C8C23×C12711yescharacteristic
119C2×Q8—42no—
120C2×D4—21no—
121C22×C4—41no—
122Q16—84no—
123D8—22no—
124M16—82no—
125C2×C8—21no—
126C2×C8—41no—
127C2×C8D8×C12711yescharacteristic
128C2×C8D8×C12711yescharacteristic
129C2×C8C2×D4×C12711yescharacteristic
130C2×C8#41×C12711yescharacteristic
131C4⋊C4—21no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C22⋊C4—41no—
135C42C2×D4×C12711yescharacteristic
136C16—42no—
137C23—41no—
138Q8—84no—
139D4—41no—
140D4—41no—
141C2×C4—41no—
142C2×C4—81no—
143C2×C4—81no—
144C2×C4—82no—
145C2×C4#121×C12711yescharacteristic
146C2×C4C2×D8×C12711yescharacteristic
147C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
148C8—22no—
149C8—21no—
150C8—21no—
151C8—81no—
152C8SD32×C12712yes—
153C8#137×C12712yes—
154C22—81no—
155C22—81no—
156C22—81no—
157C22#459×C12711yescharacteristic
158C4—21no—
159C4—81no—
160C4—162no—
161C4#470×C12711yescharacteristic
162C4#473×C12711yescharacteristic
163C4C2×SD32×C12711yescharacteristic
164C4#510×C12711yescharacteristic
165C2—161no—
166C2C127×#168911yescharacteristic
167C2C127×#220811yescharacteristic
168C2C127×#221311yescharacteristic
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×#1365C2semidirect
80. #12499C127direct (N × H)
86. #1713C2×C127semidirect
88. #1367C2×C127semidirect
89. #1365C2×C127semidirect
90. C127#12499direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22262
C127×#17132
C127×#15892
C127×#13672
C127×#13652
#12499127