Finite Group Databasebeta

← C127×#10635 #44574308

Subgroups — C127×#10635 #44574308

Order 32512.

294 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1960C211yesmaximal, characteristic
2C127×#1838C211yesmaximal, characteristic
3C127×#1546C212yesmaximal
4C127×#1286C212yesmaximal
5C127×#1281C211yesmaximal, characteristic
6C2×C4⋊Q8×C127C2211yescharacteristic
7#431×C127C2212yes—
8#423×C127C2212yes—
9C2×#103×C127—22no—
10C2×#97×C127C2211yescharacteristic
11#382×C127C2211yescharacteristic
12#341×C127—22no—
13#332×C127—24no—
14C22×Q8×C127—21no—
15C2×M16×C127—22no—
16C22×C8×C127D412yes—
17C4⋊Q8×C127—22no—
18C4⋊Q8×C127—21no—
19C4⋊Q8×C127D412yes—
20C2×C4⋊C4×C127—22no—
21C2×C4⋊C4×C127—21no—
22C2×C42×C127C2311yescharacteristic
23C4⋊C8×C127—22no—
24C4⋊C8×C127—22no—
25C4⋊C8×C127—22no—
26#103×C127—44no—
27C22⋊C8×C127—22no—
28#97×C127—22no—
29C4×C8×C127—22no—
30#95×C127—22no—
31C2×Q8×C127—22no—
32C2×Q8×C127—41no—
33C2×Q8×C127—42no—
34C2×Q8×C127—42no—
35C22×C4×C127—41no—
36C22×C4×C127—41no—
37C22×C4×C127C2×D411yescharacteristic
38C22×C4×C127#4112yes—
39M16×C127—42no—
40M16×C127—42no—
41C2×C8×C127—22no—
42C2×C8×C127—22no—
43C2×C8×C127—22no—
44C2×C8×C127—42no—
45C2×C8×C127—42no—
46C4⋊C4×C127—24no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127—42no—
49C42×C127C2×D411yescharacteristic
50C42×C127#4111yescharacteristic
51C42×C127#4112yes—
52C23×C127#12411yescharacteristic
53Q8×C127—44no—
54Q8×C127—82no—
55C2×C4×C127—42no—
56C2×C4×C127—42no—
57C2×C4×C127—81no—
58C2×C4×C127—81no—
59C2×C4×C127—82no—
60C2×C4×C127—81no—
61C2×C4×C127#12111yescharacteristic
62C2×C4×C127#12312yes—
63C2×C4×C127#12311yescharacteristic
64C2×C4×C127#12612yes—
65C2×C4×C127#13512yes—
66C2×C4×C127AGL(1,ℤ/8)12yes—
67C8×C127—42no—
68C8×C127—82no—
69C8×C127—82no—
70C22×C127—22no—
71C22×C127#39711yescharacteristic
72C22×C127#48811yescharacteristic
73C22×C127#49011yescharacteristic
74C4×C127—22no—
75C4×C127—22no—
76C4×C127—82no—
77C4×C127—161no—
78C4×C127#46312yes—
79C4×C127#48212yes—
80#10635C12711yesmaximal, characteristic, direct product factor, Sylow
81C2×C127—21no—
82C2×C127—21no—
83C2×C127#207311yescharacteristic
84C2×C127#208212yes—
85#1960C2×C12711yescharacteristic
86#1838C2×C12711yescharacteristic
87#1546C2×C12712yes—
88#1286C2×C12712yes—
89#1281C2×C12711yescharacteristic
90C127#1063511yescharacteristic, direct product factor, Sylow
91C2×C4⋊Q8C22×C12711yescharacteristic
92#431C22×C12712yes—
93#423C22×C12712yes—
94C2×#103—22no—
95C2×#97C22×C12711yescharacteristic
96#382C22×C12711yescharacteristic
97#341—22no—
98#332—24no—
99C22×Q8—21no—
100C2×M16—22no—
101C22×C8D4×C12712yes—
102C4⋊Q8—22no—
103C4⋊Q8—21no—
104C4⋊Q8D4×C12712yes—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C42C23×C12711yescharacteristic
108C4⋊C8—22no—
109C4⋊C8—22no—
110C4⋊C8—22no—
111#103—44no—
112C22⋊C8—22no—
113#97—22no—
114C4×C8—22no—
115#95—22no—
116C2×Q8—22no—
117C2×Q8—41no—
118C2×Q8—42no—
119C2×Q8—42no—
120C22×C4—41no—
121C22×C4—41no—
122C22×C4C2×D4×C12711yescharacteristic
123C22×C4#41×C12712yes—
124M16—42no—
125M16—42no—
126C2×C8—22no—
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—42no—
130C2×C8—42no—
131C4⋊C4—24no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C42C2×D4×C12711yescharacteristic
135C42#41×C12711yescharacteristic
136C42#41×C12712yes—
137C23#124×C12711yescharacteristic
138Q8—44no—
139Q8—82no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—81no—
143C2×C4—81no—
144C2×C4—82no—
145C2×C4—81no—
146C2×C4#121×C12711yescharacteristic
147C2×C4#123×C12712yes—
148C2×C4#123×C12711yescharacteristic
149C2×C4#126×C12712yes—
150C2×C4#135×C12712yes—
151C2×C4AGL(1,ℤ/8)×C12712yes—
152C8—42no—
153C8—82no—
154C8—82no—
155C22—22no—
156C22#397×C12711yescharacteristic
157C22#488×C12711yescharacteristic
158C22#490×C12711yescharacteristic
159C4—22no—
160C4—22no—
161C4—82no—
162C4—161no—
163C4#463×C12712yes—
164C4#482×C12712yes—
165C2—21no—
166C2—21no—
167C2C127×#207311yescharacteristic
168C2C127×#208212yes—
subgroupG/H
center, socleC22×C127#397
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
80. #10635C127direct (N × H)
90. C127#10635direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19602
C127×#18382
C127×#15462
C127×#12862
C127×#12812
#10635127