Finite Group Databasebeta

← C127×#12305 #44575978

Subgroups — C127×#12305 #44575978

Order 32512.

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

normal subgroups only

This group has 262 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×#3261C211yesmaximal, characteristic
2C127×#2239C212yesmaximal
3C127×#2103C211yesmaximal, characteristic
4C127×#1342C212yesmaximal
5C127×#1328C211yesmaximal, characteristic
6#541×C127—21no—
7#479×C127—22no—
8#470×C127C2212yes—
9#467×C127—21no—
10#462×C127—22no—
11#430×C127C2211yescharacteristic
12#424×C127C2211yescharacteristic
13#365×C127—22no—
14#362×C127—22no—
15#349×C127C2212yes—
16#344×C127—21no—
17#341×C127—21no—
18#338×C127C2211yescharacteristic
19C2×Q16×C127—21no—
20C2×Q16×C127D412yes—
21C2×M16×C127—21no—
22C2×M16×C127—21no—
23C2×M16×C127C2311yescharacteristic
24C22×C8×C127D411yescharacteristic
25C4⋊Q8×C127—21no—
26#126×C127—42no—
27#125×C127—21no—
28#125×C127—42no—
29C22⋊Q8×C127—22no—
30C4×Q8×C127—22no—
31#117×C127D411yescharacteristic
32M32×C127—22no—
33#108×C127—22no—
34#107×C127—21no—
35#106×C127D412yes—
36C4⋊C8×C127—22no—
37#103×C127—22no—
38#103×C127—22no—
39C2×Q8×C127—22no—
40C22×C4×C127C2×D411yescharacteristic
41Q16×C127—42no—
42Q16×C127—81no—
43M16×C127—41no—
44M16×C127—41no—
45M16×C127—41no—
46M16×C127—41no—
47M16×C127—41no—
48C2×C8×C127—21no—
49C2×C8×C127—41no—
50C2×C8×C127—41no—
51C2×C8×C127—41no—
52C2×C8×C127C2×D412yes—
53C4⋊C4×C127—21no—
54C4⋊C4×C127—22no—
55C4⋊C4×C127—42no—
56C4⋊C4×C127—42no—
57C4⋊C4×C127—42no—
58C4⋊C4×C127—42no—
59C22⋊C4×C127—42no—
60C22⋊C4×C127SD1612yes—
61C42×C127—21no—
62C42×C127—42no—
63C16×C127—42no—
64C23×C127C2×SD1611yescharacteristic
65Q8×C127—42no—
66Q8×C127—42no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127—22no—
70C2×C4×C127—42no—
71C2×C4×C127—42no—
72C2×C4×C127#12011yescharacteristic
73C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
74C8×C127—22no—
75C8×C127—41no—
76C8×C127—81no—
77C8×C127—81no—
78C22×C127—21no—
79C22×C127—41no—
80C22×C127#45011yescharacteristic
81C4×C127—21no—
82C4×C127—42no—
83C4×C127—82no—
84C4×C127—82no—
85C4×C127#45411yescharacteristic
86C4×C127#45811yescharacteristic
87#12305C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—21no—
89C2×C127—41no—
90C2×C127#161611yescharacteristic
91#3261C2×C12711yescharacteristic
92#2239C2×C12712yes—
93#2103C2×C12711yescharacteristic
94#1342C2×C12712yes—
95#1328C2×C12711yescharacteristic
96C127#1230511yescharacteristic, direct product factor, Sylow
97#541—21no—
98#479—22no—
99#470C22×C12712yes—
100#467—21no—
101#462—22no—
102#430C22×C12711yescharacteristic
103#424C22×C12711yescharacteristic
104#365—22no—
105#362—22no—
106#349C22×C12712yes—
107#344—21no—
108#341—21no—
109#338C22×C12711yescharacteristic
110C2×Q16—21no—
111C2×Q16D4×C12712yes—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16C23×C12711yescharacteristic
115C22×C8D4×C12711yescharacteristic
116C4⋊Q8—21no—
117#126—42no—
118#125—21no—
119#125—42no—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117D4×C12711yescharacteristic
123M32—22no—
124#108—22no—
125#107—21no—
126#106D4×C12712yes—
127C4⋊C8—22no—
128#103—22no—
129#103—22no—
130C2×Q8—22no—
131C22×C4C2×D4×C12711yescharacteristic
132Q16—42no—
133Q16—81no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8C2×D4×C12712yes—
144C4⋊C4—21no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C22⋊C4—42no—
151C22⋊C4SD16×C12712yes—
152C42—21no—
153C42—42no—
154C16—42no—
155C23C2×SD16×C12711yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4#120×C12711yescharacteristic
164C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22#450×C12711yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4#454×C12711yescharacteristic
177C4#458×C12711yescharacteristic
178C2—21no—
179C2—41no—
180C2C127×#161611yescharacteristic
subgroupG/H
center, socleC2×C127#1616
commutator, Frattini, cosocleC2×M16C23×C127
prime radicalC23×C127C2×SD16
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
87. #12305C127direct (N × H)
96. C127#12305direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32612
C127×#22392
C127×#21032
C127×#13422
C127×#13282
#12305127