Finite Group Databasebeta

← C127×#10529 #44574202

Subgroups — C127×#10529 #44574202

Order 32512.

326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3255C211yesmaximal, characteristic
2C127×#1838C211yesmaximal, characteristic
3C127×#1559C212yesmaximal
4C127×#1531C212yesmaximal
5C127×#1307C211yesmaximal, characteristic
6#533×C127C2212yes—
7#475×C127—22no—
8#470×C127—22no—
9#462×C127—22no—
10#432×C127C2212yes—
11#423×C127C2211yescharacteristic
12#423×C127C2211yescharacteristic
13C2×#97×C127C2211yescharacteristic
14#341×C127—22no—
15#333×C127—22no—
16#332×C127—22no—
17#330×C127—24no—
18C2×Q16×C127—22no—
19C2×M16×C127—21no—
20C2×M16×C127D412yes—
21C22×C8×C127—21no—
22C4⋊Q8×C127D412yes—
23C4⋊Q8×C127D412yes—
24#125×C127—22no—
25C22⋊Q8×C127—22no—
26C22⋊Q8×C127—22no—
27C4×Q8×C127—22no—
28C4×Q8×C127—22no—
29#117×C127—22no—
30C2×C42×C127C2311yescharacteristic
31#106×C127—22no—
32C4⋊C8×C127—22no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35#103×C127—24no—
36C22⋊C8×C127—22no—
37#97×C127—22no—
38#97×C127—21no—
39#97×C127D412yes—
40C2×Q8×C127—22no—
41C2×Q8×C127—22no—
42C22×C4×C127C2×D411yescharacteristic
43C22×C4×C127#4112yes—
44Q16×C127—82no—
45M16×C127—42no—
46M16×C127—42no—
47C2×C8×C127—22no—
48C2×C8×C127—22no—
49C2×C8×C127—41no—
50C2×C8×C127—41no—
51C2×C8×C127—41no—
52C2×C8×C127—42no—
53C4⋊C4×C127—22no—
54C4⋊C4×C127—22no—
55C4⋊C4×C127—22no—
56C4⋊C4×C127—22no—
57C4⋊C4×C127—42no—
58C4⋊C4×C127—42no—
59C22⋊C4×C127—42no—
60C42×C127—42no—
61C42×C127C2×D412yes—
62C42×C127C2×D411yescharacteristic
63C42×C127#4111yescharacteristic
64C23×C127#12411yescharacteristic
65Q8×C127—42no—
66Q8×C127—42no—
67Q8×C127—82no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—42no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127#12011yescharacteristic
74C2×C4×C127#12112yes—
75C2×C4×C127#12111yescharacteristic
76C2×C4×C127#12312yes—
77C8×C127—42no—
78C8×C127—42no—
79C8×C127—82no—
80C8×C127—81no—
81C22×C127—22no—
82C22×C127—21no—
83C22×C127#39411yescharacteristic
84C4×C127—22no—
85C4×C127—22no—
86C4×C127—21no—
87C4×C127—82no—
88C4×C127—82no—
89C4×C127#45411yescharacteristic
90C4×C127#45511yescharacteristic
91#10529C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127—41no—
93C2×C127#204011yescharacteristic
94C2×C127#204912yes—
95#3255C2×C12711yescharacteristic
96#1838C2×C12711yescharacteristic
97#1559C2×C12712yes—
98#1531C2×C12712yes—
99#1307C2×C12711yescharacteristic
100C127#1052911yescharacteristic, direct product factor, Sylow
101#533C22×C12712yes—
102#475—22no—
103#470—22no—
104#462—22no—
105#432C22×C12712yes—
106#423C22×C12711yescharacteristic
107#423C22×C12711yescharacteristic
108C2×#97C22×C12711yescharacteristic
109#341—22no—
110#333—22no—
111#332—22no—
112#330—24no—
113C2×Q16—22no—
114C2×M16—21no—
115C2×M16D4×C12712yes—
116C22×C8—21no—
117C4⋊Q8D4×C12712yes—
118C4⋊Q8D4×C12712yes—
119#125—22no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124#117—22no—
125C2×C42C23×C12711yescharacteristic
126#106—22no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130#103—24no—
131C22⋊C8—22no—
132#97—22no—
133#97—21no—
134#97D4×C12712yes—
135C2×Q8—22no—
136C2×Q8—22no—
137C22×C4C2×D4×C12711yescharacteristic
138C22×C4#41×C12712yes—
139Q16—82no—
140M16—42no—
141M16—42no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8—41no—
147C2×C8—42no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C22⋊C4—42no—
155C42—42no—
156C42C2×D4×C12712yes—
157C42C2×D4×C12711yescharacteristic
158C42#41×C12711yescharacteristic
159C23#124×C12711yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—82no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4#120×C12711yescharacteristic
169C2×C4#121×C12712yes—
170C2×C4#121×C12711yescharacteristic
171C2×C4#123×C12712yes—
172C8—42no—
173C8—42no—
174C8—82no—
175C8—81no—
176C22—21no—
177C22—22no—
178C22#394×C12711yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—82no—
183C4—82no—
184C4#454×C12711yescharacteristic
185C4#455×C12711yescharacteristic
186C2—41no—
187C2C127×#204011yescharacteristic
188C2C127×#204912yes—
subgroupG/H
center, socleC22×C127#394
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
91. #10529C127direct (N × H)
100. C127#10529direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32552
C127×#18382
C127×#15592
C127×#15312
C127×#13072
#10529127