Finite Group Databasebeta

← C127×#11915 #44575588

Subgroups — C127×#11915 #44575588

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×#3138C211yesmaximal, characteristic
2C127×#2165C212yesmaximal, complemented
3C127×#1355C214yesmaximal, complemented
4#533×C127C411yescharacteristic
5C2×#127×C127C411yescharacteristic
6#490×C127C412yes—
7#490×C127C2212yes—
8#486×C127—22no—
9#418×C127—22no—
10C4×M16×C127C2211yescharacteristic
11#364×C127—22no—
12#349×C127—22no—
13#347×C127C2214yescomplemented
14C22×D4×C127—21no—
15C22×D4×C127—41no—
16C2×M16×C127D412yes—
17C4⋊Q8×C127—21no—
18#127×C127—21no—
19#127×C127—41no—
20#127×C127C2×C412yes—
21#125×C127C2×C412yes—
22C22⋊Q8×C127—41no—
23C4×Q8×C127—41no—
24#117×C127—21no—
25C2×C42×C127C2×C411yescharacteristic
26M32×C127—24no—
27#102×C127—24no—
28#102×C127—24no—
29#97×C127C2×C411yescharacteristic
30#97×C127C2311yescharacteristic
31C4×C8×C127D412yes—
32C24×C127—41no—
33C2×Q8×C127—41no—
34C2×D4×C127—22no—
35C2×D4×C127—44no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38C2×D4×C127—41no—
39C2×D4×C127—84no—
40C22×C4×C127—21no—
41C22×C4×C127C22⋊C411yescharacteristic
42M16×C127—42no—
43C2×C8×C127C22⋊C412yes—
44C2×C8×C127C2×D412yes—
45C4⋊C4×C127—22no—
46C4⋊C4×C127—42no—
47C4⋊C4×C127—41no—
48C22⋊C4×C127—41no—
49C42×C127—21no—
50C42×C127—41no—
51C42×C127C22⋊C411yescharacteristic
52C42×C127C22×C411yescharacteristic
53C16×C127—44no—
54C23×C127—42no—
55C23×C127—82no—
56C23×C127—84no—
57C23×C127#10011yescharacteristic
58Q8×C127—82no—
59D4×C127—44no—
60D4×C127—82no—
61D4×C127—84no—
62D4×C127—84no—
63C2×C4×C127—21no—
64C2×C4×C127—22no—
65C2×C4×C127—21no—
66C2×C4×C127—42no—
67C2×C4×C127—42no—
68C2×C4×C127#10011yescharacteristic
69C2×C4×C127C2×C22⋊C411yescharacteristic
70C8×C127—22no—
71C8×C127—22no—
72C22×C127—21no—
73C22×C127—41no—
74C22×C127—84no—
75C22×C127—82no—
76C22×C127—164no—
77C22×C127C2×#10011yescharacteristic
78C4×C127—22no—
79C4×C127—21no—
80C4×C127—41no—
81C4×C127—82no—
82C4×C127#42112yes—
83#11915C12711yesmaximal, characteristic, direct product factor, Sylow
84C2×C127—21no—
85C2×C127—41no—
86C2×C127—162no—
87C2×C127#153311yescharacteristic
88#3138C2×C12711yescharacteristic
89#2165C2×C12712yescomplemented
90#1355C2×C12714yescomplemented
91C127#1191511yescharacteristic, direct product factor, Sylow
92#533C4×C12711yescharacteristic
93C2×#127C4×C12711yescharacteristic
94#490C4×C12712yes—
95#490C22×C12712yes—
96#486—22no—
97#418—22no—
98C4×M16C22×C12711yescharacteristic
99#364—22no—
100#349—22no—
101#347C22×C12714yescomplemented
102C22×D4—21no—
103C22×D4—41no—
104C2×M16D4×C12712yes—
105C4⋊Q8—21no—
106#127—21no—
107#127—41no—
108#127C2×C4×C12712yes—
109#125C2×C4×C12712yes—
110C22⋊Q8—41no—
111C4×Q8—41no—
112#117—21no—
113C2×C42C2×C4×C12711yescharacteristic
114M32—24no—
115#102—24no—
116#102—24no—
117#97C2×C4×C12711yescharacteristic
118#97C23×C12711yescharacteristic
119C4×C8D4×C12712yes—
120C24—41no—
121C2×Q8—41no—
122C2×D4—22no—
123C2×D4—44no—
124C2×D4—42no—
125C2×D4—42no—
126C2×D4—41no—
127C2×D4—84no—
128C22×C4—21no—
129C22×C4C22⋊C4×C12711yescharacteristic
130M16—42no—
131C2×C8C22⋊C4×C12712yes—
132C2×C8C2×D4×C12712yes—
133C4⋊C4—22no—
134C4⋊C4—42no—
135C4⋊C4—41no—
136C22⋊C4—41no—
137C42—21no—
138C42—41no—
139C42C22⋊C4×C12711yescharacteristic
140C42C22×C4×C12711yescharacteristic
141C16—44no—
142C23—42no—
143C23—82no—
144C23—84no—
145C23#100×C12711yescharacteristic
146Q8—82no—
147D4—44no—
148D4—82no—
149D4—84no—
150D4—84no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4#100×C12711yescharacteristic
157C2×C4C2×C22⋊C4×C12711yescharacteristic
158C8—22no—
159C8—22no—
160C22—21no—
161C22—41no—
162C22—84no—
163C22—82no—
164C22—164no—
165C22C2×#100×C12711yescharacteristic
166C4—22no—
167C4—21no—
168C4—41no—
169C4—82no—
170C4#421×C12712yes—
171C2—21no—
172C2—41no—
173C2—162no—
174C2C127×#153311yescharacteristic
subgroupG/H
center, socleC2×C127#1533
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radicalC2×#127×C127C4
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2165C2semidirect
3. C127×#1355C2semidirect
13. #347×C127C22semidirect
83. #11915C127direct (N × H)
89. #2165C2×C127semidirect
90. #1355C2×C127semidirect
91. C127#11915direct (N × H)
101. #347C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31382
C127×#21652
C127×#13552
#11915127