Finite Group Databasebeta

← C127×#11917 #44575590

Subgroups — C127×#11917 #44575590

Order 32512.

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

normal subgroups only

This group has 280 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×#3142C211yesmaximal, characteristic
2C127×#2165C212yesmaximal, complemented
3C127×#1356C212yesmaximal, complemented
4C127×#1355C212yesmaximal, complemented
5#532×C127C411yescharacteristic
6C2×#125×C127C411yescharacteristic
7#491×C127C411yescharacteristic
8#491×C127C2211yescharacteristic
9#490×C127C411yescharacteristic
10#490×C127C2211yescharacteristic
11#488×C127—22no—
12#417×C127—22no—
13C4×M16×C127C2211yescharacteristic
14#364×C127—22no—
15#349×C127—22no—
16#347×C127C2214yes—
17C2×#41×C127—21no—
18C2×M16×C127D412yes—
19C4⋊Q8×C127C2×C411yescharacteristic
20#127×C127C2×C411yescharacteristic
21#125×C127—21no—
22#125×C127—41no—
23#125×C127C2×C411yescharacteristic
24#125×C127C2×C411yescharacteristic
25#124×C127—21no—
26#121×C127—41no—
27C4×D4×C127—41no—
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127—41no—
30C2×C42×C127C2×C411yescharacteristic
31M32×C127—24no—
32#103×C127—22no—
33#103×C127—22no—
34#102×C127—22no—
35#102×C127—22no—
36#97×C127C2×C411yescharacteristic
37#97×C127C2311yescharacteristic
38C4×C8×C127D412yes—
39#41×C127—44no—
40C2×Q8×C127—21no—
41C2×D4×C127—21no—
42C2×D4×C127—41no—
43C2×D4×C127—41no—
44C22×C4×C127—21no—
45C22×C4×C127—41no—
46C22×C4×C127—41no—
47C22×C4×C127C22⋊C411yescharacteristic
48M16×C127—42no—
49C2×C8×C127C22⋊C412yes—
50C2×C8×C127C2×D412yes—
51C4⋊C4×C127—21no—
52C4⋊C4×C127—21no—
53C4⋊C4×C127—41no—
54C4⋊C4×C127—41no—
55C4⋊C4×C127—41no—
56C4⋊C4×C127—42no—
57C4⋊C4×C127—41no—
58C22⋊C4×C127—42no—
59C42×C127—21no—
60C42×C127C22⋊C411yescharacteristic
61C42×C127C22×C411yescharacteristic
62C16×C127—44no—
63C23×C127—41no—
64C23×C127#10011yescharacteristic
65Q8×C127—42no—
66D4×C127—42no—
67D4×C127—82no—
68D4×C127—82no—
69C2×C4×C127—22no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127—82no—
76C2×C4×C127—81no—
77C2×C4×C127—82no—
78C2×C4×C127#10011yescharacteristic
79C2×C4×C127C2×C22⋊C411yescharacteristic
80C8×C127—22no—
81C8×C127—22no—
82C22×C127—21no—
83C22×C127—41no—
84C22×C127—82no—
85C22×C127—81no—
86C22×C127C2×#10011yescharacteristic
87C4×C127—21no—
88C4×C127—41no—
89C4×C127—41no—
90C4×C127—81no—
91C4×C127—81no—
92C4×C127—81no—
93C4×C127#42112yes—
94#11917C12711yesmaximal, characteristic, direct product factor, Sylow
95C2×C127—21no—
96C2×C127—41no—
97C2×C127—161no—
98C2×C127#153311yescharacteristic
99#3142C2×C12711yescharacteristic
100#2165C2×C12712yescomplemented
101#1356C2×C12712yescomplemented
102#1355C2×C12712yescomplemented
103C127#1191711yescharacteristic, direct product factor, Sylow
104#532C4×C12711yescharacteristic
105C2×#125C4×C12711yescharacteristic
106#491C4×C12711yescharacteristic
107#491C22×C12711yescharacteristic
108#490C4×C12711yescharacteristic
109#490C22×C12711yescharacteristic
110#488—22no—
111#417—22no—
112C4×M16C22×C12711yescharacteristic
113#364—22no—
114#349—22no—
115#347C22×C12714yes—
116C2×#41—21no—
117C2×M16D4×C12712yes—
118C4⋊Q8C2×C4×C12711yescharacteristic
119#127C2×C4×C12711yescharacteristic
120#125—21no—
121#125—41no—
122#125C2×C4×C12711yescharacteristic
123#125C2×C4×C12711yescharacteristic
124#124—21no—
125#121—41no—
126C4×D4—41no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—41no—
129C2×C42C2×C4×C12711yescharacteristic
130M32—24no—
131#103—22no—
132#103—22no—
133#102—22no—
134#102—22no—
135#97C2×C4×C12711yescharacteristic
136#97C23×C12711yescharacteristic
137C4×C8D4×C12712yes—
138#41—44no—
139C2×Q8—21no—
140C2×D4—21no—
141C2×D4—41no—
142C2×D4—41no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4—41no—
146C22×C4C22⋊C4×C12711yescharacteristic
147M16—42no—
148C2×C8C22⋊C4×C12712yes—
149C2×C8C2×D4×C12712yes—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—41no—
155C4⋊C4—42no—
156C4⋊C4—41no—
157C22⋊C4—42no—
158C42—21no—
159C42C22⋊C4×C12711yescharacteristic
160C42C22×C4×C12711yescharacteristic
161C16—44no—
162C23—41no—
163C23#100×C12711yescharacteristic
164Q8—42no—
165D4—42no—
166D4—82no—
167D4—82no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—82no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4#100×C12711yescharacteristic
178C2×C4C2×C22⋊C4×C12711yescharacteristic
179C8—22no—
180C8—22no—
181C22—21no—
182C22—41no—
183C22—82no—
184C22—81no—
185C22C2×#100×C12711yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—81no—
191C4—81no—
192C4#421×C12712yes—
193C2—21no—
194C2—41no—
195C2—161no—
196C2C127×#153311yescharacteristic
subgroupG/H
center, socleC2×C127#1533
commutatorC42C22×C4×C127
Frattini, cosocle#97C23×C127
prime radical#532×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×#1356C2semidirect
4. C127×#1355C2semidirect
94. #11917C127direct (N × H)
100. #2165C2×C127semidirect
101. #1356C2×C127semidirect
102. #1355C2×C127semidirect
103. C127#11917direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31422
C127×#21652
C127×#13562
C127×#13552
#11917127