Finite Group Databasebeta

← C127×#11920 #44575593

Subgroups — C127×#11920 #44575593

Order 32512.

400 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 138 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×#3147C211yesmaximal, characteristic
2C2×#364×C127C212yesmaximal, complemented
3C127×#1358C212yesmaximal, complemented
4C127×#1357C212yesmaximal, complemented
5C2×#135×C127—22no—
6#532×C127C412yes—
7C2×M32×C127—22no—
8#495×C127—22no—
9#494×C127C2211yescharacteristic
10#493×C127C2211yescharacteristic
11#492×C127C412yes—
12C2×C4×C8×C127C2211yescharacteristic
13#364×C127—22no—
14#364×C127C2214yes—
15C2×#41×C127—22no—
16#135×C127—42no—
17#135×C127—42no—
18#135×C127—42no—
19#135×C127—42no—
20C2×Q16×C127—22no—
21C2×SD16×C127—24no—
22C2×D8×C127—22no—
23C22×C8×C127D412yes—
24C4⋊Q8×C127C2×C412yes—
25#127×C127C2×C412yes—
26#124×C127—22no—
27#121×C127—42no—
28C4×D4×C127—42no—
29C2×C42×C127C2×C411yescharacteristic
30M32×C127—24no—
31M32×C127—42no—
32C2×C16×C127—42no—
33C4×C8×C127C2×C411yescharacteristic
34C4×C8×C127D412yes—
35C4×C8×C127C2311yescharacteristic
36#41×C127—44no—
37#41×C127—44no—
38C2×Q8×C127—22no—
39C2×D4×C127—22no—
40C2×D4×C127—42no—
41C2×D4×C127—42no—
42C22×C4×C127—21no—
43C22×C4×C127—42no—
44C22×C4×C127C22⋊C411yescharacteristic
45Q16×C127—42no—
46Q16×C127—42no—
47SD16×C127—44no—
48SD16×C127—44no—
49D8×C127—42no—
50D8×C127—42no—
51C2×C8×C127C22⋊C412yes—
52C2×C8×C127D812yes—
53C2×C8×C127D812yes—
54C2×C8×C127SD1612yes—
55C2×C8×C127SD1612yes—
56C2×C8×C127C2×D412yes—
57C4⋊C4×C127—42no—
58C22⋊C4×C127—44no—
59C42×C127—21no—
60C42×C127C22⋊C411yescharacteristic
61C42×C127C22×C411yescharacteristic
62C16×C127—44no—
63C23×C127—42no—
64C23×C127#10011yescharacteristic
65Q8×C127—44no—
66D4×C127—44no—
67D4×C127—84no—
68D4×C127—84no—
69C2×C4×C127—21no—
70C2×C4×C127—21no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127—82no—
74C2×C4×C127—82no—
75C2×C4×C127#10011yescharacteristic
76C2×C4×C127#10212yes—
77C2×C4×C127#10212yes—
78C2×C4×C127C2×C22⋊C411yescharacteristic
79C8×C127#10212yes—
80C8×C127#10212yes—
81C8×C127C2×D812yes—
82C8×C127C2×SD1612yes—
83C22×C127—41no—
84C22×C127—84no—
85C22×C127—82no—
86C22×C127#33112yes—
87C22×C127C2×#10011yescharacteristic
88C4×C127—22no—
89C4×C127—41no—
90C4×C127—82no—
91C4×C127#33111yescharacteristic
92C4×C127#33111yescharacteristic
93C4×C127C2×#10212yes—
94#11920C12711yesmaximal, characteristic, direct product factor, Sylow
95C2×C127—21no—
96C2×C127—22no—
97C2×C127—162no—
98C2×C127C2×#33111yescharacteristic
99#3147C2×C12711yescharacteristic
100C2×#364C2×C12712yescomplemented
101#1358C2×C12712yescomplemented
102#1357C2×C12712yescomplemented
103C127#1192011yescharacteristic, direct product factor, Sylow
104C2×#135—22no—
105#532C4×C12712yes—
106C2×M32—22no—
107#495—22no—
108#494C22×C12711yescharacteristic
109#493C22×C12711yescharacteristic
110#492C4×C12712yes—
111C2×C4×C8C22×C12711yescharacteristic
112#364—22no—
113#364C22×C12714yes—
114C2×#41—22no—
115#135—42no—
116#135—42no—
117#135—42no—
118#135—42no—
119C2×Q16—22no—
120C2×SD16—24no—
121C2×D8—22no—
122C22×C8D4×C12712yes—
123C4⋊Q8C2×C4×C12712yes—
124#127C2×C4×C12712yes—
125#124—22no—
126#121—42no—
127C4×D4—42no—
128C2×C42C2×C4×C12711yescharacteristic
129M32—24no—
130M32—42no—
131C2×C16—42no—
132C4×C8C2×C4×C12711yescharacteristic
133C4×C8D4×C12712yes—
134C4×C8C23×C12711yescharacteristic
135#41—44no—
136#41—44no—
137C2×Q8—22no—
138C2×D4—22no—
139C2×D4—42no—
140C2×D4—42no—
141C22×C4—21no—
142C22×C4—42no—
143C22×C4C22⋊C4×C12711yescharacteristic
144Q16—42no—
145Q16—42no—
146SD16—44no—
147SD16—44no—
148D8—42no—
149D8—42no—
150C2×C8C22⋊C4×C12712yes—
151C2×C8D8×C12712yes—
152C2×C8D8×C12712yes—
153C2×C8SD16×C12712yes—
154C2×C8SD16×C12712yes—
155C2×C8C2×D4×C12712yes—
156C4⋊C4—42no—
157C22⋊C4—44no—
158C42—21no—
159C42C22⋊C4×C12711yescharacteristic
160C42C22×C4×C12711yescharacteristic
161C16—44no—
162C23—42no—
163C23#100×C12711yescharacteristic
164Q8—44no—
165D4—44no—
166D4—84no—
167D4—84no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—82no—
173C2×C4—82no—
174C2×C4#100×C12711yescharacteristic
175C2×C4#102×C12712yes—
176C2×C4#102×C12712yes—
177C2×C4C2×C22⋊C4×C12711yescharacteristic
178C8#102×C12712yes—
179C8#102×C12712yes—
180C8C2×D8×C12712yes—
181C8C2×SD16×C12712yes—
182C22—41no—
183C22—84no—
184C22—82no—
185C22#331×C12712yes—
186C22C2×#100×C12711yescharacteristic
187C4—22no—
188C4—41no—
189C4—82no—
190C4#331×C12711yescharacteristic
191C4#331×C12711yescharacteristic
192C4C2×#102×C12712yes—
193C2—21no—
194C2—22no—
195C2—162no—
196C2C2×#331×C12711yescharacteristic
subgroupG/H
centerC4×C127#331
commutatorC42C22×C4×C127
Frattini, cosocleC4×C8C23×C127
socleC2×C127C2×#331
prime radicalC127×#3147C2
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#364×C127C2semidirect
3. C127×#1358C2semidirect
4. C127×#1357C2semidirect
94. #11920C127direct (N × H)
100. C2×#364C2×C127semidirect
101. #1358C2×C127semidirect
102. #1357C2×C127semidirect
103. C127#11920direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31472
C2×#364×C1272
C127×#13582
C127×#13572
#11920127