Finite Group Databasebeta

← C127×#12311 #44575984

Subgroups — C127×#12311 #44575984

Order 32512.

366 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3293C211yesmaximal, characteristic, complemented
2C127×#2213C212yesmaximal, complemented
3C127×#1709C211yesmaximal, characteristic, complemented
4C127×#1358C211yesmaximal, characteristic, complemented
5C127×#1335C212yesmaximal, complemented
6#578×C127—22no—
7#509×C127—22no—
8#494×C127C2211yescharacteristic
9#493×C127C2211yescharacteristic
10#486×C127—22no—
11#473×C127—22no—
12#456×C127—22no—
13#443×C127C2212yes—
14#364×C127C2212yes—
15#361×C127—22no—
16C82×C127C2211yescharacteristic
172−1+4×C127—22no—
18#137×C127—24no—
19#137×C127—44no—
20#135×C127—42no—
21#135×C127D412yes—
22C2×Q16×C127—22no—
23C2×Q16×C127—42no—
24C2×D8×C127—22no—
25#131×C127—22no—
26C4⋊Q8×C127D412yes—
27#127×C127—21no—
28SD32×C127—42no—
29D16×C127—42no—
30M32×C127—22no—
31#108×C127D412yes—
32#104×C127—22no—
33#102×C127—44no—
34#101×C127—22no—
35C4×C8×C127—21no—
36C4×C8×C127C2311yescharacteristic
37#41×C127—22no—
38#41×C127—44no—
39#41×C127—82no—
40C2×Q8×C127—22no—
41C2×Q8×C127—44no—
42C2×D4×C127—42no—
43C2×D4×C127—41no—
44Q16×C127—44no—
45Q16×C127—42no—
46Q16×C127—42no—
47Q16×C127D812yes—
48SD16×C127—22no—
49SD16×C127—44no—
50D8×C127—42no—
51D8×C127—42no—
52D8×C127D812yes—
53M16×C127—22no—
54M16×C127—42no—
55C2×C8×C127—22no—
56C2×C8×C127—42no—
57C2×C8×C127C2×D412yes—
58C4⋊C4×C127—42no—
59C42×C127C2×D411yescharacteristic
60C16×C127—42no—
61C23×C127—81no—
62Q8×C127—22no—
63Q8×C127—44no—
64Q8×C127—82no—
65D4×C127—22no—
66D4×C127—42no—
67D4×C127—84no—
68D4×C127—82no—
69D4×C127—82no—
70C2×C4×C127—21no—
71C2×C4×C127—42no—
72C2×C4×C127—42no—
73C2×C4×C127—84no—
74C2×C4×C127#12011yescharacteristic
75C8×C127—42no—
76C8×C127—42no—
77C8×C127C2×D812yes—
78C8×C127AGL(1,ℤ/8)12yes—
79C22×C127—42no—
80C22×C127—162no—
81C22×C127—161no—
82C22×C127#45311yescharacteristic
83C4×C127—22no—
84C4×C127—42no—
85C4×C127—82no—
86C4×C127#44712yes—
87#12311C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—21no—
89C2×C127—82no—
90C2×C127—321no—
91C2×C127#161911yescharacteristic
92#3293C2×C12711yescharacteristic, complemented
93#2213C2×C12712yescomplemented
94#1709C2×C12711yescharacteristic, complemented
95#1358C2×C12711yescharacteristic, complemented
96#1335C2×C12712yescomplemented
97C127#1231111yescharacteristic, direct product factor, Sylow
98#578—22no—
99#509—22no—
100#494C22×C12711yescharacteristic
101#493C22×C12711yescharacteristic
102#486—22no—
103#473—22no—
104#456—22no—
105#443C22×C12712yes—
106#364C22×C12712yes—
107#361—22no—
108C82C22×C12711yescharacteristic
1092−1+4—22no—
110#137—24no—
111#137—44no—
112#135—42no—
113#135D4×C12712yes—
114C2×Q16—22no—
115C2×Q16—42no—
116C2×D8—22no—
117#131—22no—
118C4⋊Q8D4×C12712yes—
119#127—21no—
120SD32—42no—
121D16—42no—
122M32—22no—
123#108D4×C12712yes—
124#104—22no—
125#102—44no—
126#101—22no—
127C4×C8—21no—
128C4×C8C23×C12711yescharacteristic
129#41—22no—
130#41—44no—
131#41—82no—
132C2×Q8—22no—
133C2×Q8—44no—
134C2×D4—42no—
135C2×D4—41no—
136Q16—44no—
137Q16—42no—
138Q16—42no—
139Q16D8×C12712yes—
140SD16—22no—
141SD16—44no—
142D8—42no—
143D8—42no—
144D8D8×C12712yes—
145M16—22no—
146M16—42no—
147C2×C8—22no—
148C2×C8—42no—
149C2×C8C2×D4×C12712yes—
150C4⋊C4—42no—
151C42C2×D4×C12711yescharacteristic
152C16—42no—
153C23—81no—
154Q8—22no—
155Q8—44no—
156Q8—82no—
157D4—22no—
158D4—42no—
159D4—84no—
160D4—82no—
161D4—82no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—84no—
166C2×C4#120×C12711yescharacteristic
167C8—42no—
168C8—42no—
169C8C2×D8×C12712yes—
170C8AGL(1,ℤ/8)×C12712yes—
171C22—42no—
172C22—162no—
173C22—161no—
174C22#453×C12711yescharacteristic
175C4—22no—
176C4—42no—
177C4—82no—
178C4#447×C12712yes—
179C2—21no—
180C2—82no—
181C2—321no—
182C2C127×#161911yescharacteristic
subgroupG/H
center, socleC2×C127#1619
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3293C2semidirect
2. C127×#2213C2semidirect
3. C127×#1709C2semidirect
4. C127×#1358C2semidirect
5. C127×#1335C2semidirect
87. #12311C127direct (N × H)
92. #3293C2×C127semidirect
93. #2213C2×C127semidirect
94. #1709C2×C127semidirect
95. #1358C2×C127semidirect
96. #1335C2×C127semidirect
97. C127#12311direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32932
C127×#22132
C127×#17092
C127×#13582
C127×#13352
#12311127