Finite Group Databasebeta

← C127×#1922 #30634874

Subgroups — C127×#1922 #30634874

Order 16256.

186 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 96 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
1#427×C127C211yesmaximal, characteristic
2#424×C127C211yesmaximal, characteristic
3#405×C127C211yesmaximal, characteristic
4#341×C127C211yesmaximal, characteristic
5#339×C127C211yesmaximal, characteristic
6#339×C127C211yesmaximal, characteristic
7#336×C127C211yesmaximal, characteristic
8C2×M16×C127C2211yescharacteristic
9C2×M16×C127C2211yescharacteristic
10C22×C8×C127C2211yescharacteristic
11C22×C8×C127C2211yescharacteristic
12#117×C127C2211yescharacteristic
13#117×C127C2211yescharacteristic
14C2×C42×C127C2211yescharacteristic
15#107×C127C411yescharacteristic, complemented
16#107×C127C411yescharacteristic, complemented
17#106×C127C411yescharacteristic, complemented
18#106×C127C411yescharacteristic, complemented
19C4⋊C8×C127—21no—
20C4⋊C8×C127—21no—
21#97×C127—21no—
22C4×C8×C127—21no—
23C22×C4×C127—21no—
24C22×C4×C127C2311yescharacteristic
25M16×C127—21no—
26M16×C127—21no—
27M16×C127—21no—
28M16×C127Q812yes—
29C2×C8×C127—21no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127—21no—
33C2×C8×C127—21no—
34C2×C8×C127—21no—
35C2×C8×C127C2×C411yescharacteristic
36C2×C8×C127C2×C411yescharacteristic
37C2×C8×C127D411yescharacteristic
38C2×C8×C127D411yescharacteristic
39C4⋊C4×C127C2×C411yescharacteristic
40C4⋊C4×C127C2×C411yescharacteristic
41C4⋊C4×C127C2×C411yescharacteristic
42C4⋊C4×C127C2×C411yescharacteristic
43C22⋊C4×C127—21no—
44C22⋊C4×C127—21no—
45C42×C127—21no—
46C42×C127—21no—
47C42×C127—21no—
48C42×C127—21no—
49C23×C127#4111yescharacteristic
50C2×C4×C127—22no—
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127—21no—
54C2×C4×C127—21no—
55C2×C4×C127—41no—
56C2×C4×C127—41no—
57C2×C4×C127C22×C411yescharacteristic
58C2×C4×C127C2×D411yescharacteristic
59C2×C4×C127C2×Q811yescharacteristic
60C2×C4×C127#4111yescharacteristic
61C2×C4×C127#4111yescharacteristic
62C2×C4×C127#4111yescharacteristic
63C8×C127—21no—
64C8×C127—21no—
65C8×C127—22no—
66C8×C127—21no—
67C8×C127—21no—
68C8×C127—41no—
69C22×C127—21no—
70C22×C127—21no—
71C22×C127C4×D411yescharacteristic
72C22×C127#12511yescharacteristic
73C22×C127#12611yescharacteristic
74C4×C127—42no—
75C4×C127—41no—
76C4×C127—41no—
77C4×C127—41no—
78C4×C127—41no—
79C4×C127#11711yescharacteristic
80C4×C127C4×Q811yescharacteristic
81C4×C127C22⋊Q811yescharacteristic
82C4×C127#12311yescharacteristic
83C2×C127—21no—
84C2×C127—21no—
85C2×C127#38711yescharacteristic
86C2×C127#44311yescharacteristic
87C2×C127#44411yescharacteristic
88#1922C12711yesmaximal, characteristic, direct product factor, Sylow
89C127#192211yescharacteristic, direct product factor, Sylow
90#427C2×C12711yescharacteristic
91#424C2×C12711yescharacteristic
92#405C2×C12711yescharacteristic
93#341C2×C12711yescharacteristic
94#339C2×C12711yescharacteristic
95#339C2×C12711yescharacteristic
96#336C2×C12711yescharacteristic
97C2×M16C22×C12711yescharacteristic
98C2×M16C22×C12711yescharacteristic
99C22×C8C22×C12711yescharacteristic
100C22×C8C22×C12711yescharacteristic
101#117C22×C12711yescharacteristic
102#117C22×C12711yescharacteristic
103C2×C42C22×C12711yescharacteristic
104#107C4×C12711yescharacteristic, complemented
105#107C4×C12711yescharacteristic, complemented
106#106C4×C12711yescharacteristic, complemented
107#106C4×C12711yescharacteristic, complemented
108C4⋊C8—21no—
109C4⋊C8—21no—
110#97—21no—
111C4×C8—21no—
112C22×C4—21no—
113C22×C4C23×C12711yescharacteristic
114M16—21no—
115M16—21no—
116M16—21no—
117M16Q8×C12712yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8C2×C4×C12711yescharacteristic
125C2×C8C2×C4×C12711yescharacteristic
126C2×C8D4×C12711yescharacteristic
127C2×C8D4×C12711yescharacteristic
128C4⋊C4C2×C4×C12711yescharacteristic
129C4⋊C4C2×C4×C12711yescharacteristic
130C4⋊C4C2×C4×C12711yescharacteristic
131C4⋊C4C2×C4×C12711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C42—21no—
135C42—21no—
136C42—21no—
137C42—21no—
138C23#41×C12711yescharacteristic
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4C22×C4×C12711yescharacteristic
147C2×C4C2×D4×C12711yescharacteristic
148C2×C4C2×Q8×C12711yescharacteristic
149C2×C4#41×C12711yescharacteristic
150C2×C4#41×C12711yescharacteristic
151C2×C4#41×C12711yescharacteristic
152C8—21no—
153C8—21no—
154C8—22no—
155C8—21no—
156C8—21no—
157C8—41no—
158C22—21no—
159C22—21no—
160C22C4×D4×C12711yescharacteristic
161C22#125×C12711yescharacteristic
162C22#126×C12711yescharacteristic
163C4—42no—
164C4—41no—
165C4—41no—
166C4—41no—
167C4—41no—
168C4#117×C12711yescharacteristic
169C4C4×Q8×C12711yescharacteristic
170C4C22⋊Q8×C12711yescharacteristic
171C4#123×C12711yescharacteristic
172C2—21no—
173C2—21no—
174C2#387×C12711yescharacteristic
175C2#443×C12711yescharacteristic
176C2#444×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
socleC22×C127C4×D4
prime radicalC23×C127#41
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
15. #107×C127C4semidirect
16. #107×C127C4semidirect
17. #106×C127C4semidirect
18. #106×C127C4semidirect
88. #1922C127direct (N × H)
89. C127#1922direct (N × H)
104. #107C4×C127semidirect
105. #107C4×C127semidirect
106. #106C4×C127semidirect
107. #106C4×C127semidirect

Maximal subgroups

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

subgroupindex
#427×C1272
#424×C1272
#405×C1272
#341×C1272
#339×C1272
#336×C1272
#1922127