Finite Group Databasebeta

← C127×#1892 #30634844

Subgroups — C127×#1892 #30634844

Order 16256.

380 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 144 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
1C23×C8×C127C211yesmaximal, characteristic
2C2×C22⋊Q8×C127C211yesmaximal, characteristic
3C2×#103×C127C212yesmaximal, complemented
4#380×C127C211yesmaximal, characteristic
5#340×C127C212yesmaximal, complemented
6C22×Q8×C127C2211yescharacteristic
7C23×C4×C127C2211yescharacteristic
8C22×C8×C127—22no—
9C22×C8×C127—24no—
10C22×C8×C127C2212yes—
11C22⋊Q8×C127—22no—
12C22⋊Q8×C127C414yescomplemented
13C2×C4⋊C4×C127—21no—
14C2×C4⋊C4×C127C2212yes—
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C22⋊C4×C127—21no—
17C2×C22⋊C4×C127—21no—
18#103×C127—24no—
19#95×C127—21no—
20C24×C127D411yescharacteristic
21C2×Q8×C127—21no—
22C2×Q8×C127—22no—
23C2×Q8×C127—22no—
24C2×Q8×C127C2×C412yes—
25C22×C4×C127—22no—
26C22×C4×C127—22no—
27C22×C4×C127—21no—
28C22×C4×C127—21no—
29C22×C4×C127—22no—
30C22×C4×C127C2×C412yes—
31C22×C4×C127D411yescharacteristic
32C22×C4×C127D412yes—
33C22×C4×C127C2311yescharacteristic
34C2×C8×C127—28no—
35C2×C8×C127—22no—
36C2×C8×C127—22no—
37C2×C8×C127D414yes—
38C4⋊C4×C127—24no—
39C4⋊C4×C127—21no—
40C4⋊C4×C127—22no—
41C4⋊C4×C127—22no—
42C4⋊C4×C127C2×C412yes—
43C22⋊C4×C127—24no—
44C22⋊C4×C127—42no—
45C23×C127—22no—
46C23×C127—22no—
47C23×C127C22⋊C412yes—
48C23×C127SD1612yes—
49C23×C127Q1612yes—
50C23×C127C2×D411yescharacteristic
51Q8×C127—24no—
52Q8×C127—41no—
53Q8×C127—41no—
54C2×C4×C127—22no—
55C2×C4×C127—24no—
56C2×C4×C127—22no—
57C2×C4×C127—22no—
58C2×C4×C127—22no—
59C2×C4×C127—22no—
60C2×C4×C127—42no—
61C2×C4×C127—42no—
62C2×C4×C127—42no—
63C2×C4×C127—42no—
64C2×C4×C127—42no—
65C2×C4×C127C22⋊C412yes—
66C2×C4×C127C22×C411yescharacteristic
67C2×C4×C127C2×D412yes—
68C2×C4×C127C2×D411yescharacteristic
69C2×C4×C127#4112yes—
70C8×C127—24no—
71C22×C127—22no—
72C22×C127—22no—
73C22×C127—24no—
74C22×C127—24no—
75C22×C127#10314yescomplemented
76C22×C127C2×C22⋊C411yescharacteristic
77C22×C127#12112yes—
78C22×C127C2×SD1611yescharacteristic
79C22×C127C2×Q1611yescharacteristic
80C22×C127#13512yes—
81C4×C127—22no—
82C4×C127—42no—
83C4×C127—42no—
84C4×C127—82no—
85C4×C127C4×D412yes—
86C4×C127#12011yescharacteristic
87C4×C127#12311yescharacteristic
88C2×C127—24no—
89C2×C127#38611yescharacteristic
90C2×C127C2×#10311yescharacteristic
91C2×C127#41611yescharacteristic
92C2×C127#46512yes—
93C2×C127#46712yes—
94#1892C12711yesmaximal, characteristic, direct product factor, Sylow
95C127#189211yescharacteristic, direct product factor, Sylow
96C23×C8C2×C12711yescharacteristic
97C2×C22⋊Q8C2×C12711yescharacteristic
98C2×#103C2×C12712yescomplemented
99#380C2×C12711yescharacteristic
100#340C2×C12712yescomplemented
101C22×Q8C22×C12711yescharacteristic
102C23×C4C22×C12711yescharacteristic
103C22×C8—22no—
104C22×C8—24no—
105C22×C8C22×C12712yes—
106C22⋊Q8—22no—
107C22⋊Q8C4×C12714yescomplemented
108C2×C4⋊C4—21no—
109C2×C4⋊C4C22×C12712yes—
110C2×C4⋊C4C22×C12711yescharacteristic
111C2×C22⋊C4—21no—
112C2×C22⋊C4—21no—
113#103—24no—
114#95—21no—
115C24D4×C12711yescharacteristic
116C2×Q8—21no—
117C2×Q8—22no—
118C2×Q8—22no—
119C2×Q8C2×C4×C12712yes—
120C22×C4—22no—
121C22×C4—22no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—22no—
125C22×C4C2×C4×C12712yes—
126C22×C4D4×C12711yescharacteristic
127C22×C4D4×C12712yes—
128C22×C4C23×C12711yescharacteristic
129C2×C8—28no—
130C2×C8—22no—
131C2×C8—22no—
132C2×C8D4×C12714yes—
133C4⋊C4—24no—
134C4⋊C4—21no—
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4C2×C4×C12712yes—
138C22⋊C4—24no—
139C22⋊C4—42no—
140C23—22no—
141C23—22no—
142C23C22⋊C4×C12712yes—
143C23SD16×C12712yes—
144C23Q16×C12712yes—
145C23C2×D4×C12711yescharacteristic
146Q8—24no—
147Q8—41no—
148Q8—41no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4C22⋊C4×C12712yes—
161C2×C4C22×C4×C12711yescharacteristic
162C2×C4C2×D4×C12712yes—
163C2×C4C2×D4×C12711yescharacteristic
164C2×C4#41×C12712yes—
165C8—24no—
166C22—22no—
167C22—22no—
168C22—24no—
169C22—24no—
170C22#103×C12714yescomplemented
171C22C2×C22⋊C4×C12711yescharacteristic
172C22#121×C12712yes—
173C22C2×SD16×C12711yescharacteristic
174C22C2×Q16×C12711yescharacteristic
175C22#135×C12712yes—
176C4—22no—
177C4—42no—
178C4—42no—
179C4—82no—
180C4C4×D4×C12712yes—
181C4#120×C12711yescharacteristic
182C4#123×C12711yescharacteristic
183C2—24no—
184C2#386×C12711yescharacteristic
185C2C2×#103×C12711yescharacteristic
186C2#416×C12711yescharacteristic
187C2#465×C12712yes—
188C2#467×C12712yes—
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC24×C127D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#103×C127C2semidirect
5. #340×C127C2semidirect
12. C22⋊Q8×C127C4semidirect
75. C22×C127#103semidirect
94. #1892C127direct (N × H)
95. C127#1892direct (N × H)
98. C2×#103C2×C127semidirect
100. #340C2×C127semidirect
107. C22⋊Q8C4×C127semidirect
170. C22#103×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C8×C1272
C2×C22⋊Q8×C1272
C2×#103×C1272
#380×C1272
#340×C1272
#1892127