Finite Group Databasebeta

← C127×#1893 #30634845

Subgroups — C127×#1893 #30634845

Order 16256.

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

normal subgroups only

This group has 432 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, complemented
2C2×#121×C127C211yesmaximal, characteristic
3C2×#102×C127C212yesmaximal, complemented
4#380×C127C211yesmaximal, characteristic, complemented
5#340×C127C212yesmaximal, complemented
6C22×D4×C127—21no—
7C22×D4×C127C2211yescharacteristic
8C23×C4×C127C2211yescharacteristic
9C22×C8×C127—22no—
10C22×C8×C127—24no—
11C22×C8×C127C2212yes—
12#121×C127—22no—
13#121×C127C414yescomplemented
14C2×C4⋊C4×C127C2212yes—
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C22⋊C4×C127—21no—
17C2×C22⋊C4×C127—21no—
18#102×C127—24no—
19#95×C127—21no—
20C24×C127—21no—
21C24×C127D411yescharacteristic
22C2×D4×C127—24no—
23C2×D4×C127—22no—
24C2×D4×C127—21no—
25C2×D4×C127—22no—
26C2×D4×C127—42no—
27C2×D4×C127—42no—
28C2×D4×C127C2×C412yes—
29C22×C4×C127—22no—
30C22×C4×C127—22no—
31C22×C4×C127—21no—
32C22×C4×C127—22no—
33C22×C4×C127C2×C412yes—
34C22×C4×C127D411yescharacteristic
35C22×C4×C127D412yes—
36C22×C4×C127C2311yescharacteristic
37C2×C8×C127—28no—
38C2×C8×C127—22no—
39C2×C8×C127—22no—
40C2×C8×C127D414yescomplemented
41C4⋊C4×C127—21no—
42C4⋊C4×C127—22no—
43C4⋊C4×C127—22no—
44C4⋊C4×C127C2×C412yes—
45C22⋊C4×C127—24no—
46C22⋊C4×C127—42no—
47C23×C127—22no—
48C23×C127—22no—
49C23×C127—22no—
50C23×C127—42no—
51C23×C127—41no—
52C23×C127—41no—
53C23×C127—42no—
54C23×C127C22⋊C412yes—
55C23×C127D812yes—
56C23×C127SD1612yes—
57C23×C127C2×D411yescharacteristic
58D4×C127—24no—
59D4×C127—48no—
60D4×C127—41no—
61D4×C127—41no—
62C2×C4×C127—22no—
63C2×C4×C127—24no—
64C2×C4×C127—22no—
65C2×C4×C127—22no—
66C2×C4×C127—22no—
67C2×C4×C127—41no—
68C2×C4×C127—41no—
69C2×C4×C127—42no—
70C2×C4×C127—42no—
71C2×C4×C127—42no—
72C2×C4×C127C22⋊C412yes—
73C2×C4×C127C22×C411yescharacteristic
74C2×C4×C127C2×D412yes—
75C2×C4×C127C2×D411yescharacteristic
76C2×C4×C127#4112yes—
77C8×C127—24no—
78C22×C127—22no—
79C22×C127—22no—
80C22×C127—24no—
81C22×C127—24no—
82C22×C127—42no—
83C22×C127—42no—
84C22×C127—42no—
85C22×C127—82no—
86C22×C127—82no—
87C22×C127#10214yescomplemented
88C22×C127C2×C22⋊C411yescharacteristic
89C22×C127#12112yes—
90C22×C127C2×D811yescharacteristic
91C22×C127C2×SD1611yescharacteristic
92C22×C127#13512yes—
93C4×C127—22no—
94C4×C127—42no—
95C4×C127—82no—
96C4×C127C4×D412yes—
97C4×C127#12011yescharacteristic
98C4×C127#12311yescharacteristic
99C2×C127—24no—
100C2×C127—82no—
101C2×C127#38611yescharacteristic
102C2×C127C2×#10211yescharacteristic
103C2×C127#41611yescharacteristic
104C2×C127#46512yes—
105C2×C127#46612yes—
106#1893C12711yesmaximal, characteristic, direct product factor, Sylow
107C127#189311yescharacteristic, direct product factor, Sylow
108C23×C8C2×C12711yescharacteristic, complemented
109C2×#121C2×C12711yescharacteristic
110C2×#102C2×C12712yescomplemented
111#380C2×C12711yescharacteristic, complemented
112#340C2×C12712yescomplemented
113C22×D4—21no—
114C22×D4C22×C12711yescharacteristic
115C23×C4C22×C12711yescharacteristic
116C22×C8—22no—
117C22×C8—24no—
118C22×C8C22×C12712yes—
119#121—22no—
120#121C4×C12714yescomplemented
121C2×C4⋊C4C22×C12712yes—
122C2×C4⋊C4C22×C12711yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4—21no—
125#102—24no—
126#95—21no—
127C24—21no—
128C24D4×C12711yescharacteristic
129C2×D4—24no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—22no—
133C2×D4—42no—
134C2×D4—42no—
135C2×D4C2×C4×C12712yes—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—22no—
140C22×C4C2×C4×C12712yes—
141C22×C4D4×C12711yescharacteristic
142C22×C4D4×C12712yes—
143C22×C4C23×C12711yescharacteristic
144C2×C8—28no—
145C2×C8—22no—
146C2×C8—22no—
147C2×C8D4×C12714yescomplemented
148C4⋊C4—21no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4C2×C4×C12712yes—
152C22⋊C4—24no—
153C22⋊C4—42no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23—42no—
161C23C22⋊C4×C12712yes—
162C23D8×C12712yes—
163C23SD16×C12712yes—
164C23C2×D4×C12711yescharacteristic
165D4—24no—
166D4—48no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4C22⋊C4×C12712yes—
180C2×C4C22×C4×C12711yescharacteristic
181C2×C4C2×D4×C12712yes—
182C2×C4C2×D4×C12711yescharacteristic
183C2×C4#41×C12712yes—
184C8—24no—
185C22—22no—
186C22—22no—
187C22—24no—
188C22—24no—
189C22—42no—
190C22—42no—
191C22—42no—
192C22—82no—
193C22—82no—
194C22#102×C12714yescomplemented
195C22C2×C22⋊C4×C12711yescharacteristic
196C22#121×C12712yes—
197C22C2×D8×C12711yescharacteristic
198C22C2×SD16×C12711yescharacteristic
199C22#135×C12712yes—
200C4—22no—
201C4—42no—
202C4—82no—
203C4C4×D4×C12712yes—
204C4#120×C12711yescharacteristic
205C4#123×C12711yescharacteristic
206C2—24no—
207C2—82no—
208C2#386×C12711yescharacteristic
209C2C2×#102×C12711yescharacteristic
210C2#416×C12711yescharacteristic
211C2#465×C12712yes—
212C2#466×C12712yes—
subgroupG/H
center, socleC23×C127C2×D4
commutatorC2×C4C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC2×#121×C127C2
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
1. C23×C8×C127C2semidirect
3. C2×#102×C127C2semidirect
4. #380×C127C2semidirect
5. #340×C127C2semidirect
13. #121×C127C4semidirect
40. C2×C8×C127D4semidirect
87. C22×C127#102semidirect
106. #1893C127direct (N × H)
107. C127#1893direct (N × H)
108. C23×C8C2×C127semidirect
110. C2×#102C2×C127semidirect
111. #380C2×C127semidirect
112. #340C2×C127semidirect
120. #121C4×C127semidirect
147. C2×C8D4×C127semidirect
194. C22#102×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×#121×C1272
C2×#102×C1272
#380×C1272
#340×C1272
#1893127