Finite Group Databasebeta

← C127×#1901 #30634853

Subgroups — C127×#1901 #30634853

Order 16256.

338 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C22×M16×C127C211yesmaximal, characteristic
2C2×C22⋊Q8×C127C211yesmaximal, characteristic
3C2×#101×C127C212yesmaximal, complemented
4#407×C127C211yesmaximal, characteristic
5#343×C127C212yesmaximal, complemented
6C22×Q8×C127C2211yescharacteristic
7C23×C4×C127C2211yescharacteristic
8C2×M16×C127—21no—
9C2×M16×C127—24no—
10C2×M16×C127C2212yes—
11C2×M16×C127C2212yes—
12C22×C8×C127—21no—
13C22⋊Q8×C127—21no—
14C22⋊Q8×C127—21no—
15C22⋊Q8×C127—21no—
16C22⋊Q8×C127—21no—
17C2×C4⋊C4×C127C412yes—
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C22⋊C4×C127C412yes—
20#101×C127—24no—
21C22⋊C8×C127—21no—
22C22⋊C8×C127—21no—
23C24×C127C2×C411yescharacteristic
24C2×Q8×C127—22no—
25C2×Q8×C127—21no—
26C2×Q8×C127—21no—
27C2×Q8×C127—22no—
28C22×C4×C127—22no—
29C22×C4×C127—22no—
30C22×C4×C127C2×C412yes—
31C22×C4×C127C2×C411yescharacteristic
32C22×C4×C127C2×C412yes—
33C22×C4×C127D411yescharacteristic
34C22×C4×C127D411yescharacteristic
35C22×C4×C127D411yescharacteristic
36C22×C4×C127D411yescharacteristic
37C22×C4×C127C2311yescharacteristic
38M16×C127—24no—
39M16×C127—22no—
40M16×C127—22no—
41M16×C127—22no—
42M16×C127D414yes—
43C2×C8×C127—24no—
44C2×C8×C127—22no—
45C2×C8×C127—22no—
46C4⋊C4×C127—22no—
47C4⋊C4×C127—22no—
48C4⋊C4×C127—21no—
49C4⋊C4×C127—21no—
50C22⋊C4×C127—22no—
51C22⋊C4×C127—22no—
52C23×C127—22no—
53C23×C127—22no—
54C23×C127—41no—
55C23×C127C22⋊C411yescharacteristic
56C23×C127C22⋊C411yescharacteristic
57C23×C127C22×C411yescharacteristic
58Q8×C127—41no—
59Q8×C127—42no—
60Q8×C127—41no—
61C2×C4×C127—22no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—22no—
65C2×C4×C127—22no—
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—22no—
69C2×C4×C127—22no—
70C2×C4×C127—24no—
71C2×C4×C127—42no—
72C2×C4×C127C22⋊C411yescharacteristic
73C2×C4×C127C22⋊C411yescharacteristic
74C2×C4×C127C2×D412yes—
75C2×C4×C127C2×D411yescharacteristic
76C2×C4×C127C2×D411yescharacteristic
77C2×C4×C127#4112yes—
78C8×C127—24no—
79C8×C127—42no—
80C22×C127—21no—
81C22×C127—21no—
82C22×C127—21no—
83C22×C127—21no—
84C22×C127—21no—
85C22×C127—21no—
86C22×C127—21no—
87C22×C127—44no—
88C22×C127#10112yescomplemented
89C22×C127C2×C22⋊C411yescharacteristic
90C22×C127C4×D412yes—
91C4×C127—21no—
92C4×C127—21no—
93C4×C127—42no—
94C4×C127—42no—
95C4×C127#12011yescharacteristic
96C4×C127#12112yes—
97C4×C127#12311yescharacteristic
98C2×C127—22no—
99C2×C127—22no—
100C2×C127—41no—
101C2×C127#38611yescharacteristic
102C2×C127C2×#10111yescharacteristic
103C2×C127#41311yescharacteristic
104#1901C12711yesmaximal, characteristic, direct product factor, Sylow
105C127#190111yescharacteristic, direct product factor, Sylow
106C22×M16C2×C12711yescharacteristic
107C2×C22⋊Q8C2×C12711yescharacteristic
108C2×#101C2×C12712yescomplemented
109#407C2×C12711yescharacteristic
110#343C2×C12712yescomplemented
111C22×Q8C22×C12711yescharacteristic
112C23×C4C22×C12711yescharacteristic
113C2×M16—21no—
114C2×M16—24no—
115C2×M16C22×C12712yes—
116C2×M16C22×C12712yes—
117C22×C8—21no—
118C22⋊Q8—21no—
119C22⋊Q8—21no—
120C22⋊Q8—21no—
121C22⋊Q8—21no—
122C2×C4⋊C4C4×C12712yes—
123C2×C4⋊C4C22×C12711yescharacteristic
124C2×C22⋊C4C4×C12712yes—
125#101—24no—
126C22⋊C8—21no—
127C22⋊C8—21no—
128C24C2×C4×C12711yescharacteristic
129C2×Q8—22no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—22no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4C2×C4×C12712yes—
136C22×C4C2×C4×C12711yescharacteristic
137C22×C4C2×C4×C12712yes—
138C22×C4D4×C12711yescharacteristic
139C22×C4D4×C12711yescharacteristic
140C22×C4D4×C12711yescharacteristic
141C22×C4D4×C12711yescharacteristic
142C22×C4C23×C12711yescharacteristic
143M16—24no—
144M16—22no—
145M16—22no—
146M16—22no—
147M16D4×C12714yes—
148C2×C8—24no—
149C2×C8—22no—
150C2×C8—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C23—22no—
158C23—22no—
159C23—41no—
160C23C22⋊C4×C12711yescharacteristic
161C23C22⋊C4×C12711yescharacteristic
162C23C22×C4×C12711yescharacteristic
163Q8—41no—
164Q8—42no—
165Q8—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—42no—
177C2×C4C22⋊C4×C12711yescharacteristic
178C2×C4C22⋊C4×C12711yescharacteristic
179C2×C4C2×D4×C12712yes—
180C2×C4C2×D4×C12711yescharacteristic
181C2×C4C2×D4×C12711yescharacteristic
182C2×C4#41×C12712yes—
183C8—24no—
184C8—42no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22#101×C12712yescomplemented
194C22C2×C22⋊C4×C12711yescharacteristic
195C22C4×D4×C12712yes—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4#120×C12711yescharacteristic
201C4#121×C12712yes—
202C4#123×C12711yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2#386×C12711yescharacteristic
207C2C2×#101×C12711yescharacteristic
208C2#413×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×C22⋊C4
commutatorC23C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC24×C127C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#101×C127C2semidirect
5. #343×C127C2semidirect
88. C22×C127#101semidirect
104. #1901C127direct (N × H)
105. C127#1901direct (N × H)
108. C2×#101C2×C127semidirect
110. #343C2×C127semidirect
193. C22#101×C127semidirect

Maximal subgroups

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

subgroupindex
C22×M16×C1272
C2×C22⋊Q8×C1272
C2×#101×C1272
#407×C1272
#343×C1272
#1901127