Finite Group Databasebeta

← C127×#2041 #30634993

Subgroups — C127×#2041 #30634993

Order 16256.

402 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C2×#127×C127C211yesmaximal, characteristic
2C2×#102×C127C212yesmaximal, complemented
3C2×#102×C127C212yesmaximal, complemented
4#389×C127C211yesmaximal, characteristic, complemented
5#336×C127C211yesmaximal, characteristic, complemented
6C22×D4×C127—21no—
7C22×D4×C127—21no—
8C22×D4×C127C2212yes—
9C22×C8×C127C2212yes—
10#127×C127—24no—
11C2×C4⋊C4×C127—21no—
12C2×C4⋊C4×C127C2211yescharacteristic
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C42×C127C2211yescharacteristic
15#102×C127—24no—
16#102×C127—24no—
17#95×C127—21no—
18C24×C127—22no—
19C2×D4×C127—24no—
20C2×D4×C127—24no—
21C2×D4×C127—22no—
22C2×D4×C127—22no—
23C2×D4×C127—22no—
24C2×D4×C127—22no—
25C2×D4×C127—22no—
26C2×D4×C127—42no—
27C2×D4×C127—42no—
28C2×D4×C127—42no—
29C2×D4×C127—42no—
30C2×D4×C127D414yes—
31C22×C4×C127—21no—
32C22×C4×C127—21no—
33C22×C4×C127D411yescharacteristic
34C22×C4×C127D411yescharacteristic
35C22×C4×C127C2311yescharacteristic
36C2×C8×C127—22no—
37C2×C8×C127—22no—
38C2×C8×C127—22no—
39C4⋊C4×C127—21no—
40C4⋊C4×C127—22no—
41C4⋊C4×C127—42no—
42C4⋊C4×C127D412yescomplemented
43C42×C127—22no—
44C23×C127—24no—
45C23×C127—42no—
46C23×C127—42no—
47C23×C127—42no—
48C23×C127—42no—
49C23×C127—42no—
50C23×C127—42no—
51C23×C127C2×D411yescharacteristic
52D4×C127—24no—
53D4×C127—24no—
54D4×C127—48no—
55D4×C127—48no—
56D4×C127—42no—
57D4×C127—42no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127—22no—
63C2×C4×C127—41no—
64C2×C4×C127—41no—
65C2×C4×C127—41no—
66C2×C4×C127—41no—
67C2×C4×C127—41no—
68C2×C4×C127D812yes—
69C2×C4×C127SD1612yes—
70C2×C4×C127C2×D411yescharacteristic
71C2×C4×C127C2×D412yes—
72C2×C4×C127#4112yes—
73C2×C4×C127#4111yescharacteristic
74C8×C127—42no—
75C22×C127—44no—
76C22×C127—44no—
77C22×C127—44no—
78C22×C127—82no—
79C22×C127—82no—
80C22×C127—82no—
81C22×C127—82no—
82C22×C127#12011yescharacteristic
83C22×C127#12111yescharacteristic
84C22×C127#12411yescharacteristic
85C22×C127C2×D811yescharacteristic
86C22×C127C2×SD1611yescharacteristic
87C22×C127AGL(1,ℤ/8)11yescharacteristic
88C22×C127AGL(1,ℤ/8)11yescharacteristic
89C4×C127—22no—
90C4×C127—22no—
91C4×C127—42no—
92C4×C127—81no—
93C4×C127#12112yes—
94C4×C127#12312yes—
95C2×C127—84no—
96C2×C127#39411yescharacteristic
97C2×C127#44711yescharacteristic
98C2×C127#45011yescharacteristic
99C2×C127#45911yescharacteristic
100C2×C127#46011yescharacteristic
101C2×C127#48611yescharacteristic
102C2×C127#49011yescharacteristic
103#2041C12711yesmaximal, characteristic, direct product factor, Sylow
104C127#204111yescharacteristic, direct product factor, Sylow
105C2×#127C2×C12711yescharacteristic
106C2×#102C2×C12712yescomplemented
107C2×#102C2×C12712yescomplemented
108#389C2×C12711yescharacteristic, complemented
109#336C2×C12711yescharacteristic, complemented
110C22×D4—21no—
111C22×D4—21no—
112C22×D4C22×C12712yes—
113C22×C8C22×C12712yes—
114#127—24no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4C22×C12711yescharacteristic
117C2×C4⋊C4C22×C12711yescharacteristic
118C2×C42C22×C12711yescharacteristic
119#102—24no—
120#102—24no—
121#95—21no—
122C24—22no—
123C2×D4—24no—
124C2×D4—24no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—42no—
131C2×D4—42no—
132C2×D4—42no—
133C2×D4—42no—
134C2×D4D4×C12714yes—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4D4×C12711yescharacteristic
138C22×C4D4×C12711yescharacteristic
139C22×C4C23×C12711yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—22no—
143C4⋊C4—21no—
144C4⋊C4—22no—
145C4⋊C4—42no—
146C4⋊C4D4×C12712yescomplemented
147C42—22no—
148C23—24no—
149C23—42no—
150C23—42no—
151C23—42no—
152C23—42no—
153C23—42no—
154C23—42no—
155C23C2×D4×C12711yescharacteristic
156D4—24no—
157D4—24no—
158D4—48no—
159D4—48no—
160D4—42no—
161D4—42no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4D8×C12712yes—
173C2×C4SD16×C12712yes—
174C2×C4C2×D4×C12711yescharacteristic
175C2×C4C2×D4×C12712yes—
176C2×C4#41×C12712yes—
177C2×C4#41×C12711yescharacteristic
178C8—42no—
179C22—44no—
180C22—44no—
181C22—44no—
182C22—82no—
183C22—82no—
184C22—82no—
185C22—82no—
186C22#120×C12711yescharacteristic
187C22#121×C12711yescharacteristic
188C22#124×C12711yescharacteristic
189C22C2×D8×C12711yescharacteristic
190C22C2×SD16×C12711yescharacteristic
191C22AGL(1,ℤ/8)×C12711yescharacteristic
192C22AGL(1,ℤ/8)×C12711yescharacteristic
193C4—22no—
194C4—22no—
195C4—42no—
196C4—81no—
197C4#121×C12712yes—
198C4#123×C12712yes—
199C2—84no—
200C2#394×C12711yescharacteristic
201C2#447×C12711yescharacteristic
202C2#450×C12711yescharacteristic
203C2#459×C12711yescharacteristic
204C2#460×C12711yescharacteristic
205C2#486×C12711yescharacteristic
206C2#490×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC2×#127×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#102×C127C2semidirect
3. C2×#102×C127C2semidirect
4. #389×C127C2semidirect
5. #336×C127C2semidirect
42. C4⋊C4×C127D4semidirect
103. #2041C127direct (N × H)
104. C127#2041direct (N × H)
106. C2×#102C2×C127semidirect
107. C2×#102C2×C127semidirect
108. #389C2×C127semidirect
109. #336C2×C127semidirect
146. C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#127×C1272
C2×#102×C1272
#389×C1272
#336×C1272
#2041127