Finite Group Databasebeta

← C127×#3058 #30636010

Subgroups — C127×#3058 #30636010

Order 16256.

524 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 200 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×D8×C127C211yesmaximal, characteristic, complemented
2C2×#131×C127C211yesmaximal, characteristic, complemented
3#535×C127C212yesmaximal, complemented
4#469×C127C214yesmaximal, complemented
5#466×C127C214yesmaximal, complemented
6#427×C127C211yesmaximal, characteristic, complemented
7#418×C127C212yesmaximal, complemented
8C2×#41×C127C2211yescharacteristic
9C22×D4×C127C2212yes—
10C2×D8×C127—24no—
11C2×D8×C127C2212yes—
12C2×D8×C127C2212yes—
13#131×C127—24no—
14C2×M16×C127C2211yescharacteristic
15C2×M16×C127C2212yescomplemented
16C22×C8×C127C2211yescharacteristic
17C22×C8×C127C2212yescomplemented
18#127×C127—22no—
19#124×C127—22no—
20#121×C127C2218yescomplemented
21#120×C127—24no—
22#117×C127C2212yes—
23#107×C127C2212yescomplemented
24#106×C127C2212yescomplemented
25#102×C127C2218yescomplemented
26C24×C127—22no—
27#41×C127—22no—
28#41×C127—22no—
29C2×Q8×C127D411yescharacteristic
30C2×D4×C127—28no—
31C2×D4×C127—24no—
32C2×D4×C127—22no—
33C2×D4×C127—24no—
34C2×D4×C127D412yes—
35C2×D4×C127D411yescharacteristic
36C2×D4×C127C2314yes—
37C22×C4×C127C2312yes—
38C22×C4×C127C2311yescharacteristic
39D8×C127—24no—
40D8×C127—24no—
41M16×C127—22no—
42M16×C127—24no—
43C2×C8×C127—24no—
44C2×C8×C127D414yescomplemented
45C2×C8×C127C2312yes—
46C2×C8×C127C2311yescharacteristic
47C2×C8×C127C2311yescharacteristic
48C4⋊C4×C127C2314yes—
49C22⋊C4×C127—22no—
50C22⋊C4×C127—28no—
51C42×C127—22no—
52C23×C127—24no—
53C23×C127—44no—
54C23×C127—84no—
55C23×C127C2×D412yes—
56C23×C127C2×D411yescharacteristic
57Q8×C127—22no—
58D4×C127—24no—
59D4×C127—22no—
60D4×C127—24no—
61D4×C127—24no—
62D4×C127—44no—
63D4×C127—88no—
64C2×C4×C127—22no—
65C2×C4×C127—22no—
66C2×C4×C127—24no—
67C2×C4×C127C2×D412yes—
68C2×C4×C127C2×D411yescharacteristic
69C2×C4×C127C2×D412yes—
70C2×C4×C127#4112yes—
71C2×C4×C127C2411yescharacteristic
72C8×C127—22no—
73C8×C127C2×D412yes—
74C8×C127C2×D412yes—
75C22×C127—22no—
76C22×C127—22no—
77C22×C127—24no—
78C22×C127—44no—
79C22×C127—48no—
80C22×C127—88no—
81C22×C127#12112yes—
82C22×C127C22×D411yescharacteristic
83C4×C127—22no—
84C4×C127—44no—
85C4×C127#12112yes—
86C4×C127C22×D411yescharacteristic
87C4×C127C2×#4111yescharacteristic
88C2×C127—22no—
89C2×C127—42no—
90C2×C127—84no—
91C2×C127C2×#12111yescharacteristic
92C2×C127#57612yes—
93#3058C12711yesmaximal, characteristic, direct product factor, Sylow
94C127#305811yescharacteristic, direct product factor, Sylow
95C22×D8C2×C12711yescharacteristic, complemented
96C2×#131C2×C12711yescharacteristic, complemented
97#535C2×C12712yescomplemented
98#469C2×C12714yescomplemented
99#466C2×C12714yescomplemented
100#427C2×C12711yescharacteristic, complemented
101#418C2×C12712yescomplemented
102C2×#41C22×C12711yescharacteristic
103C22×D4C22×C12712yes—
104C2×D8—24no—
105C2×D8C22×C12712yes—
106C2×D8C22×C12712yes—
107#131—24no—
108C2×M16C22×C12711yescharacteristic
109C2×M16C22×C12712yescomplemented
110C22×C8C22×C12711yescharacteristic
111C22×C8C22×C12712yescomplemented
112#127—22no—
113#124—22no—
114#121C22×C12718yescomplemented
115#120—24no—
116#117C22×C12712yes—
117#107C22×C12712yescomplemented
118#106C22×C12712yescomplemented
119#102C22×C12718yescomplemented
120C24—22no—
121#41—22no—
122#41—22no—
123C2×Q8D4×C12711yescharacteristic
124C2×D4—28no—
125C2×D4—24no—
126C2×D4—22no—
127C2×D4—24no—
128C2×D4D4×C12712yes—
129C2×D4D4×C12711yescharacteristic
130C2×D4C23×C12714yes—
131C22×C4C23×C12712yes—
132C22×C4C23×C12711yescharacteristic
133D8—24no—
134D8—24no—
135M16—22no—
136M16—24no—
137C2×C8—24no—
138C2×C8D4×C12714yescomplemented
139C2×C8C23×C12712yes—
140C2×C8C23×C12711yescharacteristic
141C2×C8C23×C12711yescharacteristic
142C4⋊C4C23×C12714yes—
143C22⋊C4—22no—
144C22⋊C4—28no—
145C42—22no—
146C23—24no—
147C23—44no—
148C23—84no—
149C23C2×D4×C12712yes—
150C23C2×D4×C12711yescharacteristic
151Q8—22no—
152D4—24no—
153D4—22no—
154D4—24no—
155D4—24no—
156D4—44no—
157D4—88no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4C2×D4×C12712yes—
162C2×C4C2×D4×C12711yescharacteristic
163C2×C4C2×D4×C12712yes—
164C2×C4#41×C12712yes—
165C2×C4C24×C12711yescharacteristic
166C8—22no—
167C8C2×D4×C12712yes—
168C8C2×D4×C12712yes—
169C22—22no—
170C22—22no—
171C22—24no—
172C22—44no—
173C22—48no—
174C22—88no—
175C22#121×C12712yes—
176C22C22×D4×C12711yescharacteristic
177C4—22no—
178C4—44no—
179C4#121×C12712yes—
180C4C22×D4×C12711yescharacteristic
181C4C2×#41×C12711yescharacteristic
182C2—22no—
183C2—42no—
184C2—84no—
185C2C2×#121×C12711yescharacteristic
186C2#576×C12712yes—
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×D8×C127C2semidirect
2. C2×#131×C127C2semidirect
3. #535×C127C2semidirect
4. #469×C127C2semidirect
5. #466×C127C2semidirect
6. #427×C127C2semidirect
7. #418×C127C2semidirect
15. C2×M16×C127C22semidirect
17. C22×C8×C127C22semidirect
20. #121×C127C22semidirect
23. #107×C127C22semidirect
24. #106×C127C22semidirect
25. #102×C127C22semidirect
44. C2×C8×C127D4semidirect
93. #3058C127direct (N × H)
94. C127#3058direct (N × H)
95. C22×D8C2×C127semidirect
96. C2×#131C2×C127semidirect
97. #535C2×C127semidirect
98. #469C2×C127semidirect
99. #466C2×C127semidirect
100. #427C2×C127semidirect
101. #418C2×C127semidirect
109. C2×M16C22×C127semidirect
111. C22×C8C22×C127semidirect
114. #121C22×C127semidirect
117. #107C22×C127semidirect
118. #106C22×C127semidirect
119. #102C22×C127semidirect
138. C2×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D8×C1272
C2×#131×C1272
#535×C1272
#469×C1272
#466×C1272
#427×C1272
#418×C1272
#3058127