Finite Group Databasebeta

← C127×#2016 #30634968

Subgroups — C127×#2016 #30634968

Order 16256.

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

normal subgroups only

This group has 370 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×Q16×C127C212yesmaximal
2C2×C4⋊Q8×C127C211yesmaximal, characteristic
3C2×#103×C127C212yesmaximal
4#391×C127C211yesmaximal, characteristic
5#336×C127C211yesmaximal, characteristic
6C22×Q8×C127C2212yes—
7C22×Q8×C127C2211yescharacteristic
8C2×Q16×C127—24no—
9C2×Q16×C127—24no—
10C2×Q16×C127—24no—
11C22×C8×C127C2212yes—
12C4⋊Q8×C127—24no—
13C2×C4⋊C4×C127—22no—
14C2×C4⋊C4×C127C2211yescharacteristic
15C2×C42×C127C2211yescharacteristic
16#103×C127—24no—
17#95×C127—22no—
18C2×Q8×C127—22no—
19C2×Q8×C127—21no—
20C2×Q8×C127—22no—
21C2×Q8×C127—22no—
22C2×Q8×C127—22no—
23C2×Q8×C127—22no—
24C2×Q8×C127—22no—
25C2×Q8×C127—22no—
26C2×Q8×C127D414yes—
27C2×Q8×C127D412yes—
28C22×C4×C127—21no—
29C22×C4×C127—22no—
30C22×C4×C127—21no—
31C22×C4×C127D412yes—
32C22×C4×C127C2311yescharacteristic
33Q16×C127—216no—
34C2×C8×C127—22no—
35C2×C8×C127—22no—
36C2×C8×C127D414yes—
37C4⋊C4×C127—28no—
38C4⋊C4×C127—22no—
39C42×C127—22no—
40C23×C127C2×D411yescharacteristic
41Q8×C127—24no—
42Q8×C127—24no—
43Q8×C127—24no—
44Q8×C127—42no—
45Q8×C127—42no—
46Q8×C127—42no—
47C2×C4×C127—22no—
48C2×C4×C127—22no—
49C2×C4×C127—24no—
50C2×C4×C127—22no—
51C2×C4×C127—41no—
52C2×C4×C127—42no—
53C2×C4×C127—41no—
54C2×C4×C127—42no—
55C2×C4×C127—41no—
56C2×C4×C127—42no—
57C2×C4×C127Q1614yescomplemented
58C2×C4×C127C2×D411yescharacteristic
59C2×C4×C127C2×D412yes—
60C2×C4×C127C2×D412yes—
61C2×C4×C127#4111yescharacteristic
62C8×C127—24no—
63C22×C127#12011yescharacteristic
64C22×C127#12111yescharacteristic
65C22×C127#12711yescharacteristic
66C22×C127C2×Q1612yes—
67C22×C127#13712yes—
68C4×C127—24no—
69C4×C127—44no—
70C4×C127—42no—
71C4×C127—81no—
72C4×C127#12012yes—
73C4×C127#12112yes—
74C2×C127#39211yescharacteristic
75C2×C127#45112yes—
76C2×C127#46212yes—
77C2×C127#49411yescharacteristic
78C2×C127#49711yescharacteristic
79#2016C12711yesmaximal, characteristic, direct product factor, Sylow
80C127#201611yescharacteristic, direct product factor, Sylow
81C22×Q16C2×C12712yes—
82C2×C4⋊Q8C2×C12711yescharacteristic
83C2×#103C2×C12712yes—
84#391C2×C12711yescharacteristic
85#336C2×C12711yescharacteristic
86C22×Q8C22×C12712yes—
87C22×Q8C22×C12711yescharacteristic
88C2×Q16—24no—
89C2×Q16—24no—
90C2×Q16—24no—
91C22×C8C22×C12712yes—
92C4⋊Q8—24no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4C22×C12711yescharacteristic
95C2×C42C22×C12711yescharacteristic
96#103—24no—
97#95—22no—
98C2×Q8—22no—
99C2×Q8—21no—
100C2×Q8—22no—
101C2×Q8—22no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—22no—
106C2×Q8D4×C12714yes—
107C2×Q8D4×C12712yes—
108C22×C4—21no—
109C22×C4—22no—
110C22×C4—21no—
111C22×C4D4×C12712yes—
112C22×C4C23×C12711yescharacteristic
113Q16—216no—
114C2×C8—22no—
115C2×C8—22no—
116C2×C8D4×C12714yes—
117C4⋊C4—28no—
118C4⋊C4—22no—
119C42—22no—
120C23C2×D4×C12711yescharacteristic
121Q8—24no—
122Q8—24no—
123Q8—24no—
124Q8—42no—
125Q8—42no—
126Q8—42no—
127C2×C4—22no—
128C2×C4—22no—
129C2×C4—24no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—41no—
134C2×C4—42no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4Q16×C12714yescomplemented
138C2×C4C2×D4×C12711yescharacteristic
139C2×C4C2×D4×C12712yes—
140C2×C4C2×D4×C12712yes—
141C2×C4#41×C12711yescharacteristic
142C8—24no—
143C22#120×C12711yescharacteristic
144C22#121×C12711yescharacteristic
145C22#127×C12711yescharacteristic
146C22C2×Q16×C12712yes—
147C22#137×C12712yes—
148C4—24no—
149C4—44no—
150C4—42no—
151C4—81no—
152C4#120×C12712yes—
153C4#121×C12712yes—
154C2#392×C12711yescharacteristic
155C2#451×C12712yes—
156C2#462×C12712yes—
157C2#494×C12711yescharacteristic
158C2#497×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
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
57. C2×C4×C127Q16semidirect
79. #2016C127direct (N × H)
80. C127#2016direct (N × H)
137. C2×C4Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×C1272
C2×C4⋊Q8×C1272
C2×#103×C1272
#391×C1272
#336×C1272
#2016127