Finite Group Databasebeta

← C127×#1915 #30634867

Subgroups — C127×#1915 #30634867

Order 16256.

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

normal subgroups only

This group has 308 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
1#568×C127C211yesmaximal, characteristic
2#536×C127C211yesmaximal, characteristic
3#413×C127C211yesmaximal, characteristic
4C2×#101×C127C212yesmaximal, complemented
5#344×C127C212yesmaximal, complemented
6C2×#41×C127C2211yescharacteristic
7C22×Q8×C127C2211yescharacteristic
8#131×C127—24no—
9C2×M16×C127—22no—
10C2×M16×C127C2212yes—
11C2×M16×C127C2212yes—
12C4⋊Q8×C127—21no—
13#124×C127—21no—
14#123×C127C414yes—
15C22⋊Q8×C127—22no—
16#117×C127C2211yescharacteristic
17#101×C127—21no—
18#101×C127—24no—
19#100×C127—21no—
20#41×C127—22no—
21#41×C127—22no—
22C2×Q8×C127—22no—
23C2×Q8×C127—21no—
24C2×Q8×C127—21no—
25C2×Q8×C127—22no—
26C2×Q8×C127D411yescharacteristic
27C2×D4×C127C2×C412yes—
28C2×D4×C127D411yescharacteristic
29C22×C4×C127C2×C412yes—
30C22×C4×C127D412yes—
31C22×C4×C127C2311yescharacteristic
32M16×C127—24no—
33M16×C127—22no—
34M16×C127—22no—
35M16×C127—22no—
36M16×C127D414yes—
37C2×C8×C127—24no—
38C2×C8×C127—22no—
39C2×C8×C127—22no—
40C4⋊C4×C127—24no—
41C4⋊C4×C127—21no—
42C22⋊C4×C127—24no—
43C22⋊C4×C127C2×C412yes—
44C42×C127—21no—
45C23×C127C22⋊C412yes—
46C23×C127C22×C411yescharacteristic
47Q8×C127—22no—
48Q8×C127—41no—
49Q8×C127—42no—
50Q8×C127—41no—
51D4×C127—24no—
52D4×C127—22no—
53C2×C4×C127—22no—
54C2×C4×C127—22no—
55C2×C4×C127—22no—
56C2×C4×C127—22no—
57C2×C4×C127—24no—
58C2×C4×C127C22⋊C412yes—
59C2×C4×C127C2×D412yes—
60C2×C4×C127C2×D411yescharacteristic
61C2×C4×C127C2×D411yescharacteristic
62C2×C4×C127#4112yes—
63C8×C127—24no—
64C8×C127—42no—
65C22×C127—22no—
66C22×C127—41no—
67C22×C127—42no—
68C22×C127C2×C22⋊C411yescharacteristic
69C22×C127C4×D412yes—
70C4×C127—22no—
71C4×C127—42no—
72C4×C127—42no—
73C4×C127#12011yescharacteristic
74C4×C127#12112yes—
75C4×C127#12311yescharacteristic
76C2×C127—21no—
77C2×C127—22no—
78C2×C127—42no—
79C2×C127#38611yescharacteristic
80#1915C12711yesmaximal, characteristic, direct product factor, Sylow
81C127#191511yescharacteristic, direct product factor, Sylow
82#568C2×C12711yescharacteristic
83#536C2×C12711yescharacteristic
84#413C2×C12711yescharacteristic
85C2×#101C2×C12712yescomplemented
86#344C2×C12712yescomplemented
87C2×#41C22×C12711yescharacteristic
88C22×Q8C22×C12711yescharacteristic
89#131—24no—
90C2×M16—22no—
91C2×M16C22×C12712yes—
92C2×M16C22×C12712yes—
93C4⋊Q8—21no—
94#124—21no—
95#123C4×C12714yes—
96C22⋊Q8—22no—
97#117C22×C12711yescharacteristic
98#101—21no—
99#101—24no—
100#100—21no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—21no—
105C2×Q8—21no—
106C2×Q8—22no—
107C2×Q8D4×C12711yescharacteristic
108C2×D4C2×C4×C12712yes—
109C2×D4D4×C12711yescharacteristic
110C22×C4C2×C4×C12712yes—
111C22×C4D4×C12712yes—
112C22×C4C23×C12711yescharacteristic
113M16—24no—
114M16—22no—
115M16—22no—
116M16—22no—
117M16D4×C12714yes—
118C2×C8—24no—
119C2×C8—22no—
120C2×C8—22no—
121C4⋊C4—24no—
122C4⋊C4—21no—
123C22⋊C4—24no—
124C22⋊C4C2×C4×C12712yes—
125C42—21no—
126C23C22⋊C4×C12712yes—
127C23C22×C4×C12711yescharacteristic
128Q8—22no—
129Q8—41no—
130Q8—42no—
131Q8—41no—
132D4—24no—
133D4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4C22⋊C4×C12712yes—
140C2×C4C2×D4×C12712yes—
141C2×C4C2×D4×C12711yescharacteristic
142C2×C4C2×D4×C12711yescharacteristic
143C2×C4#41×C12712yes—
144C8—24no—
145C8—42no—
146C22—22no—
147C22—41no—
148C22—42no—
149C22C2×C22⋊C4×C12711yescharacteristic
150C22C4×D4×C12712yes—
151C4—22no—
152C4—42no—
153C4—42no—
154C4#120×C12711yescharacteristic
155C4#121×C12712yes—
156C4#123×C12711yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#386×C12711yescharacteristic
subgroupG/H
center, socleC2×C127#386
commutatorC23C22×C4×C127
Frattini, cosocleC22×C4C23×C127
prime radicalC2×#41×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#101×C127C2semidirect
5. #344×C127C2semidirect
80. #1915C127direct (N × H)
81. C127#1915direct (N × H)
85. C2×#101C2×C127semidirect
86. #344C2×C127semidirect

Maximal subgroups

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

subgroupindex
#568×C1272
#536×C1272
#413×C1272
C2×#101×C1272
#344×C1272
#1915127