Finite Group Databasebeta

← C127×#7319 #44570992

Subgroups — C127×#7319 #44570992

Order 32512.

456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C127×#1785C212yesmaximal
2C127×#1782C211yesmaximal, characteristic
3C22×#41×C127C2211yescharacteristic
4C2×#101×C127—22no—
5C2×#100×C127—22no—
6C2×#99×C127—22no—
7#407×C127C414yescomplemented
8#381×C127C412yes—
9C2×#41×C127—42no—
10C2×#41×C127—44no—
11C22×Q8×C127D411yescharacteristic
12C22×D4×C127D412yes—
13C22×D4×C127Q811yescharacteristic
14C23×C4×C127C2×C412yes—
15C23×C4×C127C2×C411yescharacteristic
16C2×M16×C127—24no—
17C2×C22⋊C4×C127—22no—
18#101×C127—44no—
19#100×C127—44no—
20#99×C127—44no—
21C22⋊C8×C127—44no—
22#95×C127—42no—
23C24×C127C22⋊C411yescharacteristic
24C24×C127C4⋊C412yes—
25#41×C127—416no—
26C2×Q8×C127—24no—
27C2×Q8×C127—41no—
28C2×D4×C127—24no—
29C2×D4×C127—24no—
30C2×D4×C127—42no—
31C2×D4×C127—41no—
32C2×D4×C127—42no—
33C22×C4×C127—22no—
34C22×C4×C127—24no—
35C22×C4×C127—42no—
36C22×C4×C127—42no—
37C22×C4×C127—42no—
38C22×C4×C127—42no—
39C22×C4×C127C4211yescharacteristic
40C22×C4×C127C22⋊C412yes—
41C22×C4×C127C4⋊C411yescharacteristic
42M16×C127—44no—
43M16×C127—44no—
44C2×C8×C127—44no—
45C22⋊C4×C127—44no—
46C23×C127—22no—
47C23×C127—22no—
48C23×C127—22no—
49C23×C127—22no—
50C23×C127—81no—
51C23×C127—82no—
52C23×C127#9511yescharacteristic
53C23×C127#9912yes—
54Q8×C127—44no—
55D4×C127—48no—
56D4×C127—44no—
57C2×C4×C127—22no—
58C2×C4×C127—22no—
59C2×C4×C127—21no—
60C2×C4×C127—22no—
61C2×C4×C127—21no—
62C2×C4×C127—22no—
63C2×C4×C127—48no—
64C2×C4×C127—44no—
65C2×C4×C127—82no—
66C2×C4×C127—84no—
67C2×C4×C127#9914yes—
68C8×C127—84no—
69C22×C127—22no—
70C22×C127—41no—
71C22×C127—42no—
72C22×C127—44no—
73C22×C127—42no—
74C22×C127—82no—
75C22×C127—82no—
76C22×C127—82no—
77C22×C127#34211yescharacteristic
78C22×C127#34212yes—
79C4×C127—24no—
80C4×C127—41no—
81C4×C127—41no—
82C4×C127—162no—
83#7319C12711yesmaximal, characteristic, direct product factor, Sylow
84C2×C127—21no—
85C2×C127—22no—
86C2×C127—42no—
87C2×C127—82no—
88C2×C127#130411yescharacteristic
89#1785C2×C12712yes—
90#1782C2×C12711yescharacteristic
91C127#731911yescharacteristic, direct product factor, Sylow
92C22×#41C22×C12711yescharacteristic
93C2×#101—22no—
94C2×#100—22no—
95C2×#99—22no—
96#407C4×C12714yescomplemented
97#381C4×C12712yes—
98C2×#41—42no—
99C2×#41—44no—
100C22×Q8D4×C12711yescharacteristic
101C22×D4D4×C12712yes—
102C22×D4Q8×C12711yescharacteristic
103C23×C4C2×C4×C12712yes—
104C23×C4C2×C4×C12711yescharacteristic
105C2×M16—24no—
106C2×C22⋊C4—22no—
107#101—44no—
108#100—44no—
109#99—44no—
110C22⋊C8—44no—
111#95—42no—
112C24C22⋊C4×C12711yescharacteristic
113C24C4⋊C4×C12712yes—
114#41—416no—
115C2×Q8—24no—
116C2×Q8—41no—
117C2×D4—24no—
118C2×D4—24no—
119C2×D4—42no—
120C2×D4—41no—
121C2×D4—42no—
122C22×C4—22no—
123C22×C4—24no—
124C22×C4—42no—
125C22×C4—42no—
126C22×C4—42no—
127C22×C4—42no—
128C22×C4C42×C12711yescharacteristic
129C22×C4C22⋊C4×C12712yes—
130C22×C4C4⋊C4×C12711yescharacteristic
131M16—44no—
132M16—44no—
133C2×C8—44no—
134C22⋊C4—44no—
135C23—22no—
136C23—22no—
137C23—22no—
138C23—22no—
139C23—81no—
140C23—82no—
141C23#95×C12711yescharacteristic
142C23#99×C12712yes—
143Q8—44no—
144D4—48no—
145D4—44no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—22no—
152C2×C4—48no—
153C2×C4—44no—
154C2×C4—82no—
155C2×C4—84no—
156C2×C4#99×C12714yes—
157C8—84no—
158C22—22no—
159C22—41no—
160C22—42no—
161C22—44no—
162C22—42no—
163C22—82no—
164C22—82no—
165C22—82no—
166C22#342×C12711yescharacteristic
167C22#342×C12712yes—
168C4—24no—
169C4—41no—
170C4—41no—
171C4—162no—
172C2—21no—
173C2—22no—
174C2—42no—
175C2—82no—
176C2C127×#130411yescharacteristic
subgroupG/H
center, socleC2×C127#1304
commutatorC22×C4C42×C127
Frattini, cosocleC22×#41C22×C127
prime radicalC22×#41×C127C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C23×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
7. #407×C127C4semidirect
83. #7319C127direct (N × H)
91. C127#7319direct (N × H)
96. #407C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#17852
C127×#17822
#7319127