Finite Group Databasebeta

← C127×#12455 #44576128

Subgroups — C127×#12455 #44576128

Order 32512.

206 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2252C211yesmaximal, characteristic, complemented
2C127×#2169C211yesmaximal, characteristic
3C127×#1675C212yesmaximal
4C127×#1372C211yesmaximal, characteristic, complemented
5C127×#1365C212yesmaximal, complemented
6C2×M32×C127—21no—
7#500×C127C2212yes—
8#476×C127—22no—
9C8×D4×C127C2211yescharacteristic
10#366×C127—21no—
11#366×C127—21no—
12C4⋊C16×C127C2211yescharacteristic
13C22⋊C16×C127—21no—
14C4×C16×C127C2211yescharacteristic
15#335×C127C2212yes—
16#333×C127—22no—
17C22×C8×C127—21no—
18C4⋊Q8×C127—22no—
19C4×D4×C127D411yescharacteristic
20M32×C127—42no—
21C2×C16×C127—21no—
22C2×C16×C127D411yescharacteristic
23C2×C16×C127D411yescharacteristic
24#107×C127—22no—
25#107×C127—22no—
26#106×C127—42no—
27C4⋊C8×C127—22no—
28C4⋊C8×C127D411yescharacteristic
29#102×C127—42no—
30C22⋊C8×C127—21no—
31C4×C8×C127C2311yescharacteristic
32C2×Q8×C127—42no—
33C2×D4×C127D811yescharacteristic
34C22×C4×C127—21no—
35C2×C8×C127—21no—
36C2×C8×C127—41no—
37C2×C8×C127—41no—
38C2×C8×C127—42no—
39C2×C8×C127C2×D411yescharacteristic
40C2×C8×C127#4111yescharacteristic
41C4⋊C4×C127—42no—
42C4⋊C4×C127—42no—
43C4⋊C4×C127D811yescharacteristic
44C22⋊C4×C127—21no—
45C42×C127C2×D411yescharacteristic
46C16×C127—21no—
47C16×C127—41no—
48C16×C127SD1612yes—
49C23×C127—21no—
50Q8×C127—162no—
51D4×C127—22no—
52C2×C4×C127—21no—
53C2×C4×C127—41no—
54C2×C4×C127—41no—
55C2×C4×C127—82no—
56C2×C4×C127#12111yescharacteristic
57C2×C4×C127C2×D811yescharacteristic
58C2×C4×C127#13511yescharacteristic
59C8×C127—21no—
60C8×C127—41no—
61C8×C127—82no—
62C8×C127C2×SD1611yescharacteristic
63C8×C127#13711yescharacteristic
64C22×C127—41no—
65C22×C127—41no—
66C22×C127—41no—
67C22×C127#46611yescharacteristic
68C4×C127—21no—
69C4×C127—41no—
70C4×C127—162no—
71C4×C127#46111yescharacteristic
72C4×C127#47311yescharacteristic
73C4×C127#51012yes—
74#12455C12711yesmaximal, characteristic, direct product factor, Sylow
75C2×C127—81no—
76C2×C127#167311yescharacteristic
77C2×C127#221911yescharacteristic
78C2×C127#222111yescharacteristic
79#2252C2×C12711yescharacteristic, complemented
80#2169C2×C12711yescharacteristic
81#1675C2×C12712yes—
82#1372C2×C12711yescharacteristic, complemented
83#1365C2×C12712yescomplemented
84C127#1245511yescharacteristic, direct product factor, Sylow
85C2×M32—21no—
86#500C22×C12712yes—
87#476—22no—
88C8×D4C22×C12711yescharacteristic
89#366—21no—
90#366—21no—
91C4⋊C16C22×C12711yescharacteristic
92C22⋊C16—21no—
93C4×C16C22×C12711yescharacteristic
94#335C22×C12712yes—
95#333—22no—
96C22×C8—21no—
97C4⋊Q8—22no—
98C4×D4D4×C12711yescharacteristic
99M32—42no—
100C2×C16—21no—
101C2×C16D4×C12711yescharacteristic
102C2×C16D4×C12711yescharacteristic
103#107—22no—
104#107—22no—
105#106—42no—
106C4⋊C8—22no—
107C4⋊C8D4×C12711yescharacteristic
108#102—42no—
109C22⋊C8—21no—
110C4×C8C23×C12711yescharacteristic
111C2×Q8—42no—
112C2×D4D8×C12711yescharacteristic
113C22×C4—21no—
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—41no—
117C2×C8—42no—
118C2×C8C2×D4×C12711yescharacteristic
119C2×C8#41×C12711yescharacteristic
120C4⋊C4—42no—
121C4⋊C4—42no—
122C4⋊C4D8×C12711yescharacteristic
123C22⋊C4—21no—
124C42C2×D4×C12711yescharacteristic
125C16—21no—
126C16—41no—
127C16SD16×C12712yes—
128C23—21no—
129Q8—162no—
130D4—22no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—82no—
135C2×C4#121×C12711yescharacteristic
136C2×C4C2×D8×C12711yescharacteristic
137C2×C4#135×C12711yescharacteristic
138C8—21no—
139C8—41no—
140C8—82no—
141C8C2×SD16×C12711yescharacteristic
142C8#137×C12711yescharacteristic
143C22—41no—
144C22—41no—
145C22—41no—
146C22#466×C12711yescharacteristic
147C4—21no—
148C4—41no—
149C4—162no—
150C4#461×C12711yescharacteristic
151C4#473×C12711yescharacteristic
152C4#510×C12712yes—
153C2—81no—
154C2C127×#167311yescharacteristic
155C2C127×#221911yescharacteristic
156C2C127×#222111yescharacteristic
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC2×D4×C127D8
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2252C2semidirect
4. C127×#1372C2semidirect
5. C127×#1365C2semidirect
74. #12455C127direct (N × H)
79. #2252C2×C127semidirect
82. #1372C2×C127semidirect
83. #1365C2×C127semidirect
84. C127#12455direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22522
C127×#21692
C127×#16752
C127×#13722
C127×#13652
#12455127