Finite Group Databasebeta

← C127×#12434 #44576107

Subgroups — C127×#12434 #44576107

Order 32512.

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

normal subgroups only

This group has 230 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×#2247C211yesmaximal, characteristic, complemented
2C127×#2169C211yesmaximal, characteristic
3C127×#1669C212yesmaximal
4C127×#1372C211yesmaximal, characteristic, complemented
5C127×#1362C212yesmaximal, complemented
6C2×Q32×C127—21no—
7C2×Q32×C127—21no—
8C2×M32×C127—21no—
9#494×C127C2212yes—
10#474×C127—22no—
11C8×D4×C127C2211yescharacteristic
12C4⋊C16×C127C2211yescharacteristic
13C22⋊C16×C127—21no—
14C4×C16×C127C2211yescharacteristic
15#335×C127C2212yes—
16#332×C127—22no—
17C2×Q16×C127—22no—
18C2×Q16×C127—22no—
19C22×C8×C127—21no—
20C4⋊Q8×C127—22no—
21C4×D4×C127D411yescharacteristic
22Q32×C127—42no—
23Q32×C127—42no—
24M32×C127—42no—
25C2×C16×C127—21no—
26C2×C16×C127D411yescharacteristic
27C2×C16×C127D411yescharacteristic
28#107×C127—42no—
29C4⋊C8×C127—22no—
30C4⋊C8×C127D411yescharacteristic
31#102×C127—42no—
32C22⋊C8×C127—21no—
33C4×C8×C127C2311yescharacteristic
34C2×Q8×C127—42no—
35C2×D4×C127D811yescharacteristic
36C22×C4×C127—21no—
37Q16×C127—42no—
38Q16×C127—42no—
39Q16×C127—82no—
40C2×C8×C127—21no—
41C2×C8×C127—41no—
42C2×C8×C127—41no—
43C2×C8×C127—42no—
44C2×C8×C127C2×D411yescharacteristic
45C2×C8×C127#4111yescharacteristic
46C4⋊C4×C127—42no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127D811yescharacteristic
49C22⋊C4×C127—21no—
50C42×C127C2×D411yescharacteristic
51C16×C127—21no—
52C16×C127—41no—
53C16×C127D812yes—
54C23×C127—21no—
55Q8×C127—82no—
56Q8×C127—82no—
57D4×C127—22no—
58C2×C4×C127—21no—
59C2×C4×C127—41no—
60C2×C4×C127—41no—
61C2×C4×C127—82no—
62C2×C4×C127#12111yescharacteristic
63C2×C4×C127C2×D811yescharacteristic
64C2×C4×C127#13511yescharacteristic
65C8×C127—21no—
66C8×C127—41no—
67C8×C127—82no—
68C8×C127C2×D811yescharacteristic
69C8×C127AGL(1,ℤ/8)11yescharacteristic
70C22×C127—41no—
71C22×C127—41no—
72C22×C127—41no—
73C22×C127#46611yescharacteristic
74C4×C127—21no—
75C4×C127—41no—
76C4×C127—162no—
77C4×C127#45911yescharacteristic
78C4×C127#47211yescharacteristic
79C4×C127#51012yes—
80#12434C12711yesmaximal, characteristic, direct product factor, Sylow
81C2×C127—81no—
82C2×C127#166711yescharacteristic
83C2×C127#221911yescharacteristic
84C2×C127#222211yescharacteristic
85#2247C2×C12711yescharacteristic, complemented
86#2169C2×C12711yescharacteristic
87#1669C2×C12712yes—
88#1372C2×C12711yescharacteristic, complemented
89#1362C2×C12712yescomplemented
90C127#1243411yescharacteristic, direct product factor, Sylow
91C2×Q32—21no—
92C2×Q32—21no—
93C2×M32—21no—
94#494C22×C12712yes—
95#474—22no—
96C8×D4C22×C12711yescharacteristic
97C4⋊C16C22×C12711yescharacteristic
98C22⋊C16—21no—
99C4×C16C22×C12711yescharacteristic
100#335C22×C12712yes—
101#332—22no—
102C2×Q16—22no—
103C2×Q16—22no—
104C22×C8—21no—
105C4⋊Q8—22no—
106C4×D4D4×C12711yescharacteristic
107Q32—42no—
108Q32—42no—
109M32—42no—
110C2×C16—21no—
111C2×C16D4×C12711yescharacteristic
112C2×C16D4×C12711yescharacteristic
113#107—42no—
114C4⋊C8—22no—
115C4⋊C8D4×C12711yescharacteristic
116#102—42no—
117C22⋊C8—21no—
118C4×C8C23×C12711yescharacteristic
119C2×Q8—42no—
120C2×D4D8×C12711yescharacteristic
121C22×C4—21no—
122Q16—42no—
123Q16—42no—
124Q16—82no—
125C2×C8—21no—
126C2×C8—41no—
127C2×C8—41no—
128C2×C8—42no—
129C2×C8C2×D4×C12711yescharacteristic
130C2×C8#41×C12711yescharacteristic
131C4⋊C4—42no—
132C4⋊C4—42no—
133C4⋊C4D8×C12711yescharacteristic
134C22⋊C4—21no—
135C42C2×D4×C12711yescharacteristic
136C16—21no—
137C16—41no—
138C16D8×C12712yes—
139C23—21no—
140Q8—82no—
141Q8—82no—
142D4—22no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—82no—
147C2×C4#121×C12711yescharacteristic
148C2×C4C2×D8×C12711yescharacteristic
149C2×C4#135×C12711yescharacteristic
150C8—21no—
151C8—41no—
152C8—82no—
153C8C2×D8×C12711yescharacteristic
154C8AGL(1,ℤ/8)×C12711yescharacteristic
155C22—41no—
156C22—41no—
157C22—41no—
158C22#466×C12711yescharacteristic
159C4—21no—
160C4—41no—
161C4—162no—
162C4#459×C12711yescharacteristic
163C4#472×C12711yescharacteristic
164C4#510×C12712yes—
165C2—81no—
166C2C127×#166711yescharacteristic
167C2C127×#221911yescharacteristic
168C2C127×#222211yescharacteristic
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×#2247C2semidirect
4. C127×#1372C2semidirect
5. C127×#1362C2semidirect
80. #12434C127direct (N × H)
85. #2247C2×C127semidirect
88. #1372C2×C127semidirect
89. #1362C2×C127semidirect
90. C127#12434direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22472
C127×#21692
C127×#16692
C127×#13722
C127×#13622
#12434127