Finite Group Databasebeta

← C127×#12445 #44576118

Subgroups — C127×#12445 #44576118

Order 32512.

234 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 86 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×#2224C212yesmaximal
2C127×#1713C211yesmaximal, characteristic, complemented
3C8×D8×C127C211yesmaximal, characteristic
4C127×#1370C211yesmaximal, characteristic, complemented
5C127×#1364C212yesmaximal, complemented
6#500×C127—21no—
7#500×C127C2212yes—
8#494×C127—21no—
9C4×D8×C127C2211yescharacteristic
10C8×D4×C127—21no—
11#366×C127—22no—
12C4⋊C16×C127C2212yes—
13#357×C127—22no—
14#335×C127C2211yescharacteristic
15D4⋊C8×C127—21no—
16C82×C127C2211yescharacteristic
17C2×Q16×C127—41no—
18C2×Q16×C127—41no—
19C2×D8×C127D411yescharacteristic
20C22×C8×C127—41no—
21C4⋊Q8×C127—22no—
22C4×D4×C127—21no—
23C2×C16×C127—22no—
24#107×C127—22no—
25#107×C127—22no—
26#107×C127—42no—
27#107×C127D411yescharacteristic
28C4⋊C8×C127—21no—
29#102×C127—21no—
30C22⋊C8×C127—41no—
31C4×C8×C127D411yescharacteristic
32C4×C8×C127D411yescharacteristic
33C4×C8×C127C2311yescharacteristic
34C2×Q8×C127—42no—
35C2×D4×C127—21no—
36C22×C4×C127—41no—
37Q16×C127—82no—
38Q16×C127—82no—
39D8×C127—21no—
40D8×C127Q1612yescomplemented
41C2×C8×C127—21no—
42C2×C8×C127—41no—
43C2×C8×C127—82no—
44C2×C8×C127D811yescharacteristic
45C2×C8×C127D811yescharacteristic
46C2×C8×C127C2×D411yescharacteristic
47C2×C8×C127#4111yescharacteristic
48C4⋊C4×C127—21no—
49C4⋊C4×C127—42no—
50C4⋊C4×C127—42no—
51C22⋊C4×C127—41no—
52C42×C127C2×D411yescharacteristic
53C16×C127—42no—
54C23×C127—41no—
55Q8×C127—82no—
56Q8×C127—82no—
57D4×C127—22no—
58D4×C127—41no—
59C2×C4×C127—41no—
60C2×C4×C127—81no—
61C2×C4×C127—81no—
62C2×C4×C127—82no—
63C2×C4×C127#12111yescharacteristic
64C2×C4×C127C2×D811yescharacteristic
65C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
66C8×C127—22no—
67C8×C127—21no—
68C8×C127—21no—
69C8×C127—81no—
70C8×C127D1612yes—
71C8×C127C2×Q1611yescharacteristic
72C8×C127#13511yescharacteristic
73C22×C127—42no—
74C22×C127—81no—
75C22×C127—81no—
76C22×C127#45911yescharacteristic
77C4×C127—21no—
78C4×C127—81no—
79C4×C127—162no—
80C4×C127#46711yescharacteristic
81C4×C127#47311yescharacteristic
82C4×C127C2×D1611yescharacteristic
83C4×C127#50911yescharacteristic
84#12445C12711yesmaximal, characteristic, direct product factor, Sylow
85C2×C127—82no—
86C2×C127#166911yescharacteristic
87C2×C127#220611yescharacteristic
88C2×C127#221411yescharacteristic
89#2224C2×C12712yes—
90#1713C2×C12711yescharacteristic, complemented
91C8×D8C2×C12711yescharacteristic
92#1370C2×C12711yescharacteristic, complemented
93#1364C2×C12712yescomplemented
94C127#1244511yescharacteristic, direct product factor, Sylow
95#500—21no—
96#500C22×C12712yes—
97#494—21no—
98C4×D8C22×C12711yescharacteristic
99C8×D4—21no—
100#366—22no—
101C4⋊C16C22×C12712yes—
102#357—22no—
103#335C22×C12711yescharacteristic
104D4⋊C8—21no—
105C82C22×C12711yescharacteristic
106C2×Q16—41no—
107C2×Q16—41no—
108C2×D8D4×C12711yescharacteristic
109C22×C8—41no—
110C4⋊Q8—22no—
111C4×D4—21no—
112C2×C16—22no—
113#107—22no—
114#107—22no—
115#107—42no—
116#107D4×C12711yescharacteristic
117C4⋊C8—21no—
118#102—21no—
119C22⋊C8—41no—
120C4×C8D4×C12711yescharacteristic
121C4×C8D4×C12711yescharacteristic
122C4×C8C23×C12711yescharacteristic
123C2×Q8—42no—
124C2×D4—21no—
125C22×C4—41no—
126Q16—82no—
127Q16—82no—
128D8—21no—
129D8Q16×C12712yescomplemented
130C2×C8—21no—
131C2×C8—41no—
132C2×C8—82no—
133C2×C8D8×C12711yescharacteristic
134C2×C8D8×C12711yescharacteristic
135C2×C8C2×D4×C12711yescharacteristic
136C2×C8#41×C12711yescharacteristic
137C4⋊C4—21no—
138C4⋊C4—42no—
139C4⋊C4—42no—
140C22⋊C4—41no—
141C42C2×D4×C12711yescharacteristic
142C16—42no—
143C23—41no—
144Q8—82no—
145Q8—82no—
146D4—22no—
147D4—41no—
148C2×C4—41no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—82no—
152C2×C4#121×C12711yescharacteristic
153C2×C4C2×D8×C12711yescharacteristic
154C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
155C8—22no—
156C8—21no—
157C8—21no—
158C8—81no—
159C8D16×C12712yes—
160C8C2×Q16×C12711yescharacteristic
161C8#135×C12711yescharacteristic
162C22—42no—
163C22—81no—
164C22—81no—
165C22#459×C12711yescharacteristic
166C4—21no—
167C4—81no—
168C4—162no—
169C4#467×C12711yescharacteristic
170C4#473×C12711yescharacteristic
171C4C2×D16×C12711yescharacteristic
172C4#509×C12711yescharacteristic
173C2—82no—
174C2C127×#166911yescharacteristic
175C2C127×#220611yescharacteristic
176C2C127×#221411yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC2×D8×C127D4
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1713C2semidirect
4. C127×#1370C2semidirect
5. C127×#1364C2semidirect
40. D8×C127Q16semidirect
84. #12445C127direct (N × H)
90. #1713C2×C127semidirect
92. #1370C2×C127semidirect
93. #1364C2×C127semidirect
94. C127#12445direct (N × H)
129. D8Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22242
C127×#17132
C8×D8×C1272
C127×#13702
C127×#13642
#12445127