Finite Group Databasebeta

← C127×#13459 #44577132

Subgroups — C127×#13459 #44577132

Order 32512.

318 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3162C211yesmaximal, characteristic
2C127×#2155C212yesmaximal
3C127×#1946C211yesmaximal, characteristic
4C127×#1384C212yesmaximal
5C127×#1375C211yesmaximal, characteristic
6#533×C127—21no—
7C2×M32×C127C2212yes—
8#501×C127—24no—
9C2×#108×C127C2211yescharacteristic
10#427×C127—21no—
11#427×C127C2212yes—
12#427×C127C2211yescharacteristic
13#424×C127—21no—
14C2×#97×C127C2211yescharacteristic
15#365×C127—24no—
16#339×C127—21no—
17C2×M16×C127—21no—
18C22×C8×C127D411yescharacteristic
19C22×C8×C127C2311yescharacteristic
20C4⋊Q8×C127—22no—
21#125×C127—22no—
22C22⋊Q8×C127—42no—
23C4×Q8×C127—42no—
24#117×C127—22no—
25#117×C127—21no—
26C2×C42×C127D411yescharacteristic
27M32×C127—22no—
28M32×C127—22no—
29C2×C16×C127Q814yescomplemented
30#108×C127—22no—
31#107×C127—22no—
32#107×C127—22no—
33#107×C127—21no—
34#106×C127—22no—
35#106×C127D414yes—
36#106×C127Q812yescomplemented
37C4⋊C8×C127—42no—
38#97×C127—22no—
39C2×Q8×C127—42no—
40C22×C4×C127—21no—
41C22×C4×C127C2×D411yescharacteristic
42M16×C127—41no—
43M16×C127—41no—
44C2×C8×C127—21no—
45C2×C8×C127—21no—
46C2×C8×C127—41no—
47C2×C8×C127SD1612yes—
48C2×C8×C127C2×D412yes—
49C2×C8×C127C2×Q812yes—
50C2×C8×C127C2×Q811yescharacteristic
51C2×C8×C127#4111yescharacteristic
52C4⋊C4×C127—24no—
53C4⋊C4×C127—22no—
54C4⋊C4×C127—44no—
55C4⋊C4×C127—42no—
56C22⋊C4×C127—41no—
57C22⋊C4×C127—42no—
58C42×C127—21no—
59C42×C127—41no—
60C42×C127—42no—
61C42×C127SD1612yes—
62C16×C127—24no—
63C23×C127AGL(1,ℤ/8)11yescharacteristic
64Q8×C127—84no—
65C2×C4×C127—22no—
66C2×C4×C127—44no—
67C2×C4×C127—42no—
68C2×C4×C127—81no—
69C2×C4×C127#12011yescharacteristic
70C2×C4×C127C22⋊Q811yescharacteristic
71C2×C4×C127C4⋊Q811yescharacteristic
72C2×C4×C127C2×SD1611yescharacteristic
73C2×C4×C127C2×SD1611yescharacteristic
74C2×C4×C127#13711yescharacteristic
75C8×C127—22no—
76C8×C127—81no—
77C8×C127C22⋊Q812yes—
78C8×C127C4⋊Q812yes—
79C22×C127—41no—
80C22×C127#45011yescharacteristic
81C22×C127#47611yescharacteristic
82C22×C127#50111yescharacteristic
83C4×C127—42no—
84C4×C127—82no—
85C4×C127—84no—
86C4×C127#39511yescharacteristic
87C4×C127#44811yescharacteristic
88C4×C127#47511yescharacteristic
89C4×C127#49811yescharacteristic
90#13459C12711yesmaximal, characteristic, direct product factor, Sylow
91C2×C127—21no—
92C2×C127—21no—
93C2×C127—21no—
94C2×C127#205811yescharacteristic
95#3162C2×C12711yescharacteristic
96#2155C2×C12712yes—
97#1946C2×C12711yescharacteristic
98#1384C2×C12712yes—
99#1375C2×C12711yescharacteristic
100C127#1345911yescharacteristic, direct product factor, Sylow
101#533—21no—
102C2×M32C22×C12712yes—
103#501—24no—
104C2×#108C22×C12711yescharacteristic
105#427—21no—
106#427C22×C12712yes—
107#427C22×C12711yescharacteristic
108#424—21no—
109C2×#97C22×C12711yescharacteristic
110#365—24no—
111#339—21no—
112C2×M16—21no—
113C22×C8D4×C12711yescharacteristic
114C22×C8C23×C12711yescharacteristic
115C4⋊Q8—22no—
116#125—22no—
117C22⋊Q8—42no—
118C4×Q8—42no—
119#117—22no—
120#117—21no—
121C2×C42D4×C12711yescharacteristic
122M32—22no—
123M32—22no—
124C2×C16Q8×C12714yescomplemented
125#108—22no—
126#107—22no—
127#107—22no—
128#107—21no—
129#106—22no—
130#106D4×C12714yes—
131#106Q8×C12712yescomplemented
132C4⋊C8—42no—
133#97—22no—
134C2×Q8—42no—
135C22×C4—21no—
136C22×C4C2×D4×C12711yescharacteristic
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—41no—
142C2×C8SD16×C12712yes—
143C2×C8C2×D4×C12712yes—
144C2×C8C2×Q8×C12712yes—
145C2×C8C2×Q8×C12711yescharacteristic
146C2×C8#41×C12711yescharacteristic
147C4⋊C4—24no—
148C4⋊C4—22no—
149C4⋊C4—44no—
150C4⋊C4—42no—
151C22⋊C4—41no—
152C22⋊C4—42no—
153C42—21no—
154C42—41no—
155C42—42no—
156C42SD16×C12712yes—
157C16—24no—
158C23AGL(1,ℤ/8)×C12711yescharacteristic
159Q8—84no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—81no—
164C2×C4#120×C12711yescharacteristic
165C2×C4C22⋊Q8×C12711yescharacteristic
166C2×C4C4⋊Q8×C12711yescharacteristic
167C2×C4C2×SD16×C12711yescharacteristic
168C2×C4C2×SD16×C12711yescharacteristic
169C2×C4#137×C12711yescharacteristic
170C8—22no—
171C8—81no—
172C8C22⋊Q8×C12712yes—
173C8C4⋊Q8×C12712yes—
174C22—41no—
175C22#450×C12711yescharacteristic
176C22#476×C12711yescharacteristic
177C22#501×C12711yescharacteristic
178C4—42no—
179C4—84no—
180C4—82no—
181C4#395×C12711yescharacteristic
182C4#448×C12711yescharacteristic
183C4#475×C12711yescharacteristic
184C4#498×C12711yescharacteristic
185C2—21no—
186C2—21no—
187C2—21no—
188C2C127×#205811yescharacteristic
subgroupG/H
centerC4×C127#498
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2058
prime radicalC23×C127AGL(1,ℤ/8)
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
29. C2×C16×C127Q8semidirect
36. #106×C127Q8semidirect
90. #13459C127direct (N × H)
100. C127#13459direct (N × H)
124. C2×C16Q8×C127semidirect
131. #106Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31622
C127×#21552
C127×#19462
C127×#13842
C127×#13752
#13459127