Finite Group Databasebeta

← C127×#13508 #44577181

Subgroups — C127×#13508 #44577181

Order 32512.

284 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2159C212yesmaximal
2C127×#1945C211yesmaximal, characteristic
3C127×#1845C211yesmaximal, characteristic
4C127×#1387C212yesmaximal
5C127×#1376C211yesmaximal, characteristic
6C2×M32×C127C2212yes—
7C2×#108×C127C2211yescharacteristic
8#427×C127C2211yescharacteristic
9C2×#107×C127—21no—
10C2×#107×C127C2212yes—
11#424×C127—21no—
12C2×C4×C8×C127C2211yescharacteristic
13#384×C127—21no—
14#367×C127—22no—
15#366×C127—22no—
16#339×C127—21no—
17C2×M16×C127—21no—
18C22×C8×C127D411yescharacteristic
19C22×C8×C127C2311yescharacteristic
20#117×C127—21no—
21C2×C4⋊C4×C127—22no—
22C2×C4⋊C4×C127—42no—
23C2×C42×C127D411yescharacteristic
24M32×C127—22no—
25M32×C127Q814yes—
26C2×C16×C127—22no—
27#108×C127—22no—
28#107×C127—22no—
29#107×C127—22no—
30#107×C127—42no—
31#107×C127D411yescharacteristic
32#107×C127D411yescharacteristic
33#106×C127—21no—
34C4⋊C8×C127—42no—
35C4×C8×C127—22no—
36C22×C4×C127—21no—
37C22×C4×C127—42no—
38C22×C4×C127C2×D411yescharacteristic
39M16×C127—41no—
40M16×C127—41no—
41C2×C8×C127—21no—
42C2×C8×C127—21no—
43C2×C8×C127—41no—
44C2×C8×C127D812yes—
45C2×C8×C127C2×D411yescharacteristic
46C2×C8×C127C2×Q812yes—
47C2×C8×C127#4112yes—
48C2×C8×C127#4111yescharacteristic
49C4⋊C4×C127—21no—
50C4⋊C4×C127—21no—
51C4⋊C4×C127—42no—
52C4⋊C4×C127—42no—
53C4⋊C4×C127—84no—
54C22⋊C4×C127—41no—
55C42×C127—21no—
56C42×C127—41no—
57C42×C127Q1612yes—
58C16×C127—24no—
59C23×C127AGL(1,ℤ/8)11yescharacteristic
60C2×C4×C127—22no—
61C2×C4×C127—22no—
62C2×C4×C127—22no—
63C2×C4×C127—41no—
64C2×C4×C127—41no—
65C2×C4×C127—84no—
66C2×C4×C127—82no—
67C2×C4×C127#12111yescharacteristic
68C2×C4×C127#12311yescharacteristic
69C2×C4×C127C4⋊Q811yescharacteristic
70C2×C4×C127C2×D811yescharacteristic
71C2×C4×C127C2×Q1611yescharacteristic
72C2×C4×C127#13711yescharacteristic
73C8×C127—22no—
74C8×C127—81no—
75C8×C127C22⋊Q812yes—
76C8×C127#12512yes—
77C22×C127—21no—
78C22×C127—21no—
79C22×C127#45911yescharacteristic
80C22×C127#48411yescharacteristic
81C22×C127#50111yescharacteristic
82C4×C127—24no—
83C4×C127—81no—
84C4×C127—81no—
85C4×C127—162no—
86C4×C127#39811yescharacteristic
87C4×C127#46211yescharacteristic
88C4×C127#48011yescharacteristic
89C4×C127#50011yescharacteristic
90#13508C12711yesmaximal, characteristic, direct product factor, Sylow
91C2×C127—21no—
92C2×C127—21no—
93C2×C127#208311yescharacteristic
94C2×C127#221311yescharacteristic
95C2×C127#221411yescharacteristic
96#2159C2×C12712yes—
97#1945C2×C12711yescharacteristic
98#1845C2×C12711yescharacteristic
99#1387C2×C12712yes—
100#1376C2×C12711yescharacteristic
101C127#1350811yescharacteristic, direct product factor, Sylow
102C2×M32C22×C12712yes—
103C2×#108C22×C12711yescharacteristic
104#427C22×C12711yescharacteristic
105C2×#107—21no—
106C2×#107C22×C12712yes—
107#424—21no—
108C2×C4×C8C22×C12711yescharacteristic
109#384—21no—
110#367—22no—
111#366—22no—
112#339—21no—
113C2×M16—21no—
114C22×C8D4×C12711yescharacteristic
115C22×C8C23×C12711yescharacteristic
116#117—21no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—42no—
119C2×C42D4×C12711yescharacteristic
120M32—22no—
121M32Q8×C12714yes—
122C2×C16—22no—
123#108—22no—
124#107—22no—
125#107—22no—
126#107—42no—
127#107D4×C12711yescharacteristic
128#107D4×C12711yescharacteristic
129#106—21no—
130C4⋊C8—42no—
131C4×C8—22no—
132C22×C4—21no—
133C22×C4—42no—
134C22×C4C2×D4×C12711yescharacteristic
135M16—41no—
136M16—41no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8D8×C12712yes—
141C2×C8C2×D4×C12711yescharacteristic
142C2×C8C2×Q8×C12712yes—
143C2×C8#41×C12712yes—
144C2×C8#41×C12711yescharacteristic
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—84no—
150C22⋊C4—41no—
151C42—21no—
152C42—41no—
153C42Q16×C12712yes—
154C16—24no—
155C23AGL(1,ℤ/8)×C12711yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—84no—
162C2×C4—82no—
163C2×C4#121×C12711yescharacteristic
164C2×C4#123×C12711yescharacteristic
165C2×C4C4⋊Q8×C12711yescharacteristic
166C2×C4C2×D8×C12711yescharacteristic
167C2×C4C2×Q16×C12711yescharacteristic
168C2×C4#137×C12711yescharacteristic
169C8—22no—
170C8—81no—
171C8C22⋊Q8×C12712yes—
172C8#125×C12712yes—
173C22—21no—
174C22—21no—
175C22#459×C12711yescharacteristic
176C22#484×C12711yescharacteristic
177C22#501×C12711yescharacteristic
178C4—24no—
179C4—81no—
180C4—81no—
181C4—162no—
182C4#398×C12711yescharacteristic
183C4#462×C12711yescharacteristic
184C4#480×C12711yescharacteristic
185C4#500×C12711yescharacteristic
186C2—21no—
187C2—21no—
188C2C127×#208311yescharacteristic
189C2C127×#221311yescharacteristic
190C2C127×#221411yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC23×C127AGL(1,ℤ/8)
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
90. #13508C127direct (N × H)
101. C127#13508direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21592
C127×#19452
C127×#18452
C127×#13872
C127×#13762
#13508127