Finite Group Databasebeta

← C127×#13702 #44577375

Subgroups — C127×#13702 #44577375

Order 32512.

184 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C2×SD64×C127C211yesmaximal, characteristic, complemented
2C127×#2258C211yesmaximal, characteristic, complemented
3C127×#2222C211yesmaximal, characteristic, complemented
4C127×#2221C211yesmaximal, characteristic
5C127×#1425C211yesmaximal, characteristic, complemented
6C127×#1420C211yesmaximal, characteristic, complemented
7C127×#1419C211yesmaximal, characteristic, complemented
8C2×Q32×C127C2211yescharacteristic
9C2×D16×C127C2211yescharacteristic
10#504×C127C2211yescharacteristic
11#473×C127—21no—
12#472×C127—21no—
13SD64×C127—21no—
14SD64×C127—21no—
15M64×C127—21no—
16M64×C127C2211yescharacteristic
17C2×C32×C127—21no—
18C2×C32×C127C2211yescharacteristic
19#368×C127C2211yescharacteristic
20#368×C127C2211yescharacteristic
21#362×C127—21no—
22#361×C127—21no—
23#137×C127—41no—
24AGL(1,ℤ/8)×C127—41no—
25C2×Q16×C127—21no—
26C2×D8×C127—21no—
27#131×C127D411yescharacteristic
28Q32×C127—21no—
29Q32×C127—21no—
30D16×C127—21no—
31D16×C127—21no—
32M32×C127—21no—
33M32×C127D411yescharacteristic
34C2×C16×C127—21no—
35C2×C16×C127C2311yescharacteristic
36#108×C127—21no—
37#108×C127—21no—
38#101×C127—41no—
39#100×C127—41no—
40C32×C127—21no—
41C32×C127D411yescharacteristic
42C32×C127D411yescharacteristic
43#41×C127D811yescharacteristic
44C2×Q8×C127—41no—
45C2×D4×C127—41no—
46Q16×C127—41no—
47Q16×C127—41no—
48Q16×C127—81no—
49SD16×C127—81no—
50SD16×C127—81no—
51D8×C127—41no—
52D8×C127—41no—
53D8×C127—81no—
54M16×C127—21no—
55M16×C127—41no—
56M16×C127—41no—
57M16×C127D811yescharacteristic
58C2×C8×C127—21no—
59C2×C8×C127C2×D411yescharacteristic
60C16×C127—21no—
61C16×C127C2×D411yescharacteristic
62C16×C127#4111yescharacteristic
63C23×C127—81no—
64Q8×C127—81no—
65Q8×C127—81no—
66Q8×C127D1611yescharacteristic
67D4×C127—21no—
68D4×C127—81no—
69D4×C127—81no—
70D4×C127D1611yescharacteristic
71C2×C4×C127—21no—
72C2×C4×C127—81no—
73C2×C4×C127C2×D811yescharacteristic
74C8×C127—21no—
75C8×C127—81no—
76C8×C127—81no—
77C8×C127#12111yescharacteristic
78C8×C127#13511yescharacteristic
79C22×C127—21no—
80C22×C127—161no—
81C22×C127—321no—
82C22×C127#50811yescharacteristic
83C4×C127—21no—
84C4×C127—161no—
85C4×C127#46611yescharacteristic
86C4×C127C2×D1611yescharacteristic
87#13702C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—21no—
89C2×C127—41no—
90C2×C127—321no—
91C2×C127#221511yescharacteristic
92C2×SD64C2×C12711yescharacteristic, complemented
93#2258C2×C12711yescharacteristic, complemented
94#2222C2×C12711yescharacteristic, complemented
95#2221C2×C12711yescharacteristic
96#1425C2×C12711yescharacteristic, complemented
97#1420C2×C12711yescharacteristic, complemented
98#1419C2×C12711yescharacteristic, complemented
99C127#1370211yescharacteristic, direct product factor, Sylow
100C2×Q32C22×C12711yescharacteristic
101C2×D16C22×C12711yescharacteristic
102#504C22×C12711yescharacteristic
103#473—21no—
104#472—21no—
105SD64—21no—
106SD64—21no—
107M64—21no—
108M64C22×C12711yescharacteristic
109C2×C32—21no—
110C2×C32C22×C12711yescharacteristic
111#368C22×C12711yescharacteristic
112#368C22×C12711yescharacteristic
113#362—21no—
114#361—21no—
115#137—41no—
116AGL(1,ℤ/8)—41no—
117C2×Q16—21no—
118C2×D8—21no—
119#131D4×C12711yescharacteristic
120Q32—21no—
121Q32—21no—
122D16—21no—
123D16—21no—
124M32—21no—
125M32D4×C12711yescharacteristic
126C2×C16—21no—
127C2×C16C23×C12711yescharacteristic
128#108—21no—
129#108—21no—
130#101—41no—
131#100—41no—
132C32—21no—
133C32D4×C12711yescharacteristic
134C32D4×C12711yescharacteristic
135#41D8×C12711yescharacteristic
136C2×Q8—41no—
137C2×D4—41no—
138Q16—41no—
139Q16—41no—
140Q16—81no—
141SD16—81no—
142SD16—81no—
143D8—41no—
144D8—41no—
145D8—81no—
146M16—21no—
147M16—41no—
148M16—41no—
149M16D8×C12711yescharacteristic
150C2×C8—21no—
151C2×C8C2×D4×C12711yescharacteristic
152C16—21no—
153C16C2×D4×C12711yescharacteristic
154C16#41×C12711yescharacteristic
155C23—81no—
156Q8—81no—
157Q8—81no—
158Q8D16×C12711yescharacteristic
159D4—21no—
160D4—81no—
161D4—81no—
162D4D16×C12711yescharacteristic
163C2×C4—21no—
164C2×C4—81no—
165C2×C4C2×D8×C12711yescharacteristic
166C8—21no—
167C8—81no—
168C8—81no—
169C8#121×C12711yescharacteristic
170C8#135×C12711yescharacteristic
171C22—21no—
172C22—161no—
173C22—321no—
174C22#508×C12711yescharacteristic
175C4—21no—
176C4—161no—
177C4#466×C12711yescharacteristic
178C4C2×D16×C12711yescharacteristic
179C2—21no—
180C2—41no—
181C2—321no—
182C2C127×#221511yescharacteristic
subgroupG/H
center, socleC2×C127#2215
commutator, Frattini, cosocleC2×C16C23×C127
prime radicalC127×#2221C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ #131×C127 ◁ #504×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×SD64×C127C2semidirect
2. C127×#2258C2semidirect
3. C127×#2222C2semidirect
5. C127×#1425C2semidirect
6. C127×#1420C2semidirect
7. C127×#1419C2semidirect
87. #13702C127direct (N × H)
92. C2×SD64C2×C127semidirect
93. #2258C2×C127semidirect
94. #2222C2×C127semidirect
96. #1425C2×C127semidirect
97. #1420C2×C127semidirect
98. #1419C2×C127semidirect
99. C127#13702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×SD64×C1272
C127×#22582
C127×#22222
C127×#22212
C127×#14252
C127×#14202
C127×#14192
#13702127