Finite Group Databasebeta

← C127×#13486 #44577159

Subgroups — C127×#13486 #44577159

Order 32512.

296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2148C212yesmaximal
2C127×#1975C211yesmaximal, characteristic
3C127×#1849C211yesmaximal, characteristic, complemented
4C127×#1388C212yesmaximal, complemented
5C127×#1375C211yesmaximal, characteristic, complemented
6C2×#135×C127C2211yescharacteristic
7C2×M32×C127C2212yes—
8C2×#108×C127—21no—
9C2×#108×C127C2212yes—
10C2×#108×C127C2211yescharacteristic
11#423×C127—21no—
12C2×#104×C127—21no—
13#408×C127—21no—
14C2×#97×C127C2211yescharacteristic
15#362×C127—22no—
16#361×C127—22no—
17C2×#41×C127—21no—
18#135×C127—22no—
19#135×C127—22no—
20C2×Q16×C127D411yescharacteristic
21C2×SD16×C127—21no—
22C2×D8×C127D411yescharacteristic
23C2×M16×C127—21no—
24C2×M16×C127—22no—
25C22×C8×C127D411yescharacteristic
26C22×C8×C127C2311yescharacteristic
27C2×C42×C127D411yescharacteristic
28M32×C127—22no—
29M32×C127—22no—
30C2×C16×C127—22no—
31#108×C127—22no—
32#108×C127—22no—
33#108×C127—22no—
34#108×C127—42no—
35C4⋊C8×C127—42no—
36#104×C127—42no—
37C22⋊C8×C127—42no—
38#97×C127—22no—
39#41×C127—41no—
40#41×C127—41no—
41#41×C127—41no—
42#41×C127—41no—
43C2×Q8×C127—21no—
44C2×D4×C127—21no—
45C2×D4×C127—41no—
46C22×C4×C127—21no—
47C22×C4×C127—41no—
48C22×C4×C127C2×D411yescharacteristic
49Q16×C127—22no—
50SD16×C127—42no—
51D8×C127—22no—
52M16×C127—42no—
53M16×C127—41no—
54M16×C127—41no—
55M16×C127—42no—
56C2×C8×C127—21no—
57C2×C8×C127—21no—
58C2×C8×C127—42no—
59C2×C8×C127—41no—
60C2×C8×C127SD1612yes—
61C2×C8×C127C2×D411yescharacteristic
62C2×C8×C127#4112yes—
63C2×C8×C127#4112yes—
64C2×C8×C127#4111yescharacteristic
65C42×C127—21no—
66C42×C127D812yes—
67C16×C127—42no—
68C23×C127—41no—
69C23×C127#13711yescharacteristic
70Q8×C127—41no—
71Q8×C127—41no—
72D4×C127—41no—
73D4×C127—41no—
74D4×C127—81no—
75D4×C127—81no—
76C2×C4×C127—22no—
77C2×C4×C127—41no—
78C2×C4×C127—81no—
79C2×C4×C127—81no—
80C2×C4×C127—81no—
81C2×C4×C127#12111yescharacteristic
82C2×C4×C127#12311yescharacteristic
83C2×C4×C127#12411yescharacteristic
84C2×C4×C127C2×D811yescharacteristic
85C2×C4×C127C2×SD1611yescharacteristic
86C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
87C8×C127—22no—
88C8×C127—82no—
89C8×C127—81no—
90C8×C127#12312yes—
91C8×C127#12612yes—
92C22×C127—41no—
93C22×C127—82no—
94C22×C127—81no—
95C22×C127#46111yescharacteristic
96C22×C127#48011yescharacteristic
97C22×C127#48911yescharacteristic
98C4×C127—42no—
99C4×C127—81no—
100C4×C127#39711yescharacteristic
101C4×C127#45911yescharacteristic
102C4×C127#48111yescharacteristic
103C4×C127#48611yescharacteristic
104#13486C12711yesmaximal, characteristic, direct product factor, Sylow
105C2×C127—21no—
106C2×C127—21no—
107C2×C127—21no—
108C2×C127—161no—
109C2×C127#207111yescharacteristic
110#2148C2×C12712yes—
111#1975C2×C12711yescharacteristic
112#1849C2×C12711yescharacteristic, complemented
113#1388C2×C12712yescomplemented
114#1375C2×C12711yescharacteristic, complemented
115C127#1348611yescharacteristic, direct product factor, Sylow
116C2×#135C22×C12711yescharacteristic
117C2×M32C22×C12712yes—
118C2×#108—21no—
119C2×#108C22×C12712yes—
120C2×#108C22×C12711yescharacteristic
121#423—21no—
122C2×#104—21no—
123#408—21no—
124C2×#97C22×C12711yescharacteristic
125#362—22no—
126#361—22no—
127C2×#41—21no—
128#135—22no—
129#135—22no—
130C2×Q16D4×C12711yescharacteristic
131C2×SD16—21no—
132C2×D8D4×C12711yescharacteristic
133C2×M16—21no—
134C2×M16—22no—
135C22×C8D4×C12711yescharacteristic
136C22×C8C23×C12711yescharacteristic
137C2×C42D4×C12711yescharacteristic
138M32—22no—
139M32—22no—
140C2×C16—22no—
141#108—22no—
142#108—22no—
143#108—22no—
144#108—42no—
145C4⋊C8—42no—
146#104—42no—
147C22⋊C8—42no—
148#97—22no—
149#41—41no—
150#41—41no—
151#41—41no—
152#41—41no—
153C2×Q8—21no—
154C2×D4—21no—
155C2×D4—41no—
156C22×C4—21no—
157C22×C4—41no—
158C22×C4C2×D4×C12711yescharacteristic
159Q16—22no—
160SD16—42no—
161D8—22no—
162M16—42no—
163M16—41no—
164M16—41no—
165M16—42no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—42no—
169C2×C8—41no—
170C2×C8SD16×C12712yes—
171C2×C8C2×D4×C12711yescharacteristic
172C2×C8#41×C12712yes—
173C2×C8#41×C12712yes—
174C2×C8#41×C12711yescharacteristic
175C42—21no—
176C42D8×C12712yes—
177C16—42no—
178C23—41no—
179C23#137×C12711yescharacteristic
180Q8—41no—
181Q8—41no—
182D4—41no—
183D4—41no—
184D4—81no—
185D4—81no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4#121×C12711yescharacteristic
192C2×C4#123×C12711yescharacteristic
193C2×C4#124×C12711yescharacteristic
194C2×C4C2×D8×C12711yescharacteristic
195C2×C4C2×SD16×C12711yescharacteristic
196C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
197C8—22no—
198C8—82no—
199C8—81no—
200C8#123×C12712yes—
201C8#126×C12712yes—
202C22—41no—
203C22—82no—
204C22—81no—
205C22#461×C12711yescharacteristic
206C22#480×C12711yescharacteristic
207C22#489×C12711yescharacteristic
208C4—42no—
209C4—81no—
210C4#397×C12711yescharacteristic
211C4#459×C12711yescharacteristic
212C4#481×C12711yescharacteristic
213C4#486×C12711yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—161no—
218C2C127×#207111yescharacteristic
subgroupG/H
centerC4×C127#486
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2071
prime radicalC2×#135×C127C22
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
3. C127×#1849C2semidirect
4. C127×#1388C2semidirect
5. C127×#1375C2semidirect
104. #13486C127direct (N × H)
112. #1849C2×C127semidirect
113. #1388C2×C127semidirect
114. #1375C2×C127semidirect
115. C127#13486direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21482
C127×#19752
C127×#18492
C127×#13882
C127×#13752
#13486127