Finite Group Databasebeta

← C127×#13485 #44577158

Subgroups — C127×#13485 #44577158

Order 32512.

314 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2139C212yesmaximal
2C127×#1974C211yesmaximal, characteristic
3C127×#1846C211yesmaximal, characteristic, complemented
4C127×#1387C212yesmaximal, complemented
5C127×#1376C211yesmaximal, characteristic, complemented
6C2×#135×C127C2211yescharacteristic
7C2×M32×C127C2212yes—
8C2×#108×C127C2211yescharacteristic
9C2×#107×C127C2212yes—
10C2×#106×C127—21no—
11C2×#104×C127—21no—
12#408×C127—21no—
13C2×C4×C8×C127C2211yescharacteristic
14#382×C127—21no—
15#358×C127—22no—
16#357×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—
24C22×C8×C127D411yescharacteristic
25C22×C8×C127C2311yescharacteristic
26C2×C4⋊C4×C127—22no—
27C2×C42×C127D411yescharacteristic
28M32×C127—22no—
29M32×C127—22no—
30C2×C16×C127—22no—
31#108×C127—22no—
32#107×C127—22no—
33#107×C127—22no—
34#106×C127—42no—
35#104×C127—42no—
36C22⋊C8×C127—42no—
37C4×C8×C127—22no—
38#95×C127—42no—
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×C127—42no—
49C22×C4×C127C2×D411yescharacteristic
50Q16×C127—22no—
51SD16×C127—42no—
52D8×C127—22no—
53M16×C127—41no—
54M16×C127—41no—
55C2×C8×C127—21no—
56C2×C8×C127—21no—
57C2×C8×C127—41no—
58C2×C8×C127D812yes—
59C2×C8×C127C2×D411yescharacteristic
60C2×C8×C127#4112yes—
61C2×C8×C127#4112yes—
62C2×C8×C127#4111yescharacteristic
63C4⋊C4×C127—42no—
64C4⋊C4×C127—42no—
65C42×C127—21no—
66C42×C127SD1612yes—
67C16×C127—42no—
68C23×C127—41no—
69C23×C127AGL(1,ℤ/8)11yescharacteristic
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—42no—
78C2×C4×C127—41no—
79C2×C4×C127—81no—
80C2×C4×C127—81no—
81C2×C4×C127—84no—
82C2×C4×C127—82no—
83C2×C4×C127#12111yescharacteristic
84C2×C4×C127#12311yescharacteristic
85C2×C4×C127#12411yescharacteristic
86C2×C4×C127C2×D811yescharacteristic
87C2×C4×C127C2×SD1611yescharacteristic
88C2×C4×C127#13711yescharacteristic
89C8×C127—22no—
90C8×C127—81no—
91C8×C127#12312yes—
92C8×C127#12612yes—
93C22×C127—22no—
94C22×C127—81no—
95C22×C127—82no—
96C22×C127#45911yescharacteristic
97C22×C127#48111yescharacteristic
98C22×C127#48911yescharacteristic
99C4×C127—42no—
100C4×C127—81no—
101C4×C127—162no—
102C4×C127#39711yescharacteristic
103C4×C127#46111yescharacteristic
104C4×C127#48011yescharacteristic
105C4×C127#48611yescharacteristic
106#13485C12711yesmaximal, characteristic, direct product factor, Sylow
107C2×C127—21no—
108C2×C127—21no—
109C2×C127—161no—
110C2×C127#207111yescharacteristic
111C2×C127#221212yes—
112#2139C2×C12712yes—
113#1974C2×C12711yescharacteristic
114#1846C2×C12711yescharacteristic, complemented
115#1387C2×C12712yescomplemented
116#1376C2×C12711yescharacteristic, complemented
117C127#1348511yescharacteristic, direct product factor, Sylow
118C2×#135C22×C12711yescharacteristic
119C2×M32C22×C12712yes—
120C2×#108C22×C12711yescharacteristic
121C2×#107C22×C12712yes—
122C2×#106—21no—
123C2×#104—21no—
124#408—21no—
125C2×C4×C8C22×C12711yescharacteristic
126#382—21no—
127#358—22no—
128#357—22no—
129C2×#41—21no—
130#135—22no—
131#135—22no—
132C2×Q16D4×C12711yescharacteristic
133C2×SD16—21no—
134C2×D8D4×C12711yescharacteristic
135C2×M16—21no—
136C22×C8D4×C12711yescharacteristic
137C22×C8C23×C12711yescharacteristic
138C2×C4⋊C4—22no—
139C2×C42D4×C12711yescharacteristic
140M32—22no—
141M32—22no—
142C2×C16—22no—
143#108—22no—
144#107—22no—
145#107—22no—
146#106—42no—
147#104—42no—
148C22⋊C8—42no—
149C4×C8—22no—
150#95—42no—
151#41—41no—
152#41—41no—
153#41—41no—
154#41—41no—
155C2×Q8—21no—
156C2×D4—21no—
157C2×D4—41no—
158C22×C4—21no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4C2×D4×C12711yescharacteristic
162Q16—22no—
163SD16—42no—
164D8—22no—
165M16—41no—
166M16—41no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—41no—
170C2×C8D8×C12712yes—
171C2×C8C2×D4×C12711yescharacteristic
172C2×C8#41×C12712yes—
173C2×C8#41×C12712yes—
174C2×C8#41×C12711yescharacteristic
175C4⋊C4—42no—
176C4⋊C4—42no—
177C42—21no—
178C42SD16×C12712yes—
179C16—42no—
180C23—41no—
181C23AGL(1,ℤ/8)×C12711yescharacteristic
182Q8—41no—
183Q8—41no—
184D4—41no—
185D4—41no—
186D4—81no—
187D4—81no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—84no—
194C2×C4—82no—
195C2×C4#121×C12711yescharacteristic
196C2×C4#123×C12711yescharacteristic
197C2×C4#124×C12711yescharacteristic
198C2×C4C2×D8×C12711yescharacteristic
199C2×C4C2×SD16×C12711yescharacteristic
200C2×C4#137×C12711yescharacteristic
201C8—22no—
202C8—81no—
203C8#123×C12712yes—
204C8#126×C12712yes—
205C22—22no—
206C22—81no—
207C22—82no—
208C22#459×C12711yescharacteristic
209C22#481×C12711yescharacteristic
210C22#489×C12711yescharacteristic
211C4—42no—
212C4—81no—
213C4—162no—
214C4#397×C12711yescharacteristic
215C4#461×C12711yescharacteristic
216C4#480×C12711yescharacteristic
217C4#486×C12711yescharacteristic
218C2—21no—
219C2—21no—
220C2—161no—
221C2C127×#207111yescharacteristic
222C2C127×#221212yes—
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
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
3. C127×#1846C2semidirect
4. C127×#1387C2semidirect
5. C127×#1376C2semidirect
106. #13485C127direct (N × H)
114. #1846C2×C127semidirect
115. #1387C2×C127semidirect
116. #1376C2×C127semidirect
117. C127#13485direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21392
C127×#19742
C127×#18462
C127×#13872
C127×#13762
#13485127