Finite Group Databasebeta

← C127×#13482 #44577155

Subgroups — C127×#13482 #44577155

Order 32512.

362 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 122 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×#357×C127C212yesmaximal
2C127×#1970C211yesmaximal, characteristic
3C127×#1846C211yesmaximal, characteristic, complemented
4C127×#1380C212yesmaximal, complemented
5C127×#1374C211yesmaximal, characteristic, complemented
6C22×D8×C127C2211yescharacteristic
7C22×C16×C127C2212yes—
8C2×#107×C127C2212yes—
9C2×#107×C127C2211yescharacteristic
10C2×#106×C127—21no—
11C2×#102×C127—21no—
12C2×C4×C8×C127C2211yescharacteristic
13#390×C127—21no—
14#382×C127—21no—
15#357×C127—24no—
16C22×D4×C127—21no—
17C2×D8×C127—22no—
18C2×D8×C127—22no—
19C2×D8×C127—21no—
20C2×D8×C127D412yes—
21C22×C8×C127D411yescharacteristic
22C22×C8×C127C2311yescharacteristic
23C2×C4⋊C4×C127—22no—
24C2×C4⋊C4×C127—21no—
25C2×C22⋊C4×C127—42no—
26C2×C42×C127D411yescharacteristic
27C2×C16×C127—22no—
28C2×C16×C127—22no—
29C2×C16×C127—22no—
30#107×C127—22no—
31#107×C127—22no—
32#107×C127—22no—
33#106×C127—42no—
34#102×C127—42no—
35C4×C8×C127—22no—
36#95×C127—42no—
37C24×C127—41no—
38C2×D4×C127—22no—
39C2×D4×C127—41no—
40C2×D4×C127—41no—
41C2×D4×C127—41no—
42C2×D4×C127—41no—
43C2×D4×C127—41no—
44C22×C4×C127—42no—
45C22×C4×C127—41no—
46C22×C4×C127D812yes—
47C22×C4×C127C2×D411yescharacteristic
48D8×C127—24no—
49D8×C127—42no—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×C8×C127SD1612yes—
53C2×C8×C127C2×D411yescharacteristic
54C2×C8×C127#4112yes—
55C2×C8×C127#4112yes—
56C2×C8×C127#4111yescharacteristic
57C4⋊C4×C127—42no—
58C4⋊C4×C127—41no—
59C4⋊C4×C127—41no—
60C4⋊C4×C127—42no—
61C22⋊C4×C127—84no—
62C42×C127—21no—
63C42×C127—21no—
64C16×C127—42no—
65C23×C127—42no—
66C23×C127—81no—
67C23×C127—81no—
68C23×C127—82no—
69C23×C127—82no—
70C23×C127C2×D811yescharacteristic
71D4×C127—42no—
72D4×C127—42no—
73D4×C127—81no—
74D4×C127—81no—
75C2×C4×C127—22no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—82no—
79C2×C4×C127—81no—
80C2×C4×C127—82no—
81C2×C4×C127—82no—
82C2×C4×C127—82no—
83C2×C4×C127#12111yescharacteristic
84C2×C4×C127#12311yescharacteristic
85C2×C4×C127#12411yescharacteristic
86C2×C4×C127C2×SD1611yescharacteristic
87C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
88C2×C4×C127#13711yescharacteristic
89C8×C127—22no—
90C8×C127#12312yes—
91C8×C127#12612yes—
92C22×C127—82no—
93C22×C127—84no—
94C22×C127—162no—
95C22×C127—161no—
96C22×C127—161no—
97C22×C127#45911yescharacteristic
98C22×C127#48011yescharacteristic
99C22×C127#48611yescharacteristic
100C22×C127#50812yes—
101C22×C127#50912yes—
102C4×C127—42no—
103C4×C127—162no—
104C4×C127—161no—
105C4×C127#39711yescharacteristic
106C4×C127#46111yescharacteristic
107C4×C127#48111yescharacteristic
108C4×C127#48911yescharacteristic
109#13482C12711yesmaximal, characteristic, direct product factor, Sylow
110C2×C127—162no—
111C2×C127#207111yescharacteristic
112C2×C127#221012yes—
113C2×C127#223412yes—
114C2×C127#224211yescharacteristic
115C2×C127#224411yescharacteristic
116C2×#357C2×C12712yes—
117#1970C2×C12711yescharacteristic
118#1846C2×C12711yescharacteristic, complemented
119#1380C2×C12712yescomplemented
120#1374C2×C12711yescharacteristic, complemented
121C127#1348211yescharacteristic, direct product factor, Sylow
122C22×D8C22×C12711yescharacteristic
123C22×C16C22×C12712yes—
124C2×#107C22×C12712yes—
125C2×#107C22×C12711yescharacteristic
126C2×#106—21no—
127C2×#102—21no—
128C2×C4×C8C22×C12711yescharacteristic
129#390—21no—
130#382—21no—
131#357—24no—
132C22×D4—21no—
133C2×D8—22no—
134C2×D8—22no—
135C2×D8—21no—
136C2×D8D4×C12712yes—
137C22×C8D4×C12711yescharacteristic
138C22×C8C23×C12711yescharacteristic
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C22⋊C4—42no—
142C2×C42D4×C12711yescharacteristic
143C2×C16—22no—
144C2×C16—22no—
145C2×C16—22no—
146#107—22no—
147#107—22no—
148#107—22no—
149#106—42no—
150#102—42no—
151C4×C8—22no—
152#95—42no—
153C24—41no—
154C2×D4—22no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C22×C4—42no—
161C22×C4—41no—
162C22×C4D8×C12712yes—
163C22×C4C2×D4×C12711yescharacteristic
164D8—24no—
165D8—42no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8SD16×C12712yes—
169C2×C8C2×D4×C12711yescharacteristic
170C2×C8#41×C12712yes—
171C2×C8#41×C12712yes—
172C2×C8#41×C12711yescharacteristic
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C22⋊C4—84no—
178C42—21no—
179C42—21no—
180C16—42no—
181C23—42no—
182C23—82no—
183C23—82no—
184C23—81no—
185C23—81no—
186C23C2×D8×C12711yescharacteristic
187D4—42no—
188D4—42no—
189D4—81no—
190D4—81no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—82no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—82no—
198C2×C4—81no—
199C2×C4#121×C12711yescharacteristic
200C2×C4#123×C12711yescharacteristic
201C2×C4#124×C12711yescharacteristic
202C2×C4C2×SD16×C12711yescharacteristic
203C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
204C2×C4#137×C12711yescharacteristic
205C8—22no—
206C8#123×C12712yes—
207C8#126×C12712yes—
208C22—82no—
209C22—84no—
210C22—162no—
211C22—161no—
212C22—161no—
213C22#459×C12711yescharacteristic
214C22#480×C12711yescharacteristic
215C22#486×C12711yescharacteristic
216C22#508×C12712yes—
217C22#509×C12712yes—
218C4—42no—
219C4—162no—
220C4—161no—
221C4#397×C12711yescharacteristic
222C4#461×C12711yescharacteristic
223C4#481×C12711yescharacteristic
224C4#489×C12711yescharacteristic
225C2—162no—
226C2C127×#207111yescharacteristic
227C2C127×#221012yes—
228C2C127×#223412yes—
229C2C127×#224211yescharacteristic
230C2C127×#224411yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×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×#1380C2semidirect
5. C127×#1374C2semidirect
109. #13482C127direct (N × H)
118. #1846C2×C127semidirect
119. #1380C2×C127semidirect
120. #1374C2×C127semidirect
121. C127#13482direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#357×C1272
C127×#19702
C127×#18462
C127×#13802
C127×#13742
#13482127