Finite Group Databasebeta

← C127×#13075 #44576748

Subgroups — C127×#13075 #44576748

Order 32512.

458 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 146 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×#3407C211yesmaximal, characteristic
2C127×#3059C211yesmaximal, characteristic
3C127×#2141C212yesmaximal, complemented
4C127×#1812C211yesmaximal, characteristic
5C127×#1384C212yesmaximal, complemented
6C22×Q16×C127C2211yescharacteristic
7C2×#131×C127C2211yescharacteristic
8#536×C127—21no—
9#504×C127—24no—
10C2×M32×C127—22no—
11C2×M32×C127C2212yes—
12#470×C127C414yescomplemented
13#467×C127—22no—
14#427×C127C2212yes—
15#427×C127C2211yescharacteristic
16#419×C127—21no—
17#410×C127—21no—
18#358×C127—24no—
19H(3,ℤ/4)×C127—21no—
20C2×#41×C127D411yescharacteristic
21C22×Q8×C127—21no—
22C2×Q16×C127—22no—
23C2×Q16×C127—21no—
24C2×Q16×C127—22no—
25C2×Q16×C127C2×C412yes—
26#131×C127—22no—
27#131×C127—22no—
28C2×M16×C127C2×C412yes—
29C2×M16×C127D411yescharacteristic
30C22×C8×C127D412yes—
31C22×C8×C127C2311yescharacteristic
32C4⋊Q8×C127—41no—
33#124×C127—41no—
34#123×C127—42no—
35C22⋊Q8×C127—24no—
36#117×C127—21no—
37#117×C127—22no—
38M32×C127—24no—
39M32×C127—22no—
40M32×C127—22no—
41C2×C16×C127—24no—
42C2×C16×C127D414yes—
43#107×C127—21no—
44#107×C127—22no—
45#106×C127—22no—
46#106×C127C2×C412yes—
47#103×C127—24no—
48#99×C127—42no—
49#41×C127—22no—
50#41×C127—22no—
51C2×Q8×C127—22no—
52C2×Q8×C127—41no—
53C2×Q8×C127—42no—
54C2×Q8×C127—42no—
55C2×Q8×C127SD1611yescharacteristic
56C2×D4×C127D812yes—
57C2×D4×C127SD1611yescharacteristic
58C22×C4×C127—41no—
59C22×C4×C127C22⋊C412yes—
60C22×C4×C127C2×D411yescharacteristic
61Q16×C127—24no—
62Q16×C127—41no—
63Q16×C127—41no—
64M16×C127—22no—
65M16×C127—24no—
66C2×C8×C127—22no—
67C2×C8×C127—22no—
68C2×C8×C127C22⋊C412yes—
69C2×C8×C127C22×C411yescharacteristic
70C2×C8×C127C2×D412yes—
71C2×C8×C127C2×D411yescharacteristic
72C2×C8×C127#4112yes—
73C4⋊C4×C127—22no—
74C4⋊C4×C127—44no—
75C4⋊C4×C127—42no—
76C22⋊C4×C127—44no—
77C22⋊C4×C127—41no—
78C22⋊C4×C127—42no—
79C42×C127—41no—
80C42×C127—42no—
81C16×C127—24no—
82C23×C127#10212yes—
83C23×C127C2×D811yescharacteristic
84Q8×C127—22no—
85Q8×C127—42no—
86Q8×C127—42no—
87Q8×C127—82no—
88D4×C127—24no—
89D4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—42no—
93C2×C4×C127—42no—
94C2×C4×C127—82no—
95C2×C4×C127—82no—
96C2×C4×C127#10212yes—
97C2×C4×C127C2×C22⋊C411yescharacteristic
98C2×C4×C127#12112yes—
99C2×C4×C127C2×SD1611yescharacteristic
100C2×C4×C127#13512yes—
101C8×C127—22no—
102C8×C127C4×D412yes—
103C8×C127#12011yescharacteristic
104C8×C127#12311yescharacteristic
105C22×C127—22no—
106C22×C127—41no—
107C22×C127—42no—
108C22×C127C2×#10211yescharacteristic
109C22×C127#46612yes—
110C4×C127—22no—
111C4×C127—82no—
112C4×C127—82no—
113C4×C127—162no—
114C4×C127#38611yescharacteristic
115C4×C127#41611yescharacteristic
116C4×C127#46512yes—
117#13075C12711yesmaximal, characteristic, direct product factor, Sylow
118C2×C127—21no—
119C2×C127—22no—
120C2×C127—42no—
121C2×C127#189311yescharacteristic
122#3407C2×C12711yescharacteristic
123#3059C2×C12711yescharacteristic
124#2141C2×C12712yescomplemented
125#1812C2×C12711yescharacteristic
126#1384C2×C12712yescomplemented
127C127#1307511yescharacteristic, direct product factor, Sylow
128C22×Q16C22×C12711yescharacteristic
129C2×#131C22×C12711yescharacteristic
130#536—21no—
131#504—24no—
132C2×M32—22no—
133C2×M32C22×C12712yes—
134#470C4×C12714yescomplemented
135#467—22no—
136#427C22×C12712yes—
137#427C22×C12711yescharacteristic
138#419—21no—
139#410—21no—
140#358—24no—
141H(3,ℤ/4)—21no—
142C2×#41D4×C12711yescharacteristic
143C22×Q8—21no—
144C2×Q16—22no—
145C2×Q16—21no—
146C2×Q16—22no—
147C2×Q16C2×C4×C12712yes—
148#131—22no—
149#131—22no—
150C2×M16C2×C4×C12712yes—
151C2×M16D4×C12711yescharacteristic
152C22×C8D4×C12712yes—
153C22×C8C23×C12711yescharacteristic
154C4⋊Q8—41no—
155#124—41no—
156#123—42no—
157C22⋊Q8—24no—
158#117—21no—
159#117—22no—
160M32—24no—
161M32—22no—
162M32—22no—
163C2×C16—24no—
164C2×C16D4×C12714yes—
165#107—21no—
166#107—22no—
167#106—22no—
168#106C2×C4×C12712yes—
169#103—24no—
170#99—42no—
171#41—22no—
172#41—22no—
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8SD16×C12711yescharacteristic
178C2×D4D8×C12712yes—
179C2×D4SD16×C12711yescharacteristic
180C22×C4—41no—
181C22×C4C22⋊C4×C12712yes—
182C22×C4C2×D4×C12711yescharacteristic
183Q16—24no—
184Q16—41no—
185Q16—41no—
186M16—22no—
187M16—24no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8C22⋊C4×C12712yes—
191C2×C8C22×C4×C12711yescharacteristic
192C2×C8C2×D4×C12712yes—
193C2×C8C2×D4×C12711yescharacteristic
194C2×C8#41×C12712yes—
195C4⋊C4—22no—
196C4⋊C4—44no—
197C4⋊C4—42no—
198C22⋊C4—44no—
199C22⋊C4—41no—
200C22⋊C4—42no—
201C42—41no—
202C42—42no—
203C16—24no—
204C23#102×C12712yes—
205C23C2×D8×C12711yescharacteristic
206Q8—22no—
207Q8—42no—
208Q8—42no—
209Q8—82no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—82no—
217C2×C4—82no—
218C2×C4#102×C12712yes—
219C2×C4C2×C22⋊C4×C12711yescharacteristic
220C2×C4#121×C12712yes—
221C2×C4C2×SD16×C12711yescharacteristic
222C2×C4#135×C12712yes—
223C8—22no—
224C8C4×D4×C12712yes—
225C8#120×C12711yescharacteristic
226C8#123×C12711yescharacteristic
227C22—22no—
228C22—41no—
229C22—42no—
230C22C2×#102×C12711yescharacteristic
231C22#466×C12712yes—
232C4—22no—
233C4—82no—
234C4—82no—
235C4—162no—
236C4#386×C12711yescharacteristic
237C4#416×C12711yescharacteristic
238C4#465×C12712yes—
239C2—21no—
240C2—22no—
241C2—42no—
242C2C127×#189311yescharacteristic
subgroupG/H
center, socleC2×C127#1893
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#2141C2semidirect
5. C127×#1384C2semidirect
12. #470×C127C4semidirect
117. #13075C127direct (N × H)
124. #2141C2×C127semidirect
126. #1384C2×C127semidirect
127. C127#13075direct (N × H)
134. #470C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34072
C127×#30592
C127×#21412
C127×#18122
C127×#13842
#13075127