Finite Group Databasebeta

← C127×#13074 #44576747

Subgroups — C127×#13074 #44576747

Order 32512.

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

normal subgroups only

This group has 490 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, complemented
2C127×#3058C211yesmaximal, characteristic
3C127×#2140C212yesmaximal, complemented
4C127×#1812C211yesmaximal, characteristic, complemented
5C127×#1384C212yesmaximal, complemented
6C22×D8×C127C2211yescharacteristic
7C2×#131×C127C2211yescharacteristic
8#535×C127—21no—
9#504×C127—24no—
10C2×M32×C127—22no—
11C2×M32×C127C2212yes—
12#469×C127C414yescomplemented
13#466×C127—22no—
14#427×C127C2212yes—
15#427×C127C2211yescharacteristic
16#418×C127—21no—
17#410×C127—21no—
18#357×C127—24no—
19H(3,ℤ/4)×C127—21no—
20C2×#41×C127D411yescharacteristic
21C22×D4×C127—21no—
22C2×D8×C127—22no—
23C2×D8×C127—21no—
24C2×D8×C127—22no—
25C2×D8×C127C2×C412yes—
26#131×C127—22no—
27#131×C127—22no—
28C2×M16×C127C2×C412yes—
29C2×M16×C127D411yescharacteristic
30C22×C8×C127D412yes—
31C22×C8×C127C2311yescharacteristic
32#127×C127—41no—
33#124×C127—41no—
34#121×C127—24no—
35#120×C127—42no—
36#117×C127—21no—
37#117×C127—22no—
38M32×C127—24no—
39M32×C127—22no—
40M32×C127—22no—
41C2×C16×C127—24no—
42C2×C16×C127D414yescomplemented
43#107×C127—21no—
44#107×C127—22no—
45#106×C127—22no—
46#106×C127C2×C412yes—
47#102×C127—24no—
48#99×C127—42no—
49C24×C127—41no—
50#41×C127—22no—
51#41×C127—22no—
52C2×Q8×C127SD1611yescharacteristic
53C2×D4×C127—22no—
54C2×D4×C127—44no—
55C2×D4×C127—42no—
56C2×D4×C127—41no—
57C2×D4×C127—42no—
58C2×D4×C127D812yes—
59C2×D4×C127SD1611yescharacteristic
60C22×C4×C127C22⋊C412yes—
61C22×C4×C127C2×D411yescharacteristic
62D8×C127—24no—
63D8×C127—41no—
64D8×C127—41no—
65M16×C127—22no—
66M16×C127—24no—
67C2×C8×C127—22no—
68C2×C8×C127—22no—
69C2×C8×C127C22⋊C412yes—
70C2×C8×C127C22×C411yescharacteristic
71C2×C8×C127C2×D412yes—
72C2×C8×C127C2×D411yescharacteristic
73C2×C8×C127#4112yes—
74C4⋊C4×C127—22no—
75C4⋊C4×C127—42no—
76C22⋊C4×C127—41no—
77C22⋊C4×C127—44no—
78C22⋊C4×C127—42no—
79C42×C127—41no—
80C42×C127—42no—
81C16×C127—24no—
82C23×C127—42no—
83C23×C127—82no—
84C23×C127—162no—
85C23×C127#10212yes—
86C23×C127C2×D811yescharacteristic
87Q8×C127—22no—
88D4×C127—24no—
89D4×C127—22no—
90D4×C127—42no—
91D4×C127—42no—
92D4×C127—82no—
93D4×C127—164no—
94C2×C4×C127—22no—
95C2×C4×C127—22no—
96C2×C4×C127—42no—
97C2×C4×C127—82no—
98C2×C4×C127#10212yes—
99C2×C4×C127C2×C22⋊C411yescharacteristic
100C2×C4×C127#12112yes—
101C2×C4×C127C2×SD1611yescharacteristic
102C2×C4×C127#13512yes—
103C8×C127—22no—
104C8×C127C4×D412yes—
105C8×C127#12011yescharacteristic
106C8×C127#12311yescharacteristic
107C22×C127—22no—
108C22×C127—41no—
109C22×C127—42no—
110C22×C127—84no—
111C22×C127—82no—
112C22×C127—164no—
113C22×C127C2×#10211yescharacteristic
114C22×C127#46612yes—
115C4×C127—22no—
116C4×C127—82no—
117C4×C127—162no—
118C4×C127#38611yescharacteristic
119C4×C127#41611yescharacteristic
120C4×C127#46512yes—
121#13074C12711yesmaximal, characteristic, direct product factor, Sylow
122C2×C127—21no—
123C2×C127—22no—
124C2×C127—42no—
125C2×C127—162no—
126C2×C127#189311yescharacteristic
127#3407C2×C12711yescharacteristic, complemented
128#3058C2×C12711yescharacteristic
129#2140C2×C12712yescomplemented
130#1812C2×C12711yescharacteristic, complemented
131#1384C2×C12712yescomplemented
132C127#1307411yescharacteristic, direct product factor, Sylow
133C22×D8C22×C12711yescharacteristic
134C2×#131C22×C12711yescharacteristic
135#535—21no—
136#504—24no—
137C2×M32—22no—
138C2×M32C22×C12712yes—
139#469C4×C12714yescomplemented
140#466—22no—
141#427C22×C12712yes—
142#427C22×C12711yescharacteristic
143#418—21no—
144#410—21no—
145#357—24no—
146H(3,ℤ/4)—21no—
147C2×#41D4×C12711yescharacteristic
148C22×D4—21no—
149C2×D8—22no—
150C2×D8—21no—
151C2×D8—22no—
152C2×D8C2×C4×C12712yes—
153#131—22no—
154#131—22no—
155C2×M16C2×C4×C12712yes—
156C2×M16D4×C12711yescharacteristic
157C22×C8D4×C12712yes—
158C22×C8C23×C12711yescharacteristic
159#127—41no—
160#124—41no—
161#121—24no—
162#120—42no—
163#117—21no—
164#117—22no—
165M32—24no—
166M32—22no—
167M32—22no—
168C2×C16—24no—
169C2×C16D4×C12714yescomplemented
170#107—21no—
171#107—22no—
172#106—22no—
173#106C2×C4×C12712yes—
174#102—24no—
175#99—42no—
176C24—41no—
177#41—22no—
178#41—22no—
179C2×Q8SD16×C12711yescharacteristic
180C2×D4—22no—
181C2×D4—44no—
182C2×D4—42no—
183C2×D4—41no—
184C2×D4—42no—
185C2×D4D8×C12712yes—
186C2×D4SD16×C12711yescharacteristic
187C22×C4C22⋊C4×C12712yes—
188C22×C4C2×D4×C12711yescharacteristic
189D8—24no—
190D8—41no—
191D8—41no—
192M16—22no—
193M16—24no—
194C2×C8—22no—
195C2×C8—22no—
196C2×C8C22⋊C4×C12712yes—
197C2×C8C22×C4×C12711yescharacteristic
198C2×C8C2×D4×C12712yes—
199C2×C8C2×D4×C12711yescharacteristic
200C2×C8#41×C12712yes—
201C4⋊C4—22no—
202C4⋊C4—42no—
203C22⋊C4—41no—
204C22⋊C4—44no—
205C22⋊C4—42no—
206C42—41no—
207C42—42no—
208C16—24no—
209C23—42no—
210C23—82no—
211C23—162no—
212C23#102×C12712yes—
213C23C2×D8×C12711yescharacteristic
214Q8—22no—
215D4—24no—
216D4—22no—
217D4—42no—
218D4—42no—
219D4—82no—
220D4—164no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4#102×C12712yes—
226C2×C4C2×C22⋊C4×C12711yescharacteristic
227C2×C4#121×C12712yes—
228C2×C4C2×SD16×C12711yescharacteristic
229C2×C4#135×C12712yes—
230C8—22no—
231C8C4×D4×C12712yes—
232C8#120×C12711yescharacteristic
233C8#123×C12711yescharacteristic
234C22—22no—
235C22—41no—
236C22—42no—
237C22—84no—
238C22—82no—
239C22—164no—
240C22C2×#102×C12711yescharacteristic
241C22#466×C12712yes—
242C4—22no—
243C4—82no—
244C4—162no—
245C4#386×C12711yescharacteristic
246C4#416×C12711yescharacteristic
247C4#465×C12712yes—
248C2—21no—
249C2—22no—
250C2—42no—
251C2—162no—
252C2C127×#189311yescharacteristic
subgroupG/H
center, socleC2×C127#1893
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3058C2
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
1. C127×#3407C2semidirect
3. C127×#2140C2semidirect
4. C127×#1812C2semidirect
5. C127×#1384C2semidirect
12. #469×C127C4semidirect
42. C2×C16×C127D4semidirect
121. #13074C127direct (N × H)
127. #3407C2×C127semidirect
129. #2140C2×C127semidirect
130. #1812C2×C127semidirect
131. #1384C2×C127semidirect
132. C127#13074direct (N × H)
139. #469C4×C127semidirect
169. C2×C16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34072
C127×#30582
C127×#21402
C127×#18122
C127×#13842
#13074127