Finite Group Databasebeta

← C127×#13079 #44576752

Subgroups — C127×#13079 #44576752

Order 32512.

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

normal subgroups only

This group has 486 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
3C2×#361×C127C212yesmaximal, complemented
4C127×#1813C211yesmaximal, characteristic, complemented
5C127×#1389C212yesmaximal, complemented
6C22×D8×C127C2211yescharacteristic
7C2×#131×C127C2211yescharacteristic
8#535×C127—21no—
9#504×C127—24no—
10C2×M32×C127—22no—
11C2×M32×C127C2212yes—
12#469×C127C414yes—
13#466×C127—22no—
14C2×#108×C127C2212yes—
15#427×C127C2211yescharacteristic
16#418×C127—21no—
17#413×C127—21no—
18#361×C127—24no—
19#338×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×C127—22no—
29C2×M16×C127C2×C412yes—
30C2×M16×C127D411yescharacteristic
31C22×C8×C127D412yes—
32C22×C8×C127C2311yescharacteristic
33#127×C127—41no—
34#124×C127—41no—
35#121×C127—24no—
36#120×C127—42no—
37#117×C127—21no—
38M32×C127—24no—
39M32×C127—22no—
40M32×C127D414yescomplemented
41C2×C16×C127—24no—
42C2×C16×C127—22no—
43#108×C127—22no—
44#108×C127—22no—
45#107×C127—21no—
46#106×C127C2×C412yes—
47#102×C127—24no—
48#101×C127—41no—
49#100×C127—41no—
50C24×C127—41no—
51#41×C127—22no—
52#41×C127—22no—
53C2×Q8×C127D811yescharacteristic
54C2×D4×C127—22no—
55C2×D4×C127—44no—
56C2×D4×C127—42no—
57C2×D4×C127—41no—
58C2×D4×C127—42no—
59C2×D4×C127D811yescharacteristic
60C2×D4×C127SD1612yes—
61C22×C4×C127C22⋊C412yes—
62C22×C4×C127C2×D411yescharacteristic
63D8×C127—24no—
64D8×C127—41no—
65D8×C127—41no—
66M16×C127—22no—
67M16×C127—24no—
68M16×C127—42no—
69M16×C127—42no—
70C2×C8×C127—22no—
71C2×C8×C127—22no—
72C2×C8×C127—42no—
73C2×C8×C127C22⋊C412yes—
74C2×C8×C127C22×C411yescharacteristic
75C2×C8×C127C2×D412yes—
76C2×C8×C127C2×D411yescharacteristic
77C2×C8×C127#4112yes—
78C4⋊C4×C127—22no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—44no—
81C42×C127—41no—
82C16×C127—24no—
83C23×C127—42no—
84C23×C127—82no—
85C23×C127—162no—
86C23×C127#10212yes—
87C23×C127C2×SD1611yescharacteristic
88Q8×C127—22no—
89D4×C127—24no—
90D4×C127—22no—
91D4×C127—42no—
92D4×C127—42no—
93D4×C127—82no—
94D4×C127—164no—
95C2×C4×C127—22no—
96C2×C4×C127—22no—
97C2×C4×C127—42no—
98C2×C4×C127#10212yes—
99C2×C4×C127C2×C22⋊C411yescharacteristic
100C2×C4×C127#12112yes—
101C2×C4×C127C2×D811yescharacteristic
102C2×C4×C127#13512yes—
103C8×C127—22no—
104C8×C127—82no—
105C8×C127C4×D412yes—
106C8×C127#12011yescharacteristic
107C8×C127#12311yescharacteristic
108C22×C127—22no—
109C22×C127—41no—
110C22×C127—42no—
111C22×C127—84no—
112C22×C127—82no—
113C22×C127—164no—
114C22×C127C2×#10211yescharacteristic
115C22×C127#46512yes—
116C4×C127—22no—
117C4×C127—82no—
118C4×C127#38611yescharacteristic
119C4×C127#41611yescharacteristic
120C4×C127#46612yes—
121#13079C12711yesmaximal, 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
129C2×#361C2×C12712yescomplemented
130#1813C2×C12711yescharacteristic, complemented
131#1389C2×C12712yescomplemented
132C127#1307911yescharacteristic, direct product factor, Sylow
133C22×D8C22×C12711yescharacteristic
134C2×#131C22×C12711yescharacteristic
135#535—21no—
136#504—24no—
137C2×M32—22no—
138C2×M32C22×C12712yes—
139#469C4×C12714yes—
140#466—22no—
141C2×#108C22×C12712yes—
142#427C22×C12711yescharacteristic
143#418—21no—
144#413—21no—
145#361—24no—
146#338—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×M16—22no—
156C2×M16C2×C4×C12712yes—
157C2×M16D4×C12711yescharacteristic
158C22×C8D4×C12712yes—
159C22×C8C23×C12711yescharacteristic
160#127—41no—
161#124—41no—
162#121—24no—
163#120—42no—
164#117—21no—
165M32—24no—
166M32—22no—
167M32D4×C12714yescomplemented
168C2×C16—24no—
169C2×C16—22no—
170#108—22no—
171#108—22no—
172#107—21no—
173#106C2×C4×C12712yes—
174#102—24no—
175#101—41no—
176#100—41no—
177C24—41no—
178#41—22no—
179#41—22no—
180C2×Q8D8×C12711yescharacteristic
181C2×D4—22no—
182C2×D4—44no—
183C2×D4—42no—
184C2×D4—41no—
185C2×D4—42no—
186C2×D4D8×C12711yescharacteristic
187C2×D4SD16×C12712yes—
188C22×C4C22⋊C4×C12712yes—
189C22×C4C2×D4×C12711yescharacteristic
190D8—24no—
191D8—41no—
192D8—41no—
193M16—22no—
194M16—24no—
195M16—42no—
196M16—42no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—42no—
200C2×C8C22⋊C4×C12712yes—
201C2×C8C22×C4×C12711yescharacteristic
202C2×C8C2×D4×C12712yes—
203C2×C8C2×D4×C12711yescharacteristic
204C2×C8#41×C12712yes—
205C4⋊C4—22no—
206C22⋊C4—41no—
207C22⋊C4—44no—
208C42—41no—
209C16—24no—
210C23—42no—
211C23—82no—
212C23—162no—
213C23#102×C12712yes—
214C23C2×SD16×C12711yescharacteristic
215Q8—22no—
216D4—24no—
217D4—22no—
218D4—42no—
219D4—42no—
220D4—82no—
221D4—164no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4#102×C12712yes—
226C2×C4C2×C22⋊C4×C12711yescharacteristic
227C2×C4#121×C12712yes—
228C2×C4C2×D8×C12711yescharacteristic
229C2×C4#135×C12712yes—
230C8—22no—
231C8—82no—
232C8C4×D4×C12712yes—
233C8#120×C12711yescharacteristic
234C8#123×C12711yescharacteristic
235C22—22no—
236C22—41no—
237C22—42no—
238C22—84no—
239C22—82no—
240C22—164no—
241C22C2×#102×C12711yescharacteristic
242C22#465×C12712yes—
243C4—22no—
244C4—82no—
245C4#386×C12711yescharacteristic
246C4#416×C12711yescharacteristic
247C4#466×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. C2×#361×C127C2semidirect
4. C127×#1813C2semidirect
5. C127×#1389C2semidirect
40. M32×C127D4semidirect
121. #13079C127direct (N × H)
127. #3407C2×C127semidirect
129. C2×#361C2×C127semidirect
130. #1813C2×C127semidirect
131. #1389C2×C127semidirect
132. C127#13079direct (N × H)
167. M32D4×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
C2×#361×C1272
C127×#18132
C127×#13892
#13079127