Finite Group Databasebeta

← C127×#13078 #44576751

Subgroups — C127×#13078 #44576751

Order 32512.

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

normal subgroups only

This group has 454 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
3C2×#362×C127C212yesmaximal, complemented
4C127×#1813C211yesmaximal, characteristic
5C127×#1389C212yesmaximal, complemented
6C22×Q16×C127C2211yescharacteristic
7C2×#131×C127C2211yescharacteristic
8#536×C127—21no—
9#504×C127—24no—
10C2×M32×C127—22no—
11C2×M32×C127C2212yes—
12#470×C127C414yes—
13#467×C127—22no—
14C2×#108×C127C2212yes—
15#427×C127C2211yescharacteristic
16#419×C127—21no—
17#413×C127—21no—
18#362×C127—24no—
19#338×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×C127—22no—
29C2×M16×C127C2×C412yes—
30C2×M16×C127D411yescharacteristic
31C22×C8×C127D412yes—
32C22×C8×C127C2311yescharacteristic
33C4⋊Q8×C127—41no—
34#124×C127—41no—
35#123×C127—42no—
36C22⋊Q8×C127—24no—
37#117×C127—21no—
38M32×C127—24no—
39M32×C127—22no—
40M32×C127D414yes—
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#103×C127—24no—
48#101×C127—41no—
49#100×C127—41no—
50#41×C127—22no—
51#41×C127—22no—
52C2×Q8×C127—22no—
53C2×Q8×C127—41no—
54C2×Q8×C127—42no—
55C2×Q8×C127—42no—
56C2×Q8×C127D811yescharacteristic
57C2×D4×C127D811yescharacteristic
58C2×D4×C127SD1612yes—
59C22×C4×C127—41no—
60C22×C4×C127C22⋊C412yes—
61C22×C4×C127C2×D411yescharacteristic
62Q16×C127—24no—
63Q16×C127—41no—
64Q16×C127—41no—
65M16×C127—22no—
66M16×C127—24no—
67M16×C127—42no—
68M16×C127—42no—
69C2×C8×C127—22no—
70C2×C8×C127—22no—
71C2×C8×C127—42no—
72C2×C8×C127C22⋊C412yes—
73C2×C8×C127C22×C411yescharacteristic
74C2×C8×C127C2×D412yes—
75C2×C8×C127C2×D411yescharacteristic
76C2×C8×C127#4112yes—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—44no—
79C22⋊C4×C127—44no—
80C22⋊C4×C127—41no—
81C42×C127—41no—
82C16×C127—24no—
83C23×C127#10212yes—
84C23×C127C2×SD1611yescharacteristic
85Q8×C127—22no—
86Q8×C127—42no—
87Q8×C127—42no—
88Q8×C127—82no—
89D4×C127—24no—
90D4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—22no—
93C2×C4×C127—42no—
94C2×C4×C127—42no—
95C2×C4×C127—82no—
96C2×C4×C127#10212yes—
97C2×C4×C127C2×C22⋊C411yescharacteristic
98C2×C4×C127#12112yes—
99C2×C4×C127C2×D811yescharacteristic
100C2×C4×C127#13512yes—
101C8×C127—22no—
102C8×C127—82no—
103C8×C127C4×D412yes—
104C8×C127#12011yescharacteristic
105C8×C127#12311yescharacteristic
106C22×C127—22no—
107C22×C127—41no—
108C22×C127—42no—
109C22×C127C2×#10211yescharacteristic
110C22×C127#46512yes—
111C4×C127—22no—
112C4×C127—82no—
113C4×C127—82no—
114C4×C127#38611yescharacteristic
115C4×C127#41611yescharacteristic
116C4×C127#46612yes—
117#13078C12711yesmaximal, characteristic, direct product factor, Sylow
118C2×C127—21no—
119C2×C127—22no—
120C2×C127—42no—
121C2×C127#189311yescharacteristic
122#3407C2×C12711yescharacteristic
123#3059C2×C12711yescharacteristic
124C2×#362C2×C12712yescomplemented
125#1813C2×C12711yescharacteristic
126#1389C2×C12712yescomplemented
127C127#1307811yescharacteristic, direct product factor, Sylow
128C22×Q16C22×C12711yescharacteristic
129C2×#131C22×C12711yescharacteristic
130#536—21no—
131#504—24no—
132C2×M32—22no—
133C2×M32C22×C12712yes—
134#470C4×C12714yes—
135#467—22no—
136C2×#108C22×C12712yes—
137#427C22×C12711yescharacteristic
138#419—21no—
139#413—21no—
140#362—24no—
141#338—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×M16—22no—
151C2×M16C2×C4×C12712yes—
152C2×M16D4×C12711yescharacteristic
153C22×C8D4×C12712yes—
154C22×C8C23×C12711yescharacteristic
155C4⋊Q8—41no—
156#124—41no—
157#123—42no—
158C22⋊Q8—24no—
159#117—21no—
160M32—24no—
161M32—22no—
162M32D4×C12714yes—
163C2×C16—24no—
164C2×C16—22no—
165#108—22no—
166#108—22no—
167#107—21no—
168#106C2×C4×C12712yes—
169#103—24no—
170#101—41no—
171#100—41no—
172#41—22no—
173#41—22no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8D8×C12711yescharacteristic
179C2×D4D8×C12711yescharacteristic
180C2×D4SD16×C12712yes—
181C22×C4—41no—
182C22×C4C22⋊C4×C12712yes—
183C22×C4C2×D4×C12711yescharacteristic
184Q16—24no—
185Q16—41no—
186Q16—41no—
187M16—22no—
188M16—24no—
189M16—42no—
190M16—42no—
191C2×C8—22no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8C22⋊C4×C12712yes—
195C2×C8C22×C4×C12711yescharacteristic
196C2×C8C2×D4×C12712yes—
197C2×C8C2×D4×C12711yescharacteristic
198C2×C8#41×C12712yes—
199C4⋊C4—22no—
200C4⋊C4—44no—
201C22⋊C4—44no—
202C22⋊C4—41no—
203C42—41no—
204C16—24no—
205C23#102×C12712yes—
206C23C2×SD16×C12711yescharacteristic
207Q8—22no—
208Q8—42no—
209Q8—42no—
210Q8—82no—
211D4—24no—
212D4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—82no—
218C2×C4#102×C12712yes—
219C2×C4C2×C22⋊C4×C12711yescharacteristic
220C2×C4#121×C12712yes—
221C2×C4C2×D8×C12711yescharacteristic
222C2×C4#135×C12712yes—
223C8—22no—
224C8—82no—
225C8C4×D4×C12712yes—
226C8#120×C12711yescharacteristic
227C8#123×C12711yescharacteristic
228C22—22no—
229C22—41no—
230C22—42no—
231C22C2×#102×C12711yescharacteristic
232C22#465×C12712yes—
233C4—22no—
234C4—82no—
235C4—82no—
236C4#386×C12711yescharacteristic
237C4#416×C12711yescharacteristic
238C4#466×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. C2×#362×C127C2semidirect
5. C127×#1389C2semidirect
117. #13078C127direct (N × H)
124. C2×#362C2×C127semidirect
126. #1389C2×C127semidirect
127. C127#13078direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34072
C127×#30592
C2×#362×C1272
C127×#18132
C127×#13892
#13078127