Finite Group Databasebeta

← C127×#13066 #44576739

Subgroups — C127×#13066 #44576739

Order 32512.

484 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M32×C127C211yesmaximal, characteristic
2C2×#467×C127C211yesmaximal, characteristic
3C2×#362×C127C212yesmaximal, complemented
4C127×#1810C211yesmaximal, characteristic
5C127×#1387C212yesmaximal, complemented
6C22×Q16×C127C2211yescharacteristic
7C23×C8×C127C2211yescharacteristic
8C2×C22⋊Q8×C127—21no—
9C2×M32×C127—21no—
10C2×M32×C127—24no—
11C2×M32×C127C2212yes—
12C22×C16×C127—21no—
13#467×C127—21no—
14#467×C127—21no—
15#467×C127C412yes—
16#467×C127C412yes—
17C2×#108×C127C2212yes—
18C2×#107×C127C2211yescharacteristic
19C2×#103×C127—21no—
20#407×C127—21no—
21#362×C127—24no—
22#341×C127—21no—
23C22×Q8×C127—21no—
24C23×C4×C127D411yescharacteristic
25C2×Q16×C127—22no—
26C2×Q16×C127—21no—
27C2×Q16×C127—22no—
28C2×Q16×C127C2×C412yes—
29C2×M16×C127—22no—
30C22×C8×C127—22no—
31C22×C8×C127—22no—
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127C2×C411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22×C8×C127C2311yescharacteristic
38C22⋊Q8×C127—22no—
39C22⋊Q8×C127—22no—
40C22⋊Q8×C127—41no—
41C22⋊Q8×C127—41no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—41no—
44C2×C22⋊C4×C127—41no—
45M32×C127—24no—
46M32×C127—22no—
47M32×C127D414yes—
48C2×C16×C127—24no—
49C2×C16×C127—22no—
50#108×C127—22no—
51#108×C127—22no—
52#107×C127—21no—
53#107×C127C2×C412yes—
54#103×C127—22no—
55#103×C127—22no—
56C22⋊C8×C127—41no—
57C22⋊C8×C127—41no—
58C24×C127SD1611yescharacteristic
59C2×Q8×C127—22no—
60C2×Q8×C127—41no—
61C2×Q8×C127—42no—
62C2×Q8×C127—42no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127D811yescharacteristic
70C22×C4×C127D811yescharacteristic
71C22×C4×C127SD1611yescharacteristic
72C22×C4×C127C2×D411yescharacteristic
73Q16×C127—24no—
74Q16×C127—41no—
75Q16×C127—41no—
76M16×C127—42no—
77M16×C127—42no—
78C2×C8×C127—22no—
79C2×C8×C127—22no—
80C2×C8×C127—22no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—21no—
84C2×C8×C127—21no—
85C2×C8×C127—42no—
86C2×C8×C127C22⋊C411yescharacteristic
87C2×C8×C127C22⋊C411yescharacteristic
88C2×C8×C127C22×C411yescharacteristic
89C2×C8×C127C2×D412yes—
90C2×C8×C127C2×D411yescharacteristic
91C2×C8×C127#4112yes—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—42no—
95C4⋊C4×C127—41no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—42no—
98C16×C127—24no—
99C23×C127—22no—
100C23×C127—22no—
101C23×C127—41no—
102C23×C127#10211yescharacteristic
103C23×C127#10211yescharacteristic
104C23×C127C2×SD1611yescharacteristic
105Q8×C127—42no—
106Q8×C127—42no—
107Q8×C127—82no—
108C2×C4×C127—22no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—22no—
114C2×C4×C127—22no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—82no—
118C2×C4×C127—82no—
119C2×C4×C127#10211yescharacteristic
120C2×C4×C127#10211yescharacteristic
121C2×C4×C127C2×C22⋊C411yescharacteristic
122C2×C4×C127#12112yes—
123C2×C4×C127C2×D811yescharacteristic
124C2×C4×C127#13512yes—
125C8×C127—21no—
126C8×C127—21no—
127C8×C127—82no—
128C8×C127C4×D412yes—
129C8×C127#12011yescharacteristic
130C8×C127#12311yescharacteristic
131C22×C127—21no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127—21no—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—44no—
139C22×C127#36212yescomplemented
140C22×C127C2×#10211yescharacteristic
141C22×C127#46512yes—
142C4×C127—21no—
143C4×C127—21no—
144C4×C127—82no—
145C4×C127—82no—
146C4×C127#38611yescharacteristic
147C4×C127#41611yescharacteristic
148C4×C127#46612yes—
149#13066C12711yesmaximal, characteristic, direct product factor, Sylow
150C2×C127—22no—
151C2×C127—22no—
152C2×C127—41no—
153C2×C127#189311yescharacteristic
154C2×C127C2×#36211yescharacteristic
155C2×C127#214811yescharacteristic
156C22×M32C2×C12711yescharacteristic
157C2×#467C2×C12711yescharacteristic
158C2×#362C2×C12712yescomplemented
159#1810C2×C12711yescharacteristic
160#1387C2×C12712yescomplemented
161C127#1306611yescharacteristic, direct product factor, Sylow
162C22×Q16C22×C12711yescharacteristic
163C23×C8C22×C12711yescharacteristic
164C2×C22⋊Q8—21no—
165C2×M32—21no—
166C2×M32—24no—
167C2×M32C22×C12712yes—
168C22×C16—21no—
169#467—21no—
170#467—21no—
171#467C4×C12712yes—
172#467C4×C12712yes—
173C2×#108C22×C12712yes—
174C2×#107C22×C12711yescharacteristic
175C2×#103—21no—
176#407—21no—
177#362—24no—
178#341—21no—
179C22×Q8—21no—
180C23×C4D4×C12711yescharacteristic
181C2×Q16—22no—
182C2×Q16—21no—
183C2×Q16—22no—
184C2×Q16C2×C4×C12712yes—
185C2×M16—22no—
186C22×C8—22no—
187C22×C8—22no—
188C22×C8C2×C4×C12711yescharacteristic
189C22×C8C2×C4×C12711yescharacteristic
190C22×C8D4×C12711yescharacteristic
191C22×C8D4×C12711yescharacteristic
192C22×C8D4×C12711yescharacteristic
193C22×C8C23×C12711yescharacteristic
194C22⋊Q8—22no—
195C22⋊Q8—22no—
196C22⋊Q8—41no—
197C22⋊Q8—41no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—41no—
200C2×C22⋊C4—41no—
201M32—24no—
202M32—22no—
203M32D4×C12714yes—
204C2×C16—24no—
205C2×C16—22no—
206#108—22no—
207#108—22no—
208#107—21no—
209#107C2×C4×C12712yes—
210#103—22no—
211#103—22no—
212C22⋊C8—41no—
213C22⋊C8—41no—
214C24SD16×C12711yescharacteristic
215C2×Q8—22no—
216C2×Q8—41no—
217C2×Q8—42no—
218C2×Q8—42no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4C22⋊C4×C12711yescharacteristic
224C22×C4C22⋊C4×C12711yescharacteristic
225C22×C4D8×C12711yescharacteristic
226C22×C4D8×C12711yescharacteristic
227C22×C4SD16×C12711yescharacteristic
228C22×C4C2×D4×C12711yescharacteristic
229Q16—24no—
230Q16—41no—
231Q16—41no—
232M16—42no—
233M16—42no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—42no—
242C2×C8C22⋊C4×C12711yescharacteristic
243C2×C8C22⋊C4×C12711yescharacteristic
244C2×C8C22×C4×C12711yescharacteristic
245C2×C8C2×D4×C12712yes—
246C2×C8C2×D4×C12711yescharacteristic
247C2×C8#41×C12712yes—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C16—24no—
255C23—22no—
256C23—22no—
257C23—41no—
258C23#102×C12711yescharacteristic
259C23#102×C12711yescharacteristic
260C23C2×SD16×C12711yescharacteristic
261Q8—42no—
262Q8—42no—
263Q8—82no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4#102×C12711yescharacteristic
276C2×C4#102×C12711yescharacteristic
277C2×C4C2×C22⋊C4×C12711yescharacteristic
278C2×C4#121×C12712yes—
279C2×C4C2×D8×C12711yescharacteristic
280C2×C4#135×C12712yes—
281C8—21no—
282C8—21no—
283C8—82no—
284C8C4×D4×C12712yes—
285C8#120×C12711yescharacteristic
286C8#123×C12711yescharacteristic
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—44no—
295C22#362×C12712yescomplemented
296C22C2×#102×C12711yescharacteristic
297C22#465×C12712yes—
298C4—21no—
299C4—21no—
300C4—82no—
301C4—82no—
302C4#386×C12711yescharacteristic
303C4#416×C12711yescharacteristic
304C4#466×C12712yes—
305C2—22no—
306C2—22no—
307C2—41no—
308C2C127×#189311yescharacteristic
309C2C2×#362×C12711yescharacteristic
310C2C127×#214811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#362×C127C2semidirect
5. C127×#1387C2semidirect
139. C22×C127#362semidirect
149. #13066C127direct (N × H)
158. C2×#362C2×C127semidirect
160. #1387C2×C127semidirect
161. C127#13066direct (N × H)
295. C22#362×C127semidirect

Maximal subgroups

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

subgroupindex
C22×M32×C1272
C2×#467×C1272
C2×#362×C1272
C127×#18102
C127×#13872
#13066127