Finite Group Databasebeta

← C127×#11709 #44575382

Subgroups — C127×#11709 #44575382

Order 32512.

450 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3050C211yesmaximal, characteristic
2C2×C22⋊C16×C127C211yesmaximal, characteristic, complemented
3C2×#341×C127C211yesmaximal, characteristic, complemented
4C127×#1350C212yesmaximal, complemented
5C127×#1349C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic
7C22×M16×C127—21no—
8C23×C8×C127C2211yescharacteristic
9#525×C127—21no—
10C22×C16×C127—21no—
11#467×C127C411yescharacteristic
12#467×C127C2211yescharacteristic
13#466×C127C411yescharacteristic
14#466×C127C2211yescharacteristic
15#465×C127—21no—
16#465×C127—21no—
17#427×C127C411yescharacteristic
18#416×C127—21no—
19C22⋊C16×C127—21no—
20C22⋊C16×C127C2212yes—
21#341×C127—21no—
22#341×C127C2212yes—
23C2×#41×C127—21no—
24C23×C4×C127D411yescharacteristic
25#135×C127—42no—
26C2×Q16×C127C2×C411yescharacteristic
27C2×SD16×C127—21no—
28C2×D8×C127C2×C411yescharacteristic
29C2×M16×C127—24no—
30C2×M16×C127—22no—
31C2×M16×C127—42no—
32C2×M16×C127—41no—
33C22×C8×C127—42no—
34C22×C8×C127—41no—
35C22×C8×C127C2×C411yescharacteristic
36C22×C8×C127C2×C411yescharacteristic
37C22×C8×C127D411yescharacteristic
38C22×C8×C127D411yescharacteristic
39C22×C8×C127D411yescharacteristic
40C22×C8×C127C2311yescharacteristic
41#123×C127—41no—
42C22⋊Q8×C127—21no—
43C22⋊Q8×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46#120×C127—41no—
47C4×D4×C127—41no—
48C4×D4×C127—41no—
49#117×C127—21no—
50C2×C16×C127—22no—
51C2×C16×C127—42no—
52#107×C127C2×C411yescharacteristic
53#107×C127C2×C411yescharacteristic
54#106×C127—21no—
55#103×C127—21no—
56#103×C127—21no—
57#102×C127—21no—
58#102×C127—21no—
59C24×C127SD1611yescharacteristic
60#41×C127—42no—
61#41×C127—42no—
62C2×Q8×C127—21no—
63C2×D4×C127—21no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127—41no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—41no—
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127D811yescharacteristic
73C22×C4×C127D811yescharacteristic
74C22×C4×C127SD1611yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76Q16×C127—41no—
77SD16×C127—42no—
78D8×C127—41no—
79M16×C127—24no—
80M16×C127—44no—
81M16×C127—42no—
82C2×C8×C127—22no—
83C2×C8×C127—22no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—44no—
89C2×C8×C127—42no—
90C2×C8×C127C22⋊C411yescharacteristic
91C2×C8×C127C22⋊C411yescharacteristic
92C2×C8×C127C22×C411yescharacteristic
93C2×C8×C127C2×D411yescharacteristic
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C42×C127—41no—
104C16×C127—42no—
105C23×C127—22no—
106C23×C127—22no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127#10211yescharacteristic
110C23×C127#10211yescharacteristic
111C23×C127C2×SD1611yescharacteristic
112Q8×C127—41no—
113Q8×C127—41no—
114D4×C127—41no—
115D4×C127—41no—
116D4×C127—82no—
117D4×C127—82no—
118D4×C127—82no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—82no—
130C2×C4×C127#9912yes—
131C2×C4×C127#10211yescharacteristic
132C2×C4×C127#10211yescharacteristic
133C2×C4×C127#10412yes—
134C2×C4×C127C2×C22⋊C411yescharacteristic
135C2×C4×C127C2×D811yescharacteristic
136C8×C127—21no—
137C8×C127—21no—
138C8×C127—21no—
139C8×C127—21no—
140C8×C127—44no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—44no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127#32712yes—
153C22×C127#35912yes—
154C22×C127C2×#10211yescharacteristic
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—81no—
158C4×C127—81no—
159C4×C127—81no—
160C4×C127#32712yes—
161C4×C127C2×#9911yescharacteristic
162C4×C127C2×#10411yescharacteristic
163#11709C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—22no—
165C2×C127—22no—
166C2×C127—41no—
167C2×C127—161no—
168C2×C127C2×#32711yescharacteristic
169C2×C127C2×#35911yescharacteristic
170C2×C127#214811yescharacteristic
171#3050C2×C12711yescharacteristic
172C2×C22⋊C16C2×C12711yescharacteristic, complemented
173C2×#341C2×C12711yescharacteristic, complemented
174#1350C2×C12712yescomplemented
175#1349C2×C12712yescomplemented
176C127#1170911yescharacteristic, direct product factor, Sylow
177C2×#135C4×C12711yescharacteristic
178C22×M16—21no—
179C23×C8C22×C12711yescharacteristic
180#525—21no—
181C22×C16—21no—
182#467C4×C12711yescharacteristic
183#467C22×C12711yescharacteristic
184#466C4×C12711yescharacteristic
185#466C22×C12711yescharacteristic
186#465—21no—
187#465—21no—
188#427C4×C12711yescharacteristic
189#416—21no—
190C22⋊C16—21no—
191C22⋊C16C22×C12712yes—
192#341—21no—
193#341C22×C12712yes—
194C2×#41—21no—
195C23×C4D4×C12711yescharacteristic
196#135—42no—
197C2×Q16C2×C4×C12711yescharacteristic
198C2×SD16—21no—
199C2×D8C2×C4×C12711yescharacteristic
200C2×M16—24no—
201C2×M16—22no—
202C2×M16—42no—
203C2×M16—41no—
204C22×C8—42no—
205C22×C8—41no—
206C22×C8C2×C4×C12711yescharacteristic
207C22×C8C2×C4×C12711yescharacteristic
208C22×C8D4×C12711yescharacteristic
209C22×C8D4×C12711yescharacteristic
210C22×C8D4×C12711yescharacteristic
211C22×C8C23×C12711yescharacteristic
212#123—41no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215#121—21no—
216#121—21no—
217#120—41no—
218C4×D4—41no—
219C4×D4—41no—
220#117—21no—
221C2×C16—22no—
222C2×C16—42no—
223#107C2×C4×C12711yescharacteristic
224#107C2×C4×C12711yescharacteristic
225#106—21no—
226#103—21no—
227#103—21no—
228#102—21no—
229#102—21no—
230C24SD16×C12711yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—41no—
241C22×C4C22⋊C4×C12711yescharacteristic
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4D8×C12711yescharacteristic
244C22×C4D8×C12711yescharacteristic
245C22×C4SD16×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247Q16—41no—
248SD16—42no—
249D8—41no—
250M16—24no—
251M16—44no—
252M16—42no—
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—44no—
260C2×C8—42no—
261C2×C8C22⋊C4×C12711yescharacteristic
262C2×C8C22⋊C4×C12711yescharacteristic
263C2×C8C22×C4×C12711yescharacteristic
264C2×C8C2×D4×C12711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C42—41no—
275C16—42no—
276C23—22no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23#102×C12711yescharacteristic
281C23#102×C12711yescharacteristic
282C23C2×SD16×C12711yescharacteristic
283Q8—41no—
284Q8—41no—
285D4—41no—
286D4—41no—
287D4—82no—
288D4—82no—
289D4—82no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—82no—
301C2×C4#99×C12712yes—
302C2×C4#102×C12711yescharacteristic
303C2×C4#102×C12711yescharacteristic
304C2×C4#104×C12712yes—
305C2×C4C2×C22⋊C4×C12711yescharacteristic
306C2×C4C2×D8×C12711yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C8—44no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—44no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22#327×C12712yes—
324C22#359×C12712yes—
325C22C2×#102×C12711yescharacteristic
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4#327×C12712yes—
332C4C2×#99×C12711yescharacteristic
333C4C2×#104×C12711yescharacteristic
334C2—22no—
335C2—22no—
336C2—41no—
337C2—161no—
338C2C2×#327×C12711yescharacteristic
339C2C2×#359×C12711yescharacteristic
340C2C127×#214811yescharacteristic
subgroupG/H
centerC2×C4×C127#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×#102
prime radicalC127×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C16×C127C2semidirect
3. C2×#341×C127C2semidirect
4. C127×#1350C2semidirect
5. C127×#1349C2semidirect
163. #11709C127direct (N × H)
172. C2×C22⋊C16C2×C127semidirect
173. C2×#341C2×C127semidirect
174. #1350C2×C127semidirect
175. #1349C2×C127semidirect
176. C127#11709direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30502
C2×C22⋊C16×C1272
C2×#341×C1272
C127×#13502
C127×#13492
#11709127