Finite Group Databasebeta

← C127×#11894 #44575567

Subgroups — C127×#11894 #44575567

Order 32512.

394 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3050C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic, complemented
3C127×#1810C211yesmaximal, characteristic, complemented
4C127×#1350C212yesmaximal, complemented
5C127×#1349C212yesmaximal, complemented
6C2×#135×C127C411yescharacteristic
7C23×C8×C127C2211yescharacteristic
8#525×C127—21no—
9C2×M32×C127—21no—
10#467×C127C411yescharacteristic
11#467×C127C2211yescharacteristic
12#466×C127C411yescharacteristic
13#466×C127C2211yescharacteristic
14#465×C127—21no—
15#465×C127—21no—
16C2×#108×C127—21no—
17#427×C127C411yescharacteristic
18#416×C127—21no—
19#407×C127—21no—
20C22⋊C16×C127—21no—
21C22⋊C16×C127C2212yes—
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—22no—
30C22×C8×C127—42no—
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127C2311yescharacteristic
37#123×C127—41no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40#121×C127—21no—
41#121×C127—21no—
42#120×C127—41no—
43C4×D4×C127—41no—
44C4×D4×C127—41no—
45#117×C127—21no—
46M32×C127—42no—
47C2×C16×C127—22no—
48#108×C127—42no—
49#107×C127C2×C411yescharacteristic
50#107×C127C2×C411yescharacteristic
51#106×C127—21no—
52#103×C127—21no—
53#103×C127—21no—
54#102×C127—21no—
55#102×C127—21no—
56C22⋊C8×C127—41no—
57C22⋊C8×C127—41no—
58C24×C127SD1611yescharacteristic
59#41×C127—42no—
60#41×C127—42no—
61C2×Q8×C127—21no—
62C2×D4×C127—21no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127D811yescharacteristic
72C22×C4×C127D811yescharacteristic
73C22×C4×C127SD1611yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75Q16×C127—41no—
76SD16×C127—42no—
77D8×C127—41no—
78M16×C127—42no—
79M16×C127—42no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—22no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127—42no—
87C2×C8×C127C22⋊C411yescharacteristic
88C2×C8×C127C22⋊C411yescharacteristic
89C2×C8×C127C22×C411yescharacteristic
90C2×C8×C127C2×D411yescharacteristic
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C42×C127—41no—
101C16×C127—42no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127#10211yescharacteristic
107C23×C127#10211yescharacteristic
108C23×C127C2×SD1611yescharacteristic
109Q8×C127—41no—
110Q8×C127—41no—
111D4×C127—41no—
112D4×C127—41no—
113D4×C127—82no—
114D4×C127—82no—
115D4×C127—82no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—82no—
129C2×C4×C127#10211yescharacteristic
130C2×C4×C127#10211yescharacteristic
131C2×C4×C127C2×C22⋊C411yescharacteristic
132C2×C4×C127C2×D811yescharacteristic
133C8×C127—21no—
134C8×C127—21no—
135C8×C127—21no—
136C8×C127—82no—
137C8×C127#9912yes—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—44no—
148C22×C127—81no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127C2×#10211yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—81no—
156C4×C127—81no—
157C4×C127—81no—
158C4×C127C2×#9911yescharacteristic
159C4×C127#42111yescharacteristic
160#11894C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—41no—
162C2×C127—41no—
163C2×C127—41no—
164C2×C127—161no—
165C2×C127#151911yescharacteristic
166C2×C127#214311yescharacteristic
167C2×C127#214811yescharacteristic
168#3050C2×C12711yescharacteristic
169#2112C2×C12711yescharacteristic, complemented
170#1810C2×C12711yescharacteristic, complemented
171#1350C2×C12712yescomplemented
172#1349C2×C12712yescomplemented
173C127#1189411yescharacteristic, direct product factor, Sylow
174C2×#135C4×C12711yescharacteristic
175C23×C8C22×C12711yescharacteristic
176#525—21no—
177C2×M32—21no—
178#467C4×C12711yescharacteristic
179#467C22×C12711yescharacteristic
180#466C4×C12711yescharacteristic
181#466C22×C12711yescharacteristic
182#465—21no—
183#465—21no—
184C2×#108—21no—
185#427C4×C12711yescharacteristic
186#416—21no—
187#407—21no—
188C22⋊C16—21no—
189C22⋊C16C22×C12712yes—
190#341C22×C12712yes—
191C2×#41—21no—
192C23×C4D4×C12711yescharacteristic
193#135—42no—
194C2×Q16C2×C4×C12711yescharacteristic
195C2×SD16—21no—
196C2×D8C2×C4×C12711yescharacteristic
197C2×M16—22no—
198C22×C8—42no—
199C22×C8C2×C4×C12711yescharacteristic
200C22×C8C2×C4×C12711yescharacteristic
201C22×C8D4×C12711yescharacteristic
202C22×C8D4×C12711yescharacteristic
203C22×C8D4×C12711yescharacteristic
204C22×C8C23×C12711yescharacteristic
205#123—41no—
206C22⋊Q8—21no—
207C22⋊Q8—21no—
208#121—21no—
209#121—21no—
210#120—41no—
211C4×D4—41no—
212C4×D4—41no—
213#117—21no—
214M32—42no—
215C2×C16—22no—
216#108—42no—
217#107C2×C4×C12711yescharacteristic
218#107C2×C4×C12711yescharacteristic
219#106—21no—
220#103—21no—
221#103—21no—
222#102—21no—
223#102—21no—
224C22⋊C8—41no—
225C22⋊C8—41no—
226C24SD16×C12711yescharacteristic
227#41—42no—
228#41—42no—
229C2×Q8—21no—
230C2×D4—21no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4C22⋊C4×C12711yescharacteristic
239C22×C4D8×C12711yescharacteristic
240C22×C4D8×C12711yescharacteristic
241C22×C4SD16×C12711yescharacteristic
242C22×C4C2×D4×C12711yescharacteristic
243Q16—41no—
244SD16—42no—
245D8—41no—
246M16—42no—
247M16—42no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—42no—
255C2×C8C22⋊C4×C12711yescharacteristic
256C2×C8C22⋊C4×C12711yescharacteristic
257C2×C8C22×C4×C12711yescharacteristic
258C2×C8C2×D4×C12711yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—41no—
269C16—42no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23#102×C12711yescharacteristic
275C23#102×C12711yescharacteristic
276C23C2×SD16×C12711yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—82no—
282D4—82no—
283D4—82no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—82no—
297C2×C4#102×C12711yescharacteristic
298C2×C4#102×C12711yescharacteristic
299C2×C4C2×C22⋊C4×C12711yescharacteristic
300C2×C4C2×D8×C12711yescharacteristic
301C8—21no—
302C8—21no—
303C8—21no—
304C8—82no—
305C8#99×C12712yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—44no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22C2×#102×C12711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4C2×#99×C12711yescharacteristic
327C4#421×C12711yescharacteristic
328C2—41no—
329C2—41no—
330C2—41no—
331C2—161no—
332C2C127×#151911yescharacteristic
333C2C127×#214311yescharacteristic
334C2C127×#214811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3050C2
LCSG ▷ C2×C8 ▷ C2×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
2. C127×#2112C2semidirect
3. C127×#1810C2semidirect
4. C127×#1350C2semidirect
5. C127×#1349C2semidirect
160. #11894C127direct (N × H)
169. #2112C2×C127semidirect
170. #1810C2×C127semidirect
171. #1350C2×C127semidirect
172. #1349C2×C127semidirect
173. C127#11894direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30502
C127×#21122
C127×#18102
C127×#13502
C127×#13492
#11894127