Finite Group Databasebeta

← C127×#13033 #44576706

Subgroups — C127×#13033 #44576706

Order 32512.

498 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C127C211yesmaximal, characteristic
2C127×#2948C211yesmaximal, characteristic, complemented
3C127×#2145C211yesmaximal, characteristic, complemented
4C127×#2140C211yesmaximal, characteristic, complemented
5C127×#1976C211yesmaximal, characteristic, complemented
6C127×#1384C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×D8×C127C2211yescharacteristic
10#518×C127—21no—
11#509×C127—22no—
12#509×C127—22no—
13C2×SD32×C127C412yescomplemented
14C2×D16×C127C412yescomplemented
15C2×M32×C127C2211yescharacteristic
16C2×M32×C127C2211yescharacteristic
17#442×C127—22no—
18C4×D8×C127—22no—
19#427×C127C2211yescharacteristic
20#427×C127C2211yescharacteristic
21#421×C127—21no—
22#418×C127—21no—
23#410×C127—21no—
24#405×C127C2211yescharacteristic
25#360×C127—22no—
26#357×C127—22no—
27C2×#41×C127—21no—
28C22×D4×C127—21no—
29#135×C127—21no—
30#135×C127—21no—
31#135×C127—21no—
32#135×C127—21no—
33C2×Q16×C127C2×C411yescharacteristic, complemented
34C2×SD16×C127—21no—
35C2×D8×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—21no—
38C2×D8×C127C2×C412yes—
39C2×D8×C127C2×C411yescharacteristic, complemented
40C2×D8×C127D412yes—
41C2×D8×C127D412yes—
42C2×M16×C127D411yescharacteristic
43C22×C8×C127C2311yescharacteristic
44C4×D4×C127—24no—
45C4×D4×C127—42no—
46#117×C127—21no—
47#117×C127—21no—
48#117×C127D411yescharacteristic
49C2×C22⋊C4×C127—42no—
50SD32×C127—24no—
51D16×C127—24no—
52M32×C127—21no—
53M32×C127—21no—
54M32×C127—21no—
55M32×C127—21no—
56C2×C16×C127—21no—
57C2×C16×C127C2×C412yescomplemented
58#107×C127—21no—
59#107×C127—21no—
60#106×C127—21no—
61#106×C127D412yes—
62#104×C127—42no—
63#102×C127—24no—
64#99×C127—42no—
65#97×C127—21no—
66C4×C8×C127—21no—
67C24×C127—41no—
68#41×C127—41no—
69#41×C127—41no—
70#41×C127—41no—
71#41×C127—41no—
72C2×Q8×C127—21no—
73C2×D4×C127—22no—
74C2×D4×C127—21no—
75C2×D4×C127—22no—
76C2×D4×C127—22no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C22×C4×C127—44no—
82C22×C4×C127—41no—
83C22×C4×C127C2×D411yescharacteristic
84Q16×C127—21no—
85Q16×C127—21no—
86SD16×C127—41no—
87SD16×C127—41no—
88D8×C127—21no—
89D8×C127—22no—
90D8×C127—21no—
91D8×C127—22no—
92D8×C127—22no—
93D8×C127C22⋊C414yes—
94M16×C127—21no—
95M16×C127—21no—
96C2×C8×C127—21no—
97C2×C8×C127C22×C411yescharacteristic
98C2×C8×C127C2×D411yescharacteristic
99C2×C8×C127C2×D411yescharacteristic
100C2×C8×C127C2×D411yescharacteristic
101C2×C8×C127#4111yescharacteristic
102C2×C8×C127#4111yescharacteristic
103C4⋊C4×C127—21no—
104C4⋊C4×C127—22no—
105C4⋊C4×C127—41no—
106C22⋊C4×C127—44no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127D812yes—
110C42×C127—21no—
111C42×C127—41no—
112C42×C127—41no—
113C16×C127—22no—
114C16×C127—41no—
115C23×C127—42no—
116C23×C127—42no—
117C23×C127—42no—
118C23×C127—41no—
119C23×C127—162no—
120C23×C127C2×D811yescharacteristic
121Q8×C127—41no—
122Q8×C127—41no—
123D4×C127—24no—
124D4×C127—41no—
125D4×C127—42no—
126D4×C127—41no—
127D4×C127—42no—
128D4×C127—42no—
129D4×C127—81no—
130D4×C127—81no—
131C2×C4×C127—22no—
132C2×C4×C127—41no—
133C2×C4×C127—42no—
134C2×C4×C127—81no—
135C2×C4×C127—81no—
136C2×C4×C127—81no—
137C2×C4×C127—164no—
138C2×C4×C127C4×D411yescharacteristic
139C2×C4×C127#12011yescharacteristic
140C2×C4×C127#12111yescharacteristic
141C2×C4×C127#13511yescharacteristic
142C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
144C8×C127—41no—
145C8×C127C2×C22⋊C411yescharacteristic
146C8×C127C4×D411yescharacteristic
147C8×C127#12111yescharacteristic
148C8×C127#12311yescharacteristic
149C22×C127—41no—
150C22×C127—44no—
151C22×C127—84no—
152C22×C127—81no—
153C22×C127—162no—
154C22×C127—162no—
155C22×C127—161no—
156C22×C127C4×D811yescharacteristic
157C22×C127#44711yescharacteristic
158C22×C127#45911yescharacteristic
159C4×C127—42no—
160C4×C127—82no—
161C4×C127—81no—
162C4×C127—161no—
163C4×C127#38611yescharacteristic
164C4×C127#44211yescharacteristic
165C4×C127#44911yescharacteristic
166C4×C127#46311yescharacteristic
167#13033C12711yesmaximal, characteristic, direct product factor, Sylow
168C2×C127—21no—
169C2×C127—21no—
170C2×C127—21no—
171C2×C127—84no—
172C2×C127—161no—
173C2×C127#187911yescharacteristic
174C2×#509C2×C12711yescharacteristic
175#2948C2×C12711yescharacteristic, complemented
176#2145C2×C12711yescharacteristic, complemented
177#2140C2×C12711yescharacteristic, complemented
178#1976C2×C12711yescharacteristic, complemented
179#1384C2×C12711yescharacteristic, complemented
180#1378C2×C12711yescharacteristic, complemented
181C127#1303311yescharacteristic, direct product factor, Sylow
182C2×#135C22×C12711yescharacteristic
183C22×D8C22×C12711yescharacteristic
184#518—21no—
185#509—22no—
186#509—22no—
187C2×SD32C4×C12712yescomplemented
188C2×D16C4×C12712yescomplemented
189C2×M32C22×C12711yescharacteristic
190C2×M32C22×C12711yescharacteristic
191#442—22no—
192C4×D8—22no—
193#427C22×C12711yescharacteristic
194#427C22×C12711yescharacteristic
195#421—21no—
196#418—21no—
197#410—21no—
198#405C22×C12711yescharacteristic
199#360—22no—
200#357—22no—
201C2×#41—21no—
202C22×D4—21no—
203#135—21no—
204#135—21no—
205#135—21no—
206#135—21no—
207C2×Q16C2×C4×C12711yescharacteristic, complemented
208C2×SD16—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C2×C4×C12712yes—
213C2×D8C2×C4×C12711yescharacteristic, complemented
214C2×D8D4×C12712yes—
215C2×D8D4×C12712yes—
216C2×M16D4×C12711yescharacteristic
217C22×C8C23×C12711yescharacteristic
218C4×D4—24no—
219C4×D4—42no—
220#117—21no—
221#117—21no—
222#117D4×C12711yescharacteristic
223C2×C22⋊C4—42no—
224SD32—24no—
225D16—24no—
226M32—21no—
227M32—21no—
228M32—21no—
229M32—21no—
230C2×C16—21no—
231C2×C16C2×C4×C12712yescomplemented
232#107—21no—
233#107—21no—
234#106—21no—
235#106D4×C12712yes—
236#104—42no—
237#102—24no—
238#99—42no—
239#97—21no—
240C4×C8—21no—
241C24—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245#41—41no—
246C2×Q8—21no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C22×C4—44no—
256C22×C4—41no—
257C22×C4C2×D4×C12711yescharacteristic
258Q16—21no—
259Q16—21no—
260SD16—41no—
261SD16—41no—
262D8—21no—
263D8—22no—
264D8—21no—
265D8—22no—
266D8—22no—
267D8C22⋊C4×C12714yes—
268M16—21no—
269M16—21no—
270C2×C8—21no—
271C2×C8C22×C4×C12711yescharacteristic
272C2×C8C2×D4×C12711yescharacteristic
273C2×C8C2×D4×C12711yescharacteristic
274C2×C8C2×D4×C12711yescharacteristic
275C2×C8#41×C12711yescharacteristic
276C2×C8#41×C12711yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—41no—
280C22⋊C4—44no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4D8×C12712yes—
284C42—21no—
285C42—41no—
286C42—41no—
287C16—22no—
288C16—41no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—41no—
293C23—162no—
294C23C2×D8×C12711yescharacteristic
295Q8—41no—
296Q8—41no—
297D4—24no—
298D4—41no—
299D4—42no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—164no—
312C2×C4C4×D4×C12711yescharacteristic
313C2×C4#120×C12711yescharacteristic
314C2×C4#121×C12711yescharacteristic
315C2×C4#135×C12711yescharacteristic
316C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
317C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
318C8—41no—
319C8C2×C22⋊C4×C12711yescharacteristic
320C8C4×D4×C12711yescharacteristic
321C8#121×C12711yescharacteristic
322C8#123×C12711yescharacteristic
323C22—41no—
324C22—44no—
325C22—84no—
326C22—81no—
327C22—162no—
328C22—162no—
329C22—161no—
330C22C4×D8×C12711yescharacteristic
331C22#447×C12711yescharacteristic
332C22#459×C12711yescharacteristic
333C4—42no—
334C4—82no—
335C4—81no—
336C4—161no—
337C4#386×C12711yescharacteristic
338C4#442×C12711yescharacteristic
339C4#449×C12711yescharacteristic
340C4#463×C12711yescharacteristic
341C2—21no—
342C2—21no—
343C2—21no—
344C2—84no—
345C2—161no—
346C2C127×#187911yescharacteristic
subgroupG/H
center, socleC2×C127#1879
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2948C2semidirect
3. C127×#2145C2semidirect
4. C127×#2140C2semidirect
5. C127×#1976C2semidirect
6. C127×#1384C2semidirect
7. C127×#1378C2semidirect
13. C2×SD32×C127C4semidirect
14. C2×D16×C127C4semidirect
33. C2×Q16×C127C2×C4semidirect
39. C2×D8×C127C2×C4semidirect
57. C2×C16×C127C2×C4semidirect
167. #13033C127direct (N × H)
175. #2948C2×C127semidirect
176. #2145C2×C127semidirect
177. #2140C2×C127semidirect
178. #1976C2×C127semidirect
179. #1384C2×C127semidirect
180. #1378C2×C127semidirect
181. C127#13033direct (N × H)
187. C2×SD32C4×C127semidirect
188. C2×D16C4×C127semidirect
207. C2×Q16C2×C4×C127semidirect
213. C2×D8C2×C4×C127semidirect
231. C2×C16C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C127×#29482
C127×#21452
C127×#21402
C127×#19762
C127×#13842
C127×#13782
#13033127