Finite Group Databasebeta

← C127×#8902 #44572575

Subgroups — C127×#8902 #44572575

Order 32512.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2906C211yesmaximal, characteristic
2C127×#1806C211yesmaximal, characteristic
3C127×#1571C211yesmaximal, characteristic, complemented
4C127×#1567C211yesmaximal, characteristic, complemented
5C127×#1476C211yesmaximal, characteristic
6C127×#1303C211yesmaximal, characteristic, complemented
7C127×#1279C211yesmaximal, characteristic, complemented
8C2×#131×C127—21no—
9C4×#41×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#424×C127—21no—
12#424×C127—22no—
13#423×C127—21no—
14#423×C127C2211yescharacteristic
15#423×C127C2211yescharacteristic
16C2×C4⋊C8×C127—21no—
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#104×C127—21no—
19C2×C4×C8×C127C2211yescharacteristic
20C4×C4⋊C4×C127C2211yescharacteristic
21#339×C127—21no—
22#335×C127—22no—
23#335×C127—21no—
24#335×C127—21no—
25Q8⋊C8×C127C411yescharacteristic, complemented
26Q8⋊C8×C127C411yescharacteristic, complemented
27D4⋊C8×C127C411yescharacteristic, complemented
28D4⋊C8×C127C411yescharacteristic, complemented
29C2×#41×C127D411yescharacteristic
30#131×C127—42no—
31#131×C127—42no—
32C2×M16×C127—22no—
33C2×M16×C127—21no—
34C2×M16×C127—21no—
35C22×C8×C127—22no—
36C22×C8×C127—21no—
37C22×C8×C127—21no—
38C4×Q8×C127C2×C411yescharacteristic
39C4×Q8×C127Q811yescharacteristic
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C4×D4×C127C2×C411yescharacteristic
43C4×D4×C127Q811yescharacteristic
44#117×C127—21no—
45#117×C127D411yescharacteristic
46C2×C4⋊C4×C127—21no—
47C2×C42×C127—21no—
48C2×C42×C127—21no—
49C2×C42×C127C2311yescharacteristic
50C4⋊C8×C127—22no—
51C4⋊C8×C127—22no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127C2×C411yescharacteristic
57C4⋊C8×C127C2×C411yescharacteristic
58C4⋊C8×C127D411yescharacteristic
59C4⋊C8×C127D411yescharacteristic
60C4⋊C8×C127D412yes—
61#104×C127—42no—
62C22⋊C8×C127—21no—
63C4×C8×C127—21no—
64C4×C8×C127—21no—
65C4×C8×C127C2×C411yescharacteristic
66C4×C8×C127C2×C411yescharacteristic
67#95×C127—21no—
68#41×C127—21no—
69#41×C127—21no—
70#41×C127D812yes—
71#41×C127Q1612yes—
72C2×Q8×C127C4⋊C411yescharacteristic
73C2×D4×C127—21no—
74C2×D4×C127C4⋊C411yescharacteristic
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—41no—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127#4111yescharacteristic
81C22×C4×C127#4111yescharacteristic
82M16×C127—44no—
83M16×C127—41no—
84M16×C127—41no—
85M16×C127—41no—
86M16×C127—41no—
87C2×C8×C127—21no—
88C2×C8×C127—21no—
89C2×C8×C127—21no—
90C2×C8×C127—21no—
91C2×C8×C127—21no—
92C2×C8×C127—22no—
93C2×C8×C127—21no—
94C2×C8×C127—42no—
95C2×C8×C127—44no—
96C2×C8×C127—41no—
97C2×C8×C127—41no—
98C2×C8×C127—41no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—22no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127C4⋊C411yescharacteristic
104C4⋊C4×C127C4⋊C411yescharacteristic
105C22⋊C4×C127—21no—
106C22⋊C4×C127—21no—
107C22⋊C4×C127—21no—
108C42×C127—21no—
109C42×C127—21no—
110C42×C127—21no—
111C42×C127—41no—
112C42×C127—41no—
113C42×C127C22×C411yescharacteristic
114C42×C127C2×D411yescharacteristic
115C42×C127C2×D411yescharacteristic
116C42×C127C2×Q811yescharacteristic
117C23×C127—21no—
118C23×C127#12311yescharacteristic
119Q8×C127—21no—
120Q8×C127#10712yes—
121D4×C127—22no—
122D4×C127—22no—
123D4×C127—21no—
124D4×C127#10712yes—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—42no—
136C2×C4×C127—81no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127C2×C4⋊C411yescharacteristic
140C2×C4×C127C4×D411yescharacteristic
141C2×C4×C127C4×D411yescharacteristic
142C2×C4×C127#12011yescharacteristic
143C2×C4×C127C22⋊Q811yescharacteristic
144C2×C4×C127C22⋊Q811yescharacteristic
145C2×C4×C127C2×D811yescharacteristic
146C2×C4×C127C2×Q1611yescharacteristic
147C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C127#13711yescharacteristic
149C8×C127—22no—
150C8×C127—41no—
151C8×C127—41no—
152C8×C127—41no—
153C8×C127—41no—
154C8×C127—42no—
155C8×C127—41no—
156C8×C127—81no—
157C22×C127—21no—
158C22×C127—21no—
159C22×C127—22no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127#38511yescharacteristic
163C22×C127#48011yescharacteristic
164C22×C127#48411yescharacteristic
165C4×C127—22no—
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—41no—
170C4×C127—41no—
171C4×C127—82no—
172C4×C127C2×#10711yescharacteristic
173C4×C127#42811yescharacteristic
174C4×C127#44311yescharacteristic
175C4×C127#44411yescharacteristic
176C4×C127#44711yescharacteristic
177C4×C127#45111yescharacteristic
178#8902C12711yesmaximal, characteristic, direct product factor, Sylow
179C2×C127—21no—
180C2×C127—21no—
181C2×C127—42no—
182C2×C127#185211yescharacteristic
183C2×C127#186111yescharacteristic
184C2×C127#186611yescharacteristic
185#2906C2×C12711yescharacteristic
186#1806C2×C12711yescharacteristic
187#1571C2×C12711yescharacteristic, complemented
188#1567C2×C12711yescharacteristic, complemented
189#1476C2×C12711yescharacteristic
190#1303C2×C12711yescharacteristic, complemented
191#1279C2×C12711yescharacteristic, complemented
192C127#890211yescharacteristic, direct product factor, Sylow
193C2×#131—21no—
194C4×#41C22×C12711yescharacteristic
195#431C22×C12711yescharacteristic
196#424—21no—
197#424—22no—
198#423—21no—
199#423C22×C12711yescharacteristic
200#423C22×C12711yescharacteristic
201C2×C4⋊C8—21no—
202C2×C4⋊C8C22×C12711yescharacteristic
203C2×#104—21no—
204C2×C4×C8C22×C12711yescharacteristic
205C4×C4⋊C4C22×C12711yescharacteristic
206#339—21no—
207#335—22no—
208#335—21no—
209#335—21no—
210Q8⋊C8C4×C12711yescharacteristic, complemented
211Q8⋊C8C4×C12711yescharacteristic, complemented
212D4⋊C8C4×C12711yescharacteristic, complemented
213D4⋊C8C4×C12711yescharacteristic, complemented
214C2×#41D4×C12711yescharacteristic
215#131—42no—
216#131—42no—
217C2×M16—22no—
218C2×M16—21no—
219C2×M16—21no—
220C22×C8—22no—
221C22×C8—21no—
222C22×C8—21no—
223C4×Q8C2×C4×C12711yescharacteristic
224C4×Q8Q8×C12711yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4C2×C4×C12711yescharacteristic
228C4×D4Q8×C12711yescharacteristic
229#117—21no—
230#117D4×C12711yescharacteristic
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C23×C12711yescharacteristic
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C12711yescharacteristic
242C4⋊C8C2×C4×C12711yescharacteristic
243C4⋊C8D4×C12711yescharacteristic
244C4⋊C8D4×C12711yescharacteristic
245C4⋊C8D4×C12712yes—
246#104—42no—
247C22⋊C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×C4×C12711yescharacteristic
251C4×C8C2×C4×C12711yescharacteristic
252#95—21no—
253#41—21no—
254#41—21no—
255#41D8×C12712yes—
256#41Q16×C12712yes—
257C2×Q8C4⋊C4×C12711yescharacteristic
258C2×D4—21no—
259C2×D4C4⋊C4×C12711yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4C2×D4×C12711yescharacteristic
265C22×C4#41×C12711yescharacteristic
266C22×C4#41×C12711yescharacteristic
267M16—44no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—41no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—44no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4C4⋊C4×C12711yescharacteristic
289C4⋊C4C4⋊C4×C12711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—41no—
297C42—41no—
298C42C22×C4×C12711yescharacteristic
299C42C2×D4×C12711yescharacteristic
300C42C2×D4×C12711yescharacteristic
301C42C2×Q8×C12711yescharacteristic
302C23—21no—
303C23#123×C12711yescharacteristic
304Q8—21no—
305Q8#107×C12712yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#107×C12712yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4C2×C4⋊C4×C12711yescharacteristic
325C2×C4C4×D4×C12711yescharacteristic
326C2×C4C4×D4×C12711yescharacteristic
327C2×C4#120×C12711yescharacteristic
328C2×C4C22⋊Q8×C12711yescharacteristic
329C2×C4C22⋊Q8×C12711yescharacteristic
330C2×C4C2×D8×C12711yescharacteristic
331C2×C4C2×Q16×C12711yescharacteristic
332C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
333C2×C4#137×C12711yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—41no—
339C8—42no—
340C8—41no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#385×C12711yescharacteristic
348C22#480×C12711yescharacteristic
349C22#484×C12711yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4C2×#107×C12711yescharacteristic
358C4#428×C12711yescharacteristic
359C4#443×C12711yescharacteristic
360C4#444×C12711yescharacteristic
361C4#447×C12711yescharacteristic
362C4#451×C12711yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2C127×#185211yescharacteristic
367C2C127×#186111yescharacteristic
368C2C127×#186611yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#385
prime radicalC2×#41×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1571C2semidirect
4. C127×#1567C2semidirect
6. C127×#1303C2semidirect
7. C127×#1279C2semidirect
25. Q8⋊C8×C127C4semidirect
26. Q8⋊C8×C127C4semidirect
27. D4⋊C8×C127C4semidirect
28. D4⋊C8×C127C4semidirect
178. #8902C127direct (N × H)
187. #1571C2×C127semidirect
188. #1567C2×C127semidirect
190. #1303C2×C127semidirect
191. #1279C2×C127semidirect
192. C127#8902direct (N × H)
210. Q8⋊C8C4×C127semidirect
211. Q8⋊C8C4×C127semidirect
212. D4⋊C8C4×C127semidirect
213. D4⋊C8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29062
C127×#18062
C127×#15712
C127×#15672
C127×#14762
C127×#13032
C127×#12792
#8902127