Finite Group Databasebeta

← C127×#8831 #44572504

Subgroups — C127×#8831 #44572504

Order 32512.

500 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#431×C127C211yesmaximal, characteristic
2C127×#1797C211yesmaximal, characteristic
3C4×C22⋊C8×C127C211yesmaximal, characteristic
4C2×#335×C127C211yesmaximal, characteristic, complemented
5C2×#334×C127C211yesmaximal, characteristic, complemented
6C127×#1277C211yesmaximal, characteristic, complemented
7C127×#1277C211yesmaximal, characteristic, complemented
8C22×C42×C127C2211yescharacteristic
9#431×C127—22no—
10#431×C127—22no—
11C2×C4⋊C8×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×C4⋊C8×C127C2211yescharacteristic
15C2×C22⋊C8×C127—21no—
16C2×C22⋊C8×C127—21no—
17C2×C22⋊C8×C127C411yescharacteristic
18C2×C22⋊C8×C127C411yescharacteristic
19C2×C4×C8×C127—21no—
20C2×C4×C8×C127C2211yescharacteristic
21C2×C4×C8×C127C2211yescharacteristic
22#336×C127—21no—
23#336×C127C411yescharacteristic
24#336×C127C411yescharacteristic
25#335×C127—22no—
26#334×C127—22no—
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D411yescharacteristic
29C23×C4×C127Q811yescharacteristic
30C22×C8×C127—21no—
31C22×C8×C127—21no—
32C22×C8×C127—21no—
33C22×C8×C127—21no—
34C22×C8×C127C2×C411yescharacteristic
35C22×C8×C127C2×C411yescharacteristic
36C22×C8×C127C2×C411yescharacteristic
37C22×C8×C127C2×C411yescharacteristic
38C2×C42×C127—21no—
39C2×C42×C127—21no—
40C2×C42×C127—21no—
41C2×C42×C127—21no—
42C2×C42×C127C2×C411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C2×C42×C127Q811yescharacteristic
45C2×C42×C127C2311yescharacteristic
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127D412yes—
53C4⋊C8×C127D412yes—
54C22⋊C8×C127—24no—
55C22⋊C8×C127—22no—
56C22⋊C8×C127—42no—
57C22⋊C8×C127C814yescomplemented
58C4×C8×C127—24no—
59C4×C8×C127—21no—
60C4×C8×C127—21no—
61C4×C8×C127—21no—
62C4×C8×C127—21no—
63C24×C127C4⋊C411yescharacteristic
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—22no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—41no—
78C22×C4×C127C4⋊C411yescharacteristic
79C22×C4×C127C4⋊C411yescharacteristic
80C22×C4×C127C4⋊C411yescharacteristic
81C22×C4×C127C2×C812yes—
82C22×C4×C127M1612yes—
83C22×C4×C127C22×C411yescharacteristic
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×Q811yescharacteristic
86C2×C8×C127—21no—
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—22no—
94C2×C8×C127—21no—
95C2×C8×C127—21no—
96C2×C8×C127—21no—
97C2×C8×C127—21no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127—41no—
101C2×C8×C127—41no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127—41no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127C2×C812yes—
109C2×C8×C127C2×C812yes—
110C42×C127—21no—
111C42×C127—21no—
112C42×C127—21no—
113C42×C127—21no—
114C42×C127—21no—
115C42×C127—21no—
116C42×C127C2×D411yescharacteristic
117C42×C127C2×D411yescharacteristic
118C42×C127#4111yescharacteristic
119C42×C127#4111yescharacteristic
120C23×C127—21no—
121C23×C127—21no—
122C23×C127—21no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127C4⋊C812yes—
127C23×C127C2×C4⋊C411yescharacteristic
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—22no—
137C2×C4×C127—22no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127C4⋊C812yes—
148C2×C4×C127#10812yes—
149C2×C4×C127C4×D411yescharacteristic
150C2×C4×C127C4×D411yescharacteristic
151C2×C4×C127#12011yescharacteristic
152C2×C4×C127C22⋊Q811yescharacteristic
153C2×C4×C127C22⋊Q811yescharacteristic
154C2×C4×C127#12311yescharacteristic
155C2×C4×C127C22×C811yescharacteristic
156C2×C4×C127C2×M1611yescharacteristic
157C2×C4×C127#13111yescharacteristic
158C2×C4×C127#13111yescharacteristic
159C2×C4×C127#13511yescharacteristic
160C2×C4×C127#13511yescharacteristic
161C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C127#13711yescharacteristic
163C8×C127—22no—
164C8×C127—22no—
165C8×C127—41no—
166C8×C127—41no—
167C8×C127—42no—
168C8×C127—42no—
169C8×C127—81no—
170C8×C127—81no—
171C22×C127—22no—
172C22×C127—22no—
173C22×C127—22no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127—41no—
178C22×C127#38511yescharacteristic
179C22×C127C2×C4⋊C811yescharacteristic
180C22×C127#42411yescharacteristic
181C22×C127#42711yescharacteristic
182C22×C127#42811yescharacteristic
183C22×C127C2×#10811yescharacteristic
184C22×C127#43011yescharacteristic
185C4×C127—22no—
186C4×C127—22no—
187C4×C127—21no—
188C4×C127—21no—
189C4×C127—41no—
190C4×C127C8×D411yescharacteristic
191C4×C127C8×D411yescharacteristic
192C4×C127#43511yescharacteristic
193C4×C127#43511yescharacteristic
194C4×C127#44911yescharacteristic
195C4×C127#45211yescharacteristic
196C4×C127#48211yescharacteristic
197C4×C127#48511yescharacteristic
198#8831C12711yesmaximal, characteristic, direct product factor, Sylow
199C2×C127—42no—
200C2×C127#156411yescharacteristic
201C2×C127#156511yescharacteristic
202C2×C127#157211yescharacteristic
203C2×C127#157411yescharacteristic
204C2×C127#185011yescharacteristic
205C2×C127#185411yescharacteristic
206C2×C127#185511yescharacteristic
207C2×#431C2×C12711yescharacteristic
208#1797C2×C12711yescharacteristic
209C4×C22⋊C8C2×C12711yescharacteristic
210C2×#335C2×C12711yescharacteristic, complemented
211C2×#334C2×C12711yescharacteristic, complemented
212#1277C2×C12711yescharacteristic, complemented
213#1277C2×C12711yescharacteristic, complemented
214C127#883111yescharacteristic, direct product factor, Sylow
215C22×C42C22×C12711yescharacteristic
216#431—22no—
217#431—22no—
218C2×C4⋊C8C22×C12711yescharacteristic
219C2×C4⋊C8C22×C12711yescharacteristic
220C2×C4⋊C8C22×C12711yescharacteristic
221C2×C4⋊C8C22×C12711yescharacteristic
222C2×C22⋊C8—21no—
223C2×C22⋊C8—21no—
224C2×C22⋊C8C4×C12711yescharacteristic
225C2×C22⋊C8C4×C12711yescharacteristic
226C2×C4×C8—21no—
227C2×C4×C8C22×C12711yescharacteristic
228C2×C4×C8C22×C12711yescharacteristic
229#336—21no—
230#336C4×C12711yescharacteristic
231#336C4×C12711yescharacteristic
232#335—22no—
233#334—22no—
234C23×C4C2×C4×C12711yescharacteristic
235C23×C4D4×C12711yescharacteristic
236C23×C4Q8×C12711yescharacteristic
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8C2×C4×C12711yescharacteristic
242C22×C8C2×C4×C12711yescharacteristic
243C22×C8C2×C4×C12711yescharacteristic
244C22×C8C2×C4×C12711yescharacteristic
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C2×C4×C12711yescharacteristic
250C2×C42D4×C12711yescharacteristic
251C2×C42Q8×C12711yescharacteristic
252C2×C42C23×C12711yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C12712yes—
260C4⋊C8D4×C12712yes—
261C22⋊C8—24no—
262C22⋊C8—22no—
263C22⋊C8—42no—
264C22⋊C8C8×C12714yescomplemented
265C4×C8—24no—
266C4×C8—21no—
267C4×C8—21no—
268C4×C8—21no—
269C4×C8—21no—
270C24C4⋊C4×C12711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4C4⋊C4×C12711yescharacteristic
286C22×C4C4⋊C4×C12711yescharacteristic
287C22×C4C4⋊C4×C12711yescharacteristic
288C22×C4C2×C8×C12712yes—
289C22×C4M16×C12712yes—
290C22×C4C22×C4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292C22×C4C2×Q8×C12711yescharacteristic
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8C2×C8×C12712yes—
316C2×C8C2×C8×C12712yes—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—21no—
323C42C2×D4×C12711yescharacteristic
324C42C2×D4×C12711yescharacteristic
325C42#41×C12711yescharacteristic
326C42#41×C12711yescharacteristic
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23C4⋊C8×C12712yes—
334C23C2×C4⋊C4×C12711yescharacteristic
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4C4⋊C8×C12712yes—
355C2×C4#108×C12712yes—
356C2×C4C4×D4×C12711yescharacteristic
357C2×C4C4×D4×C12711yescharacteristic
358C2×C4#120×C12711yescharacteristic
359C2×C4C22⋊Q8×C12711yescharacteristic
360C2×C4C22⋊Q8×C12711yescharacteristic
361C2×C4#123×C12711yescharacteristic
362C2×C4C22×C8×C12711yescharacteristic
363C2×C4C2×M16×C12711yescharacteristic
364C2×C4#131×C12711yescharacteristic
365C2×C4#131×C12711yescharacteristic
366C2×C4#135×C12711yescharacteristic
367C2×C4#135×C12711yescharacteristic
368C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
369C2×C4#137×C12711yescharacteristic
370C8—22no—
371C8—22no—
372C8—41no—
373C8—41no—
374C8—42no—
375C8—42no—
376C8—81no—
377C8—81no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22#385×C12711yescharacteristic
386C22C2×C4⋊C8×C12711yescharacteristic
387C22#424×C12711yescharacteristic
388C22#427×C12711yescharacteristic
389C22#428×C12711yescharacteristic
390C22C2×#108×C12711yescharacteristic
391C22#430×C12711yescharacteristic
392C4—22no—
393C4—22no—
394C4—21no—
395C4—21no—
396C4—41no—
397C4C8×D4×C12711yescharacteristic
398C4C8×D4×C12711yescharacteristic
399C4#435×C12711yescharacteristic
400C4#435×C12711yescharacteristic
401C4#449×C12711yescharacteristic
402C4#452×C12711yescharacteristic
403C4#482×C12711yescharacteristic
404C4#485×C12711yescharacteristic
405C2—42no—
406C2C127×#156411yescharacteristic
407C2C127×#156511yescharacteristic
408C2C127×#157211yescharacteristic
409C2C127×#157411yescharacteristic
410C2C127×#185011yescharacteristic
411C2C127×#185411yescharacteristic
412C2C127×#185511yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×C42C23×C127
socleC23×C127C2×C4⋊C4
prime radicalC24×C127C4⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#335×C127C2semidirect
5. C2×#334×C127C2semidirect
6. C127×#1277C2semidirect
7. C127×#1277C2semidirect
57. C22⋊C8×C127C8semidirect
198. #8831C127direct (N × H)
210. C2×#335C2×C127semidirect
211. C2×#334C2×C127semidirect
212. #1277C2×C127semidirect
213. #1277C2×C127semidirect
214. C127#8831direct (N × H)
264. C22⋊C8C8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C1272
C127×#17972
C4×C22⋊C8×C1272
C2×#335×C1272
C2×#334×C1272
C127×#12772
#8831127