Finite Group Databasebeta

← C127×#21083 #44584756

Subgroups — C127×#21083 #44584756

Order 32512.

1178 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#416×C127C211yesmaximal, characteristic
2C2×#416×C127C211yesmaximal, characteristic
3C22×C4×C8×C127C211yesmaximal, characteristic, complemented
4C127×#2297C211yesmaximal, characteristic
5C127×#2296C211yesmaximal, characteristic, complemented
6C127×#1934C214yesmaximal, complemented
7C127×#1933C214yesmaximal, complemented
8C127×#1735C211yesmaximal, characteristic, complemented
9C127×#1735C211yesmaximal, characteristic, complemented
10C22×#41×C127C2211yescharacteristic
11C23×C8×C127C2211yescharacteristic
12C23×C8×C127C2211yescharacteristic
13C2×#117×C127C2211yescharacteristic
14C2×#117×C127C2211yescharacteristic
15C2×#117×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17#416×C127—24no—
18#416×C127C418yescomplemented
19C2×#103×C127C2212yes—
20C2×#103×C127C2212yes—
21C2×#102×C127C2212yes—
22C2×#102×C127C2212yes—
23C2×C4×C8×C127—24no—
24C2×C4×C8×C127C2214yes—
25#391×C127C2212yes—
26#390×C127C2212yes—
27#389×C127C2214yes—
28#386×C127—22no—
29#385×C127—22no—
30C4×C4⋊C4×C127—22no—
31C4×C22⋊C4×C127—22no—
32#340×C127C2214yes—
33#340×C127C2214yes—
34C2×#41×C127—22no—
35C2×#41×C127—22no—
36C2×#41×C127—22no—
37C2×#41×C127—22no—
38C2×#41×C127—22no—
39C2×#41×C127C2×C414yes—
40C22×Q8×C127C2311yescharacteristic
41C22×D4×C127—21no—
42C22×D4×C127C2311yescharacteristic
43C23×C4×C127—21no—
44C23×C4×C127D412yes—
45C23×C4×C127C2311yescharacteristic
46C22×C8×C127—22no—
47C22×C8×C127—22no—
48C22×C8×C127—22no—
49C22×C8×C127—22no—
50C22×C8×C127C2×C414yes—
51C22×C8×C127D414yes—
52C22×C8×C127C2312yes—
53C22×C8×C127C2312yes—
54#117×C127—22no—
55#117×C127—22no—
56#117×C127—22no—
57#117×C127—22no—
58#117×C127—22no—
59#117×C127C2×C414yes—
60C2×C4⋊C4×C127—24no—
61C2×C4⋊C4×C127C2312yes—
62C2×C4⋊C4×C127C2312yes—
63C2×C4⋊C4×C127C2312yes—
64C2×C22⋊C4×C127—21no—
65C2×C22⋊C4×C127—21no—
66C2×C22⋊C4×C127—21no—
67C2×C22⋊C4×C127—24no—
68C2×C42×C127—22no—
69C2×C42×C127—21no—
70C2×C42×C127—22no—
71C2×C42×C127—21no—
72C2×C42×C127—21no—
73C2×C42×C127D412yes—
74C2×C42×C127C2312yes—
75#103×C127—24no—
76#103×C127C2×C418yescomplemented
77#102×C127—24no—
78#102×C127C2×C418yescomplemented
79C4×C8×C127—28no—
80#95×C127—24no—
81#95×C127—24no—
82C24×C127—21no—
83C24×C127C2×D411yescharacteristic
84#41×C127—28no—
85#41×C127—28no—
86#41×C127—44no—
87#41×C127—44no—
88C2×Q8×C127—21no—
89C2×Q8×C127—21no—
90C2×Q8×C127—21no—
91C2×Q8×C127—21no—
92C2×Q8×C127—21no—
93C2×Q8×C127C22×C412yes—
94C2×D4×C127—24no—
95C2×D4×C127—21no—
96C2×D4×C127—21no—
97C2×D4×C127—21no—
98C2×D4×C127—21no—
99C2×D4×C127—21no—
100C2×D4×C127—42no—
101C2×D4×C127—42no—
102C2×D4×C127C22×C412yes—
103C22×C4×C127—24no—
104C22×C4×C127—28no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—24no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—42no—
111C22×C4×C127—42no—
112C22×C4×C127C22×C412yes—
113C22×C4×C127C2×D414yes—
114C22×C4×C127C2×D412yes—
115C22×C4×C127C2×D411yescharacteristic
116C22×C4×C127#4112yes—
117C22×C4×C127#4112yes—
118C22×C4×C127#4112yes—
119C22×C4×C127#4112yes—
120C22×C4×C127C2411yescharacteristic
121C2×C8×C127—28no—
122C2×C8×C127—28no—
123C2×C8×C127—22no—
124C2×C8×C127—22no—
125C2×C8×C127—22no—
126C2×C8×C127—22no—
127C2×C8×C127C22×C414yes—
128C2×C8×C127C2×D414yes—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—48no—
135C4⋊C4×C127C22×C414yes—
136C22⋊C4×C127—24no—
137C22⋊C4×C127—42no—
138C22⋊C4×C127—42no—
139C22⋊C4×C127—48no—
140C42×C127—24no—
141C42×C127—24no—
142C42×C127—22no—
143C42×C127—22no—
144C42×C127—42no—
145C42×C127—42no—
146C23×C127—24no—
147C23×C127—22no—
148C23×C127—41no—
149C23×C127—41no—
150C23×C127—44no—
151C23×C127C4×D412yes—
152C23×C127#12112yes—
153C23×C127#12412yes—
154C23×C127C22×D411yescharacteristic
155Q8×C127—22no—
156Q8×C127—22no—
157Q8×C127—41no—
158Q8×C127—41no—
159D4×C127—22no—
160D4×C127—22no—
161D4×C127—48no—
162D4×C127—41no—
163D4×C127—41no—
164C2×C4×C127—216no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—22no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—44no—
172C2×C4×C127—48no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—44no—
176C2×C4×C127—44no—
177C2×C4×C127#11714yes—
178C2×C4×C127C4×D414yes—
179C2×C4×C127C4×D412yes—
180C2×C4×C127#12112yes—
181C2×C4×C127#12314yes—
182C2×C4×C127#12412yes—
183C2×C4×C127#12614yes—
184C2×C4×C127#13518yes—
185C2×C4×C127C23×C411yescharacteristic
186C2×C4×C127C22×D411yescharacteristic
187C2×C4×C127C2×#4111yescharacteristic
188C2×C4×C127C2×#4111yescharacteristic
189C2×C4×C127C2×#4111yescharacteristic
190C2×C4×C127C2×#4111yescharacteristic
191C8×C127—24no—
192C8×C127—24no—
193C22×C127—24no—
194C22×C127—24no—
195C22×C127—24no—
196C22×C127—44no—
197C22×C127—42no—
198C22×C127—82no—
199C22×C127—82no—
200C22×C127#38814yes—
201C22×C127C2×C4×D411yescharacteristic
202C22×C127C2×#12111yescharacteristic
203C22×C127C2×#12411yescharacteristic
204C22×C127C2×#13514yes—
205C4×C127—28no—
206C4×C127—44no—
207C4×C127—42no—
208C4×C127—82no—
209C4×C127—82no—
210C4×C127#38814yes—
211C4×C127C2×#11711yescharacteristic
212C4×C127C2×C4×D411yescharacteristic
213C4×C127C2×#12311yescharacteristic
214C4×C127C2×#12611yescharacteristic
215#21083C12711yesmaximal, characteristic, direct product factor, Sylow
216C2×C127—24no—
217C2×C127—82no—
218C2×C127C2×#38811yescharacteristic
219C2×C127C4×#13512yes—
220C2×C127#305012yes—
221C2×C127#313112yes—
222C2×#416C2×C12711yescharacteristic
223C2×#416C2×C12711yescharacteristic
224C22×C4×C8C2×C12711yescharacteristic, complemented
225#2297C2×C12711yescharacteristic
226#2296C2×C12711yescharacteristic, complemented
227#1934C2×C12714yescomplemented
228#1933C2×C12714yescomplemented
229#1735C2×C12711yescharacteristic, complemented
230#1735C2×C12711yescharacteristic, complemented
231C127#2108311yescharacteristic, direct product factor, Sylow
232C22×#41C22×C12711yescharacteristic
233C23×C8C22×C12711yescharacteristic
234C23×C8C22×C12711yescharacteristic
235C2×#117C22×C12711yescharacteristic
236C2×#117C22×C12711yescharacteristic
237C2×#117C22×C12711yescharacteristic
238C22×C42C22×C12711yescharacteristic
239#416—24no—
240#416C4×C12718yescomplemented
241C2×#103C22×C12712yes—
242C2×#103C22×C12712yes—
243C2×#102C22×C12712yes—
244C2×#102C22×C12712yes—
245C2×C4×C8—24no—
246C2×C4×C8C22×C12714yes—
247#391C22×C12712yes—
248#390C22×C12712yes—
249#389C22×C12714yes—
250#386—22no—
251#385—22no—
252C4×C4⋊C4—22no—
253C4×C22⋊C4—22no—
254#340C22×C12714yes—
255#340C22×C12714yes—
256C2×#41—22no—
257C2×#41—22no—
258C2×#41—22no—
259C2×#41—22no—
260C2×#41—22no—
261C2×#41C2×C4×C12714yes—
262C22×Q8C23×C12711yescharacteristic
263C22×D4—21no—
264C22×D4C23×C12711yescharacteristic
265C23×C4—21no—
266C23×C4D4×C12712yes—
267C23×C4C23×C12711yescharacteristic
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8C2×C4×C12714yes—
273C22×C8D4×C12714yes—
274C22×C8C23×C12712yes—
275C22×C8C23×C12712yes—
276#117—22no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117—22no—
281#117C2×C4×C12714yes—
282C2×C4⋊C4—24no—
283C2×C4⋊C4C23×C12712yes—
284C2×C4⋊C4C23×C12712yes—
285C2×C4⋊C4C23×C12712yes—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—24no—
290C2×C42—21no—
291C2×C42—22no—
292C2×C42—22no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42D4×C12712yes—
296C2×C42C23×C12712yes—
297#103—24no—
298#103C2×C4×C12718yescomplemented
299#102—24no—
300#102C2×C4×C12718yescomplemented
301C4×C8—28no—
302#95—24no—
303#95—24no—
304C24—21no—
305C24C2×D4×C12711yescharacteristic
306#41—28no—
307#41—28no—
308#41—44no—
309#41—44no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8C22×C4×C12712yes—
316C2×D4—24no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—42no—
323C2×D4—42no—
324C2×D4C22×C4×C12712yes—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4C22×C4×C12712yes—
335C22×C4C2×D4×C12714yes—
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4C2×D4×C12712yes—
338C22×C4#41×C12712yes—
339C22×C4#41×C12712yes—
340C22×C4#41×C12712yes—
341C22×C4#41×C12712yes—
342C22×C4C24×C12711yescharacteristic
343C2×C8—28no—
344C2×C8—28no—
345C2×C8—22no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8C22×C4×C12714yes—
350C2×C8C2×D4×C12714yes—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—22no—
354C4⋊C4—22no—
355C4⋊C4—22no—
356C4⋊C4—48no—
357C4⋊C4C22×C4×C12714yes—
358C22⋊C4—24no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—48no—
362C42—24no—
363C42—24no—
364C42—22no—
365C42—22no—
366C42—42no—
367C42—42no—
368C23—24no—
369C23—22no—
370C23—41no—
371C23—41no—
372C23—44no—
373C23C4×D4×C12712yes—
374C23#121×C12712yes—
375C23#124×C12712yes—
376C23C22×D4×C12711yescharacteristic
377Q8—22no—
378Q8—22no—
379Q8—41no—
380Q8—41no—
381D4—22no—
382D4—22no—
383D4—48no—
384D4—41no—
385D4—41no—
386C2×C4—216no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—44no—
394C2×C4—48no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4#117×C12714yes—
400C2×C4C4×D4×C12714yes—
401C2×C4C4×D4×C12712yes—
402C2×C4#121×C12712yes—
403C2×C4#123×C12714yes—
404C2×C4#124×C12712yes—
405C2×C4#126×C12714yes—
406C2×C4#135×C12718yes—
407C2×C4C23×C4×C12711yescharacteristic
408C2×C4C22×D4×C12711yescharacteristic
409C2×C4C2×#41×C12711yescharacteristic
410C2×C4C2×#41×C12711yescharacteristic
411C2×C4C2×#41×C12711yescharacteristic
412C2×C4C2×#41×C12711yescharacteristic
413C8—24no—
414C8—24no—
415C22—24no—
416C22—24no—
417C22—24no—
418C22—44no—
419C22—42no—
420C22—82no—
421C22—82no—
422C22#388×C12714yes—
423C22C2×C4×D4×C12711yescharacteristic
424C22C2×#121×C12711yescharacteristic
425C22C2×#124×C12711yescharacteristic
426C22C2×#135×C12714yes—
427C4—28no—
428C4—44no—
429C4—42no—
430C4—82no—
431C4—82no—
432C4#388×C12714yes—
433C4C2×#117×C12711yescharacteristic
434C4C2×C4×D4×C12711yescharacteristic
435C4C2×#123×C12711yescharacteristic
436C4C2×#126×C12711yescharacteristic
437C2—24no—
438C2—82no—
439C2C2×#388×C12711yescharacteristic
440C2C4×#135×C12712yes—
441C2C127×#305012yes—
442C2C127×#313112yes—
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC22×#41×C127C22
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
3. C22×C4×C8×C127C2semidirect
5. C127×#2296C2semidirect
6. C127×#1934C2semidirect
7. C127×#1933C2semidirect
8. C127×#1735C2semidirect
9. C127×#1735C2semidirect
18. #416×C127C4semidirect
76. #103×C127C2×C4semidirect
78. #102×C127C2×C4semidirect
215. #21083C127direct (N × H)
224. C22×C4×C8C2×C127semidirect
226. #2296C2×C127semidirect
227. #1934C2×C127semidirect
228. #1933C2×C127semidirect
229. #1735C2×C127semidirect
230. #1735C2×C127semidirect
231. C127#21083direct (N × H)
240. #416C4×C127semidirect
298. #103C2×C4×C127semidirect
300. #102C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#416×C1272
C22×C4×C8×C1272
C127×#22972
C127×#22962
C127×#19342
C127×#19332
C127×#17352
#21083127