Finite Group Databasebeta

← C127×#18510 #44582183

Subgroups — C127×#18510 #44582183

Order 32512.

1062 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3483C211yesmaximal, characteristic, complemented
2C127×#3147C211yesmaximal, characteristic, complemented
3C127×#3106C212yesmaximal, complemented
4C127×#1634C211yesmaximal, characteristic, complemented
5C127×#1633C211yesmaximal, characteristic, complemented
6C127×#1631C212yesmaximal, complemented
7C127×#1624C211yesmaximal, characteristic, complemented
8C127×#1623C211yesmaximal, characteristic, complemented
9C127×#1621C212yesmaximal, complemented
10C127×#1543C211yesmaximal, characteristic, complemented
11C127×#1476C212yesmaximal, complemented
12C2×#135×C127—22no—
13Q82×C127C2211yescharacteristic
14#555×C127—22no—
15#555×C127—22no—
16#555×C127C2211yescharacteristic
17#550×C127—22no—
18#550×C127C2212yes—
19#532×C127—22no—
20#532×C127—22no—
21#532×C127C2211yescharacteristic
22#532×C127C2211yescharacteristic
23C4×#41×C127—22no—
24C4×#41×C127C2212yes—
25#495×C127—22no—
26#494×C127C2211yescharacteristic
27#493×C127C2211yescharacteristic
28#492×C127C2211yescharacteristic
29#492×C127C2211yescharacteristic
30#482×C127—22no—
31#477×C127C2212yes—
32#476×C127C2212yes—
33#460×C127C2212yes—
34#459×C127C2212yes—
35#449×C127—22no—
36C4×SD16×C127—22no—
37C4×D8×C127—22no—
38#431×C127C2212yes—
39C2×C4×C8×C127C2211yescharacteristic
40#333×C127C2211yescharacteristic
41#333×C127C2211yescharacteristic
42#331×C127C2212yes—
43Q8⋊C8×C127C2212yes—
44Q8⋊C8×C127C2212yes—
45D4⋊C8×C127C2212yes—
46D4⋊C8×C127C2212yes—
47C2×#41×C127—22no—
48C2×#41×C127—22no—
49C2×#41×C127—21no—
50C2×#41×C127D412yes—
51C2×#41×C127D412yes—
52#135×C127—48no—
53C2×Q16×C127—22no—
54C2×SD16×C127—22no—
55C2×SD16×C127—22no—
56C2×SD16×C127—22no—
57C2×D8×C127—22no—
58C2×D8×C127—22no—
59C22×C8×C127—21no—
60C4⋊Q8×C127—22no—
61C4⋊Q8×C127—22no—
62C4⋊Q8×C127C2311yescharacteristic
63C4⋊Q8×C127C2311yescharacteristic
64#127×C127—22no—
65#127×C127—22no—
66#127×C127C2311yescharacteristic
67#127×C127C2311yescharacteristic
68#124×C127—22no—
69#124×C127—24no—
70#124×C127—22no—
71#124×C127—21no—
72#124×C127D412yes—
73#121×C127—24no—
74#121×C127—24no—
75#121×C127—22no—
76#121×C127—24no—
77#121×C127—22no—
78#121×C127—22no—
79#121×C127—22no—
80C4×Q8×C127—22no—
81C4×Q8×C127D412yes—
82C4×Q8×C127C2312yes—
83C4×D4×C127—24no—
84C4×D4×C127—24no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127D412yes—
91C4×D4×C127C2312yes—
92#117×C127—24no—
93#117×C127—22no—
94#117×C127—22no—
95#117×C127D412yes—
96C2×C42×C127—22no—
97C2×C42×C127—22no—
98C2×C42×C127C2311yescharacteristic
99#107×C127—22no—
100#106×C127—22no—
101C4⋊C8×C127C2312yes—
102C4⋊C8×C127C2312yes—
103#103×C127—22no—
104#102×C127—22no—
105#102×C127—22no—
106#102×C127—22no—
107C22⋊C8×C127—22no—
108C4×C8×C127—21no—
109C4×C8×C127—22no—
110C4×C8×C127C2311yescharacteristic
111C4×C8×C127C2311yescharacteristic
112#41×C127—24no—
113#41×C127—42no—
114#41×C127—44no—
115#41×C127—44no—
116#41×C127—44no—
117#41×C127—44no—
118#41×C127—84no—
119C2×Q8×C127—22no—
120C2×Q8×C127—21no—
121C2×Q8×C127C2×D412yes—
122C2×Q8×C127C2×D412yes—
123C2×D4×C127—24no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—24no—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—22no—
130C2×D4×C127—21no—
131C2×D4×C127—41no—
132C2×D4×C127C2×D412yes—
133C2×D4×C127C2×D412yes—
134C22×C4×C127—24no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—41no—
140C22×C4×C127C2×D412yes—
141C22×C4×C127C2×D411yescharacteristic
142Q16×C127—44no—
143SD16×C127—44no—
144SD16×C127—44no—
145SD16×C127—44no—
146D8×C127—44no—
147D8×C127—44no—
148C2×C8×C127—24no—
149C2×C8×C127—21no—
150C2×C8×C127—21no—
151C2×C8×C127—22no—
152C2×C8×C127—22no—
153C4⋊C4×C127—24no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127C2×D412yes—
159C4⋊C4×C127C2×D412yes—
160C22⋊C4×C127—24no—
161C22⋊C4×C127—24no—
162C22⋊C4×C127—22no—
163C22⋊C4×C127—24no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—42no—
167C42×C127—22no—
168C42×C127—22no—
169C42×C127—22no—
170C42×C127—22no—
171C42×C127—22no—
172C42×C127C2×D411yescharacteristic
173C42×C127C2×D412yes—
174C42×C127C2411yescharacteristic
175C23×C127—22no—
176C23×C127—22no—
177C23×C127—41no—
178C23×C127#12011yescharacteristic
179Q8×C127—22no—
180Q8×C127—42no—
181Q8×C127—42no—
182Q8×C127—82no—
183Q8×C127#13514yescomplemented
184D4×C127—22no—
185D4×C127—22no—
186D4×C127—44no—
187D4×C127—42no—
188D4×C127—48no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—42no—
194D4×C127—82no—
195D4×C127—82no—
196D4×C127—84no—
197D4×C127—82no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—44no—
206C2×C4×C127—48no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—44no—
210C2×C4×C127—44no—
211C2×C4×C127—41no—
212C2×C4×C127—82no—
213C2×C4×C127#12012yes—
214C2×C4×C127#12011yescharacteristic
215C2×C4×C127C22×D411yescharacteristic
216C2×C4×C127C22×D412yes—
217C8×C127—22no—
218C8×C127—22no—
219C8×C127—42no—
220C8×C127—42no—
221C22×C127—22no—
222C22×C127—21no—
223C22×C127—42no—
224C22×C127—44no—
225C22×C127—42no—
226C22×C127—42no—
227C22×C127—42no—
228C22×C127—82no—
229C22×C127—81no—
230C22×C127C2×#12011yescharacteristic
231C4×C127—22no—
232C4×C127—24no—
233C4×C127—21no—
234C4×C127—42no—
235C4×C127—42no—
236C4×C127—42no—
237C4×C127—81no—
238C4×C127#45312yes—
239C4×C127C2×#13512yes—
240C4×C127#57512yes—
241#18510C12711yesmaximal, characteristic, direct product factor, Sylow
242C2×C127—41no—
243C2×C127—82no—
244C2×C127—82no—
245C2×C127—161no—
246C2×C127#300212yes—
247C2×C127C2×#45311yescharacteristic
248#3483C2×C12711yescharacteristic, complemented
249#3147C2×C12711yescharacteristic, complemented
250#3106C2×C12712yescomplemented
251#1634C2×C12711yescharacteristic, complemented
252#1633C2×C12711yescharacteristic, complemented
253#1631C2×C12712yescomplemented
254#1624C2×C12711yescharacteristic, complemented
255#1623C2×C12711yescharacteristic, complemented
256#1621C2×C12712yescomplemented
257#1543C2×C12711yescharacteristic, complemented
258#1476C2×C12712yescomplemented
259C127#1851011yescharacteristic, direct product factor, Sylow
260C2×#135—22no—
261Q82C22×C12711yescharacteristic
262#555—22no—
263#555—22no—
264#555C22×C12711yescharacteristic
265#550—22no—
266#550C22×C12712yes—
267#532—22no—
268#532—22no—
269#532C22×C12711yescharacteristic
270#532C22×C12711yescharacteristic
271C4×#41—22no—
272C4×#41C22×C12712yes—
273#495—22no—
274#494C22×C12711yescharacteristic
275#493C22×C12711yescharacteristic
276#492C22×C12711yescharacteristic
277#492C22×C12711yescharacteristic
278#482—22no—
279#477C22×C12712yes—
280#476C22×C12712yes—
281#460C22×C12712yes—
282#459C22×C12712yes—
283#449—22no—
284C4×SD16—22no—
285C4×D8—22no—
286#431C22×C12712yes—
287C2×C4×C8C22×C12711yescharacteristic
288#333C22×C12711yescharacteristic
289#333C22×C12711yescharacteristic
290#331C22×C12712yes—
291Q8⋊C8C22×C12712yes—
292Q8⋊C8C22×C12712yes—
293D4⋊C8C22×C12712yes—
294D4⋊C8C22×C12712yes—
295C2×#41—22no—
296C2×#41—22no—
297C2×#41—21no—
298C2×#41D4×C12712yes—
299C2×#41D4×C12712yes—
300#135—48no—
301C2×Q16—22no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×D8—22no—
306C2×D8—22no—
307C22×C8—21no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8C23×C12711yescharacteristic
311C4⋊Q8C23×C12711yescharacteristic
312#127—22no—
313#127—22no—
314#127C23×C12711yescharacteristic
315#127C23×C12711yescharacteristic
316#124—22no—
317#124—24no—
318#124—22no—
319#124—21no—
320#124D4×C12712yes—
321#121—24no—
322#121—24no—
323#121—22no—
324#121—24no—
325#121—22no—
326#121—22no—
327#121—22no—
328C4×Q8—22no—
329C4×Q8D4×C12712yes—
330C4×Q8C23×C12712yes—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4D4×C12712yes—
339C4×D4C23×C12712yes—
340#117—24no—
341#117—22no—
342#117—22no—
343#117D4×C12712yes—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42C23×C12711yescharacteristic
347#107—22no—
348#106—22no—
349C4⋊C8C23×C12712yes—
350C4⋊C8C23×C12712yes—
351#103—22no—
352#102—22no—
353#102—22no—
354#102—22no—
355C22⋊C8—22no—
356C4×C8—21no—
357C4×C8—22no—
358C4×C8C23×C12711yescharacteristic
359C4×C8C23×C12711yescharacteristic
360#41—24no—
361#41—42no—
362#41—44no—
363#41—44no—
364#41—44no—
365#41—44no—
366#41—84no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8C2×D4×C12712yes—
370C2×Q8C2×D4×C12712yes—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—41no—
380C2×D4C2×D4×C12712yes—
381C2×D4C2×D4×C12712yes—
382C22×C4—24no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—41no—
388C22×C4C2×D4×C12712yes—
389C22×C4C2×D4×C12711yescharacteristic
390Q16—44no—
391SD16—44no—
392SD16—44no—
393SD16—44no—
394D8—44no—
395D8—44no—
396C2×C8—24no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—22no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4C2×D4×C12712yes—
407C4⋊C4C2×D4×C12712yes—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—22no—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—42no—
415C42—22no—
416C42—22no—
417C42—22no—
418C42—22no—
419C42—22no—
420C42C2×D4×C12712yes—
421C42C2×D4×C12711yescharacteristic
422C42C24×C12711yescharacteristic
423C23—22no—
424C23—22no—
425C23—41no—
426C23#120×C12711yescharacteristic
427Q8—22no—
428Q8—42no—
429Q8—42no—
430Q8—82no—
431Q8#135×C12714yescomplemented
432D4—22no—
433D4—22no—
434D4—44no—
435D4—42no—
436D4—48no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4—82no—
443D4—82no—
444D4—84no—
445D4—82no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—44no—
454C2×C4—48no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—44no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4#120×C12712yes—
462C2×C4#120×C12711yescharacteristic
463C2×C4C22×D4×C12711yescharacteristic
464C2×C4C22×D4×C12712yes—
465C8—22no—
466C8—22no—
467C8—42no—
468C8—42no—
469C22—22no—
470C22—21no—
471C22—42no—
472C22—44no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—82no—
477C22—81no—
478C22C2×#120×C12711yescharacteristic
479C4—22no—
480C4—24no—
481C4—21no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—81no—
486C4#453×C12712yes—
487C4C2×#135×C12712yes—
488C4#575×C12712yes—
489C2—41no—
490C2—82no—
491C2—82no—
492C2—161no—
493C2C127×#300212yes—
494C2C2×#453×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
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
1. C127×#3483C2semidirect
2. C127×#3147C2semidirect
3. C127×#3106C2semidirect
4. C127×#1634C2semidirect
5. C127×#1633C2semidirect
6. C127×#1631C2semidirect
7. C127×#1624C2semidirect
8. C127×#1623C2semidirect
9. C127×#1621C2semidirect
10. C127×#1543C2semidirect
11. C127×#1476C2semidirect
183. Q8×C127#135semidirect
241. #18510C127direct (N × H)
248. #3483C2×C127semidirect
249. #3147C2×C127semidirect
250. #3106C2×C127semidirect
251. #1634C2×C127semidirect
252. #1633C2×C127semidirect
253. #1631C2×C127semidirect
254. #1624C2×C127semidirect
255. #1623C2×C127semidirect
256. #1621C2×C127semidirect
257. #1543C2×C127semidirect
258. #1476C2×C127semidirect
259. C127#18510direct (N × H)
431. Q8#135×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34832
C127×#31472
C127×#31062
C127×#16342
C127×#16332
C127×#16312
C127×#16242
C127×#16232
C127×#16212
C127×#15432
C127×#14762
#18510127