Finite Group Databasebeta

← C4×#473×C127 #44585227

Subgroups — C4×#473×C127 #44585227

Order 32512.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#473×C127C211yesmaximal, characteristic
2C4×#137×C127C212yesmaximal
3C2×C4×Q16×C127C211yesmaximal, characteristic, complemented
4C4×#131×C127C211yesmaximal, characteristic
5C127×#1979C211yesmaximal, characteristic, complemented
6C127×#1952C211yesmaximal, characteristic, complemented
7C127×#1930C212yesmaximal, complemented
8C127×#1908C212yesmaximal
9C127×#1816C211yesmaximal, characteristic
10C4×#108×C127C211yesmaximal, characteristic, complemented
11C4×#101×C127C212yesmaximal, complemented
12C2×#137×C127C2212yes—
13C22×Q16×C127C2211yescharacteristic
14C2×#131×C127C2211yescharacteristic
15C2×#131×C127C2211yescharacteristic
16C4×#41×C127C2211yescharacteristic
17C2×C4×Q8×C127C2212yes—
18#473×C127C418yesdirect product factor
19#441×C127—22no—
20#440×C127—22no—
21C4×Q16×C127—22no—
22C4×Q16×C127—21no—
23C4×Q16×C127—21no—
24C4×Q16×C127—21no—
25C4×Q16×C127—21no—
26C4×SD16×C127—22no—
27C2×#108×C127C2211yescharacteristic
28C2×#108×C127C2211yescharacteristic
29#428×C127C2212yes—
30C2×#107×C127C2211yescharacteristic
31#419×C127C2212yes—
32#417×C127C2212yes—
33C2×#103×C127C2212yes—
34C2×#101×C127C2212yes—
35C2×#101×C127C2212yes—
36#405×C127—21no—
37#405×C127—21no—
38#405×C127C2211yescharacteristic
39#405×C127C2211yescharacteristic
40C4×M16×C127—21no—
41C4×M16×C127C2211yescharacteristic
42C4×M16×C127C2212yes—
43C2×C4×C8×C127—21no—
44C2×C4×C8×C127C2211yescharacteristic
45#343×C127C2212yes—
46#343×C127C2212yes—
47#341×C127C2212yes—
48C2×#41×C127C2311yescharacteristic
49C22×Q8×C127C2312yes—
50#137×C127—24no—
51#137×C127C2×C418yes—
52C2×Q16×C127—22no—
53C2×Q16×C127—21no—
54C2×Q16×C127—21no—
55C2×Q16×C127—22no—
56C2×Q16×C127C2×C414yescomplemented
57C2×SD16×C127—22no—
58#131×C127—22no—
59#131×C127—22no—
60#131×C127—22no—
61#131×C127C2×C414yes—
62C2×M16×C127—21no—
63C2×M16×C127—21no—
64C2×M16×C127C2312yes—
65C2×M16×C127C2311yescharacteristic
66C2×M16×C127C2312yes—
67C2×M16×C127C2311yescharacteristic
68C22×C8×C127—21no—
69C22×C8×C127—21no—
70C22×C8×C127C2311yescharacteristic
71C22×C8×C127C2311yescharacteristic
72C4×Q8×C127—22no—
73C4×Q8×C127—22no—
74C4×Q8×C127—22no—
75C4×Q8×C127—22no—
76C4×Q8×C127D411yescharacteristic
77C4×Q8×C127D411yescharacteristic
78C4×D4×C127—21no—
79C4×D4×C127—21no—
80C4×D4×C127D411yescharacteristic
81C4×D4×C127D411yescharacteristic
82#117×C127—21no—
83#117×C127C2311yescharacteristic
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127C2312yes—
86C2×C42×C127—21no—
87C2×C42×C127—22no—
88C2×C42×C127C2311yescharacteristic
89#108×C127—22no—
90#108×C127C2×C414yescomplemented
91#107×C127—21no—
92#107×C127—21no—
93#107×C127—22no—
94#106×C127—22no—
95#103×C127—22no—
96#103×C127—22no—
97#103×C127—22no—
98#103×C127—22no—
99#103×C127—22no—
100#102×C127—22no—
101#101×C127—24no—
102#101×C127C2×C418yescomplemented
103#97×C127—21no—
104#97×C127—21no—
105#97×C127—21no—
106#97×C127—22no—
107C4×C8×C127—21no—
108C4×C8×C127—21no—
109C4×C8×C127—21no—
110C4×C8×C127—22no—
111C4×C8×C127D411yescharacteristic
112C4×C8×C127D411yescharacteristic
113C4×C8×C127D411yescharacteristic
114C4×C8×C127D411yescharacteristic
115#41×C127—21no—
116#41×C127—21no—
117#41×C127C22×C412yes—
118#41×C127#4112yes—
119C2×Q8×C127—22no—
120C2×Q8×C127—22no—
121C2×Q8×C127—22no—
122C2×Q8×C127—22no—
123C2×Q8×C127—22no—
124C2×Q8×C127C22×C414yes—
125C2×Q8×C127C2×D411yescharacteristic
126C2×D4×C127—21no—
127C2×D4×C127C2×D411yescharacteristic
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—21no—
131C22×C4×C127—21no—
132C22×C4×C127—22no—
133C22×C4×C127#4111yescharacteristic
134C22×C4×C127#4111yescharacteristic
135C22×C4×C127C2411yescharacteristic
136Q16×C127—28no—
137Q16×C127—24no—
138Q16×C127—24no—
139SD16×C127—28no—
140M16×C127—24no—
141M16×C127—21no—
142M16×C127—21no—
143M16×C127—22no—
144M16×C127—24no—
145M16×C127—22no—
146M16×C127—22no—
147M16×C127C22×C412yes—
148M16×C127C22×C414yes—
149M16×C127#4112yes—
150C2×C8×C127—24no—
151C2×C8×C127—21no—
152C2×C8×C127—21no—
153C2×C8×C127—22no—
154C2×C8×C127—21no—
155C2×C8×C127—21no—
156C2×C8×C127—24no—
157C2×C8×C127—22no—
158C2×C8×C127C22×C412yes—
159C2×C8×C127C2×D411yescharacteristic
160C2×C8×C127C2×D411yescharacteristic
161C2×C8×C127C2×D411yescharacteristic
162C2×C8×C127C2×D411yescharacteristic
163C2×C8×C127#4112yes—
164C4⋊C4×C127—21no—
165C4⋊C4×C127—21no—
166C4⋊C4×C127—22no—
167C4⋊C4×C127—22no—
168C4⋊C4×C127—42no—
169C4⋊C4×C127—42no—
170C4⋊C4×C127C2×D411yescharacteristic
171C4⋊C4×C127C2×D411yescharacteristic
172C22⋊C4×C127—21no—
173C22⋊C4×C127—21no—
174C22⋊C4×C127—21no—
175C42×C127—21no—
176C42×C127—21no—
177C42×C127—21no—
178C42×C127—42no—
179C42×C127—42no—
180C42×C127C2×D411yescharacteristic
181C42×C127C2×D411yescharacteristic
182C42×C127C2×D411yescharacteristic
183C42×C127C2×D411yescharacteristic
184C23×C127—21no—
185C23×C127C2×#4111yescharacteristic
186Q8×C127—21no—
187Q8×C127—24no—
188Q8×C127—24no—
189Q8×C127—42no—
190Q8×C127—42no—
191Q8×C127C4×D412yes—
192D4×C127—22no—
193D4×C127—22no—
194D4×C127—21no—
195D4×C127C4×D412yes—
196C2×C4×C127—21no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—24no—
201C2×C4×C127—21no—
202C2×C4×C127—21no—
203C2×C4×C127—41no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—82no—
210C2×C4×C127#12111yescharacteristic
211C2×C4×C127#12111yescharacteristic
212C2×C4×C127#12111yescharacteristic
213C2×C4×C127#12111yescharacteristic
214C2×C4×C127C23×C411yescharacteristic
215C2×C4×C127C22×D411yescharacteristic
216C2×C4×C127C22×D411yescharacteristic
217C2×C4×C127C2×#4111yescharacteristic
218C2×C4×C127C2×#4111yescharacteristic
219C2×C4×C127C2×#4111yescharacteristic
220C8×C127—22no—
221C8×C127—24no—
222C8×C127—21no—
223C8×C127—22no—
224C8×C127—21no—
225C8×C127—42no—
226C8×C127C4×D412yes—
227C8×C127C4×D412yes—
228C22×C127—21no—
229C22×C127—21no—
230C22×C127—22no—
231C22×C127—41no—
232C22×C127—41no—
233C22×C127C4×#4111yescharacteristic
234C22×C127C2×#12111yescharacteristic
235C22×C127#52911yescharacteristic
236C4×C127—21no—
237C4×C127—21no—
238C4×C127—21no—
239C4×C127—22no—
240C4×C127—41no—
241C4×C127—41no—
242C4×C127—44no—
243C4×C127—82no—
244C4×C127#47312yesdirect product factor
245C4×C127C2×C4×D411yescharacteristic
246C4×C127C2×C4×D411yescharacteristic
247C4×C127#52511yescharacteristic
248C4×C127#53211yescharacteristic
249C4×#473C12711yesmaximal, characteristic, direct product factor, Sylow
250C2×C127—21no—
251C2×C127—21no—
252C2×C127—42no—
253C2×C127C4×#12111yescharacteristic
254C2×C127C2×#47311yescharacteristic
255C2×C127#306711yescharacteristic
256C2×#473C2×C12711yescharacteristic
257C4×#137C2×C12712yes—
258C2×C4×Q16C2×C12711yescharacteristic, complemented
259C4×#131C2×C12711yescharacteristic
260#1979C2×C12711yescharacteristic, complemented
261#1952C2×C12711yescharacteristic, complemented
262#1930C2×C12712yescomplemented
263#1908C2×C12712yes—
264#1816C2×C12711yescharacteristic
265C4×#108C2×C12711yescharacteristic, complemented
266C4×#101C2×C12712yescomplemented
267C127C4×#47311yescharacteristic, direct product factor, Sylow
268C2×#137C22×C12712yes—
269C22×Q16C22×C12711yescharacteristic
270C2×#131C22×C12711yescharacteristic
271C2×#131C22×C12711yescharacteristic
272C4×#41C22×C12711yescharacteristic
273C2×C4×Q8C22×C12712yes—
274#473C4×C12718yesdirect product factor
275#441—22no—
276#440—22no—
277C4×Q16—22no—
278C4×Q16—21no—
279C4×Q16—21no—
280C4×Q16—21no—
281C4×Q16—21no—
282C4×SD16—22no—
283C2×#108C22×C12711yescharacteristic
284C2×#108C22×C12711yescharacteristic
285#428C22×C12712yes—
286C2×#107C22×C12711yescharacteristic
287#419C22×C12712yes—
288#417C22×C12712yes—
289C2×#103C22×C12712yes—
290C2×#101C22×C12712yes—
291C2×#101C22×C12712yes—
292#405—21no—
293#405—21no—
294#405C22×C12711yescharacteristic
295#405C22×C12711yescharacteristic
296C4×M16—21no—
297C4×M16C22×C12711yescharacteristic
298C4×M16C22×C12712yes—
299C2×C4×C8—21no—
300C2×C4×C8C22×C12711yescharacteristic
301#343C22×C12712yes—
302#343C22×C12712yes—
303#341C22×C12712yes—
304C2×#41C23×C12711yescharacteristic
305C22×Q8C23×C12712yes—
306#137—24no—
307#137C2×C4×C12718yes—
308C2×Q16—22no—
309C2×Q16—21no—
310C2×Q16—21no—
311C2×Q16—22no—
312C2×Q16C2×C4×C12714yescomplemented
313C2×SD16—22no—
314#131—22no—
315#131—22no—
316#131—22no—
317#131C2×C4×C12714yes—
318C2×M16—21no—
319C2×M16—21no—
320C2×M16C23×C12712yes—
321C2×M16C23×C12711yescharacteristic
322C2×M16C23×C12712yes—
323C2×M16C23×C12711yescharacteristic
324C22×C8—21no—
325C22×C8—21no—
326C22×C8C23×C12711yescharacteristic
327C22×C8C23×C12711yescharacteristic
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×Q8—22no—
332C4×Q8D4×C12711yescharacteristic
333C4×Q8D4×C12711yescharacteristic
334C4×D4—21no—
335C4×D4—21no—
336C4×D4D4×C12711yescharacteristic
337C4×D4D4×C12711yescharacteristic
338#117—21no—
339#117C23×C12711yescharacteristic
340C2×C4⋊C4—22no—
341C2×C4⋊C4C23×C12712yes—
342C2×C42—21no—
343C2×C42—22no—
344C2×C42C23×C12711yescharacteristic
345#108—22no—
346#108C2×C4×C12714yescomplemented
347#107—21no—
348#107—21no—
349#107—22no—
350#106—22no—
351#103—22no—
352#103—22no—
353#103—22no—
354#103—22no—
355#103—22no—
356#102—22no—
357#101—24no—
358#101C2×C4×C12718yescomplemented
359#97—21no—
360#97—21no—
361#97—21no—
362#97—22no—
363C4×C8—21no—
364C4×C8—21no—
365C4×C8—21no—
366C4×C8—22no—
367C4×C8D4×C12711yescharacteristic
368C4×C8D4×C12711yescharacteristic
369C4×C8D4×C12711yescharacteristic
370C4×C8D4×C12711yescharacteristic
371#41—21no—
372#41—21no—
373#41C22×C4×C12712yes—
374#41#41×C12712yes—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8C22×C4×C12714yes—
381C2×Q8C2×D4×C12711yescharacteristic
382C2×D4—21no—
383C2×D4C2×D4×C12711yescharacteristic
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4#41×C12711yescharacteristic
390C22×C4#41×C12711yescharacteristic
391C22×C4C24×C12711yescharacteristic
392Q16—28no—
393Q16—24no—
394Q16—24no—
395SD16—28no—
396M16—24no—
397M16—21no—
398M16—21no—
399M16—22no—
400M16—24no—
401M16—22no—
402M16—22no—
403M16C22×C4×C12712yes—
404M16C22×C4×C12714yes—
405M16#41×C12712yes—
406C2×C8—24no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—24no—
413C2×C8—22no—
414C2×C8C22×C4×C12712yes—
415C2×C8C2×D4×C12711yescharacteristic
416C2×C8C2×D4×C12711yescharacteristic
417C2×C8C2×D4×C12711yescharacteristic
418C2×C8C2×D4×C12711yescharacteristic
419C2×C8#41×C12712yes—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4C2×D4×C12711yescharacteristic
427C4⋊C4C2×D4×C12711yescharacteristic
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C42—21no—
432C42—21no—
433C42—21no—
434C42—42no—
435C42—42no—
436C42C2×D4×C12711yescharacteristic
437C42C2×D4×C12711yescharacteristic
438C42C2×D4×C12711yescharacteristic
439C42C2×D4×C12711yescharacteristic
440C23—21no—
441C23C2×#41×C12711yescharacteristic
442Q8—21no—
443Q8—24no—
444Q8—24no—
445Q8—42no—
446Q8—42no—
447Q8C4×D4×C12712yes—
448D4—22no—
449D4—22no—
450D4—21no—
451D4C4×D4×C12712yes—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4#121×C12711yescharacteristic
467C2×C4#121×C12711yescharacteristic
468C2×C4#121×C12711yescharacteristic
469C2×C4#121×C12711yescharacteristic
470C2×C4C23×C4×C12711yescharacteristic
471C2×C4C22×D4×C12711yescharacteristic
472C2×C4C22×D4×C12711yescharacteristic
473C2×C4C2×#41×C12711yescharacteristic
474C2×C4C2×#41×C12711yescharacteristic
475C2×C4C2×#41×C12711yescharacteristic
476C8—22no—
477C8—24no—
478C8—21no—
479C8—22no—
480C8—21no—
481C8—42no—
482C8C4×D4×C12712yes—
483C8C4×D4×C12712yes—
484C22—21no—
485C22—21no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22C4×#41×C12711yescharacteristic
490C22C2×#121×C12711yescharacteristic
491C22#529×C12711yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—22no—
496C4—41no—
497C4—41no—
498C4—44no—
499C4—82no—
500C4#473×C12712yesdirect product factor
501C4C2×C4×D4×C12711yescharacteristic
502C4C2×C4×D4×C12711yescharacteristic
503C4#525×C12711yescharacteristic
504C4#532×C12711yescharacteristic
505C2—21no—
506C2—21no—
507C2—42no—
508C2C4×#121×C12711yescharacteristic
509C2C2×#473×C12711yescharacteristic
510C2C127×#306711yescharacteristic
subgroupG/H
centerC2×C4×C127#121
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C2×#121
prime radicalC2×#41×C127C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q16×C127C2semidirect
5. C127×#1979C2semidirect
6. C127×#1952C2semidirect
7. C127×#1930C2semidirect
10. C4×#108×C127C2semidirect
11. C4×#101×C127C2semidirect
18. #473×C127C4direct (N × H)
56. C2×Q16×C127C2×C4semidirect
90. #108×C127C2×C4semidirect
102. #101×C127C2×C4semidirect
244. C4×C127#473direct (N × H)
249. C4×#473C127direct (N × H)
258. C2×C4×Q16C2×C127semidirect
260. #1979C2×C127semidirect
261. #1952C2×C127semidirect
262. #1930C2×C127semidirect
265. C4×#108C2×C127semidirect
266. C4×#101C2×C127semidirect
267. C127C4×#473direct (N × H)
274. #473C4×C127direct (N × H)
312. C2×Q16C2×C4×C127semidirect
346. #108C2×C4×C127semidirect
358. #101C2×C4×C127semidirect
500. C4#473×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#473×C1272
C4×#137×C1272
C2×C4×Q16×C1272
C4×#131×C1272
C127×#19792
C127×#19522
C127×#19302
C127×#19082
C127×#18162
C4×#108×C1272
C4×#101×C1272
C4×#473127