Finite Group Databasebeta

← C127×#11339 #44575012

Subgroups — C127×#11339 #44575012

Order 32512.

806 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C127C211yesmaximal, characteristic
2C127×#2317C211yesmaximal, characteristic
3C2×#382×C127C211yesmaximal, characteristic
4C2×#343×C127C211yesmaximal, characteristic
5C127×#1736C211yesmaximal, characteristic
6C2×#339×C127C211yesmaximal, characteristic
7C2×#339×C127C211yesmaximal, characteristic
8C22×M16×C127C2211yescharacteristic
9C22×M16×C127C2211yescharacteristic
10C2×#117×C127C2211yescharacteristic
11C2×#117×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C42×C127C2211yescharacteristic
15#428×C127—22no—
16#428×C127—22no—
17C2×#107×C127—21no—
18C2×#106×C127—21no—
19#389×C127—22no—
20#385×C127—22no—
21#384×C127—21no—
22#382×C127—21no—
23#382×C127—22no—
24#382×C127—22no—
25C2×#95×C127—22no—
26#343×C127—22no—
27#340×C127—22no—
28#339×C127—22no—
29#339×C127C414yescomplemented
30C23×C4×C127—21no—
31C23×C4×C127—21no—
32C23×C4×C127D412yes—
33C23×C4×C127C2311yescharacteristic
34C2×M16×C127—21no—
35C2×M16×C127—21no—
36C2×M16×C127—21no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C2×M16×C127—21no—
42C2×M16×C127C2×C412yes—
43C2×M16×C127D412yes—
44C2×M16×C127Q812yes—
45C2×M16×C127Q812yes—
46C22×C8×C127—21no—
47C22×C8×C127—21no—
48#117×C127—21no—
49#117×C127—21no—
50#117×C127—21no—
51#117×C127—21no—
52#117×C127—21no—
53#117×C127—21no—
54#117×C127C2×C412yes—
55#117×C127Q812yes—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127—21no—
58C2×C4⋊C4×C127—21no—
59C2×C4⋊C4×C127—21no—
60C2×C4⋊C4×C127—21no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—24no—
68C2×C4⋊C4×C127D412yes—
69C2×C4⋊C4×C127D411yescharacteristic
70C2×C4⋊C4×C127D411yescharacteristic
71C2×C4⋊C4×C127D412yes—
72C2×C22⋊C4×C127—21no—
73C2×C22⋊C4×C127—21no—
74C2×C42×C127—21no—
75C2×C42×C127—21no—
76C2×C42×C127—21no—
77C2×C42×C127—21no—
78C2×C42×C127—21no—
79C2×C42×C127C2×C412yes—
80C2×C42×C127D412yes—
81C2×C42×C127Q812yes—
82#107×C127—24no—
83#106×C127—24no—
84#95×C127—28no—
85#95×C127—24no—
86C24×C127C2×D411yescharacteristic
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—22no—
97C22×C4×C127—42no—
98C22×C4×C127—42no—
99C22×C4×C127—44no—
100C22×C4×C127—44no—
101C22×C4×C127—41no—
102C22×C4×C127—41no—
103C22×C4×C127C22×C411yescharacteristic
104C22×C4×C127C2×D411yescharacteristic
105C22×C4×C127C2×D411yescharacteristic
106C22×C4×C127C2×D411yescharacteristic
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×Q811yescharacteristic
110C22×C4×C127C2×Q811yescharacteristic
111C22×C4×C127C2×Q811yescharacteristic
112C22×C4×C127C2×Q811yescharacteristic
113C22×C4×C127#4111yescharacteristic
114C22×C4×C127#4111yescharacteristic
115C22×C4×C127#4111yescharacteristic
116C22×C4×C127#4111yescharacteristic
117M16×C127—22no—
118M16×C127—22no—
119M16×C127—22no—
120M16×C127—22no—
121M16×C127—22no—
122M16×C127—41no—
123M16×C127—41no—
124M16×C127C4⋊C414yescomplemented
125C2×C8×C127—22no—
126C2×C8×C127—22no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—41no—
130C2×C8×C127—41no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—41no—
139C4⋊C4×C127—41no—
140C4⋊C4×C127—41no—
141C4⋊C4×C127—41no—
142C4⋊C4×C127—41no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127—84no—
145C4⋊C4×C127C4⋊C414yes—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—41no—
149C22⋊C4×C127—41no—
150C42×C127—22no—
151C42×C127—22no—
152C42×C127—22no—
153C42×C127—22no—
154C42×C127—22no—
155C42×C127—41no—
156C42×C127—41no—
157C42×C127C4⋊C414yescomplemented
158C23×C127—22no—
159C23×C127—22no—
160C23×C127C4×D411yescharacteristic
161C23×C127#12011yescharacteristic
162C23×C127#12011yescharacteristic
163C23×C127#12111yescharacteristic
164C23×C127C22⋊Q811yescharacteristic
165C23×C127C22⋊Q811yescharacteristic
166C23×C127C4⋊Q811yescharacteristic
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—44no—
170C2×C4×C127—44no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—44no—
176C2×C4×C127—44no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—44no—
184C2×C4×C127—82no—
185C2×C4×C127—82no—
186C2×C4×C127—82no—
187C2×C4×C127C2×C4⋊C411yescharacteristic
188C2×C4×C127C2×C4⋊C411yescharacteristic
189C2×C4×C127C2×C4⋊C411yescharacteristic
190C2×C4×C127C4×D411yescharacteristic
191C2×C4×C127C4×D411yescharacteristic
192C2×C4×C127C4×Q811yescharacteristic
193C2×C4×C127#12011yescharacteristic
194C2×C4×C127#12111yescharacteristic
195C2×C4×C127#12111yescharacteristic
196C2×C4×C127C22⋊Q811yescharacteristic
197C2×C4×C127C22⋊Q811yescharacteristic
198C2×C4×C127C22⋊Q811yescharacteristic
199C2×C4×C127C22⋊Q811yescharacteristic
200C2×C4×C127C22⋊Q811yescharacteristic
201C2×C4×C127C22⋊Q811yescharacteristic
202C2×C4×C127C22⋊Q811yescharacteristic
203C2×C4×C127#12311yescharacteristic
204C2×C4×C127#12311yescharacteristic
205C2×C4×C127#12311yescharacteristic
206C2×C4×C127#12511yescharacteristic
207C2×C4×C127#12511yescharacteristic
208C2×C4×C127#12511yescharacteristic
209C2×C4×C127#12711yescharacteristic
210C2×C4×C127C4⋊Q811yescharacteristic
211C2×C4×C127C4⋊Q811yescharacteristic
212C2×C4×C127C4⋊Q811yescharacteristic
213C2×C4×C127C4⋊Q811yescharacteristic
214C2×C4×C127C4⋊Q811yescharacteristic
215C8×C127—24no—
216C8×C127—42no—
217C22×C127—22no—
218C22×C127—22no—
219C22×C127—22no—
220C22×C127—22no—
221C22×C127—21no—
222C22×C127—21no—
223C22×C127—21no—
224C22×C127—21no—
225C22×C127#38511yescharacteristic
226C22×C127#38511yescharacteristic
227C22×C127#38911yescharacteristic
228C22×C127#39211yescharacteristic
229C22×C127#39511yescharacteristic
230C22×C127#39511yescharacteristic
231C22×C127#39811yescharacteristic
232C22×C127#45412yes—
233C22×C127#45512yes—
234C4×C127—44no—
235C4×C127—44no—
236C4×C127—81no—
237C4×C127—82no—
238C4×C127—81no—
239C4×C127—82no—
240C4×C127#38411yescharacteristic
241C4×C127#38511yescharacteristic
242C4×C127#38911yescharacteristic
243C4×C127#38911yescharacteristic
244C4×C127#39511yescharacteristic
245C4×C127#39811yescharacteristic
246C4×C127#39811yescharacteristic
247C4×C127#39911yescharacteristic
248#11339C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—21no—
250C2×C127—21no—
251C2×C127—21no—
252C2×C127—21no—
253C2×C127#144411yescharacteristic
254C2×C127#186012yes—
255C2×C127#200311yescharacteristic
256C2×C127#200411yescharacteristic
257C2×C127#206112yes—
258C2×#428C2×C12711yescharacteristic
259#2317C2×C12711yescharacteristic
260C2×#382C2×C12711yescharacteristic
261C2×#343C2×C12711yescharacteristic
262#1736C2×C12711yescharacteristic
263C2×#339C2×C12711yescharacteristic
264C2×#339C2×C12711yescharacteristic
265C127#1133911yescharacteristic, direct product factor, Sylow
266C22×M16C22×C12711yescharacteristic
267C22×M16C22×C12711yescharacteristic
268C2×#117C22×C12711yescharacteristic
269C2×#117C22×C12711yescharacteristic
270C22×C4⋊C4C22×C12711yescharacteristic
271C22×C4⋊C4C22×C12711yescharacteristic
272C22×C42C22×C12711yescharacteristic
273#428—22no—
274#428—22no—
275C2×#107—21no—
276C2×#106—21no—
277#389—22no—
278#385—22no—
279#384—21no—
280#382—21no—
281#382—22no—
282#382—22no—
283C2×#95—22no—
284#343—22no—
285#340—22no—
286#339—22no—
287#339C4×C12714yescomplemented
288C23×C4—21no—
289C23×C4—21no—
290C23×C4D4×C12712yes—
291C23×C4C23×C12711yescharacteristic
292C2×M16—21no—
293C2×M16—21no—
294C2×M16—21no—
295C2×M16—21no—
296C2×M16—21no—
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16C2×C4×C12712yes—
301C2×M16D4×C12712yes—
302C2×M16Q8×C12712yes—
303C2×M16Q8×C12712yes—
304C22×C8—21no—
305C22×C8—21no—
306#117—21no—
307#117—21no—
308#117—21no—
309#117—21no—
310#117—21no—
311#117—21no—
312#117C2×C4×C12712yes—
313#117Q8×C12712yes—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4D4×C12712yes—
327C2×C4⋊C4D4×C12711yescharacteristic
328C2×C4⋊C4D4×C12711yescharacteristic
329C2×C4⋊C4D4×C12712yes—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42C2×C4×C12712yes—
338C2×C42D4×C12712yes—
339C2×C42Q8×C12712yes—
340#107—24no—
341#106—24no—
342#95—28no—
343#95—24no—
344C24C2×D4×C12711yescharacteristic
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C22×C4×C12711yescharacteristic
362C22×C4C2×D4×C12711yescharacteristic
363C22×C4C2×D4×C12711yescharacteristic
364C22×C4C2×D4×C12711yescharacteristic
365C22×C4C2×D4×C12711yescharacteristic
366C22×C4C2×D4×C12711yescharacteristic
367C22×C4C2×Q8×C12711yescharacteristic
368C22×C4C2×Q8×C12711yescharacteristic
369C22×C4C2×Q8×C12711yescharacteristic
370C22×C4C2×Q8×C12711yescharacteristic
371C22×C4#41×C12711yescharacteristic
372C22×C4#41×C12711yescharacteristic
373C22×C4#41×C12711yescharacteristic
374C22×C4#41×C12711yescharacteristic
375M16—22no—
376M16—22no—
377M16—22no—
378M16—22no—
379M16—22no—
380M16—41no—
381M16—41no—
382M16C4⋊C4×C12714yescomplemented
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—41no—
388C2×C8—41no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—84no—
403C4⋊C4C4⋊C4×C12714yes—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C42—22no—
409C42—22no—
410C42—22no—
411C42—22no—
412C42—22no—
413C42—41no—
414C42—41no—
415C42C4⋊C4×C12714yescomplemented
416C23—22no—
417C23—22no—
418C23C4×D4×C12711yescharacteristic
419C23#120×C12711yescharacteristic
420C23#120×C12711yescharacteristic
421C23#121×C12711yescharacteristic
422C23C22⋊Q8×C12711yescharacteristic
423C23C22⋊Q8×C12711yescharacteristic
424C23C4⋊Q8×C12711yescharacteristic
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4C2×C4⋊C4×C12711yescharacteristic
446C2×C4C2×C4⋊C4×C12711yescharacteristic
447C2×C4C2×C4⋊C4×C12711yescharacteristic
448C2×C4C4×D4×C12711yescharacteristic
449C2×C4C4×D4×C12711yescharacteristic
450C2×C4C4×Q8×C12711yescharacteristic
451C2×C4#120×C12711yescharacteristic
452C2×C4#121×C12711yescharacteristic
453C2×C4#121×C12711yescharacteristic
454C2×C4C22⋊Q8×C12711yescharacteristic
455C2×C4C22⋊Q8×C12711yescharacteristic
456C2×C4C22⋊Q8×C12711yescharacteristic
457C2×C4C22⋊Q8×C12711yescharacteristic
458C2×C4C22⋊Q8×C12711yescharacteristic
459C2×C4C22⋊Q8×C12711yescharacteristic
460C2×C4C22⋊Q8×C12711yescharacteristic
461C2×C4#123×C12711yescharacteristic
462C2×C4#123×C12711yescharacteristic
463C2×C4#123×C12711yescharacteristic
464C2×C4#125×C12711yescharacteristic
465C2×C4#125×C12711yescharacteristic
466C2×C4#125×C12711yescharacteristic
467C2×C4#127×C12711yescharacteristic
468C2×C4C4⋊Q8×C12711yescharacteristic
469C2×C4C4⋊Q8×C12711yescharacteristic
470C2×C4C4⋊Q8×C12711yescharacteristic
471C2×C4C4⋊Q8×C12711yescharacteristic
472C2×C4C4⋊Q8×C12711yescharacteristic
473C8—24no—
474C8—42no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22#385×C12711yescharacteristic
484C22#385×C12711yescharacteristic
485C22#389×C12711yescharacteristic
486C22#392×C12711yescharacteristic
487C22#395×C12711yescharacteristic
488C22#395×C12711yescharacteristic
489C22#398×C12711yescharacteristic
490C22#454×C12712yes—
491C22#455×C12712yes—
492C4—44no—
493C4—44no—
494C4—82no—
495C4—81no—
496C4—82no—
497C4—81no—
498C4#384×C12711yescharacteristic
499C4#385×C12711yescharacteristic
500C4#389×C12711yescharacteristic
501C4#389×C12711yescharacteristic
502C4#395×C12711yescharacteristic
503C4#398×C12711yescharacteristic
504C4#398×C12711yescharacteristic
505C4#399×C12711yescharacteristic
506C2—21no—
507C2—21no—
508C2—21no—
509C2—21no—
510C2C127×#144411yescharacteristic
511C2C127×#186012yes—
512C2C127×#200311yescharacteristic
513C2C127×#200411yescharacteristic
514C2C127×#206112yes—
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
29. #339×C127C4semidirect
124. M16×C127C4⋊C4semidirect
157. C42×C127C4⋊C4semidirect
248. #11339C127direct (N × H)
265. C127#11339direct (N × H)
287. #339C4×C127semidirect
382. M16C4⋊C4×C127semidirect
415. C42C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C1272
C127×#23172
C2×#382×C1272
C2×#343×C1272
C127×#17362
C2×#339×C1272
#11339127