Finite Group Databasebeta

← C127×#11333 #44575006

Subgroups — C127×#11333 #44575006

Order 32512.

726 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2911C211yesmaximal, characteristic
2C2×#428×C127C211yesmaximal, characteristic
3C127×#2317C211yesmaximal, characteristic
4C2×#344×C127C211yesmaximal, characteristic
5C127×#1740C211yesmaximal, characteristic
6C127×#1736C211yesmaximal, characteristic
7C127×#1733C211yesmaximal, characteristic
8C22×M16×C127C2211yescharacteristic
9C22×M16×C127C2211yescharacteristic
10C2×#117×C127C2211yescharacteristic
11C2×#117×C127C2211yescharacteristic
12C2×#117×C127C2211yescharacteristic
13C2×#117×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15#428×C127—22no—
16#428×C127—22no—
17#428×C127—21no—
18#428×C127—21no—
19#428×C127—21no—
20#428×C127—21no—
21#427×C127—22no—
22C2×#107×C127—21no—
23C2×#106×C127—21no—
24#389×C127—22no—
25#385×C127—22no—
26#384×C127—21no—
27#382×C127—21no—
28#344×C127C414yescomplemented
29#342×C127—22no—
30#340×C127—22no—
31#339×C127—22no—
32C23×C4×C127—21no—
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×C127C2×C412yes—
42C2×M16×C127C2×C412yes—
43C2×M16×C127D412yes—
44C2×M16×C127Q812yes—
45C2×M16×C127Q812yes—
46C22×C8×C127—21no—
47C22×C8×C127D412yes—
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×C127—21no—
55#117×C127—21no—
56#117×C127—21no—
57#117×C127—21no—
58#117×C127—21no—
59#117×C127—21no—
60#117×C127—21no—
61#117×C127C2×C412yes—
62#117×C127Q812yes—
63#117×C127Q812yes—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127—21no—
67C2×C4⋊C4×C127—21no—
68C2×C4⋊C4×C127—21no—
69C2×C4⋊C4×C127—21no—
70C2×C4⋊C4×C127—21no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127D412yes—
73C2×C4⋊C4×C127D411yescharacteristic
74C2×C4⋊C4×C127D411yescharacteristic
75C2×C4⋊C4×C127D411yescharacteristic
76C2×C4⋊C4×C127D411yescharacteristic
77C2×C22⋊C4×C127—21no—
78C2×C22⋊C4×C127—21no—
79C2×C22⋊C4×C127—21no—
80C2×C22⋊C4×C127D412yes—
81C2×C42×C127—21no—
82C2×C42×C127—21no—
83C2×C42×C127—21no—
84C2×C42×C127—21no—
85#107×C127—24no—
86#107×C127—22no—
87#107×C127—22no—
88#106×C127—24no—
89#106×C127—22no—
90#106×C127—22no—
91#95×C127—24no—
92C24×C127C2×D411yescharacteristic
93C22×C4×C127—22no—
94C22×C4×C127—21no—
95C22×C4×C127—22no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127—82no—
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—22no—
123M16×C127—22no—
124M16×C127C4⋊C414yescomplemented
125C2×C8×C127—22no—
126C2×C8×C127—22no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127C4⋊C414yescomplemented
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—21no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—21no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—21no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—21no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—41no—
145C4⋊C4×C127—41no—
146C4⋊C4×C127—41no—
147C4⋊C4×C127—84no—
148C22⋊C4×C127—22no—
149C22⋊C4×C127—22no—
150C22⋊C4×C127—41no—
151C22⋊C4×C127—41no—
152C22⋊C4×C127—41no—
153C22⋊C4×C127—41no—
154C22⋊C4×C127—41no—
155C22⋊C4×C127C4⋊C414yes—
156C42×C127—22no—
157C42×C127—22no—
158C42×C127—22no—
159C42×C127—41no—
160C42×C127—41no—
161C42×C127—41no—
162C42×C127—41no—
163C42×C127—41no—
164C23×C127—41no—
165C23×C127—41no—
166C23×C127C2×C4⋊C411yescharacteristic
167C23×C127#12011yescharacteristic
168C23×C127#12111yescharacteristic
169C23×C127C22⋊Q811yescharacteristic
170C23×C127#12311yescharacteristic
171C23×C127#12711yescharacteristic
172C23×C127C4⋊Q811yescharacteristic
173C2×C4×C127—24no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—44no—
178C2×C4×C127—42no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—81no—
186C2×C4×C127—81no—
187C2×C4×C127—82no—
188C2×C4×C127—82no—
189C2×C4×C127—81no—
190C2×C4×C127—81no—
191C2×C4×C127C2×C4⋊C411yescharacteristic
192C2×C4×C127C2×C4⋊C411yescharacteristic
193C2×C4×C127C4×D411yescharacteristic
194C2×C4×C127C4×D411yescharacteristic
195C2×C4×C127C4×D411yescharacteristic
196C2×C4×C127C4×Q811yescharacteristic
197C2×C4×C127#12011yescharacteristic
198C2×C4×C127#12011yescharacteristic
199C2×C4×C127#12111yescharacteristic
200C2×C4×C127#12111yescharacteristic
201C2×C4×C127C22⋊Q811yescharacteristic
202C2×C4×C127C22⋊Q811yescharacteristic
203C2×C4×C127C22⋊Q811yescharacteristic
204C2×C4×C127C22⋊Q811yescharacteristic
205C2×C4×C127C22⋊Q811yescharacteristic
206C2×C4×C127C22⋊Q811yescharacteristic
207C2×C4×C127C22⋊Q811yescharacteristic
208C2×C4×C127C22⋊Q811yescharacteristic
209C2×C4×C127#12311yescharacteristic
210C2×C4×C127#12311yescharacteristic
211C2×C4×C127#12511yescharacteristic
212C2×C4×C127#12511yescharacteristic
213C2×C4×C127#12511yescharacteristic
214C2×C4×C127C4⋊Q811yescharacteristic
215C2×C4×C127C4⋊Q811yescharacteristic
216C2×C4×C127C4⋊Q811yescharacteristic
217C2×C4×C127C4⋊Q811yescharacteristic
218C2×C4×C127C4⋊Q811yescharacteristic
219C8×C127—24no—
220C8×C127—24no—
221C22×C127—21no—
222C22×C127—21no—
223C22×C127—21no—
224C22×C127—21no—
225C22×C127—21no—
226C22×C127—21no—
227C22×C127—41no—
228C22×C127—41no—
229C22×C127—41no—
230C22×C127—41no—
231C22×C127#38411yescharacteristic
232C22×C127#38511yescharacteristic
233C22×C127#38911yescharacteristic
234C22×C127#39211yescharacteristic
235C22×C127#39511yescharacteristic
236C22×C127#39811yescharacteristic
237C22×C127#39911yescharacteristic
238C4×C127—44no—
239C4×C127—82no—
240C4×C127—81no—
241C4×C127—82no—
242C4×C127—81no—
243C4×C127—81no—
244C4×C127—81no—
245C4×C127#38511yescharacteristic
246C4×C127#38511yescharacteristic
247C4×C127#38911yescharacteristic
248C4×C127#38911yescharacteristic
249C4×C127#39511yescharacteristic
250C4×C127#39511yescharacteristic
251C4×C127#39811yescharacteristic
252C4×C127#39811yescharacteristic
253#11333C12711yesmaximal, characteristic, direct product factor, Sylow
254C2×C127—21no—
255C2×C127—21no—
256C2×C127—21no—
257C2×C127—21no—
258C2×C127—21no—
259C2×C127—21no—
260C2×C127#144411yescharacteristic
261C2×C127#200811yescharacteristic
262C2×C127#200911yescharacteristic
263#2911C2×C12711yescharacteristic
264C2×#428C2×C12711yescharacteristic
265#2317C2×C12711yescharacteristic
266C2×#344C2×C12711yescharacteristic
267#1740C2×C12711yescharacteristic
268#1736C2×C12711yescharacteristic
269#1733C2×C12711yescharacteristic
270C127#1133311yescharacteristic, direct product factor, Sylow
271C22×M16C22×C12711yescharacteristic
272C22×M16C22×C12711yescharacteristic
273C2×#117C22×C12711yescharacteristic
274C2×#117C22×C12711yescharacteristic
275C2×#117C22×C12711yescharacteristic
276C2×#117C22×C12711yescharacteristic
277C22×C4⋊C4C22×C12711yescharacteristic
278#428—22no—
279#428—22no—
280#428—21no—
281#428—21no—
282#428—21no—
283#428—21no—
284#427—22no—
285C2×#107—21no—
286C2×#106—21no—
287#389—22no—
288#385—22no—
289#384—21no—
290#382—21no—
291#344C4×C12714yescomplemented
292#342—22no—
293#340—22no—
294#339—22no—
295C23×C4—21no—
296C23×C4C23×C12711yescharacteristic
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16—21no—
303C2×M16—21no—
304C2×M16C2×C4×C12712yes—
305C2×M16C2×C4×C12712yes—
306C2×M16D4×C12712yes—
307C2×M16Q8×C12712yes—
308C2×M16Q8×C12712yes—
309C22×C8—21no—
310C22×C8D4×C12712yes—
311#117—21no—
312#117—21no—
313#117—21no—
314#117—21no—
315#117—21no—
316#117—21no—
317#117—21no—
318#117—21no—
319#117—21no—
320#117—21no—
321#117—21no—
322#117—21no—
323#117—21no—
324#117C2×C4×C12712yes—
325#117Q8×C12712yes—
326#117Q8×C12712yes—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4D4×C12712yes—
336C2×C4⋊C4D4×C12711yescharacteristic
337C2×C4⋊C4D4×C12711yescharacteristic
338C2×C4⋊C4D4×C12711yescharacteristic
339C2×C4⋊C4D4×C12711yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4D4×C12712yes—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348#107—24no—
349#107—22no—
350#107—22no—
351#106—24no—
352#106—22no—
353#106—22no—
354#95—24no—
355C24C2×D4×C12711yescharacteristic
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—82no—
366C22×C4C22×C4×C12711yescharacteristic
367C22×C4C2×D4×C12711yescharacteristic
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C2×D4×C12711yescharacteristic
370C22×C4C2×D4×C12711yescharacteristic
371C22×C4C2×D4×C12711yescharacteristic
372C22×C4C2×Q8×C12711yescharacteristic
373C22×C4C2×Q8×C12711yescharacteristic
374C22×C4C2×Q8×C12711yescharacteristic
375C22×C4C2×Q8×C12711yescharacteristic
376C22×C4#41×C12711yescharacteristic
377C22×C4#41×C12711yescharacteristic
378C22×C4#41×C12711yescharacteristic
379C22×C4#41×C12711yescharacteristic
380M16—22no—
381M16—22no—
382M16—22no—
383M16—22no—
384M16—22no—
385M16—22no—
386M16—22no—
387M16C4⋊C4×C12714yescomplemented
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8C4⋊C4×C12714yescomplemented
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—84no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4C4⋊C4×C12714yes—
419C42—22no—
420C42—22no—
421C42—22no—
422C42—41no—
423C42—41no—
424C42—41no—
425C42—41no—
426C42—41no—
427C23—41no—
428C23—41no—
429C23C2×C4⋊C4×C12711yescharacteristic
430C23#120×C12711yescharacteristic
431C23#121×C12711yescharacteristic
432C23C22⋊Q8×C12711yescharacteristic
433C23#123×C12711yescharacteristic
434C23#127×C12711yescharacteristic
435C23C4⋊Q8×C12711yescharacteristic
436C2×C4—24no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4C2×C4⋊C4×C12711yescharacteristic
455C2×C4C2×C4⋊C4×C12711yescharacteristic
456C2×C4C4×D4×C12711yescharacteristic
457C2×C4C4×D4×C12711yescharacteristic
458C2×C4C4×D4×C12711yescharacteristic
459C2×C4C4×Q8×C12711yescharacteristic
460C2×C4#120×C12711yescharacteristic
461C2×C4#120×C12711yescharacteristic
462C2×C4#121×C12711yescharacteristic
463C2×C4#121×C12711yescharacteristic
464C2×C4C22⋊Q8×C12711yescharacteristic
465C2×C4C22⋊Q8×C12711yescharacteristic
466C2×C4C22⋊Q8×C12711yescharacteristic
467C2×C4C22⋊Q8×C12711yescharacteristic
468C2×C4C22⋊Q8×C12711yescharacteristic
469C2×C4C22⋊Q8×C12711yescharacteristic
470C2×C4C22⋊Q8×C12711yescharacteristic
471C2×C4C22⋊Q8×C12711yescharacteristic
472C2×C4#123×C12711yescharacteristic
473C2×C4#123×C12711yescharacteristic
474C2×C4#125×C12711yescharacteristic
475C2×C4#125×C12711yescharacteristic
476C2×C4#125×C12711yescharacteristic
477C2×C4C4⋊Q8×C12711yescharacteristic
478C2×C4C4⋊Q8×C12711yescharacteristic
479C2×C4C4⋊Q8×C12711yescharacteristic
480C2×C4C4⋊Q8×C12711yescharacteristic
481C2×C4C4⋊Q8×C12711yescharacteristic
482C8—24no—
483C8—24no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22#384×C12711yescharacteristic
495C22#385×C12711yescharacteristic
496C22#389×C12711yescharacteristic
497C22#392×C12711yescharacteristic
498C22#395×C12711yescharacteristic
499C22#398×C12711yescharacteristic
500C22#399×C12711yescharacteristic
501C4—44no—
502C4—82no—
503C4—82no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—81no—
508C4#385×C12711yescharacteristic
509C4#385×C12711yescharacteristic
510C4#389×C12711yescharacteristic
511C4#389×C12711yescharacteristic
512C4#395×C12711yescharacteristic
513C4#395×C12711yescharacteristic
514C4#398×C12711yescharacteristic
515C4#398×C12711yescharacteristic
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2—21no—
521C2—21no—
522C2C127×#144411yescharacteristic
523C2C127×#200811yescharacteristic
524C2C127×#200911yescharacteristic
subgroupG/H
center, socleC22×C127#392
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
28. #344×C127C4semidirect
124. M16×C127C4⋊C4semidirect
130. C2×C8×C127C4⋊C4semidirect
253. #11333C127direct (N × H)
270. C127#11333direct (N × H)
291. #344C4×C127semidirect
387. M16C4⋊C4×C127semidirect
393. C2×C8C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29112
C2×#428×C1272
C127×#23172
C2×#344×C1272
C127×#17402
C127×#17362
C127×#17332
#11333127