Finite Group Databasebeta

← C127×#11692 #44575365

Subgroups — C127×#11692 #44575365

Order 32512.

670 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2617C211yesmaximal, characteristic
2C2×#342×C127C211yesmaximal, characteristic, complemented
3C2×#323×C127C211yesmaximal, characteristic, complemented
4C127×#1344C212yesmaximal, complemented
5C127×#1343C212yesmaximal, complemented
6C2×#121×C127C411yescharacteristic, complemented
7C2×#120×C127—21no—
8C22×C22⋊C4×C127—21no—
9C22×C22⋊C4×C127C2211yescharacteristic
10C2×C22⋊C8×C127—21no—
11#397×C127C411yescharacteristic, complemented
12#397×C127C2211yescharacteristic
13#394×C127—21no—
14#394×C127—21no—
15#392×C127C411yescharacteristic, complemented
16#392×C127C2211yescharacteristic
17#386×C127—21no—
18#380×C127C411yescharacteristic, complemented
19#342×C127—21no—
20#342×C127C2212yes—
21#323×C127—21no—
22#323×C127C2212yes—
23C25×C127D411yescharacteristic
24C22×D4×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127—21no—
27C22×D4×C127C2×C411yescharacteristic, complemented
28C23×C4×C127—41no—
29C23×C4×C127C2×C411yescharacteristic
30C23×C4×C127D411yescharacteristic
31C22×C8×C127—41no—
32#121×C127—41no—
33#121×C127—41no—
34#120×C127—42no—
35#120×C127—42no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
38C2×C22⋊C4×C127—24no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—41no—
47C2×C22⋊C4×C127—41no—
48C2×C22⋊C4×C127—41no—
49C2×C22⋊C4×C127—42no—
50C2×C22⋊C4×C127C2×C411yescharacteristic
51C2×C22⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127D411yescharacteristic
53C2×C22⋊C4×C127C2311yescharacteristic
54C22⋊C8×C127—22no—
55C22⋊C8×C127—41no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127C2×C411yescharacteristic, complemented
59#95×C127C2×C411yescharacteristic, complemented
60C24×C127—21no—
61C24×C127—21no—
62C24×C127—22no—
63C24×C127—21no—
64C24×C127—81no—
65C24×C127—81no—
66C24×C127C22⋊C411yescharacteristic
67C24×C127C22⋊C411yescharacteristic
68C24×C127D812yes—
69C24×C127SD1612yes—
70C24×C127C2×D411yescharacteristic
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—42no—
75C2×D4×C127—42no—
76C2×D4×C127—42no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—81no—
80C2×D4×C127—81no—
81C2×D4×C127—81no—
82C2×D4×C127—81no—
83C2×D4×C127—81no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—44no—
92C22×C4×C127—42no—
93C22×C4×C127—81no—
94C22×C4×C127—81no—
95C22×C4×C127—82no—
96C22×C4×C127—82no—
97C22×C4×C127C22⋊C411yescharacteristic
98C22×C4×C127C22⋊C411yescharacteristic
99C22×C4×C127C22×C411yescharacteristic
100C22×C4×C127C2×D411yescharacteristic
101C2×C8×C127—42no—
102C2×C8×C127—82no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—81no—
105C22⋊C4×C127—24no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—42no—
111C22⋊C4×C127—44no—
112C22⋊C4×C127—42no—
113C22⋊C4×C127—42no—
114C22⋊C4×C127—42no—
115C22⋊C4×C127—41no—
116C22⋊C4×C127—41no—
117C22⋊C4×C127—81no—
118C22⋊C4×C127—81no—
119C23×C127—22no—
120C23×C127—22no—
121C23×C127—21no—
122C23×C127—21no—
123C23×C127—22no—
124C23×C127—22no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—41no—
128C23×C127—41no—
129C23×C127—42no—
130C23×C127—42no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—81no—
143C23×C127—81no—
144C23×C127—82no—
145C23×C127—82no—
146C23×C127—84no—
147C23×C127#9911yescharacteristic
148C23×C127#9911yescharacteristic
149C23×C127#10212yes—
150C23×C127#10212yes—
151C23×C127#10412yes—
152C23×C127C2×C22⋊C411yescharacteristic
153C23×C127C2×D811yescharacteristic
154C23×C127C2×SD1611yescharacteristic
155D4×C127—82no—
156D4×C127—84no—
157D4×C127—82no—
158D4×C127—82no—
159D4×C127—82no—
160D4×C127—82no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—21no—
164C2×C4×C127—21no—
165C2×C4×C127—42no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—44no—
171C2×C4×C127—41no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—41no—
179C2×C4×C127—41no—
180C2×C4×C127—81no—
181C2×C4×C127—81no—
182C2×C4×C127—81no—
183C2×C4×C127—88no—
184C2×C4×C127—82no—
185C2×C4×C127—82no—
186C8×C127—82no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—21no—
194C22×C127—22no—
195C22×C127—21no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—42no—
199C22×C127—41no—
200C22×C127—41no—
201C22×C127—44no—
202C22×C127—44no—
203C22×C127—41no—
204C22×C127—41no—
205C22×C127—41no—
206C22×C127—41no—
207C22×C127—81no—
208C22×C127—81no—
209C22×C127—82no—
210C22×C127—82no—
211C22×C127—81no—
212C22×C127—81no—
213C22×C127—81no—
214C22×C127—81no—
215C22×C127—81no—
216C22×C127—81no—
217C22×C127—81no—
218C22×C127#32712yes—
219C22×C127#32712yes—
220C22×C127C2×#9911yescharacteristic
221C22×C127C2×#10211yescharacteristic
222C22×C127C2×#10411yescharacteristic
223C4×C127—41no—
224C4×C127—41no—
225C4×C127—41no—
226C4×C127—41no—
227C4×C127—81no—
228C4×C127—81no—
229C4×C127—84no—
230C4×C127—81no—
231#11692C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—21no—
233C2×C127—22no—
234C2×C127—21no—
235C2×C127—22no—
236C2×C127—41no—
237C2×C127—42no—
238C2×C127—41no—
239C2×C127—161no—
240C2×C127C2×#32711yescharacteristic
241C2×C127#212111yescharacteristic
242C2×C127#212711yescharacteristic
243#2617C2×C12711yescharacteristic
244C2×#342C2×C12711yescharacteristic, complemented
245C2×#323C2×C12711yescharacteristic, complemented
246#1344C2×C12712yescomplemented
247#1343C2×C12712yescomplemented
248C127#1169211yescharacteristic, direct product factor, Sylow
249C2×#121C4×C12711yescharacteristic, complemented
250C2×#120—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4C22×C12711yescharacteristic
253C2×C22⋊C8—21no—
254#397C4×C12711yescharacteristic, complemented
255#397C22×C12711yescharacteristic
256#394—21no—
257#394—21no—
258#392C4×C12711yescharacteristic, complemented
259#392C22×C12711yescharacteristic
260#386—21no—
261#380C4×C12711yescharacteristic, complemented
262#342—21no—
263#342C22×C12712yes—
264#323—21no—
265#323C22×C12712yes—
266C25D4×C12711yescharacteristic
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4C2×C4×C12711yescharacteristic, complemented
271C23×C4—41no—
272C23×C4C2×C4×C12711yescharacteristic
273C23×C4D4×C12711yescharacteristic
274C22×C8—41no—
275#121—41no—
276#121—41no—
277#120—42no—
278#120—42no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
281C2×C22⋊C4—24no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—41no—
290C2×C22⋊C4—41no—
291C2×C22⋊C4—41no—
292C2×C22⋊C4—42no—
293C2×C22⋊C4C2×C4×C12711yescharacteristic
294C2×C22⋊C4D4×C12711yescharacteristic
295C2×C22⋊C4D4×C12711yescharacteristic
296C2×C22⋊C4C23×C12711yescharacteristic
297C22⋊C8—22no—
298C22⋊C8—41no—
299#95—21no—
300#95—21no—
301#95C2×C4×C12711yescharacteristic, complemented
302#95C2×C4×C12711yescharacteristic, complemented
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—81no—
308C24—81no—
309C24C22⋊C4×C12711yescharacteristic
310C24C22⋊C4×C12711yescharacteristic
311C24D8×C12712yes—
312C24SD16×C12712yes—
313C24C2×D4×C12711yescharacteristic
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—42no—
318C2×D4—42no—
319C2×D4—42no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—81no—
323C2×D4—81no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4—81no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—44no—
335C22×C4—42no—
336C22×C4—81no—
337C22×C4—81no—
338C22×C4—82no—
339C22×C4—82no—
340C22×C4C22⋊C4×C12711yescharacteristic
341C22×C4C22⋊C4×C12711yescharacteristic
342C22×C4C22×C4×C12711yescharacteristic
343C22×C4C2×D4×C12711yescharacteristic
344C2×C8—42no—
345C2×C8—82no—
346C4⋊C4—41no—
347C4⋊C4—81no—
348C22⋊C4—24no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—42no—
354C22⋊C4—44no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—81no—
361C22⋊C4—81no—
362C23—22no—
363C23—22no—
364C23—21no—
365C23—21no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—41no—
371C23—41no—
372C23—42no—
373C23—42no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—81no—
386C23—81no—
387C23—82no—
388C23—82no—
389C23—84no—
390C23#99×C12711yescharacteristic
391C23#99×C12711yescharacteristic
392C23#102×C12712yes—
393C23#102×C12712yes—
394C23#104×C12712yes—
395C23C2×C22⋊C4×C12711yescharacteristic
396C23C2×D8×C12711yescharacteristic
397C23C2×SD16×C12711yescharacteristic
398D4—82no—
399D4—84no—
400D4—82no—
401D4—82no—
402D4—82no—
403D4—82no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—88no—
427C2×C4—82no—
428C2×C4—82no—
429C8—82no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—21no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—41no—
443C22—41no—
444C22—44no—
445C22—44no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—81no—
451C22—81no—
452C22—82no—
453C22—82no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#327×C12712yes—
462C22#327×C12712yes—
463C22C2×#99×C12711yescharacteristic
464C22C2×#102×C12711yescharacteristic
465C22C2×#104×C12711yescharacteristic
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—81no—
471C4—81no—
472C4—84no—
473C4—81no—
474C2—21no—
475C2—22no—
476C2—21no—
477C2—22no—
478C2—41no—
479C2—42no—
480C2—41no—
481C2—161no—
482C2C2×#327×C12711yescharacteristic
483C2C127×#212111yescharacteristic
484C2C127×#212711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC127×#2617C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#342×C127C2semidirect
3. C2×#323×C127C2semidirect
4. C127×#1344C2semidirect
5. C127×#1343C2semidirect
6. C2×#121×C127C4semidirect
11. #397×C127C4semidirect
15. #392×C127C4semidirect
18. #380×C127C4semidirect
27. C22×D4×C127C2×C4semidirect
37. C2×C4⋊C4×C127C2×C4semidirect
58. #95×C127C2×C4semidirect
59. #95×C127C2×C4semidirect
231. #11692C127direct (N × H)
244. C2×#342C2×C127semidirect
245. C2×#323C2×C127semidirect
246. #1344C2×C127semidirect
247. #1343C2×C127semidirect
248. C127#11692direct (N × H)
249. C2×#121C4×C127semidirect
254. #397C4×C127semidirect
258. #392C4×C127semidirect
261. #380C4×C127semidirect
270. C22×D4C2×C4×C127semidirect
280. C2×C4⋊C4C2×C4×C127semidirect
301. #95C2×C4×C127semidirect
302. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26172
C2×#342×C1272
C2×#323×C1272
C127×#13442
C127×#13432
#11692127