Finite Group Databasebeta

← C127×#9341 #44573014

Subgroups — C127×#9341 #44573014

Order 32512.

534 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3193C211yesmaximal, characteristic
2C127×#2377C211yesmaximal, characteristic
3C127×#1996C211yesmaximal, characteristic, complemented
4C127×#1511C211yesmaximal, characteristic, complemented
5C127×#1507C211yesmaximal, characteristic
6C127×#1305C211yesmaximal, characteristic, complemented
7C127×#1284C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×#121×C127C2211yescharacteristic
10#484×C127—21no—
11#480×C127C412yescomplemented
12#468×C127—22no—
13#450×C127—21no—
14#448×C127C412yescomplemented
15#407×C127C2211yescharacteristic
16#407×C127C2211yescharacteristic
17#390×C127—21no—
18#388×C127—21no—
19#387×C127—21no—
20#386×C127—21no—
21#386×C127—21no—
22#385×C127—21no—
23#381×C127C2211yescharacteristic
24#380×C127C2211yescharacteristic
25C4×C22⋊C4×C127C2211yescharacteristic
26#342×C127—21no—
27#342×C127—21no—
28#328×C127—21no—
29#328×C127—21no—
30#327×C127—22no—
31C22×Q8×C127C2×C411yescharacteristic, complemented
32C22×D4×C127—21no—
33C22×D4×C127D411yescharacteristic
34C23×C4×C127—21no—
35C23×C4×C127C2311yescharacteristic
36C2×SD16×C127—22no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43#121×C127—21no—
44#121×C127—21no—
45#121×C127C2×C412yes—
46#121×C127D412yes—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127—21no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127D411yescharacteristic
60C2×C22⋊C4×C127D411yescharacteristic
61C2×C42×C127—21no—
62C2×C42×C127—21no—
63#107×C127—22no—
64#103×C127—22no—
65#102×C127—22no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127—21no—
68C22⋊C8×C127—21no—
69C22⋊C8×C127C2×C412yescomplemented
70#95×C127—21no—
71#95×C127—21no—
72#95×C127—21no—
73#95×C127—21no—
74#95×C127—21no—
75#95×C127D411yescharacteristic
76#95×C127D411yescharacteristic
77C24×C127—21no—
78C24×C127C2×D411yescharacteristic
79C2×Q8×C127—21no—
80C2×Q8×C127—21no—
81C2×Q8×C127—81no—
82C2×D4×C127—22no—
83C2×D4×C127—22no—
84C2×D4×C127—21no—
85C2×D4×C127—81no—
86C2×D4×C127—81no—
87C2×D4×C127—81no—
88C2×D4×C127C22⋊C412yes—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—41no—
97C22×C4×C127—81no—
98C22×C4×C127—81no—
99C22×C4×C127—81no—
100C22×C4×C127—81no—
101C22×C4×C127C22×C411yescharacteristic
102C22×C4×C127C2×D411yescharacteristic
103C22×C4×C127C2×D411yescharacteristic
104C22×C4×C127C2×D411yescharacteristic
105C22×C4×C127#4111yescharacteristic
106C22×C4×C127#4111yescharacteristic
107SD16×C127—82no—
108M16×C127—81no—
109M16×C127—81no—
110C2×C8×C127—22no—
111C2×C8×C127—41no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—41no—
117C4⋊C4×C127—81no—
118C4⋊C4×C127—81no—
119C4⋊C4×C127C22⋊C412yes—
120C22⋊C4×C127—22no—
121C22⋊C4×C127—22no—
122C22⋊C4×C127—22no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—41no—
127C22⋊C4×C127—41no—
128C22⋊C4×C127—81no—
129C22⋊C4×C127—81no—
130C22⋊C4×C127—81no—
131C22⋊C4×C127—81no—
132C42×C127—81no—
133C42×C127—81no—
134C23×C127—21no—
135C23×C127—21no—
136C23×C127—22no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127C4×D411yescharacteristic
146C23×C127#12011yescharacteristic
147C23×C127#12111yescharacteristic
148Q8×C127—42no—
149Q8×C127—81no—
150D4×C127—42no—
151D4×C127—81no—
152D4×C127—82no—
153D4×C127—82no—
154C2×C4×C127—22no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—42no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
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—81no—
179C2×C4×C127—81no—
180C2×C4×C127—84no—
181C2×C4×C127—81no—
182C2×C4×C127—81no—
183C2×C4×C127C2×C22⋊C411yescharacteristic
184C2×C4×C127C4×D411yescharacteristic
185C2×C4×C127#12111yescharacteristic
186C2×C4×C127#12311yescharacteristic
187C8×C127—42no—
188C8×C127—81no—
189C22×C127—21no—
190C22×C127—21no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—42no—
198C22×C127—42no—
199C22×C127—42no—
200C22×C127—81no—
201C22×C127—81no—
202C22×C127—81no—
203C22×C127—81no—
204C22×C127—81no—
205C22×C127—81no—
206C22×C127#38611yescharacteristic
207C22×C127#45511yescharacteristic
208C22×C127#45611yescharacteristic
209C4×C127—21no—
210C4×C127—21no—
211C4×C127—21no—
212C4×C127—21no—
213C4×C127—42no—
214C4×C127—81no—
215C4×C127—81no—
216C4×C127—81no—
217C4×C127—81no—
218C4×C127—82no—
219C4×C127—81no—
220C4×C127—81no—
221#9341C12711yesmaximal, characteristic, direct product factor, Sylow
222C2×C127—21no—
223C2×C127—21no—
224C2×C127—41no—
225C2×C127—41no—
226C2×C127—82no—
227C2×C127#188211yescharacteristic
228C2×C127#190411yescharacteristic
229C2×C127#191311yescharacteristic
230#3193C2×C12711yescharacteristic
231#2377C2×C12711yescharacteristic
232#1996C2×C12711yescharacteristic, complemented
233#1511C2×C12711yescharacteristic, complemented
234#1507C2×C12711yescharacteristic
235#1305C2×C12711yescharacteristic, complemented
236#1284C2×C12711yescharacteristic, complemented
237C127#934111yescharacteristic, direct product factor, Sylow
238C2×C22⋊Q8C22×C12711yescharacteristic
239C2×#121C22×C12711yescharacteristic
240#484—21no—
241#480C4×C12712yescomplemented
242#468—22no—
243#450—21no—
244#448C4×C12712yescomplemented
245#407C22×C12711yescharacteristic
246#407C22×C12711yescharacteristic
247#390—21no—
248#388—21no—
249#387—21no—
250#386—21no—
251#386—21no—
252#385—21no—
253#381C22×C12711yescharacteristic
254#380C22×C12711yescharacteristic
255C4×C22⋊C4C22×C12711yescharacteristic
256#342—21no—
257#342—21no—
258#328—21no—
259#328—21no—
260#327—22no—
261C22×Q8C2×C4×C12711yescharacteristic, complemented
262C22×D4—21no—
263C22×D4D4×C12711yescharacteristic
264C23×C4—21no—
265C23×C4C23×C12711yescharacteristic
266C2×SD16—22no—
267C2×M16—21no—
268C2×M16—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273#121—21no—
274#121—21no—
275#121C2×C4×C12712yes—
276#121D4×C12712yes—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
281C2×C4⋊C4D4×C12711yescharacteristic
282C2×C22⋊C4—21no—
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⋊C4D4×C12711yescharacteristic
290C2×C22⋊C4D4×C12711yescharacteristic
291C2×C42—21no—
292C2×C42—21no—
293#107—22no—
294#103—22no—
295#102—22no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8C2×C4×C12712yescomplemented
300#95—21no—
301#95—21no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95D4×C12711yescharacteristic
306#95D4×C12711yescharacteristic
307C24—21no—
308C24C2×D4×C12711yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—81no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—21no—
315C2×D4—81no—
316C2×D4—81no—
317C2×D4—81no—
318C2×D4C22⋊C4×C12712yes—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—81no—
328C22×C4—81no—
329C22×C4—81no—
330C22×C4—81no—
331C22×C4C22×C4×C12711yescharacteristic
332C22×C4C2×D4×C12711yescharacteristic
333C22×C4C2×D4×C12711yescharacteristic
334C22×C4C2×D4×C12711yescharacteristic
335C22×C4#41×C12711yescharacteristic
336C22×C4#41×C12711yescharacteristic
337SD16—82no—
338M16—81no—
339M16—81no—
340C2×C8—22no—
341C2×C8—41no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—81no—
348C4⋊C4—81no—
349C4⋊C4C22⋊C4×C12712yes—
350C22⋊C4—22no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—81no—
359C22⋊C4—81no—
360C22⋊C4—81no—
361C22⋊C4—81no—
362C42—81no—
363C42—81no—
364C23—21no—
365C23—21no—
366C23—22no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23C4×D4×C12711yescharacteristic
376C23#120×C12711yescharacteristic
377C23#121×C12711yescharacteristic
378Q8—42no—
379Q8—81no—
380D4—42no—
381D4—81no—
382D4—82no—
383D4—82no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—84no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4C2×C22⋊C4×C12711yescharacteristic
414C2×C4C4×D4×C12711yescharacteristic
415C2×C4#121×C12711yescharacteristic
416C2×C4#123×C12711yescharacteristic
417C8—42no—
418C8—81no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22#386×C12711yescharacteristic
437C22#455×C12711yescharacteristic
438C22#456×C12711yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—42no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4—82no—
449C4—81no—
450C4—81no—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—82no—
456C2C127×#188211yescharacteristic
457C2C127×#190411yescharacteristic
458C2C127×#191311yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#121×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1996C2semidirect
4. C127×#1511C2semidirect
6. C127×#1305C2semidirect
7. C127×#1284C2semidirect
11. #480×C127C4semidirect
14. #448×C127C4semidirect
31. C22×Q8×C127C2×C4semidirect
50. C2×C4⋊C4×C127C2×C4semidirect
69. C22⋊C8×C127C2×C4semidirect
221. #9341C127direct (N × H)
232. #1996C2×C127semidirect
233. #1511C2×C127semidirect
235. #1305C2×C127semidirect
236. #1284C2×C127semidirect
237. C127#9341direct (N × H)
241. #480C4×C127semidirect
244. #448C4×C127semidirect
261. C22×Q8C2×C4×C127semidirect
280. C2×C4⋊C4C2×C4×C127semidirect
299. C22⋊C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31932
C127×#23772
C127×#19962
C127×#15112
C127×#15072
C127×#13052
C127×#12842
#9341127