Finite Group Databasebeta

← C127×#8485 #44572158

Subgroups — C127×#8485 #44572158

Order 32512.

630 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3563C211yesmaximal, characteristic
2C127×#1998C211yesmaximal, characteristic, complemented
3C127×#1559C211yesmaximal, characteristic, complemented
4C127×#1529C211yesmaximal, characteristic
5C127×#1495C211yesmaximal, characteristic
6C127×#1485C211yesmaximal, characteristic, complemented
7C127×#1470C211yesmaximal, characteristic, complemented
8#564×C127—21no—
9#563×C127—21no—
10#557×C127—21no—
11#554×C127—21no—
12#552×C127—21no—
13#552×C127—22no—
14#552×C127—21no—
15#544×C127—21no—
16#544×C127C412yes—
17#541×C127—21no—
18#541×C127—22no—
19#539×C127C412yes—
20#533×C127C2211yescharacteristic
21#529×C127C2211yescharacteristic
22C2×#125×C127C2211yescharacteristic
23#432×C127C2211yescharacteristic
24#431×C127C2211yescharacteristic
25#423×C127C2211yescharacteristic
26C4×M16×C127C2211yescharacteristic
27#343×C127—21no—
28#343×C127—21no—
29#333×C127—21no—
30#332×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33Q8⋊C8×C127—22no—
34Q8⋊C8×C127—21no—
35D4⋊C8×C127—21no—
36#324×C127—22no—
37C2×M16×C127—21no—
38C2×M16×C127—21no—
39C4⋊Q8×C127—21no—
40C4⋊Q8×C127—22no—
41C4⋊Q8×C127—22no—
42C4⋊Q8×C127D411yescharacteristic
43C4⋊Q8×C127D411yescharacteristic
44#126×C127—22no—
45#126×C127—22no—
46#126×C127—22no—
47#126×C127—22no—
48#126×C127—21no—
49#125×C127—22no—
50#125×C127—22no—
51#125×C127—22no—
52#125×C127—22no—
53#125×C127—21no—
54#125×C127—22no—
55#125×C127—22no—
56#125×C127—22no—
57#125×C127—22no—
58#125×C127—21no—
59#125×C127—21no—
60#125×C127—21no—
61#125×C127—21no—
62#125×C127—21no—
63#125×C127D411yescharacteristic
64#124×C127D411yescharacteristic
65#123×C127—22no—
66#123×C127—22no—
67#123×C127—21no—
68C22⋊Q8×C127—21no—
69C22⋊Q8×C127—21no—
70C22⋊Q8×C127—22no—
71C22⋊Q8×C127—22no—
72C22⋊Q8×C127—22no—
73C22⋊Q8×C127—22no—
74C22⋊Q8×C127—21no—
75C22⋊Q8×C127C2×C411yescharacteristic
76C22⋊Q8×C127C2×C412yes—
77#121×C127C2×C411yescharacteristic
78C4×Q8×C127—21no—
79C4×Q8×C127—22no—
80C4×Q8×C127—21no—
81C4×Q8×C127—21no—
82C4×Q8×C127D411yescharacteristic
83C4×Q8×C127D412yes—
84C4×D4×C127—22no—
85C4×D4×C127—21no—
86C4×D4×C127D411yescharacteristic
87#117×C127—22no—
88#117×C127—21no—
89#117×C127—22no—
90#117×C127—21no—
91#117×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127C2×C412yes—
94C2×C4⋊C4×C127D412yes—
95C2×C4⋊C4×C127D411yescharacteristic
96C2×C4⋊C4×C127D411yescharacteristic
97C2×C42×C127C2311yescharacteristic
98C4⋊C8×C127—21no—
99C4⋊C8×C127—21no—
100C4⋊C8×C127—21no—
101C4⋊C8×C127—21no—
102C22⋊C8×C127—21no—
103C22⋊C8×C127—21no—
104#97×C127—21no—
105#97×C127—21no—
106C4×C8×C127—21no—
107C4×C8×C127—21no—
108C2×Q8×C127—22no—
109C2×Q8×C127—21no—
110C2×Q8×C127C22⋊C412yes—
111C2×Q8×C127C22⋊C411yescharacteristic
112C2×D4×C127—21no—
113C2×D4×C127C22⋊C411yescharacteristic
114C22×C4×C127—22no—
115C22×C4×C127—21no—
116C22×C4×C127C22⋊C412yes—
117C22×C4×C127C22⋊C412yes—
118C22×C4×C127C22×C411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121M16×C127—22no—
122M16×C127—41no—
123M16×C127—42no—
124C2×C8×C127—41no—
125C2×C8×C127—41no—
126C2×C8×C127—41no—
127C2×C8×C127—41no—
128C4⋊C4×C127—22no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—22no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—21no—
141C4⋊C4×C127—21no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127C22⋊C411yescharacteristic
154C4⋊C4×C127C22⋊C411yescharacteristic
155C4⋊C4×C127C22⋊C412yes—
156C22⋊C4×C127—22no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—22no—
159C22⋊C4×C127—22no—
160C22⋊C4×C127—21no—
161C22⋊C4×C127—21no—
162C22⋊C4×C127—21no—
163C22⋊C4×C127—21no—
164C22⋊C4×C127—21no—
165C42×C127—22no—
166C42×C127—22no—
167C42×C127—22no—
168C42×C127—22no—
169C42×C127—21no—
170C42×C127C2×D411yescharacteristic
171C42×C127C2×D411yescharacteristic
172C42×C127C2×D411yescharacteristic
173C42×C127C2×D411yescharacteristic
174C23×C127—21no—
175C23×C127C2×C22⋊C411yescharacteristic
176Q8×C127—41no—
177Q8×C127—42no—
178Q8×C127—41no—
179Q8×C127—41no—
180Q8×C127—82no—
181D4×C127—41no—
182D4×C127—42no—
183C2×C4×C127—21no—
184C2×C4×C127—21no—
185C2×C4×C127—22no—
186C2×C4×C127—21no—
187C2×C4×C127—21no—
188C2×C4×C127—22no—
189C2×C4×C127—21no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—41no—
193C2×C4×C127—41no—
194C2×C4×C127—41no—
195C2×C4×C127—41no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—82no—
199C2×C4×C127C2×C22⋊C411yescharacteristic
200C2×C4×C127C2×C22⋊C411yescharacteristic
201C2×C4×C127#12011yescharacteristic
202C2×C4×C127#12011yescharacteristic
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127#12011yescharacteristic
205C8×C127—42no—
206C8×C127—81no—
207C8×C127—81no—
208C8×C127—81no—
209C22×C127—21no—
210C22×C127—21no—
211C22×C127—21no—
212C22×C127—41no—
213C22×C127—41no—
214C22×C127—41no—
215C22×C127#37911yescharacteristic
216C4×C127—21no—
217C4×C127—21no—
218C4×C127—21no—
219C4×C127—21no—
220C4×C127—21no—
221C4×C127—41no—
222C4×C127—42no—
223C4×C127—42no—
224C4×C127—41no—
225C4×C127—42no—
226C4×C127—42no—
227C4×C127—41no—
228C4×C127#45411yescharacteristic
229C4×C127#45611yescharacteristic
230#8485C12711yesmaximal, characteristic, direct product factor, Sylow
231C2×C127—41no—
232C2×C127—81no—
233C2×C127#179111yescharacteristic
234C2×C127#179311yescharacteristic
235C2×C127#179611yescharacteristic
236#3563C2×C12711yescharacteristic
237#1998C2×C12711yescharacteristic, complemented
238#1559C2×C12711yescharacteristic, complemented
239#1529C2×C12711yescharacteristic
240#1495C2×C12711yescharacteristic
241#1485C2×C12711yescharacteristic, complemented
242#1470C2×C12711yescharacteristic, complemented
243C127#848511yescharacteristic, direct product factor, Sylow
244#564—21no—
245#563—21no—
246#557—21no—
247#554—21no—
248#552—21no—
249#552—22no—
250#552—21no—
251#544—21no—
252#544C4×C12712yes—
253#541—21no—
254#541—22no—
255#539C4×C12712yes—
256#533C22×C12711yescharacteristic
257#529C22×C12711yescharacteristic
258C2×#125C22×C12711yescharacteristic
259#432C22×C12711yescharacteristic
260#431C22×C12711yescharacteristic
261#423C22×C12711yescharacteristic
262C4×M16C22×C12711yescharacteristic
263#343—21no—
264#343—21no—
265#333—21no—
266#332—21no—
267#330—21no—
268#329—21no—
269Q8⋊C8—22no—
270Q8⋊C8—21no—
271D4⋊C8—21no—
272#324—22no—
273C2×M16—21no—
274C2×M16—21no—
275C4⋊Q8—21no—
276C4⋊Q8—22no—
277C4⋊Q8—22no—
278C4⋊Q8D4×C12711yescharacteristic
279C4⋊Q8D4×C12711yescharacteristic
280#126—22no—
281#126—22no—
282#126—22no—
283#126—22no—
284#126—21no—
285#125—22no—
286#125—22no—
287#125—22no—
288#125—22no—
289#125—21no—
290#125—22no—
291#125—22no—
292#125—22no—
293#125—22no—
294#125—21no—
295#125—21no—
296#125—21no—
297#125—21no—
298#125—21no—
299#125D4×C12711yescharacteristic
300#124D4×C12711yescharacteristic
301#123—22no—
302#123—22no—
303#123—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—22no—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—21no—
311C22⋊Q8C2×C4×C12711yescharacteristic
312C22⋊Q8C2×C4×C12712yes—
313#121C2×C4×C12711yescharacteristic
314C4×Q8—21no—
315C4×Q8—22no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×Q8D4×C12711yescharacteristic
319C4×Q8D4×C12712yes—
320C4×D4—22no—
321C4×D4—21no—
322C4×D4D4×C12711yescharacteristic
323#117—22no—
324#117—21no—
325#117—22no—
326#117—21no—
327#117—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4C2×C4×C12712yes—
330C2×C4⋊C4D4×C12712yes—
331C2×C4⋊C4D4×C12711yescharacteristic
332C2×C4⋊C4D4×C12711yescharacteristic
333C2×C42C23×C12711yescharacteristic
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340#97—21no—
341#97—21no—
342C4×C8—21no—
343C4×C8—21no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8C22⋊C4×C12712yes—
347C2×Q8C22⋊C4×C12711yescharacteristic
348C2×D4—21no—
349C2×D4C22⋊C4×C12711yescharacteristic
350C22×C4—22no—
351C22×C4—21no—
352C22×C4C22⋊C4×C12712yes—
353C22×C4C22⋊C4×C12712yes—
354C22×C4C22×C4×C12711yescharacteristic
355C22×C4C2×D4×C12711yescharacteristic
356C22×C4C2×D4×C12711yescharacteristic
357M16—22no—
358M16—41no—
359M16—42no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4C22⋊C4×C12711yescharacteristic
390C4⋊C4C22⋊C4×C12711yescharacteristic
391C4⋊C4C22⋊C4×C12712yes—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C42—22no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—21no—
406C42C2×D4×C12711yescharacteristic
407C42C2×D4×C12711yescharacteristic
408C42C2×D4×C12711yescharacteristic
409C42C2×D4×C12711yescharacteristic
410C23—21no—
411C23C2×C22⋊C4×C12711yescharacteristic
412Q8—41no—
413Q8—42no—
414Q8—41no—
415Q8—41no—
416Q8—82no—
417D4—41no—
418D4—42no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4C2×C22⋊C4×C12711yescharacteristic
436C2×C4C2×C22⋊C4×C12711yescharacteristic
437C2×C4#120×C12711yescharacteristic
438C2×C4#120×C12711yescharacteristic
439C2×C4#120×C12711yescharacteristic
440C2×C4#120×C12711yescharacteristic
441C8—42no—
442C8—81no—
443C8—81no—
444C8—81no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22#379×C12711yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—42no—
458C4—42no—
459C4—41no—
460C4—41no—
461C4—42no—
462C4—42no—
463C4—41no—
464C4#454×C12711yescharacteristic
465C4#456×C12711yescharacteristic
466C2—41no—
467C2—81no—
468C2C127×#179111yescharacteristic
469C2C127×#179311yescharacteristic
470C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#121×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1998C2semidirect
3. C127×#1559C2semidirect
6. C127×#1485C2semidirect
7. C127×#1470C2semidirect
230. #8485C127direct (N × H)
237. #1998C2×C127semidirect
238. #1559C2×C127semidirect
241. #1485C2×C127semidirect
242. #1470C2×C127semidirect
243. C127#8485direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35632
C127×#19982
C127×#15592
C127×#15292
C127×#14952
C127×#14852
C127×#14702
#8485127