Finite Group Databasebeta

← C127×#8434 #44572107

Subgroups — C127×#8434 #44572107

Order 32512.

760 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3506C211yesmaximal, characteristic
2C127×#1804C211yesmaximal, characteristic, complemented
3C127×#1542C211yesmaximal, characteristic, complemented
4C127×#1518C211yesmaximal, characteristic, complemented
5C127×#1517C211yesmaximal, characteristic, complemented
6C127×#1480C211yesmaximal, characteristic, complemented
7C127×#1478C211yesmaximal, characteristic, complemented
8#559×C127—22no—
9#556×C127C412yescomplemented
10#555×C127—21no—
11#553×C127—22no—
12#550×C127C412yescomplemented
13#547×C127—21no—
14#538×C127—22no—
15#535×C127—21no—
16#533×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#525×C127—22no—
19#520×C127—21no—
20C2×C4×D4×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×#102×C127—21no—
25#382×C127C2211yescharacteristic
26#340×C127—21no—
27#333×C127—21no—
28#332×C127—21no—
29#328×C127—22no—
30#327×C127—22no—
31D4⋊C8×C127—22no—
32D4⋊C8×C127—22no—
33C2×#41×C127—22no—
34C2×#41×C127—21no—
35C22×D4×C127D411yescharacteristic
36C23×C4×C127—21no—
37C22×C8×C127—21no—
38C4⋊Q8×C127C2×C411yescharacteristic
39C4⋊Q8×C127D411yescharacteristic
40C4⋊Q8×C127D411yescharacteristic
41#127×C127—22no—
42#127×C127C2×C411yescharacteristic
43#126×C127—24no—
44#125×C127—21no—
45#124×C127—24no—
46#124×C127—22no—
47#124×C127—21no—
48#123×C127—24no—
49#123×C127—24no—
50C22⋊Q8×C127—22no—
51C22⋊Q8×C127—21no—
52C22⋊Q8×C127D412yes—
53#121×C127—22no—
54#121×C127—22no—
55#121×C127—24no—
56#121×C127—21no—
57#121×C127—22no—
58#121×C127D412yes—
59#120×C127—24no—
60C4×Q8×C127—22no—
61C4×Q8×C127—21no—
62C4×Q8×C127C2×C412yes—
63C4×D4×C127—24no—
64C4×D4×C127—24no—
65C4×D4×C127—22no—
66C4×D4×C127—21no—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69C4×D4×C127C2×C412yes—
70C4×D4×C127D412yes—
71C4×D4×C127D412yes—
72#117×C127—22no—
73#117×C127—21no—
74#117×C127—22no—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127D411yescharacteristic
78C2×C22⋊C4×C127—21no—
79C2×C42×C127C2311yescharacteristic
80C4⋊C8×C127—21no—
81C4⋊C8×C127—21no—
82C4⋊C8×C127—21no—
83C4⋊C8×C127—21no—
84#102×C127—42no—
85C22⋊C8×C127—21no—
86C22⋊C8×C127—21no—
87C4×C8×C127—21no—
88C4×C8×C127—21no—
89#95×C127—21no—
90#95×C127—21no—
91C24×C127—21no—
92#41×C127—41no—
93#41×C127—41no—
94#41×C127—41no—
95#41×C127—41no—
96#41×C127—84no—
97C2×Q8×C127—21no—
98C2×Q8×C127—21no—
99C2×Q8×C127C22⋊C412yes—
100C2×D4×C127—22no—
101C2×D4×C127—24no—
102C2×D4×C127—24no—
103C2×D4×C127—21no—
104C2×D4×C127—21no—
105C2×D4×C127—21no—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—21no—
109C2×D4×C127—21no—
110C2×D4×C127C22⋊C412yes—
111C2×D4×C127C22⋊C412yes—
112C22×C4×C127—24no—
113C22×C4×C127—21no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—41no—
118C22×C4×C127—82no—
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127C2×D411yescharacteristic
122C2×C8×C127—41no—
123C2×C8×C127—41no—
124C2×C8×C127—41no—
125C2×C8×C127—41no—
126C2×C8×C127—41no—
127C4⋊C4×C127—24no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—21no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—21no—
135C4⋊C4×C127—41no—
136C4⋊C4×C127—41no—
137C4⋊C4×C127C22⋊C412yes—
138C4⋊C4×C127C22⋊C412yes—
139C4⋊C4×C127C22⋊C412yes—
140C22⋊C4×C127—24no—
141C22⋊C4×C127—24no—
142C22⋊C4×C127—24no—
143C22⋊C4×C127—22no—
144C22⋊C4×C127—22no—
145C22⋊C4×C127—22no—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—22no—
148C42×C127—24no—
149C42×C127—22no—
150C42×C127C22×C411yescharacteristic
151C42×C127C2×D411yescharacteristic
152C42×C127C2×D411yescharacteristic
153C42×C127C2×D411yescharacteristic
154C23×C127—22no—
155C23×C127—22no—
156C23×C127—41no—
157C23×C127—41no—
158C23×C127—81no—
159C23×C127—81no—
160C23×C127#12011yescharacteristic
161Q8×C127—42no—
162Q8×C127—41no—
163Q8×C127—41no—
164Q8×C127—81no—
165D4×C127—22no—
166D4×C127—22no—
167D4×C127—42no—
168D4×C127—42no—
169D4×C127—42no—
170D4×C127—42no—
171D4×C127—41no—
172D4×C127—41no—
173D4×C127—41no—
174D4×C127—41no—
175D4×C127—84no—
176D4×C127—84no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—44no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—82no—
187C2×C4×C127—81no—
188C2×C4×C127—84no—
189C2×C4×C127—81no—
190C2×C4×C127—81no—
191C2×C4×C127—81no—
192C2×C4×C127C2×C22⋊C411yescharacteristic
193C2×C4×C127C2×C22⋊C411yescharacteristic
194C2×C4×C127C2×C22⋊C411yescharacteristic
195C2×C4×C127#12011yescharacteristic
196C2×C4×C127#12011yescharacteristic
197C2×C4×C127#12011yescharacteristic
198C2×C4×C127#13511yescharacteristic
199C2×C4×C127#13511yescharacteristic
200C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C127#13711yescharacteristic
202C8×C127—81no—
203C8×C127—81no—
204C8×C127—81no—
205C22×C127—21no—
206C22×C127—21no—
207C22×C127—42no—
208C22×C127—42no—
209C22×C127—42no—
210C22×C127—42no—
211C22×C127—42no—
212C22×C127—42no—
213C22×C127—82no—
214C22×C127—82no—
215C22×C127#37911yescharacteristic
216C22×C127#44911yescharacteristic
217C22×C127#45211yescharacteristic
218C4×C127—21no—
219C4×C127—21no—
220C4×C127—21no—
221C4×C127—21no—
222C4×C127—42no—
223C4×C127—42no—
224C4×C127—42no—
225C4×C127—42no—
226C4×C127—161no—
227C4×C127#41611yescharacteristic
228C4×C127#41711yescharacteristic
229C4×C127#44911yescharacteristic
230C4×C127#45211yescharacteristic
231#8434C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—21no—
233C2×C127—21no—
234C2×C127—82no—
235C2×C127—82no—
236C2×C127#178811yescharacteristic
237C2×C127#179411yescharacteristic
238C2×C127#179511yescharacteristic
239#3506C2×C12711yescharacteristic
240#1804C2×C12711yescharacteristic, complemented
241#1542C2×C12711yescharacteristic, complemented
242#1518C2×C12711yescharacteristic, complemented
243#1517C2×C12711yescharacteristic, complemented
244#1480C2×C12711yescharacteristic, complemented
245#1478C2×C12711yescharacteristic, complemented
246C127#843411yescharacteristic, direct product factor, Sylow
247#559—22no—
248#556C4×C12712yescomplemented
249#555—21no—
250#553—22no—
251#550C4×C12712yescomplemented
252#547—21no—
253#538—22no—
254#535—21no—
255#533C22×C12711yescharacteristic
256#532C22×C12711yescharacteristic
257#525—22no—
258#520—21no—
259C2×C4×D4C22×C12711yescharacteristic
260#431C22×C12711yescharacteristic
261#431C22×C12711yescharacteristic
262C2×C4⋊C8C22×C12711yescharacteristic
263C2×#102—21no—
264#382C22×C12711yescharacteristic
265#340—21no—
266#333—21no—
267#332—21no—
268#328—22no—
269#327—22no—
270D4⋊C8—22no—
271D4⋊C8—22no—
272C2×#41—22no—
273C2×#41—21no—
274C22×D4D4×C12711yescharacteristic
275C23×C4—21no—
276C22×C8—21no—
277C4⋊Q8C2×C4×C12711yescharacteristic
278C4⋊Q8D4×C12711yescharacteristic
279C4⋊Q8D4×C12711yescharacteristic
280#127—22no—
281#127C2×C4×C12711yescharacteristic
282#126—24no—
283#125—21no—
284#124—24no—
285#124—22no—
286#124—21no—
287#123—24no—
288#123—24no—
289C22⋊Q8—22no—
290C22⋊Q8—21no—
291C22⋊Q8D4×C12712yes—
292#121—22no—
293#121—22no—
294#121—24no—
295#121—21no—
296#121—22no—
297#121D4×C12712yes—
298#120—24no—
299C4×Q8—22no—
300C4×Q8—21no—
301C4×Q8C2×C4×C12712yes—
302C4×D4—24no—
303C4×D4—24no—
304C4×D4—22no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4C2×C4×C12712yes—
309C4×D4D4×C12712yes—
310C4×D4D4×C12712yes—
311#117—22no—
312#117—21no—
313#117—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4D4×C12711yescharacteristic
317C2×C22⋊C4—21no—
318C2×C42C23×C12711yescharacteristic
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323#102—42no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C4×C8—21no—
327C4×C8—21no—
328#95—21no—
329#95—21no—
330C24—21no—
331#41—41no—
332#41—41no—
333#41—41no—
334#41—41no—
335#41—84no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8C22⋊C4×C12712yes—
339C2×D4—22no—
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4C22⋊C4×C12712yes—
350C2×D4C22⋊C4×C12712yes—
351C22×C4—24no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—41no—
357C22×C4—82no—
358C22×C4C2×D4×C12711yescharacteristic
359C22×C4C2×D4×C12711yescharacteristic
360C22×C4C2×D4×C12711yescharacteristic
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C22⋊C4×C12712yes—
377C4⋊C4C22⋊C4×C12712yes—
378C4⋊C4C22⋊C4×C12712yes—
379C22⋊C4—24no—
380C22⋊C4—24no—
381C22⋊C4—24no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—24no—
388C42—22no—
389C42C22×C4×C12711yescharacteristic
390C42C2×D4×C12711yescharacteristic
391C42C2×D4×C12711yescharacteristic
392C42C2×D4×C12711yescharacteristic
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—81no—
398C23—81no—
399C23#120×C12711yescharacteristic
400Q8—42no—
401Q8—41no—
402Q8—41no—
403Q8—81no—
404D4—22no—
405D4—22no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—84no—
415D4—84no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—84no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4C2×C22⋊C4×C12711yescharacteristic
432C2×C4C2×C22⋊C4×C12711yescharacteristic
433C2×C4C2×C22⋊C4×C12711yescharacteristic
434C2×C4#120×C12711yescharacteristic
435C2×C4#120×C12711yescharacteristic
436C2×C4#120×C12711yescharacteristic
437C2×C4#135×C12711yescharacteristic
438C2×C4#135×C12711yescharacteristic
439C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
440C2×C4#137×C12711yescharacteristic
441C8—81no—
442C8—81no—
443C8—81no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—82no—
453C22—82no—
454C22#379×C12711yescharacteristic
455C22#449×C12711yescharacteristic
456C22#452×C12711yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—161no—
466C4#416×C12711yescharacteristic
467C4#417×C12711yescharacteristic
468C4#449×C12711yescharacteristic
469C4#452×C12711yescharacteristic
470C2—21no—
471C2—21no—
472C2—82no—
473C2—82no—
474C2C127×#178811yescharacteristic
475C2C127×#179411yescharacteristic
476C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3506C2
LCSG ▷ C42 ▷ 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×#1804C2semidirect
3. C127×#1542C2semidirect
4. C127×#1518C2semidirect
5. C127×#1517C2semidirect
6. C127×#1480C2semidirect
7. C127×#1478C2semidirect
9. #556×C127C4semidirect
12. #550×C127C4semidirect
231. #8434C127direct (N × H)
240. #1804C2×C127semidirect
241. #1542C2×C127semidirect
242. #1518C2×C127semidirect
243. #1517C2×C127semidirect
244. #1480C2×C127semidirect
245. #1478C2×C127semidirect
246. C127#8434direct (N × H)
248. #556C4×C127semidirect
251. #550C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35062
C127×#18042
C127×#15422
C127×#15182
C127×#15172
C127×#14802
C127×#14782
#8434127