Finite Group Databasebeta

← C127×#8348 #44572021

Subgroups — C127×#8348 #44572021

Order 32512.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3491C211yesmaximal, characteristic
2C127×#1750C211yesmaximal, characteristic, complemented
3C127×#1532C212yesmaximal, complemented
4C127×#1494C212yesmaximal, complemented
5C127×#1464C211yesmaximal, characteristic, complemented
6#552×C127—22no—
7#552×C127—22no—
8#551×C127—22no—
9#551×C127—22no—
10#543×C127C411yescharacteristic
11#539×C127—21no—
12#539×C127C412yes—
13#534×C127C411yescharacteristic
14#529×C127—21no—
15#529×C127C2212yes—
16C2×#123×C127—21no—
17#518×C127—21no—
18C2×#117×C127C2211yescharacteristic
19#432×C127C2212yescomplemented
20C2×C22⋊C8×C127—21no—
21C2×#97×C127C2211yescharacteristic, complemented
22C2×C4×C8×C127C2211yescharacteristic, complemented
23#336×C127—21no—
24#330×C127—22no—
25#329×C127—22no—
26Q8⋊C8×C127—22no—
27D4⋊C8×C127—22no—
28#324×C127—21no—
29#323×C127—21no—
30C22×D4×C127—21no—
31C23×C4×C127D411yescharacteristic
32C22×C8×C127—21no—
33C22×C8×C127—21no—
34#126×C127—22no—
35#126×C127—22no—
36#126×C127—22no—
37#126×C127—22no—
38#125×C127—21no—
39#125×C127—22no—
40#125×C127—22no—
41#125×C127D412yes—
42#124×C127—21no—
43#124×C127D412yes—
44#123×C127—22no—
45#123×C127—22no—
46#123×C127—22no—
47#123×C127—22no—
48#123×C127—22no—
49#123×C127—22no—
50#123×C127—22no—
51C22⋊Q8×C127—22no—
52C22⋊Q8×C127—22no—
53C22⋊Q8×C127—22no—
54C22⋊Q8×C127—21no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127C2×C412yes—
57#121×C127—21no—
58#121×C127C2×C412yes—
59#120×C127—22no—
60C4×Q8×C127—21no—
61C4×Q8×C127D412yes—
62C4×D4×C127—22no—
63C4×D4×C127—22no—
64C4×D4×C127—21no—
65C4×D4×C127—22no—
66C4×D4×C127—22no—
67C4×D4×C127D412yes—
68#117×C127—22no—
69#117×C127—22no—
70#117×C127—22no—
71#117×C127—22no—
72#117×C127—22no—
73C2×C4⋊C4×C127—21no—
74C2×C4⋊C4×C127—21no—
75C2×C4⋊C4×C127C2×C411yescharacteristic
76C2×C4⋊C4×C127D411yescharacteristic
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—21no—
79C2×C22⋊C4×C127—21no—
80C2×C22⋊C4×C127—21no—
81C2×C22⋊C4×C127C2×C411yescharacteristic
82C2×C22⋊C4×C127D411yescharacteristic
83C2×C42×C127D411yescharacteristic
84C2×C42×C127C2311yescharacteristic
85C4⋊C8×C127—22no—
86C22⋊C8×C127—24no—
87C22⋊C8×C127—22no—
88#97×C127—22no—
89#97×C127—22no—
90C4×C8×C127—22no—
91C24×C127—21no—
92C24×C127C22⋊C411yescharacteristic
93C2×Q8×C127—21no—
94C2×Q8×C127C22⋊C412yes—
95C2×D4×C127—22no—
96C2×D4×C127—22no—
97C2×D4×C127—21no—
98C2×D4×C127—42no—
99C2×D4×C127—42no—
100C2×D4×C127C22⋊C412yes—
101C22×C4×C127—21no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—22no—
109C22×C4×C127—41no—
110C22×C4×C127C22⋊C411yescharacteristic
111C22×C4×C127C22⋊C411yescharacteristic
112C22×C4×C127C22⋊C411yescharacteristic
113C22×C4×C127C22×C411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C2×C8×C127—22no—
117C2×C8×C127—22no—
118C2×C8×C127—41no—
119C2×C8×C127—41no—
120C2×C8×C127—41no—
121C2×C8×C127—41no—
122C2×C8×C127—42no—
123C4⋊C4×C127—22no—
124C4⋊C4×C127—22no—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—21no—
128C4⋊C4×C127—21no—
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×C127C22⋊C412yes—
136C4⋊C4×C127C22⋊C412yes—
137C22⋊C4×C127—22no—
138C22⋊C4×C127—22no—
139C22⋊C4×C127—22no—
140C22⋊C4×C127—22no—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—22no—
143C22⋊C4×C127—22no—
144C22⋊C4×C127—22no—
145C22⋊C4×C127—22no—
146C22⋊C4×C127—22no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—22no—
149C42×C127—22no—
150C42×C127—21no—
151C42×C127—21no—
152C42×C127—22no—
153C42×C127C2×D412yes—
154C42×C127C2×D412yes—
155C23×C127—21no—
156C23×C127—21no—
157C23×C127—22no—
158C23×C127—41no—
159C23×C127—41no—
160C23×C127—42no—
161C23×C127—81no—
162C23×C127—81no—
163C23×C127#10412yes—
164C23×C127C2×C22⋊C411yescharacteristic
165Q8×C127—42no—
166Q8×C127—81no—
167D4×C127—42no—
168D4×C127—44no—
169D4×C127—42no—
170D4×C127—42no—
171D4×C127—81no—
172C2×C4×C127—21no—
173C2×C4×C127—21no—
174C2×C4×C127—21no—
175C2×C4×C127—21no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—21no—
180C2×C4×C127—21no—
181C2×C4×C127—21no—
182C2×C4×C127—41no—
183C2×C4×C127—41no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—41no—
188C2×C4×C127—41no—
189C2×C4×C127—82no—
190C2×C4×C127—81no—
191C2×C4×C127—82no—
192C2×C4×C127—81no—
193C2×C4×C127C2×C22⋊C412yes—
194C2×C4×C127#12012yes—
195C2×C4×C127#12011yescharacteristic
196C2×C4×C127#12011yescharacteristic
197C8×C127—42no—
198C8×C127—42no—
199C8×C127—82no—
200C22×C127—21no—
201C22×C127—21no—
202C22×C127—22no—
203C22×C127—42no—
204C22×C127—41no—
205C22×C127—41no—
206C22×C127—42no—
207C22×C127—42no—
208C22×C127—42no—
209C22×C127—81no—
210C22×C127—162no—
211C22×C127#37911yescharacteristic
212C22×C127C2×#10411yescharacteristic
213C22×C127#42111yescharacteristic
214C4×C127—22no—
215C4×C127—21no—
216C4×C127—21no—
217C4×C127—22no—
218C4×C127—41no—
219C4×C127—42no—
220C4×C127—41no—
221C4×C127—42no—
222C4×C127—41no—
223C4×C127—42no—
224#8348C12711yesmaximal, characteristic, direct product factor, Sylow
225C2×C127—21no—
226C2×C127—21no—
227C2×C127—42no—
228C2×C127—82no—
229C2×C127#178911yescharacteristic
230C2×C127#179111yescharacteristic
231C2×C127#179411yescharacteristic
232#3491C2×C12711yescharacteristic
233#1750C2×C12711yescharacteristic, complemented
234#1532C2×C12712yescomplemented
235#1494C2×C12712yescomplemented
236#1464C2×C12711yescharacteristic, complemented
237C127#834811yescharacteristic, direct product factor, Sylow
238#552—22no—
239#552—22no—
240#551—22no—
241#551—22no—
242#543C4×C12711yescharacteristic
243#539—21no—
244#539C4×C12712yes—
245#534C4×C12711yescharacteristic
246#529—21no—
247#529C22×C12712yes—
248C2×#123—21no—
249#518—21no—
250C2×#117C22×C12711yescharacteristic
251#432C22×C12712yescomplemented
252C2×C22⋊C8—21no—
253C2×#97C22×C12711yescharacteristic, complemented
254C2×C4×C8C22×C12711yescharacteristic, complemented
255#336—21no—
256#330—22no—
257#329—22no—
258Q8⋊C8—22no—
259D4⋊C8—22no—
260#324—21no—
261#323—21no—
262C22×D4—21no—
263C23×C4D4×C12711yescharacteristic
264C22×C8—21no—
265C22×C8—21no—
266#126—22no—
267#126—22no—
268#126—22no—
269#126—22no—
270#125—21no—
271#125—22no—
272#125—22no—
273#125D4×C12712yes—
274#124—21no—
275#124D4×C12712yes—
276#123—22no—
277#123—22no—
278#123—22no—
279#123—22no—
280#123—22no—
281#123—22no—
282#123—22no—
283C22⋊Q8—22no—
284C22⋊Q8—22no—
285C22⋊Q8—22no—
286C22⋊Q8—21no—
287C22⋊Q8—22no—
288C22⋊Q8C2×C4×C12712yes—
289#121—21no—
290#121C2×C4×C12712yes—
291#120—22no—
292C4×Q8—21no—
293C4×Q8D4×C12712yes—
294C4×D4—22no—
295C4×D4—22no—
296C4×D4—21no—
297C4×D4—22no—
298C4×D4—22no—
299C4×D4D4×C12712yes—
300#117—22no—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4C2×C4×C12711yescharacteristic
308C2×C4⋊C4D4×C12711yescharacteristic
309C2×C22⋊C4—22no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4C2×C4×C12711yescharacteristic
314C2×C22⋊C4D4×C12711yescharacteristic
315C2×C42D4×C12711yescharacteristic
316C2×C42C23×C12711yescharacteristic
317C4⋊C8—22no—
318C22⋊C8—24no—
319C22⋊C8—22no—
320#97—22no—
321#97—22no—
322C4×C8—22no—
323C24—21no—
324C24C22⋊C4×C12711yescharacteristic
325C2×Q8—21no—
326C2×Q8C22⋊C4×C12712yes—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—42no—
332C2×D4C22⋊C4×C12712yes—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4C22⋊C4×C12711yescharacteristic
343C22×C4C22⋊C4×C12711yescharacteristic
344C22×C4C22⋊C4×C12711yescharacteristic
345C22×C4C22×C4×C12711yescharacteristic
346C22×C4C2×D4×C12711yescharacteristic
347C22×C4C2×D4×C12711yescharacteristic
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—42no—
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4C22⋊C4×C12712yes—
368C4⋊C4C22⋊C4×C12712yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C42—22no—
382C42—21no—
383C42—21no—
384C42—22no—
385C42C2×D4×C12712yes—
386C42C2×D4×C12712yes—
387C23—21no—
388C23—21no—
389C23—22no—
390C23—41no—
391C23—41no—
392C23—42no—
393C23—81no—
394C23—81no—
395C23#104×C12712yes—
396C23C2×C22⋊C4×C12711yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—42no—
400D4—44no—
401D4—42no—
402D4—42no—
403D4—81no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4C2×C22⋊C4×C12712yes—
426C2×C4#120×C12711yescharacteristic
427C2×C4#120×C12711yescharacteristic
428C2×C4#120×C12712yes—
429C8—42no—
430C8—42no—
431C8—82no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—42no—
436C22—41no—
437C22—41no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—81no—
442C22—162no—
443C22#379×C12711yescharacteristic
444C22C2×#104×C12711yescharacteristic
445C22#421×C12711yescharacteristic
446C4—21no—
447C4—21no—
448C4—22no—
449C4—22no—
450C4—41no—
451C4—42no—
452C4—41no—
453C4—42no—
454C4—41no—
455C4—42no—
456C2—21no—
457C2—21no—
458C2—42no—
459C2—82no—
460C2C127×#178911yescharacteristic
461C2C127×#179111yescharacteristic
462C2C127×#179411yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#534×C127C4
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×#1750C2semidirect
3. C127×#1532C2semidirect
4. C127×#1494C2semidirect
5. C127×#1464C2semidirect
19. #432×C127C22semidirect
21. C2×#97×C127C22semidirect
22. C2×C4×C8×C127C22semidirect
224. #8348C127direct (N × H)
233. #1750C2×C127semidirect
234. #1532C2×C127semidirect
235. #1494C2×C127semidirect
236. #1464C2×C127semidirect
237. C127#8348direct (N × H)
251. #432C22×C127semidirect
253. C2×#97C22×C127semidirect
254. C2×C4×C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34912
C127×#17502
C127×#15322
C127×#14942
C127×#14642
#8348127