Finite Group Databasebeta

← C127×#11024 #44574697

Subgroups — C127×#11024 #44574697

Order 32512.

1390 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
1C23×Q16×C127C211yesmaximal, characteristic
2C22×#103×C127C212yesmaximal
3C2×#391×C127C212yesmaximal
4C2×#340×C127C211yesmaximal, characteristic
5C2×#336×C127C211yesmaximal, characteristic
6C23×Q8×C127C2212yes—
7C22×Q16×C127—24no—
8C22×Q16×C127—24no—
9C22×Q16×C127—22no—
10C22×Q16×C127—22no—
11C22×Q16×C127C414yescomplemented
12C23×C8×C127C2211yescharacteristic
13C23×C8×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16C2×#103×C127—24no—
17C2×#103×C127—24no—
18C2×#103×C127—24no—
19#391×C127—24no—
20#391×C127—24no—
21C2×#95×C127—24no—
22#340×C127—22no—
23#336×C127—22no—
24C22×Q8×C127—22no—
25C22×Q8×C127—22no—
26C22×Q8×C127—22no—
27C22×Q8×C127—22no—
28C22×Q8×C127—22no—
29C22×Q8×C127—22no—
30C22×Q8×C127—22no—
31C22×Q8×C127—22no—
32C22×Q8×C127—22no—
33C22×Q8×C127—22no—
34C22×Q8×C127—22no—
35C22×Q8×C127C2×C414yes—
36C22×Q8×C127D414yes—
37C22×Q8×C127D414yes—
38C23×C4×C127—22no—
39C23×C4×C127—22no—
40C23×C4×C127D412yes—
41C23×C4×C127C2311yescharacteristic
42C2×Q16×C127—28no—
43C2×Q16×C127—28no—
44C2×Q16×C127—216no—
45C2×Q16×C127—216no—
46C2×Q16×C127—28no—
47C22×C8×C127—22no—
48C22×C8×C127—22no—
49C22×C8×C127—21no—
50C22×C8×C127—22no—
51C22×C8×C127—22no—
52C22×C8×C127—21no—
53C22×C8×C127C2×C412yes—
54C22×C8×C127D412yes—
55C22×C8×C127D412yes—
56C22×C8×C127D412yes—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127D414yes—
63C2×C42×C127—21no—
64C2×C42×C127—22no—
65C2×C42×C127—22no—
66C2×C42×C127—21no—
67#103×C127—216no—
68#95×C127—216no—
69C24×C127C2×D411yescharacteristic
70C2×Q8×C127—24no—
71C2×Q8×C127—24no—
72C2×Q8×C127—24no—
73C2×Q8×C127—24no—
74C2×Q8×C127—24no—
75C2×Q8×C127—24no—
76C2×Q8×C127—24no—
77C2×Q8×C127—24no—
78C2×Q8×C127—24no—
79C2×Q8×C127—24no—
80C2×Q8×C127—24no—
81C2×Q8×C127—24no—
82C2×Q8×C127—24no—
83C2×Q8×C127—24no—
84C2×Q8×C127—24no—
85C2×Q8×C127—42no—
86C2×Q8×C127—42no—
87C2×Q8×C127—42no—
88C2×Q8×C127—42no—
89C2×Q8×C127—42no—
90C2×Q8×C127—42no—
91C2×Q8×C127—42no—
92C2×Q8×C127—42no—
93C2×Q8×C127—42no—
94C2×Q8×C127—42no—
95C2×Q8×C127—42no—
96C2×Q8×C127—42no—
97C2×Q8×C127C22⋊C418yes—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—22no—
102C22×C4×C127—24no—
103C22×C4×C127—22no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—42no—
107C22×C4×C127—42no—
108C22×C4×C127—42no—
109C22×C4×C127—42no—
110C22×C4×C127—42no—
111C22×C4×C127—42no—
112C22×C4×C127—44no—
113C22×C4×C127—44no—
114C22×C4×C127Q1614yescomplemented
115C22×C4×C127C22×C411yescharacteristic
116C22×C4×C127C2×D412yes—
117C22×C4×C127C2×D412yes—
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D411yescharacteristic
120C22×C4×C127C2×D411yescharacteristic
121C22×C4×C127C2×D412yes—
122C22×C4×C127#4111yescharacteristic
123C22×C4×C127#4112yes—
124C22×C4×C127#4111yescharacteristic
125Q16×C127—232no—
126C2×C8×C127—24no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—24no—
130C2×C8×C127—24no—
131C2×C8×C127—22no—
132C2×C8×C127—41no—
133C2×C8×C127—42no—
134C2×C8×C127—41no—
135C2×C8×C127C22⋊C414yes—
136C4⋊C4×C127—24no—
137C4⋊C4×C127—24no—
138C4⋊C4×C127—42no—
139C4⋊C4×C127—42no—
140C42×C127—41no—
141C42×C127—42no—
142C42×C127—41no—
143C23×C127C4×D411yescharacteristic
144C23×C127#12012yes—
145C23×C127#12112yes—
146C23×C127#12111yescharacteristic
147C23×C127#12711yescharacteristic
148C23×C127C2×Q1612yes—
149C23×C127#13512yes—
150C23×C127#13714yes—
151Q8×C127—28no—
152Q8×C127—28no—
153Q8×C127—44no—
154Q8×C127—44no—
155Q8×C127—44no—
156Q8×C127—44no—
157Q8×C127—44no—
158Q8×C127—44no—
159C2×C4×C127—28no—
160C2×C4×C127—28no—
161C2×C4×C127—24no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—42no—
165C2×C4×C127—44no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127—44no—
170C2×C4×C127—42no—
171C2×C4×C127—44no—
172C2×C4×C127—48no—
173C2×C4×C127—84no—
174C2×C4×C127—82no—
175C2×C4×C127—82no—
176C2×C4×C127C2×C22⋊C412yes—
177C2×C4×C127C2×C22⋊C411yescharacteristic
178C2×C4×C127C4×D411yescharacteristic
179C2×C4×C127C4×D412yes—
180C2×C4×C127#12011yescharacteristic
181C2×C4×C127#12011yescharacteristic
182C2×C4×C127#12012yes—
183C2×C4×C127#12012yes—
184C2×C4×C127#12112yes—
185C2×C4×C127#12112yes—
186C2×C4×C127#12112yes—
187C2×C4×C127#12112yes—
188C2×C4×C127#12111yescharacteristic
189C2×C4×C127#12312yes—
190C2×C4×C127#12312yes—
191C2×C4×C127#12411yescharacteristic
192C2×C4×C127#12411yescharacteristic
193C2×C4×C127#12711yescharacteristic
194C8×C127—24no—
195C8×C127—42no—
196C22×C127#38612yes—
197C22×C127#39011yescharacteristic
198C22×C127#39211yescharacteristic
199C22×C127#39212yes—
200C22×C127#39411yescharacteristic
201C22×C127C4×Q1612yes—
202C22×C127#44112yes—
203C22×C127#45114yes—
204C22×C127#45214yes—
205C22×C127#46214yes—
206C22×C127#46414yes—
207C22×C127#46712yes—
208C22×C127#47012yes—
209C22×C127#49411yescharacteristic
210C22×C127#49511yescharacteristic
211C22×C127#49712yes—
212C4×C127—48no—
213C4×C127—44no—
214C4×C127—84no—
215C4×C127#37911yescharacteristic
216C4×C127#38612yes—
217C4×C127#39011yescharacteristic
218C4×C127#39211yescharacteristic
219C4×C127#39411yescharacteristic
220C4×C127#39412yes—
221#11024C12711yesmaximal, characteristic, direct product factor, Sylow
222C2×C127#143811yescharacteristic
223C2×C127#187814yes—
224C2×C127#196911yescharacteristic
225C2×C127#197111yescharacteristic
226C2×C127#200112yes—
227C2×C127#201512yes—
228C2×C127#201612yes—
229C2×C127#205612yes—
230C23×Q16C2×C12711yescharacteristic
231C22×#103C2×C12712yes—
232C2×#391C2×C12712yes—
233C2×#340C2×C12711yescharacteristic
234C2×#336C2×C12711yescharacteristic
235C127#1102411yescharacteristic, direct product factor, Sylow
236C23×Q8C22×C12712yes—
237C22×Q16—24no—
238C22×Q16—24no—
239C22×Q16—22no—
240C22×Q16—22no—
241C22×Q16C4×C12714yescomplemented
242C23×C8C22×C12711yescharacteristic
243C23×C8C22×C12711yescharacteristic
244C22×C4⋊C4C22×C12712yes—
245C22×C42C22×C12711yescharacteristic
246C2×#103—24no—
247C2×#103—24no—
248C2×#103—24no—
249#391—24no—
250#391—24no—
251C2×#95—24no—
252#340—22no—
253#336—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8C2×C4×C12714yes—
266C22×Q8D4×C12714yes—
267C22×Q8D4×C12714yes—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4D4×C12712yes—
271C23×C4C23×C12711yescharacteristic
272C2×Q16—28no—
273C2×Q16—28no—
274C2×Q16—216no—
275C2×Q16—216no—
276C2×Q16—28no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8—21no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—21no—
283C22×C8C2×C4×C12712yes—
284C22×C8D4×C12712yes—
285C22×C8D4×C12712yes—
286C22×C8D4×C12712yes—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4D4×C12714yes—
293C2×C42—21no—
294C2×C42—22no—
295C2×C42—22no—
296C2×C42—21no—
297#103—216no—
298#95—216no—
299C24C2×D4×C12711yescharacteristic
300C2×Q8—24no—
301C2×Q8—24no—
302C2×Q8—24no—
303C2×Q8—24no—
304C2×Q8—24no—
305C2×Q8—24no—
306C2×Q8—24no—
307C2×Q8—24no—
308C2×Q8—24no—
309C2×Q8—24no—
310C2×Q8—24no—
311C2×Q8—24no—
312C2×Q8—24no—
313C2×Q8—24no—
314C2×Q8—24no—
315C2×Q8—42no—
316C2×Q8—42no—
317C2×Q8—42no—
318C2×Q8—42no—
319C2×Q8—42no—
320C2×Q8—42no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—42no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8C22⋊C4×C12718yes—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—44no—
343C22×C4—44no—
344C22×C4Q16×C12714yescomplemented
345C22×C4C22×C4×C12711yescharacteristic
346C22×C4C2×D4×C12712yes—
347C22×C4C2×D4×C12712yes—
348C22×C4C2×D4×C12711yescharacteristic
349C22×C4C2×D4×C12711yescharacteristic
350C22×C4C2×D4×C12711yescharacteristic
351C22×C4C2×D4×C12712yes—
352C22×C4#41×C12711yescharacteristic
353C22×C4#41×C12712yes—
354C22×C4#41×C12711yescharacteristic
355Q16—232no—
356C2×C8—24no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—24no—
360C2×C8—24no—
361C2×C8—22no—
362C2×C8—41no—
363C2×C8—42no—
364C2×C8—41no—
365C2×C8C22⋊C4×C12714yes—
366C4⋊C4—24no—
367C4⋊C4—24no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C42—41no—
371C42—42no—
372C42—41no—
373C23C4×D4×C12711yescharacteristic
374C23#120×C12712yes—
375C23#121×C12712yes—
376C23#121×C12711yescharacteristic
377C23#127×C12711yescharacteristic
378C23C2×Q16×C12712yes—
379C23#135×C12712yes—
380C23#137×C12714yes—
381Q8—28no—
382Q8—28no—
383Q8—44no—
384Q8—44no—
385Q8—44no—
386Q8—44no—
387Q8—44no—
388Q8—44no—
389C2×C4—28no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—48no—
403C2×C4—82no—
404C2×C4—84no—
405C2×C4—82no—
406C2×C4C2×C22⋊C4×C12712yes—
407C2×C4C2×C22⋊C4×C12711yescharacteristic
408C2×C4C4×D4×C12711yescharacteristic
409C2×C4C4×D4×C12712yes—
410C2×C4#120×C12711yescharacteristic
411C2×C4#120×C12711yescharacteristic
412C2×C4#120×C12712yes—
413C2×C4#120×C12712yes—
414C2×C4#121×C12712yes—
415C2×C4#121×C12712yes—
416C2×C4#121×C12712yes—
417C2×C4#121×C12712yes—
418C2×C4#121×C12711yescharacteristic
419C2×C4#123×C12712yes—
420C2×C4#123×C12712yes—
421C2×C4#124×C12711yescharacteristic
422C2×C4#124×C12711yescharacteristic
423C2×C4#127×C12711yescharacteristic
424C8—24no—
425C8—42no—
426C22#386×C12712yes—
427C22#390×C12711yescharacteristic
428C22#392×C12711yescharacteristic
429C22#392×C12712yes—
430C22#394×C12711yescharacteristic
431C22C4×Q16×C12712yes—
432C22#441×C12712yes—
433C22#451×C12714yes—
434C22#452×C12714yes—
435C22#462×C12714yes—
436C22#464×C12714yes—
437C22#467×C12712yes—
438C22#470×C12712yes—
439C22#494×C12711yescharacteristic
440C22#495×C12711yescharacteristic
441C22#497×C12712yes—
442C4—48no—
443C4—44no—
444C4—84no—
445C4#379×C12711yescharacteristic
446C4#386×C12712yes—
447C4#390×C12711yescharacteristic
448C4#392×C12711yescharacteristic
449C4#394×C12711yescharacteristic
450C4#394×C12712yes—
451C2C127×#143811yescharacteristic
452C2C127×#187814yes—
453C2C127×#196911yescharacteristic
454C2C127×#197111yescharacteristic
455C2C127×#200112yes—
456C2C127×#201512yes—
457C2C127×#201612yes—
458C2C127×#205612yes—
subgroupG/H
center, socle, prime radicalC24×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
11. C22×Q16×C127C4semidirect
114. C22×C4×C127Q16semidirect
221. #11024C127direct (N × H)
235. C127#11024direct (N × H)
241. C22×Q16C4×C127semidirect
344. C22×C4Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C23×Q16×C1272
C22×#103×C1272
C2×#391×C1272
C2×#340×C1272
C2×#336×C1272
#11024127