Finite Group Databasebeta

← C2×C127×#1933 #44584754

Subgroups — C2×C127×#1933 #44584754

Order 32512.

1246 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
1C22×#103×C127C211yesmaximal, characteristic
2C22×#103×C127C211yesmaximal, characteristic
3C22×C4×C8×C127C211yesmaximal, characteristic
4C2×#391×C127C211yesmaximal, characteristic
5C2×#389×C127C211yesmaximal, characteristic
6C127×#1933C218yesmaximal, direct product factor
7C2×#340×C127C211yesmaximal, characteristic
8C2×#340×C127C211yesmaximal, characteristic
9C23×Q8×C127C2211yescharacteristic
10C23×C8×C127C2211yescharacteristic
11C23×C8×C127C2211yescharacteristic
12C22×C4⋊C4×C127—21no—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17C2×#103×C127—24no—
18C2×#103×C127C418yescomplemented
19C2×#103×C127C2214yes—
20C2×#103×C127C2214yes—
21C2×C4×C8×C127—24no—
22C2×C4×C8×C127C2214yes—
23#391×C127—22no—
24#391×C127C2214yes—
25#389×C127—22no—
26#389×C127C2214yes—
27C2×#95×C127—21no—
28C2×#95×C127—21no—
29C2×#95×C127—21no—
30#340×C127C2214yes—
31#340×C127C2214yes—
32C22×Q8×C127—21no—
33C22×Q8×C127—22no—
34C22×Q8×C127—22no—
35C22×Q8×C127—22no—
36C22×Q8×C127—22no—
37C22×Q8×C127—22no—
38C22×Q8×C127C2×C414yes—
39C22×Q8×C127C2312yes—
40C23×C4×C127—21no—
41C23×C4×C127—21no—
42C23×C4×C127—21no—
43C23×C4×C127—21no—
44C23×C4×C127D411yescharacteristic
45C23×C4×C127D411yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C22×C8×C127—22no—
48C22×C8×C127—22no—
49C22×C8×C127—22no—
50C22×C8×C127—22no—
51C22×C8×C127C2×C414yes—
52C22×C8×C127D414yes—
53C22×C8×C127C2312yes—
54C22×C8×C127C2312yes—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—44no—
65C2×C4⋊C4×C127C2×C414yes—
66C2×C4⋊C4×C127C2312yes—
67C2×C4⋊C4×C127C2312yes—
68C2×C4⋊C4×C127C2312yes—
69C2×C42×C127—22no—
70C2×C42×C127—22no—
71C2×C42×C127D412yes—
72C2×C42×C127C2312yes—
73#103×C127—28no—
74#103×C127C2×C4116yescomplemented
75C4×C8×C127—28no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—24no—
79C24×C127C2×D411yescharacteristic
80C2×Q8×C127—24no—
81C2×Q8×C127—22no—
82C2×Q8×C127—28no—
83C2×Q8×C127—28no—
84C2×Q8×C127—22no—
85C2×Q8×C127—22no—
86C2×Q8×C127—22no—
87C2×Q8×C127—22no—
88C2×Q8×C127—42no—
89C2×Q8×C127—44no—
90C2×Q8×C127—42no—
91C2×Q8×C127—44no—
92C2×Q8×C127C22×C414yes—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—42no—
104C22×C4×C127—42no—
105C22×C4×C127—42no—
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—42no—
113C22×C4×C127SD1614yes—
114C22×C4×C127Q1614yes—
115C22×C4×C127C22×C412yes—
116C22×C4×C127C2×D412yes—
117C22×C4×C127C2×D412yes—
118C22×C4×C127C2×D411yescharacteristic
119C22×C4×C127C2×D412yes—
120C22×C4×C127#4112yes—
121C22×C4×C127#4112yes—
122C22×C4×C127#4112yes—
123C22×C4×C127#4112yes—
124C22×C4×C127C2411yescharacteristic
125C2×C8×C127—28no—
126C2×C8×C127—28no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—22no—
130C2×C8×C127—22no—
131C2×C8×C127C22×C414yes—
132C2×C8×C127C2×D414yes—
133C4⋊C4×C127—24no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—42no—
140C4⋊C4×C127—42no—
141C4⋊C4×C127—48no—
142C4⋊C4×C127C22×C414yes—
143C42×C127—24no—
144C42×C127—22no—
145C42×C127—22no—
146C23×C127C4×D412yes—
147C23×C127#12112yes—
148C23×C127#12412yes—
149C23×C127C2×SD1612yes—
150C23×C127C2×Q1612yes—
151C23×C127#13512yes—
152C23×C127#13512yes—
153C23×C127C22×D411yescharacteristic
154Q8×C127—24no—
155Q8×C127—24no—
156Q8×C127—42no—
157Q8×C127—42no—
158Q8×C127—48no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—28no—
164C2×C4×C127—28no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—42no—
170C2×C4×C127—42no—
171C2×C4×C127—48no—
172C2×C4×C127—48no—
173C2×C4×C127—42no—
174C2×C4×C127—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—84no—
180C2×C4×C127—84no—
181C2×C4×C127#11714yes—
182C2×C4×C127C4×D414yes—
183C2×C4×C127C4×D412yes—
184C2×C4×C127#12112yes—
185C2×C4×C127#12314yes—
186C2×C4×C127#12412yes—
187C2×C4×C127#12614yes—
188C2×C4×C127C2×SD1614yes—
189C2×C4×C127C2×Q1614yes—
190C2×C4×C127C23×C411yescharacteristic
191C2×C4×C127C22×D411yescharacteristic
192C2×C4×C127C2×#4111yescharacteristic
193C2×C4×C127C2×#4111yescharacteristic
194C2×C4×C127C2×#4111yescharacteristic
195C2×C4×C127C2×#4111yescharacteristic
196C8×C127—24no—
197C8×C127—24no—
198C22×C127#38814yes—
199C22×C127C4×SD1614yes—
200C22×C127C4×Q1614yes—
201C22×C127#46514yes—
202C22×C127#46714yes—
203C22×C127#48714yes—
204C22×C127#48814yes—
205C22×C127C2×C4×D411yescharacteristic
206C22×C127C2×#12111yescharacteristic
207C22×C127C2×#12411yescharacteristic
208C22×C127C22×SD1611yescharacteristic
209C22×C127C22×Q1611yescharacteristic
210C22×C127C2×#13511yescharacteristic
211C22×C127C2×#13511yescharacteristic
212C4×C127—24no—
213C4×C127—24no—
214C4×C127—44no—
215C4×C127—44no—
216C4×C127—82no—
217C4×C127—82no—
218C4×C127#38814yes—
219C4×C127C2×#11711yescharacteristic
220C4×C127C2×C4×D411yescharacteristic
221C4×C127C2×#12311yescharacteristic
222C4×C127C2×#12611yescharacteristic
223C2×#1933C12711yesmaximal, characteristic, direct product factor, Sylow
224C2×C127#193318yesdirect product factor
225C2×C127C2×#38811yescharacteristic
226C2×C127C2×C4×SD1611yescharacteristic
227C2×C127C2×C4×Q1611yescharacteristic
228C2×C127C2×#46511yescharacteristic
229C2×C127C2×#46711yescharacteristic
230C2×C127C2×#48711yescharacteristic
231C2×C127C2×#48811yescharacteristic
232C22×#103C2×C12711yescharacteristic
233C22×#103C2×C12711yescharacteristic
234C22×C4×C8C2×C12711yescharacteristic
235C2×#391C2×C12711yescharacteristic
236C2×#389C2×C12711yescharacteristic
237#1933C2×C12718yesdirect product factor
238C2×#340C2×C12711yescharacteristic
239C2×#340C2×C12711yescharacteristic
240C127C2×#193311yescharacteristic, direct product factor, Sylow
241C23×Q8C22×C12711yescharacteristic
242C23×C8C22×C12711yescharacteristic
243C23×C8C22×C12711yescharacteristic
244C22×C4⋊C4—21no—
245C22×C4⋊C4C22×C12711yescharacteristic
246C22×C4⋊C4C22×C12711yescharacteristic
247C22×C4⋊C4C22×C12711yescharacteristic
248C22×C42C22×C12711yescharacteristic
249C2×#103—24no—
250C2×#103C4×C12718yescomplemented
251C2×#103C22×C12714yes—
252C2×#103C22×C12714yes—
253C2×C4×C8—24no—
254C2×C4×C8C22×C12714yes—
255#391—22no—
256#391C22×C12714yes—
257#389—22no—
258#389C22×C12714yes—
259C2×#95—21no—
260C2×#95—21no—
261C2×#95—21no—
262#340C22×C12714yes—
263#340C22×C12714yes—
264C22×Q8—21no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8C2×C4×C12714yes—
271C22×Q8C23×C12712yes—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4D4×C12711yescharacteristic
277C23×C4D4×C12711yescharacteristic
278C23×C4C23×C12711yescharacteristic
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8C2×C4×C12714yes—
284C22×C8D4×C12714yes—
285C22×C8C23×C12712yes—
286C22×C8C23×C12712yes—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4C2×C4×C12714yes—
298C2×C4⋊C4C23×C12712yes—
299C2×C4⋊C4C23×C12712yes—
300C2×C4⋊C4C23×C12712yes—
301C2×C42—22no—
302C2×C42—22no—
303C2×C42D4×C12712yes—
304C2×C42C23×C12712yes—
305#103—28no—
306#103C2×C4×C127116yescomplemented
307C4×C8—28no—
308#95—24no—
309#95—24no—
310#95—24no—
311C24C2×D4×C12711yescharacteristic
312C2×Q8—24no—
313C2×Q8—22no—
314C2×Q8—28no—
315C2×Q8—28no—
316C2×Q8—22no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—42no—
321C2×Q8—44no—
322C2×Q8—42no—
323C2×Q8—44no—
324C2×Q8C22×C4×C12714yes—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4SD16×C12714yes—
346C22×C4Q16×C12714yes—
347C22×C4C22×C4×C12712yes—
348C22×C4C2×D4×C12712yes—
349C22×C4C2×D4×C12712yes—
350C22×C4C2×D4×C12711yescharacteristic
351C22×C4C2×D4×C12712yes—
352C22×C4#41×C12712yes—
353C22×C4#41×C12712yes—
354C22×C4#41×C12712yes—
355C22×C4#41×C12712yes—
356C22×C4C24×C12711yescharacteristic
357C2×C8—28no—
358C2×C8—28no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8C22×C4×C12714yes—
364C2×C8C2×D4×C12714yes—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—48no—
374C4⋊C4C22×C4×C12714yes—
375C42—24no—
376C42—22no—
377C42—22no—
378C23C4×D4×C12712yes—
379C23#121×C12712yes—
380C23#124×C12712yes—
381C23C2×SD16×C12712yes—
382C23C2×Q16×C12712yes—
383C23#135×C12712yes—
384C23#135×C12712yes—
385C23C22×D4×C12711yescharacteristic
386Q8—24no—
387Q8—24no—
388Q8—42no—
389Q8—42no—
390Q8—48no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—28no—
396C2×C4—28no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—48no—
404C2×C4—48no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—84no—
412C2×C4—84no—
413C2×C4#117×C12714yes—
414C2×C4C4×D4×C12714yes—
415C2×C4C4×D4×C12712yes—
416C2×C4#121×C12712yes—
417C2×C4#123×C12714yes—
418C2×C4#124×C12712yes—
419C2×C4#126×C12714yes—
420C2×C4C2×SD16×C12714yes—
421C2×C4C2×Q16×C12714yes—
422C2×C4C23×C4×C12711yescharacteristic
423C2×C4C22×D4×C12711yescharacteristic
424C2×C4C2×#41×C12711yescharacteristic
425C2×C4C2×#41×C12711yescharacteristic
426C2×C4C2×#41×C12711yescharacteristic
427C2×C4C2×#41×C12711yescharacteristic
428C8—24no—
429C8—24no—
430C22#388×C12714yes—
431C22C4×SD16×C12714yes—
432C22C4×Q16×C12714yes—
433C22#465×C12714yes—
434C22#467×C12714yes—
435C22#487×C12714yes—
436C22#488×C12714yes—
437C22C2×C4×D4×C12711yescharacteristic
438C22C2×#121×C12711yescharacteristic
439C22C2×#124×C12711yescharacteristic
440C22C22×SD16×C12711yescharacteristic
441C22C22×Q16×C12711yescharacteristic
442C22C2×#135×C12711yescharacteristic
443C22C2×#135×C12711yescharacteristic
444C4—24no—
445C4—24no—
446C4—44no—
447C4—44no—
448C4—82no—
449C4—82no—
450C4#388×C12714yes—
451C4C2×#117×C12711yescharacteristic
452C4C2×C4×D4×C12711yescharacteristic
453C4C2×#123×C12711yescharacteristic
454C4C2×#126×C12711yescharacteristic
455C2C127×#193318yesdirect product factor
456C2C2×#388×C12711yescharacteristic
457C2C2×C4×SD16×C12711yescharacteristic
458C2C2×C4×Q16×C12711yescharacteristic
459C2C2×#465×C12711yescharacteristic
460C2C2×#467×C12711yescharacteristic
461C2C2×#487×C12711yescharacteristic
462C2C2×#488×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C127×#1933C2direct (N × H)
18. C2×#103×C127C4semidirect
74. #103×C127C2×C4semidirect
223. C2×#1933C127direct (N × H)
224. C2×C127#1933direct (N × H)
237. #1933C2×C127direct (N × H)
240. C127C2×#1933direct (N × H)
250. C2×#103C4×C127semidirect
306. #103C2×C4×C127semidirect
455. C2C127×#1933direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#103×C1272
C22×C4×C8×C1272
C2×#391×C1272
C2×#389×C1272
C127×#19332
C2×#340×C1272
C2×#1933127