Finite Group Databasebeta

← C2×C127×#1826 #44584377

Subgroups — C2×C127×#1826 #44584377

Order 32512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C127C211yesmaximal, characteristic
2C2×#407×C127C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
4C127×#1826C218yesmaximal, direct product factor
5C2×#339×C127C214yesmaximal, complemented
6C24×C4×C127C2211yescharacteristic
7C22×M16×C127C2212yes—
8C2×#117×C127—21no—
9C2×#117×C127—22no—
10C2×#117×C127—22no—
11C2×#117×C127—21no—
12C2×#117×C127C412yescomplemented
13C2×#117×C127C414yescomplemented
14C2×#117×C127C2212yes—
15C2×#117×C127C2214yes—
16C22×C4⋊C4×C127C411yescharacteristic, complemented
17C22×C4⋊C4×C127C411yescharacteristic, complemented
18C22×C22⋊C4×C127—21no—
19C22×C22⋊C4×C127—21no—
20C22×C42×C127—21no—
21C22×C42×C127C2212yes—
22#407×C127—22no—
23#407×C127C2214yes—
24C2×C22⋊C8×C127—21no—
25C2×C22⋊C8×C127—21no—
26C4×C22⋊C4×C127—22no—
27C4×C22⋊C4×C127C2214yes—
28C2×#95×C127—21no—
29#339×C127C22116yescomplemented
30C25×C127D411yescharacteristic
31C23×C4×C127—28no—
32C23×C4×C127—21no—
33C23×C4×C127—21no—
34C23×C4×C127—22no—
35C23×C4×C127C2×C411yescharacteristic
36C23×C4×C127C2×C412yes—
37C23×C4×C127C2×C411yescharacteristic
38C23×C4×C127D411yescharacteristic
39C23×C4×C127D412yes—
40C23×C4×C127D412yes—
41C23×C4×C127D411yescharacteristic
42C23×C4×C127D411yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C2×M16×C127—22no—
46C2×M16×C127—28no—
47C2×M16×C127C2314yes—
48C22×C8×C127—22no—
49#117×C127—24no—
50#117×C127—24no—
51#117×C127—24no—
52#117×C127—22no—
53#117×C127—24no—
54#117×C127—22no—
55#117×C127—24no—
56#117×C127C2×C414yes—
57#117×C127C2×C418yescomplemented
58#117×C127C2314yes—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127C2×C412yes—
64C2×C4⋊C4×C127C2×C412yes—
65C2×C4⋊C4×C127C2×C414yescomplemented
66C2×C4⋊C4×C127C2×C414yescomplemented
67C2×C22⋊C4×C127—28no—
68C2×C22⋊C4×C127—24no—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—24no—
72C2×C22⋊C4×C127—24no—
73C2×C42×C127—24no—
74C2×C42×C127—22no—
75C2×C42×C127—24no—
76C2×C42×C127—22no—
77C2×C42×C127—28no—
78C2×C42×C127—22no—
79C2×C42×C127C2314yes—
80C22⋊C8×C127—24no—
81C22⋊C8×C127—24no—
82#95×C127—24no—
83C24×C127—24no—
84C24×C127—24no—
85C24×C127—42no—
86C24×C127C22⋊C411yescharacteristic
87C24×C127C22⋊C412yes—
88C24×C127C22⋊C411yescharacteristic
89C24×C127C2×D412yes—
90C24×C127C2×D411yescharacteristic
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—28no—
94C22×C4×C127—24no—
95C22×C4×C127—28no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—28no—
99C22×C4×C127—28no—
100C22×C4×C127—28no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—44no—
107C22×C4×C127—44no—
108C22×C4×C127—44no—
109C22×C4×C127—44no—
110C22×C4×C127C22⋊C411yescharacteristic
111C22×C4×C127C22⋊C412yes—
112C22×C4×C127C22⋊C411yescharacteristic
113C22×C4×C127C22⋊C412yes—
114C22×C4×C127C22⋊C412yes—
115C22×C4×C127C22⋊C412yes—
116C22×C4×C127C22⋊C412yes—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C22×C412yes—
119C22×C4×C127C22×C411yescharacteristic
120C22×C4×C127C22×C411yescharacteristic
121C22×C4×C127C2×D412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127#4118yes—
128C22×C4×C127C2411yescharacteristic
129M16×C127—28no—
130M16×C127—44no—
131C2×C8×C127—24no—
132C2×C8×C127—44no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—24no—
136C4⋊C4×C127—24no—
137C4⋊C4×C127C22×C414yes—
138C4⋊C4×C127C22×C414yes—
139C22⋊C4×C127—216no—
140C22⋊C4×C127—24no—
141C22⋊C4×C127—28no—
142C22⋊C4×C127—24no—
143C42×C127—24no—
144C42×C127—28no—
145C42×C127—24no—
146C42×C127—28no—
147C42×C127—44no—
148C23×C127—22no—
149C23×C127—22no—
150C23×C127—22no—
151C23×C127—22no—
152C23×C127—24no—
153C23×C127—24no—
154C23×C127—22no—
155C23×C127—24no—
156C23×C127—24no—
157C23×C127—22no—
158C23×C127—22no—
159C23×C127—42no—
160C23×C127—42no—
161C23×C127—416no—
162C23×C127#10414yes—
163C23×C127C2×C22⋊C412yes—
164C23×C127C2×C22⋊C411yescharacteristic
165C23×C127C2×C22⋊C412yes—
166C23×C127C2×C22⋊C411yescharacteristic
167C23×C127#12314yes—
168C23×C127C22×D411yescharacteristic
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—28no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—416no—
185C2×C4×C127—44no—
186C2×C4×C127—48no—
187C2×C4×C127—44no—
188C2×C4×C127—48no—
189C2×C4×C127—44no—
190C2×C4×C127—44no—
191C2×C4×C127C2×C22⋊C412yes—
192C2×C4×C127C2×C22⋊C412yes—
193C2×C4×C127C2×C22⋊C411yescharacteristic
194C2×C4×C127C2×C22⋊C411yescharacteristic
195C2×C4×C127#11714yes—
196C2×C4×C127#11714yes—
197C2×C4×C127#12314yes—
198C2×C4×C127#12314yes—
199C2×C4×C127#12314yes—
200C2×C4×C127C23×C411yescharacteristic
201C2×C4×C127C22×D411yescharacteristic
202C2×C4×C127C2×#4114yes—
203C8×C127—44no—
204C22×C127—28no—
205C22×C127—28no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—22no—
209C22×C127—21no—
210C22×C127—21no—
211C22×C127—22no—
212C22×C127—22no—
213C22×C127—22no—
214C22×C127—22no—
215C22×C127—48no—
216C22×C127—48no—
217C22×C127—44no—
218C22×C127#38112yes—
219C22×C127#38112yes—
220C22×C127C2×#10414yes—
221C22×C127C2×#10412yes—
222C22×C127#42112yes—
223C22×C127C22×C22⋊C411yescharacteristic
224C22×C127C2×#12312yes—
225C4×C127—22no—
226C4×C127—22no—
227C4×C127—48no—
228C4×C127—44no—
229C4×C127—44no—
230C4×C127#38112yes—
231C4×C127#38112yes—
232C4×C127C2×#11712yes—
233C4×C127C2×#12312yes—
234C2×#1826C12711yesmaximal, characteristic, direct product factor, Sylow
235C2×C127—22no—
236C2×C127—22no—
237C2×C127—24no—
238C2×C127—42no—
239C2×C127#182614yesdirect product factor
240C2×C127C2×#38111yescharacteristic
241C2×C127C22×#10411yescharacteristic
242C2×C127C2×#42111yescharacteristic
243C22×#117C2×C12711yescharacteristic
244C2×#407C2×C12711yescharacteristic
245C2×C4×C22⋊C4C2×C12711yescharacteristic
246#1826C2×C12718yesdirect product factor
247C2×#339C2×C12714yescomplemented
248C127C2×#182611yescharacteristic, direct product factor, Sylow
249C24×C4C22×C12711yescharacteristic
250C22×M16C22×C12712yes—
251C2×#117—21no—
252C2×#117—22no—
253C2×#117—21no—
254C2×#117—22no—
255C2×#117C4×C12712yescomplemented
256C2×#117C4×C12714yescomplemented
257C2×#117C22×C12712yes—
258C2×#117C22×C12714yes—
259C22×C4⋊C4C4×C12711yescharacteristic, complemented
260C22×C4⋊C4C4×C12711yescharacteristic, complemented
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263C22×C42—21no—
264C22×C42C22×C12712yes—
265#407—22no—
266#407C22×C12714yes—
267C2×C22⋊C8—21no—
268C2×C22⋊C8—21no—
269C4×C22⋊C4—22no—
270C4×C22⋊C4C22×C12714yes—
271C2×#95—21no—
272#339C22×C127116yescomplemented
273C25D4×C12711yescharacteristic
274C23×C4—28no—
275C23×C4—21no—
276C23×C4—21no—
277C23×C4—22no—
278C23×C4C2×C4×C12711yescharacteristic
279C23×C4C2×C4×C12712yes—
280C23×C4C2×C4×C12711yescharacteristic
281C23×C4D4×C12711yescharacteristic
282C23×C4D4×C12712yes—
283C23×C4D4×C12711yescharacteristic
284C23×C4D4×C12712yes—
285C23×C4D4×C12711yescharacteristic
286C23×C4C23×C12712yes—
287C23×C4C23×C12711yescharacteristic
288C2×M16—22no—
289C2×M16—28no—
290C2×M16C23×C12714yes—
291C22×C8—22no—
292#117—24no—
293#117—24no—
294#117—24no—
295#117—22no—
296#117—24no—
297#117—22no—
298#117—24no—
299#117C2×C4×C12714yes—
300#117C2×C4×C12718yescomplemented
301#117C23×C12714yes—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4C2×C4×C12712yes—
307C2×C4⋊C4C2×C4×C12712yes—
308C2×C4⋊C4C2×C4×C12714yescomplemented
309C2×C4⋊C4C2×C4×C12714yescomplemented
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C42—24no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—24no—
320C2×C42—28no—
321C2×C42—22no—
322C2×C42C23×C12714yes—
323C22⋊C8—24no—
324C22⋊C8—24no—
325#95—24no—
326C24—24no—
327C24—24no—
328C24—42no—
329C24C22⋊C4×C12711yescharacteristic
330C24C22⋊C4×C12712yes—
331C24C22⋊C4×C12711yescharacteristic
332C24C2×D4×C12712yes—
333C24C2×D4×C12711yescharacteristic
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—28no—
337C22×C4—24no—
338C22×C4—28no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—28no—
342C22×C4—28no—
343C22×C4—28no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4—44no—
353C22×C4C22⋊C4×C12711yescharacteristic
354C22×C4C22⋊C4×C12712yes—
355C22×C4C22⋊C4×C12711yescharacteristic
356C22×C4C22⋊C4×C12712yes—
357C22×C4C22⋊C4×C12712yes—
358C22×C4C22⋊C4×C12712yes—
359C22×C4C22⋊C4×C12712yes—
360C22×C4C22×C4×C12712yes—
361C22×C4C22×C4×C12712yes—
362C22×C4C22×C4×C12711yescharacteristic
363C22×C4C22×C4×C12711yescharacteristic
364C22×C4C2×D4×C12712yes—
365C22×C4C2×D4×C12712yes—
366C22×C4C2×D4×C12712yes—
367C22×C4C2×D4×C12711yescharacteristic
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C2×D4×C12711yescharacteristic
370C22×C4#41×C12718yes—
371C22×C4C24×C12711yescharacteristic
372M16—28no—
373M16—44no—
374C2×C8—24no—
375C2×C8—44no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—24no—
379C4⋊C4—24no—
380C4⋊C4C22×C4×C12714yes—
381C4⋊C4C22×C4×C12714yes—
382C22⋊C4—216no—
383C22⋊C4—24no—
384C22⋊C4—28no—
385C22⋊C4—24no—
386C42—24no—
387C42—28no—
388C42—24no—
389C42—28no—
390C42—44no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—24no—
396C23—24no—
397C23—22no—
398C23—24no—
399C23—24no—
400C23—22no—
401C23—22no—
402C23—42no—
403C23—42no—
404C23—416no—
405C23#104×C12714yes—
406C23C2×C22⋊C4×C12712yes—
407C23C2×C22⋊C4×C12711yescharacteristic
408C23C2×C22⋊C4×C12712yes—
409C23C2×C22⋊C4×C12711yescharacteristic
410C23#123×C12714yes—
411C23C22×D4×C12711yescharacteristic
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—416no—
428C2×C4—44no—
429C2×C4—48no—
430C2×C4—44no—
431C2×C4—48no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4C2×C22⋊C4×C12712yes—
435C2×C4C2×C22⋊C4×C12712yes—
436C2×C4C2×C22⋊C4×C12711yescharacteristic
437C2×C4C2×C22⋊C4×C12711yescharacteristic
438C2×C4#117×C12714yes—
439C2×C4#117×C12714yes—
440C2×C4#123×C12714yes—
441C2×C4#123×C12714yes—
442C2×C4#123×C12714yes—
443C2×C4C23×C4×C12711yescharacteristic
444C2×C4C22×D4×C12711yescharacteristic
445C2×C4C2×#41×C12714yes—
446C8—44no—
447C22—28no—
448C22—28no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—48no—
459C22—48no—
460C22—44no—
461C22#381×C12712yes—
462C22#381×C12712yes—
463C22C2×#104×C12714yes—
464C22C2×#104×C12712yes—
465C22#421×C12712yes—
466C22C22×C22⋊C4×C12711yescharacteristic
467C22C2×#123×C12712yes—
468C4—22no—
469C4—22no—
470C4—48no—
471C4—44no—
472C4—44no—
473C4#381×C12712yes—
474C4#381×C12712yes—
475C4C2×#117×C12712yes—
476C4C2×#123×C12712yes—
477C2—22no—
478C2—22no—
479C2—24no—
480C2—42no—
481C2C127×#182614yesdirect product factor
482C2C2×#381×C12711yescharacteristic
483C2C22×#104×C12711yescharacteristic
484C2C2×#421×C12711yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C2×C22⋊C4
prime radicalC25×C127D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1826C2direct (N × H)
5. C2×#339×C127C2semidirect
12. C2×#117×C127C4semidirect
13. C2×#117×C127C4semidirect
16. C22×C4⋊C4×C127C4semidirect
17. C22×C4⋊C4×C127C4semidirect
29. #339×C127C22semidirect
57. #117×C127C2×C4semidirect
65. C2×C4⋊C4×C127C2×C4semidirect
66. C2×C4⋊C4×C127C2×C4semidirect
234. C2×#1826C127direct (N × H)
239. C2×C127#1826direct (N × H)
246. #1826C2×C127direct (N × H)
247. C2×#339C2×C127semidirect
248. C127C2×#1826direct (N × H)
255. C2×#117C4×C127semidirect
256. C2×#117C4×C127semidirect
259. C22×C4⋊C4C4×C127semidirect
260. C22×C4⋊C4C4×C127semidirect
272. #339C22×C127semidirect
300. #117C2×C4×C127semidirect
308. C2×C4⋊C4C2×C4×C127semidirect
309. C2×C4⋊C4C2×C4×C127semidirect
481. C2C127×#1826direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#117×C1272
C2×#407×C1272
C2×C4×C22⋊C4×C1272
C127×#18262
C2×#339×C1272
C2×#1826127