Finite Group Databasebeta

← C2×C127×#1638 #44582166

Subgroups — C2×C127×#1638 #44582166

Order 32512.

946 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C127C211yesmaximal, characteristic
2C2×#487×C127C211yesmaximal, characteristic, complemented
3C2×#477×C127C211yesmaximal, characteristic, complemented
4C2×#476×C127C211yesmaximal, characteristic
5C127×#1638C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic
9#556×C127—22no—
10#556×C127—22no—
11#556×C127—22no—
12#556×C127C2214yes—
13C2×C4⋊Q8×C127C2211yescharacteristic
14C2×C4⋊Q8×C127C2211yescharacteristic
15C2×#126×C127—22no—
16C2×#124×C127—21no—
17C2×C22⋊Q8×C127—21no—
18C2×C4×Q8×C127—21no—
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21C2×#117×C127—21no—
22#487×C127—22no—
23#487×C127C2214yescomplemented
24#477×C127—22no—
25#477×C127C2214yescomplemented
26#476×C127—22no—
27#476×C127C2214yes—
28C2×#107×C127—21no—
29C2×#106×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127—21no—
33C2×#103×C127—22no—
34C2×#102×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic
36#332×C127C2214yescomplemented
37Q8⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yes—
39C22×Q8×C127—21no—
40C22×Q8×C127—21no—
41C22×Q8×C127D411yescharacteristic
42C22×D4×C127D411yescharacteristic
43C23×C4×C127—21no—
44C22×C8×C127—21no—
45C22×C8×C127—21no—
46C22×C8×C127—21no—
47C4⋊Q8×C127—21no—
48C4⋊Q8×C127—21no—
49C4⋊Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127D412yes—
53C4⋊Q8×C127C2312yes—
54C4⋊Q8×C127C2312yes—
55#126×C127—28no—
56#126×C127—28no—
57#124×C127—24no—
58#124×C127—24no—
59C22⋊Q8×C127—24no—
60C22⋊Q8×C127—24no—
61C4×Q8×C127—24no—
62C4×Q8×C127—24no—
63C4×Q8×C127—21no—
64C4×Q8×C127—21no—
65C4×Q8×C127D412yes—
66C4×Q8×C127C2312yes—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69C4×D4×C127D412yes—
70C4×D4×C127C2312yes—
71#117×C127—24no—
72#117×C127—24no—
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127—21no—
75C2×C4⋊C4×C127—21no—
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127D411yescharacteristic
79C2×C4⋊C4×C127D411yescharacteristic
80C2×C4⋊C4×C127D412yes—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—21no—
84C2×C42×C127—22no—
85C2×C42×C127—21no—
86C2×C42×C127C2311yescharacteristic
87#107×C127—24no—
88#106×C127—24no—
89C4⋊C8×C127—21no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127C2312yes—
92C4⋊C8×C127C2312yes—
93#103×C127—24no—
94#103×C127—28no—
95#102×C127—24no—
96C4×C8×C127—21no—
97C4×C8×C127C2312yes—
98C24×C127—21no—
99C2×Q8×C127—21no—
100C2×Q8×C127—22no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—44no—
106C2×Q8×C127—41no—
107C2×Q8×C127—42no—
108C2×Q8×C127—42no—
109C2×Q8×C127C2×D412yes—
110C2×D4×C127—21no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127C2×D412yes—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—42no—
121C22×C4×C127—42no—
122C22×C4×C127—41no—
123C22×C4×C127C2×D411yescharacteristic
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C2×C8×C127—22no—
127C2×C8×C127—22no—
128C2×C8×C127—22no—
129C2×C8×C127—42no—
130C2×C8×C127—42no—
131C2×C8×C127—42no—
132C4⋊C4×C127—28no—
133C4⋊C4×C127—22no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—21no—
136C4⋊C4×C127—21no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—41no—
143C4⋊C4×C127—41no—
144C4⋊C4×C127C2×D414yes—
145C4⋊C4×C127C2×D412yes—
146C4⋊C4×C127C2×D412yes—
147C22⋊C4×C127—28no—
148C22⋊C4×C127—28no—
149C22⋊C4×C127—22no—
150C22⋊C4×C127—22no—
151C42×C127—28no—
152C42×C127—22no—
153C42×C127—22no—
154C42×C127C2×D411yescharacteristic
155C42×C127C2×D411yescharacteristic
156C42×C127C2×D411yescharacteristic
157C42×C127C2411yescharacteristic
158C23×C127—22no—
159C23×C127—42no—
160C23×C127—42no—
161C23×C127—42no—
162C23×C127#12011yescharacteristic
163Q8×C127—22no—
164Q8×C127—22no—
165Q8×C127—44no—
166Q8×C127—42no—
167Q8×C127—42no—
168Q8×C127—42no—
169Q8×C127—44no—
170Q8×C127—82no—
171D4×C127—22no—
172D4×C127—22no—
173D4×C127—42no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—24no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—44no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—44no—
186C2×C4×C127—42no—
187C2×C4×C127—82no—
188C2×C4×C127#12011yescharacteristic
189C2×C4×C127#12011yescharacteristic
190C2×C4×C127#12011yescharacteristic
191C2×C4×C127#13512yes—
192C2×C4×C127#13512yes—
193C2×C4×C127#13712yes—
194C2×C4×C127#13712yes—
195C2×C4×C127C22×D411yescharacteristic
196C2×C4×C127C22×D411yescharacteristic
197C2×C4×C127C22×D411yescharacteristic
198C8×C127—42no—
199C8×C127—42no—
200C8×C127—42no—
201C22×C127—42no—
202C22×C127—42no—
203C22×C127—42no—
204C22×C127—84no—
205C22×C127#45212yes—
206C22×C127#45212yes—
207C22×C127#45412yes—
208C22×C127C2×#12011yescharacteristic
209C4×C127—21no—
210C4×C127—21no—
211C4×C127—42no—
212C4×C127—42no—
213C4×C127—44no—
214C4×C127—42no—
215C4×C127—82no—
216C4×C127#45212yes—
217C4×C127#45212yes—
218C4×C127C2×#13511yescharacteristic
219C4×C127C2×#13511yescharacteristic
220C4×C127C2×#13711yescharacteristic
221C4×C127C2×#13711yescharacteristic
222C2×#1638C12711yesmaximal, characteristic, direct product factor, Sylow
223C2×C127—82no—
224C2×C127#163814yesdirect product factor
225C2×C127C2×#45211yescharacteristic
226C2×C127C2×#45211yescharacteristic
227C2×C127C2×#45411yescharacteristic
228C2×#556C2×C12711yescharacteristic
229C2×#487C2×C12711yescharacteristic, complemented
230C2×#477C2×C12711yescharacteristic, complemented
231C2×#476C2×C12711yescharacteristic
232#1638C2×C12718yesdirect product factor
233C2×#332C2×C12711yescharacteristic, complemented
234C2×Q8⋊C8C2×C12711yescharacteristic, complemented
235C2×D4⋊C8C2×C12711yescharacteristic
236C127C2×#163811yescharacteristic, direct product factor, Sylow
237#556—22no—
238#556—22no—
239#556—22no—
240#556C22×C12714yes—
241C2×C4⋊Q8C22×C12711yescharacteristic
242C2×C4⋊Q8C22×C12711yescharacteristic
243C2×#126—22no—
244C2×#124—21no—
245C2×C22⋊Q8—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8C22×C12711yescharacteristic
248C2×C4×D4C22×C12711yescharacteristic
249C2×#117—21no—
250#487—22no—
251#487C22×C12714yescomplemented
252#477—22no—
253#477C22×C12714yescomplemented
254#476—22no—
255#476C22×C12714yes—
256C2×#107—21no—
257C2×#106—21no—
258C2×C4⋊C8C22×C12711yescharacteristic
259C2×C4⋊C8C22×C12711yescharacteristic
260C2×#103—21no—
261C2×#103—22no—
262C2×#102—21no—
263C2×C4×C8C22×C12711yescharacteristic
264#332C22×C12714yescomplemented
265Q8⋊C8C22×C12714yescomplemented
266D4⋊C8C22×C12714yes—
267C22×Q8—21no—
268C22×Q8—21no—
269C22×Q8D4×C12711yescharacteristic
270C22×D4D4×C12711yescharacteristic
271C23×C4—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C4⋊Q8—21no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8D4×C12712yes—
281C4⋊Q8C23×C12712yes—
282C4⋊Q8C23×C12712yes—
283#126—28no—
284#126—28no—
285#124—24no—
286#124—24no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C4×Q8—24no—
290C4×Q8—24no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8D4×C12712yes—
294C4×Q8C23×C12712yes—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4D4×C12712yes—
298C4×D4C23×C12712yes—
299#117—24no—
300#117—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4D4×C12711yescharacteristic
307C2×C4⋊C4D4×C12711yescharacteristic
308C2×C4⋊C4D4×C12712yes—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—21no—
312C2×C42—22no—
313C2×C42—21no—
314C2×C42C23×C12711yescharacteristic
315#107—24no—
316#106—24no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8C23×C12712yes—
320C4⋊C8C23×C12712yes—
321#103—24no—
322#103—28no—
323#102—24no—
324C4×C8—21no—
325C4×C8C23×C12712yes—
326C24—21no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—22no—
330C2×Q8—22no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—44no—
334C2×Q8—41no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8C2×D4×C12712yes—
338C2×D4—21no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4C2×D4×C12712yes—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4C2×D4×C12711yescharacteristic
352C22×C4C2×D4×C12711yescharacteristic
353C22×C4C2×D4×C12711yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—42no—
358C2×C8—42no—
359C2×C8—42no—
360C4⋊C4—28no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4C2×D4×C12714yes—
373C4⋊C4C2×D4×C12712yes—
374C4⋊C4C2×D4×C12712yes—
375C22⋊C4—28no—
376C22⋊C4—28no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C42—28no—
380C42—22no—
381C42—22no—
382C42C2×D4×C12711yescharacteristic
383C42C2×D4×C12711yescharacteristic
384C42C2×D4×C12711yescharacteristic
385C42C24×C12711yescharacteristic
386C23—22no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23#120×C12711yescharacteristic
391Q8—22no—
392Q8—22no—
393Q8—44no—
394Q8—42no—
395Q8—42no—
396Q8—42no—
397Q8—44no—
398Q8—82no—
399D4—22no—
400D4—22no—
401D4—42no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—82no—
416C2×C4#120×C12711yescharacteristic
417C2×C4#120×C12711yescharacteristic
418C2×C4#120×C12711yescharacteristic
419C2×C4#135×C12712yes—
420C2×C4#135×C12712yes—
421C2×C4#137×C12712yes—
422C2×C4#137×C12712yes—
423C2×C4C22×D4×C12711yescharacteristic
424C2×C4C22×D4×C12711yescharacteristic
425C2×C4C22×D4×C12711yescharacteristic
426C8—42no—
427C8—42no—
428C8—42no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—84no—
433C22#452×C12712yes—
434C22#452×C12712yes—
435C22#454×C12712yes—
436C22C2×#120×C12711yescharacteristic
437C4—21no—
438C4—21no—
439C4—42no—
440C4—42no—
441C4—44no—
442C4—42no—
443C4—82no—
444C4#452×C12712yes—
445C4#452×C12712yes—
446C4C2×#135×C12711yescharacteristic
447C4C2×#135×C12711yescharacteristic
448C4C2×#137×C12711yescharacteristic
449C4C2×#137×C12711yescharacteristic
450C2—82no—
451C2C127×#163814yesdirect product factor
452C2C2×#452×C12711yescharacteristic
453C2C2×#452×C12711yescharacteristic
454C2C2×#454×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#487×C127C2semidirect
3. C2×#477×C127C2semidirect
5. C127×#1638C2direct (N × H)
6. C2×#332×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
23. #487×C127C22semidirect
25. #477×C127C22semidirect
36. #332×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
222. C2×#1638C127direct (N × H)
224. C2×C127#1638direct (N × H)
229. C2×#487C2×C127semidirect
230. C2×#477C2×C127semidirect
232. #1638C2×C127direct (N × H)
233. C2×#332C2×C127semidirect
234. C2×Q8⋊C8C2×C127semidirect
236. C127C2×#1638direct (N × H)
251. #487C22×C127semidirect
253. #477C22×C127semidirect
264. #332C22×C127semidirect
265. Q8⋊C8C22×C127semidirect
451. C2C127×#1638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#556×C1272
C2×#487×C1272
C2×#477×C1272
C2×#476×C1272
C127×#16382
C2×#332×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1638127