Finite Group Databasebeta

← C127×#8406 #44572079

Subgroups — C127×#8406 #44572079

Order 32512.

868 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C127C211yesmaximal, characteristic
2C127×#1872C212yesmaximal
3C2×#328×C127C212yesmaximal
4C2×#324×C127C211yesmaximal, characteristic
5C127×#1441C211yesmaximal, characteristic
6#544×C127—24no—
7#544×C127—22no—
8#544×C127C414yescomplemented
9C2×C4⋊Q8×C127—22no—
10C2×#125×C127—22no—
11C2×C22⋊Q8×C127—21no—
12C2×C22⋊Q8×C127C2212yes—
13C2×#117×C127—21no—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C2×#103×C127—22no—
17C2×C22⋊C8×C127C2212yes—
18C2×#95×C127—21no—
19C2×#95×C127—21no—
20C2×#95×C127C2211yescharacteristic
21#340×C127—22no—
22#328×C127—24no—
23#324×C127—22no—
24C22×Q8×C127—21no—
25C22×Q8×C127D412yes—
26C23×C4×C127—21no—
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C23×C4×C127C2311yescharacteristic
31C22×C8×C127—22no—
32C4⋊Q8×C127—28no—
33C4⋊Q8×C127—28no—
34#125×C127—28no—
35#125×C127—28no—
36C22⋊Q8×C127—24no—
37C22⋊Q8×C127—24no—
38C22⋊Q8×C127—22no—
39C22⋊Q8×C127—22no—
40C22⋊Q8×C127C2×C414yes—
41C22⋊Q8×C127D414yes—
42#117×C127—24no—
43#117×C127—24no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—42no—
53C2×C4⋊C4×C127C2×C412yes—
54C2×C4⋊C4×C127D412yes—
55C2×C4⋊C4×C127D412yes—
56C2×C22⋊C4×C127—22no—
57C2×C42×C127—22no—
58#103×C127—44no—
59C22⋊C8×C127—22no—
60C22⋊C8×C127—22no—
61#95×C127—22no—
62#95×C127—42no—
63#95×C127—42no—
64C24×C127C2×D411yescharacteristic
65C2×Q8×C127—24no—
66C2×Q8×C127—22no—
67C2×Q8×C127—42no—
68C2×Q8×C127—42no—
69C2×Q8×C127—81no—
70C2×Q8×C127—81no—
71C2×Q8×C127C22⋊C414yes—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127—41no—
89C22×C4×C127—41no—
90C22×C4×C127—41no—
91C22×C4×C127—41no—
92C22×C4×C127—41no—
93C22×C4×C127—41no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127—41no—
98C22×C4×C127C22⋊C412yes—
99C22×C4×C127C22⋊C412yes—
100C22×C4×C127SD1612yes—
101C22×C4×C127Q1612yes—
102C22×C4×C127C22×C411yescharacteristic
103C22×C4×C127C2×D412yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D411yescharacteristic
106C2×C8×C127—42no—
107C2×C8×C127—42no—
108C2×C8×C127—42no—
109C4⋊C4×C127—24no—
110C4⋊C4×C127—24no—
111C4⋊C4×C127—24no—
112C4⋊C4×C127—28no—
113C4⋊C4×C127—24no—
114C4⋊C4×C127—24no—
115C4⋊C4×C127—24no—
116C4⋊C4×C127—24no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127—24no—
119C4⋊C4×C127—42no—
120C4⋊C4×C127C22⋊C414yes—
121C22⋊C4×C127—24no—
122C22⋊C4×C127—24no—
123C42×C127—28no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—21no—
128C23×C127C2×C22⋊C411yescharacteristic
129C23×C127#12011yescharacteristic
130C23×C127#12011yescharacteristic
131C23×C127C2×SD1611yescharacteristic
132C23×C127C2×Q1611yescharacteristic
133C23×C127#13711yescharacteristic
134C23×C127#13711yescharacteristic
135Q8×C127—44no—
136Q8×C127—82no—
137Q8×C127—84no—
138C2×C4×C127—22no—
139C2×C4×C127—22no—
140C2×C4×C127—22no—
141C2×C4×C127—22no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—22no—
145C2×C4×C127—22no—
146C2×C4×C127—24no—
147C2×C4×C127—24no—
148C2×C4×C127—22no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—42no—
152C2×C4×C127—42no—
153C2×C4×C127—42no—
154C2×C4×C127—41no—
155C2×C4×C127—42no—
156C2×C4×C127—41no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—42no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—81no—
166C2×C4×C127—81no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127—81no—
170C2×C4×C127—81no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127—81no—
174C2×C4×C127#10314yescomplemented
175C2×C4×C127C2×C22⋊C412yes—
176C2×C4×C127#12012yes—
177C8×C127—82no—
178C22×C127—21no—
179C22×C127—21no—
180C22×C127—21no—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—21no—
190C22×C127#37911yescharacteristic
191C22×C127C2×#10311yescharacteristic
192C22×C127#41911yescharacteristic
193C22×C127#44811yescharacteristic
194C22×C127#44811yescharacteristic
195C22×C127#45111yescharacteristic
196C22×C127#45111yescharacteristic
197C22×C127#45411yescharacteristic
198C22×C127#45611yescharacteristic
199C22×C127B(4,𝔽2)11yescharacteristic
200C22×C127#45811yescharacteristic
201C4×C127—24no—
202C4×C127—22no—
203C4×C127—22no—
204C4×C127—44no—
205C4×C127—42no—
206C4×C127—44no—
207C4×C127—82no—
208C4×C127—82no—
209#8406C12711yesmaximal, characteristic, direct product factor, Sylow
210C2×C127—21no—
211C2×C127—21no—
212C2×C127—21no—
213C2×C127—21no—
214C2×C127#159911yescharacteristic
215C2×C127#160511yescharacteristic
216C2×C127#161111yescharacteristic
217C2×C127#161711yescharacteristic
218C2×C127#178711yescharacteristic
219C2×C127#179011yescharacteristic
220C2×C127#179311yescharacteristic
221C2×#544C2×C12711yescharacteristic
222#1872C2×C12712yes—
223C2×#328C2×C12712yes—
224C2×#324C2×C12711yescharacteristic
225#1441C2×C12711yescharacteristic
226C127#840611yescharacteristic, direct product factor, Sylow
227#544—24no—
228#544—22no—
229#544C4×C12714yescomplemented
230C2×C4⋊Q8—22no—
231C2×#125—22no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C22×C12712yes—
234C2×#117—21no—
235C22×C4⋊C4C22×C12711yescharacteristic
236C22×C4⋊C4C22×C12711yescharacteristic
237C2×#103—22no—
238C2×C22⋊C8C22×C12712yes—
239C2×#95—21no—
240C2×#95—21no—
241C2×#95C22×C12711yescharacteristic
242#340—22no—
243#328—24no—
244#324—22no—
245C22×Q8—21no—
246C22×Q8D4×C12712yes—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4D4×C12711yescharacteristic
250C23×C4D4×C12711yescharacteristic
251C23×C4C23×C12711yescharacteristic
252C22×C8—22no—
253C4⋊Q8—28no—
254C4⋊Q8—28no—
255#125—28no—
256#125—28no—
257C22⋊Q8—24no—
258C22⋊Q8—24no—
259C22⋊Q8—22no—
260C22⋊Q8—22no—
261C22⋊Q8C2×C4×C12714yes—
262C22⋊Q8D4×C12714yes—
263#117—24no—
264#117—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4C2×C4×C12712yes—
275C2×C4⋊C4D4×C12712yes—
276C2×C4⋊C4D4×C12712yes—
277C2×C22⋊C4—22no—
278C2×C42—22no—
279#103—44no—
280C22⋊C8—22no—
281C22⋊C8—22no—
282#95—22no—
283#95—42no—
284#95—42no—
285C24C2×D4×C12711yescharacteristic
286C2×Q8—24no—
287C2×Q8—22no—
288C2×Q8—42no—
289C2×Q8—42no—
290C2×Q8—81no—
291C2×Q8—81no—
292C2×Q8C22⋊C4×C12714yes—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4C22⋊C4×C12712yes—
320C22×C4C22⋊C4×C12712yes—
321C22×C4SD16×C12712yes—
322C22×C4Q16×C12712yes—
323C22×C4C22×C4×C12711yescharacteristic
324C22×C4C2×D4×C12712yes—
325C22×C4C2×D4×C12712yes—
326C22×C4C2×D4×C12711yescharacteristic
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—28no—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—42no—
341C4⋊C4C22⋊C4×C12714yes—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C42—28no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23C2×C22⋊C4×C12711yescharacteristic
350C23#120×C12711yescharacteristic
351C23#120×C12711yescharacteristic
352C23C2×SD16×C12711yescharacteristic
353C23C2×Q16×C12711yescharacteristic
354C23#137×C12711yescharacteristic
355C23#137×C12711yescharacteristic
356Q8—44no—
357Q8—82no—
358Q8—84no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4#103×C12714yescomplemented
396C2×C4C2×C22⋊C4×C12712yes—
397C2×C4#120×C12712yes—
398C8—82no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22#379×C12711yescharacteristic
412C22C2×#103×C12711yescharacteristic
413C22#419×C12711yescharacteristic
414C22#448×C12711yescharacteristic
415C22#448×C12711yescharacteristic
416C22#451×C12711yescharacteristic
417C22#451×C12711yescharacteristic
418C22#454×C12711yescharacteristic
419C22#456×C12711yescharacteristic
420C22B(4,𝔽2)×C12711yescharacteristic
421C22#458×C12711yescharacteristic
422C4—24no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—44no—
427C4—44no—
428C4—82no—
429C4—82no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2C127×#159911yescharacteristic
435C2C127×#160511yescharacteristic
436C2C127×#161111yescharacteristic
437C2C127×#161711yescharacteristic
438C2C127×#178711yescharacteristic
439C2C127×#179011yescharacteristic
440C2C127×#179311yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
8. #544×C127C4semidirect
174. C2×C4×C127#103semidirect
209. #8406C127direct (N × H)
226. C127#8406direct (N × H)
229. #544C4×C127semidirect
395. C2×C4#103×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1272
C127×#18722
C2×#328×C1272
C2×#324×C1272
C127×#14412
#8406127