Finite Group Databasebeta

← C127×#21825 #44585498

Subgroups — C127×#21825 #44585498

Order 32512.

1474 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic
2C127×#2280C212yesmaximal
3C127×#1996C218yesmaximal, complemented
4C127×#1819C214yesmaximal
5C23×Q8×C127C411yescharacteristic, complemented
6C24×C4×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—22no—
8C2×C22⋊Q8×C127—22no—
9C2×C22⋊Q8×C127—22no—
10C2×C22⋊Q8×C127—22no—
11C2×C22⋊Q8×C127C414yescomplemented
12C2×C22⋊Q8×C127C2214yes—
13C2×#117×C127—22no—
14C22×C4⋊C4×C127C411yescharacteristic, complemented
15C22×C4⋊C4×C127C412yescomplemented
16C22×C22⋊C4×C127C2212yes—
17#381×C127—22no—
18#380×C127—22no—
19#380×C127C2214yes—
20#379×C127C2214yes—
21C4×C22⋊C4×C127—22no—
22C4×C22⋊C4×C127C2214yes—
23#342×C127C22116yes—
24C25×C127C2311yescharacteristic
25C22×Q8×C127—22no—
26C22×Q8×C127—21no—
27C22×Q8×C127—21no—
28C22×Q8×C127—44no—
29C22×Q8×C127C2×C414yes—
30C23×C4×C127—44no—
31C23×C4×C127C2×C411yescharacteristic
32C23×C4×C127C2×C412yes—
33C23×C4×C127C2×C412yes—
34C23×C4×C127C2×C411yescharacteristic
35C23×C4×C127C2×C412yes—
36C23×C4×C127D412yes—
37C23×C4×C127D412yes—
38C23×C4×C127D412yes—
39C23×C4×C127D412yes—
40C23×C4×C127C2312yes—
41C22⋊Q8×C127—24no—
42C22⋊Q8×C127—24no—
43C22⋊Q8×C127—24no—
44C22⋊Q8×C127—24no—
45C22⋊Q8×C127—24no—
46C22⋊Q8×C127—24no—
47C22⋊Q8×C127—24no—
48C22⋊Q8×C127—24no—
49#117×C127—48no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127C2×C414yes—
58C2×C4⋊C4×C127C2×C418yes—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127C2×C414yes—
64C2×C22⋊C4×C127C2318yes—
65C2×C22⋊C4×C127C2314yes—
66C2×C42×C127—24no—
67#95×C127—24no—
68#95×C127—24no—
69C24×C127—24no—
70C24×C127—42no—
71C24×C127—42no—
72C24×C127C22×C411yescharacteristic
73C24×C127C22×C411yescharacteristic
74C24×C127C2×D412yes—
75C24×C127C2×D412yes—
76C24×C127C2411yescharacteristic
77C2×Q8×C127—24no—
78C2×Q8×C127—24no—
79C2×Q8×C127—48no—
80C2×Q8×C127—44no—
81C2×Q8×C127—48no—
82C2×Q8×C127—44no—
83C22×C4×C127—28no—
84C22×C4×C127—24no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—28no—
90C22×C4×C127—44no—
91C22×C4×C127—44no—
92C22×C4×C127—44no—
93C22×C4×C127—44no—
94C22×C4×C127—42no—
95C22×C4×C127—44no—
96C22×C4×C127—44no—
97C22×C4×C127—44no—
98C22×C4×C127C22⋊C412yes—
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C22⋊C412yes—
101C22×C4×C127C22⋊C412yes—
102C22×C4×C127C22⋊C412yes—
103C22×C4×C127C22⋊C411yescharacteristic
104C22×C4×C127C22⋊C411yescharacteristic
105C22×C4×C127C22⋊C412yes—
106C22×C4×C127C22⋊C412yes—
107C22×C4×C127C22⋊C411yescharacteristic
108C22×C4×C127C22×C412yes—
109C22×C4×C127C22×C414yes—
110C22×C4×C127C22×C414yes—
111C22×C4×C127C22×C412yes—
112C22×C4×C127C2×D412yes—
113C22×C4×C127C2×D412yes—
114C22×C4×C127C2×D412yes—
115C22×C4×C127C2×D412yes—
116C4⋊C4×C127—24no—
117C4⋊C4×C127—24no—
118C4⋊C4×C127—28no—
119C4⋊C4×C127—28no—
120C4⋊C4×C127—48no—
121C22⋊C4×C127—28no—
122C22⋊C4×C127—28no—
123C22⋊C4×C127—216no—
124C22⋊C4×C127—48no—
125C22⋊C4×C127—48no—
126C42×C127—48no—
127C23×C127—22no—
128C23×C127—22no—
129C23×C127—22no—
130C23×C127—22no—
131C23×C127—24no—
132C23×C127—24no—
133C23×C127—24no—
134C23×C127—24no—
135C23×C127—41no—
136C23×C127—42no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—42no—
140C23×C127—41no—
141C23×C127—416no—
142C23×C127C2×C22⋊C412yes—
143C23×C127C2×C22⋊C411yescharacteristic
144C23×C127C2×C22⋊C411yescharacteristic
145C23×C127C23×C411yescharacteristic
146C23×C127C22×D412yes—
147C23×C1272−1+414yes—
148Q8×C127—48no—
149Q8×C127—48no—
150C2×C4×C127—24no—
151C2×C4×C127—22no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—24no—
155C2×C4×C127—24no—
156C2×C4×C127—24no—
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127—44no—
170C2×C4×C127—44no—
171C2×C4×C127—44no—
172C2×C4×C127—44no—
173C2×C4×C127—48no—
174C2×C4×C127—48no—
175C2×C4×C127—48no—
176C2×C4×C127#9914yes—
177C2×C4×C127C2×C22⋊C412yes—
178C2×C4×C127C2×C22⋊C412yes—
179C2×C4×C127C2×C22⋊C412yes—
180C2×C4×C127C2×C22⋊C412yes—
181C22×C127—28no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—22no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—22no—
190C22×C127—22no—
191C22×C127—22no—
192C22×C127—22no—
193C22×C127—44no—
194C22×C127—48no—
195C22×C127—48no—
196C22×C127—44no—
197C22×C127C2×#9912yes—
198C22×C127#41012yes—
199C22×C127C22×C22⋊C411yescharacteristic
200C22×C127#51912yes—
201C22×C127#53614yes—
202C4×C127—22no—
203C4×C127—22no—
204C4×C127—22no—
205C4×C127—44no—
206C4×C127—44no—
207C4×C127—88no—
208C4×C127C2×#9914yes—
209#21825C12711yesmaximal, characteristic, direct product factor, Sylow
210C2×C127—24no—
211C2×C127—22no—
212C2×C127—22no—
213C2×C127—22no—
214C2×C127—42no—
215C2×C127#231011yescharacteristic
216C2×C127C22×#9911yescharacteristic
217C2×C127C2×#41011yescharacteristic
218C22×C22⋊Q8C2×C12711yescharacteristic
219#2280C2×C12712yes—
220#1996C2×C12718yescomplemented
221#1819C2×C12714yes—
222C127#2182511yescharacteristic, direct product factor, Sylow
223C23×Q8C4×C12711yescharacteristic, complemented
224C24×C4C22×C12711yescharacteristic
225C2×C22⋊Q8—22no—
226C2×C22⋊Q8—22no—
227C2×C22⋊Q8—22no—
228C2×C22⋊Q8—22no—
229C2×C22⋊Q8C4×C12714yescomplemented
230C2×C22⋊Q8C22×C12714yes—
231C2×#117—22no—
232C22×C4⋊C4C4×C12711yescharacteristic, complemented
233C22×C4⋊C4C4×C12712yescomplemented
234C22×C22⋊C4C22×C12712yes—
235#381—22no—
236#380—22no—
237#380C22×C12714yes—
238#379C22×C12714yes—
239C4×C22⋊C4—22no—
240C4×C22⋊C4C22×C12714yes—
241#342C22×C127116yes—
242C25C23×C12711yescharacteristic
243C22×Q8—22no—
244C22×Q8—21no—
245C22×Q8—21no—
246C22×Q8—44no—
247C22×Q8C2×C4×C12714yes—
248C23×C4—44no—
249C23×C4C2×C4×C12711yescharacteristic
250C23×C4C2×C4×C12712yes—
251C23×C4C2×C4×C12712yes—
252C23×C4C2×C4×C12711yescharacteristic
253C23×C4C2×C4×C12712yes—
254C23×C4D4×C12712yes—
255C23×C4D4×C12712yes—
256C23×C4D4×C12712yes—
257C23×C4D4×C12712yes—
258C23×C4C23×C12712yes—
259C22⋊Q8—24no—
260C22⋊Q8—24no—
261C22⋊Q8—24no—
262C22⋊Q8—24no—
263C22⋊Q8—24no—
264C22⋊Q8—24no—
265C22⋊Q8—24no—
266C22⋊Q8—24no—
267#117—48no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4C2×C4×C12714yes—
276C2×C4⋊C4C2×C4×C12718yes—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—24no—
281C2×C22⋊C4C2×C4×C12714yes—
282C2×C22⋊C4C23×C12718yes—
283C2×C22⋊C4C23×C12714yes—
284C2×C42—24no—
285#95—24no—
286#95—24no—
287C24—24no—
288C24—42no—
289C24—42no—
290C24C22×C4×C12711yescharacteristic
291C24C22×C4×C12711yescharacteristic
292C24C2×D4×C12712yes—
293C24C2×D4×C12712yes—
294C24C24×C12711yescharacteristic
295C2×Q8—24no—
296C2×Q8—24no—
297C2×Q8—48no—
298C2×Q8—44no—
299C2×Q8—48no—
300C2×Q8—44no—
301C22×C4—28no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—28no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—44no—
316C22×C4C22⋊C4×C12712yes—
317C22×C4C22⋊C4×C12711yescharacteristic
318C22×C4C22⋊C4×C12712yes—
319C22×C4C22⋊C4×C12712yes—
320C22×C4C22⋊C4×C12712yes—
321C22×C4C22⋊C4×C12711yescharacteristic
322C22×C4C22⋊C4×C12711yescharacteristic
323C22×C4C22⋊C4×C12712yes—
324C22×C4C22⋊C4×C12712yes—
325C22×C4C22⋊C4×C12711yescharacteristic
326C22×C4C22×C4×C12712yes—
327C22×C4C22×C4×C12714yes—
328C22×C4C22×C4×C12714yes—
329C22×C4C22×C4×C12712yes—
330C22×C4C2×D4×C12712yes—
331C22×C4C2×D4×C12712yes—
332C22×C4C2×D4×C12712yes—
333C22×C4C2×D4×C12712yes—
334C4⋊C4—24no—
335C4⋊C4—24no—
336C4⋊C4—28no—
337C4⋊C4—28no—
338C4⋊C4—48no—
339C22⋊C4—28no—
340C22⋊C4—28no—
341C22⋊C4—216no—
342C22⋊C4—48no—
343C22⋊C4—48no—
344C42—48no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—24no—
350C23—24no—
351C23—24no—
352C23—24no—
353C23—41no—
354C23—42no—
355C23—41no—
356C23—41no—
357C23—42no—
358C23—41no—
359C23—416no—
360C23C2×C22⋊C4×C12712yes—
361C23C2×C22⋊C4×C12711yescharacteristic
362C23C2×C22⋊C4×C12711yescharacteristic
363C23C23×C4×C12711yescharacteristic
364C23C22×D4×C12712yes—
365C232−1+4×C12714yes—
366Q8—48no—
367Q8—48no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—48no—
392C2×C4—48no—
393C2×C4—48no—
394C2×C4#99×C12714yes—
395C2×C4C2×C22⋊C4×C12712yes—
396C2×C4C2×C22⋊C4×C12712yes—
397C2×C4C2×C22⋊C4×C12712yes—
398C2×C4C2×C22⋊C4×C12712yes—
399C22—28no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—44no—
412C22—48no—
413C22—48no—
414C22—44no—
415C22C2×#99×C12712yes—
416C22#410×C12712yes—
417C22C22×C22⋊C4×C12711yescharacteristic
418C22#519×C12712yes—
419C22#536×C12714yes—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—44no—
424C4—44no—
425C4—88no—
426C4C2×#99×C12714yes—
427C2—24no—
428C2—22no—
429C2—22no—
430C2—22no—
431C2—42no—
432C2C127×#231011yescharacteristic
433C2C22×#99×C12711yescharacteristic
434C2C2×#410×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1996C2semidirect
5. C23×Q8×C127C4semidirect
11. C2×C22⋊Q8×C127C4semidirect
14. C22×C4⋊C4×C127C4semidirect
15. C22×C4⋊C4×C127C4semidirect
209. #21825C127direct (N × H)
220. #1996C2×C127semidirect
222. C127#21825direct (N × H)
223. C23×Q8C4×C127semidirect
229. C2×C22⋊Q8C4×C127semidirect
232. C22×C4⋊C4C4×C127semidirect
233. C22×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C127×#22802
C127×#19962
C127×#18192
#21825127