Finite Group Databasebeta

← C127×#17304 #44580977

Subgroups — C127×#17304 #44580977

Order 32512.

970 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1445C211yesmaximal, characteristic
2C127×#1444C211yesmaximal, characteristic
3C127×#1443C212yesmaximal
4C127×#1442C212yesmaximal
5C127×#1442C211yesmaximal, characteristic
6C127×#1442C212yesmaximal
7C127×#1441C212yesmaximal
8C127×#1441C212yesmaximal
9C127×#1441C212yesmaximal
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C2×#95×C127C2211yescharacteristic
16C2×#95×C127C2212yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2212yes—
19C2×#95×C127C2211yescharacteristic
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C23×C4×C127C2312yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2311yescharacteristic
38C23×C4×C127C2312yes—
39C23×C4×C127C2311yescharacteristic
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—41no—
43C2×C4⋊C4×C127—41no—
44C2×C4⋊C4×C127—42no—
45C2×C4⋊C4×C127—42no—
46C2×C4⋊C4×C127—42no—
47C2×C4⋊C4×C127—42no—
48C2×C4⋊C4×C127—41no—
49C2×C4⋊C4×C127—41no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—42no—
52C2×C4⋊C4×C127Q814yes—
53#95×C127—22no—
54#95×C127—24no—
55#95×C127—24no—
56#95×C127—24no—
57#95×C127—22no—
58#95×C127—42no—
59#95×C127—42no—
60#95×C127—42no—
61#95×C127—42no—
62#95×C127—41no—
63#95×C127—42no—
64#95×C127—41no—
65#95×C127—42no—
66#95×C127—42no—
67#95×C127—42no—
68#95×C127—42no—
69C24×C127C2411yescharacteristic
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—21no—
79C22×C4×C127—22no—
80C22×C4×C127—21no—
81C22×C4×C127—22no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—21no—
90C22×C4×C127—22no—
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127C2×Q812yes—
123C22×C4×C127C2×Q814yes—
124C22×C4×C127#4112yes—
125C22×C4×C127#4114yes—
126C22×C4×C127#4112yes—
127C4⋊C4×C127—44no—
128C4⋊C4×C127—48no—
129C4⋊C4×C127—48no—
130C4⋊C4×C127—44no—
131C4⋊C4×C127—44no—
132C23×C127C22×Q811yescharacteristic
133C23×C127C2×#4111yescharacteristic
134C23×C127C2×#4112yes—
135C23×C127C2×#4111yescharacteristic
136C23×C127H(5,𝔽2)12yes—
137C23×C127H(5,𝔽2)11yescharacteristic
138C23×C127H(5,𝔽2)12yes—
139C23×C127H(5,𝔽2)11yescharacteristic
140C23×C1272−1+411yescharacteristic
141C23×C1272−1+412yes—
142C23×C1272−1+411yescharacteristic
143C2×C4×C127—24no—
144C2×C4×C127—24no—
145C2×C4×C127—22no—
146C2×C4×C127—24no—
147C2×C4×C127—22no—
148C2×C4×C127—22no—
149C2×C4×C127—24no—
150C2×C4×C127—24no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—24no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—42no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—42no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—42no—
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—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C22×C127#53812yes—
201C22×C127#53812yes—
202C22×C127#53911yescharacteristic
203C22×C127#53912yes—
204C22×C127#53911yescharacteristic
205C22×C127#54112yes—
206C22×C127#54212yes—
207C22×C127#54311yescharacteristic
208C22×C127#54412yes—
209C22×C127#55212yes—
210C22×C127#55312yes—
211C22×C127#55412yes—
212C22×C127#55511yescharacteristic
213C22×C127#55511yescharacteristic
214C22×C127#55711yescharacteristic
215C22×C127#55711yescharacteristic
216C22×C127#56011yescharacteristic
217C22×C127#56011yescharacteristic
218C22×C127#56212yes—
219C22×C127#56212yes—
220C22×C127#56311yescharacteristic
221C22×C127#56312yes—
222C22×C127#56311yescharacteristic
223C4×C127—42no—
224C4×C127—42no—
225C4×C127—42no—
226C4×C127—44no—
227C4×C127—44no—
228C4×C127—82no—
229C4×C127—82no—
230C4×C127—82no—
231C4×C127—82no—
232#17304C12711yesmaximal, characteristic, direct product factor, Sylow
233C2×C127#276911yescharacteristic
234C2×C127#277412yes—
235C2×C127#278112yes—
236C2×C127#278411yescharacteristic
237C2×C127#279511yescharacteristic
238C2×C127#280212yes—
239C2×C127#280911yescharacteristic
240C2×C127#282611yescharacteristic
241C2×C127#283112yes—
242C2×C127#283411yescharacteristic
243C2×C127#284111yescharacteristic
244#1445C2×C12711yescharacteristic
245#1444C2×C12711yescharacteristic
246#1443C2×C12712yes—
247#1442C2×C12712yes—
248#1442C2×C12711yescharacteristic
249#1442C2×C12712yes—
250#1441C2×C12712yes—
251#1441C2×C12712yes—
252#1441C2×C12712yes—
253C127#1730411yescharacteristic, direct product factor, Sylow
254C22×C4⋊C4C22×C12712yes—
255C22×C4⋊C4C22×C12712yes—
256C22×C4⋊C4C22×C12711yescharacteristic
257C22×C4⋊C4C22×C12711yescharacteristic
258C22×C4⋊C4C22×C12711yescharacteristic
259C2×#95C22×C12711yescharacteristic
260C2×#95C22×C12712yes—
261C2×#95C22×C12712yes—
262C2×#95C22×C12712yes—
263C2×#95C22×C12711yescharacteristic
264C2×#95C22×C12712yes—
265C2×#95C22×C12712yes—
266C2×#95C22×C12712yes—
267C2×#95C22×C12712yes—
268C2×#95C22×C12712yes—
269C2×#95C22×C12712yes—
270C2×#95C22×C12712yes—
271C2×#95C22×C12712yes—
272C2×#95C22×C12712yes—
273C2×#95C22×C12711yescharacteristic
274C2×#95C22×C12711yescharacteristic
275C23×C4C23×C12712yes—
276C23×C4C23×C12712yes—
277C23×C4C23×C12712yes—
278C23×C4C23×C12712yes—
279C23×C4C23×C12712yes—
280C23×C4C23×C12711yescharacteristic
281C23×C4C23×C12711yescharacteristic
282C23×C4C23×C12712yes—
283C23×C4C23×C12711yescharacteristic
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4Q8×C12714yes—
297#95—22no—
298#95—24no—
299#95—24no—
300#95—24no—
301#95—22no—
302#95—42no—
303#95—42no—
304#95—42no—
305#95—42no—
306#95—41no—
307#95—42no—
308#95—41no—
309#95—42no—
310#95—42no—
311#95—42no—
312#95—42no—
313C24C24×C12711yescharacteristic
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4C2×Q8×C12712yes—
367C22×C4C2×Q8×C12714yes—
368C22×C4#41×C12712yes—
369C22×C4#41×C12714yes—
370C22×C4#41×C12712yes—
371C4⋊C4—44no—
372C4⋊C4—48no—
373C4⋊C4—48no—
374C4⋊C4—44no—
375C4⋊C4—44no—
376C23C22×Q8×C12711yescharacteristic
377C23C2×#41×C12711yescharacteristic
378C23C2×#41×C12712yes—
379C23C2×#41×C12711yescharacteristic
380C23H(5,𝔽2)×C12712yes—
381C23H(5,𝔽2)×C12711yescharacteristic
382C23H(5,𝔽2)×C12712yes—
383C23H(5,𝔽2)×C12711yescharacteristic
384C232−1+4×C12711yescharacteristic
385C232−1+4×C12712yes—
386C232−1+4×C12711yescharacteristic
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C22#538×C12712yes—
445C22#538×C12712yes—
446C22#539×C12711yescharacteristic
447C22#539×C12712yes—
448C22#539×C12711yescharacteristic
449C22#541×C12712yes—
450C22#542×C12712yes—
451C22#543×C12711yescharacteristic
452C22#544×C12712yes—
453C22#552×C12712yes—
454C22#553×C12712yes—
455C22#554×C12712yes—
456C22#555×C12711yescharacteristic
457C22#555×C12711yescharacteristic
458C22#557×C12711yescharacteristic
459C22#557×C12711yescharacteristic
460C22#560×C12711yescharacteristic
461C22#560×C12711yescharacteristic
462C22#562×C12712yes—
463C22#562×C12712yes—
464C22#563×C12711yescharacteristic
465C22#563×C12712yes—
466C22#563×C12711yescharacteristic
467C4—42no—
468C4—42no—
469C4—42no—
470C4—44no—
471C4—44no—
472C4—82no—
473C4—82no—
474C4—82no—
475C4—82no—
476C2C127×#276911yescharacteristic
477C2C127×#277412yes—
478C2C127×#278112yes—
479C2C127×#278411yescharacteristic
480C2C127×#279511yescharacteristic
481C2C127×#280212yes—
482C2C127×#280911yescharacteristic
483C2C127×#282611yescharacteristic
484C2C127×#283112yes—
485C2C127×#283411yescharacteristic
486C2C127×#284111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
232. #17304C127direct (N × H)
253. C127#17304direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#14452
C127×#14442
C127×#14432
C127×#14422
C127×#14412
#17304127