Finite Group Databasebeta

← C127×#17065 #44580738

Subgroups — C127×#17065 #44580738

Order 32512.

1102 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387×C127C211yesmaximal, characteristic
2C2×#384×C127C211yesmaximal, characteristic
3C127×#1445C212yesmaximal
4C127×#1445C212yesmaximal
5C127×#1442C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1441C212yesmaximal
8C127×#1441C212yesmaximal
9C127×#1434C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16#387×C127—24no—
17#384×C127—24no—
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2211yescharacteristic
22C2×#95×C127C2211yescharacteristic
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2214yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2214yes—
28C2×#95×C127C2214yes—
29C23×C4×C127C2314yes—
30C23×C4×C127C2311yescharacteristic
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2314yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2311yescharacteristic
38C2×C4⋊C4×C127—22no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—44no—
48C2×C4⋊C4×C127—44no—
49C2×C4⋊C4×C127Q814yes—
50C2×C42×C127—24no—
51C2×C42×C127D414yes—
52#95×C127—22no—
53#95×C127—22no—
54#95×C127—22no—
55#95×C127—22no—
56#95×C127—24no—
57#95×C127—24no—
58#95×C127—24no—
59#95×C127—44no—
60#95×C127—44no—
61#95×C127—44no—
62#95×C127—44no—
63C24×C127C2411yescharacteristic
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
84C22×C4×C127—22no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127C2×D412yes—
101C22×C4×C127C2×D412yes—
102C22×C4×C127C2×D412yes—
103C22×C4×C127C2×Q812yes—
104C22×C4×C127C2×Q812yes—
105C22×C4×C127C2×Q812yes—
106C22×C4×C127#4112yes—
107C22×C4×C127#4114yes—
108C22×C4×C127#4114yes—
109C4⋊C4×C127—28no—
110C4⋊C4×C127—48no—
111C4⋊C4×C127—48no—
112C4⋊C4×C127—44no—
113C4⋊C4×C127—48no—
114C42×C127—28no—
115C23×C127C22×D411yescharacteristic
116C23×C127C22×Q811yescharacteristic
117C23×C127C2×#4111yescharacteristic
118C23×C127C2×#4112yes—
119C23×C127C2×#4112yes—
120C23×C127H(5,𝔽2)12yes—
121C23×C127H(5,𝔽2)12yes—
122C23×C1272−1+412yes—
123C23×C1272−1+412yes—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—28no—
131C2×C4×C127—28no—
132C2×C4×C127—24no—
133C2×C4×C127—24no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—24no—
137C2×C4×C127—24no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—41no—
145C2×C4×C127—44no—
146C2×C4×C127—44no—
147C2×C4×C127—44no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—44no—
154C2×C4×C127—44no—
155C2×C4×C127—44no—
156C2×C4×C127—44no—
157C2×C4×C127—44no—
158C2×C4×C127—44no—
159C2×C4×C127—44no—
160C2×C4×C127—44no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127C22⋊Q814yes—
167C2×C4×C127#12314yes—
168C2×C4×C127#12414yes—
169C22×C127C2×C22⋊Q811yescharacteristic
170C22×C127C2×#12311yescharacteristic
171C22×C127C2×#12411yescharacteristic
172C22×C127#53511yescharacteristic
173C22×C127#53511yescharacteristic
174C22×C127#53611yescharacteristic
175C22×C127#53611yescharacteristic
176C22×C127#53914yes—
177C22×C127#54014yes—
178C22×C127#54212yes—
179C22×C127#54412yes—
180C22×C127#55214yes—
181C22×C127#55312yes—
182C22×C127#55412yes—
183C22×C127#55612yes—
184C22×C127#55712yes—
185C22×C127#56314yes—
186C4×C127—24no—
187C4×C127—24no—
188C4×C127—24no—
189C4×C127—42no—
190C4×C127—42no—
191C4×C127—81no—
192C4×C127—81no—
193C4×C127—84no—
194C4×C127—84no—
195#17065C12711yesmaximal, characteristic, direct product factor, Sylow
196C2×C127#248711yescharacteristic
197C2×C127#250311yescharacteristic
198C2×C127#256811yescharacteristic
199C2×C127#262311yescharacteristic
200C2×C127#262811yescharacteristic
201C2×C127#264111yescharacteristic
202C2×C127#279114yes—
203C2×C127#279314yes—
204C2×C127#282111yescharacteristic
205C2×#387C2×C12711yescharacteristic
206C2×#384C2×C12711yescharacteristic
207#1445C2×C12712yes—
208#1445C2×C12712yes—
209#1442C2×C12712yes—
210#1442C2×C12712yes—
211#1441C2×C12712yes—
212#1441C2×C12712yes—
213#1434C2×C12711yescharacteristic
214C127#1706511yescharacteristic, direct product factor, Sylow
215C22×C4⋊C4C22×C12711yescharacteristic
216C22×C4⋊C4C22×C12712yes—
217C22×C4⋊C4C22×C12711yescharacteristic
218C22×C4⋊C4C22×C12712yes—
219C22×C4⋊C4C22×C12712yes—
220C22×C42C22×C12711yescharacteristic
221#387—24no—
222#384—24no—
223C2×#95C22×C12712yes—
224C2×#95C22×C12712yes—
225C2×#95C22×C12712yes—
226C2×#95C22×C12711yescharacteristic
227C2×#95C22×C12711yescharacteristic
228C2×#95C22×C12711yescharacteristic
229C2×#95C22×C12711yescharacteristic
230C2×#95C22×C12714yes—
231C2×#95C22×C12714yes—
232C2×#95C22×C12714yes—
233C2×#95C22×C12714yes—
234C23×C4C23×C12714yes—
235C23×C4C23×C12711yescharacteristic
236C23×C4C23×C12711yescharacteristic
237C23×C4C23×C12714yes—
238C23×C4C23×C12711yescharacteristic
239C23×C4C23×C12711yescharacteristic
240C23×C4C23×C12711yescharacteristic
241C23×C4C23×C12711yescharacteristic
242C23×C4C23×C12711yescharacteristic
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4Q8×C12714yes—
255C2×C42—24no—
256C2×C42D4×C12714yes—
257#95—22no—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—24no—
262#95—24no—
263#95—24no—
264#95—44no—
265#95—44no—
266#95—44no—
267#95—44no—
268C24C24×C12711yescharacteristic
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4C2×D4×C12712yes—
306C22×C4C2×D4×C12712yes—
307C22×C4C2×D4×C12712yes—
308C22×C4C2×Q8×C12712yes—
309C22×C4C2×Q8×C12712yes—
310C22×C4C2×Q8×C12712yes—
311C22×C4#41×C12712yes—
312C22×C4#41×C12714yes—
313C22×C4#41×C12714yes—
314C4⋊C4—28no—
315C4⋊C4—48no—
316C4⋊C4—48no—
317C4⋊C4—44no—
318C4⋊C4—48no—
319C42—28no—
320C23C22×D4×C12711yescharacteristic
321C23C22×Q8×C12711yescharacteristic
322C23C2×#41×C12711yescharacteristic
323C23C2×#41×C12712yes—
324C23C2×#41×C12712yes—
325C23H(5,𝔽2)×C12712yes—
326C23H(5,𝔽2)×C12712yes—
327C232−1+4×C12712yes—
328C232−1+4×C12712yes—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4C22⋊Q8×C12714yes—
372C2×C4#123×C12714yes—
373C2×C4#124×C12714yes—
374C22C2×C22⋊Q8×C12711yescharacteristic
375C22C2×#123×C12711yescharacteristic
376C22C2×#124×C12711yescharacteristic
377C22#535×C12711yescharacteristic
378C22#535×C12711yescharacteristic
379C22#536×C12711yescharacteristic
380C22#536×C12711yescharacteristic
381C22#539×C12714yes—
382C22#540×C12714yes—
383C22#542×C12712yes—
384C22#544×C12712yes—
385C22#552×C12714yes—
386C22#553×C12712yes—
387C22#554×C12712yes—
388C22#556×C12712yes—
389C22#557×C12712yes—
390C22#563×C12714yes—
391C4—24no—
392C4—24no—
393C4—24no—
394C4—42no—
395C4—42no—
396C4—81no—
397C4—84no—
398C4—84no—
399C4—81no—
400C2C127×#248711yescharacteristic
401C2C127×#250311yescharacteristic
402C2C127×#256811yescharacteristic
403C2C127×#262311yescharacteristic
404C2C127×#262811yescharacteristic
405C2C127×#264111yescharacteristic
406C2C127×#279114yes—
407C2C127×#279314yes—
408C2C127×#282111yescharacteristic
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
195. #17065C127direct (N × H)
214. C127#17065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#387×C1272
C2×#384×C1272
C127×#14452
C127×#14422
C127×#14412
C127×#14342
#17065127