Finite Group Databasebeta

← C127×#17061 #44580734

Subgroups — C127×#17061 #44580734

Order 32512.

1230 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C212yesmaximal
2C2×#387×C127C211yesmaximal, characteristic
3C2×#384×C127C211yesmaximal, characteristic
4C127×#1445C212yesmaximal
5C127×#1444C212yesmaximal
6C127×#1444C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1441C212yesmaximal
9C127×#1434C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2214yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2212yes—
16C22×C42×C127C2211yescharacteristic
17#398×C127—28no—
18#387×C127—24no—
19#384×C127—24no—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2214yes—
28C2×#95×C127C2214yes—
29C2×#95×C127C2212yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2311yescharacteristic
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2314yes—
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2311yescharacteristic
38C23×C4×C127C2311yescharacteristic
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—22no—
45C2×C4⋊C4×C127—28no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—44no—
50C2×C4⋊C4×C127—44no—
51C2×C4⋊C4×C127—44no—
52C2×C4⋊C4×C127—44no—
53C2×C4⋊C4×C127D414yes—
54C2×C42×C127—24no—
55C2×C42×C127D414yes—
56#95×C127—22no—
57#95×C127—22no—
58#95×C127—22no—
59#95×C127—22no—
60#95×C127—24no—
61#95×C127—28no—
62#95×C127—24no—
63#95×C127—44no—
64#95×C127—44no—
65#95×C127Q818yes—
66C24×C127C2411yescharacteristic
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—21no—
74C22×C4×C127—24no—
75C22×C4×C127—21no—
76C22×C4×C127—24no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—22no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—24no—
85C22×C4×C127—22no—
86C22×C4×C127—24no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127C2×D412yes—
103C22×C4×C127C2×D412yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2×D412yes—
108C22×C4×C127C2×Q818yes—
109C22×C4×C127C2×Q814yes—
110C22×C4×C127#4112yes—
111C22×C4×C127#4114yes—
112C4⋊C4×C127—28no—
113C4⋊C4×C127—48no—
114C4⋊C4×C127—48no—
115C4⋊C4×C127—416no—
116C4⋊C4×C127—48no—
117C4⋊C4×C127—44no—
118C42×C127—28no—
119C23×C127C22×D411yescharacteristic
120C23×C127C22×D411yescharacteristic
121C23×C127C22×Q812yes—
122C23×C127C2×#4111yescharacteristic
123C23×C127C2×#4112yes—
124C23×C127H(5,𝔽2)12yes—
125C23×C127H(5,𝔽2)12yes—
126C23×C1272−1+412yes—
127C23×C1272−1+412yes—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—22no—
131C2×C4×C127—22no—
132C2×C4×C127—22no—
133C2×C4×C127—22no—
134C2×C4×C127—28no—
135C2×C4×C127—24no—
136C2×C4×C127—24no—
137C2×C4×C127—28no—
138C2×C4×C127—22no—
139C2×C4×C127—22no—
140C2×C4×C127—24no—
141C2×C4×C127—28no—
142C2×C4×C127—24no—
143C2×C4×C127—28no—
144C2×C4×C127—28no—
145C2×C4×C127—41no—
146C2×C4×C127—44no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—44no—
151C2×C4×C127—42no—
152C2×C4×C127—44no—
153C2×C4×C127—42no—
154C2×C4×C127—44no—
155C2×C4×C127—44no—
156C2×C4×C127—41no—
157C2×C4×C127—44no—
158C2×C4×C127—44no—
159C2×C4×C127—44no—
160C2×C4×C127—41no—
161C2×C4×C127—44no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127—44no—
170C2×C4×C127#12114yes—
171C2×C4×C127#12314yes—
172C2×C4×C127C4⋊Q814yes—
173C22×C127C2×#12111yescharacteristic
174C22×C127C2×#12311yescharacteristic
175C22×C127C2×C4⋊Q811yescharacteristic
176C22×C127#53511yescharacteristic
177C22×C127#53511yescharacteristic
178C22×C127#53512yes—
179C22×C127#53611yescharacteristic
180C22×C127#53611yescharacteristic
181C22×C127#53914yes—
182C22×C127#54012yes—
183C22×C127#54414yes—
184C22×C127#54712yes—
185C22×C127D4×Q812yes—
186C22×C127#55212yes—
187C22×C127#55414yes—
188C22×C127#55712yes—
189C22×C127#56314yes—
190C4×C127—24no—
191C4×C127—24no—
192C4×C127—24no—
193C4×C127—42no—
194C4×C127—48no—
195C4×C127—42no—
196C4×C127—81no—
197C4×C127—84no—
198C4×C127—81no—
199#17061C12711yesmaximal, characteristic, direct product factor, Sylow
200C2×C127#248611yescharacteristic
201C2×C127#250211yescharacteristic
202C2×C127#254611yescharacteristic
203C2×C127#261911yescharacteristic
204C2×C127#262311yescharacteristic
205C2×C127#266011yescharacteristic
206C2×C127#272014yes—
207C2×C127#279114yes—
208C2×C127#282111yescharacteristic
209C2×#398C2×C12712yes—
210C2×#387C2×C12711yescharacteristic
211C2×#384C2×C12711yescharacteristic
212#1445C2×C12712yes—
213#1444C2×C12712yes—
214#1444C2×C12712yes—
215#1442C2×C12712yes—
216#1441C2×C12712yes—
217#1434C2×C12711yescharacteristic
218C127#1706111yescharacteristic, direct product factor, Sylow
219C22×C4⋊C4C22×C12712yes—
220C22×C4⋊C4C22×C12711yescharacteristic
221C22×C4⋊C4C22×C12711yescharacteristic
222C22×C4⋊C4C22×C12714yes—
223C22×C4⋊C4C22×C12712yes—
224C22×C4⋊C4C22×C12712yes—
225C22×C42C22×C12711yescharacteristic
226#398—28no—
227#387—24no—
228#384—24no—
229C2×#95C22×C12712yes—
230C2×#95C22×C12714yes—
231C2×#95C22×C12712yes—
232C2×#95C22×C12711yescharacteristic
233C2×#95C22×C12711yescharacteristic
234C2×#95C22×C12711yescharacteristic
235C2×#95C22×C12711yescharacteristic
236C2×#95C22×C12714yes—
237C2×#95C22×C12714yes—
238C2×#95C22×C12712yes—
239C23×C4C23×C12714yes—
240C23×C4C23×C12711yescharacteristic
241C23×C4C23×C12711yescharacteristic
242C23×C4C23×C12711yescharacteristic
243C23×C4C23×C12711yescharacteristic
244C23×C4C23×C12714yes—
245C23×C4C23×C12711yescharacteristic
246C23×C4C23×C12711yescharacteristic
247C23×C4C23×C12711yescharacteristic
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—44no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4—44no—
261C2×C4⋊C4—44no—
262C2×C4⋊C4D4×C12714yes—
263C2×C42—24no—
264C2×C42D4×C12714yes—
265#95—22no—
266#95—22no—
267#95—22no—
268#95—22no—
269#95—24no—
270#95—28no—
271#95—24no—
272#95—44no—
273#95—44no—
274#95Q8×C12718yes—
275C24C24×C12711yescharacteristic
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—24no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—24no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4C2×D4×C12712yes—
312C22×C4C2×D4×C12712yes—
313C22×C4C2×D4×C12712yes—
314C22×C4C2×D4×C12712yes—
315C22×C4C2×D4×C12712yes—
316C22×C4C2×D4×C12712yes—
317C22×C4C2×Q8×C12718yes—
318C22×C4C2×Q8×C12714yes—
319C22×C4#41×C12712yes—
320C22×C4#41×C12714yes—
321C4⋊C4—28no—
322C4⋊C4—48no—
323C4⋊C4—48no—
324C4⋊C4—416no—
325C4⋊C4—48no—
326C4⋊C4—44no—
327C42—28no—
328C23C22×D4×C12711yescharacteristic
329C23C22×D4×C12711yescharacteristic
330C23C22×Q8×C12712yes—
331C23C2×#41×C12711yescharacteristic
332C23C2×#41×C12712yes—
333C23H(5,𝔽2)×C12712yes—
334C23H(5,𝔽2)×C12712yes—
335C232−1+4×C12712yes—
336C232−1+4×C12712yes—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—28no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—28no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—28no—
351C2×C4—24no—
352C2×C4—28no—
353C2×C4—28no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—44no—
360C2×C4—42no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—41no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4#121×C12714yes—
380C2×C4#123×C12714yes—
381C2×C4C4⋊Q8×C12714yes—
382C22C2×#121×C12711yescharacteristic
383C22C2×#123×C12711yescharacteristic
384C22C2×C4⋊Q8×C12711yescharacteristic
385C22#535×C12711yescharacteristic
386C22#535×C12712yes—
387C22#535×C12711yescharacteristic
388C22#536×C12711yescharacteristic
389C22#536×C12711yescharacteristic
390C22#539×C12714yes—
391C22#540×C12712yes—
392C22#544×C12714yes—
393C22#547×C12712yes—
394C22D4×Q8×C12712yes—
395C22#552×C12712yes—
396C22#554×C12714yes—
397C22#557×C12712yes—
398C22#563×C12714yes—
399C4—24no—
400C4—24no—
401C4—24no—
402C4—42no—
403C4—48no—
404C4—42no—
405C4—84no—
406C4—81no—
407C4—81no—
408C2C127×#248611yescharacteristic
409C2C127×#250211yescharacteristic
410C2C127×#254611yescharacteristic
411C2C127×#261911yescharacteristic
412C2C127×#262311yescharacteristic
413C2C127×#266011yescharacteristic
414C2C127×#272014yes—
415C2C127×#279114yes—
416C2C127×#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
199. #17061C127direct (N × H)
218. C127#17061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C2×#387×C1272
C2×#384×C1272
C127×#14452
C127×#14442
C127×#14422
C127×#14412
C127×#14342
#17061127