Finite Group Databasebeta

← C127×#8332 #44572005

Subgroups — C127×#8332 #44572005

Order 32512.

1156 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C127C211yesmaximal, characteristic
2C127×#1817C211yesmaximal, characteristic, complemented
3C2×#327×C127C214yesmaximal, complemented
4C127×#1434C211yesmaximal, characteristic, complemented
5C22×#41×C127—21no—
6#532×C127—28no—
7C2×C4⋊Q8×C127C411yescharacteristic, complemented
8C2×#127×C127C411yescharacteristic, complemented
9C2×#124×C127—21no—
10C2×#121×C127—21no—
11C2×#121×C127C2212yes—
12C2×C4×D4×C127—21no—
13C2×C4×D4×C127C412yescomplemented
14C22×C42×C127C2211yescharacteristic
15C2×C22⋊C8×C127C2212yes—
16C2×#95×C127—21no—
17C2×#95×C127—21no—
18C2×#95×C127C2212yes—
19#336×C127—21no—
20#336×C127—21no—
21#327×C127—28no—
22C2×#41×C127—28no—
23C2×#41×C127—44no—
24C2×#41×C127—42no—
25C2×#41×C127—42no—
26C22×Q8×C127—21no—
27C22×D4×C127—22no—
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127C2×C412yes—
31C23×C4×C127—22no—
32C23×C4×C127—22no—
33C23×C4×C127D411yescharacteristic
34C23×C4×C127D411yescharacteristic
35C23×C4×C127C2311yescharacteristic
36C22×C8×C127—22no—
37C4⋊Q8×C127—24no—
38#127×C127—24no—
39#124×C127—28no—
40#121×C127—28no—
41#121×C127—24no—
42#121×C127D418yes—
43C4×D4×C127—28no—
44C4×D4×C127—24no—
45C4×D4×C127—24no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127C2×C412yes—
48C2×C22⋊C4×C127—22no—
49C2×C22⋊C4×C127—22no—
50C2×C42×C127—24no—
51C2×C42×C127C2×C411yescharacteristic
52C2×C42×C127C2×C411yescharacteristic
53C2×C42×C127D411yescharacteristic
54C2×C42×C127D411yescharacteristic
55C22⋊C8×C127—24no—
56#95×C127—24no—
57#95×C127—24no—
58#95×C127—42no—
59C24×C127—22no—
60C24×C127C2×D411yescharacteristic
61#41×C127—416no—
62#41×C127—416no—
63C2×Q8×C127—24no—
64C2×Q8×C127—42no—
65C2×Q8×C127—42no—
66C2×D4×C127—24no—
67C2×D4×C127—24no—
68C2×D4×C127—28no—
69C2×D4×C127—22no—
70C2×D4×C127—42no—
71C2×D4×C127—42no—
72C2×D4×C127—42no—
73C2×D4×C127—42no—
74C2×D4×C127—42no—
75C2×D4×C127—42no—
76C2×D4×C127—44no—
77C2×D4×C127—42no—
78C2×D4×C127—42no—
79C2×D4×C127C22⋊C414yes—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—28no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—24no—
87C22×C4×C127—41no—
88C22×C4×C127—41no—
89C22×C4×C127—41no—
90C22×C4×C127—44no—
91C22×C4×C127—44no—
92C22×C4×C127—42no—
93C22×C4×C127—42no—
94C22×C4×C127—42no—
95C22×C4×C127—42no—
96C22×C4×C127—42no—
97C22×C4×C127—42no—
98C22×C4×C127C22⋊C411yescharacteristic
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C22⋊C411yescharacteristic
101C22×C4×C127C22⋊C411yescharacteristic
102C22×C4×C127D812yes—
103C22×C4×C127SD1612yes—
104C22×C4×C127C22×C411yescharacteristic
105C22×C4×C127C2×D411yescharacteristic
106C22×C4×C127C2×D414yes—
107C2×C8×C127—42no—
108C2×C8×C127—42no—
109C2×C8×C127—42no—
110C4⋊C4×C127—24no—
111C4⋊C4×C127—22no—
112C4⋊C4×C127C22⋊C414yes—
113C22⋊C4×C127—28no—
114C22⋊C4×C127—28no—
115C42×C127—22no—
116C42×C127—22no—
117C42×C127—22no—
118C42×C127—22no—
119C23×C127—21no—
120C23×C127—21no—
121C23×C127—21no—
122C23×C127—21no—
123C23×C127—24no—
124C23×C127—42no—
125C23×C127—42no—
126C23×C127—42no—
127C23×C127—42no—
128C23×C127—42no—
129C23×C127—42no—
130C23×C127C2×C22⋊C411yescharacteristic
131C23×C127#12012yes—
132C23×C127C2×D811yescharacteristic
133C23×C127C2×SD1611yescharacteristic
134C23×C127AGL(1,ℤ/8)12yes—
135Q8×C127—48no—
136D4×C127—44no—
137D4×C127—44no—
138D4×C127—48no—
139D4×C127—48no—
140D4×C127—48no—
141D4×C127—48no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—21no—
145C2×C4×C127—21no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—21no—
155C2×C4×C127—24no—
156C2×C4×C127—21no—
157C2×C4×C127—21no—
158C2×C4×C127—44no—
159C2×C4×C127—44no—
160C2×C4×C127—416no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127—82no—
167C2×C4×C127—82no—
168C2×C4×C127—82no—
169C2×C4×C127—82no—
170C2×C4×C127#10212yes—
171C2×C4×C127#10212yes—
172C2×C4×C127#10412yes—
173C2×C4×C127C2×C22⋊C412yes—
174C2×C4×C127#12012yes—
175C8×C127—82no—
176C22×C127—21no—
177C22×C127—21no—
178C22×C127—22no—
179C22×C127—22no—
180C22×C127—21no—
181C22×C127—21no—
182C22×C127—22no—
183C22×C127—22no—
184C22×C127—44no—
185C22×C127—44no—
186C22×C127—44no—
187C22×C127—82no—
188C22×C127—82no—
189C22×C127—82no—
190C22×C127—82no—
191C22×C127#37911yescharacteristic
192C22×C127#41011yescharacteristic
193C22×C127#41011yescharacteristic
194C22×C127C2×#10211yescharacteristic
195C22×C127#41811yescharacteristic
196C22×C127C2×#10411yescharacteristic
197C22×C127#42111yescharacteristic
198C22×C127#44712yes—
199C22×C127#45012yes—
200C4×C127—22no—
201C4×C127—22no—
202C4×C127—22no—
203C4×C127—22no—
204C4×C127—22no—
205C4×C127—44no—
206C4×C127—41no—
207C4×C127—84no—
208#8332C12711yesmaximal, characteristic, direct product factor, Sylow
209C2×C127—22no—
210C2×C127—22no—
211C2×C127—84no—
212C2×C127#150211yescharacteristic
213C2×C127#150511yescharacteristic
214C2×C127#151411yescharacteristic
215C2×C127#151711yescharacteristic
216C2×C127#178211yescharacteristic
217C2×C127#178611yescharacteristic
218C2×C127#178911yescharacteristic
219C2×#532C2×C12711yescharacteristic
220#1817C2×C12711yescharacteristic, complemented
221C2×#327C2×C12714yescomplemented
222#1434C2×C12711yescharacteristic, complemented
223C127#833211yescharacteristic, direct product factor, Sylow
224C22×#41—21no—
225#532—28no—
226C2×C4⋊Q8C4×C12711yescharacteristic, complemented
227C2×#127C4×C12711yescharacteristic, complemented
228C2×#124—21no—
229C2×#121—21no—
230C2×#121C22×C12712yes—
231C2×C4×D4—21no—
232C2×C4×D4C4×C12712yescomplemented
233C22×C42C22×C12711yescharacteristic
234C2×C22⋊C8C22×C12712yes—
235C2×#95—21no—
236C2×#95—21no—
237C2×#95C22×C12712yes—
238#336—21no—
239#336—21no—
240#327—28no—
241C2×#41—28no—
242C2×#41—44no—
243C2×#41—42no—
244C2×#41—42no—
245C22×Q8—21no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4—21no—
249C22×D4C2×C4×C12712yes—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4D4×C12711yescharacteristic
253C23×C4D4×C12711yescharacteristic
254C23×C4C23×C12711yescharacteristic
255C22×C8—22no—
256C4⋊Q8—24no—
257#127—24no—
258#124—28no—
259#121—28no—
260#121—24no—
261#121D4×C12718yes—
262C4×D4—28no—
263C4×D4—24no—
264C4×D4—24no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C12712yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C42—24no—
270C2×C42C2×C4×C12711yescharacteristic
271C2×C42C2×C4×C12711yescharacteristic
272C2×C42D4×C12711yescharacteristic
273C2×C42D4×C12711yescharacteristic
274C22⋊C8—24no—
275#95—24no—
276#95—24no—
277#95—42no—
278C24—22no—
279C24C2×D4×C12711yescharacteristic
280#41—416no—
281#41—416no—
282C2×Q8—24no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×D4—24no—
286C2×D4—24no—
287C2×D4—28no—
288C2×D4—22no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—42no—
294C2×D4—42no—
295C2×D4—44no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4C22⋊C4×C12714yes—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—28no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—44no—
310C22×C4—44no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4C22⋊C4×C12711yescharacteristic
318C22×C4C22⋊C4×C12711yescharacteristic
319C22×C4C22⋊C4×C12711yescharacteristic
320C22×C4C22⋊C4×C12711yescharacteristic
321C22×C4D8×C12712yes—
322C22×C4SD16×C12712yes—
323C22×C4C22×C4×C12711yescharacteristic
324C22×C4C2×D4×C12711yescharacteristic
325C22×C4C2×D4×C12714yes—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C4⋊C4—24no—
330C4⋊C4—22no—
331C4⋊C4C22⋊C4×C12714yes—
332C22⋊C4—28no—
333C22⋊C4—28no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—24no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23C2×C22⋊C4×C12711yescharacteristic
350C23#120×C12712yes—
351C23C2×D8×C12711yescharacteristic
352C23C2×SD16×C12711yescharacteristic
353C23AGL(1,ℤ/8)×C12712yes—
354Q8—48no—
355D4—44no—
356D4—48no—
357D4—44no—
358D4—48no—
359D4—48no—
360D4—48no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—21no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—416no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4#102×C12712yes—
390C2×C4#102×C12712yes—
391C2×C4#104×C12712yes—
392C2×C4C2×C22⋊C4×C12712yes—
393C2×C4#120×C12712yes—
394C8—82no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22—21no—
400C22—21no—
401C22—22no—
402C22—22no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22#379×C12711yescharacteristic
411C22#410×C12711yescharacteristic
412C22#410×C12711yescharacteristic
413C22C2×#102×C12711yescharacteristic
414C22#418×C12711yescharacteristic
415C22C2×#104×C12711yescharacteristic
416C22#421×C12711yescharacteristic
417C22#447×C12712yes—
418C22#450×C12712yes—
419C4—22no—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—44no—
425C4—41no—
426C4—84no—
427C2—22no—
428C2—22no—
429C2—84no—
430C2C127×#150211yescharacteristic
431C2C127×#150511yescharacteristic
432C2C127×#151411yescharacteristic
433C2C127×#151711yescharacteristic
434C2C127×#178211yescharacteristic
435C2C127×#178611yescharacteristic
436C2C127×#178911yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#532×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1817C2semidirect
3. C2×#327×C127C2semidirect
4. C127×#1434C2semidirect
7. C2×C4⋊Q8×C127C4semidirect
8. C2×#127×C127C4semidirect
13. C2×C4×D4×C127C4semidirect
208. #8332C127direct (N × H)
220. #1817C2×C127semidirect
221. C2×#327C2×C127semidirect
222. #1434C2×C127semidirect
223. C127#8332direct (N × H)
226. C2×C4⋊Q8C4×C127semidirect
227. C2×#127C4×C127semidirect
232. C2×C4×D4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1272
C127×#18172
C2×#327×C1272
C127×#14342
#8332127