Finite Group Databasebeta

← C127×#8360 #44572033

Subgroups — C127×#8360 #44572033

Order 32512.

846 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C127C211yesmaximal, characteristic
2C127×#1826C212yesmaximal, complemented
3C4×#99×C127C211yesmaximal, characteristic, complemented
4C127×#1507C212yesmaximal, complemented
5C127×#1465C211yesmaximal, characteristic, complemented
6#555×C127—24no—
7#555×C127—24no—
8C2×C4⋊Q8×C127C411yescharacteristic, complemented
9C2×#124×C127—21no—
10C2×#124×C127—21no—
11C2×#121×C127—21no—
12C2×#121×C127C411yescharacteristic, complemented
13C2×#121×C127C2211yescharacteristic
14C2×C4×D4×C127C411yescharacteristic, complemented
15C2×C4×D4×C127C2211yescharacteristic
16C2×#117×C127—21no—
17C2×#117×C127C411yescharacteristic, complemented
18C2×#117×C127C2211yescharacteristic
19C2×#99×C127—21no—
20#407×C127C2212yes—
21C4×C22⋊C4×C127C2212yes—
22#342×C127—21no—
23#339×C127—24no—
24#327×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C22×Q8×C127—21no—
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127C2×C411yescharacteristic
31C22×D4×C127D411yescharacteristic
32C23×C4×C127—21no—
33C23×C4×C127C2×C411yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C2×M16×C127—22no—
36C4⋊Q8×C127—22no—
37C4⋊Q8×C127—22no—
38#124×C127—28no—
39#124×C127—28no—
40#121×C127—28no—
41#121×C127—22no—
42#121×C127—22no—
43#121×C127—22no—
44#121×C127D414yes—
45C4×D4×C127—22no—
46C4×D4×C127—22no—
47C4×D4×C127—22no—
48C4×D4×C127—22no—
49#117×C127—28no—
50#117×C127—22no—
51#117×C127—22no—
52#117×C127—22no—
53#117×C127D414yes—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127C2×C411yescharacteristic
56C2×C4⋊C4×C127C2×C411yescharacteristic
57C2×C4⋊C4×C127C2×C411yescharacteristic
58C2×C4⋊C4×C127D411yescharacteristic
59C2×C22⋊C4×C127—21no—
60C2×C22⋊C4×C127—21no—
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—21no—
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127D411yescharacteristic
66C2×C22⋊C4×C127D411yescharacteristic
67C2×C42×C127—21no—
68C2×C42×C127—21no—
69C2×C42×C127—22no—
70C2×C42×C127C2×C411yescharacteristic
71#99×C127—24no—
72C22⋊C8×C127—22no—
73C22⋊C8×C127—22no—
74#95×C127—22no—
75C24×C127—21no—
76C24×C127C22⋊C411yescharacteristic
77C24×C127C2×D411yescharacteristic
78C2×Q8×C127—24no—
79C2×Q8×C127—82no—
80C2×D4×C127—22no—
81C2×D4×C127—24no—
82C2×D4×C127—24no—
83C2×D4×C127—22no—
84C2×D4×C127—21no—
85C2×D4×C127—41no—
86C2×D4×C127—42no—
87C2×D4×C127—82no—
88C2×D4×C127—82no—
89C2×D4×C127C22⋊C412yes—
90C22×C4×C127—24no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—42no—
97C22×C4×C127—42no—
98C22×C4×C127—42no—
99C22×C4×C127—42no—
100C22×C4×C127—42no—
101C22×C4×C127C22⋊C411yescharacteristic
102C22×C4×C127C22⋊C411yescharacteristic
103C22×C4×C127C22⋊C411yescharacteristic
104C22×C4×C127C22×C411yescharacteristic
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2×D411yescharacteristic
108M16×C127—44no—
109C2×C8×C127—42no—
110C4⋊C4×C127—24no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—22no—
115C4⋊C4×C127C22⋊C412yes—
116C4⋊C4×C127C22⋊C412yes—
117C4⋊C4×C127C22⋊C412yes—
118C22⋊C4×C127—24no—
119C22⋊C4×C127—24no—
120C22⋊C4×C127—24no—
121C22⋊C4×C127—24no—
122C22⋊C4×C127—22no—
123C22⋊C4×C127—24no—
124C22⋊C4×C127—22no—
125C22⋊C4×C127—24no—
126C22⋊C4×C127—42no—
127C42×C127—24no—
128C42×C127—21no—
129C42×C127—21no—
130C42×C127—24no—
131C42×C127—44no—
132C23×C127—21no—
133C23×C127—21no—
134C23×C127—21no—
135C23×C127—22no—
136C23×C127—21no—
137C23×C127—21no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—42no—
141C23×C127—42no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127—41no—
146C23×C127C2×C22⋊C411yescharacteristic
147C23×C127#12012yes—
148Q8×C127—84no—
149D4×C127—44no—
150D4×C127—42no—
151D4×C127—42no—
152D4×C127—84no—
153D4×C127—84no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—24no—
157C2×C4×C127—22no—
158C2×C4×C127—21no—
159C2×C4×C127—22no—
160C2×C4×C127—21no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—41no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—48no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—42no—
172C2×C4×C127—41no—
173C2×C4×C127—41no—
174C2×C4×C127—44no—
175C2×C4×C127—82no—
176C2×C4×C127—82no—
177C2×C4×C127#10412yes—
178C2×C4×C127C2×C22⋊C411yescharacteristic
179C2×C4×C127C2×C22⋊C411yescharacteristic
180C2×C4×C127#12012yes—
181C8×C127—82no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—22no—
185C22×C127—22no—
186C22×C127—22no—
187C22×C127—41no—
188C22×C127—42no—
189C22×C127—41no—
190C22×C127—42no—
191C22×C127—42no—
192C22×C127—41no—
193C22×C127—81no—
194C22×C127—81no—
195C22×C127—81no—
196C22×C127—81no—
197C22×C127—82no—
198C22×C127—82no—
199C22×C127#37911yescharacteristic
200C22×C127C2×#10411yescharacteristic
201C22×C127#42111yescharacteristic
202C4×C127—22no—
203C4×C127—21no—
204C4×C127—22no—
205C4×C127—42no—
206C4×C127—42no—
207C4×C127—41no—
208C4×C127—41no—
209C4×C127—42no—
210C4×C127—84no—
211C4×C127#41012yes—
212#8360C12711yesmaximal, characteristic, direct product factor, Sylow
213C2×C127—21no—
214C2×C127—21no—
215C2×C127—42no—
216C2×C127—81no—
217C2×C127—82no—
218C2×C127#178211yescharacteristic
219C2×C127#178911yescharacteristic
220C2×C127#179511yescharacteristic
221C2×#555C2×C12711yescharacteristic
222#1826C2×C12712yescomplemented
223C4×#99C2×C12711yescharacteristic, complemented
224#1507C2×C12712yescomplemented
225#1465C2×C12711yescharacteristic, complemented
226C127#836011yescharacteristic, direct product factor, Sylow
227#555—24no—
228#555—24no—
229C2×C4⋊Q8C4×C12711yescharacteristic, complemented
230C2×#124—21no—
231C2×#124—21no—
232C2×#121—21no—
233C2×#121C4×C12711yescharacteristic, complemented
234C2×#121C22×C12711yescharacteristic
235C2×C4×D4C4×C12711yescharacteristic, complemented
236C2×C4×D4C22×C12711yescharacteristic
237C2×#117—21no—
238C2×#117C4×C12711yescharacteristic, complemented
239C2×#117C22×C12711yescharacteristic
240C2×#99—21no—
241#407C22×C12712yes—
242C4×C22⋊C4C22×C12712yes—
243#342—21no—
244#339—24no—
245#327—24no—
246#324—21no—
247#323—21no—
248C22×Q8—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4C2×C4×C12711yescharacteristic
252C22×D4D4×C12711yescharacteristic
253C23×C4—21no—
254C23×C4C2×C4×C12711yescharacteristic
255C23×C4C23×C12711yescharacteristic
256C2×M16—22no—
257C4⋊Q8—22no—
258C4⋊Q8—22no—
259#124—28no—
260#124—28no—
261#121—28no—
262#121—22no—
263#121—22no—
264#121—22no—
265#121D4×C12714yes—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—22no—
270#117—28no—
271#117—22no—
272#117—22no—
273#117—22no—
274#117D4×C12714yes—
275C2×C4⋊C4—21no—
276C2×C4⋊C4C2×C4×C12711yescharacteristic
277C2×C4⋊C4C2×C4×C12711yescharacteristic
278C2×C4⋊C4C2×C4×C12711yescharacteristic
279C2×C4⋊C4D4×C12711yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4D4×C12711yescharacteristic
287C2×C22⋊C4D4×C12711yescharacteristic
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—22no—
291C2×C42C2×C4×C12711yescharacteristic
292#99—24no—
293C22⋊C8—22no—
294C22⋊C8—22no—
295#95—22no—
296C24—21no—
297C24C22⋊C4×C12711yescharacteristic
298C24C2×D4×C12711yescharacteristic
299C2×Q8—24no—
300C2×Q8—82no—
301C2×D4—22no—
302C2×D4—24no—
303C2×D4—24no—
304C2×D4—22no—
305C2×D4—21no—
306C2×D4—41no—
307C2×D4—42no—
308C2×D4—82no—
309C2×D4—82no—
310C2×D4C22⋊C4×C12712yes—
311C22×C4—24no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4C22⋊C4×C12711yescharacteristic
323C22×C4C22⋊C4×C12711yescharacteristic
324C22×C4C22⋊C4×C12711yescharacteristic
325C22×C4C22×C4×C12711yescharacteristic
326C22×C4C2×D4×C12712yes—
327C22×C4C2×D4×C12712yes—
328C22×C4C2×D4×C12711yescharacteristic
329M16—44no—
330C2×C8—42no—
331C4⋊C4—24no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4C22⋊C4×C12712yes—
337C4⋊C4C22⋊C4×C12712yes—
338C4⋊C4C22⋊C4×C12712yes—
339C22⋊C4—24no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—24no—
345C22⋊C4—22no—
346C22⋊C4—24no—
347C22⋊C4—42no—
348C42—24no—
349C42—21no—
350C42—21no—
351C42—24no—
352C42—44no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—22no—
357C23—21no—
358C23—21no—
359C23—41no—
360C23—41no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23C2×C22⋊C4×C12711yescharacteristic
368C23#120×C12712yes—
369Q8—84no—
370D4—44no—
371D4—42no—
372D4—42no—
373D4—84no—
374D4—84no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—48no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—82no—
397C2×C4—82no—
398C2×C4#104×C12712yes—
399C2×C4C2×C22⋊C4×C12711yescharacteristic
400C2×C4C2×C22⋊C4×C12711yescharacteristic
401C2×C4#120×C12712yes—
402C8—82no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—41no—
409C22—42no—
410C22—42no—
411C22—41no—
412C22—42no—
413C22—41no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22#379×C12711yescharacteristic
421C22C2×#104×C12711yescharacteristic
422C22#421×C12711yescharacteristic
423C4—22no—
424C4—21no—
425C4—22no—
426C4—41no—
427C4—42no—
428C4—42no—
429C4—42no—
430C4—41no—
431C4—84no—
432C4#410×C12712yes—
433C2—21no—
434C2—21no—
435C2—42no—
436C2—82no—
437C2—81no—
438C2C127×#178211yescharacteristic
439C2C127×#178911yescharacteristic
440C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×#555×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1826C2semidirect
3. C4×#99×C127C2semidirect
4. C127×#1507C2semidirect
5. C127×#1465C2semidirect
8. C2×C4⋊Q8×C127C4semidirect
12. C2×#121×C127C4semidirect
14. C2×C4×D4×C127C4semidirect
17. C2×#117×C127C4semidirect
212. #8360C127direct (N × H)
222. #1826C2×C127semidirect
223. C4×#99C2×C127semidirect
224. #1507C2×C127semidirect
225. #1465C2×C127semidirect
226. C127#8360direct (N × H)
229. C2×C4⋊Q8C4×C127semidirect
233. C2×#121C4×C127semidirect
235. C2×C4×D4C4×C127semidirect
238. C2×#117C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1272
C127×#18262
C4×#99×C1272
C127×#15072
C127×#14652
#8360127