Finite Group Databasebeta

← C127×#13225 #44576898

Subgroups — C127×#13225 #44576898

Order 32512.

602 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2544C211yesmaximal, characteristic
2C2×#354×C127C212yesmaximal, complemented
3C2×#353×C127C212yesmaximal
4C127×#1799C211yesmaximal, characteristic, complemented
5C4×#99×C127C211yesmaximal, characteristic, complemented
6C2×#127×C127C2211yescharacteristic
7C2×#124×C127C411yescharacteristic, complemented
8C2×#124×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10C2×#99×C127C2212yes—
11C2×#99×C127C2212yes—
12#394×C127—21no—
13#394×C127—21no—
14#391×C127C411yescharacteristic, complemented
15#390×C127C411yescharacteristic, complemented
16#386×C127—21no—
17#386×C127—21no—
18#380×C127—21no—
19C4×C4⋊C4×C127C411yescharacteristic, complemented
20C4×C22⋊C4×C127—21no—
21#354×C127—24no—
22#353×C127—24no—
23#342×C127—21no—
24#342×C127—21no—
25C22×Q8×C127C2×C411yescharacteristic
26C22×D4×C127—21no—
27C22×D4×C127—21no—
28C22×D4×C127C2×C411yescharacteristic
29C22×D4×C127C2311yescharacteristic
30C23×C4×C127D411yescharacteristic
31C23×C4×C127D411yescharacteristic
32#127×C127—22no—
33#127×C127—22no—
34#124×C127—22no—
35#124×C127—22no—
36#124×C127—41no—
37#124×C127—41no—
38C4×D4×C127—41no—
39C4×D4×C127—41no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—41no—
42C2×C4⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—21no—
48C2×C22⋊C4×C127—22no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127D411yescharacteristic
53C2×C42×C127—41no—
54C2×C42×C127C2×C411yescharacteristic
55C2×C42×C127C2×C411yescharacteristic
56C2×C42×C127C2×C411yescharacteristic
57#99×C127—22no—
58#99×C127—22no—
59#99×C127—22no—
60#99×C127D414yes—
61#95×C127—21no—
62#95×C127—21no—
63#95×C127—21no—
64#95×C127—41no—
65#95×C127—41no—
66C24×C127—21no—
67C24×C127C2×D411yescharacteristic
68C24×C127C2×D411yescharacteristic
69C2×Q8×C127—22no—
70C2×Q8×C127—41no—
71C2×Q8×C127—41no—
72C2×D4×C127—22no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C2×D4×C127—42no—
78C2×D4×C127—42no—
79C2×D4×C127—42no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C2×D4×C127—81no—
83C2×D4×C127—81no—
84C2×D4×C127C2×D412yes—
85C2×D4×C127#4112yes—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—42no—
94C22×C4×C127—42no—
95C22×C4×C127—81no—
96C22×C4×C127—81no—
97C22×C4×C127C22⋊C411yescharacteristic
98C22×C4×C127C22⋊C411yescharacteristic
99C22×C4×C127C22⋊C411yescharacteristic
100C22×C4×C127C22⋊C411yescharacteristic
101C22×C4×C127C22×C411yescharacteristic
102C4⋊C4×C127—41no—
103C4⋊C4×C127—42no—
104C4⋊C4×C127—82no—
105C22⋊C4×C127—24no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—42no—
109C22⋊C4×C127—42no—
110C22⋊C4×C127—42no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C22⋊C4×C127—42no—
116C22⋊C4×C127—42no—
117C22⋊C4×C127—81no—
118C22⋊C4×C127—81no—
119C42×C127—21no—
120C42×C127—21no—
121C42×C127—22no—
122C42×C127—22no—
123C42×C127—82no—
124C23×C127—21no—
125C23×C127—21no—
126C23×C127—21no—
127C23×C127—21no—
128C23×C127—41no—
129C23×C127—41no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127C2×C22⋊C411yescharacteristic
140C23×C127#12112yes—
141C23×C127#12411yescharacteristic
142C23×C127#12711yescharacteristic
143Q8×C127—82no—
144D4×C127—42no—
145D4×C127—42no—
146D4×C127—82no—
147D4×C127—84no—
148D4×C127—82no—
149D4×C127—82no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—22no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—41no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—44no—
165C2×C4×C127—41no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—41no—
169C2×C4×C127—41no—
170C2×C4×C127—41no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127—82no—
174C2×C4×C127—82no—
175C2×C4×C127—82no—
176C2×C4×C127—82no—
177C2×C4×C127—82no—
178C2×C4×C127#9911yescharacteristic
179C2×C4×C127#9911yescharacteristic
180C2×C4×C127C4×D412yes—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—22no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—42no—
187C22×C127—41no—
188C22×C127—41no—
189C22×C127—41no—
190C22×C127—41no—
191C22×C127—41no—
192C22×C127—41no—
193C22×C127—81no—
194C22×C127—81no—
195C22×C127—81no—
196C22×C127—81no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—81no—
200C22×C127—81no—
201C22×C127—81no—
202C22×C127#39011yescharacteristic
203C22×C127C2×#9911yescharacteristic
204C22×C127#41011yescharacteristic
205C4×C127—21no—
206C4×C127—21no—
207C4×C127—22no—
208C4×C127—42no—
209C4×C127—41no—
210C4×C127—41no—
211C4×C127—41no—
212C4×C127—81no—
213C4×C127—84no—
214C4×C127—81no—
215C4×C127—162no—
216#13225C12711yesmaximal, characteristic, direct product factor, Sylow
217C2×C127—21no—
218C2×C127—21no—
219C2×C127—42no—
220C2×C127—41no—
221C2×C127—41no—
222C2×C127—161no—
223C2×C127#196411yescharacteristic
224C2×C127#212611yescharacteristic
225C2×C127#212711yescharacteristic
226#2544C2×C12711yescharacteristic
227C2×#354C2×C12712yescomplemented
228C2×#353C2×C12712yes—
229#1799C2×C12711yescharacteristic, complemented
230C4×#99C2×C12711yescharacteristic, complemented
231C127#1322511yescharacteristic, direct product factor, Sylow
232C2×#127C22×C12711yescharacteristic
233C2×#124C4×C12711yescharacteristic, complemented
234C2×#124C22×C12711yescharacteristic
235C2×C4×D4C22×C12711yescharacteristic
236C2×#99C22×C12712yes—
237C2×#99C22×C12712yes—
238#394—21no—
239#394—21no—
240#391C4×C12711yescharacteristic, complemented
241#390C4×C12711yescharacteristic, complemented
242#386—21no—
243#386—21no—
244#380—21no—
245C4×C4⋊C4C4×C12711yescharacteristic, complemented
246C4×C22⋊C4—21no—
247#354—24no—
248#353—24no—
249#342—21no—
250#342—21no—
251C22×Q8C2×C4×C12711yescharacteristic
252C22×D4—21no—
253C22×D4—21no—
254C22×D4C2×C4×C12711yescharacteristic
255C22×D4C23×C12711yescharacteristic
256C23×C4D4×C12711yescharacteristic
257C23×C4D4×C12711yescharacteristic
258#127—22no—
259#127—22no—
260#124—22no—
261#124—22no—
262#124—41no—
263#124—41no—
264C4×D4—41no—
265C4×D4—41no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4C2×C4×C12711yescharacteristic
269C2×C22⋊C4—22no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4D4×C12711yescharacteristic
278C2×C22⋊C4D4×C12711yescharacteristic
279C2×C42—41no—
280C2×C42C2×C4×C12711yescharacteristic
281C2×C42C2×C4×C12711yescharacteristic
282C2×C42C2×C4×C12711yescharacteristic
283#99—22no—
284#99—22no—
285#99—22no—
286#99D4×C12714yes—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—41no—
291#95—41no—
292C24—21no—
293C24C2×D4×C12711yescharacteristic
294C24C2×D4×C12711yescharacteristic
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—81no—
309C2×D4—81no—
310C2×D4C2×D4×C12712yes—
311C2×D4#41×C12712yes—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—81no—
322C22×C4—81no—
323C22×C4C22⋊C4×C12711yescharacteristic
324C22×C4C22⋊C4×C12711yescharacteristic
325C22×C4C22⋊C4×C12711yescharacteristic
326C22×C4C22⋊C4×C12711yescharacteristic
327C22×C4C22×C4×C12711yescharacteristic
328C4⋊C4—41no—
329C4⋊C4—42no—
330C4⋊C4—82no—
331C22⋊C4—24no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—42no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—81no—
344C22⋊C4—81no—
345C42—21no—
346C42—21no—
347C42—22no—
348C42—22no—
349C42—82no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23C2×C22⋊C4×C12711yescharacteristic
366C23#121×C12712yes—
367C23#124×C12711yescharacteristic
368C23#127×C12711yescharacteristic
369Q8—82no—
370D4—42no—
371D4—42no—
372D4—82no—
373D4—84no—
374D4—82no—
375D4—82no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—82no—
400C2×C4—82no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4#99×C12711yescharacteristic
405C2×C4#99×C12711yescharacteristic
406C2×C4C4×D4×C12712yes—
407C22—21no—
408C22—21no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—42no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22#390×C12711yescharacteristic
429C22C2×#99×C12711yescharacteristic
430C22#410×C12711yescharacteristic
431C4—21no—
432C4—21no—
433C4—22no—
434C4—42no—
435C4—41no—
436C4—41no—
437C4—41no—
438C4—81no—
439C4—84no—
440C4—81no—
441C4—162no—
442C2—21no—
443C2—21no—
444C2—42no—
445C2—41no—
446C2—41no—
447C2—161no—
448C2C127×#196411yescharacteristic
449C2C127×#212611yescharacteristic
450C2C127×#212711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC22×D4C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#354×C127C2semidirect
4. C127×#1799C2semidirect
5. C4×#99×C127C2semidirect
7. C2×#124×C127C4semidirect
14. #391×C127C4semidirect
15. #390×C127C4semidirect
19. C4×C4⋊C4×C127C4semidirect
216. #13225C127direct (N × H)
227. C2×#354C2×C127semidirect
229. #1799C2×C127semidirect
230. C4×#99C2×C127semidirect
231. C127#13225direct (N × H)
233. C2×#124C4×C127semidirect
240. #391C4×C127semidirect
241. #390C4×C127semidirect
245. C4×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#25442
C2×#354×C1272
C2×#353×C1272
C127×#17992
C4×#99×C1272
#13225127