Finite Group Databasebeta

← C127×#11716 #44575389

Subgroups — C127×#11716 #44575389

Order 32512.

592 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2626C211yesmaximal, characteristic
2C2×#342×C127C211yesmaximal, characteristic
3C2×#323×C127C211yesmaximal, characteristic
4C127×#1352C212yesmaximal, complemented
5C127×#1351C212yesmaximal, complemented
6C2×C22⋊Q8×C127C411yescharacteristic, complemented
7C22×C22⋊C4×C127—21no—
8C22×C22⋊C4×C127C2211yescharacteristic
9C2×C22⋊C8×C127—21no—
10#399×C127C411yescharacteristic, complemented
11#399×C127C2211yescharacteristic
12#396×C127—21no—
13#396×C127—21no—
14#393×C127C411yescharacteristic, complemented
15#393×C127C2211yescharacteristic
16#385×C127—21no—
17#380×C127C411yescharacteristic, complemented
18#379×C127—21no—
19#342×C127—21no—
20#342×C127C2212yes—
21#323×C127—21no—
22#323×C127C2212yes—
23C25×C127D411yescharacteristic
24C22×Q8×C127C2×C411yescharacteristic, complemented
25C23×C4×C127—41no—
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C22×C8×C127—41no—
29C22⋊Q8×C127—41no—
30C22⋊Q8×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
36C2×C22⋊C4×C127—24no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—41no—
45C2×C22⋊C4×C127—41no—
46C2×C22⋊C4×C127—41no—
47C2×C22⋊C4×C127—42no—
48C2×C22⋊C4×C127C2×C411yescharacteristic
49C2×C22⋊C4×C127D411yescharacteristic
50C2×C22⋊C4×C127D411yescharacteristic
51C2×C22⋊C4×C127C2311yescharacteristic
52C22⋊C8×C127—22no—
53C22⋊C8×C127—41no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127C2×C411yescharacteristic, complemented
57#95×C127C2×C411yescharacteristic, complemented
58C24×C127—21no—
59C24×C127—21no—
60C24×C127—22no—
61C24×C127—81no—
62C24×C127—81no—
63C24×C127C22⋊C411yescharacteristic
64C24×C127C22⋊C411yescharacteristic
65C24×C127SD1612yes—
66C24×C127Q1612yes—
67C24×C127C2×D411yescharacteristic
68C2×Q8×C127—41no—
69C2×Q8×C127—81no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—44no—
79C22×C4×C127—42no—
80C22×C4×C127—81no—
81C22×C4×C127—81no—
82C22×C4×C127—82no—
83C22×C4×C127—82no—
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22⋊C411yescharacteristic
86C22×C4×C127C22×C411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88C2×C8×C127—42no—
89C2×C8×C127—82no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—42no—
92C4⋊C4×C127—81no—
93C4⋊C4×C127—81no—
94C4⋊C4×C127—81no—
95C22⋊C4×C127—24no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—44no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—42no—
104C22⋊C4×C127—42no—
105C22⋊C4×C127—81no—
106C22⋊C4×C127—81no—
107C22⋊C4×C127—81no—
108C22⋊C4×C127—81no—
109C23×C127—22no—
110C23×C127—22no—
111C23×C127—21no—
112C23×C127—21no—
113C23×C127—22no—
114C23×C127—22no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—42no—
120C23×C127—42no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127—81no—
126C23×C127—81no—
127C23×C127—82no—
128C23×C127—82no—
129C23×C127—84no—
130C23×C127#9911yescharacteristic
131C23×C127#9911yescharacteristic
132C23×C127#10312yes—
133C23×C127#10312yes—
134C23×C127#10412yes—
135C23×C127C2×C22⋊C411yescharacteristic
136C23×C127C2×SD1611yescharacteristic
137C23×C127C2×Q1611yescharacteristic
138Q8×C127—82no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—42no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—44no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—81no—
162C2×C4×C127—81no—
163C2×C4×C127—81no—
164C2×C4×C127—88no—
165C2×C4×C127—82no—
166C2×C4×C127—82no—
167C8×C127—82no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—21no—
173C22×C127—21no—
174C22×C127—21no—
175C22×C127—22no—
176C22×C127—21no—
177C22×C127—42no—
178C22×C127—42no—
179C22×C127—42no—
180C22×C127—41no—
181C22×C127—41no—
182C22×C127—44no—
183C22×C127—44no—
184C22×C127—41no—
185C22×C127—41no—
186C22×C127—41no—
187C22×C127—41no—
188C22×C127—81no—
189C22×C127—81no—
190C22×C127—82no—
191C22×C127—82no—
192C22×C127#32812yes—
193C22×C127#32812yes—
194C22×C127C2×#9911yescharacteristic
195C22×C127C2×#10311yescharacteristic
196C22×C127C2×#10411yescharacteristic
197C4×C127—41no—
198C4×C127—41no—
199C4×C127—41no—
200C4×C127—41no—
201C4×C127—81no—
202C4×C127—81no—
203C4×C127—84no—
204C4×C127—81no—
205C4×C127—81no—
206#11716C12711yesmaximal, characteristic, direct product factor, Sylow
207C2×C127—21no—
208C2×C127—22no—
209C2×C127—21no—
210C2×C127—22no—
211C2×C127—41no—
212C2×C127—42no—
213C2×C127—41no—
214C2×C127C2×#32811yescharacteristic
215C2×C127#212111yescharacteristic
216C2×C127#212711yescharacteristic
217#2626C2×C12711yescharacteristic
218C2×#342C2×C12711yescharacteristic
219C2×#323C2×C12711yescharacteristic
220#1352C2×C12712yescomplemented
221#1351C2×C12712yescomplemented
222C127#1171611yescharacteristic, direct product factor, Sylow
223C2×C22⋊Q8C4×C12711yescharacteristic, complemented
224C22×C22⋊C4—21no—
225C22×C22⋊C4C22×C12711yescharacteristic
226C2×C22⋊C8—21no—
227#399C4×C12711yescharacteristic, complemented
228#399C22×C12711yescharacteristic
229#396—21no—
230#396—21no—
231#393C4×C12711yescharacteristic, complemented
232#393C22×C12711yescharacteristic
233#385—21no—
234#380C4×C12711yescharacteristic, complemented
235#379—21no—
236#342—21no—
237#342C22×C12712yes—
238#323—21no—
239#323C22×C12712yes—
240C25D4×C12711yescharacteristic
241C22×Q8C2×C4×C12711yescharacteristic, complemented
242C23×C4—41no—
243C23×C4C2×C4×C12711yescharacteristic
244C23×C4D4×C12711yescharacteristic
245C22×C8—41no—
246C22⋊Q8—41no—
247C22⋊Q8—41no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
253C2×C22⋊C4—24no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—41no—
262C2×C22⋊C4—41no—
263C2×C22⋊C4—41no—
264C2×C22⋊C4—42no—
265C2×C22⋊C4C2×C4×C12711yescharacteristic
266C2×C22⋊C4D4×C12711yescharacteristic
267C2×C22⋊C4D4×C12711yescharacteristic
268C2×C22⋊C4C23×C12711yescharacteristic
269C22⋊C8—22no—
270C22⋊C8—41no—
271#95—21no—
272#95—21no—
273#95C2×C4×C12711yescharacteristic, complemented
274#95C2×C4×C12711yescharacteristic, complemented
275C24—21no—
276C24—21no—
277C24—22no—
278C24—81no—
279C24—81no—
280C24C22⋊C4×C12711yescharacteristic
281C24C22⋊C4×C12711yescharacteristic
282C24SD16×C12712yes—
283C24Q16×C12712yes—
284C24C2×D4×C12711yescharacteristic
285C2×Q8—41no—
286C2×Q8—81no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—44no—
296C22×C4—42no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—82no—
300C22×C4—82no—
301C22×C4C22⋊C4×C12711yescharacteristic
302C22×C4C22⋊C4×C12711yescharacteristic
303C22×C4C22×C4×C12711yescharacteristic
304C22×C4C2×D4×C12711yescharacteristic
305C2×C8—42no—
306C2×C8—82no—
307C4⋊C4—41no—
308C4⋊C4—42no—
309C4⋊C4—81no—
310C4⋊C4—81no—
311C4⋊C4—81no—
312C22⋊C4—24no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—44no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—81no—
323C22⋊C4—81no—
324C22⋊C4—81no—
325C22⋊C4—81no—
326C23—22no—
327C23—22no—
328C23—21no—
329C23—21no—
330C23—22no—
331C23—22no—
332C23—21no—
333C23—21no—
334C23—41no—
335C23—41no—
336C23—42no—
337C23—42no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—81no—
343C23—81no—
344C23—82no—
345C23—82no—
346C23—84no—
347C23#99×C12711yescharacteristic
348C23#99×C12711yescharacteristic
349C23#103×C12712yes—
350C23#103×C12712yes—
351C23#104×C12712yes—
352C23C2×C22⋊C4×C12711yescharacteristic
353C23C2×SD16×C12711yescharacteristic
354C23C2×Q16×C12711yescharacteristic
355Q8—82no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—88no—
382C2×C4—82no—
383C2×C4—82no—
384C8—82no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—42no—
395C22—42no—
396C22—42no—
397C22—41no—
398C22—41no—
399C22—44no—
400C22—44no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—82no—
408C22—82no—
409C22#328×C12712yes—
410C22#328×C12712yes—
411C22C2×#99×C12711yescharacteristic
412C22C2×#103×C12711yescharacteristic
413C22C2×#104×C12711yescharacteristic
414C4—41no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—81no—
419C4—81no—
420C4—84no—
421C4—81no—
422C4—81no—
423C2—21no—
424C2—22no—
425C2—21no—
426C2—22no—
427C2—41no—
428C2—42no—
429C2—41no—
430C2C2×#328×C12711yescharacteristic
431C2C127×#212111yescharacteristic
432C2C127×#212711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC25×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1352C2semidirect
5. C127×#1351C2semidirect
6. C2×C22⋊Q8×C127C4semidirect
10. #399×C127C4semidirect
14. #393×C127C4semidirect
17. #380×C127C4semidirect
24. C22×Q8×C127C2×C4semidirect
35. C2×C4⋊C4×C127C2×C4semidirect
56. #95×C127C2×C4semidirect
57. #95×C127C2×C4semidirect
206. #11716C127direct (N × H)
220. #1352C2×C127semidirect
221. #1351C2×C127semidirect
222. C127#11716direct (N × H)
223. C2×C22⋊Q8C4×C127semidirect
227. #399C4×C127semidirect
231. #393C4×C127semidirect
234. #380C4×C127semidirect
241. C22×Q8C2×C4×C127semidirect
252. C2×C4⋊C4C2×C4×C127semidirect
273. #95C2×C4×C127semidirect
274. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26262
C2×#342×C1272
C2×#323×C1272
C127×#13522
C127×#13512
#11716127