Finite Group Databasebeta

← C127×#8341 #44572014

Subgroups — C127×#8341 #44572014

Order 32512.

1082 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C127C211yesmaximal, characteristic
2C127×#1797C211yesmaximal, characteristic, complemented
3C127×#1797C211yesmaximal, characteristic, complemented
4C2×#332×C127C212yesmaximal, complemented
5C2×#331×C127C212yesmaximal, complemented
6C22×#41×C127—21no—
7#532×C127—24no—
8#532×C127—24no—
9C2×C4⋊Q8×C127C2211yescharacteristic
10C2×#127×C127C2211yescharacteristic
11C2×#124×C127—21no—
12C2×#121×C127—21no—
13C2×#121×C127C412yes—
14C2×C4×D4×C127—21no—
15C2×C4×D4×C127C412yes—
16C22×C42×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2212yes—
18C2×C4⋊C8×C127C2212yes—
19C2×C22⋊C8×C127—21no—
20C2×C22⋊C8×C127—21no—
21#336×C127—21no—
22#336×C127—21no—
23#332×C127—24no—
24#331×C127—24no—
25C2×#41×C127—28no—
26C2×#41×C127—44no—
27C2×#41×C127—42no—
28C2×#41×C127—42no—
29C22×Q8×C127—21no—
30C22×D4×C127—22no—
31C22×D4×C127—21no—
32C22×D4×C127—21no—
33C22×D4×C127C2×C412yes—
34C23×C4×C127—22no—
35C23×C4×C127C2×C411yescharacteristic
36C23×C4×C127D411yescharacteristic
37C23×C4×C127D411yescharacteristic
38C22×C8×C127—22no—
39C22×C8×C127—22no—
40C4⋊Q8×C127—22no—
41C4⋊Q8×C127D414yes—
42#127×C127—22no—
43#127×C127D414yes—
44#124×C127—28no—
45#121×C127—28no—
46#121×C127—24no—
47#121×C127—24no—
48C4×D4×C127—28no—
49C4×D4×C127—24no—
50C4×D4×C127—24no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127C2×C412yes—
53C2×C22⋊C4×C127—22no—
54C2×C22⋊C4×C127—22no—
55C2×C42×C127—22no—
56C2×C42×C127—22no—
57C2×C42×C127C2×C411yescharacteristic
58C2×C42×C127D411yescharacteristic
59C2×C42×C127D411yescharacteristic
60C2×C42×C127C2311yescharacteristic
61C4⋊C8×C127—22no—
62C4⋊C8×C127—22no—
63C4⋊C8×C127—22no—
64C4⋊C8×C127—22no—
65C22⋊C8×C127—42no—
66C22⋊C8×C127—42no—
67C24×C127—22no—
68C24×C127C22⋊C411yescharacteristic
69#41×C127—416no—
70#41×C127—416no—
71C2×Q8×C127—24no—
72C2×Q8×C127—41no—
73C2×Q8×C127—41no—
74C2×Q8×C127—42no—
75C2×D4×C127—28no—
76C2×D4×C127—22no—
77C2×D4×C127—24no—
78C2×D4×C127—24no—
79C2×D4×C127—42no—
80C2×D4×C127—42no—
81C2×D4×C127—44no—
82C2×D4×C127—44no—
83C2×D4×C127—41no—
84C2×D4×C127—41no—
85C2×D4×C127—42no—
86C2×D4×C127—41no—
87C2×D4×C127—42no—
88C2×D4×C127—41no—
89C2×D4×C127C22⋊C414yes—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—28no—
93C22×C4×C127—22no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127—44no—
103C22×C4×C127—44no—
104C22×C4×C127C22⋊C411yescharacteristic
105C22×C4×C127C22⋊C411yescharacteristic
106C22×C4×C127C22⋊C411yescharacteristic
107C22×C4×C127D812yes—
108C22×C4×C127SD1612yes—
109C22×C4×C127C22×C411yescharacteristic
110C22×C4×C127C2×D411yescharacteristic
111C22×C4×C127C2×D411yescharacteristic
112C2×C8×C127—42no—
113C2×C8×C127—42no—
114C2×C8×C127—42no—
115C2×C8×C127—42no—
116C2×C8×C127—42no—
117C2×C8×C127—42no—
118C4⋊C4×C127—22no—
119C4⋊C4×C127—24no—
120C4⋊C4×C127C22⋊C414yes—
121C22⋊C4×C127—28no—
122C22⋊C4×C127—28no—
123C42×C127—21no—
124C42×C127—21no—
125C42×C127—22no—
126C42×C127—22no—
127C42×C127C2×D412yes—
128C42×C127C2×D412yes—
129C23×C127—21no—
130C23×C127—21no—
131C23×C127—21no—
132C23×C127—21no—
133C23×C127—21no—
134C23×C127—21no—
135C23×C127—24no—
136C23×C127—42no—
137C23×C127—42no—
138C23×C127—42no—
139C23×C127—42no—
140C23×C127—42no—
141C23×C127—42no—
142C23×C127#10212yes—
143C23×C127C2×C22⋊C411yescharacteristic
144Q8×C127—44no—
145Q8×C127—44no—
146D4×C127—44no—
147D4×C127—44no—
148D4×C127—416no—
149D4×C127—44no—
150D4×C127—44no—
151D4×C127—44no—
152D4×C127—44no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—21no—
160C2×C4×C127—21no—
161C2×C4×C127—24no—
162C2×C4×C127—21no—
163C2×C4×C127—21no—
164C2×C4×C127—21no—
165C2×C4×C127—21no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—416no—
169C2×C4×C127—42no—
170C2×C4×C127—42no—
171C2×C4×C127—42no—
172C2×C4×C127—42no—
173C2×C4×C127#10212yes—
174C2×C4×C127C2×C22⋊C411yescharacteristic
175C2×C4×C127C2×C22⋊C411yescharacteristic
176C2×C4×C127#12012yes—
177C2×C4×C127#12012yes—
178C2×C4×C127C2×D811yescharacteristic
179C2×C4×C127C2×SD1611yescharacteristic
180C2×C4×C127#13512yes—
181C2×C4×C127AGL(1,ℤ/8)12yes—
182C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C127#13711yescharacteristic
184C8×C127—82no—
185C8×C127—82no—
186C22×C127—22no—
187C22×C127—22no—
188C22×C127—22no—
189C22×C127—41no—
190C22×C127—41no—
191C22×C127—41no—
192C22×C127—41no—
193C22×C127—44no—
194C22×C127—44no—
195C22×C127—44no—
196C22×C127—82no—
197C22×C127—82no—
198C22×C127—82no—
199C22×C127—82no—
200C22×C127#37911yescharacteristic
201C22×C127#41311yescharacteristic
202C22×C127#41311yescharacteristic
203C22×C127C2×#10211yescharacteristic
204C22×C127#41611yescharacteristic
205C22×C127#41711yescharacteristic
206C22×C127#41811yescharacteristic
207C4×C127—21no—
208C4×C127—21no—
209C4×C127—22no—
210C4×C127—41no—
211C4×C127—44no—
212C4×C127—41no—
213C4×C127#44712yes—
214C4×C127#44912yes—
215C4×C127#45012yes—
216C4×C127#45212yes—
217#8341C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—42no—
219C2×C127—84no—
220C2×C127#154011yescharacteristic
221C2×C127#154711yescharacteristic
222C2×C127#155311yescharacteristic
223C2×C127#155711yescharacteristic
224C2×C127#178511yescharacteristic
225C2×C127#178611yescharacteristic
226C2×C127#178811yescharacteristic
227C2×#532C2×C12711yescharacteristic
228#1797C2×C12711yescharacteristic, complemented
229#1797C2×C12711yescharacteristic, complemented
230C2×#332C2×C12712yescomplemented
231C2×#331C2×C12712yescomplemented
232C127#834111yescharacteristic, direct product factor, Sylow
233C22×#41—21no—
234#532—24no—
235#532—24no—
236C2×C4⋊Q8C22×C12711yescharacteristic
237C2×#127C22×C12711yescharacteristic
238C2×#124—21no—
239C2×#121—21no—
240C2×#121C4×C12712yes—
241C2×C4×D4—21no—
242C2×C4×D4C4×C12712yes—
243C22×C42C22×C12711yescharacteristic
244C2×C4⋊C8C22×C12712yes—
245C2×C4⋊C8C22×C12712yes—
246C2×C22⋊C8—21no—
247C2×C22⋊C8—21no—
248#336—21no—
249#336—21no—
250#332—24no—
251#331—24no—
252C2×#41—28no—
253C2×#41—44no—
254C2×#41—42no—
255C2×#41—42no—
256C22×Q8—21no—
257C22×D4—22no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4C2×C4×C12712yes—
261C23×C4—22no—
262C23×C4C2×C4×C12711yescharacteristic
263C23×C4D4×C12711yescharacteristic
264C23×C4D4×C12711yescharacteristic
265C22×C8—22no—
266C22×C8—22no—
267C4⋊Q8—22no—
268C4⋊Q8D4×C12714yes—
269#127—22no—
270#127D4×C12714yes—
271#124—28no—
272#121—28no—
273#121—24no—
274#121—24no—
275C4×D4—28no—
276C4×D4—24no—
277C4×D4—24no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4C2×C4×C12712yes—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C42—22no—
283C2×C42—22no—
284C2×C42C2×C4×C12711yescharacteristic
285C2×C42D4×C12711yescharacteristic
286C2×C42D4×C12711yescharacteristic
287C2×C42C23×C12711yescharacteristic
288C4⋊C8—22no—
289C4⋊C8—22no—
290C4⋊C8—22no—
291C4⋊C8—22no—
292C22⋊C8—42no—
293C22⋊C8—42no—
294C24—22no—
295C24C22⋊C4×C12711yescharacteristic
296#41—416no—
297#41—416no—
298C2×Q8—24no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8—42no—
302C2×D4—28no—
303C2×D4—22no—
304C2×D4—24no—
305C2×D4—24no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—44no—
309C2×D4—44no—
310C2×D4—41no—
311C2×D4—41no—
312C2×D4—42no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—41no—
316C2×D4C22⋊C4×C12714yes—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—28no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—44no—
330C22×C4—44no—
331C22×C4C22⋊C4×C12711yescharacteristic
332C22×C4C22⋊C4×C12711yescharacteristic
333C22×C4C22⋊C4×C12711yescharacteristic
334C22×C4D8×C12712yes—
335C22×C4SD16×C12712yes—
336C22×C4C22×C4×C12711yescharacteristic
337C22×C4C2×D4×C12711yescharacteristic
338C22×C4C2×D4×C12711yescharacteristic
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C4⋊C4—22no—
346C4⋊C4—24no—
347C4⋊C4C22⋊C4×C12714yes—
348C22⋊C4—28no—
349C22⋊C4—28no—
350C42—21no—
351C42—21no—
352C42—22no—
353C42—22no—
354C42C2×D4×C12712yes—
355C42C2×D4×C12712yes—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—24no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23#102×C12712yes—
370C23C2×C22⋊C4×C12711yescharacteristic
371Q8—44no—
372Q8—44no—
373D4—44no—
374D4—44no—
375D4—416no—
376D4—44no—
377D4—44no—
378D4—44no—
379D4—44no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—24no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—416no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4#102×C12712yes—
401C2×C4C2×C22⋊C4×C12711yescharacteristic
402C2×C4C2×C22⋊C4×C12711yescharacteristic
403C2×C4#120×C12712yes—
404C2×C4#120×C12712yes—
405C2×C4C2×D8×C12711yescharacteristic
406C2×C4C2×SD16×C12711yescharacteristic
407C2×C4#135×C12712yes—
408C2×C4AGL(1,ℤ/8)×C12712yes—
409C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
410C2×C4#137×C12711yescharacteristic
411C8—82no—
412C8—82no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—44no—
421C22—44no—
422C22—44no—
423C22—82no—
424C22—82no—
425C22—82no—
426C22—82no—
427C22#379×C12711yescharacteristic
428C22#413×C12711yescharacteristic
429C22#413×C12711yescharacteristic
430C22C2×#102×C12711yescharacteristic
431C22#416×C12711yescharacteristic
432C22#417×C12711yescharacteristic
433C22#418×C12711yescharacteristic
434C4—21no—
435C4—21no—
436C4—22no—
437C4—41no—
438C4—44no—
439C4—41no—
440C4#447×C12712yes—
441C4#449×C12712yes—
442C4#450×C12712yes—
443C4#452×C12712yes—
444C2—42no—
445C2—84no—
446C2C127×#154011yescharacteristic
447C2C127×#154711yescharacteristic
448C2C127×#155311yescharacteristic
449C2C127×#155711yescharacteristic
450C2C127×#178511yescharacteristic
451C2C127×#178611yescharacteristic
452C2C127×#178811yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×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×#1797C2semidirect
3. C127×#1797C2semidirect
4. C2×#332×C127C2semidirect
5. C2×#331×C127C2semidirect
217. #8341C127direct (N × H)
228. #1797C2×C127semidirect
229. #1797C2×C127semidirect
230. C2×#332C2×C127semidirect
231. C2×#331C2×C127semidirect
232. C127#8341direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#532×C1272
C127×#17972
C2×#332×C1272
C2×#331×C1272
#8341127