Finite Group Databasebeta

← C127×#9240 #44572913

Subgroups — C127×#9240 #44572913

Order 32512.

452 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C127C211yesmaximal, characteristic
2C127×#2924C211yesmaximal, characteristic
3C127×#1826C211yesmaximal, characteristic
4C127×#1508C211yesmaximal, characteristic
5C127×#1472C211yesmaximal, characteristic
6C127×#1293C211yesmaximal, characteristic
7C127×#1282C211yesmaximal, characteristic
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×#117×C127C2211yescharacteristic
10#485×C127—21no—
11#485×C127—21no—
12#485×C127—21no—
13#485×C127—21no—
14#433×C127—22no—
15#432×C127—21no—
16#431×C127—21no—
17C2×#107×C127C411yescharacteristic, complemented
18C2×#106×C127C411yescharacteristic, complemented
19#424×C127—21no—
20C2×#103×C127C411yescharacteristic, complemented
21C2×#103×C127C411yescharacteristic, complemented
22#407×C127C2211yescharacteristic
23#407×C127C2211yescharacteristic
24C2×C22⋊C8×C127C2211yescharacteristic
25C2×C22⋊C8×C127C2211yescharacteristic
26#405×C127—21no—
27C4×C22⋊C4×C127C2211yescharacteristic
28#339×C127—21no—
29#339×C127—21no—
30#328×C127—22no—
31#324×C127—21no—
32#324×C127—21no—
33C22×Q8×C127C2×C411yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C2×M16×C127—21no—
36C2×M16×C127—21no—
37C22×C8×C127—21no—
38C22×C8×C127C2×C411yescharacteristic
39C22×C8×C127C2×C411yescharacteristic
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43C22⋊Q8×C127—21no—
44#117×C127—21no—
45#117×C127—21no—
46#117×C127D411yescharacteristic
47#117×C127D411yescharacteristic
48#117×C127D411yescharacteristic
49#117×C127D411yescharacteristic
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127C2×C411yescharacteristic
52C2×C4⋊C4×C127C2×C411yescharacteristic
53C2×C4⋊C4×C127C2×C411yescharacteristic
54C2×C22⋊C4×C127—21no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C42×C127—21no—
58C2×C42×C127—21no—
59#107×C127—21no—
60#107×C127—21no—
61#106×C127—21no—
62#106×C127—21no—
63C4⋊C8×C127—22no—
64C4⋊C8×C127—22no—
65#103×C127—21no—
66#103×C127—21no—
67#103×C127—21no—
68#103×C127—21no—
69C22⋊C8×C127—21no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C22⋊C8×C127—21no—
75C22⋊C8×C127D411yescharacteristic
76C22⋊C8×C127D411yescharacteristic
77C22⋊C8×C127D412yes—
78#97×C127—22no—
79C4×C8×C127—22no—
80#95×C127—21no—
81C24×C127#4111yescharacteristic
82C2×Q8×C127—21no—
83C2×Q8×C127—21no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—41no—
91C22×C4×C127—41no—
92C22×C4×C127—41no—
93C22×C4×C127C22×C411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127C2×D411yescharacteristic
96C22×C4×C127C2×D411yescharacteristic
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127#4111yescharacteristic
99M16×C127—41no—
100M16×C127—41no—
101M16×C127—41no—
102M16×C127—41no—
103C2×C8×C127—21no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—22no—
107C2×C8×C127—21no—
108C2×C8×C127—41no—
109C2×C8×C127—41no—
110C2×C8×C127—41no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127C22⋊C411yescharacteristic
120C4⋊C4×C127C22⋊C411yescharacteristic
121C4⋊C4×C127C22⋊C411yescharacteristic
122C4⋊C4×C127C22⋊C411yescharacteristic
123C22⋊C4×C127—21no—
124C22⋊C4×C127—21no—
125C22⋊C4×C127—21no—
126C22⋊C4×C127—21no—
127C22⋊C4×C127—22no—
128C22⋊C4×C127—41no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—41no—
131C42×C127—21no—
132C42×C127—21no—
133C42×C127—21no—
134C42×C127—21no—
135C42×C127—41no—
136C42×C127—41no—
137C23×C127—21no—
138C23×C127—21no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127C4×D411yescharacteristic
142C23×C127#12111yescharacteristic
143C23×C127#12311yescharacteristic
144Q8×C127—41no—
145Q8×C127—41no—
146Q8×C127—81no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—42no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—41no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127—81no—
170C2×C4×C127—81no—
171C2×C4×C127C2×C22⋊C411yescharacteristic
172C2×C4×C127C4×D411yescharacteristic
173C2×C4×C127#12011yescharacteristic
174C2×C4×C127#12111yescharacteristic
175C8×C127—41no—
176C8×C127—41no—
177C8×C127—42no—
178C8×C127—41no—
179C8×C127—41no—
180C8×C127—81no—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—21no—
188C22×C127—21no—
189C22×C127—81no—
190C22×C127—81no—
191C22×C127#38611yescharacteristic
192C22×C127#44311yescharacteristic
193C22×C127#44411yescharacteristic
194C4×C127—21no—
195C4×C127—21no—
196C4×C127—21no—
197C4×C127—41no—
198C4×C127—41no—
199C4×C127—41no—
200C4×C127—41no—
201C4×C127—82no—
202C4×C127—81no—
203C4×C127—81no—
204C4×C127#41011yescharacteristic
205C4×C127#41011yescharacteristic
206#9240C12711yesmaximal, characteristic, direct product factor, Sylow
207C2×C127—21no—
208C2×C127—21no—
209C2×C127—41no—
210C2×C127—41no—
211C2×C127#187611yescharacteristic
212C2×C127#189911yescharacteristic
213C2×C127#190211yescharacteristic
214C2×#485C2×C12711yescharacteristic
215#2924C2×C12711yescharacteristic
216#1826C2×C12711yescharacteristic
217#1508C2×C12711yescharacteristic
218#1472C2×C12711yescharacteristic
219#1293C2×C12711yescharacteristic
220#1282C2×C12711yescharacteristic
221C127#924011yescharacteristic, direct product factor, Sylow
222C2×C22⋊Q8C22×C12711yescharacteristic
223C2×#117C22×C12711yescharacteristic
224#485—21no—
225#485—21no—
226#485—21no—
227#485—21no—
228#433—22no—
229#432—21no—
230#431—21no—
231C2×#107C4×C12711yescharacteristic, complemented
232C2×#106C4×C12711yescharacteristic, complemented
233#424—21no—
234C2×#103C4×C12711yescharacteristic, complemented
235C2×#103C4×C12711yescharacteristic, complemented
236#407C22×C12711yescharacteristic
237#407C22×C12711yescharacteristic
238C2×C22⋊C8C22×C12711yescharacteristic
239C2×C22⋊C8C22×C12711yescharacteristic
240#405—21no—
241C4×C22⋊C4C22×C12711yescharacteristic
242#339—21no—
243#339—21no—
244#328—22no—
245#324—21no—
246#324—21no—
247C22×Q8C2×C4×C12711yescharacteristic
248C23×C4C23×C12711yescharacteristic
249C2×M16—21no—
250C2×M16—21no—
251C22×C8—21no—
252C22×C8C2×C4×C12711yescharacteristic
253C22×C8C2×C4×C12711yescharacteristic
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117D4×C12711yescharacteristic
261#117D4×C12711yescharacteristic
262#117D4×C12711yescharacteristic
263#117D4×C12711yescharacteristic
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×C4×C12711yescharacteristic
266C2×C4⋊C4C2×C4×C12711yescharacteristic
267C2×C4⋊C4C2×C4×C12711yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C42—21no—
272C2×C42—21no—
273#107—21no—
274#107—21no—
275#106—21no—
276#106—21no—
277C4⋊C8—22no—
278C4⋊C8—22no—
279#103—21no—
280#103—21no—
281#103—21no—
282#103—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8D4×C12711yescharacteristic
290C22⋊C8D4×C12711yescharacteristic
291C22⋊C8D4×C12712yes—
292#97—22no—
293C4×C8—22no—
294#95—21no—
295C24#41×C12711yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4C22×C4×C12711yescharacteristic
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4C2×D4×C12711yescharacteristic
310C22×C4C2×D4×C12711yescharacteristic
311C22×C4C2×D4×C12711yescharacteristic
312C22×C4#41×C12711yescharacteristic
313M16—41no—
314M16—41no—
315M16—41no—
316M16—41no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—22no—
321C2×C8—21no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C12711yescharacteristic
334C4⋊C4C22⋊C4×C12711yescharacteristic
335C4⋊C4C22⋊C4×C12711yescharacteristic
336C4⋊C4C22⋊C4×C12711yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—22no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—41no—
350C42—41no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23C4×D4×C12711yescharacteristic
356C23#121×C12711yescharacteristic
357C23#123×C12711yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
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—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C22⋊C4×C12711yescharacteristic
386C2×C4C4×D4×C12711yescharacteristic
387C2×C4#120×C12711yescharacteristic
388C2×C4#121×C12711yescharacteristic
389C8—41no—
390C8—41no—
391C8—42no—
392C8—41no—
393C8—41no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#386×C12711yescharacteristic
406C22#443×C12711yescharacteristic
407C22#444×C12711yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—82no—
416C4—81no—
417C4—81no—
418C4#410×C12711yescharacteristic
419C4#410×C12711yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2C127×#187611yescharacteristic
425C2C127×#189911yescharacteristic
426C2C127×#190211yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127#41
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
17. C2×#107×C127C4semidirect
18. C2×#106×C127C4semidirect
20. C2×#103×C127C4semidirect
21. C2×#103×C127C4semidirect
206. #9240C127direct (N × H)
221. C127#9240direct (N × H)
231. C2×#107C4×C127semidirect
232. C2×#106C4×C127semidirect
234. C2×#103C4×C127semidirect
235. C2×#103C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1272
C127×#29242
C127×#18262
C127×#15082
C127×#14722
C127×#12932
C127×#12822
#9240127