Finite Group Databasebeta

← C127×#9526 #44573199

Subgroups — C127×#9526 #44573199

Order 32512.

482 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3095C211yesmaximal, characteristic
2C127×#2332C211yesmaximal, characteristic
3C127×#1826C211yesmaximal, characteristic
4C127×#1820C211yesmaximal, characteristic
5C127×#1511C211yesmaximal, characteristic
6C127×#1306C211yesmaximal, characteristic
7C127×#1284C211yesmaximal, characteristic
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×#117×C127C2211yescharacteristic
10#485×C127—22no—
11#484×C127C412yescomplemented
12#483×C127C412yescomplemented
13#428×C127—21no—
14#419×C127—21no—
15#407×C127C2211yescharacteristic
16#407×C127C2211yescharacteristic
17#391×C127—21no—
18#388×C127—21no—
19#388×C127—21no—
20#387×C127—21no—
21#387×C127—21no—
22#381×C127C2211yescharacteristic
23#381×C127C2211yescharacteristic
24C4×C4⋊C4×C127—21no—
25C4×C22⋊C4×C127C2211yescharacteristic
26#342×C127—21no—
27#342×C127—21no—
28#339×C127—21no—
29#339×C127—21no—
30#328×C127—22no—
31C22×Q8×C127D411yescharacteristic
32C23×C4×C127C2311yescharacteristic
33C2×M16×C127—21no—
34C2×M16×C127—21no—
35C22⋊Q8×C127—21no—
36C22⋊Q8×C127—21no—
37C22⋊Q8×C127C2×C412yes—
38C22⋊Q8×C127D412yes—
39#117×C127—21no—
40#117×C127—21no—
41#117×C127—21no—
42#117×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127C2×C411yescharacteristic
47C2×C4⋊C4×C127C2×C411yescharacteristic
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127D411yescharacteristic
54C2×C22⋊C4×C127D411yescharacteristic
55C2×C42×C127—21no—
56C2×C42×C127—21no—
57C2×C42×C127—21no—
58C2×C42×C127D411yescharacteristic
59C2×C42×C127D411yescharacteristic
60#107×C127—22no—
61#106×C127—22no—
62#103×C127—22no—
63#103×C127—22no—
64C22⋊C8×C127—21no—
65C22⋊C8×C127—21no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127C2×C412yes—
68#95×C127—21no—
69#95×C127—21no—
70#95×C127—21no—
71#95×C127—21no—
72#95×C127—21no—
73#95×C127—21no—
74#95×C127—21no—
75#95×C127—21no—
76#95×C127—21no—
77C24×C127C2×D411yescharacteristic
78C2×Q8×C127—21no—
79C2×Q8×C127—41no—
80C2×Q8×C127—41no—
81C2×Q8×C127C22⋊C412yes—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
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×C127#4111yescharacteristic
98C22×C4×C127#4111yescharacteristic
99M16×C127—41no—
100M16×C127—41no—
101M16×C127—41no—
102M16×C127—41no—
103C2×C8×C127—22no—
104C2×C8×C127—41no—
105C4⋊C4×C127—22no—
106C4⋊C4×C127—22no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—21no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—21no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—42no—
113C4⋊C4×C127—81no—
114C4⋊C4×C127C22⋊C412yes—
115C22⋊C4×C127—22no—
116C22⋊C4×C127—22no—
117C22⋊C4×C127—42no—
118C22⋊C4×C127—41no—
119C22⋊C4×C127—41no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C42×C127—41no—
125C42×C127—41no—
126C42×C127—42no—
127C42×C127—41no—
128C42×C127—41no—
129C42×C127—81no—
130C23×C127—21no—
131C23×C127—21no—
132C23×C127—41no—
133C23×C127—41no—
134C23×C127C4×D411yescharacteristic
135C23×C127#12011yescharacteristic
136C23×C127#12111yescharacteristic
137Q8×C127—42no—
138Q8×C127—81no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—22no—
144C2×C4×C127—22no—
145C2×C4×C127—22no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
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—41no—
162C2×C4×C127—41no—
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×C127—81no—
172C2×C4×C127C2×C22⋊C411yescharacteristic
173C2×C4×C127C4×D411yescharacteristic
174C2×C4×C127#12111yescharacteristic
175C2×C4×C127#12311yescharacteristic
176C8×C127—42no—
177C8×C127—81no—
178C22×C127—21no—
179C22×C127—21no—
180C22×C127—21no—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—81no—
187C22×C127—81no—
188C22×C127#38611yescharacteristic
189C22×C127#45811yescharacteristic
190C22×C127#45811yescharacteristic
191C4×C127—21no—
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—21no—
195C4×C127—42no—
196C4×C127—42no—
197C4×C127—42no—
198C4×C127—81no—
199C4×C127—81no—
200C4×C127—81no—
201C4×C127—81no—
202C4×C127—81no—
203C4×C127—161no—
204#9526C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127—21no—
206C2×C127—21no—
207C2×C127—41no—
208C2×C127—41no—
209C2×C127#189011yescharacteristic
210C2×C127#190511yescharacteristic
211C2×C127#190611yescharacteristic
212#3095C2×C12711yescharacteristic
213#2332C2×C12711yescharacteristic
214#1826C2×C12711yescharacteristic
215#1820C2×C12711yescharacteristic
216#1511C2×C12711yescharacteristic
217#1306C2×C12711yescharacteristic
218#1284C2×C12711yescharacteristic
219C127#952611yescharacteristic, direct product factor, Sylow
220C2×C22⋊Q8C22×C12711yescharacteristic
221C2×#117C22×C12711yescharacteristic
222#485—22no—
223#484C4×C12712yescomplemented
224#483C4×C12712yescomplemented
225#428—21no—
226#419—21no—
227#407C22×C12711yescharacteristic
228#407C22×C12711yescharacteristic
229#391—21no—
230#388—21no—
231#388—21no—
232#387—21no—
233#387—21no—
234#381C22×C12711yescharacteristic
235#381C22×C12711yescharacteristic
236C4×C4⋊C4—21no—
237C4×C22⋊C4C22×C12711yescharacteristic
238#342—21no—
239#342—21no—
240#339—21no—
241#339—21no—
242#328—22no—
243C22×Q8D4×C12711yescharacteristic
244C23×C4C23×C12711yescharacteristic
245C2×M16—21no—
246C2×M16—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8C2×C4×C12712yes—
250C22⋊Q8D4×C12712yes—
251#117—21no—
252#117—21no—
253#117—21no—
254#117—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4C2×C4×C12711yescharacteristic
259C2×C4⋊C4C2×C4×C12711yescharacteristic
260C2×C4⋊C4D4×C12711yescharacteristic
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4D4×C12711yescharacteristic
266C2×C22⋊C4D4×C12711yescharacteristic
267C2×C42—21no—
268C2×C42—21no—
269C2×C42—21no—
270C2×C42D4×C12711yescharacteristic
271C2×C42D4×C12711yescharacteristic
272#107—22no—
273#106—22no—
274#103—22no—
275#103—22no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8C2×C4×C12712yes—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289C24C2×D4×C12711yescharacteristic
290C2×Q8—21no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8C22⋊C4×C12712yes—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C22×C4×C12711yescharacteristic
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4#41×C12711yescharacteristic
310C22×C4#41×C12711yescharacteristic
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315C2×C8—22no—
316C2×C8—41no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—42no—
325C4⋊C4—81no—
326C4⋊C4C22⋊C4×C12712yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—42no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C42—41no—
337C42—41no—
338C42—42no—
339C42—41no—
340C42—41no—
341C42—81no—
342C23—21no—
343C23—21no—
344C23—41no—
345C23—41no—
346C23C4×D4×C12711yescharacteristic
347C23#120×C12711yescharacteristic
348C23#121×C12711yescharacteristic
349Q8—42no—
350Q8—81no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
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—41no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4C2×C22⋊C4×C12711yescharacteristic
385C2×C4C4×D4×C12711yescharacteristic
386C2×C4#121×C12711yescharacteristic
387C2×C4#123×C12711yescharacteristic
388C8—42no—
389C8—81no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22#386×C12711yescharacteristic
401C22#458×C12711yescharacteristic
402C22#458×C12711yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—81no—
411C4—81no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—161no—
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2C127×#189011yescharacteristic
421C2C127×#190511yescharacteristic
422C2C127×#190611yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
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
11. #484×C127C4semidirect
12. #483×C127C4semidirect
204. #9526C127direct (N × H)
219. C127#9526direct (N × H)
223. #484C4×C127semidirect
224. #483C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30952
C127×#23322
C127×#18262
C127×#18202
C127×#15112
C127×#13062
C127×#12842
#9526127