Finite Group Databasebeta

← C127×#9969 #44573642

Subgroups — C127×#9969 #44573642

Order 32512.

658 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C127C211yesmaximal, characteristic, complemented
2C2×#481×C127C211yesmaximal, characteristic
3C127×#2639C211yesmaximal, characteristic
4C2×#328×C127C211yesmaximal, characteristic, complemented
5C2×#327×C127C211yesmaximal, characteristic
6C127×#1445C211yesmaximal, characteristic, complemented
7C127×#1280C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×#121×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11#484×C127—22no—
12#484×C127—22no—
13#481×C127—22no—
14#481×C127—22no—
15C2×#107×C127—21no—
16C2×#106×C127—21no—
17C2×#103×C127—21no—
18C2×#102×C127—21no—
19C2×C22⋊C8×C127C2211yescharacteristic
20C2×C22⋊C8×C127C2211yescharacteristic
21#400×C127—21no—
22#397×C127—21no—
23#394×C127—21no—
24#393×C127—21no—
25#386×C127—22no—
26C2×#95×C127—22no—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2211yescharacteristic
29#328×C127—22no—
30#327×C127—22no—
31C22×Q8×C127D411yescharacteristic
32C22×D4×C127—21no—
33C22×D4×C127D411yescharacteristic
34C23×C4×C127—21no—
35C23×C4×C127—21no—
36C23×C4×C127D412yes—
37C23×C4×C127C2311yescharacteristic
38C22×C8×C127—21no—
39C22×C8×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43C22⋊Q8×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46#121×C127—21no—
47#121×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127D412yes—
55C2×C4⋊C4×C127D411yescharacteristic
56C2×C4⋊C4×C127D411yescharacteristic
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—22no—
61#107×C127—24no—
62#106×C127—24no—
63#103×C127—24no—
64#102×C127—24no—
65C22⋊C8×C127—21no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127D412yes—
68C22⋊C8×C127D412yes—
69#95×C127—22no—
70#95×C127—22no—
71#95×C127—21no—
72#95×C127—21no—
73#95×C127—21no—
74#95×C127—21no—
75#95×C127—44no—
76C24×C127—21no—
77C24×C127C2×D411yescharacteristic
78C2×Q8×C127—21no—
79C2×Q8×C127—21no—
80C2×Q8×C127—42no—
81C2×D4×C127—21no—
82C2×D4×C127—21no—
83C2×D4×C127—42no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C2×D4×C127—42no—
87C2×D4×C127—42no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—42no—
97C22×C4×C127—42no—
98C22×C4×C127—42no—
99C22×C4×C127—42no—
100C22×C4×C127—41no—
101C22×C4×C127—42no—
102C22×C4×C127—42no—
103C22×C4×C127—41no—
104C22×C4×C127—41no—
105C22×C4×C127—41no—
106C22×C4×C127—42no—
107C22×C4×C127C2×D411yescharacteristic
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127C2×D411yescharacteristic
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127#4111yescharacteristic
113C2×C8×C127—22no—
114C2×C8×C127—22no—
115C2×C8×C127—42no—
116C2×C8×C127—42no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127—22no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—41no—
124C4⋊C4×C127—41no—
125C4⋊C4×C127—41no—
126C4⋊C4×C127—41no—
127C22⋊C4×C127—41no—
128C22⋊C4×C127—41no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—41no—
131C22⋊C4×C127—82no—
132C22⋊C4×C127—82no—
133C23×C127—21no—
134C23×C127—21no—
135C23×C127—22no—
136C23×C127—41no—
137C23×C127—42no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—42no—
141C23×C127#12011yescharacteristic
142C23×C127#12111yescharacteristic
143C23×C127#12711yescharacteristic
144C23×C127#13512yes—
145C23×C127#13712yes—
146Q8×C127—42no—
147Q8×C127—81no—
148D4×C127—42no—
149D4×C127—81no—
150D4×C127—82no—
151D4×C127—81no—
152D4×C127—81no—
153C2×C4×C127—22no—
154C2×C4×C127—22no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—44no—
160C2×C4×C127—42no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—41no—
170C2×C4×C127—42no—
171C2×C4×C127—41no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127—82no—
175C2×C4×C127—81no—
176C2×C4×C127—82no—
177C2×C4×C127—81no—
178C2×C4×C127—81no—
179C2×C4×C127—81no—
180C2×C4×C127—82no—
181C2×C4×C127#12011yescharacteristic
182C2×C4×C127#12011yescharacteristic
183C2×C4×C127#12111yescharacteristic
184C2×C4×C127#12111yescharacteristic
185C8×C127—42no—
186C8×C127—42no—
187C22×C127—22no—
188C22×C127—22no—
189C22×C127—22no—
190C22×C127—22no—
191C22×C127—21no—
192C22×C127—21no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—82no—
196C22×C127—82no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—81no—
200C22×C127#39211yescharacteristic
201C22×C127#45212yes—
202C22×C127#45311yescharacteristic
203C22×C127#45411yescharacteristic
204C22×C127#45812yes—
205C22×C127#46412yes—
206C22×C127#49511yescharacteristic
207C22×C127#49711yescharacteristic
208C4×C127—21no—
209C4×C127—21no—
210C4×C127—21no—
211C4×C127—21no—
212C4×C127—82no—
213C4×C127—82no—
214C4×C127—81no—
215C4×C127—82no—
216C4×C127—81no—
217C4×C127—81no—
218#9969C12711yesmaximal, characteristic, direct product factor, Sylow
219C2×C127—21no—
220C2×C127—22no—
221C2×C127—21no—
222C2×C127—161no—
223C2×C127#161512yes—
224C2×C127#161812yes—
225C2×C127#200611yescharacteristic
226C2×C127#201511yescharacteristic
227C2×C127#202211yescharacteristic
228C2×#484C2×C12711yescharacteristic, complemented
229C2×#481C2×C12711yescharacteristic
230#2639C2×C12711yescharacteristic
231C2×#328C2×C12711yescharacteristic, complemented
232C2×#327C2×C12711yescharacteristic
233#1445C2×C12711yescharacteristic, complemented
234#1280C2×C12711yescharacteristic, complemented
235C127#996911yescharacteristic, direct product factor, Sylow
236C2×C22⋊Q8C22×C12711yescharacteristic
237C2×#121C22×C12711yescharacteristic
238C22×C4⋊C4C22×C12711yescharacteristic
239#484—22no—
240#484—22no—
241#481—22no—
242#481—22no—
243C2×#107—21no—
244C2×#106—21no—
245C2×#103—21no—
246C2×#102—21no—
247C2×C22⋊C8C22×C12711yescharacteristic
248C2×C22⋊C8C22×C12711yescharacteristic
249#400—21no—
250#397—21no—
251#394—21no—
252#393—21no—
253#386—22no—
254C2×#95—22no—
255C2×#95C22×C12711yescharacteristic
256C2×#95C22×C12711yescharacteristic
257#328—22no—
258#327—22no—
259C22×Q8D4×C12711yescharacteristic
260C22×D4—21no—
261C22×D4D4×C12711yescharacteristic
262C23×C4—21no—
263C23×C4—21no—
264C23×C4D4×C12712yes—
265C23×C4C23×C12711yescharacteristic
266C22×C8—21no—
267C22×C8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4D4×C12712yes—
283C2×C4⋊C4D4×C12711yescharacteristic
284C2×C4⋊C4D4×C12711yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—22no—
289#107—24no—
290#106—24no—
291#103—24no—
292#102—24no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8D4×C12712yes—
296C22⋊C8D4×C12712yes—
297#95—22no—
298#95—22no—
299#95—21no—
300#95—21no—
301#95—21no—
302#95—21no—
303#95—44no—
304C24—21no—
305C24C2×D4×C12711yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—42no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—42no—
315C2×D4—42no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—41no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—42no—
335C22×C4C2×D4×C12711yescharacteristic
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4C2×D4×C12711yescharacteristic
338C22×C4C2×D4×C12711yescharacteristic
339C22×C4C2×D4×C12711yescharacteristic
340C22×C4#41×C12711yescharacteristic
341C2×C8—22no—
342C2×C8—22no—
343C2×C8—42no—
344C2×C8—42no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—82no—
360C22⋊C4—82no—
361C23—21no—
362C23—21no—
363C23—22no—
364C23—41no—
365C23—42no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23#120×C12711yescharacteristic
370C23#121×C12711yescharacteristic
371C23#127×C12711yescharacteristic
372C23#135×C12712yes—
373C23#137×C12712yes—
374Q8—42no—
375Q8—81no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—82no—
380D4—81no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—82no—
403C2×C4—81no—
404C2×C4—82no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—82no—
409C2×C4#120×C12711yescharacteristic
410C2×C4#120×C12711yescharacteristic
411C2×C4#121×C12711yescharacteristic
412C2×C4#121×C12711yescharacteristic
413C8—42no—
414C8—42no—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—82no—
424C22—82no—
425C22—81no—
426C22—81no—
427C22—81no—
428C22#392×C12711yescharacteristic
429C22#452×C12712yes—
430C22#453×C12711yescharacteristic
431C22#454×C12711yescharacteristic
432C22#458×C12712yes—
433C22#464×C12712yes—
434C22#495×C12711yescharacteristic
435C22#497×C12711yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—82no—
442C4—82no—
443C4—81no—
444C4—81no—
445C4—81no—
446C2—21no—
447C2—21no—
448C2—22no—
449C2—161no—
450C2C127×#161512yes—
451C2C127×#161812yes—
452C2C127×#200611yescharacteristic
453C2C127×#201511yescharacteristic
454C2C127×#202211yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC2×#121×C127C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#484×C127C2semidirect
4. C2×#328×C127C2semidirect
6. C127×#1445C2semidirect
7. C127×#1280C2semidirect
218. #9969C127direct (N × H)
228. C2×#484C2×C127semidirect
231. C2×#328C2×C127semidirect
233. #1445C2×C127semidirect
234. #1280C2×C127semidirect
235. C127#9969direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#484×C1272
C2×#481×C1272
C127×#26392
C2×#328×C1272
C2×#327×C1272
C127×#14452
C127×#12802
#9969127