Finite Group Databasebeta

← C127×#9497 #44573170

Subgroups — C127×#9497 #44573170

Order 32512.

1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2403C211yesmaximal, characteristic
2C127×#2309C211yesmaximal, characteristic, complemented
3C127×#1781C212yesmaximal, complemented
4C127×#1781C211yesmaximal, characteristic, complemented
5C127×#1304C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C23×D4×C127C2211yescharacteristic
8C2×#120×C127—21no—
9C2×#120×C127C412yescomplemented
10C2×#117×C127—21no—
11C2×#99×C127—22no—
12C2×#99×C127—24no—
13#392×C127—22no—
14#390×C127—24no—
15#386×C127—21no—
16#386×C127C412yescomplemented
17#379×C127—21no—
18#379×C127C2212yes—
19#379×C127C2211yescharacteristic
20#379×C127C2212yes—
21C25×C127C2×C411yescharacteristic
22C25×C127D411yescharacteristic
23C25×C127C2311yescharacteristic
24C22×D4×C127—21no—
25C22×D4×C127—22no—
26C22×D4×C127—22no—
27C22×D4×C127—22no—
28C22×D4×C127—21no—
29C22×D4×C127—22no—
30C22×D4×C127—22no—
31C22×D4×C127—44no—
32C22×D4×C127—44no—
33C22×D4×C127C2×C412yes—
34C22×D4×C127D412yes—
35C23×C4×C127C2×C411yescharacteristic
36C23×C4×C127D411yescharacteristic
37#120×C127—44no—
38#120×C127—44no—
39#117×C127—44no—
40C2×C4⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—22no—
46C2×C22⋊C4×C127—22no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127—22no—
49C2×C22⋊C4×C127—22no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—22no—
52C2×C22⋊C4×C127C2×C412yes—
53C2×C22⋊C4×C127D414yescomplemented
54C2×C42×C127—22no—
55#99×C127—48no—
56#99×C127—44no—
57#95×C127—22no—
58C24×C127—21no—
59C24×C127—21no—
60C24×C127—22no—
61C24×C127—21no—
62C24×C127—42no—
63C24×C127—42no—
64C24×C127—42no—
65C24×C127—42no—
66C24×C127—42no—
67C24×C127—42no—
68C24×C127—81no—
69C24×C127—81no—
70C24×C127—81no—
71C24×C127C22⋊C412yes—
72C24×C127C22×C411yescharacteristic
73C24×C127C2×D411yescharacteristic
74C24×C127C2×D411yescharacteristic
75C24×C127C2×D412yes—
76C24×C127#4112yes—
77C2×D4×C127—28no—
78C2×D4×C127—24no—
79C2×D4×C127—24no—
80C2×D4×C127—24no—
81C2×D4×C127—24no—
82C2×D4×C127—24no—
83C2×D4×C127—42no—
84C2×D4×C127—42no—
85C2×D4×C127—44no—
86C2×D4×C127—44no—
87C2×D4×C127—48no—
88C2×D4×C127—42no—
89C2×D4×C127—44no—
90C2×D4×C127—42no—
91C2×D4×C127—44no—
92C2×D4×C127—42no—
93C2×D4×C127—44no—
94C2×D4×C127—41no—
95C2×D4×C127—42no—
96C2×D4×C127—41no—
97C2×D4×C127—44no—
98C2×D4×C127—44no—
99C2×D4×C127—82no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—24no—
103C22×C4×C127—21no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—24no—
107C22×C4×C127—42no—
108C22×C4×C127—42no—
109C22×C4×C127C22⋊C412yes—
110C4⋊C4×C127—44no—
111C22⋊C4×C127—44no—
112C22⋊C4×C127—44no—
113C22⋊C4×C127—42no—
114C22⋊C4×C127—44no—
115C22⋊C4×C127—44no—
116C22⋊C4×C127—42no—
117C22⋊C4×C127—44no—
118C22⋊C4×C127—44no—
119C22⋊C4×C127—82no—
120C22⋊C4×C127—82no—
121C22⋊C4×C127—81no—
122C22⋊C4×C127—82no—
123C22⋊C4×C127—82no—
124C42×C127—44no—
125C23×C127—22no—
126C23×C127—22no—
127C23×C127—22no—
128C23×C127—22no—
129C23×C127—24no—
130C23×C127—22no—
131C23×C127—24no—
132C23×C127—22no—
133C23×C127—22no—
134C23×C127—22no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—42no—
139C23×C127—41no—
140C23×C127—42no—
141C23×C127—41no—
142C23×C127—42no—
143C23×C127—42no—
144C23×C127—42no—
145C23×C127—42no—
146C23×C127—42no—
147C23×C127—42no—
148C23×C127—41no—
149C23×C127—42no—
150C23×C127—42no—
151C23×C127—42no—
152C23×C127—42no—
153C23×C127—41no—
154C23×C127—42no—
155C23×C127—42no—
156C23×C127—81no—
157C23×C127—81no—
158C23×C127—82no—
159C23×C127—82no—
160C23×C127—88no—
161C23×C127—88no—
162C23×C127—88no—
163C23×C127C2×C22⋊C411yescharacteristic
164C23×C127C4×D412yes—
165C23×C127#12011yescharacteristic
166C23×C127#12112yes—
167C23×C127#12311yescharacteristic
168D4×C127—48no—
169D4×C127—48no—
170D4×C127—48no—
171D4×C127—44no—
172D4×C127—44no—
173D4×C127—88no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—24no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—24no—
181C2×C4×C127—41no—
182C2×C4×C127—42no—
183C2×C4×C127—41no—
184C2×C4×C127—44no—
185C2×C4×C127—42no—
186C2×C4×C127—44no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—44no—
190C2×C4×C127—82no—
191C2×C4×C127—82no—
192C2×C4×C127—82no—
193C2×C4×C127#9914yescomplemented
194C22×C127—21no—
195C22×C127—21no—
196C22×C127—21no—
197C22×C127—21no—
198C22×C127—22no—
199C22×C127—22no—
200C22×C127—21no—
201C22×C127—21no—
202C22×C127—22no—
203C22×C127—22no—
204C22×C127—22no—
205C22×C127—22no—
206C22×C127—21no—
207C22×C127—44no—
208C22×C127—44no—
209C22×C127—44no—
210C22×C127—44no—
211C22×C127—42no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127—84no—
216C22×C127—82no—
217C22×C127—82no—
218C22×C127—84no—
219C22×C127—82no—
220C22×C127—84no—
221C22×C127—84no—
222C22×C127—84no—
223C22×C127—84no—
224C22×C127—81no—
225C22×C127—81no—
226C22×C127#38611yescharacteristic
227C22×C127C2×#9912yes—
228C22×C127B(4,𝔽2)12yes—
229C4×C127—24no—
230C4×C127—42no—
231C4×C127—84no—
232C4×C127—82no—
233C4×C127—162no—
234#9497C12711yesmaximal, characteristic, direct product factor, Sylow
235C2×C127—22no—
236C2×C127—22no—
237C2×C127—42no—
238C2×C127—42no—
239C2×C127—41no—
240C2×C127—82no—
241C2×C127—82no—
242C2×C127#188911yescharacteristic
243C2×C127#189811yescharacteristic
244C2×C127#191311yescharacteristic
245#2403C2×C12711yescharacteristic
246#2309C2×C12711yescharacteristic, complemented
247#1781C2×C12712yescomplemented
248#1781C2×C12711yescharacteristic, complemented
249#1304C2×C12712yescomplemented
250C127#949711yescharacteristic, direct product factor, Sylow
251C23×D4C22×C12711yescharacteristic
252C23×D4C22×C12711yescharacteristic
253C2×#120—21no—
254C2×#120C4×C12712yescomplemented
255C2×#117—21no—
256C2×#99—22no—
257C2×#99—24no—
258#392—22no—
259#390—24no—
260#386—21no—
261#386C4×C12712yescomplemented
262#379—21no—
263#379C22×C12712yes—
264#379C22×C12711yescharacteristic
265#379C22×C12712yes—
266C25C2×C4×C12711yescharacteristic
267C25D4×C12711yescharacteristic
268C25C23×C12711yescharacteristic
269C22×D4—21no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—21no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4C2×C4×C12712yes—
279C22×D4D4×C12712yes—
280C23×C4C2×C4×C12711yescharacteristic
281C23×C4D4×C12711yescharacteristic
282#120—44no—
283#120—44no—
284#117—44no—
285C2×C4⋊C4—22no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4C2×C4×C12712yes—
298C2×C22⋊C4D4×C12714yescomplemented
299C2×C42—22no—
300#99—48no—
301#99—44no—
302#95—22no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—21no—
307C24—42no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—42no—
312C24—42no—
313C24—81no—
314C24—81no—
315C24—81no—
316C24C22⋊C4×C12712yes—
317C24C22×C4×C12711yescharacteristic
318C24C2×D4×C12711yescharacteristic
319C24C2×D4×C12711yescharacteristic
320C24C2×D4×C12712yes—
321C24#41×C12712yes—
322C2×D4—28no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—24no—
327C2×D4—24no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—44no—
332C2×D4—48no—
333C2×D4—42no—
334C2×D4—44no—
335C2×D4—42no—
336C2×D4—44no—
337C2×D4—42no—
338C2×D4—44no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—82no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—24no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C22⋊C4×C12712yes—
355C4⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—42no—
359C22⋊C4—44no—
360C22⋊C4—44no—
361C22⋊C4—42no—
362C22⋊C4—44no—
363C22⋊C4—44no—
364C22⋊C4—82no—
365C22⋊C4—82no—
366C22⋊C4—81no—
367C22⋊C4—82no—
368C22⋊C4—82no—
369C42—44no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—22no—
374C23—24no—
375C23—22no—
376C23—24no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—41no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—81no—
402C23—81no—
403C23—82no—
404C23—82no—
405C23—88no—
406C23—88no—
407C23—88no—
408C23C2×C22⋊C4×C12711yescharacteristic
409C23C4×D4×C12712yes—
410C23#120×C12711yescharacteristic
411C23#121×C12712yes—
412C23#123×C12711yescharacteristic
413D4—48no—
414D4—48no—
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#99×C12714yescomplemented
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—21no—
452C22—44no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—84no—
461C22—82no—
462C22—82no—
463C22—84no—
464C22—82no—
465C22—84no—
466C22—84no—
467C22—84no—
468C22—84no—
469C22—81no—
470C22—81no—
471C22#386×C12711yescharacteristic
472C22C2×#99×C12712yes—
473C22B(4,𝔽2)×C12712yes—
474C4—24no—
475C4—42no—
476C4—82no—
477C4—84no—
478C4—162no—
479C2—22no—
480C2—22no—
481C2—42no—
482C2—42no—
483C2—41no—
484C2—82no—
485C2—82no—
486C2C127×#188911yescharacteristic
487C2C127×#189811yescharacteristic
488C2C127×#191311yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC24C22×C4×C127
Frattini, cosocleC25C23×C127
prime radicalC127×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2309C2semidirect
3. C127×#1781C2semidirect
4. C127×#1781C2semidirect
5. C127×#1304C2semidirect
9. C2×#120×C127C4semidirect
16. #386×C127C4semidirect
53. C2×C22⋊C4×C127D4semidirect
193. C2×C4×C127#99semidirect
234. #9497C127direct (N × H)
246. #2309C2×C127semidirect
247. #1781C2×C127semidirect
248. #1781C2×C127semidirect
249. #1304C2×C127semidirect
250. C127#9497direct (N × H)
254. C2×#120C4×C127semidirect
261. #386C4×C127semidirect
298. C2×C22⋊C4D4×C127semidirect
438. C2×C4#99×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24032
C127×#23092
C127×#17812
C127×#13042
#9497127